ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR STUDY, DEVELOPMENT, AND PRODUCTION OF FERROSPINELS APPLICABLE TO TUNING OF SEARCH RECEIVERS PROGRESS REPORT NO. 10, TASK ORDER NO. EDG-6 Period Covering January 1, 1955 to June 30, 1955 Electronic Defense'Group Department of' Electrical- Engineering By: D. M. Grimes Approved by C. F. Jefferson H. W. Welch, J N. C. Kothary Supervisor P. E. Nace L. Thomassen E. F. Westrum, Jr. M. H. Winsnes Project 2262 CONTRACT NO. DA-36-039 sc-63203 SIGNAL CORPS, DEPARTMENT OF THE ARMY DEPARITMENT OF ARMY PROJECT NO. 3-99-04-0h2 SIGNAL CORPS PROJECT 194B July, 1955

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iii TABLES TASK ORDER vi ABSTRACT viii 1. PURPOSE 1 2. PUBLICATIONS AND REPORTS 1 3. FACTUAL DATA 2 3.1 Q-Mleter Measurements 2 3.2 Iron-Rich Nickel Zinc Ferrites 17 3.3 Effect of Grain Size on Magnetic Properties 19 3.3.1 Outline of the Work 19 3.3.2 The Flux Problem 23 3.4 Cobalt, Iron, Nickel, Zinc Ferrite 27 3.5 Properties of (Nil.xZnxFe20O4) Review 32 3.5.1 The Spinel Structure 32 3.5.2 Magnetic Properties, Two Sublattice Model 39 3.5.3 Magnetic Properties: Four Sublattice Model 41 3.5.4 The Effect of Fluctuation of the Molecular 45 Field 3.6 Properties of NilxZnxFe204, Experimental and 47 Discussion 3.6.1 The Magnetic Moment 47 3.6.2 The Heat Capacity 47 3.6.3 Discussion 50 3.7 Temperature Effect on jp-Q for Differing Ferrous 60 Iron Contents 4. CONCLUSIONS 64 4.1 Q-Meter Measurements 64 4.2 Iron-Rich Nickel Zinc Ferrites 64 4.3 Effect of Grain Size on Magnetic Properties 64 4.4 Cobalt, Iron, Nickel, Zinc Ferrites 65 4.5 Structure and Properties of NilxZnxFe204 65 5. PROGRAM FOR THE NEXT INTERVAL 66 5.1 Q-Meter Measurements 66 5.2 Iron-Rich Nickel Zinc Ferrites 66 5.3 Effect of Grain Size on Magnetic Properties 66 5.4 Effect of Fluxes 66 5.5 Cobalt, Nickel, Iron, Zinc Ferrites 67 5.6 Magnetization Mechanisms 67 REFERENCES 68 DISTRIBUTION LIST 70 ii

LIST OF ILLUSTRATIONS Page Fig. 1 Permeability Spectra for Different Windings 3 Fig. 2 Permeability Spectra for Different Windings 4 Fig. 3 Permeability Spectra for Different Windings 5 Fig. 4 Permeability Spectra for Different Windings 6 Fig. 5 Q Spectra for Different Windings 7 Fig. 6 Q Spectra for Different Windings 8 Fig. 7 Incremental Permeability vs RF Field Amplitude 12 Fig. 8 Equivalent Circuit for a Domain Wall 16 Fig. 9 Ferrous Iron Content vs Firing Time for a 18 Stoichiometric Nickel-Zinc Ferrite Fig. 10 Fraction of Magnetite Formed as a Function of 20 Firing Temperature Fig. 11 Frequency Spectra of At and Q as a Function of 21 Total Iron Content Fig. 12 The A, Q Spectra of Composition Five After 22 Quenching (0) from 13750C and After Annealing (A) at 8000C. Fig. 13 X-Ray Powder Diffraction Pattern of a Ni-Zn 25 Ferrite Containing V205 and Fired at 10000C for Four Hours Fig. 14 Comparative Photomicrographs of a Polished and 26 Unpolished Ni-Zn Ferrite Containing V205 and Fired at 10000C for Four Hours Fig. 15 Comparative Photomicrographs of a Ni-Zn Ferrite 28 Fired at 13500C and a Ni-Zn Ferrite Containing V205 Fired at 950QC. Fig. 16 Comparative Measurements of jp and Q vs. Frequency 29 for Cores A-275 and B-2018-1 Fig. 17 Comparative B-H Loops of Cores A-275 and B-2018-1 30 iii

Page Fig. 18 V vs Q Variation as Magnetization Changes 33 Fig. 19 The Variation of V and Q with Magnet Current, 34 Transverse Fields Fig. 20 The Variation of A, and Q with Magnet Current, Transverse Fields Fig. 21 The Variation of V and Q with Magnet Current, 36 Transverse Fields Fig. 22 The Spinel Structure 38 Fig. 23 Possible Variations of M and X with T 42 Fig. 24 Proposed Angular Magnetization on A and B 44 Sublattices Fig. 25 Variation of Energy Difference on A and B 44 Sublattices with Atomic Number Fig. 26 Variation of Magnetic Moment with Temperature 48 for Nil xZnxFe204 Fig. 27 Plot of the a-d Plane for Different Values of i/l 49 Fig. 28 Low Temperature Heat Capacity of NilxZnxFe204 51 Fig. 29 Heat Capacity of Nil.xZnxFe204 52 Fig. 30 Possible B Sublattice Ordering Mechanism 53 Fig. 31a Heat Capacity of Lithium Ferrite 56 Fig. 31b Heat Capacity of Lithium Ferrite 57 Fig. 32 Nitrogen Cryostat 61 Fig. 33a p vs Temperature 62 Fig. 33b Q vs Temperature 63

TABLES Page Table 1 Winding Capacitance for Different Numbers of 10 Turns Table 2 Q/fn vs. n 11 Table 3 The Frequency of a Peak in,ul 13 Table 4 The Variation of Anisotropy and Magnetostriction 31 With Different Ferrites Table 5 Tabular Values of P(x) 54 Table 6 Comparative Anomaly Heights 54

TASK ORDER Title: STUDY, DEVELOPMENT, AND PRODUCTION OF FERROSPINELS APPLICABLE TO TUNING OF SEARCH RECEIVERS Purpose of Task: To further the development of ferrospinels of different incremental permeabilities and low losses, with reference to specific applications of interest to the Signal Corps such as RE' tuning units. Procedure: The approach to the general objective will includes a. The preparation, under controlled conditions, of specimens of different compositions; b. The measurement of parameters such as the incremental and initial permeabilities, the saturation inductance, the coercive force and the Q (figure of merit) at various frequencies; c. The interpretation of these magnetic parameters in terms of the composition, reaction temperature, pressure and other conditions in the preparation of the samples; d. The relationship of the solid state properties of the crystallite with the various measured magnetic parameters; e. Theoretical explanations, where possible, for the relationships found in d. above. Reports and Conferences: a. Quarterly Task Order Reports shall be submitted reporting technical detail and procress under this Task Order; b. Task Order Technical Reports of a final summary type are in general desirable and shall be prepared at the conclusion of investigations of each major phase. Such reports shall be prepared as decided in conference between the Electronic Defense Group and the Contracting Officer's Technical Representative in the Countermeasures Branch, Evans Signal Laboratory. vi

