DEFORMATION, FRACTURE, AND HARDNESS CHARACTERISTICS OF COMPOUNDS OF MANGANESE WITH GROUP VI ELEMENTS by Paul Gordon Riewald A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1968 Doctoral Committee: Professor Lawrence H. Van Vlack, Chairman Professor David K. Felbeck Associate Professor William F. Hosford Assistant Professor Orville F. Kimball Associate' Professor Donald R. Peacor

THE UNIVERSITY OF MICHIGAN DEPARTMENT OF CHEMICAL AND METALLURGICAL ENGINEERING ANN ARBOR, MICHIGAN 48104 June 14, 1968 LAWRENCE H. VAN VLACK ADMINISTRATIVE CHAIRMAN CHAIRMAN, MATERIALS AND METALLURGY DONALD L. KATZ CHAIRMAN, CHEMICAL ENGINEERING Selenium-Tellurium Development Association, Inc. 11 Broadway New York, New York 10004 Dear Sirs: The attached is a dissertation by Dr. Paul G. Riewald which was completed in May 1968 for his research work at the University of Michigan. Dr. Riewald received no personal support from the Selenium-Tellurium Development Association. However, the subject of his research was very closely associated with the sponsored work by the Selenium-Tellurium Development Association at the University of Michigan as it pertains to manganese selenide and manganese telluride and their possible use as additives to steels for freemachinability. Consequently, Dr. Riewald has agreed to permit his dissertation to become available to members of the SeleniumTellurium Development Association. Funds for its reproduction were borne by the Association's grant to The University of Michigan. Because the enclosed material is a dissertation, it is proper that Dr. Riewald should be consulted before using it for other purposes; however, he has indicated his willingness to grant that permission freely. As Chairman of the Department of Chemical and Metallurgical Engineering and as Chairman of Dr. Riewald's dissertation committee, I would like to solicit reactions from each of you in connection with the subject matter that is presented herein. In due course, it is anticipated that much of the material in this dissertation will be submitted for publication. We will try to make those papers available to the Selenium-Tellurium Development Association and its members. Sincerely yours, / Lawrence H. Van Vlack Professor and Chairman LHVV/ac Enclosure

Pages ii and iii not reproduced in this report.

TABLE OF CONTENTS Page LIST OF TABLES vii LIST OF FIGURES Viii ABSTRACT xiii CHAPTER I. INTRODUCTION 1 II. LITERATURE REVIEW 3 A. Deformation and Fracture of Nonmetallics 3 1. Deformation and Fracture Mechanisms 4 2. Cohesive Strength 7 5. Plasticity 8 4. Fracture 13 B. Hardness and Hardness Testing 17 1. Vickers Hardness 18 2. Knoop Hardness 19 C. Pertinent Information on MnO, MnS, MnSe, and MnTe 21 1. Structure and Phase Relations 21 2. Other Properties 23 III. EXPERIMENTAL PROCEDURE 29 A. Raw Materials 29 B. Materials Purification 32 C. Crystal Growth 35 1. Pure Compounds 55 2. Binary Compositions 56 D. Sample Preparation 57 1. Orienting and Cutting 57 2. Mounting and Polishing 57 E. Testing and Examination Procedure 38 1. Deformation 38 2. Fracture 40 5. Temperature Effect 40 4. Low Temperature X-ray Study 42 iv

TABLE OF CONTENTS (Continued) CHAPTER Page IV. EXPERIMENTAL RESULTS 44 A. Manganous Selenide 44 1. Plastic Deformation 44 2. Fracture 55 B. The System MnSe-MnS 57 1. Plastic Deformation 57 2. Fracture 62 3. Diamond Pyramid Hardness 64 4. Knoop Hardness 70 C. MnSe-Rich Portion of MnSe-MnTe System 77 1. Plastic Deformation 77 2. Fracture 77 3. Diamond Pyramid Hardness 77 4. Knoop Hardness 79 D. Manganous Telluride 79 1. Plastic Deformation 79 2. Fracture 85 E. MnTe-Rich Portion of MnSe-MnTe System 87 1. Plastic Deformation 87 2. Fracture 87 3. Diamond Pyramid Hardness 87 4. Knoop Hardness 88 V. DISCUSSION 89 A. Deformation Associated with the Vickers Indentation 89 B. Comparison of Deformation, Fracture, and Hardness Characteristics of Mn(Group VI) Compounds 94 C. Knoop Hardness Indentations on Anisotropic Materials 97 1. Data Available 97 2. Scope of the Problem 104 3. Treatments of Problem 106 4. Results 115 VI. CONCLUSIONS 123 APPENDIX I. TABULATION OF HARDNESS DATA 127 II. SUMMARY OF KNOOP HARDNESS ANISOTROPY THEORIES 131 1. Daniels and Dunn Method 131 2. Feng and Elbaum Method 131 v

TABLE OF CONTENTS (Concluded) Page 3. One Shear Stress Method 131 4. Two Shears Method 133 5. Integrated Average Method 138 III. OTHER SYSTEMS INVESTIGATED 140 1. MnTe-MnS System 140 2. MnSe-FeSe System 140 3. MnSe-CrSe System 141 4. MnS-FeS System 141 5. MnS-CrS System 142 REFERENCES 143 vi

LIST OF TABLES Table Page I. Knoop Hardness of MnSe 71 II. Knoop Hardness of MnS 71 III. Properties of Mn (Group VI) Compounds 96 IV. Cation-Anion Distances in Mn(Group VI) Compounds 97 V. Knoop Hardness Data for FCC and BCC Metals and MnSe 99 VI. Knoop Hardness Data for NaCl-Type Materials which Deform by (1103<110> Slip 100 VII. Knoop Hardness Calculations for (111) <110> Slip 116 VIII. Knoop Hardness Calculations for (110) <110> Slip 117 vii

LIST OF FIGURES Figure Page 1. Variation of yield stress with temperature for ionic crystals. 11 2. Diagram of the NiAs-type structure of MnTe. 22 3. Phase diagram of the system MnO-MnS. 24 4. Phase diagram of the system MnSe-MnS. 24 5. Phase diagram of the system MnTe-MnS. 25 6. Phase diagram of the system MnSe-MnTe. 25 7. Antiferromagnetic structure of MnO. 26 8. Apparatus used for the preparation of stoichiometric manganese sulfide. 30 9. Zone refining apparatus for the purification of manganese selenide and manganese telluride. 33 10. Technique used for hardness testing at -196~C, -70~C, and 135~C. 41 11. Apparatus used to obtain low temperature X-ray powder patterns of manganese selenide. 43 12. Slip traces around Vickers indentation on the (001) surface of MnSe. 45 13. Slip traces around Knoop and Vickers indentations on the (01i) surface of MnSe. 45 14. Slip traces around Vickers indentation on the (111) surface of MnSe. 46 15. Two cubic unit cells showing several low index planes and their intersections with other planes. 46 16. The (001) surface of MnSe showing cross slip on (110) planes. 48 17. Examples of Vickers impressions of unusual shapes on (a) the (001) and (b) the (011) surfaces of MnSe. 48 viii

LIST OF FIGURES (Continued) Figure Page 18. Interference micrographs around Vickers indentations on the (001) surface of MnSe when the indenter diagonals are in (a) <100> and (b) <110> directions. 50 19. Concentration of slip lines around Vickers indentation on the (001) surface of MnS. 52 20. Interference micrographs around Vickers indentations on the (001) surface of MnS when the indenter diagonals are in (a) <100> and (b) <110> directions. 53 21. (100} fracture around Vickers indentation on the (001) surface of MnSe. 56 22. Dislocation etch pits reflecting dislocations nucleated at the tip of a (100} cleavage crack. 56 23. (111) and (110) slip traces around Vickers indentation on the (001) surface of 75 MnSe —25 MnS single crystal. 58 24. (111) and (110} slip traces around Vickers indentation on the (001) surface of 50 MnSe —50 MnS single crystal. 58 25. (111} and (110) slip traces around Vickers indentation on the (001) surface of 50 MnSe-50 MnS single crystal with (100} cracking evident. 58 26. (111} and (110} slip traces around Vickers indentation on the (001) surface of 25 MnSe —75 MnS single crystal. 60 27. (111} and (110} slip traces around Vickers indentation on the (011) surface of 25 MnSe-75 MnS single crystal. 60 28. (110} slip traces around Vickers indentation on the (001) surface of MnS. 60 29. (110} slip traces around Vickers indentation on the (011) surface of MnS. 60 30. Dislocation etch pit rosette pattern on the (001) plane for MnS. 61 ix

LIST OF FIGURES (Continued) Figure Page 31. Development of dislocation etch pit rosette pattern characteristic of [110)<110> slip around Vickers indentations for MnSe-MnS solid solutions. 63 32. Average diamond pyramid hardness of MnSe-MnS solid solutions at various temperatures. 65 53. Diamond pyramid hardness vs. temperature for MnSe-MnS solid solutions. 67 34. (111) and (110) slip traces around Vickers indentation on the (001) surface of MnS when tested under liquid nitrogen. 68 35. The (001) surface of MnSe after quenching in liquid nitrogen. 68 36. Room temperature Knoop hardnesses on (001) for MnSe-MnS solid solutions. 72 37. Room temperature Knoop hardnesses on (011) for MnSe-MnS solid solutions. 73 38. Knoop hardnesses on (001) for MnSe-MnS solid solutions at -70~C. 75 39. Knoop hardnesses on (001) for MnSe-MnS solid solutions at 135~C. 76 40. Slip traces around Vickers indentation on the (001) surface of 93 MnSe-7 MnTe single crystal. 78 41. Slip traces around Knoop indentation on the (011) surface of 93 MnSe-7MnTe single crystal. 78 42. Slip traces around Vickers indentation on the (011) surface of 87 MnSe-13 MnTe single crystal. 78 43. Diamond pyramid hardnesses for MnSe-MnTe solid solutions. 80 44. Knoop hardnesses for MnSe-MnTe solid solid solutions. 81 45. Twinning around Vickers indentation on the (0001) surface of MnTe. 83 x

LIST OF FIGURES (Continued) Figure Page 46. Twinning around Knoop indentation on the (0001) surface of MnTe. 83 47. Possible orientations of (1012) twin traces in the basal plane of MnTe. 84 48. Interference micrograph around Vickers impression on the (0001) surface of MnTe. 84 49. Slip traces around Vickers indentation on the (1120) surface of MnTe. 86 50. Slip traces around Knoop impressions on the (1010) surface of MnTe when the long axis of the indenter is in (a) the [1210] and (b) the [0001] directions. 86 51. View of a (111) plane showing how flow in two <110> directions can result in net <112> flow. 90 52. (a) Dislocation or slip interaction on two adjacent (110) planes. (b) Dislocation or slip interaction on two adjacent (111) planes. 92 55. Comparison of Knoop hardness anisotropy behavior for several materials with cubic crystal structures. 101 54. (a) Orientation of (110) planes. (b) View in [001] direction with Knoop indenter in [100]. 105 55. (a) Orientation of [111) planes. (b) View in [001] direction with Knoop indenter in [110]. 103 56. (a) Orientation of (111) planes with respect to (110) plane. (b) Edge view of the (110) plane with intersecting (111) planes. 105 57. Diagram of Knoop indenter showing positions of force, slip plane, slip direction and axes of rotation for (A) Daniels and Dunn and (B) Feng and Elbaum methods of analysis. 107 58. Slip line field associated with the plane strain indentation of an isotropic material by an infinite wedge of included angle 150 degrees. 110 xi

LIST OF FIGURES Figure Page 59. Standard (001) stereographic projection of a cubic crystal showing the shear stress direction and the intersection of the facets of the Knoop indenter with the plane of projection when the long axis is in the [010] direction for the "one lateral shear" method of analysis. 112 60. Standard (001) stereographic projection of a cubic crystal showing the assumed shear stress directions for facet 1 and the intersection of the Knoop indenter with the plane of the projection for the "two shears" method of analysis when the long indenter axis is in the [010] direction. 114 61. Comparison of calculated and measured Knoop hardnesses on single crystals of manganese selenide, aluminum, and silicon ferrite using the "two shears" method of analysis. 119 62. Comparison of calculated and measured Knoop hardnesses on single crystals of manganese selenide, aluminum, and silicon ferrite using the "integrated average" method of analysis. 120 63. Comparison of various methods of estimating Knoop hardness anisotropy on cubic single crystals using manganese selenide as standard. 121 64. Assumed slip line field around indenter and direction of shear stress for the "one lateral shear" method of calculation. 132 65. Stereographic projection illustrating calculational procedure for "one lateral shear" method. 132 66. Assumed slip line field around indenter and directions of shear stress for the "two shears" method of calculation. 134 67. Stereographic projection illustrating calculational procedure for "two shears" method. 134 68. Diagram of slip line field used as an aid to calculate the work done during the indentation of an isotropic material by an infinite wedge. 137 69. Hodograph for the indentation of an isotropic material by an infinite wedge of included angle 130 degrees. 137 70. Plot of minimum (l/m) vs. orientation of shear stress for the "integrated average" method of analysis. 139 xii

ABSTRACT This investigation is concerned with the determination of slip mechanisms, fracture characteristics, and hardness relationships of compounds of manganese with Group VI elements. These compounds include MnO, MnS, MnSe, and MnTe, although the emphasis of this study is on MnSe, MnTe, and solid solutions in the systems MnSe-MnS and MnSe-MnTe. Single crystals were grown by a Bridgman technique, oriented by the backreflection Laue method and sectioned parallel to selected planes. The selected surfaces were then polished and indented with either a Vickers or Knoop diamond micro-indenter. This testing method was chosen because it was well suited to the size of the crystals utilized and readily provides information on plastic deformation and fracture mechanisms as well as on hardness. Plastic deformation mechanisms were studied by observing (1) slip traces around indentations, (2) the formation of dislocation etch pit rosette patterns, and (3) the Knoop hardness anisotropy associated with single crystal specimens. Fracture was studied by observation of cleavage planes and slip interactions around indentations. Tests were made over the temperature range -196~C to 135~C. Sodium chloride-type MnSe exhibits (1113<110> and (110}<110> as primary and secondary slip mechanisms respectively, in contrast to the (110)<110> mechanism preferred by MnS and MnO. As with MnO and MnS, the primary and secondary cleavage planes for MnSe are (100) and (110} respectively. Around surface indentations MnSe shows primarily (100) fracture due to dislocation interactions on (111) slip planes in contrast to (110) fracture in MnS resulting from dislocation interactions on (110) planes. Around Vickers indentations on MnSe and MnS, a crystallographic pile-up of material occurs which is related to flow on the crystal slip systems. While the appearance of the pile-up is similar in both MnSe and MnS, the mechanisms are different due to the different slip modes. In the continuous solid solution system MnSe-MnS, the primary slip mechanism changes gradually with composition. Manganese selenide is much softer than manganese sulfide. Substitution of sulfide for selenide ions in MnSe results in a large positive solid solution hardening deviation. The (110)<110> slip mechanism of MnS hardens much more rapidly with decreasing temperature than the (111)<110> mechanism of MnSe. At liquid nitrogen temperature MnS shows an appreciable amount of (111) slip. Manganese telluride, with the hexagonal NiAs-type structure, shows three modes of plastic deformation around Vickers and Knoop indentations: (1) (1012) twinning, (2) basal glide, and (3) pencil glide in <1120>. Primary and secondary cleavage planes are (0001) and (1010) respectively. xiii

The Knoop indentation hardness varies with crystal orientation in a different manner for MnSe than for MnS. A rigorous analysis of Knoop hardness anisotropy and the flow of material associated with the indenter is an extremely complex problem which was not satisfactorily solved in this study. However, a theory is postulated which improves for FCC and BCC metals on the only known published attempt at analysis-that of Daniels and Dunn. The changes in deformation, fracture, and hardness characteristics in Mn(Group VI) compounds are relatable to changes in other properties, and result from a regular decrease in the ionic character of the chemical bond in going from MnO to MnTe. xiv

CHAPTER I INTRODUCTI ON This investigation was undertaken to determine plastic deformation mechanisms, fracture characteristics, and hardness relations among compounds of manganese with Group VI elements, both for the pure compounds and, where possible, for binary substitutional solid solutions. The compounds include MnO, MnS, MnSe, and MnTe although the emphasis of this work was on MnSe, MnTe, and solid solutions in the systems MnSe-MnS and MnSe-MnTe. Such a study allows one to compare mechanical behavior to other material properties in a series of compounds in which the anion shows a systematic variation. Also, it serves as a first step in a much broader investigation on the role of these compounds, when present as inclusions in metal, on the plastic deformation behavior of the metal matrix (e.g., as in free machining steels). A Vickers or Knoop micro-indentation hardness procedure on single crystal specimens was chosen as the principal testing method because it is well suited to the size of the crystals utilized and readily provides information on plastic deformation and fracture mechanisms as well as on hardness. The results for each compound or solid solution system are presented in the following manner: (1) plastic deformation (slip) mechanisms, (2) fracture characteristics (due both to cleavage and slip interaction), (3) diamond pyramid (Vickers) hardness, and (4) Knoop hardness. Results are supplemented with photomicrographs and plots. 1

2 Finally, observations are rendered concerning the nature of plastic flow around and adjacent to the Vickers indenter, and attempts are made in an effort to explain the anisotropy associated with Knoop hardness tests on single crystals.