Personnel: Electronic Deknse Group: Project Physicist: Mr. D. 1. Grimes Countermeasures Branch, Evans Signal Laboratory: Project Engineer: Mr. Maurice S. Blum Components and 1haterials Branch, Squier Signal Laboratory: Project Scientist: Dr. E. Both Comments: The classification of this Task Order as Unclassified shall not preclude the classification of individual reports according to the information they contain, as determined in conference -with the Contracting Officer's Technical Representative. v. KEISER Chief, Countermeasures Branch Contracting Officer's Technical Representative vii

ABSTRACT A study of the effect of windings on a high permeability toroidal ferrite has been made. The results are presented and analyzed. An experimental study of ferrite formation from the constituent oxides is summarized. A study to determine the effect of grain size on magnetic properties is described, together with a method for decreasing the necessary firing temperature for a completed ferrite to below 10000~C. This reduces interbatch variability and allows longer life for furnace equipment. A nickel-zinc-iron-cobalt ferrite is described and results in crossed magnetic fields are given. An experimental study and a theoretical survey of the thermo and magnetic properties of some nickel zinc ferrites is described together with a description of a process for preparing ZnFe204. The effect of temperature on cores with different ferrous iron content is shown for two nickel-zinc ferrites.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN STUDY, DEVELOPMENT AND PRODUCTION OF FERROSPINELS APPLICABLE TO TUNING OF SEARCH RECEIVERS PROGRESS REPORT NO. 10, TASK ORDER NO. EDG-6 Period Covering January 1, 1955 to July 1, 1955 1. PURPOSE The purpose of this report is to summarize the progress made by Task 6 of the Electronic Defense Group from January 1, 1955 to July 1, 1955, on Signal Corps Contract No. DA-36-039 sc63203. The purpose of the task is to further the development of ferrospinels of different incremental permeabilities and low losses, with reference to specific applications of interest to the Signal Corps such as RF tuning units. The proposed program of Task EDG-6 was outlined in previous progress reports. Only those items will now be reported which have been worked on during the period. 2. PUBLICATIONS AND REPORTS Mr. D. M. Grimes attended the meeting of the American Physical Society on solid state physics held in Baltimore, Maryland, March 17, 18 and 19. No publications were issued during the past six months; however, a discussion was given regarding the specific heat of zinc ferrite at the Technical Conference on Magnetism, Pittsburgh, Pa., June 14, 15 and 16. This meeting was attended by Professor E. F. Westrum, Jr., Mr. D. M. Grimes, and Mr. P. E. Nace. 12.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The following reports will be issued during the next period: "Thermal Anomaly in Zinc Ferrite," by D. M. Grimes and E. F. Westrum, Jr.; "heat Capacity of Zinc and Related Ferrites," by E. F. Westrum, Jr., and D. M. Grimes; "Effect of V 0 on Nickel Zinc Ferrite Formation," by D. M. Grimes, C. F. Jfferson, N. C. Kothary, L. Thomassen; "Effect of Manufacturing Parameters on N1icel Zinc Ferrites," by C. F. Jefferson. 3. FACTUAL DATA 3.1 Q-Meter Measurements A series of measurements were made with the Q-meter in order to evaluate the accuracy of such measurements. The frequency and the number of turns were varied on Core A-324-2. This high permeability core was selected for the measurements in an effort to minimize the effect of leakage inductance due to variations in the windings. Figures 1 through 6 are plots of the data obtained. Note that the permeability plots are greatly expanded to show detail. The Cl curves are smooth within + 2% with the exception of the permeameter curve. The 12 and Q curves are almost as good. Two Boonton 160-A Q-meters were used in making these measurements. For frequencies below 50 kc, an external signal generator was used. External mica condensers were used to extend the tuning capacitance range of the Q-meter. Two runs were made at each frequency using windings of 15 and 30 turns. For each run, the old winding was removed and replaced. No. 28 A.W.G. formvar wire was used for the windings. The following discussion is an attempt to establish reasons for the results of the measurements, and is, in many instances, based on speculation. Further measurements would be necessary to check the validity of these assumptions. 2

TO INSET 360 8!n 0 85 n 60 //-n3 480 1 -- 4 340 I / 440- I'~V I n15 i o 30,d r n I00 IV/320 CT] \4~~~~~~~ 1~ LL.I:'I Ia'C-in —j —W 360-/ 3.4 5 n-;hIA W n 85fl a. L. n, 300 N. 280 n=l (PERMEAMETER) 270 fl I. 0.15.2.3.4.5.6.7.8.9 1.0 1.5 2 3 4 5 FREQUENCY (MC) FIG I PERMEABILITY SPECTRA FOR DIFFERENT WINDINGS MEASURED ON Q-METER CORE NO A-324-2 n = NUMBER OF TURNS

420 ~t w n 244 0 400 0 (3 Eo- 0~~~~~~~~~~~~~~~~~~~~~~ 4 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I (0 w~~~~~~~~~~~~~~~~~~~~~~ 0-~~~~~~~~~~~~~~~~~~~~~~~~ ~~~ Jao~~~~~o 340 d:~~~~~~~~~~~~o 0~~~~~~600 360 w 3400 3200305 70_ _020 15 2 FR~EQUENCY (KC) FIG 2 PERMEABILITY SPECTRA FOR DIFFERENT WINDINGS MEASURED ON Q-METER CORE NO A-324-2 fl= NUMBER OF TURNS

aT ______n____ ____ _________ f~I, 15 TO INSET I / to n= 30 0 15 n= (0 n=60 n= 30 100 L-r I fI I I I I I I.I' i to15 r! I 1 1"=15 1 I ~~ ~ ~~I -80 / m 880 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - o n 15 n -30 r7 I0 _ _ _ cr 7 w,d660 4n15 n = 853 - PEMEMTE) rr 5 n =~ n 60 z 3 40 30F n 85 -20 3 (PERM M EA METASUR) 3 4 0.25.3.4.5.6.8 1.0 1.5 2 3 4 FREQUENCY (MC) FIG 3 PERMEABILITY SPECTRA FOR DIFFERENT WINDINGS MEASURED ON 0-METER CORE NO A-324-2 n=NUMBER OF TURNS

n = 244 N _ _ _ _ _ - 7 Lcr n= 85 6 4 / 15 20 30 50 70 100 200 300 FREQUENCY (KC) FIG4 PERMEABILITY SPECTRA FOR DIFFERENT WINDINGS MEASURED ON Q-METER CORE NO A-324-2 n: NUMBER OF TURNS

SNEnl. JO E38vnN =:U Z-bZ~-V ON 303 HI313AI-O NO 03UfSV3Lt3 S9NlaNIM IN383JAlI O_- Vt133dS 0 ~~~~~~S 09~~~~~1~ (VIN) kON3fO3ll 9 ~ ~ ~ 0'1 8' 9 g' A' ~ S;*O A~~~ ~ -A.= U l j0 ___3E3E d 1- __ __ Xl_ | __ 09 = U0'"'0A 09 (U3.3I V3;ld3dl) I - U I I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~S8

tt) m 70,._ _ _ _ _ _ _ -0 e' N n 85 60 As ",b~~~~~~~~~~~~~~~~~~~u 50 CY A(r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( 5~ 0 00 0 r~~~~ 244 CY~~~N 30 20 40 __ 10 2O 0 I0 15 20 30 50 70 100 200 300 FREQUENCY (KC) FIG 6 Q SPECTRA FOR DIFFERENT WINDINGS MEASURED ON Q-METER CORE NO A-324-2 n = NUMBER OF TURNS

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The stray capacitance of the windings give an apparent pI that is higher than the true value, particularly in the vicinity of the coil's self-resonance. In terms of the indicated Q-meter capacitance, CQ, the effect of winding capacitance, Ir, is CQ + Cw P -va CQ (1) where vla is the apparent value and vlt is the true value. To estimate Clt we assume it to be essentially constant and equal to the low frequency of Ala. For each data point for which CQ is less than roughly 100, a value of 0o was calculated using Eq. 1. From these calculations an average value of CW was obtained for each winding. Table 1 gives the results of these calculations. M is the number of data points used for each calculation, and a- is the mean square deviation from the average Ow. The results show Ow to be small except for n = 15 and n = 244. The large CW at n = 244 is attributable to the two-layer winding. For n = 15, the rise in the p1i curve with frequency is probably due largely to a resonance in the material. Therefore, the pIt should have been chosen higher, which in turn would give a lower value of Gi.l Note that except for n = 244, [l increases as the number of turns is decreased. This is due to the fact that the RF magnetic fieldHRF, is too large to be a "reversible" field. If a reversible field is applied to a ferrite, one measures the initial'permeability (i.e., the slope at the origin of the magnetization curve). or higher fields irreversible wall displacements occur and the core cycles around a minor B-H loop. This introduces harmonic distortion, but the ('-rmeter measures only the fundamental component. Therefore, the permeability measured is the slope f the straight line joining the end points of the minor B-H loop. This irreverible wall motion adds to the reversible permeability, giving an incremental pereability greater than the reversible (i.e., initial) permeability. As HRF is inreased further, the core material approaches saturation and the incremental per9

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN meability must decrease toward a value of one. Curve B in Figure 7 gives an approximate picture of this behavior). TABLE 1'riTDIDIJG CAPACITANCE FOR DIFFERENT NU1J3ERS OF TURNS n M Cw(upf) (4Lf) Estimated jlt j 15 5 9.75 330 15 8 9.5 1.7 330 30 2 2.5 1.5 310 30 6 3.3.8 310 60 3 2.2.6 305 85 4 3.7 305 244 6 17 2.7 330 The Q-meter applies a voltage of about.02 volts to the series combination of the ferrite coil and the Q-meter condenser, CQ. For a coil Q of 50, there would be 1 volt across the coil. For n = 15, and c/2Tr = 1 mc, oL = 150 ohms is obtained from the data. i = e.7 ma; a nd HRF = ni amps/mneter =.025 oersteds. For HRF to be reversible, it should probably be less than.01 oersteds. Thus, we are probably operating on the rising portion of the Vl versus HRF curve. HRF a ni a ne C ne cc Q RF)L con2 con Therefore, for larger n, HRF decreases and the operating point moves down the,l ersus HRF curve. The l1 data show this effect. Table 1 shows the values of lll and n. Also, as the frequency decreases, HRF increases. Therefore, for a given n, ~ll should start rising as the frequency decreases. This effect is shown on the curves for n = 30, 60, 85 (see Figure 1). For n = 244, the core appears to be already -ell within the range of rising pL1 versus HRF by the time it gets away rom the winding capacitance effect. pL then peaks sharply (see Figure 2). This y be caused by EIRF reaching that value which gives a peak in the p.1 versus HRF curve. Then pl decreases as the frequency is further decreased, as predicted by the| O10

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Pl versus HRF curve. Another possible explanation of the 1l peak in the n = 244 curve would be the presence of a magnetostrictive resonance. Since HRFC Q Q for the various curves may be computed. f represents wn fn the frequencies at which the l1 curves start to rise with decreasing frequency. Table 2 shows the results. There was no apparent rise in tl with decreasing frequency for n = 15. However, with increasing frequencies one would expect the peaks in Figure 7 to flatten because the various irreversible wall jumps cannot respond to the higher frequency. It takes time for wall jump to go to completion because of viscous and/or inertial damping. At the higher frequencies some of the wall jumps do not contribute so much, presumably because the field reverses before the jump can be completed. The curve for n = 15 indicates that the jump in the i1 versus HRF curve is sufficiently blunted and broadened (see curve C, Figure 7) so that no Cl rise with decreasing frequency can be detected. TABLE 2 Q/fn vs. n n f(approx.) (mc) Q/fn C HRF 244.0o65 3.6 85.57 1.5 60.58 1.8 30.66 2.8 30.62 2.9 15 No HRF effect present 15 No HRF effect present For n = 244, the winding capacitance effect is probably masking the frequency at which the HRF effect begins. Therefore, f =.065 mc is too low a frequency to use in computing Q. If the correct frequency were known, perhaps Q would decrease to below 1.5. If the above suppositions are borne out by fn 11

ONl t~1-99-V Z9ZZ ZERO FREQUENCY (A) m I AY ~LOW FREQUENCY (B) EW k A -, OHHIGH FREQUENCY (C) FIG _j z w APPLIED RF FIELD, HRF FIG 7 INCREMENTAL PERMEABILITY VS RF FIELD AMPLITUDE 12