CHAPTER II LITERATURE REVIEW The following literature review summarizes previous work related to this thesis topic. It is divided into three main sections. The first covers the deformation and fracture of nonmetallic materials, while the second gives a review of hardness and hardness testing. The third section provides pertinent information on the materials considered in this investigation, namely MnO, MnS, MnSe, and MnTe. A. Deformation and Fracture of Nonmetallics Within the area of deformation and fracture of inorganic nonmetallic materials, the mechanical behavior of ionic crystals has been the most extensively studied and is probably known in greater detail than for any other crystal type (Gilman, 1961a, 1963). One reason for the relatively good understanding of ionic crystals is the simple nature of their chemical bond. Also, they can be readily cleaved to simple shapes and can be easily studied by means of direct observations of their dislocations (Gilman, 1961a). Because the materials used in this study are predominately ionic and because MnO, MnS, and MnSe possess the NaCl-type structure on which most of the previously reported work has been concentrated, much of the following will be devoted to NaCl-type ceramic materials. 5

4 1. DEFORMATION AND FRACTURE MECHANISMS Plastic deformation in crystals generally occurs by slip or twinning. Slip occurs by the relative movement of planes of atoms or ions on a slip plane (hkl) by the propagation of linear defects or dislocations in a slip direction <uvw>. Deformation by twinning consists of shearing movements of the atomic planes over one another so that the twinned and untwinned portions of the crystal are joined together with a definite mutual orientation. The twinned portion is either a mirror image of the orientation of the parent crystal in a plane called the twinning plane, or related by a rotation about an axis called the twinning axis, or both (Barrett, 1952). Rock salt-type ionic crystals usually deform by translation gliding on (110) planes in <110> directions, which are the shortest translation vectors of the crystal structure and do not require like charged ions to pass over each other (Gilman, 1961a). The (110) planes are favored over the more widely spaced (100) planes probably because glide on (100) is accompanied by electrostatic faulting as first explained by Buerger (1935). Buerger (1935) and Tammann and Salge (1927) report (111) <110> as a secondary slip system in the sodium halides at higher temperatures. Chao et al. (1964a) found that (111) <110> was a secondary slip system in MnS when indented with a Vickers diamond at room temperature. Moore (1965), however, did not detect (111) slip around Vickers indentations in MnO. At high temperatures, most rock salt-type crystals glide readily on (100) planes. Some crystals such as PbS and PbTe show (100) <011> slip at room temperature (Buerger, 1935; Gilman, 1961a). This is due to their high ionic

5 polarizability and shows that there is a tendency toward more (100) slip as the ionic character of the bonding decreases. Silver chloride and silver bromide often show little preference for any glide plane (Gilman, 1961a; Nabarro, 1964). Instead, slip appears to take place upon any plane of which the slip direction is zone axis. This is called pencil glide (Cottrell, 1953; Groves and Kelly, 1963). Uranium carbide (Van Der Walt and Sole, 1967) and titanium carbide (Williams and Schaal, 1962; Hollox and Smallman, 1966; Van Der Walt and Sole, 1967) have the NaCl-type structure but slip primarily on (111) planes. The bond in these appears to be largely a combination of metallic and covalent as evidenced by their high melting points and good electrical conductivity. Van Der Walt and Sole (1967) have attempted to explain the deformation of all crystals with the NaC1 structure. They conclude that the behavior of ionic crystals is controlled by the electrostatic nature of their bonding, but that the behavior of covalent crystals is directly related to the metallic-nonmetallic radii ratio. Crystals with r/R < 0.414 slip on (110); for 0.414 < r/R < 0.633, slip is on (111) and for r/R > 0.633, slip occurs on (100}. Fracture occurs most easily for NaCl-type crystals by cleavage on (100) (Gilman, 1961a). Van Zeggeren and Benson (1957) calculated the surface energy of (100] to be lower than (110]. Secondary cleavage planes are (110) although no (111) cleavage has been reported (Gilman, 1961a, 1963). Chao et al. (1964a) found that (100) cleavage is predominant in MnS but that the {110} fracture system becomes primary around surface indentations.

6 Such fracture develops by interaction of (011) and (101) slip near the (001) surface by a mechanism first proposed by Keh (1959, 1960). Chao et al. (1964a) also noted that minor amounts of (110) fracture can occur through the interaction of dislocation movements on the (111) slip planes. MnO also cleaves preferentially on (100) and shows (110) cracks normal to (100) around Vickers indentations (Moore, 1965). Of the many nonmetallics not possessing a NaCl-type structure, the one material most extensively studied with regard to deformation mechanism has probably been alumina, which has a hexagonal structure. Wachtman and Maxwell (1954, 1957, 1959) found that above 900~C, creep can occur on the (0001)<1120> system. The <1120> directions in A1203 are taken in the direction of close packing of interstitial holes at 30 degrees to a row of closely packed oxygen ions. Kronberg (1957) also found that slip occurred in A1203 on (0001) <1120> at high temperatures. He also reported that basal twinning could be induced by mechanical deformation. Conrad (1965) found that, in the range 1000-2000~C, sapphire deforms plastically in tension, compression, and bending by basal slip, and that twinning occurs on (0111) when compressed. Fracture generally occurred on a (0111) twinning plane. Slip has also been found to occur above 2000~C on the system (1210)<1010> (Klassen et al., 1942). Some other materials which have been investigated and for which deformation mechanisms have been identified are SiO2 (Bailey et al., 1958), diamond (Nabarro, 1964), InSb (sphalerite structure) (Nabarro, 1964), CaF2 (CaF2 structure) (Phillips, 1961; Burn and Murray, 1962), Ti02 (Sn02 structure) (Wachtman and Maxwell, 1957; Ashbee and Smallman, 1963), and CsBr (CsCl structure) (Johnson and Pask, 1964).

7 2. COHESIVE STRENGTH The chemical binding energy of a crystal determines its maximum theoretical strength limit. A convenient measure of the chemical bond strength of crystals is provided by their elastic moduli (Gilman, 1965). Tests have shown that the cohesive strength equals about ten percent of the modulus. This is an order of magnitude greater than the highest strengths which have been observed (Stokes, 1962). An important relationship is that between cohesive stress and interatomic spacing. This arises because the primary cause of binding is electrostatic attraction-a fact which is especially clear in ionic crystals where about 90 percent of the binding energy results from the electrostatic attraction of oppositely charged ions. The two factors most important in determining interatomic spacing are atom size and chemical valence (Gilman, 1961a, 1963). Indeed, Gilman (1963) shows that, for several types of binding and crystal structures, elastic moduli are very sensitive to interatomic spacing, often inversely proportional to the fourth power of interatomic distarce. High strength is always associated with high valence and short interatomic distance. Gilman (1963) has also shown an exponential relation between hardness and elastic modulus for covalent and metallic crystals. In both cases, tLe hardness is proportional to the elastic modulus, but the proportionality constants differ by a factor of 500, giving some evidence that cohesion may be strongly affected by dislocations (Gilman, 196K1). For metals, in which dislocations can move easily, the hardness is a small fraction of the modulus (about 0.5 percent), while in covalent crystals, it amounts to around 10 percent of the

8 modulus (Gilman, 1963). This is close to their cohesive strength and indicates that dislocations have great difficulty in moving through covalent crystals. The effect of increased temperature in lowering the elastic modulus is quite marked and has been investigated by a number of authors (Durand, 1936; Gait, 1948; Hunter and Siegel, 1942; Stephanov and Eidus, 1956; Tannhauser et al., 1956). Also, internal defects such as grain boundaries, cracks, and inclusions disrupt the normal short range binding and drastically lower the strength of ionic crystals (Gilman, 1963). 3. PLASTICITY Characteristically, ionic crystals are brittle (Gilman, 1963). However, when natural dislocation sources are reduced by annealing and when surface defects are removed by chemical polishing, ionic crystals can undergo appreciable plastic flow before fracture (Stokes, 1962). Indeed, Gorum et al. (1958) found that FCC and BCC ionic materials are inherently ductile rather than brittle. The greatest ductility and plastic deformation is associated with NaCl-type ionic crystals and it is on this variety that most studies have been performed. a. Dislocation Mechanisms It has been proved beyond any reasonable doubt that plastic deformation in crystals takes place through the motion of dislocation lines (Gilman, 1961a). The macroscopic deformation of a crystal is governed by three factors: (1) how many dislocations are in motion, (2) their average velocity, and (3) their individual effect (i.e., Burger's vector) (Miles, 1964).

9 Very large numbers of dislocations are needed to obtain sizable macroscopic strains, and these large numbers of dislocations are not often initially present in the crystal but must be formed during the plastic deformation process. Crystals grown under ordinary circumstances usually contain grown-in dislocations which, as Stokes (1962) found in MgO, are quite immobile and play a passive role in most deformation processes. Dislocations can be formed homogeneously by the action of stress alone, but this process is expected to occur only at very high stresses. In real crystals, small precipitates or other discontinuities can act as stress raisers and cause heterogeneous dislocation nucleation (Gilman, 1959b). Even heterogeneous nucleation cannot account for the vast bulk of dislocations that finally participate in a large plastic deformation. These appear to be formed through regenerative multiplication by either the Frank-Read (1950) mechanism or by a multiple cross glide mechanism first proposed by Koehler (1952) and Orowan (1954). In the case of LiF, there is good evidence that the multiple cross glide process provides most of the dislocation multiplication that occurs during plastic straining (Johnston and Gilman, 1959). Cross glide and dislocation intersections are also ways in which kinks and jogs can be formed. Seitz (1951) points out that kinks and jogs in ionic crystals can sometimes be charged. Under some circumstances, intersecting dislocations can react to form a a - a anew dislocation. An example is the reaction 2 [Ol] + 2 [101] -+ 2 [110]. The two dislocations lying on oblique (110} primary glide planes meet along a [111] direction and unite to form a new dislocation with the primary glide

10 vector, but lying on a (112) plane. This dislocation is relatively immobile (Kear et al., 1959), and is a type of Lomer-Cottrell lock. In MgO, slip is observed to take place by the development of dislocation bands which are usually nucleated at surface defects and widen by a dislocation multiplication mechanism. When two orthogonal dislocation bands intersect, one band produces a kinking in the other at the intersection and a crack may develop (Argon and Orowan, 1964). However, if all slip bands are parallel, or if a large number of slip bands are present, cracks become stabilized and a high ductility occurs. b. Yield Stress It was shown by Johnston and Gilman (1959, 1960) that if fresh dislocations are introduced at the surface of NaCl-type ionic crystals, the macroscopic yield stresses are determined by the stresses required to move these dislocations in the crystals. The yield stresses are not determined by (1) the stress to pull dislocations away from impurity atmospheres, (2) the stress to push dislocations through a forest of other dislocations or (3) the stress to operate Frank-Read sources. Rather they are determined by the frictional resistance of the crystal to dislocation movement (Gilman, 1961a). Yield stresses in ionic crystals are quite sensitive to temperature because of the sensitivity of dislocation motions to changes in temperature. This is shown in Figure 1 for LiF single crystals (Gilman, 1961a). However, it may be noted that only part of the yield stress is temperature dependent, as indicated by the fact that the curves for different LiF crystals lie paral

11 lel to each other as their hardnesses vary with temperature. The hardness difference is caused by different impurity contents of the crystals. 6-,!m^ ~~~~~~ 5 \ ~LiF a 5 \I\ (GILMAN,JOHNSTON) a- \ 4 \ \ HARD'CRYSTAL O- 3 SOFT'CRYSTAL/ < BEND TESTS 0 100 200 300 400 TESTING TEMPERATURE (~K) Figure 1. Variation of yield stress with temperature for ionic crystals (Gilman, 1961a). Chao et al. (1964b) have shown that the hot hardness of pure MnS and MnS containing one percent Ca impurity in solution gives a similar behavior. c. Yielding Versus Slip System An intrinsic effect of the crystal structure is the variation in yield stress with glide plane. Stepanov and Bobrikov (1957) measured this effect in NaCl single crystals between room temperature and 500~C, and found that the required stress for slip on (111) and (001) planes is higher than for (110) glide in the same <110> direction. Gilman (1959a) observed the same behavior in LiF crystals and concluded that, since the Burger's vectors for all these slips were <110> and the elastic strain energies were essentially the same, only the difference in the core structure of dislocations can explain the large dislocation mobility differences.

12 d. Plasticity and Strain Hardening Because the number of dislocation sources in the surface controls the glide, it also controls the rate of strain hardening. As the number of interfering glide bands increases, the rate of strain hardening increases, as was demonstrated by Stokes (1962). Barriers such as impurities, boundaries, and Lomer-Cottrell locks can obstruct dislocation motion. Dislocation pileup at a barrier can cause a "back-stress" which would oppose the applied stress. Thus the stress acting on the source and causing the generation of dislocations would tend to become neutralized (Parker, E. R., 1958). The rate of cross slip and therefore of both multiplication and debris formation increases with the stress applied to the crystal. e. Plasticity Versus Surface Surface conditions appear to have an appreciable effect on the plasticity of ionic crystals because "brittle" materials may fracture due to surface flaws before they have a chance to deform plastically. Also surface conditions can determine the distribution of slip and consequently, control the ductility in this way. Coblentz (1903) reported that NaCl crystals can be plastically deformed after they have been wetted. This is the well-known Joffe (1924) effect which may be largely due to the removal of gross surface defects such as microcracks and products of chemical reactions rather than due to a characteristic of ionic crystals (Gorum et al., 1958; Class et al., 1959). Milch (1909) reported that sticks of rock salt could be bent very readily after heating.

13 Schmid and Boas (1936) anld more recently Vaughn and Davisson (1959) have found that surface conditions, per se, do not have a strong influence on the fundamental event in plasticity —the mobilities of dislocations. f. Yielding and Impurities Eshelby et al. (1958) found that the addition of divalent impurities to NaCl would cause maxima and minima in the yield strength versus temperature plot. Differences in ion size cause difficulties in dislocation movement. Different valences of impurities cause both charge and size effects which lock dislocations. Results show that divalent impurities in a monovalent structure are about two orders of magnitude more effective than monovalent impurities in raising the yield stress of NaCl-type crystals (Gilman, 1961a). g. Plasticity Versus State of Stress The ability of ionics to deform plastically is dependent on the stress state. Bridgman (1952) has shown that the introduction of large hydrostatic pressures markedly increases the ductility of metals. He (1947) has also shown that the strength and ductility of NaCl and A1203 are increased by the application of hydrostatic pressure. 4. FRACTURE For a perfect crystal, the theoretical stress required for fracture along a cleavage plane is about E/s where E = elastic modulus normal to the cleavage plane (Gilman, 1963). Usually the stress is far smaller, as small as E/105. Low fracture stresses are caused by surface defects in the crystals or by plas

14 tic flow which precedes fracture and which creates very high stresses in localized regions. When both plastic flow and surface defects are eliminated, ionic crystals require very high stresses to make them fracture (Stokes, 1962; Johnston, 1963). The fracture process is considered to occur in two parts: (a) nucleation of cracks and (b) growth or propagation of cracks. Both of these will be considered separately. a. Nucleation The most important source of cracks or flaws in crystalline ceramics is the external surface. Surface deposits or reaction products can provide interfaces at which cracks may form. Stokes et al. (1960) have demonstrated that surface precipitates formed on improperly dried NaCl crystals lead to premature failure. Evidence now seems conclusive that cracks form as a result of plastic flow in regions where the motion of dislocations is impeded by some sort of barrier (Parker, 1963). This barrier may be the intersection of glide bands or the intersection of a glide band with a boundary. In each case, a stress concentration is provided by the nonhomogeneous nature of the slip process, wherein a region of localized plastic shear is constrained within an elastically strained matrix (Johnston and Parker, 1963; Low, 1963). Stokes (1958) and Washburn et al. (1959) concluded that cracks often form at the intersection of two slip bands in MgO crystals. Stokes (1958) attributed the crack formation to a Stroh (1954) mechanism whereby dislocations which piled-up at a kink band coalesced to nucleate a crack. Washburn et al.

15 (1959) associated the crack formation with a Cottrell (1953, 1958) mechanism where dislocation pile-up on two intersecting (110) slip bands leads to crack nucleation along a (100) plane. Keh et al. (1959) suggested that the mechanism for (110) cracks might be that dislocations on two intersecting (110) planes pile-up against the resultant immobile dislocation on the (112) plane with a [110] vector and initiate a crack in a third (110) plane. Stokes et al. (1961) and Johnston (1963) showed that MgO crystals are brittle or ductile depending on the slip distribution. If, for example, deformation in MgO proceeds by nucleation and growth of a single glide band which spreads along the gauge length, the crystal may exhibit 7 percent or more plastic strain before fracture. However, if just two glide bands intersect at the onset of yielding, complete fracture can occur with very small macroscopic strain. Work on MgO bicrystals misoriented from each other by varying amounts showed that cracks may form at a grain boundary due to a stress concentration resulting from the inability of a glide band to penetrate a neighboring grain (Johnston et al., 1962) or from the interaction of two slip bands (one from each grain) which intersected the boundary a few microns apart (Westwood, 1961). b. Growth When Griffith's (1921) theory of crack growth by the release of elastic energy is applied to NaCl-type ionic crystals, it is found that the calculated critical crack length for propagation is much larger than anything one might

16 expect to remain undetected in the crystal (Stokes and Li, 1963; Miles, 1964). Yet fracture still occurs. It has now been shown, however, that plastic flow is itself nucleated by the microcracks and enables them to grow (Stokes and Li, 1963; Miles, 1964). Screw dislocations also have a large effect on crack propagation. A crack running perpendicular to a screw dislocation can split into two cracks (cleavage step) when it strikes the dislocation line (Gilman, 1961a). The principal energy absorbing mechanisms appear to be (1) the creation of cleavage steps as the crack advances and (2) localized plastic deformation by dislocation nucleation and movement (Gilman, 1957; Amelinckx, 1958) at the tip of the crack. In single crystals, the controlling factor in the growth of cracks is the resistance to plastic deformation at the crack tip which, in turn, is influenced by temperature, composition, and microstructure (Low, 1963). The process of blunting the crack tip and replacing the concentration of elastic stress by a more diffuse distribution of stress associated with dislocations depends upon dislocation mobility. At lower velocities, the propagation of a crack is unstable (Gilman and Stauff, 1958). Appreciable amounts of plastic flow may take place if sufficient time is available after dislocations have been nucleated by a moving crack. In the absence of cleavage step formation, dislocation nucleation, etc., a crack moves through a crystal by causing successive breakage of atomic bonds across the plane of the crack. The energy required to do this is related to the cohesive energy and is sometimes defined as the true surface energy of the crystal (Gilman, 1961la).