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN additional data, then the data in Table 2 prove interesting. The value of HRF at which a rise in 41 becomes apparent seems to increase with frequency. This is in accord with the model used for Figure 7. The value of HRF for the frequency of the peak in the a1-versus-frequency curve for which n = 244 is given by the following: HRF = ni = n Ce.02.CQQl HRF ni 0 ne -. 021LC'.038 oer. 2iT 2rwoL 2ir 2r The measured values of w, CQ, r and Q are used. If Figure 7 were independent of frequency, the frequencies of corresponding peaks in the pil-versus-f curves would be as shown in Table 3, because HRF c, assuming Q to be essentially constant. However, the frequency dependence of the curves in Figure 7 makes the frequencies for the peaks lower than those computed in Table 3. The curves were continued to a low enough frequency to encounter the predicted peaks only at a value of n = 244. Since HRF was too large to be reversible, the core was subjected to a history that would affect subsequent measureemnts unless the core was demagnetized after each measurement. Fortunately, the Q-meter tends to do this. As one TABLE 3 THE FREQUENCY OF A PEAK IN,l n f(mc) cn 244 *03 85 *086 6o.12 30.24 15.49 13

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN detunes from the resonant point at which a measurement has been made, the current drops to a small faction of its resonant value. This has the effect of cycling the core around minor loops of decreasing amplitude and producing demagnetization. However, if the core is removed from the Q-meter without having detuned, the core retains some permanent magnetization which tends to lower the values of l measured thereafter (Ref. 1). Perhaps this accounts for some of the inconsistencies in the data, such as the different curves obtained for the two different 15 turn windings, Figure 1 shows data obtained with the R.F. Permeameter. These data were obtained in two different runs. In the intervening period the core was subjected to the history introduced by some Q-meter runs. The data at 2.5 and 3.5 mc were obtained on the second run; the rest of the data were obtained on the first run. Since the second run data falls low on the curve, one suspects that the core was in a nonstable remanent state introduced by the Q-meter. All of the permeameter data falls below all of the Q-meter data. This may be due to using a smaller HRF with the permeameter as it was used in conjunction with the General Radio Twin-T impedance bridge. Also, core history may have influenced the first run to some extent, though to a lesser extent than was the case in run two. Also, the difference between the permeameter data and the lowest Q-nmeter data is roughly 10%. An expected absolute accuracy of 5% is expected for each of two different sets of equipment. One contributor to L2 and Q is the copper resistance Rcu. 1 = 1 + 1 a 2+RCu (2) Q apparent Q core Q winding (2) L = f ~ lO-17 1 n2t Bn 2 = fn2 1l Lo where Lo is a constant. RCu = nRt where Rt = ac resistance per turn. 1 ~= I2 + Rt = 2measured (3) Zmeasured 1 L,lI

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN If Rt is considered to be independent of fn, then 1'2 measured should decrease LO and Qmeasured should increase with increasing frequency and with increasing n. These effects are observed at the lower frequencies. Q is influenced by the variation of l1 with f and n, but the variation of 12 is the more influential. RCu was measured at 2 mc on a polystyrene core using 86 turns of No. 28 wire and was found to be.013 ohms per turn. Thus, RCu for the 30 turn winding would be 0.4 ohms. At 2 mc, wL was 1100 ohms and Q was 39. Then, calculating _l1 from Eq 3 gives Q = 39.6, a very minor change in Q due to copper losses. This 42 is generally the case for Q100 as long as pl is high. We know of no experimental data or hypothetical views of how 42 should vary with the magnitude of HRF. However, one can say that ~2 arises in part from energy exchanges: from magnetic energy to anisotropy energy and/or elastic energy. Certainly such exchanges result in high losses in the regions of magneto str ictive resonance, domain wall resonance, and rotational resonance. However, because of the wide range in elastic parameters, domain wall parameters, domain parameters and localized fields from point to point in a sample, one expects these losses to spread into broad ranges of the frequency spectrum where it is not apparent that they are contributors. Of course these parameters vary with HRF. The magnetostrictive constants even change sign in some materials as the applied field increases, due to differencesin the magnetic orientations. The anisotropy energy is a function of the extent to which the applied HRF rotates the various magnetic dipoles from the easy directions. Of course, hysteresis losses increase with HRF, if HRF is not a "reversible" field. Since HRF cC _ 42 should decrease and Q should increase with either increasing n or increasing f. These effects are shown by the curves (Figures 1-7). At the high frequency end of the spectrum R2 undergoes an abrupt rise, even steeper than that experienced by 41l Rt (Eq 3) makes an increased

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN contribution toiL2 at the higher frequencies because of skin effect and proximity effect. Proximity effect is probably negligible for single-layer windings on toroids because the wires are, at most, in close proximity only on the inner diameter. Only for n = 85 and n = 244 were the wires in close proximity on the inner diameter, and here the capacitance effect restricted the frequency range. Consequently, we rule out proximity effect as a significant contributor. No. 38 A.W.G. wire has no skin effect over the range of frequencies encountered (Ref. 2). No. 10-38 Litz wire has the same dc resistance as No. 28 A.W.G. wire. Thus, this Litz wire could have been used to avoid skin effect. However, for f = 1 mc, and using No. 28 wire, Rac = only 1.5 and, at 4 mc increases only to 2.2 (Ref. 3). This small amount of skin effect does not explain the steep rise in I2' nor does it explain why it is a function of n. Consider the circuit of Figure 8 where Cw is the winding capacitance L R Cw FIG 8 EQUIVALENT CIRCUIT FOR A DOMAIN WALL and L and R refer to the ferrite coil. _ __R + joL R + jwL(lo2LCW) cL2L2 (4) =[l j 2 [ - 72L R for (LCwR) i< (1 LC); o 16

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Note that w2LCQ< 1, and CW << CQ for all CQ, since CQmin = 27 Eplf for the Q-meters used. Then the condition on Eq 4 becomes wCWR <<1 which is rewritten as C2 ~ << 1, which certainly is true. Equation 4 shows that while lC1-[ 1 ~2 is proportional to the square. Thus, ~2 should rise much faster - o1 with frequency than does il as -Poo, the frequency of the coil's self-resonance. The more n increases, the more wo is lowered and, therefore, the lower the frequency at which p2 begins to rise. Q R [ - describes the manner in which Q drops due to this winding capacitance effect (see Figure 5 ). 3.2 Iron-Rich Nickel Zinc Ferrites A technical report including this subject is expected to be issued during the next period. A summary of the pertinent results follows. When a ferrite is heated to a point where the diffusion process begins, the metallic cations start to penetrate the different oxygen lattices. This results in an almost immediate formation of a basic spinel structure as seen by X-ray photographs. Along with the spinel, ferrous iron is formed. As the diffusion process continues so that the permanently divalent cations are more evenly distributed, the ferrous iron content drops and the X-ray line width in the back reflection region decreases. Figure 9 shows a plot of the ferrous iron content versus firing time for a stoichiometric nickel Zinc ferrite. The time required for the ferrous iron formation and the amount present depends, of course, very strongly on the firing temperature and the mixing procedure used. It does not depend upon whether water or acetone is used for the slurry. When excess iron is added to the system, some magnetite will be formed. The percent of the excess iron converted to magnetite depends upon the temperature in much the same manner as if it were a question of the solubility of magnetite in the base nickel zinc ferrite structure. This is seen to be an equilibrium 17

1,80 _ _ _ _ -, L60 0. __ L8 0~~~~~~~~~~~~~~~~~~~~~~~~~ Is~~~~~~~~~~~~~~~~~ I L4 t tOO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1.20, z o 09 /'.8 z 0.40 O0 W 0 040.20 I 2,3 4 5 6 7 8 9 10 20 30 40 60 80 100 TIME (MINUTES) FIG. 9 FERROUS IRON CONTENT VS FIRING TIME FOR A STOICHIOMETRIC NICKEL-ZINC FERRITE (FIRED AT 1210~C)

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN phenomena since nearly the same amount of ferrous iron is found when the material is brought to equilibrium from a lower temperature as when it is brought to equilibrium from a higher temperature. Figure 10 shows the fraction of the final value of the magnetite formed as a function of temperature and of excess iron. It is found that as the total iron increases the permeability decreases and the Q increases. Further, there exists a frequency for a maximum Q, this frequency increases with increasing iron content. Figure 11 shows the variation of iu and Q with frequency for several compositions. It is found that after the material has been annealed at 8000C, the Q Inreased with the maximnnm Q shifting to a higher freqtency (see Figure 12). This is believed to be due to either the formation of a second phase or a redistribution of the cations. If it is due to the formation of a second phase, it is not evident in an examination of the surface or from X-ray photographs. Therefore, measurements of the saturation moment will be done to test for a cation redistribution. 3.3 Effect of Grain Size on Magnetic Properties 3.3.1 Outline of the Work. In order to extend the investigations reported in Section 3.3 of Electronic Defense Group Task 6 Quarterly Progress Report No. 8, it was first necessary to establish better polishing techniques, so that fewer grains would be pulled out of the material while polishing. This work was reported in Section 3.4 of Electronic Defense Group Task 6 Quarterly Progress Report No. 9. The object of the investigation was then to obtain two cores with the same permeability, fired for different times at different temperatures. All of the other variables were to be held constant. The grain sizes in these samples 19

g-gI-Z1 3~:1 N,a3t gg-11-9 M3 0~1-99- V z9ZZ 1.0'_.9 0 LL.8 0 w.7 H z.6 J 0 a) 0 rO LL r'o 0.5 1),.4. w x o2.3 0 e z ___ 0.2 cr I ~ ~ __ _ ___ _ _ ___ _ 0"',.L.I 0 1000 1100 1200 1300 1400 TEMPERATURE (DEGREES C) FIG 10 FRACTION OF MAGNETITE FORMED AS A FUNCTION OF FIRING TEMPERATURE.

o- --- -- —' —- — 0- o Lo o o o o Ni474Zn.526Fe204: Ni474Zn.26Fe204+ 135Fe203 I I 1111,1,, I I l I - FREQUENCY (MCS.) FREQUENCY (MCS.) - ___ _._____ o L O.-L Ni,474Zn526Fe 2 04 +.570 Fe2 03 N i474Zn526Fe24 +.9375Fe2 I I I11I IIIII I I I i I FREQUENCY (MCS.) FREQUENCY (MCS.) 500 L NOTE: ALL GRAPHS TO 100 / \ SAME SCALE. 400 80 300 60 200 40 Ni 474Zn 526Fe204 + 2.0Fe2 3 100 20 0 —0- ---- -- -- --- -- — 0 — -O.1.2.3.4.6.8 1.0 2 3 4 FREQUENCY (MCS.) FIG II FREQUENCY SPECTRA OF p. AND Q AS A FUNCTION OF TOTAL IRON CONTENT. 21

gg -II-L 31 ~1-99-V Z9Zz 500 200 400 l Q 1 160 4I.1.2.3.4.5.6.8 1.0 2 3 4 5 FREQUENCY (MCS) 00 QUENCHED A A QUENCHED & ANNEALED FIG 12 THE IL, Q SPECTRA OF COMPOSITION FIVE AFTER QUENCHING FROM 13750C AND AFTER ANNEALING AT 8000C (N!474Zn526Fe2O4 +.938Fe20 3) -2 2

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN would then be compared. This approach assumed an increase in permeability with firing time. It was shortly found that the permeability goes through a maximum and then decreases, both at extended firing times and at higher firing temperatures. For work on grain size to continue, it was necessary to understand and control or avoid this decrease in order to obtain comparative measurements. It was thought that this decrease might be due to volatization of zinc. The volatility of ZnO seems to be quite varied judging from the conflicting reports in the literature. However, it was presumed that the zinc present was as the spinel and not as ZnO. Two methods of checking the volatility were tried. First, firing weighed samples at different temperatures showed that the samples did lose weight above 12000. Second, Curie point measurements were taken. Since the zinc would volatilize from the surface it must be expected that the temperature falloff of permeability should not change with Zn content, but the temperature at which the permeability approached unit would. These data were inconclusive. Since the material described above was slow cooled, it was thought that at least most of the zinc would occupy A sites, as contrasted with the quenched material described in Section 3.2. However, there is no assurance that the material is completely normal, nor can it be assumed that annealing after a high temperature fire would place all of the zinc in the A sublattice. 3.3.2 The Flux Problem. The problems introduced by the zinc seemed to demand a lower firing temperature. Our previous work had shown that V205 was instrumental in promoting grain growth at a specified temperature. Therefore, This is shown in Figures 11, 12 and 13 of Electronic Defense Group Task 6 Quarterly Progress Report No. 5. See Section 3.4.1 of Electronic Defense Group Task 6 Quarterly Progress Report No. 5. 23