17 Cracks which form in MgO at the intersection of two orthogonal (110) slip bands and propagate over a (110) plane are often blocked by neighboring glide bands (Stokes et al., 1959). The ability of a glide band to arrest a crack was first observed in NaCl by Melankolin and Regal (1956) and stems from the fact that the crack has to cut through the screw components of a very large number of dislocations making up the band. The consequence of this crack stabilization is that the total deformation preceding fracture depends critically on the distribution of slip at the onset of yielding. Temperature strongly influences the ease of crack propagation in ionic crystals. Raising the temperature increases the ductility of a crystal by increasing the mobilities of dislocations. Even when the dislocation mobility is essentially zero, however, as in silica or alumina at room temperature, cracks too small to propagate can grow progressively at a constant stress through the action of an active environment such as water vapor (Johnston, 1965). B. Hardness and Hardness Testing The indentation hardness test is probably the simplest method of measuring strength of materials but it is also the least understood in terms of stress and strain distribution (Keh, 1960). Indentation hardness tests have been used extensively to characterize polycrystalline materials and a large amount of literature has resulted which has been summarized in several books (Lysaght, 1949; Tabor, 1951; Mott, 1956). Some progress has been made in analyzing the stress and strain distribution of several types of indenters, but the results

18 cannot be applied directly to single crystals having well defined slip systems (Hill, 1950) because even the most symmetric crystals show marked anisotropy with respect to hardness and plastic flow around the indenter. Since Vickers and Knoop hardnesses were used exclusively in this study, the review will be confined to these two tests. 1. VICKERS HARDNESS The Vickers hardness test utilizes a square base diamond pyramid as the indenter. The included angle between opposite faces of the pyramid is 136 degrees. The diamond pyramid hardness number (DPH) or Vickers hardness number (VPH) is defined as the load divided by the surface area of the indentation, calculated from microscopic measurements of the impression diagonals, and is expressed in kg/mm2. The versatility of the test is due to the fact that it provides a continuous hardness scale, for a given load, from very soft to very hard materials (Dieter, 1961). Theoretically, the DPH should be independent of applied load, but in reality it decreases with increasing loads up to about 1 kg (Buckle, 1959). Care should thus be taken to specify loads when reporting microhardness readings (i.e., results for loads less than 1 kg). Of the many factors which affect the quality of microhardness readings, the most important are: (1) preparation of the specimen (polishing is necessary), (2) vibration, (3) measurement of the impression, (4) load and loading rate, (5) shape of the indenter, and (6) sensitivity of equipment (Buckle, 1959). Hardness can become a measure of the yield stress or the ease with which dislocations can move through a crystal. Westbrook (1958a) found that the

19 yield stress of NaCl was related to its Vickers hardness as: Y.S. = Hv/35, where Y.S. is the yield stress in kg/mm2 and Hv is the Vickers hardness in the same units. A linear relation between hardness and elastic modulus for other NaCl-type crystals has been shown by Gilman (1961a). Empirical correlations have also been obtained between hardness and (1) melting point (Westbrook, 1958b; Wolff, 1958), (2) surface energy of the indented material (Kuznetsov, 1957; Kolsky, 1957), and (3) the energy needed to create new surfaces at fractures (Roesler, 1956). Marsh (1963) has tried to draw a consistent picture between the DPH and the general mechanical behavior of glasses and other highly elastic isotropic materials. Tolansky and Nickols (1949, 1952) and BUckle (1954, 1959) found that Vickers indentations gave distorted impressions on single crystals of tin and aluminum and that material pile-up around the indentations is crystallographically directional and independent of the indenter orientation. Warrick (1963) studied the change in hardness of NaCl with temperature from room temperature to 1075~F. The hardness of MnS, as well as of certain types of iron and steel, has been determined between 20~ and 1000~C by Chao et al. (1964b). Keh (1960) innovated the use of etch pit techniques to study the deformation patterns around Vickers indentations in MgO at various temperatures. Chao et al. (1964a) studied dislocation rosettes and slip in MnS single crystals by this technique. 2. KNOOP HARDNESS The Knoop indenter is a diamond pyramid in which the included conical

20 angles subtended by the longer and shorter edges, respectively, are 172030' and 150~. In the plane of the specimen, the indentation has the shape of a parallelogram in which the longer diagonal is about seven times the shorter diagonal (Tabor, 1951). The construction is such that very little elastic recovery takes place in the direction of the long diagonal. The long diagonal becomes the basis of the hardness measurement which is defined as: Hk = W/A, where Hk = Knoop hardness number, W = dead weight load applied and A = unrecovered projected area of the impression. Because of the shape of the Knoop indenter, the hardness numbers are influenced by the orientation of the indenter on single crystal specimens. This hardness anisotropy of single crystals has been investigated by numerous authors on materials such as Al (Petty, 1963; Garfinkle and Garlick, 1967), Ti (Feng and Elbaum, 1958; Partridge and Roberts, 1964), Mg (Schwartz et al., 1961; Partridge and Roberts, 1964), Zn (Daniels and Dunn, 1949; Partridge and Roberts, 1964), Fe (Daniels and Dunn, 1949), Cd (Partridge and Roberts, 1964), Co (ibid.), Be (ibid.), Os (ibid.), W (Garfinkle and Garlick, 1967), and Nb (ibid.). In addition, Chao et al. (1964b) and Moore (1965) have measured the orientation dependence of Knoop hardness on the (001), (011), and (111) surfaces of MnS and MnO respectively. Because of the complex nature of this deformation problem, none of the authors has stated a successful quantitative theory to explain their results. Daniels and Dunn (1949), who investigated the hardness anisotropy on single crystals of silicon ferrite and zinc, are the only persons who have attempted to formulate a theory to explain this behavior. Their analysis is based on

21 calculating a resolved shear stress on slip planes and in slip directions assuming that four tensile forces act in directions parallel to the steepest slope of each facet of the indenter and cause material to move to the surface. This assumption has been the subject of some criticism (Mebs, 1949). C. Pertinent Information on MnO, MnS, MnSe, and MnTe 1. STRUCTURE AND PHASE RELATIONS The MnS and MnSe utilized in this investigation have the face-centered cubic NaCl-type structure. Both show two other unstable allotropic modifications (Baroni, 1938; Taylor and Kagle, 1963): a cubic zincblende (sphalerite) structure and a hexagonal wurtzite form. Manganese oxide also has the NaCl structure. Manganese telluride at room temperature has a hexagonal NiAs structure depicted in plan view in Figure 2, with a c/a ratio of 1.621. The difference between the NaCl and NiAs structure is merely one of stacking anion and cation layers. For the NaCl structure the sequence is AcBaCbAcB etc... along <111> while for the NiAs structure it is AcBcAcBc etc...along <0001>. The capital letters represent anion layers and the lower case letters, layers of the smaller cations. The exact crystal structure of MnTe may not be of the simple NiAs variety, however, because of the possible "super-lattice" often associated with NiAs-type materials as outlined by Wyckoff (1965). In addition, the problem is further complicated by a slight amount of nonstoichiometry in MnTe as reported by Johansen (1958). He found that the compound was a tel

22 ('/ ^*^/C jf0^11^ J\I Figure 2. Diagram of the hexagonal NiAs-type structure of manganese telluride looking down the c-axis. The smaller circles represent manganese atoms and the larger, tellurium. The numbers at the centers of the circles designate fractional distances above base level along the c-axis. lurium excess material with a composition range MnTe.*o02 to MnTel.013. To a very good approximation, however, the structure may be assumed to be the simple NiAs-type. MnTe transforms to the NaCl structure above 1040~C (Johnston \1 and Sestrich, 1961). The systems Mn-S, Mn-Se, and Mn-Te all show two compounds-MnS and MnS2, MnSige MnSe2. Diagram of the hexagonal NiAs-type structure of manganespectively, ll of whuride looking down the c-axis The smaller etric composition. Blitz al. (nganese atoms and the Mnarg ier, telluriu. stable and it is therefore to be expecters of that e circles designate frast to analogous compounds abof relate level along the c-axis. metals, havegood a very smation, homogeniety range. Kellmay be9) ad Kiessling (1966, the 1967) report that boype. MnS ansforms to e NaC stoichiometructure above 1040C (Johnston and Sestrich, 1961). The systems Mn-S, Mn-Se, and Mn-Te all show two compounds-MnS and MnS2, MnSe and MnSe2, and MnTe and MnTe2 (Furberg, 1953; Hansen, 1958), respectively, all of which appear to be very nearly of stoichiometric composition. Blitz et al. (1933) state that the Mn+2 ion is very stable and it is therefore to be expected that MnTe and MnTe2, in contrast to analogous compounds of related 1967) report that both MnS and MnSe are stoichiometric.

23 The system MnO-MnS was studied by Chao et al. (1963) and their results are presented in Figure 3. Mehta et al. (1967) studied the MnS-MnSe system and found a continuous series of solid solutions as shown in Figure 4. Tien et al. (1967) investigated the system MnTe-MnS and found the results shown in Figure 5. Panson and Johnston (1964) and Makovetski and Sirota (1964) studied the system MnTe-MnSe, although the latter authors determined solid solubility limits at a temperature of 800~C only. The diagram of Panson and Johnston (1964) is shown in Figure 6 where it is seen that there is extensive solid solubility above 550~C and that above 1040~C a single phase solid solution of the NaCl-type structure exists for all compositions. Kiessling et al. (1966, 1967) have investigated the solid solubility limits at 1150~C for systems of the type (Mn, Me)S and (Mn, Me)(S,Se) where Me represents the metal Ti, V, Cr, Fe, Co, or Ni. This limit was found to vary continuously with a maximum for Cr and Fe substituted in the MnS, MnSe, and MnSo.sSeo.5 lattices. 2. OTHER PROPERTIES The compounds of manganese with Group VI elements are all antiferromagnetic with Neel temperatures as shown in the following table (Squire, 1939; Kittel, 1957): Comp d Neel Temp. Compound ( OK) (LK) MnO 122 MnS 145-154 MnSe 150-165 MnTe 307

24 16. -- t 16X. LIQUID. MN S 1200. 1 >S 1 600 Iq d - U12325 MNO + MNS 0 10 20 30 40 50 60 70 80 90 100 MNO WEIGHT PERCENT M.S MNS Figure 3. The system MnO-MnS, (Chao et al., 1963). 1700...-........, 1_00 q15uid.1.5 1500 0 Lii 1400 Mn (Se, S) 4 I 1300 Solid Solution W Li a Liquid Solid o Solid 1100 x Solidus by Y ~[y diffraction 1000' MnSe 25 50 75 MnS MOLE PERCENT Figure 4. The system MnSe-MnS (Mehta et al., 1967).

25 1600 - - 1400 - D 1200 Liquid // DTA DATA n< L / ~ * Cooling a. 1000 A Heating 8710 C A A \71\' 04-MnTe + MnS 600 a - MnTe + MnS I I I I L J I L 0 10 20 30 40 50 60 70 80 90 100 MnTe MOLE % MnS MnS Figure 5. The system MnTe-MnS (Tien et al., 1967). T(C) 1100 -- 0 X-Roy Porometer A Oilotometer 900- 0 Thermol Anolysis * X-Roy Symmetry Cubic Hexogonol 500 0 Cubic + Hexogonol 0.2.4.6.8 1.0 MnSe x MnTe Mole Fraction MnTe Figure 6. The system MnSe-MnTe (Panson and Johnston, 1964).

26 +2 Above the Neel temperature, the magnetic moments of the Mn ions are randomly oriented and the material appears paramagnetic. For MnO, MnS, and MnSe +2 below their Neel temperatures, the magnetic moments of the Mn line up antiparallel along the <100> directions giving a magnetic unit cell with twice the dimensions of the chemical unit cell as shown in Figure 7. MAGNETIC i C HEMICAL UNITr CELL UNIT CELL Mn ATOMS IN MnO Figure 7. Antiferromagnetic structure of MnO below its Neel temperature. Only Mn ions are shown (Shull et al., 1951). The antiferromagnetism may also result in a slight distortion of the unit cell from cubic symmetry. Changes from FCC symmetry to (1) a slightly distorted FCC (i.e., rhombohedral) cell have been observed for MnO (Tombs and Rooksby, 1950; Shull et al., 1951), MnS (Tombs and Rooksby, 1951), NiO (Tombs and Rooksby, 1951; Slack, 1960), and FeO (Tombs and Rooksby, 1950) and to (2) a tetragonal structure in the case of CoO (Tombs and Rooksby, 1950; Greenwald, 1953). Greenwald (195) and Grazhdankina and Gurfel (1958) have investigated the thermal expansion of MnTe by X-ray lattice parameter measurements and both found a sharp contraction in the c-axis at around 310~K on cooling. The a-axis con

27 tinued to change linearly with temperature. This is due to the antiferromagnetic transformation at this temperature and suggests that the magnetic moments +2 of the Mn ions are parallel to the c-axis but anti-parallel to each other on successive (0001) planes. Also investigated have been the magnetic susceptibilities of MnO (Bizette et al., 1938; Banewicz et al., 1961), MnS (Squire, 1939; Banewicz and Lindsay, 1956), MnSe (Squire, 1959; Lindsay, 1951; Banewicz et al., 1961), and MnTe (Squire, 1939; Banewicz et al., 1961). Of particular interest are the susceptibility results of Lindsay (1951) and the thermal expansion results of Makovetski and Sirota (1963) for MnSe. Lindsay's magnetic susceptibility measurements show a large thermal hysteresis in the range -196~C to 25~C and a dependence of susceptibility on field strength-phenomena which are not observed in MnS (Banewicz and Lindsay, 1956). He proposes a theory to explain this in terms of three phases which hypothetically exist in the experimental temperature range and which possess different susceptibilities. He does not explain the nature of these phases. Makovetski and Sirota (1963) noted anomalous behavior in the thermal expansion coefficient at low temperatures and attributed it to a polymorphic change in addition to the known antiferromagnetic transformation. X-ray diffraction patterns were taken at room temperature and at 197~K after quenching in liquid nitrogen. At 197~K several additional peaks appear but the authors do not speculate on the nature of this "second phase." Kelly (1939) also observed anomalies in the specific heat-temperature curve for MnSe. The temperatures specified by Lindsay (1951), Makovetski and

28 Sirota (1963), and Kelly (1939) for the anomalous behavior differ significantly in each case. More recently, however, Makovetski and Sirota (1966) have reported that MnSe transforms to the sphalerite (cubic ZnS) modification at low temperatures. Thermal expansion coefficients have been measured for MnO (Moore, 1965), MnS (Moore, 1965), MnSe (Makovetski and Sirota, 1963), and MnTe (Greenwald, 1953; Grazhdankina and Gurfel, 1958).

CHAPTER I EXPERIMENTAL PROCEDURE A. Raw Materials Manganous sulfide (MnS) was prepared by the sulfur deoxidation of reagent grade manganous sulfate (MnS04.H20) of 99.6% purity in an apparatus shown schematically in Figure 8 (Chao et al., 1964a; Moore, 1965). Sulfur was vaporized at 410-430~C and one atmosphere pressure in a vycor tube and contacted the MnS04 powder at 900~C. The inside of the vycor tube was lined with graphite felt around the MnS04 charge and the charge itself was held on a piece of graphite resting on alumina saddles. The following reaction appears to be appropriate: MnSO4 + S2 - MnS + 2S02 Chao's (1964a) analysis of the green NaCl-type MnS prepared in this way showed 36.8 ~ 0.2% sulfur compared with 36.9% for stoichiometry. To prevent the slow oxidation of the MnS powder to MnS04, the product was melted and solidified under vacuum into ingots weighing about 60 grams each. Manganese selenide was prepared in a way similar to that used by Kelly (1939), Panson and Johnston (1964), and Mehta et al. (1967). Manganese metal powder and selenium powder, 100 mesh or more, were mixed in appropriate portions, placed in a vacuum degassed graphite crucible and encapsulated in a pyrex tube under a vacuum of about 10 microns. This was reacted at 600~C for several days. 29

30 4 50. __ 5 1. S02 exhaust 6. Graphite felt liner 2. Stirrer 7. Perforated graphite disk.Vycor eaction tube on support of A1203 saddles 3. Vycor reaction tube 4. Upper furnace, 9000C 8. Liquid sulfur 9. Lower furnace, 5. MnS04 charge hlo-430~C Figure 8. Apparatus used for the preparation of stoichiometric manganese sulfide. 4. p ss srnce gO" ~- --- Ioe ura $, ~J~nS0 —---- 2 4 —-— 30" Fi~ure -^ -- 4paau sdfrtepeaaino stoichiometric- tj;-;s slfde

31 The manganese powder was prepared by triply vacuum distilling 99.9% electrolytic manganese to remove oxides and then crushing under a nitrogen atmosphere. High purity selenium shot supplied by Canadian Copper Refiners Limited was also crushed under a nitrogen atmosphere. A typical analysis of the selenium was: Hg 0.5 ppm Te 1 ppm Pb 1 ppm Fe 0.5 ppm Cu 0.08 ppm The MnSe prepared in this way was kept in the pyrex tube until ready for use. In general, 0.5 to 1% excess selenium over the stoichiometric amount was used in the initial MnSe reaction. This excess Se could be conveniently removed by placing the MnSe at the far end of a vycor tube attached to a vacuum pump. This end was then heated to 800~C and the excess Se drawn off. X-ray examination revealed no other phases but microscopic examination revealed minor amounts of MnO in spite of precautions taken during MnSe preparation. Manganese telluride was prepared in a manner exactly analogous to that used for MnSe. A typical analysis of the high purity tellurium shot, also supplied by the Canadian Copper Refiners Limited, was: Se 370 ppm Pb 5 ppm Cu 0.3 ppm Al 2 ppm Mg 1 ppm

32 The MnTe also revealed minor amounts of MnO on microscopic examination. The reaction: Mn + Te + MnTe was more exothermic and uncontrollable than that for MnSe but the graphite crucible provided an effective heat sink. B. Materials Purification Manganous sulfide was further purified by a zone refining procedure. About 60 grams of the previously solidified MnS were crushed and remelted under a purified argon atmosphere in a graphite boat within a horizontal moving coil induction furnace. After four or five passes at a speed of 3 in./hr, the MnS developed a coarsely crystalline grain size. Microscopic and X-ray examination revealed no other phases and X-ray data, extrapolated to O = 90~ using the Nelson-Riley factor, 2 (cos2O/sin Q + cos2G/Q), gave a lattice parameter of 5.224A compared with 5.224A reported by ASTM (Card 6-018), 5.225A given by Chao et al. (1964a), and 5.2236A reported by Wyckoff (1965). Manganese selenide and manganese telluride were also purified by a zone refining technique using an apparatus like that shown in Figure 9. Both MnSe and MnTe, when melted in graphite under argon at one atmosphere total pressure, slowly decomposed to elemental Se or Te with the formation of manganese arbide. The manganese carbide decomposed upon exposure to air into a complex hydrated manganese oxide. It was necessary, therefore, to seal the graphite crucible containing the MnSe or MnTe in a fused silica tube under a pressure of about 200 mm of purified nitrogen. With this procedure, a back pressure of Se or Te was built

1 2 3 4 5 6 7 8'.................... 0 0 - -...'....... Iii]Ti'liii i|lti'le~l~iF li i iii i"|TTi|~iii i TTi~i| 1. Secondary furnace, 650-700~C. 5. Graphite crucible. 2. Moving vycor tube. 6. Two turn induction coil. 5. Fused silica protecting tube. 7. Sample to be zone refined. 4. Fused silica encapsulating tube. 8. Screw drive mechanism. Figure 9. Schematic diagram of zone refining apparatus for the purification of manganese selenide and manganese telluride.