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN lower firing temperatures were tried using cores with.75 mole of Fe203 replaced by.75 mole- of V205. A series of cores were fired between 8000 and 10000C. for four hours. This material was ball milled with acetone for six hours and dried at 1100C. The material was furnace cooled. The die used was 1-11/16" OD and 1-7/16" ID. These values were chosen to obtain a ratio of minimum to maximum diameter as close to unity as possible (see Section 3.3, Ref. 1). The spinel formation in these cores occurred between 8000 and 8500. Cores fired at 8000 were orange red, those fired at 850o were black. The 8o00 core had expanded about 1/16" in OD, while the 8500 core had undergone firing shrinkage. Cores fired at or above 900~ have a smooth surface, those fired below 900 showed a folded surface with valleys and hills in a pronounced warped pattern. The X-ray and metallographic pictures of these specimen showed no. evidence of a second phase (see Figures 13 and 14). It is presumed that the reaction goes very fast in the presence of the vanadium pentoxide. CrO3 did not have the same effect. Presumably the reaction which formed the spinel, possible exothermic, started in certain localized regions. These regions shrank and formed a superstructure which prevented the remainder from contracting when it reacted, thus giving an irregular surface. Once this shape was formed, it could not be removed by heating at higher temperatures. The grain size involved was quite large (20 microns diameter). The grain size of a core containing.75mole % V205 and fired at 950o was quite comparable with that of a core not containing the vanadium fired at 13500 (see Figure 14). One item of note was that the "spots" described previously were entirely absent.'These "spots" involved regions of abnormally high grain size. Section 3.2.4 of Electronic Defense Group Task 6 Quarterly Progress Report No. 6, April 1954. 24

rn FIG 13 X-RAY POWDER DIFFRACTION PATTERN OF A Ni-Zn FERRITE CONTAINING V205 AND FIRED AT IOOOOC FOR FOUR HOURS (SPECIMEN B-2002)

UNPOLISHED AND UNETCHED SURFACE (500X) POLISHED AND ETCHED CROSS SECTION (500X ) ETCHED WITH SnCI2 IN HCI FIG 14 COMPARATIVE PHOTOMICROGRAPHS OF A POLISHED AND UNPOLISHED Ni-Zn FERRITE CONTAINING V205 AND FIRED AT 1000~0C FOR FOUR HOURS. SPECIMEN B-4-4 26

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN It is possible that the entire ferrite now has the characteristics of the spots seen before. Considerable difficulty was involved in making good physical specimens with the larger die. The difficulty was apparently involved with the very fast reaction. The core had to be kept at as uniform a temperature as possible. This was accomplished fairly successfully by placing a toroidal ring of alundum, large enough to completely cover the specimen, directly on top of it during the firing. All such cores made to date have been slightly elliptical, having a D min/D max of about.9. The surface of these cores showed a very obvious grain pattern without polishing or etching. The significance and reason for this is not at all understood. However, if the internal structure were comparable with that at the surface it would eliminate the necessity for polishing and etching each specimen. However, comparative photomicrographs show the unpolished surfaces have a smaller mean grain size and have a larger percentage voids than do polished surfaces. (See Figure 15). Therefore, it has been concluded that all measurements should be made on polished samples. Comparative magnetic properties are shown in Figures 16 and 17 between a vanadium sample fired at 950~C. and a nickel zinc sample fired at 1250 C. Figure 16 shows the comparative Q-meter measurements, and Figure 17 shows the comparative B-H loops. 3.4 Cobalt, Iron, Nickel, Zinc Ferrites Although the exact nature of the loss mechanism is not presently understood, it is certain that coupling between magnetic and elastic lattices would result in energy dissipation. Two methods of energy transfer would be by magnetostrictive and by anisotropic coupling. 27

~ SPECIMEN A-112 (500X) PLAIN NICKEL-ZINC FERRITE CORE, FIRED FOR FOUR HOURS AT 1350 DEGREES C.,...4~~~~~~~~~~~~~~~~~~~~~~~~.... ) SPECIMEN B- 2018-2 (500X) NICKEL-ZINC FERRITE CORE CONTAINING V205 AND FIRED FOR FOUR HOURS AT 950 DEGREES C.. FIG 15 COMPARATIVE PHOTOMICROGRAPHS OF A Ni-Zn FERRITE FIRED AT 1350~C AND A Ni-Zn FERRITE CONTAINING V205. FIRED AT 950~C. 28

700 600oo o. 0 A-275 A B-2018-1 400 I 250 500 750 1000 1250 1500 1750 2000 FREQUENCY (KILOCY CLES) 15 14 13 12 0 A-275 - 10 A B-2018-1 iC - 250 500 750 1000 1250 1500 1750 2000 FREQUENCY (KILOCYCLES) FIG 16 COMPARATIVE MEASUREMENTS OF p. AND Q vs FREQUENCY FOR CORES A-275 A-275 AND B-2018-I A-275 N1-Zn.FERRITE CORE FIRED AT 1250~C FOR FOUR HOURS B-2018-I Ni-Zn FERRITE CORE CONTAINING VANADIUM FIRED AT 950~C FOR FOUR HOURS 29

A-275 B-2018-1 B= 1871 GAUSS PER INCH B= 2098 GAUSS PER INCH H= 12 OE PER INCH H= 8.65 OE PER INCH BS= 3220 GAUSS Bs= 3360 GAUSS A-275 B-2018 —I B= 1871 GAUSS PER INCH 8= 2098 GAUSS PER INCH H=l.II OE PER INCH H=,.86 OE PER INCH HC=.242 OE HC-.475 OE FIG 17 COMPARATIVE B-H LOOPS OF CORES A-275 & B-2018-1 A-275; Ni-Zn FERRITE FIRED AT 12500~C FOR FOUR HOURS B-2018-1; Ni-Zn FERRITE CORE FIRED AT 9500~C FOR FOUR HOURS (CONTAINS V2 05) 30

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN The contribution of different magnetostrictive coefficients to the effective anisotropy for constant stress is4 A K = 9/4 [(cll - C12) XI0O - 2C44 kill] The cij's represent the elastic moduli. The magnetostriction in a saturated, polycrystalline body is given by5 = 1/5 [2 X100 + 3 X1] For other values of M, Brown gets for anisotropic material X/ = 1 3 ctnh + 32 where M is defined by M-Is = ctnh r - 1/ Values of K, Xl0, 1lll1 and ~ are given in Table 4.6 TABLE 4 THE VARIATION OF ANISOTROPY ANMD NAGNETOSTRICTION WITH DIFFERENT FERRITES K k100 ll1 X(demagnetized polycrystal) Non-Fe or Co Ferrites - + Fe304 + + CoFe204 + + Since K and have different magnitudes in different ferrites, it seems that it might be possible by properly combining divalent cations to produce material with a high Curie point but small values of K and X. One major difficulty would be the problem of producing locally small coupling. (See Sec. 3.5). These values allow the possibility of varying X and K with M in such a manner as to change the character of the Q vs M curve. Since tuning units, which are the ultimate objective of these investigations operate from on or near remanance towards saturation, the above possibility becones of considerable interest. Therefore cores containing different amounts of cobalt 31