34 up which prevented the reaction of Mn with the crucible. The partial pressure of nitrogen was necessary when zone refining MnSe so that, at the zone refining temperature, a total pressure slightly greater than one atmosphere existed within the fused silica tube. The tube was thus prevented from slowly collapsing around the graphite crucible. The secondary furnace around the two-turn induction coil was necessary to prevent cracking of the fused silica tube due to phase changes in devitrified material on cooling (General Electric Co., 1964). This furnace was maintained at 650~C for MnTe and 700~C for MnSe. Eight to ten passes were made at a speed of 35 in./hr for both MnSe and MnTe. In each case the first 60 percent of the resultant ingot was used as the purified raw material. Microscopic examination revealed no other phases in either MnSe or MnTe except for an occasional inclusion which apparently was MnO. Chao et al. (1963) showed that the maximum solubility of MnO in MnS is only 1.7 weight percent. Therefore, it can reasonably be assumed that, because of the much larger ion size differences involved (ionic radii: 0 = 1.32A, S = 1l74A, -2 -2 Se = 1.91A, and Te 2.11A) (Van Vlack, 1964), the oxide solid solubility in MnSe at room temperature is very small and would be smaller yet in MnTe. Furthermore, Chao et al. (1964b) found that the effect of MnO on the hardness of MnS was small from room temperature to 1000~C. On this basis, it is assumed that the very small amounts of MnO encountered have very little effect on the properties studied.

35 X-ray powder patterns gave a lattice parameter for the NaCl-type MnSe of ao = 5.4635 which compares with 5.462A reported by ASTM (Card 11-683) and 5.45A by Taylor and Kagle (1963). Manganese telluride, which has a hexagonal NiAstype structure gave ao = 4.138A and co = 6.706A. This compares with average values of ao = 4.157A and co = 6.706A as reported by ten separate authors. Chemical analyses were performed on MnSe and MnTe using methods described by Kriege and Theodore (1966) and Vogel (1961). Manganese was determined by an EDTA titration using Eriochrome Black T as indicator and selenium and tellurium were determined gravimetrically by precipitation from S02 saturated solutions. The reader is referred to the original articles for procedural details. For MnSe, the results gave 40.5 to 41.35 Mn and 59.4 to 60.0% Se by weight. Stoichiometric MnSe is 41.Oo Mn and 59.0% Se. Kelly (1939), Kiessling et al. (1967), and Panson and Johnston (1964) report nearly stoichiometric MnSe. For MnTe the results gave 30.0 to 50.4% Mn and 69.5 to 69.8% Te by weight compared with 30.1% Mn and 69.9% Te theoretically. C. Crystal Growth 1. PURE COMPOUNDS The MnS as zone purified provided grains of sufficient size to be used in the single crystal studies. With the MnSe or MnTe about 50 grams of the material was placed in a 5 in. long x 3/8 in. I.D. vacuum degassed graphite crucible and encapsulated

36 under a pressure of 200 mm of purified nitrogen in a fused silica tube. This tube was placed in a larger vycor tube and the whole assembly lowered through an induction coil at the rate of about 3/8 in./hr. This produced single crystals of sufficient size to be used in this study. The growth of single crystals of MnTe proved to be difficult because MnTe undergoes an inversion from a NaCl-type structure to a hexagonal NiAs-type on cooling below 1040~C (Johnston and Sestrich, 1961; Tien et al., 1967). In addition, a sharp contraction of the c-axis occurs at 307-310~K due to an antiferromagnetic transformation (Greenwald, 1953; Grazhdankina and Gurfel, 1958). As a result, good quality single crystals were not obtained. Rather, a coarse-grained structure was found in which individual grains tended to be misoriented from each other by, at most, 8 to 10 degrees. For instance, when looking at a (0001) back-reflection Laue photograph, bands of spots were seen rather than rows of single spots, the total band scatter being 8 to 10 degrees at most. This could be described as a coarse mosaic structure. Quite often a "crystal' would show only two or three separate mosaic parts differing by not more than ~5 degrees from a mean value. These crystals were used whenever possible. 2. BINARY COMPOSITIONS For single crystals of other than the pure compounds, the individual components were crushed to around 50 mesh, mixed in the desired portions, placed in a graphite crucible, and sealed in fused silica as before. Each of the compositions was chemically analyzed for Se or Te or both Se and Te by the methods

37 already outlined (Vogel, 1961; Kriege and Theodore, 1966) utilizing at least two samples for each analysis. Compositions in single phase regions of the systems MnS-MnSe and MnSe-MnTe were studied. D. Sample Preparation 1. ORIENTING AND CUTTING Single crystals were cleaved from the solidified ingots, placed in a graphite crucible, sealed in a vycor tube under a vacuum of 10 microns, and annealed for 12 hours at 1000~C. Following the annealing treatment the crystals were mounted on a goniometer and oriented to the desired crystal plane by the Laue back-reflection technique. They were then transferred, maintaining orientation, to another holder and slices cut with a 0.010 in. thick rubber bonded alumina wheel on a Dimet cut-off machine. For the cubic structures (001), (011), and (111) planes were studied and the orientations were accurate to within 2 degrees. Investigated in the hexagonal systems were the (0001), (1010), and (1120) planes. These orientations were accurate to within about 8 to 10 degrees. 2. MOUNTING AND POLISHING The samples were mounted in bakelite (or solder for low temperature testing) preparatory to polishing. Samples were polished on 400 and 600 grit silicon carbide paper and then on 8 micron and 1/2 micron diamond wheels. Next they were polished with Linde B alumina powder under alcohol on a Syntron

38 vibratory polisher and etched with a solution of composition 1% conc. H2S04, 1% phosphoric acid, and 1% of a solution of saturated oxalic acid. Repolishing with 1/2 micron diamond paste and Linde B on the Syntron followed twice more. Because of the softness of the samples (about that of pure Cu or pure Fe) this procedure proved necessary to obtain good surfaces and to remove residual stresses. Subsequent Laue photographs showed no significant residual stresses in the crystals. Many electrolyte solutions were tested in an effort to develop an electrolytic polishing technique but none proved satisfactory. Throughout the polishing procedure the samples were checked for parallelism of opposite faces of the mounting material. This was necessary to insure good hardness measurements. E. Testing and Examination Procedure 1. DEFORMATION The mounted and polished samples were then indented with either a Vickers or Knoop diamond indenter on a Wilson Tukon Hardness Tester and the hardness measured. For the Vickers test the loads used were 200 or 500 grams while for the Knoop test, 100 or 200 grams. The long axis of the Knoop indenter was made parallel to the several low index crystallographic directions on each of the planes tested. Upon microscopic examination in obliquely reflected light, slip lines were directly observable around the indentations. By noting the angles which these slip traces made with each other and with known crystallographic direc

39 tions, and by plotting these traces for a given plane on a stereographic projection according to the method described in Barrett (1952), one could determine the indices of all planes capable of making such traces. By comparing the results from the different crystallographic surfaces, one could uniquely determine the plane or planes upon which slip occurred. Slip mechanisms were also studied by dislocation etch pit techniques on the (001) plane of MnSe, MnS,and compositions in the system MnS-MnSe. Chao et al. (1964a) developed an etchant for MnS of composition 1% H3P04, 1% H2SO4, and 1% of a saturated oxalic acid solution which showed a preference for etching edge dislocations intersecting (100) surfaces. The etchant also appeared to work well on (100) of MnSe, giving etch pits, as in MnS, composed of the four (1013 facets which intersect a (100) surface at 45 degrees. The etchant was generally ineffective in showing dislocations on surfaces other than the cube faces. By observing dislocation etch pit rosettes around the indentations, insights into the slip mechanism could be obtained and changes in the slip system followed. A third method utilized to study slip was that of observing Knoop hardness variations as a function of indenter orientation and sample composition. Knoop hardnesses showed anisotropic effects and were found to change relative to each other as well as in absolute value as primary slip systems changed. An interferometric technique was also used to study flow and pile-up around Vickers indentations on MnS, MnSe, and MnTe.

4o 2. FRACTURE Fracture was studied by attempting to induce cleavage on several of the crystallographic planes of the samples and by noting fracture surfaces on crushed fragments. Also, if fracturing was in evidence around indentations, the type of fracturing was noted and attempts were made to relate this to slip interactions. 3. TEMPERATURE EFFECT In addition to measurements at room temperature, Vickers and Knoop hardness tests were attempted for MnS, MnSe, and MnS-MnSe binary compositions at temperatures of 135~C, -70~C, and -196~C. For these tests, the sample mounts were cemented in a stainless steel cup and the cup filled with a suitable liquid which covered the top of the specimen and at least 1/8 of an inch of the bottom portion of the indenter. A schematic diagram of the apparatus is shown in Figure 10. In the 1350C tests, a small heating coil was placed around the sample and the sample covered with vacuum pump oil. Hardnesses at room temperature with the specimen immersed in oil did not differ from those obtained in air. For low temperature tests it was found necessary to mount the samples in solder in order to prevent sample deformation by the squeezing action of the bakelite mold. Bakelite has a thermal expansion coefficient of 40 x 10 /~C (Van Vlack, 1964) compared with 18.5 x 106/~C for MnSe (Makovetski and Sirota, 1963), and 14 x 10 /~C for MnS (Moore, 1965). This resulted in the sample being exposed to a large compressive stress on cooling, sufficient to cause it

41 lOil 1. Indenter. 2. Oil, alcohol or liquid nitrogen. 3. Insulated stainless steel cup. 4. Sample and mount. 5. Transite board. Figure 10. Diagram showing technique used for hardness testing at -196~C, -70~C, and 135~C.

42 to deform in the mold. This does, however, provide an interesting way to study plastic deformation mechanisms in low yield strength materials. In the -70~C tests, specimens were immersed under an alcohol-dry ice mixture. Room temperature hardnesses under alcohol agreed with those found in air. Those tests at -196~C were made under liquid nitrogen. 4. LOW TEMPERATURE X-RAY STUDY Finally, low temperature Debye-Scherrer X-ray diffraction patterns at -84~C and -1300C were obtained in an attempt to explain anomalous behavior in MnSe at low temperatures as observed in this study and previously by Kelly (1939), Lindsay (1951), and Makovetski and Sirota (1965). An ordinary Debye-Scherrer camera was modified to allow nitrogen vapor to pass over the specimen. The temperature was controlled by adjusting the current input to a small heating coil immersed in a dewer of liquid nitrogen. This in turn controlled the rate of vaporization of nitrogen which would then pass out of the dewer and over the sample. The lowest temperature attainable was -135~C. This was measured with a chromel-alumel thermocouple placed directly over the specimen in an apparatus shown schematically in Figure 11.

43 2y~r2^ 8 7 1. Debye-Scherrer powder camera. 6. Plastic cover with opaque liner on Debye-Scherrer 2. Insulated copper tubing. camera. 3. Heating coil. 7. Cellophane window. 4. Dewer. 8.'Sample in 0.3 mm 5. Liquid nitrogen. capillary tube. 9. Chromel-alumel thermocouple. Figure 11. Schematic diagram of apparatus used to obtain low temperature Xray powder patterns of manganese selenide.

CHAPTER IV EXPERIMENTAL RESULTS A. Manganous Selenide 1. PLASTIC DEFORMATION a. Mechanism The observation of slip traces around Vickers indentations on the (001), (011i), and (111) planes of MnSe revealed that the primary glide planes are (111). The slip directions were taken to be the close-packed directions on these planes, giving a Burgers vector a <110>. The slip mechanism (111) <110> corresponds to that found in FCC metals and in the NaCl-type compounds uranium carbide (Van Der Walt and Sole, 1967) and titanium carbide (ibid.). This is in contrast to the (110) <110> primary glide mechanism found in MnO (Moore, 1965), MnS (Chao et al., 1964a), and, indeed, in most NaCl-type materials where the chemical bonding is largely ionic. Figures 12, 13, and 14 shfow the slip lines around Vickers and Knoop indentations on the (001), (011), and (111) planes of MnSe respectively. On the (001) plane (Figure 12), the slip lines extended in <110> directions. This is consistent with the intersections of (111) planes as may be seen from Figure 15, which shows two cubic unit cells together with several low index planes. On the (011) plane, the traces were in [Ol] and <112> directions (Figure 13a shows only [011] traces) and unequivocally identified 44

45 Figure 12. Slip traces around Vickers indentation (500 gm load) on the (001) surface of MnSe single crystal. Oblique lighting. X200. (a) X250 (b) X500 Figure 13. Slip traces around Knoop and Vickers indentations on the (011) surface of MnSe single crystal. Oblique lighting.

46 Figure 14. Slip traces around Vickers indentation (500 gm load) on the (111) surface of MnSe single crystal. Oblique lighting. X250. Figure 15. Two cubic unit cells showing several low index planes and their intersections with other planes.

47 the slip planes as (111). Slip lines on the (111) plane were in <110> directions, consistent with (111) slip, but they do not provide any additional information since slip on either (100) or (110) planes would also show the same traces. Chao et al. (1964a) found that the primary slip mechanism in MnS was (110) <110> with a secondary mechanism (111)<110>. With MnSe, (110)<110> slip was observable as a secondary mechanism as seen in Figure 16. The lines in <110> directions are attributable to (111) slip while the traces in <100> directions connecting the <110> lines reveal where cross slip on (110) planes has occurred. The specimen shown in Figure 16 was mounted in bakelite and quenched to -70~C in an alcohol-dry ice solution. The differential thermal contraction between the bakelite (a = 40 x 106 /~C (Van Vlack, 1964)) and MnSe (a = 18.5 x 106 /~C (Makovetski and Sirota, 1963)) was sufficient to create a compressive stress in the MnSe great enough to cause deformation in certain regions. b. Pile-up and Sinking-in Around the Indenter For certain orientations of the Vickers diamond pyramid relative to the surface of indentation, impressions of unusual shape were observed. Two examples are shown in Figures 17a and 17b for indentations on the (001) and (011) planes respectively. Buckle (1954, 1959) observed the same shaped impression as shown in Figure 17a on the cube face of an aluminum single crystal when the indenter was oriented with its diagonals in <110> directions relative to the surface. Using an interferometric technique to observe surface contours, he concluded that the star-shape was not due to extensive elastic recovery, but

48 Figure 16. The (001) surface of MnSe single crystal mounted in bakelite and quenched to -70~C. Slip traces due to (111] glide and (110} cross slip are evident. X250. (iii':::P:ii:; 0 0 ]:..:::'i. CEL.000:000;:0:;0E iiE:'-i:f; t iiEV ~ i: ii;;:; i j L;0:00;..: i::::::: i iiT:l:: f tl? I: i:::::.'::. ab-li li i\11y;, ^^.y^- ^ ^ ii'*'''."<0V''..0 *0 * "::.... ":,' *^:fffitiS.,[;.*: " * - (a) (b) Figure 17. Examples of Vickers impressions of unusual shape on (a) the (001) and (b) the (011) surfaces of MnSe single crystals for certain orientations of the indenter. X500. i::i:i::iiil~i~i~:ii i:::;.:.$i:i:i':siiliii~i ~ii::::c-:i:::~i:i~i:i~iiii:I::'::'lii~;Q < I~l::::::: i:::':iliiliiill~j:WiiK \:::iiiii:iii~i::iii1:::::::: i::i,;:l ll;iii'ili:':j i~ji:jjl li:l:'~::':::i:i: i;~:~lili';:i~l:iiiill::i:::: ll: l ( 0 1 1 ]::::: Deoi_.. [1 00 an b)te 01 sracso Mn::e s-..'ing;le crystals fori ceti rinain

49 rather, was caused by a directional piling-up and sinking-in of material displaced by the indenter. Interference photomicrographs of Vickers impressions on the (001) surface of MnSe also revealed extensive piling-up and sinking-in of material around the indentations. Figures 18a and 18b show these elevation contours for impressions in which the indenter diagonals were in <100> and <110> directions respectively. Figure 18a is the same indentation as that shown in Figure 12. These figures indicate four hills or piled-up regions out <110> directions on the (001) surface and regions where a sinking-in occurred in <100> directions. That the areas in <110> directions were actually at a higher elevation was confirmed by microscopic focusing measurements performed at high magnification. The behavior is independent of indenter orientation and is thus a crystallographic phenomenon. The apparent abnormal pile-up in the lower right of both pictures is due to a slight "out-of-levelness" possessed by the specimen during the indentation process but is not indicative of any intrinsic effect associated with the hardness test itself. Thus, the indenter penetrating the surface causes crystallographic plastic flow leading to a piling-up and sinking-in, the form of which depends upon the symmetry of the slip systems of the crystal. The manner in which the indenter cuts these regions determines the shape of the impression. A consequence of this preferential pile-up is that, on the (001) surface, for instance, most of the slip traces were seen where the most extensive pileup occurred and significantly fewer were visible elsewhere.

i~~r~~' \~~~~~~~ ~ ~ ~ ~ ~~.~~ iiii::r:::w <:: i:::::::: i,:,::i::i:::i~ii~::::::i:::i:::::::: T ~l~~-iiil:i4 K: iii::ii~::::I:I:::l::: + \i:i,~::::j: ~i'i'ii::':i 4:- 2' i,,:,:,::,:l Figure li::i~i:3(ia): Intrfeenc xnicrograp around Vickers indentation (500 gm load) on the (001) surface of Mn:le Indenter diagonals are in <10 dietos h tppoorp hosmr lal the ~ ~ ~ ~, shap ofi: th impesson X2GO.::

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52 The concentration of slip lines in certain regions is not unique to MnSe however. It was observed by Keh (1960) in MgO at high temperatures and in MnS utilized in this study, both of which have (110}<110> as the primary glide mechanism. For example, a Vickers indentation on (001) of MnS is shown in Figure 19. Keh (1960) also observed by interferometry four hills of material in <110> directions around indentations on (001) of MgO. This was also detected on MnS as shown in Figures 20a and 20b where the indenter diagonals were in the <100> and <110> directions respectively. In Figure 20a, the pileup concentrated at the center of the sides of the indentation with no detectable sinking-in in the <100> directions. When the indenter was rotated 45 degrees (Figure 20b), material was found to be piled-up all around the indentation, but again the most extensive pile-up occurred out <110>. Figure 19. Concentration of slip lines around Vickers indentation (1000 gm load) on the (001) surface of MnS single crystal. Oblique lighting. X150.

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54............... Figure 20(b). Interference micrograph around Vickers indentation (1000 g load) on the (001o) surface of MhS. Indenter diagonals are in <110> directions. The top photograph shows more clearly the shape of the indentation. X250.

55 2. FRACTURE Manganous selenide shows fracture primarily as (100} cleavage in crushed fragments with some secondary (110) cleavage also evident. Chao et al. (1964a) found these same results for MnS and indeed, these observations are directly relatable to the behavior of other materials with the NaCl-type structure (Gilman, 1961a). Surface indentation tended to produce primarily (100) fracture as may be seen in Figure 21. It should be noted that the cracks are not concentrated at the center of the indentation edges where the greatest sinking-in occurred and consequently where one might expect the greatest "parting" tendency to be, but rather, they are concentrated near the corners of the impression in regions where perpendicular intersecting slip traces are also concentrated. These areas are the ones into which most of the displaced material has been moved and the ones where more complicated problems involving the flow of material arise. Consequently, it is likely that the (100) cracking is the result of a slip or dislocation interaction mechanism rather than simply a (100) tension cleavage crack. This will be considered in more detail in the Discussion section. In addition to the (100) fracture, minor amounts of (110)90o (i.e., a (110) plane at 90 degrees to the plane of indentation) fracture were also observed. An interesting observation was made on a sample etched with an aqueous solution of composition 1% conc. H2SO4, 1% H3P04, and 1% of a solution saturated with oxalic acid used to reveal dislocation etch pits. Lines of dislocations were seen eminating from the tip of a (1003 cleavage crack (Figure 22). The

56 Figure 21. (100) fracture around Vickers indentation on the (001) surface of MnSe single crystal. Oblique lighting. X450. Figure 22. Dislocation etch pits in (001) surface reflecting dislocations nucleated at the tip of a (100) cleavage crack in MnSe. X250.

57 dislocations apparently were nucleated at the tip of the crack in an effort to replace the concentration of elastic stress by a more diffuse distribution of stress associated with dislocations (Low, 1963). B. The System MnSe-MnS 1. PLASTIC DEFORMATION a. Slip Traces Manganous selenide and manganous sulfide were found to form a continuous series of single phase solid solutions (Mehta et al., 1967). The lattice parameter varied linearly with composition. Since each possesses a different primary glide mechanism, (111)<110> for MnSe and (110)<110> for MnS, it becomes possible to investigate the change in mechanism with composition. While (110)<110> slip was observed as a secondary mechanism in MnSe, it was not detected as slip traces around Vickers indentations. With as little as 10 a/o (atomic percent) substitution of sulfide in selenide, however, traces due to (110}<110> slip were detected. As the sulfide content increased, the amount of (110) slip became more pronounced. Figure 23 shows slip traces on the (001) surface of a sample of composition 75 a/o MnSe-25 a/o MnS. Those traces in <100> directions forming a square pattern are due to (110) slip while those in <110> are the result of (111) slip. Figures 24 and 25 show impressions on the cube face of samples of composition 50 a/o MnSe-50 a/o MnS. Again traces due to both types of slip are visible but the amount of (1103 glide has increased. The apparent variability in the density of the slip

58 Figure 23. (111) and (1103 slip traces around Vickers indentation (1000 gm load) on the (001) surface of 75 MnSe25 MnS single crystal. Oblique lighting. X250. Figure 24. (111) and (110) slip traces Figure 25. Similar to Figure around Vickers indentation (500 gm load) 24 but showing a (100) crack. on the (001) surface of 50 MnSe —50 MnS X150. single crystal. Oblique lighting. X250.

59 lines on different sides of the indenter is due to the oblique lighting technique used to illuminate the specimen. Figures 26 and 27 display the (001) and (011) surfaces of a sample of composition 25 a/o MnSe-75 a/o MnS while Figures 28 and 29 reveal the (001) and (011) surfaces of pure MnS, which show no evidence of (111) slip. Thus the primary slip mechanisms were found to change gradually with composition, both mechanisms being operative for all intermediate values studied. b. Dislocation Etch Pit Rosette Patterns It was also possible to follow the change of glide mechanism by the observation of dislocation etch pit rosette patterns around the Vickers indentations. This technique has been used successfully by Keh (1960) on MgO single crystals and by Chao et al. (1964a) on MnS. Figure 30 shows this dislocation etch pit rosette pattern on the cube face of MnS as taken from Chao et al. (1964a) and may be interpreted as follows. The indenter displaces MnS along the (110} planes in <110> directions, and, in effect, provides a dislocation "loop" which swings under the indentation emerging on the other side. Both edge and screw dislocations are identified, the edge dislocations emerging perpendicular to the (001} surface and extending out <110> directions on that surface and the screw dislocations emerging at 45 degrees to (0013 and extending in <100> directions. For MnS, the edge dislocations are more readily etched than the screw dislocations and are revealed acceptably only on the cube plane. This apparently is a consequence of the stability of the surface to the etchant which was an aqueous solution of composition 1% conc. H2S04, 1% H3P04, and 1% of a saturated solution of oxalic acid.

60 Figure 26 Figure 27 Figures 26 and 27. (111) and (1103 slip traces around Vickers indentations (1000 gm load) on the (001) and (011) planes, respectively, of 25 MnSe-75 MnS single crystals. Oblique lighting. X150. Figure o8 Figure 29 Figures 28 and 29. (110) slip traces around Vickers indentations (1000 gm load) on the (001) and (011) planes, respectively, of MnS single crystals. Oblique lighting. X150.

61 i plaes ((O) 11 plnsaddsoato ie. N' Figure 30. Dislocation etch pit rosette pattern on (001) for MhS. (A) Etched after indentation. X280. (B) Edge dislocations on the (110)90o planes. (C) (110)90o planes and dislocation lines. Burgers vector b is along <110>. (Chao et al., 1964a).

62 This same etchant also revealed dislocations on the cube faces of MnSe as evidenced by the appearance of random dislocations, small angle boundaries and, for instance, dislocations nucleated at the tip of a moving cleavage crack (Figure 22). Crystal faces other than [001} failed to reveal good etch pits. Around Vickers impressions on MnSe, however, no rosette pattern developed although random dislocations and small angle boundaries were still in evidence (Figure 31a). Further investigation led to the conclusion that the dislocation mechanism was as important as the surface stability in determining the etchability of the dislocations; that is, apparently only those dislocation lines intersecting (001) with glide plane (110) could be satisfactorily revealed by these etching techniques. This allowed a study of the change in slip mechanism by observing the development of the rosette pattern characteristic of (1103<110> glide. The results are shown in Figures 31a, 3lb, 31c, and 31d for Vickers indentations on the (001) plane of MnSe, 90 a/o MnSe-10 a/o MnS, 75 a/o MnSe-25 a/o MnS, and 50 a/o MnSe-50 a/o MnS specimens respectively. The gradual development of the rosette pattern confirms the previous conclusion of a gradual change of primary slip mechanism with composition. 2. FRACTURE The fracture modes associated with surface indentation also appeared to vary gradually with composition from primarily (100) fracture for MnSe to [1103 fracture for MnS. For example, in a specimen of composition 90 a/o MnSe-10 a/o MnrS (Figure 51b), (100) fracture was evident while in 50 a/o MnSe-50 a/o MnS

(a) (b) (c) d) Figure 351. Development of dislocation etch pit rosette pattern characteristic of {110)<110> slip around Vickers indentations for MhSe-MnS solid solutions. X250.

samples both (100) and (110) fracture were observed (Figures 25 and 31d respectively). 3. DIAMOND PYRAMID HARDNESS Figure 52 shows the variation of diamond pyramid or Vickers hardness with composition for MnSe-MnS solid solutions at -70~C, room temperature, and 135~C. No additional slip mechanisms were found over this 205~C temperature range and and it was impossible to tell if significantly different amounts of (110} <110> or (111}<110> glide took place with the temperature variation by the observation of slip traces alone. Since indentations produced distorted impressions due to pile-up around the indenter, especially on (001) in MnSe, the diagonals varied slightly in length depending on the orientation of the indenter relative to the surface. For (001) tests, the hardnesses reported were measured with the indenter diagonals in <100>, giving an impression like that shown in Figure 18a. Under these conditions, the Vickers hardnesses on the (001), (011), and (111) planes were the same within the ~4% limits of the experimental error. Manganese selenide is softer than manganese sulfide (47 kg/mm2 vs. 145 kg/mm2 at 20~C). In addition there is a large positive deviation from linearity in the solid solution hardening which accompanies the substitution of sulfide for selenide ions. The substitution of selenide for sulfide ions also produces a positive, although somewhat smaller, deviation. There is no special significance attached to the maximums which appear other than that they represent an averaging out of the two solid solution hardening effects.

65 190 500 GRAM LOAD 180 -70 170- R.T. 1 35* C 140 / - 130- - 201120- l / - CO 100- 2 0 MOLE PERCENT MNS Figure 32. Average diamond pyramid hardness of MnSe-MnS solid solutions at various temperatures.

66 It is also evident that the hardness of MnSe is much less sensitive to temperature than that of MnS. The behavior of MnSe apparently is similar to that of FCC metals which maintain their ductility down to very low temperatures. The hardness of the selenide changed about O.O4%/o0C while for the sulfide it varied about 0.14%/~C based on room temperature hardness values. A cross-plot of the hardness vs. temperature curves is shown in Figure 33. For MnS, satisfactory hardness results were obtained at liquid nitrogen temperature (-196~C). It was found that the DPH dropped off somewhat from its previously linear DPH-temperature behavior. Observation of the impressions made under liquid nitrogen showed significant amounts of (111) slip with extensive (110)900 cracking. This is shown in Figure 34. Once again it should be pointed out that the oblique lighting technique enhances the visibility of some slip traces but decreases the visibility of others. The (111) slip traces can be explained as follows. The (110)<110> slip mechanism, characteristic of MnS, apparently hardens much more with decreasing temperature than the (1114<110>, and it thus becomes possible to reach temperatures where (111)<110> slip, the secondary mechanism at room temperature, can be just as easily activated in appreciable amounts as (110)<110> glide. The hardness-temperature curve for MnS agrees well with the hot hardness results of Chao et al. (1964b) over the temperature range in common. Attempts were also made, without success, to study MnSe and the other compositions at liquid nitrogen temperature. When MnSe was cooled to -196~C either by quenching or slow cooling, whether mounted or unmounted, the surface was striated and cracked, similar to that which is shown in Figure 35. The

220..I 200 180 75 160 C) o 60__50MNS~..x~ I) 140.S w 25 MNS2.0 o 80 a. 0 60 Z MNSE 20 I I I I I I -240 -200 -160 -120 -80 -40 0 40 80 120 160 200 240 280 TEMPERATURE,'C Figure 33. Diamond pyramid hardness vs. temperature for MnSe-MnS solid solutions.

68 Figure 54. Vickers impression (500 gm load) made under liquid nitrogen on the (001) surface of MnS single crystal. Oblique lighting. X250. Figure 35. The (001) surface of MnSe after quenching in liquid nitrogen. X250.

69 room temperature hardness after cycling was around 80 kg/mm2 while at -196~C it measured about 300 kg/mm2. Similar results, but less drastic, were also obtained with the other compositions except for MnS. This suggests the possibility of a polymorphic phase change in addition to the antiferromagnetic transformation already known to exist. This explanation was offered by Lindsay (1951) and Makovetski and Sirota (1963) in an effort to explain anomalous behavior in low temperature magnetic susceptibility and thermal expansion measurements. Neither was able to explain the nature of any second phase. In a more recent paper, however, Makovetski and Sirota (1966), using neutron diffraction, discovered that MnSe transforms to its sphalerite (cubic ZnS) modification at low temperatures. They found, in experiments at -158~C, that both the antiferromagnetic form of a-MnSe (NaCl-type) and P-MnSe (sphalerite modification) were present together, and that the amount of each varied depending on the thermal history of the sample. Attempts were made to obtain low temperature back-reflection Laue X-ray photographs of single crystals of MnSe by dripping liquid nitrogen on them during exposure. These results were inconclusive. A slightly different looking cubic pattern was found which may have been twinned but which, for the most part, corresponded quite closely to that found at room temperature. It was found that the crystal could be repeatedly cycled and still remain as a single crystal. However, because of the small region of the stereographic net covered by the photograph and because of the similarity of the two patterns, no conclusive results could be obtained.

70 An attempt was also made to get a diffractometer trace of a powder specimen while cooling with liquid nitrogen. This too was not successful. The best results were obtained by blowing evaporated nitrogen gas over a powder specimen in a Debye-Scherrer camera as shown previously in Figure 11. Relatively good temperature control was attained (~4~C), but the lowest temperature achieved was -150~C and a powder pattern at that temperature showed no new phases. In fact, although the lines on the photograph were sharp, no line splitting or broadening was observed resulting from a slight atom shift characteristic of the antiferromagnetic transformation (Shull et al., 1951; Tombs and Rooksby, 1950, 1951) which is supposed to take place about -120~C. It was possible to calculate the thermal expansion coefficient from lattice parameter measurements. This was 18.5 x 10 /~C and agrees well with a value 18.0 x 10 /~C determined by Makovetski and Sirota (1963). 4. KNOOP HARDNESS The variation of Knoop hardness with orientation of the long axis of the indenter on anisotropic materials is a well known phenomenon (see Literature Review). On single crystal specimens, the hardness anisotropy is some complicated function of the particular slip systems of the Crystal most favorably oriented to accommodate the shape change imposed by the indenter. Because of the difference in primary slip mechanism, this function is different for MnSe than for MnS. The room temperature Knoop hardness results for these materials are tabulated in Tables I and II, where it is seen, for instance, that, on the (001) plane, MnSe is softer when the long axis of the indenter is parallel to <110> than when it is aligned in <100>. The reverse is true for MnS.

71 TABLE I KNOOP HARDNESS OF MnSe Plane of Direction of Long Axis of Indenter Indentation <100> <110> <111> <112> (001o 65. 43. (011) 735. 48. 54. 54. (111) 57. 57. TABLE II KNOOP HARDNESS OF MnS Plane of Direction of Long Axis of Indenter Indentation <100> <110> <111> <112> (001) 122 142 (011o 119 142 142 140 (111) 140 140 Recently, Garfinkle and Garlick (1967) observed that the variation of Knoop hardness with crystallographic orientation depended mainly on the direction of the long axis and not on the plane of the indentation; that is, if <uvw> is a hard direction on one plane, it will also be a hard direction on another plane. This is seen to be approximately true for MnSe and MnS also, even though "hard" and "soft" directions are reversed for each. It thus becomes possible to follow the transition of primary glide mechanism in the MnSe-MnS solid solution series by plotting the Knoop hardnesses for two indenter orientations. Room temperature results are shown in Figures 36 and 57 for two indenter orientations on the (001) and (O0l) planes. The

72 200 GRAM LOAD 170160- ~ 150- \ 140 6130- / - 120- / aw: A/ 50 / 4 0 L I ll M/ ILONG AXIS OF INDENTER 0 O/ PARALLEL TO' r 3. Io t e atu 1o00 DIR.': * -M -— 0 — [110] DIR. / 50-/ 40 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MIS Figure 56. Room temperature Knoop hardnesses on (001) for MnSe-MnS solid solutions.

753 180 - 200 GRAM LOAD 170~ - 160 150- 140 / 130- // cr 120 // 110 / z / U( 100 // w ~ 90- / 180 I/ LONG AXIS OF INDENTER 0 ( / PARALLEL TO: o 70 / Z / - [100] DIR. 60-/ — 0 — [oT] DIR. 50- 40 —--- 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MNS Figure 37. Room temperature Knoop hardnesses on (011) for MnSe-MnS solid solutions.

behavior shown on both plots is essentially the same-a cross-over occurs and the general shape of the curves is like that for the Vickers hardness vs. composition plot. Figure 358 indicates that similar tests at -70~C on the (001) plane showed a slight increase in the hardness of the selenide but a marked increase in the sulfide hardness, and resulted in a shift of the cross-over point of the two curves toward higher percentages of MnS. Conversely, Figure 39 shows that increasing the temperature lowered the hardness of MnSe slightly, drastically lowered the hardness of MnS from its room temperature value, and shifted the cross-over to the left. Again the results show the (110)<110> glide mechanism to be much more temperature sensitive than the (111)<110>. This would mean that, with decreased temperature, the (111)<110> system should give a greater contribution to the overall deformation for all compositions and the cross-over should be shifted to the right-the effect actually observed. Alternately, at higher temperatures, the Knoop anisotropy characteristic of (110}<110> slip should extend over a greater range of compositions as (110}<110> deformation becomes greater and the cross-over should be shifted to the left-again the effect actually observed. The results appear consistent. It is interesting to speculate on the nature of the deformation associated with Knoop indentations on single crystal specimens and to try to postulate relative hardnesses as a function of indenter orientation. This is an extremely complicated problem and its consideration will be reserved for the Discussion portion of this work.

75 190 200 GRAM LOAD 180 / 170 160 / - 150 / /: /o/, 90 / ~I30 / / z ~/ 50 001 40 10 20 30 40 50 60 70 80 90 100 solutions at -70~C. LONG AXIS OF INDENTER o PARALLEL TO -& —A LIOI03 DIR. -' —0 — IIO)] DIR. 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MNS solutions at -70~C.

76 170 200 GRAM LOAD 160150140\ - z 130- ~< > \\ ~ 130 120 / w: // z 100 A / w 90- / / 0 / PARALLEL TO'.' Y \ / --— A- LDOOI DIR. 50-/ — 0 — 1o103 DIR. - ZI00- / 40 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MNS Figure 39. Knoop hardnesses on (001) for MnSe-MnS solid solutions at 135~C.

77 C. MnSe-Rich Portion of MnSe-MnTe System 1. PLASTIC DEFORMATION Panson and Johnston (1964) studied the system MnSe-MnTe (Figure 6) and found that tellurium could be substituted for selenium in the MnSe lattice to the extent of about 15 a/o at temperatures below 500~C. In this investigation, samples containing 7 a/o and 13 a/o MnTe were studied and both compositions showed slip traces due to (111)<110> and (110} <110> glide. Figure 40 is a Vickers indentation on the (001) plane of a 93 a/o MnSe-7 a/o MnTe specimen where it was found that (110) glide was somewhat more extensive than that observed in 90 a/o MnSe-10 a/o MnS samples. Figure 41 of a Knoop impression on the (011) plane of a sample of the same composition, however, revealed traces due only to (111) slip. This is a consequence of the ease of accommodating most of the lateral displacement caused by the indenter by simple (111) slip on each side of it. Figure 42 shows slip traces around a Vickers indentation on the (011) plane of an 87 a/o MnSe-13 a/o MnTe sample where both (111) and (110) glide are evident. 2. FRACTURE As with pure MnSe, both compositions showed primarily (100) cleavage with some (110) cleavage evident in crushed fragments. Around surface indentations it was found that (110)90o fracture occurred somewhat more frequently than the (100) fracture characteristic of MnSe, especially in the 13 a/o MnTe samples. 3. DIAMOND PYRAMID HARDNESS While the Vickers hardness was essentially the same on the (001), (011),

78 Figure 40. Slip traces around Vickers impression (500 gm load) on the (001) surface of 93 MnSe —7 MnTe crystal. Oblique lighting. X250. Figure 41. Slip traces around Knoop Figure 42. Slip traces around Vickindentation on the (011) surface of ers indentation (500 gm load) on the 93 MnSe-7 MnS crystal. Oblique (011) surface of 87 MnSe —13 MnTe lighting. X250. crystal. Oblique lighting. X250.