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN and iron were made. To test pL-Q versus a parallel biasing field, the equipment developed under EDG Task 4 for use at 500Kc was used.* For transverse biasing fields the cores were wound in the usual fashion and placed between the pole faces of a magnet, as described previously (Ref. 1). The core windings led to a Q meter. Sample results are shown in Fig. 18. Similar data have been taken on the cores containing magnetite and cobalt. The results and compositions are shown in Figures 19, 20 and 21. These cores were all fired in the following manner. They were heated rapidly to 11500C. and flushed with air at all temperatures greater than 1150~C. They were taken slowly to 1375~0C., held there 30 minutes, then taken down to 12000C. for two hours. They were cooled to 11000C., then put in a N2 atmos. phere and slow cooled. Each series contained a different total iron content. Each started with zero cobalt, and each series had a constant zinc content. Cobalt was introduced at the expense of the nickel, starting with the magnitude of 1/100 of the original nickel, then approximately doubling the amount of cobalt for each new core type. Some of the data are not included. It is expected that transverse field data will be taken at frequencies up to 10 mc as well as parallel field data at 500 kc. The results shown are quite dramatic. The interpretation will be considered later. 3.5 Properties of (NilxZnxFe204), Review 3.5.1 The Spinel Structure. For spherically symmetric bonding and with repulsive forces which fall off rapidly with distance, a close packed array of atoms in energetically the most stable. This can be accomplished rith either a face-centered or a hexagonal close packed lattice when all atoms are identical. Either of these structures have about 74% of the available space occupied, * the experimental setup and the data on core A-105-1 re described in Electronic Lefense Group Task 4 Quarterly Progress Report No. 15 32

1000 400 _ 300 200 ____ 00' 60 N. 20 --- PARALLEL FIELD I ~ —- TRANSVERSE FIELD 10 - - I 1 2 3 4 5 6 8 10 20 30 40 60 80 100 200 300 FIG 18 P vs Q VARIATION AS MAGNETIZATION CHANGES A-105-I 33

500 500 300 200 100 100 80 60 40 30 20 6 I I J I I I I 1 -12 00 0 -400 0 400 800 1200 -1o200 0 1200 (F-1-2) Ni2337Cz2 663Fe204 Zn (F-2- 1) Ni2313Co023Zn2663Fe204 500 500 too - 00 10 _0 -21200 0 1200 F-3-) Ni2290Co47Zn263Fe204 (F-4-) Ni CO Zn Fe 04 500 500 100 1- 00 I~~~~~~~~~~~0 1~~I0 -12o o o 12 -2 o 1200 (P-5-i) N11963CO0374Zn2663Fe204 (F-6-1) Ni.0841C01496 Zn.266 Fe204 FIG 19 THE VARIATION OF /z,Q WITH MAGNET CURRENT TRANSVERSE FIELDS 3h

SS Z 8 3OHM 8*1-99-V Z9ZZ 300 300 10oo 00 - 50 50 - 10 O5 -1200 0 1200 -1200 0 1200 (F-7-1) Ni.4 737Zn 5263CoFe204 +.2941 Fe203 (F-8-2) N i468Zn Co Fe204+.2941 Fe 0 I.4737 052.4629Zn5263Cooosee 040+.>9413Fe20 500 500 100 -- 100 50 50 10 10 5 5 I... 1 1 I I I I I I I -1200 0 1200 -1200 o 1200 (F-9-I)0 (F-N-i) Ni.4643Zn5263Co0094Fe2O4+.294 1 Fe203 Ni4359Znb263CO0379Fe204+.2941Fe23203 100 100 Q 50 50 I I! -1200 0 1200 -1200 0 1200 FI) 3980Zn 263Co 075 7 Fe204+.294 Fe2 03 F-13-) N 1705Zn 5263Co3033Fe204+.2941Fe23 FIG 20 THE VARIATION OF /. AND Q WITH MAGNET CURRENT, TRANSVERSE FIELDS. (Fe2O3 CONTENT IS THE INITIAL CONTENT. FINAL FERROUS IRON VALUE UNKNOWN.) 35

200r- 200 too o o to 10 5 - IO IC IC I I I I II -1200 0 1200 -1200 0 1200 4Ni4739Zn5261Coo Fe2O4+.9377 Fe 0 15-1N4360 Zn 5261Co 0379Fe204+.9377Fe203 200 - 100 50 10 _ 17 5... I I I I -1200 0 1200 (F162) Ni3981Zn5261Co758Fe20 4+.9377Fe2 03 FIG 21 THE VARIATION OF IL AND Q WITH MAGNET CURRENT, TRANSVERSE FIELDS. Fe203CONTENT IS THE INITIAL CONTENT. FINAL FERROUS IRON VALUE UNKNOWN. 36

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN assuming spherical particles. For face-centered cubic arrays of spherical particles, there will be interstices surrounded by 6 spheres, corresponding to Coordination Number 6 for the center of an octahedron of spheres. This type of site will be referred to as a B site. Other interstices are surrounded by four spheres givening a Coordination Number 4 to the center of a tetrahedron of spheres. This type of site will be referred to as a A site. The mineral spinel, MgA1204 has been taken as the prototype of the spinel structure. There the larger Mg2+ cations are on the A sites, the smaller A13+ on the B sites, while the 02- form the close-packed lattice. It is to be noted that this is in contrast to the usual case where the largest cations have the largest coordination numbers. One half of a unit cell is shown in Fig. 22. The spinel structure consists of an alternating array of such blocks continuing in all three directions. The positions of cations may not be exactly in octahedral or tetrahedral centers but in positions characterized by a parameter, pL. Many materials7 crystallize, either from the melt or during solid state reactions, into this structure.'We shall, for the most part, confine our efforts to MFe204 where M is a divalent ion or ions. Barth and Posnjak8 have shown that the positions of the metallic ions can be rearranged and still preserve the spinel structure. The alternative is to have half of the trivalent ions on A sites, the remainder and the divalent ions on B sites. Verwey and Heilmann9 studied the structure of several such iron containing spinels or "ferrites" using X-ray techniques. They found that for M = Ni, Cu, Mg, Co, Fe and Mn the divalent ions were on the B sites. For M = Zn, and Cd, the divalent ions were on the A sites. They defined the latter as "normal" spinels and the former as "inverted" spinels. 37

! I I x m ~~~~i I -----— ~~I I I M I I Fe 4 (TEI ITRAHEDRAL I SITES) v 2 Al ++ 2 Fe+++ I M++, IFe+++ 6 (OCTAHEDRAL SITES) o 4 O 4 O 4 O OXYGEN FIG. 22 THE SPINEL STRUCTURE THE SPINEL STRUCTURE