79 and (111) planes, the values for the two compositions were higher than the values observed for comparable substitutions of sulfide for selenide ions. This is shown graphically in the left hand portion of Figure 43. The size of the tellurium ion is 2.11 (Goldschmidt) vs. 1.91A for the selenide ion and -2 -2 1.74A for the sulfide. Thus, the size difference between S and Se (based -2 -2 -2 on the Se radius) is 8.9% while that between Te and Se is about 10.5%. This slightly larger mismatch in the case of the telluride ion may be enough to cause the higher rate of hardening observed. 4. KNOOP HARDNESS The Knoop hardness results for both compositions followed the pattern observed for Vickers hardness. The left side of Figure 44 gives results for the (001) plane where, as with pure MnSe, the hardness is lowest when the long axis of the indenter is aligned parallel to <110>. Also, like the Vickers hardness results, the rate of hardening is greater than that observed during the substitution of sulfide for selenide ions. Similar results were found on the (011) plane. D. Manganous Telluride 1. PLASTIC DEFORMATION Three modes of plastic deformation were observed in MnTe. Indentation of the basal plane produced patterns which could be attributed to (1012) twinning and which were exactly like those observed by Partridge and Roberts (1964) on single crystals of magnesium. Twinning on (1012) planes is common

80 180- 500 GRAM LOAD 170160 / \ - 150- / (0001)\ \ ~~/ ~ PLANE 140 / \ MNSe- MNS 130- / / 120 / 6110 - %~o- / X l 90l 80 / x 70 / 60 / 50 40 —---- I I,I - I0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MNTE Figure 43. Diamond pyramid hardnesses for MnSe-MnTe solid solutions with results for the MnSe-MnS system added for reference.

190200 GRAM LOAD x 180 \ - (0001 170 PLANE \ 160 - 150- MNS-NS X (I00o> ON \0 " o.;" O R TooL} \ 2140 o5130 c:120 110 \(710 o6 / 80 cOlOO <0001> ON\\ C) I oool 80 0Z /// >O 0 70 /<110> ON z, (01 hkil} PLANE OF INDENTATION 60 (hkil> DIRECTION OF LONG AXIS \I'~ ~OF INDENTER 50 - 40' —---------- I i I I I, I, I 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT MNTE Figure 44. Knoop hardnesses for MnSe-MnTe solid solutions. Some results for the MnSe-MnS system are added for reference.

82 with HCP metals (Barrett, 1952) and geometric construction has shown that it can also occur in the compound MnTe. Basal indentations are shown in Figures 45 and 46 and the possible orientations of (1012) twin traces on the basal plane in Figure 47. The appearance of the twinning on only one side of the indenter reflects a slight misorientation of the surface which, as explained previously, because of the difficulty in growing the crystals, was accurate for the basal planes to within only about three or four degrees. It was noted that different twin systems could be activated by changing the orientation of the indenter on the surface. While reoriented twinned material may provide planes that are more favorably oriented for further deformation by slip, no slip traces were observed in these regions. In fact, no slip traces at all were seen on the basal plane, giving evidence for a <1120> slip vector. Interference photomicrographs showing surface contours around Vickers impressions on (0001) revealed that a general sinking-in or compaction took place all around the indentation (Figure 48). The interference fringes showed 6fold symmetry with the sides of the hexagon rotated 30 degrees from <1120> directions. Twinned regions were higher than untwinned regions which is as expected since (1012) twinning produces an elongation along the c-axis with c/a < \f5. The few piled-up regions that were observed (e.g., points A and B in Figure 48) occurred at or near locations of extensive twinning. The reason(s) for the general sinking-in is not understood however. Vickers indentations on (1010) and (1120) planes revealed extensive amounts of basal slip as indicated by traces parallel to [1100] in Figure 49. Also observable in Figure 49 are semicircular wavy lines extending out [1100] direc

8 Figure 45. Twinning around Vickers indentation (500 gm load) on the (0001) surface of MnTe crystal. Oblique lighting. X250. Figure 46. Twinning around Knoop impression on the (0001) surface of MnTe crystal. Oblique lighting. X500.

84 CI) TWIN (0112 TRACE / (0112) \T2To L 1q20 \ Figure 47. Possible orientations of (1012) twin traces in the basal plane of MnTe. Figure 48. Interference micrograph around Vickers impression on the (0001) surface of MnTe. X250.

85 tions. This is shown more dramatically for two orientations of the Knoop indenter on (1010) in Figures 50a and 50b. In Figure 50a, with the indenter parallel to [1210], the basal slip is observed, but for the indenter rotated 90 degrees, the wavy slip lines are seen. These are attributed to pencil glide-that is, slip taking place on numerous planes having the slip direction, which most probably is <1120>, as zone axis. Deformation by simultaneous slip on many planes using a common slip direction may also be described as extensive cross slip and is quite common at elevated temperatures for many materials (e.g., Mg (Bakarian and Mathewson, 1943) and Al (Petty, 1963)). Wavy slip lines have also been observed at room temperature in AgC1 (Gilman, 1961a), AgBr (Gilman, 1961a), a-Fe (Barrett, 1952), and Hg (Greenland, 1937). Manganese telluride itself is quite soft (DPH = 65) and consequently is labeled as a material in which dislocations can move fairly easily. It thus becomes apparent that MnTe provides the additional slip systems necessary to accommodate the indenter by this sort of extensive cross slip mechanism, otherwise called pencil glide. No twinning was evident on the prism planes. 2. FRACTURE The primary cleavage plane in MnTe was (0001) and fracture on this plane revealed bright shiny surfaces. It was also possible to induce (1010) cleavage with a knife edge revealing a lusterless surface. Both types of fracture were evident in crushed fragments. Around surface indentations, both (0001} and (1010} fracture were common at low indenter loads, but irregular cracking, which could not be inter

86 Figure 49. Slip traces around Vickers indentation (500 gm load) on the (1120) surface of MnTe. Oblique lighting. X150. (a) (b) Figure 50. Slip traces around Knoop impressions on (10a0) surfaces of MnTe single crystal with (a) long axis almost parallel to [1210] and (b) long axis about parallel to [0001]. Oblique lighting. X250.

87 preted, developed at higher loads. E. MnTe-Rich Portion of MnSe-MnTe System 1. PLASTIC DEFORMATION Figure 6 indicates that the maximum solid solubility of manganese selenide in the telluride at room temperature is less than 20 a/o. Two compositions studied in the single phase region were 91 a/o MnTe-9 a/o MnSe and 81 a/o MnTe-19 a/o MnSe and both showed the same three modes of plastic deformation as found in pure MnTe, namely, (1012) twinning, basal glide, and pencil glide in <1120>. 2. FRACTURE The fracture mechanisms were also the same as those found in pure MnTe(0001) and (1010) cleavage. 3. DIAMOND PYRAMID HARDNESS The diamond pyramid hardness results for the single phase MnTe-rich portion of the MnSe-MnTe system are indicated in the right hand portion of Figure 435. The DPH on (0001) is about 65% greater than that on (1010) for pure MuTe (107 kg/mm2 vs. 65 kg/mm2) and about 53% greater for the 81 a/o MnTe-19 a/o MnSe sample (165 kg/mm2 vs. 108 kg/mm2). The higher hardness of the basal plane reflects the difficulty of activating slip systems capable of moving material up to the surface to make room for the indenter-something which can

88 not be done by glide in <1120> directions alone because they are all parallel to (0001) and surrounding material stronglyconstrains such movement. The rate of hardening on both planes was greater than that found when MnSe was added to MnS, as shown. 4. KNOOP HARDNESS Knoop hardness results for the system are shown in the right hand portion of Figure 44. All orientations of the indenter on the basal plane gave the same hardness within the limits of the experimental error. The basal hardness was about 80% greater than for the orientation [1210] on (1010) for pure MnTe (115 kg/mm2 vs. 64 kg/mm2) and 72% greater for the 81 a/o MnTe-19 a/o MnSe sample (184 kg/mm2 vs. 107 kg/mm2). The orientation [1210] on (1010) was slightly harder than [0001] on (1010) which reflects the larger number of slip systems activated by pencil glide characteristic of the latter orientation than can be supplied by basal slip which tends to be activated by the former orientation (Figures 50a and 50b). Similar tests on the (1120) planes gave results virtually identical to those found on (1010).

CHAPTER V DISCUSSION A. Deformation Associated with the Vickers Indentation Around a Vickers indentation one would normally expect the slip and pileup to be the most pronounced at the center of each of the four sides of the indenter regardless of orientation, since it is near these regions under the indenter where the greatest material displacements must occur. Tolansky and Nickols (1949a) found this to be the case for polycrystalline, nearly isotropic specimens of sintered tungsten carbide and selected steels. When they tested single crystals of tin, however, they found a crystallographic distortion resulting in a piling-up and sinking-in of material around the indentation (Tolansky and Nickols, 1949b, 1954). These and other results are similar to the pile-up and sinking-in reported here for MnSe (Figures 18a and 18b) and MnS (Figures 20a and 20b) and must be related to the nature of the plastic flow taking place on the individual slip systems of the single crystal specimens. Figure 51 indicates how the pile-up might be related to the plastic flow taking place around the indenter for MnSe. Since the slip occurs on (111) planes, the nature of the pile-up on the (001) planes would imply that the glide direction is <112>. The Burgers vector in <112>, however, is / times that for <110> glide and from geometric considerations one can conclude that <110> slip is much more likely than slip in <112>. Thus slip in two 110 89

90 1' 1:~(0031) (.t:. Eoo]' Figure 51. View of a (111) plane showing how flow in two <110> directions can result in net <112> movement. steps seems much more feasible than a <112> motion and could result in exactly the same net displacement, as shown in Figure 51. This same sort of pile-up was previously observed by Keh (1960) on MgO when indented at high temperatures and on MnS as previously mentioned. Both these compounds possess the (110)<110> primary slip mechanism. Keh (1960) attempted to relate these hills and slip line concentrations to dislocation interactions. Dislocations on neighboring (110) planes at 45~ to (001) [designated tllO)5o1] interact and tend to pile-up. If the temperature is high enough and the dislocations can acquire enough energy, some segments of the piled-up

91 dislocations will cross glide on other (110)45o planes and form new dislocation sources on parallel glide planes. Thus dislocation pile-up and subsequent cross slip could lead to a movement of material that is equivalent to slip on two adjacent (110}45o planes, each of which has one <110> slip direction. The overall effect would be a net displacement of material in a <112> direction in the same manner as for MnSe except that now slip must take place on two planes of the (110) type instead of being able to occur in two <110> directions on a single (111) plane. An additional factor must be considered in the case of MnS and MgO however. Von Mises (1928) showed that for general homogeneous strain, the operation of five independent slip systems is necessary. The (110)<110> primary glide mechanism can provide only two (Groves and Kelly, 1965). This means that some other slip mechanisms must necessarily be operating in order to produce the shape change imposed by the indenter. Chao et al. (1964a) identified (111) <110> as a secondary slip mechanism in MnS. Although direct evidence for its operation at room temperature was not seen here, it is likely that its operation in material below the surface could also lead to a crystallographic pileup around the indentation like that found for MnSe. It was previously mentioned that fracture around Vickers indentations in MnSe occurred predominately on (100) planes. Indentations on MnS (Chao et al., 1964a) and MgO (Keh, 1960), however, showed primarily (110) fracture (Figure 20b). Keh (1960) attributed this to an interaction of dislocations on adjacent (1013 planes such as, referring to Figure 52a, a/2 [Oil] + a/2 [101] + a/2 [110].

92 t[ooi] v\ \ OoT]// [oos, Figure 52. (a) Dislocation or slip interaction on two adjacent (110) planes. (b) Dislocation or slip interaction on two adjacent (111) planes.

93 The result is an immobile edge dislocation lying on a (112) plane. Therefore, the dislocations generated on the two intersecting slip planes, (011) and (101), will pile-up against this barrier and initiate a crack in the (110) plane. If sufficient thermal energy is available, portions of the piledup dislocations could cross glide to other parallel glide planes, reducing the tendency for crack formation and leading to a material pile-up in certain crystallographic directions as explained earlier. A somewhat simpler way of viewing this problem is to note that, in Figure 52a, upward slip on two adjacent (101) planes tends to separate material along a [llO90o plane. In a similar manner, the (100} fracture in MnSe may be viewed as a consequence of the tendency for the material to undergo net <112> flow around the indenter which, as shown in Figure 52b, separates material along a 100)90o plane. It is also possible, however, to postulate several energetically favorable dislocation interactions forming sessile dislocations which act as barriers and lead to a dislocation pile-up and, in the absence of sufficient cross slip, to eventual fracture on (100). Referring to Figure 52b, two of these are as follows: (1) a/2 [110] + a/2 [110] + a/2 [020] = a[010] (2) a/2 [110] + a/2 [011] + a/2 [101]. Both of the resulting dislocations are of the edge variety and lie along the [101] intersection of the two [1113 planes. The first has a glide plane (101) and the second (010). Thus both would be expected to be relatively immobile.

It may be seen, therefore, from the preceding discussion that the plastic deformation leading to a material pile-up is quite intimately related in an inverse manner to fracture caused by barriers to plastic flow. Where slip and cross glide are easier (i.e., at higher temperatures or in MnSe vs. MnS) fracture is less and pile-up more pronounced. B. Comparison of Deformation, Fracture, and Hardness Characteristics of Mn(Group VI) Compounds The compounds of manganese with Group VI elements differ sufficiently with regard to deformation, fracture, and hardness characteristics that it becomes informative to review these differences and to try to relate them to some more basic characteristic of the compounds. Briefly, MnO (Moore, 1965) and MnS (Chao et al., 1964a), both NaCl-type materials, were found to have (1103<110> as a primary slip mechanism but MnS also showed (1113<110> as a secondary mechanism. Manganese selenide, on the other hand, revealed the primary mechanism (1113<110>, that of the FCC metals, and (110) <110> as secondary. Manganese telluride does not possess a NaCl-type structure, but rather, has the hexagonal NiAs structure more characteristic of selenides and tellurides of the transition metals (Taylor and Kagle, 1965). Manganese oxide showed extensive (100) tension cleavage cracking around Vickers indentations in addition to (110) fracture produced by slip interactions on (0113 planes. The more ductile MnS showed almost exclusively (1103 fracture around indentations while the still softer and more ductile MnSe gave (1003 fracture due to multiple slip interactions on (1113 planes.

95 The increased ductility and softness with increased anion size point to a decrease in the ionic nature of the chemical bonding as the major factor giving rise to the more metallic behavior. Numerous other properties and characteristics of these materials are listed in Table III, and all these substantiate the idea that increasing the size of the anion decreases the strength and stability of the ionic bond, thus leading to a bond more covalent-metallic in character. In going from MnO to MnTe, the melting point and hardness decrease, the color changes from light green to opaque brown-black, the electrical resistivity and band gap energy decrease, and the anion polarizabilities increase to high values. One can estimate the degree of ionic bonding in these compounds by electronegativity calculations as outlined by Pauling (1948). These results are shown in the last column of Table III and indicate that the amount of ionic bonding decreases from about 65% ionic in MnO to around 10% in MnTe. Using Goldschmidt ionic radii, one can calculate theoretical lattice parameters for these compounds assuming that they are totally ionic. A comparison between calculated and measured cation-anion distances (r+R) is shown in Table IV along with (r+R) values assuming atomic rather than ionic radii. Once more the results indicate a departure from ionic bonding toward a more covalent or metallic structure. Pauling (1948) says of such a situation: "There is little evidence for a direct transition from the extreme ionic type of bond to the metallic type; in every sequence of substances which suggests itself, transition from ionic to covalent bond type first occurs followed by transition to the metallic type. This provides support for the concept of the metallic bond as similar in nature to the covalent bond, with added freedom of motion of the electrons.

TABLE III PROPERTIES OF Mn( GROUP VI) COMPOUNDS Crystal Melting Vickers Primary Secondary Anion Electrical Band Approx. Compound Point, Color Hardness, Deformation Deformation Polarizability,4 Resistivity, Gap, % Ionic Structure CC~ kg/mm2 Mechanism Mechanism cm3 x 1024 ohm-cm eV Bond9 MnO Cubic 17801 Light 285 (110)<110> 31 65 nO6501 NaC1 green slip MnS Cubic 16201 Green 142 (110)<110> (111)<110> 10.2 -lo56 NaCl slip slip Se Cubic 15002 Br111)<110> (110)<110> 1057 o.78 20 NaC1 slip slip 64 on (1012)twin. MhTe Hex. 11705 Brown- prism plane basal slip 14.o 01778 10 NiAs black 107 on pencil glide Oah basal plane in <1020> 1. Lynch and Rudner (1966). 6. Measured at 20~C by the author. 2. Mehta et al. (1967). 7. Parker, R. (1958). 5. Johnston and Sestrich (1961). 8. Makovetski and Sirota (1965). 4. Gilman (1959a). 9. Pauling (1948). 5. DeBoer and Verwey (1957).

97 TABLE IV CATION-ANION DISTANCES FOR Mn(GROUP VI) COMPOUNDS Compound Ionic (r+R) Measured (r+R) Difference Atomic (r+R) Compound (A) _ (A) (A) (A) MnO 2.23 2.22 0.01 1.72 MnS 2.65 2.61 0.05 2.18 MnSe 2.82 2.73 0.09 2.28 MnTe 3.02 2.92 0.10 2.55 Thus it is felt that the regular variation in hardness and plastic deformation behavior is due to a change in the nature of the chemical bond which varies from an ionic-covalent bond in MnO to a largely covalent-metallic type of bond in the case of MnTe. A more metallic bond results in an increased ease of dislocation movement, a characteristic of pure metals (Gilman, 1963), and subsequent decreased hardness and increased plastic deformation before fracture. C. Knoop Hardness Indentations on Anisotropic Materials 1. DATA AVAILABLE It is well known that Knoop hardness tests on single crystal specimens give a periodic variation of hardness with crystallographic direction depending on the symmetry of the plane being tested. Results for numerous crystals and crystal structures appear in the literature and are generally uncorrelated in any fundamental way with the deformation behavior of the material. A sum

98 mary of some of the data appearing in the literature for cubic materials is presented in Tables V and VI. The first column in the tables gives the direction of the long axis of the indenter and the second, the plane on which the test was made. Table V shows data for FCC and BCC metals and for MnSe which slips on (111) planes. Table VI gives hardnesses for NaCl-type materials with the glide mechanism (110}<110>. These two classes of material illustrate two general types of behavior. In Table V, the hardnesses are greatest when the long axis of the indenter is in a <100> direction and least when in <110>, while the reverse is true for the materials in Table VI. Garfinkle and Garlick (1967) note that the hardnesses themselves, on any given material, seem to depend for the most part on the direction of the long axis of the indenter and not on the plane of indentation. It must be remembered, however, that when the long axis of the indenter is in a certain direction, one is actually measuring the hardness or resistance to deformation perpendicular to that direction since material is essentially pushed laterally normal to the long axis. It is also interesting to note that close-packed FCC metals slipping on (111) planes show hardness anisotropy behavior similar to that in BCC metals. This is understandable, however, if one realizes that a common slip mechanism in BCC materials is (1103<111>, the inverse of that found in FCC metals. Both mechanisms provide the same number of slip systems, and stresses and strains are related to each other by the same (cos X cos A) resolving factors. To determine if the percentage variation in hardness is the same for all the materials in Table V, it is helpful to plot on semi-log paper hardness vs. indenter orientation. This plot is shown in Figure 53, where the spacing of points on

TABLE V KNOOP HARDNESS DATA FOR FCC AND BCC METALS AND MnSe DOrientation Aluminum Aluminum MnSe Silicon-Ferrite3 Tungsten Niobium W-3.2 Re Direction Plane [010] (001) 18 23 65 229 399 79 362 [110] (001) 13 18 43 183 342 57 279 [100] (011) 22 23 73 239 408 84 398 [011] (011) 15 17 48 203 332 60 284 [111] (011) 15 54 195 [110] (111) 17 57 199 [112] (111) 18 57 212 1. Petty (1963). 2. Garfinkle and Garlick (1967). 3. Daniels and Dunn (1949).

100 TABLE VI KNOOP HARDNESS DATA FOR NaC1-TYPE MATERIALS WHICH DEFORM BY (110)<110o> SLIP Orientation 1 2 5 Direction Plane MnS MnS-1% Ca Mn.O LiF Directionn - Plane [010] (001) 122 166 252 88 [1101 (001) 142 184 282 94 [100] (011) 119 163 252 89 [01l ] (11l) 142 196 286 93 [111] (oil) 142 193 284 [110] (111) 14o 276 [112] (111) 140 259 1. Chao et al. (1964b). 2. Moore (1965). 5. Garfinkle and Garlick (1967).

40^KNOOP HARDNESS OF MNSE, K 700C --- -~- 4O so MN SE /M2 500 p 400 2:~~~~~~f 2o o 0 W -(2 R 90~~~~~~~~~~~~~~~~~~~~~~ 80 z 0,C 40^ X MNSE PL N Co lO IE T T O O F K Nl l D N E-Co) o 30^ — 0 20^ z- -^- ----- -- -5AL._^.,, eORET ATIO N OF (001) E10T. ^ Figure 535.. Comparison of Ioo h dn s a Cubic crystal structuresO nO ades iasw

102 the abscissa or "indenter orientation' scale was proportioned to the measured hardnesses on MnSe which was taken as a standard. The slopes of the various curves do not vary appreciably, indicating similar anisotropic hardness behavior in spite of crystal structure differences. Data are also available in the literature on Knoop hardness anisotropy results for hexagonal materials although these have not been tabulated here (Daniels and Dunn, 1949; Feng and Elbaum, 1958; Schwartz et al., 1961; Partridge and Roberts, 1964). In certain cases, one can see in qualitative terms why some indenter orientations give higher hardnesses than others for a given slip mechanism. Consider, for instance, a Knoop indentation on the (001) plane. For (110)<110> glide, the slip planes are as shown in Figure 54a, which, in plan view, would appear as in Figure 54b. When the indenter is aligned with its long axis parallel to the [100] direction, relatively simple lateral displacement by slip on two (110145O planes on each side of the indenter can occur. When aligned parallel to [110], however, the load must be relieved by complex slip utilizing several slip planes on each side of the indenter. The result is that the material is harder in <110> than <100> when the primary slip mechanism is (1103 <110>. For materials gliding on (1113 <110>, the slip planes are oriented as in Figure 55b. When the indenter is parallel to [100] on the (001) plane, the load can be relieved only by slip on at least two planes on each side of the indenter. When parallel to [110], slipping in two <110> directions on (1113 planes on each side of the indenter can accommodate most of the shape change.

001oo] ~tool] (a) (a) [h/t10 roo]O (b) (b) Figure 54. (a) Orientation of (110) planes. Figure 55. (a) Orientation of (111) planes. (b) View in [001] direction with Knoop in- (b) View in [001] direction with Knoop indenter in [100]. denter in [110].

104 This multiple glide on two planes might be expected to occur more easily than slip on four planes and would lead one to predict that <110> directions on (001) are softer than <100> for (111)<110> glide. The situation becomes more complex for indentations on (011) planes, but the hardness anisotropy can still be quite easily rationalized for materials showing (111}<110> slip. The (111) glide planes are shown in Figure 56a. Two of these will intersect a (110) plane at 35.3 degrees in the [110] direction and the two others at 90 degrees in [112] and [112] directions. An edge view of the (110) plane is shown in Figure 56b with the (111) and (1i1) planes intersecting in the [110] direction. Thus, when the indenter is aligned parallel to [110], most of the lateral displacement can be accomplished by relatively simple slip on each side of the indenter on these two planes. When parallel to [100], however, the (lll)90o planes must now play a more prominent role, and one would therefore expect the material to be softer when the long axis is in a <110> direction. It becomes much more difficult to visualize this for (011) indentations on materials showing primarily (1103<110> glide. 2. SCOPE OF THE PROBLEM An accurate quantitative analysis of the deformation associated with the Knoop indenter, however, represents a problem of tremendous complexity. A necessary first step is to define the state of stress underneath the indenter. Because of the shape of the indenter, the stress state is not uniform but depends on position in the material relative to the indenter. In addition,

105 afoot.] 0000 03"[o] Doo: ~Ilo,3l~() A (m~(b) Figure 56. (a) Orientation of (111) planes with respect to the (110) plane. (b) Edge view of the (110) plane with intersecting (111) planes. The shaded planes in (a) are shown as lines in (b).

106 anisotropy inherent in the single crystal means that strains and yield stresses vary in another complex manner. In order to solve this problem rigorously for a given indenter orientation, it would be necessary to determine all physically possible flow paths on the known slip systems capable of accommodating the shape change caused by che indenter, to calculate the work of deformation on each, and to pick the particular flow path which requires the expenditure of the least amount of work as the one most likely to describe the actual indentation process. If this were done for all orientations of the indenter, the "minium work" values at each orientation should give the relative hardnesses. An additional complication arises when the known slip mechanism cannot provide the five independent slip systems necessary to produce an arbitrary shape change with conservation of volume. The (110)<110> mechanism of NaCltype ionics, for instance, gives only two (Groves and Kelly, 1963); consequently, for these materials, it is necessary to know what other mechanisms operate in order to solve this problem accurately. Also, work hardening, indenter end effects, and possible material rotations add further complications. 3. TREATMENTS OF PROBLEM Apparently Daniels and Dunn (1949) are the only persons who have attempted a comprehensive treatment of the hardness anisotropy of single crystals. Referring to Figure 57A, they assume that the force causing deformation around each facet is a tensile force, F, parallel to the steepest slope of the facet. This assumption has been the subject of some criticism (Mebs, 1949). They

""'^^^^<*N ^c^^11^'S~p PLAH 115 00 4 o^^^ 151 eba ~ ig~1re 7. ~ agra of KxiO P in ente 8'Wing g0 sit1O nls of f orce, LVP p 19 e s3A- direct, and axe s Of rotatio. for

108 resolve this force for each facet on each of the slip planes and slip directions of the known or assumed glide mechanism using the relation: Effective Resolved Shear = ERS = F/A (cos x cos 0 cos *1 where X = the angle between the slip direction, S.D., and the effective force = the angle between the normal to the slip plane, N, and the effective force = the angle between the direction, A.R., in the slip plane perpendicular to the slip direction, and the direction, H, in the "indenter-facet" plane perpendicular to the effective force. The factor, cos A, is supposed to evaluate the constraint imposed by the indenter as material tries to rotate about axis A.R. but indenter constraints try to force it to rotate about axis H. The larger the angle between these axes, the more difficult the deformation becomes. The particular slip system with the largest resolving factor (m = cos X cos f cos V) is the one assumed to be activated first. Because of the geometrical similarity of the indenter, this "m"-factor will remain essentially the same throughout the test and it is assumed to be the one primarily responsible for determining the hardness. High "m" means low hardness so the hardness becomes proportional to (1/m). Computations based on their model apparently predicted the hardness anisotropy found in silicon ferrite. Recently, however, Garfinkle and Garlick (1967), in re-examining this model, found that Daniels and Dunn (1949) had failed to consider certain slip systems of their assumed (112)<111> glide mechanism. When these were included, little agreement was found between calculated and measured results. Similar attempts involving {110]<111> and {123]<111> slip revealed equally poor correlations, indicating a discrepancy in their theoretical treatment.

109 Feng and Elbaum (1958), in modifying the Daniels and Dunn treatment, assumed that the effective force causing deformation was a compressive force acting perpendicular to each indenter facet (Figure 57B). Garfinkle and Garlick (1967) again found little agreement between predicted hardness anisotropy and the experimental results using this technique. It was our desire to view this problem in terms of shear stresses rather than normal stresses since it is the differences in principal normal stresses which determine the shear stresses responsible for deformation (i.e., hydrostatic stresses cause no deformation). The slip line field analysis technique was selected as a logical approach to the problem. Previously Hill et al. (1947) calculated the locus of maximum shear stress for the plane strain indentation of an isotropic material by an infinite wedge. Figure 58 shows this field on both sides of an infinite wedge of included angle 130 degrees, the same as that of the Knoop indenter. This field was assumed to approximate the stress state around the indenter for the first attempt at characterizing the deformation. In triangle OAE, the principal shearing stresses are in the directions EA and OA. The principal normal stresses, always at 45 degrees to the shears, are P and Q, and, by coincidence, P = 2Q for this special case. In the fan shaped region OAB, the directions of maximum shear rotate through an angle of 57.2 degrees, while in triangle OBC, the principal directions are OB and BC. The field is symmetrical about the center of the indenter.

F i- - Figure 58. Slip line field associated with the plane strain indentation of an isotropic material by an infinite wedge of included angle 130 degrees. Principal normal stresses are P and Q (Hill et al., 1947).

111 a. One Lateral Shear In the first technique, a net shearing stress was assumed to act on each side of the indenter in directions EC and ED and to be the stress primarily responsible for the deformation associated with the indenter. These particular directions were chosen because they seemed to be consistent with a continuity of material flow and to represent a satisfactory combination of the downward shear stresses in directions EA and EF and the upward stresses in directions BC and GD. This shear stress was resolved on all twelve slip systems of the type (111}<110> and all six systems of the type (110}<110> for each orientation of the indenter. This was accomplished by use of a stereographic projection such as that shown in Figure 59 for a Knoop indentation in the [010] direction on the (001) plane. The axes "y" and "x" are parallel and perpendicular, respectively, to the shear stress on one side of the indenter. The stress was resolved using the standard formula: TD = Txy (xDiyN + ~xNiyD) = Txy(m) TND = resolved shear stress ixD = cosine of the angle between the "x"-axis and the slip direction RyN = cosine of the angle between the "y"-axis and the normal to the slip plane, etc. The particular slip system with the maximum value of "m" was assumed to be the first to operate and the one contributing most to the total deformation. The hardness was thus assumed to be proportional to (1/m) and the hard

112 010 FACET 2 FACET I loC A too x1 0 Figure 59. Standard (001) stereographic projection of a cubic crystal showing the intersection ABCD of the facets of the Knoop indenter with the plane of projection when the long axis is in the [010] direction. The lateral shear stress is assumed to act in the "y" direction on one side of the indenter.

1135 ness anisotropy could be estimated by comparing the minimum (l/m)'s for various indenter orientations. b. Two Shear Stresses In a second method of analysis, it was assumed that two shearing stresses on each facet, one downward and the other in an upward direction, were primarily responsible for the plastic flow. Each facet was taken to be one side of an infinite wedge with a corresponding slip line field associated with it. The two directions of shear were assumed to be EA and BC (Figure 58) which are the directions of principal shear stress in the triangular regions OEA and OBC of the slip line field, respectively. This is shown in stereographic projection for facet 1 in Figure 60. Lines PQ and RS are along the radii of the great circles which designate the intersection of the facets with the plane of projection. It is out these directions that the stresses are assumed to act. They are shown for facet 1 along the directions y1 for the downward shear stress (EA) and Y2 for the upward stress (BC). The directions xl and x2 are normal to y1 and Y2 respectively. Each of the shear stresses on each facet was then resolved on each of the twelve (111}<110> systems and six [110}<110> systems (for orientations showing 4-fold symmetry around the indenter, it was necessary to evaluate the "m" factors for only one facet, etc...). The minimum (1/m) values for each shear at each orientation were combined as 2 (l/mEA + l/mBC) which was then taken as proportional to the hardness. This particular mode of combination was chosen because of the interdependence of both steps in the shearing process. For instance, if all the m's for one shear were zero, the

Ali 114 [3 -— c ^^^^n 0l - oo long diagonal of indenter Figure 60. Standard (001) stereographic projection of a cubic crystal showing the assumed shear stress directions for facet 1 and the intersection of the Knoop indenter with the plane of projection for the "two shears" method of analysis when the long indenter axis is in the [010] direction. two step deformation could not occur and the hardness would be infinite. This would still be reflected in the term.(l/mEA + l/mBC). c. Integrated Average of Resolved Shear It can be shown for the indentation of an infinite wedge on an isotropic material that about half the work of deformation takes place in the fan-shaped region OAB (Figure 58), which was completely neglected in the previous treatment. It was felt that a better analytical description of the deformation

115 would be obtained if an average (1/m) value could be computed for this center region of' the slip line field and weighted with the values from the "two shears" method. Accordingly, the minimum (1/m) values were found at 10 degree intervals as the directions of maximum shear rotated from EA to BC and these were plotted vs. the degrees of rotation, G. An integrated average value was obtained and weighted with the end-point values to give one net resolving factor of: 9BC^l> Amin 2 BC EA BCmin The minimum (l/m)'s varied in value and the particular slip system on which they occurred usually changed several times during the 57.2 degree rotation. The total factor given in the above equation was taken as proportional to the hardness. 4. RESULTS The resultant hardness factors for the above three procedures together with similar calculations by the Daniels and Dunn and Feng and Elbaum methods are shown in Tables VII and VIII. Table VII is for (111]<110> slip with the hardnesses of MnSe added for reference. Table VIII shows results for (1103 <110> slip and includes the measured hardnesses of MnS and MnO for comparison. Relative hardnesses calculated by the "two shears" method of analysis matched most closely the measured values for materials listed in Table V (i.e., FCC and BCC metals and MnSe). Figure 61 shows a graphical correlation for three

TABLE VII KNOOP HARDNESS CALCULATIONS FOR (111)<110> SLIP Orientation Hardness, Daniels Feng and Lateral Two Integrated Direction Plane MnSe and Dunn Elbaum Shear Shears Average [010] (001) 65 35.62 4.26 1.91 1.40 1.540 [110] (001) 43 2.84 3.24 1.85 1.23 1.36 [100] (011) 73 3.25 35.25 1.28 1.65 1.49 [Oil] (011) 48 2.61 2.96 1.80 1.17 1.26 [111] (011) 54 2.47 3.31 1.115 1.116 1.12 [l10] (111) 57 2.70 2.81 1.21 1.34 1.27 [112] (111) 57 2.52 2.60 1.05 1.247 1.19

TABLE VIII KNOOP HARDNESS CALCULATIONS FOR (110}<110> SLIP Orientation Hardness Hardness Daniels Feng and Lateral Two Integrated Direction Plane MnS MnO and Dunn Elbaum Shear Shears Average [010] (001) 122 252 3.50 35.537 3.08 1.531 [110] (001) 142 282 7.46 3.79 35.94 1.59 [100] (Oil) 119 252 2.67 2.59 1.05 2.49 1.91 [011] (oil) 142 286 3.77 11.1 4.37 1.65 2.44 [lli] (ill) 142 284 5.24 6.29 1.80 1.84 1.84 [110] (111) 140 276 4.59 4.50 1.34 35.85 2.97 - [112] (111) 140 259 3-98 35.85 1.28 2.32 1.98

118 of these materials-aluminum, manganese selenideand silicon iron. The abscissa is the measured Knoop hardness normalized to the maximum value, which occurred at the same indenter orientation in all three materials- [100] on (011). The ordinate is the calculated hardness, (1/m) equivalent normalized by the calculated value at the indenter orientation giving the highest measured value[100] on (011). If the theory is correct, all the points should fall on a curve of slope equal to unity. While there is considerable scatter, the trend does seem to be along lines with this slope, although the softest orientation, [110] on (001), falls way out of line. It was thought that the "integrated average" method would provide a better correlation, but a plot similar to Figure 61 shown in Figure 62 indicates much greater scatter than in the "two shears" approach. A comparison between calculated and measured hardness in MnSe for all five calculational methods is shown in Figure 65. Here again, the hardness of MnSe is normalized by the highest value measured, and the calculated hardness by the calculated value at the same indenter orientation. It is clear that the "two shears" technique provides the best correlation (open circles). Similar plots for materials exhibiting (110}<110> glide show almost no correlation between measured and calculated hardnesses. This is not extremely surprising, however, since the (110)<110> mechanism alone cannot provide the five independent slip systems necessary to accommodate an arbitrary shape change, while (111}<110> slip can. If the results are not good in the latter case, they can hardly be expected to improve when other slip systems of unknown character must come into play.

119 0- MNSE 1.0- A- AL (PETTY) | - FE (DANIELS AND DUNN ) I — - 0.9 0 -jA / 0A u) 0.8 Z 0 o U __0.7 - A 0 N 0.6 0.5 0.5 0.6 07 0.8 0.9 1.0 NORMALIZED HARDNESS, MEASURED Figure 61. Comparison of calculated and measured Knoop hardnesses on single crystals of manganese selenide, aluminum, and silicon ferrite using the "two shears" method of analysis.

120. oF o - MNSE A- AL (PETTY) C] U- FE (DANIELS AND DUNN) U IJ A * I0 3 _1 /,, I / I 0. 0.7 i o O 05 6 0.7 0.8 0.9 1.0 NORMALIZED HARDNESS, MEASURED Figure 62. Comparison of calculated and measured Knoop hardnesses on single crystals of manganese selenide, aluminum, and silicon ferrite using the "integrated average" method of analysis. using the "integrated average?? method of analysis.

121 1.6 1.5 x 1.4 0 3 I o 1.2 4 0..!. * - wI 0 6 _ - DANIES AND DNN METHOD l Z X ONE LATERAL SHEAR 0.5 ~ TWO SHEARS METHOD * INTEGRATED AVERAGE METHOD 0.4 1 -— I I-I 0.5 0.6 0.7 0.8 0.9 1.0 NORMALIZED HARDNESS OF MNSE Figure 63. Comparison of various methods of estimating Knoop hardness anisotropy on cubic single crystals using manganese selenide as standard. ard.

122 In summary, several approaches were attempted in an effort to explain in more fundamental and quantitative terms the deformation and hardness anisotropy associated with Knoop indentations on single crystals. Good results were not obtained although the best correlation was found for materials slipping on [111}<110> when it was assumed that two shear stresses, one downward and the other upward, were responsible for initiating a majority of the plastic deformation. The problem is so complex, however, that it is now felt only an extremely complex theory will ever be able to explain the deformation associated with the Knoop indentation on single crystals.

CHAPTER VI CONCLUSIONS The following conclusions may be drawn from this investigation: 1. Cubic, NaCl-type manganous selenide, MnSe, exhibits (111)<110> and (110}<110> as primary and secondary slip mechanisms respectively. This is in contrast to the (110}<110> mechanism preferred by MnO and MnS. 2. As with MnO and MnS, the primary cleavage plane in MnSe is (100) with some secondary (110) cleavage also evident. Around surface indentations, however, MnSe shows primarily (100} fracture due to dislocation interactions on (111) planes, in contrast to (110) fracture common in MnS due to dislocation interactions on (110) planes. 3. Around Vickers indentations on MnSe and MnS, a crystallographic pileup of material occurs in certain regions and a sinking-in of material in others. The pile-up directions are independent of indenter orientation and unusual shaped impressions result depending on how the indenter penetrates these piledup regions. This phenomenon is related to the flow of material on crystallographic slip systems. a. For an indentation on the (001) plane of MnSe, for instance, material prefers to flow in two <110> directions on each (111) slip plane giving an apparent Burgers vector in <112> and resulting in four piled-up hills out <110> directions on (001). b. The pile-up in MnS is like that found in MnSe. In this case, however, the apparent <112> flow may be due to cross slip and disloca123

124 tion climb on adjacent (110) planes in addition to secondary slip on (111) planes. c. The preferred flow paths resulting in pile-up also result in the appearance of a majority of the slip traces being concentrated in the piled-up regions. d. For both MnSe and MnS, dislocation interactions forming barriers can lead to dislocation pile-up and eventual fracture. Where cross slip and climb can occur, material pile-up occurs and the tendency for fracturing near indentations decreases. 4. In the continuous solid solution system MnSe-MnS, the primary slip mechanism changes gradually from (lll)<110> for MnSe to (110)<110> for MnS. 5. Substitution of sulfide for selenide ions in MnSe results in a large positive solid solution hardening deviation. Substitution of selenide for sulfide ions in MnS also results in a positive, although smaller, solid solution hardening effect. a. MnSe is much softer than MnS (47 kg/mm2 vs. 145 kg/mm2). b. Within the limits of experimental error, the diamond pyramid hardness is the same on the (001), (011), and [111) planes for all compositions in the MnSe-MnS system. c. The (110)<110> slip mechanism of MnS hardens much more rapidly with decreasing temperature than the (111)<110> mechanism characteristic of MnSe such that, at liquid nitrogen temperature, MnS shows an appreciable amount of (1113 slip.

125 6. The addition of telluride ions to MnSe results in an early appearance of (110) slip and produces a slightly higher rate of solid solution hardening than for a comparable substitution of sulfide ions. 7. Manganous telluride, MnTe, having the hexagonal NiAs structure, shows three modes of plastic deformation around Vickers and Knoop indentations: (1) (1012) twinning, (2) basal glide, and (3) pencil glide in <1120>. 8. Fracture in MnTe occurs on (0001) primarily but also on (1010), both in crushed fragments and around surface indentations. 9. Solid solutions formed by substitution of selenide ions in the MnTe matrix show the same plastic deformation and fracture characteristics as MnTe. a. The basal plane is much harder than the prism planes which is a reflection of the difficulty of activating slip systems by basal indentation. b. The rate of hardening is greater than for the comparable substitution of selenide ions in the MnS matrix. 10. Knoop hardness anisotropy behavior is evident on the single crystal specimens studied. a. Manganese selenide is softest when the long axis of the Knoop indenter is in a <110> direction and hardest when it is in <100>. The reverse is true for MnS. b. The reversal of hard and soft directions in the MnSe-MnS system provides a qualitative means of following the gradual change of primary glide mechanism with composition.

126 11. A rigorous treatment of Knoop hardness anisotropy and the flow of material associated with the indenter is an extremely complex problem which cannot be explained in a manner as simple as that proposed by Daniels and Dunn. a. Of several additional procedures tried in an effort to explain this behavior, the method giving the best correlation between theory and measured results for FCC metals is one which assumes that the majority of plastic flow is caused by two shear stresses around each facet of the indenter, one acting in a downward direction, the other, upward. The correlation was much better than the Daniels and Dunn procedure but still was not considered good. b. The same approaches on NaCl-type ionic materials gliding primarily on (110}<110> showed poor correlations for all methods attempted because five independent slip systems are not available from this slip mechanism alone. 12. The changes in deformation, fracture, and hardness characteristics in compounds of manganese with Group VI elements are relatable to changes in other properties such as electrical conductivity and melting point and result from a regular decrease in the ionic character associated. with the chemical bonding as one goes from MnO to MnTe.

APPENDIX I TABULATION OF HARDNESS DATA Part I. Knoop Hardness Numbers- 200 gram load (Compositions are atom percents) MnSe 25 00 91MnSe-9MnS 25 00 Long Axis Dire tion Lon Axis Direction Plane C 01 0 < 1 1 (111> 11 2> Plane <01 0 <011)111) 11 2 oo0l1 64.9 43. {ool 1 91. 73 1.... _ fo0l1 73. 48. 54. 54. {011 94. 82. 87. 84. 111 __ 57. 1 _. 111 1 I__ 190. 193 75MnSe-25MnS 25~ C 50MnSe-50MnS 25~ 0 LPong Axis Direction P Long Axis Direction Plane I<010><011) 1 1 ane 0 1 1 1 2) 11 2 {oo0 1 14. 96. f oolOJ 149. 138. ____ {011 114. 112. 110 109. 01 1 148 146. 149 147. t1 11! 16__. 1 ii.. 1 1 i __ 147. 1141. 25MnSe-75MnS 25~ C MnS 25 "0 PleLong Axis Direction Long Axis Direction Plane 010 > 1 1 11> <i 1 P2> iane o40 < ><1 1 1 <1 12> Plane Long Axis Direction Plane Lo s Dirtn (010> (01 1> ] 1 11 11 2) ( 010)<011> <111> 1 12> 0ooi 1 72. 48. ___ 1 I001 127. 109.______ 127

128 50MnSe-50MnS -70~ 0 25MnSe-75MnS. -70~ 0 Plane on Axi Direction aneLonnn._W<010> 011> <111><112) <010>< 011> <111><1 12> {o001 165. 155. ____ __ {o 172. 172,,,____ MnS -70 "0C Mne 13500 Long Axis Direction Long Axis Direction {001 169. 188. ____ __ {ool 56. 39. ____ 75MhSe-25MnS 13500 5OMnSe-5OMnS 135~0. Long Axis Direction Long Axis Di ectio Plane o01-><Zi 1) 011> n121> Plane oo ><11> > [~001S 102. 90.1 1 9 1___ L 130. 127 ____ _ _ I_. I. _I 25MnSe-75MnS 135 0 0Mne S 135c 0 | n Long Axis Direction Pan Ion Axes rttin.vlane <o010><011>4111)11|2> Plane <010> 0110 <111> <112> _Ol- 13b, 145. ____ __{ 107. 107. 93MnSe-7MnTe 25C 0 87MnSe-13MnTe 250C Plane Long Axis Direction a Long Axis Direction Pl~ane oo>410oi6 (01 11P(112 lane 01> <011> 1 <111 <(112> {o1o l 101.'8310. 9 001 | 13 0., {~1J 100'. 88. 89.___ {O1 132.' 12b. 128,|

129 MnTe 250 0 91 MnTe-9MnSe 25~ 0 Plane Long ais direction Plane Long axis direction ane <1210>t <100oo> P 0001> lane I20> (10 /000Q1> {00011 113. 118. ji0001 149. 151.__ {1010} 51. *5 65. [10o i 73 ____90. 1120} ______ 53. 64. ______ _ 81 MTe-19MnSe 25'C Plane Long axis direction <1210> <11002 <0001> {0001? 186. 181.__ [1010 95.___ 107. Part II. Diamond Pyramid (Vickers) Hardness 500 gram load..___.. _________25 C Plane Composition toola foll0 111_ Tire MnSe 47. 47. 46. 91MnSe-9MnS 79. 84. 85. 75MnSe-25MnS 108. 115/ 115. 50MnSe-50YmS 146. 148. 148. 25MnSe-75MnS 165. 169. 169. Pure MnS 144. 144. 146. Temperature, C 0 Composition -1 98 -70 135 Pure MnSe - 50. 43. 91lMnSe-9MnS - - - 91 l~ Se-9t~. -........ -.... - 75MnSe-25MnS -300 121. 100. 50Q&Se-50MS -330 156. 1 31 25MnSe-75MnS -270 173. 144. Pure MaS 207. 187. 105.

130.Pn e'25' Composition Plane Pure MnSe 47. 47. 46. 93MnSe-7MnTe 83. 80. 87MnSe-13MnTe 1t1. 115.___ 25~ 0 Oomposition Pure MnTe 107. 64. 65. 91 AnTe-9kMSe 135 83. 83. 8lMnTe-19MnSe 165. 108. 110. All of these hardness numbers represent an average of at least five readings, and, in most cases, they are the average of ten or more.

APPENDIX II SUMMARY OF KNOOP HARDNESS ANISOTROPY THEORIES 1. DANIELS AND DUNN METHOD The Daniels and Dunn (1949) procedure has been explained quite extensively in the text. For further reference, the reader is referred to the original article. 2. FENG AND ELBAUM METHOD The Feng and Elbaum (1958) method is similar to the Daniels and Dunn (1949) method except that a compressive force perpendicular to each facet is assumed to be responsible for most of the deformation occurring during indentation. 3. ONE SHEAR STRESS METHOD This procedure has also been described extensively in the body of this report but a sample calculation will be included here. A portion of the indenter and the slip line field associated with the indentation of an infinite wedge in an isotropic material is shown in Figure 64. The direction of the assumed shear stress, Txy, is along a line from E to C on this side of the indenter. This direction is labeled "y" and direction "x" is perpendicular to it. Figure 65 is a stereographic projection showing the intersection of the facets of the indenter with the plane of indentation; the directions "x" and "y"; a slip plane normal, N; and a slip direction, D. The shear stress Txy, 131

132 Figure 64. Assumed slip line field around Knoop indenter and direction of shear stress for the "one lateral shear stress" method of calculation. long diagona long diagonal of indenter Figure 65. Stereographic projection illustrating calculational procedure for "one lateral shear stress" method.

133 is resolved in the direction, D, on the plane whose normal is N by the formula: TND = Txy( xN~yD + IxD2yN) TND xy(m), where TNr = resolved shear stress HND IxN cosine of the angle between the "x"-axis and the normal to the slip plane IyD = cosine of the angle between the "y"-axis and the slip direction, etc. For this hypothetical case: GN =54~ (yD = 820 xD = 55~ GyN = 51~ T = T (0-2) ND = xy.. m = 0.425 This factor was calculated for all the slip systems of a given type at each particular indenter orientation and the maximum "tm1-value at each orientation was assumed to be inversely proportional to the hardness. 4. TWO SHEARS METHOD In this procedure, two shear stresses, Txiy and Tx2 y shown in Figure 66, were assumed to be primarily responsible for the deformation associated with the indenter. These stress directions are shown in stereographic projection for facet 1 in Figure 67. Each facet was assumed to be one side of an in

134 INDENTER As "'"~/ B Figure 66. Assumed slip line field around Knoop indenter and directions of shear stress for the "two shears" method of calculation. R / Q A3 —/ ^. ^: ^ ] — EA 100 100 () oTi long diagonal of indenter Figure 67. Stereographic projection illustrating the calculational procedure for "two shears" method for the (111)[0[1] slip system when the long axis of the indenter is in the [010] direction on the (001) plane.

finite wedge with a slip line field associated with it. A sample calculation will be performed for the slip system (111)[011] for an indentation on the (001) plane with the long axis of the indenter in the [010] direction. Tx1yi = Txiyi( xlNyilD + xDy1N) T (0.766)(0.342) + (-o.4o7)(0.629) = Txl Y (0-006) Tx2y2 TND = X2Y2( X2N y2D + ~x2D~Y2N) Tx2y(0.078)(0.342) + (0.866)(0.629) = T (0.571) At this particular indenter orientation the largest value of "m" for the downward stress, Tx y, happens to occur on the system (111)[011] (m = 0.614) and for the upward stress, T y2, on the system (111)[101] (m = 0.842). Thus the hardness is proportional to: 2 (1/mi + l/m2) = 2 (1/0.614 + 1/0.842) = 1.408. In this procedure, any effects associated with the fan-shaped region of the slip line field, OAB, were completely neglected. It may be shown by means of a hodograph, however, that about half the work done in deforming an isotropic material takes place in this region. A hodograph is a vectorial plot of velocities of indenter and material as it deforms.

The stress perpendicular to the side of the indenter along OE (Figure 68) happens to be 4k where k is the yield stress, assuming an isotropic, nonstrain hardening material. The force per unit length, FL, is P (OE). This force resolved in a vertical direction is the force the indenter encounters as it moves downward with velocity VI (Figure 69). The rate of work done on the indenter as it moves downward is: F V = V (4k)(OE)cos 25 y I This equals the sum of the work done on the material by the indenter in the three portions of the slip line field, OEA, OAB, and OBC. F V = E kV* i y I 1 k[V* EA + V* BC + work in region OAB] LA BC now VA EA = V* BC EA BC and, by the law of sines, V* V EA I sin 65~ sin 45~ EA = V(sin 65 ) \ and, EA = 7 work on leg EA k(V sin 65 2) X total work 4k(V cos 25~) EO = 0.25

137 Figure 68. Diagram of slip line field to be used as an aid for calculating the work done in indenting an isotropic material with an infinite wedge. V: Figure 69. Hodograph for the indentation of an isotropic material by an infinite wedge of included angle 130 degrees.

138 Therefore, 1/4 of the work is done in region OAE, 1/4 in OBC, leaving 1/2 in the fan-shaped region OAB, 5. INTEGRATED AVERAGE METHOD It was felt that a better analytical description of the deformation would be obtained if an average 1/m value could be computed for this center region of the slip line field and weighted with the results from the shears Tx Yi and TX2y as found in the "two shears" method. Accordingly, the directions of principal shear stress were rotated between EA and BC and the stresses resolved at 10 degree intervals during the rotation. At each position the minimum (1/m) value was found. A plot of (1/m) min vs. angle of rotation 9 is shown in Figure 70 for (111)<110> slip and for the indenter in [010] on (001). Each continuous curve represents the variation of (l/m) with 0 for one slip system. An average value over this region was calculated by a graphical integration and weighted with the results of the "two shears" method as: (1/m) - ( 1 (1/m) + 1 (/ ) /m equiv 4 (1/mEA)min +4 B/C mmin 2 9 aver which was then taken as proportional to the hardness. In this case, (1/m) er = 1.670 and (1/m)equiv = 1.559.

139 30 -20 -10 0 10 20 30 40 DEGREES ROTATION FROM HORIZONTAL Figure 70. Plot of the minimum (l/m) vs. orientation of shear stress for the "integrated average" method when the long axis of the indenter is in the [010] direction on the (001) plane. The particular slip system responsible for the minimum value in a particular region is identified. An average value was found over the 57 degree rotation by means of a graphical integration.

APPENDIX III OTHER SYSTEMS INVESTIGATED At the onset of this investigation, several solid solution systems were selected as showing potential for a deformation study. The growth of single crystals was attempted for almost all these systems but several failed to give satisfactory results. These are listed as follows: 1. MnTe-MnS SYSTEM The MnTe-MnS system, shown in Figure 5, shows such limited single phase regions that no single crystals, other than of the pure end members, could be grown. 2. MnSe-FeSe SYSTEM Kiessling et al. (1967) have found that Fe may replace up to 42 percent of the Mn atoms in MnSe at 1150~C. It was therefore hoped that the solid solubility at room temperature would be large enough to allow single crystals of one or two compositions to be grown in the single phase region. Powders of Mn, Fe, and Se were blended, placed in graphite crucibles, sealed in vycor under vacuunm and reacted at 700~C to give material of compositions92 w/o MnSe8 w/o FeSe, and 85 w/o MnSe-15 w/o FeSe. Some of the reacted material was placed in another graphite crucible, sealed in fused silica tubing under vacuum, and lowered slowly through an induction coil, bypassing the zone refining step just to see if the process used with MnSe and MnTe was feasible here. It was anticipated that there would be a strong tendency to form iron carbide. Ap140

141 parently iron carbide did form, releasing selenium which has a high vapor pressure at 1500~C, approximately the temperature used in this run. The silica tube could not hold this pressure and exploded. The compound FeSe is thus not as stable as MnSe. Another run was attempted using an alumina crucible rather than graphite. The alumina crucible reacted extensively with the selenium in the charge, and, after a short time, the fused silica capsule shattered again. As a result, this system was abandoned. 3. MnSe-CrSe SYSTEM Kiessling et al. (1967) found that Cr may replace up to 47 percent of the Mn atoms in MnSe. Powders of Mn, Cr, and Se were mixed and reacted at 700~C in a graphite crucible sealed in vycor to give compositions of 92 w/o MnSe-8 w/o CrSe, and 85 w/o MnSe-15 w/o CrSe. When attempts were made to grow single crystals, the fused silica tube again exploded. It is felt that single crystals in the above two systems could be grown in a high pressure chamber utilizing argon or some inert gas at 150 to 200 atmospheres pressure. This, however, would have required extensive and costly construction and revision of equipment which was not deemed appropriate at this time. 4. MnS-FeS SYSTEM Iron sulfide, FeS, was prepared by reacting sulfur with high purity iron wire in an evacuated pyrex tube but no attempt was made to grow single crystals because of the explosions encountered in the previous two cases.

142 5. MnS-CrS SYSTEM Attempts were.made to manufacture CrS as a raw material by reacting stoichiometric amounts of sulfur and chromium powders. Some of the sulfur did react with the chromium, but much of it would not react even over long periods of time at 500~C (e.g., a week or more).

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