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN They found that the lattice constants for the normal spinels were larger than for the inverse spinels. This, of course, means that the inverse ferrites are more closely packed. From a combination of lattice-constant and line-intensity measurements they determined that in a mixed ferrite of Cu and Zn the zinc stayed on the A sites, the Cu on the B sites. Goodenough and Loeb have shown that a combination of covalent bonding and electrostatic bonding can account for the known spinel properties. The aforementioned ferritestlwith inverted spinel structure possess ferromagnetic properties. Those with normal spinel structure do not. Snoek was able to make ferromagnetic materials with an array of properties mixing normal and inverted spinels. Lithium ferrite also exists in the spinel structure. In this case the Li+l form an ordered f.c.c. array on the B sublattice.12 3.5.2 Magnetic Properties: Two Sublattice Model. The gross magnetic properties of the ferromagnetic spinels, or ferrites, with the inverse structure has been well established. There are several major differences from the ordinary ferromagnetic behaviour. The material does not follow the Curie-Weiss law above the Curie terperature, but is concave towards the temperature axis. The saturation moment is small —less than the sum of all atomic moments. These characteristics were explained and the temperature dependence of the sponteneous moment predicted by Neel.13 This was accomplished by extending the molecular field approximation of ferromagnetism. The ions located on A sites will be subjected to different crystalline forces than those on B sites. It is assumed that the B ions will exert antiferromagnetic forces on each other, as will also the A ions. However, the B ions exert an antiferromagnetic force on the A ions larger than the intra-A antiferromagnetic forces, and vice versa. The result 39

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN is that the B ions have their moments aligned as do the A ions, but in the opposite sense. Thus, the net moment arises from the difference of the B and the A moments. Following Ne'el, let X be the fraction of the ferric ions on the A sites, p. the fraction on the B sites. Thus, X + p = 1. For the inverted spinel, X = p = 0.5. For the normal spinel A= O, p = 1. Let the magnetization of a gram ion of ferric ions on the A sites be denoted by Na, the magnetization of a gram ion of ferric ions on the B sites by Mb. The total magnetization is then given byt N =XMa + LMb (5) The molecular field approximation assumes an effective local field at each lattice site due to the surrounding ions given by: Ha = no (lXMa - pMb) (6) Hb = no (-XMa - yPMb) The magnetic energy associated with these fields at absolute zero is given by: E = 1/2 [XHa * Mas + PI{b'Mbs] (7) Combining Equations 6 and 7 E = n /2 [aX22 + 2XM PasMbs + Y12Mbs2] (8) E is an extremum for the following four cases. I. Mas + Mbs = O. (paramagnetism) II. Mas = Mbs = the maximum value M. III. Mas = M; Mbs = - X/ M. IV. Mas = )/,a M; Mbs = M. It is to be noted that solutions III and IV represent a sublattice magnetization different from saturation at O~K, and that the slope of the M vs T curve for this specimen is nonzero at 04K, violating the so-called third law of 4o

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN thermodynamics. That the above ideas are essentially correct has been shown by Shull,14 et. al. by neutron diffraction studies of magnetite. Since then further neutron studies on NiFe204, ZnFe204, and NiSZn5Fe204 have been carried out.15 They) too, substantiate the Neel picture. In spite of all this experimental agreement, it should be emphasized that even though it can be shown that the ground state for ferromagnets is very nearly that of all moments aligned, and further,l6 that for antiferromagnets the picture of nearest neighbors with antiparallel spins is stable for extended periods of time, it is necessary to merely assume this state for ferrimagnetism. It is to be expected that the usual equations describing wall formation in ferromagnets must be altered to consider the additional sublattice. Further, since the ferric ions on A and B sites are located in different potentials it is to be expected that crystalline-dependent properties such as the Lande' g-factor and the crystalline anisotropy would be different on each sublattice. The effects of different g-factors have been observed.17 The possible magnetization curves using the two sublattice model are shown in Fig. 23. 3.5.3 Magnetic Properties: Four Sublattice Model. Yafet and Kittell8 considered a further subdivision of the structure by considering nearest neighbor interactions. They divided the A sublattice into two and the B sublattice into four face-centered cubic lattices. For zero anisotropy the four B sublattices can be lumped into two equivalent sublattices. The molecular fields acting on each sublattice can be written, analogous to Eq. 2, ass Ha,' = no (alMa + -M T M ) Ha" = n (a2Mat + clMa" -'b - ilb) (5) hl

M I/X M I/X / / / 8p T ec ep T M I/X M I/X / / / /,p T ep T M I/X M I/X / e/ T / 8. T Tc rp FIG 23 POSSIBLE VARIATIONS OF M AND X WITH T.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Hbt = no (-ii2 - 2at + ia'lb + 2bb) + ) Ibt = no (-Ma' - Ma"t + Y21b' + b' + b ) This gives rise to a magnetic energy: E -no [(al-a2 cos 2)Ma2 + aMb sin sin, + ( (6) (-._v2 cos2 ) Mb2 The angles q and 4, are defined in Fig. 24. This leads to the minimum energy conditions analogous to those of Neel: I. (f = 4 = O. This term no longer means a paramagnetic arrangement but a doubly antiferromagnetic arrangement of spins. II. q = ~ = n/2. III. 4, = rr/2, sin = Mb a2 Ma IV. a = /2, sin 4 = Ma Mb ~T2 Solutions II, III and IV correspond directly to Neel's solutions. The interpretation in this theory is a triangular spin arrangement on one sublattice for solutions III and IV. In this case the slope of the magnetization curve at T = 0 is zero. The higher temperature behaviour can be found be assuming the usual Curie law to hold using the proper molecular fields. There is no simple relationship between the high and low temperature characteristics. It is therefore possible to go from one minimum energy condition to another as the temperature changes. It is to be expected that there will be an extra specific heat contribution at the boundary between different minimum energy conditions because of the difference in the temperature dependence of the magnetic energy. According to Yafet and Kittel, it is to be expected for a mixed Ni-Zn ferrite with about 10 mole % NiO and 4o mole 3 ZnO and 50 mole % Fe203, that 43

G-11-L IJ.I 921-99-V a9ZZ Mb' FIG 24 PROPOSED ANGULAR MAGNETIZATION ON A & B SUBLATTICES. (AFTER YAFET & KITTEL) Atomic No. 25 26 27 28 29 30 Mn Fe Co Ni Cu Zn FIG 25 VARIATION OF ENERGY DIFFERENCE ON A AND B SUBLATTICES WITH ATOMIC NUMBER. (AFTER NEEL) La4

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN several such transitions should occur as the temperature of the material is varied. 3.5.4 The Effect of Fluctuations of the Molecular Field. As was pointed out by Neell9 the molecular field approximation assumes each cation to possess the average environment of the gross material. A B-site cation has 6 nearest neighbor A-sites and 6 nearest neighbor B-sites. Consider the case of RFe204. In the case of a simple normal spinel all 6 nearest neighbor A-sites will be occupied by R2+, all 6 n.n. B-sites by Fe3+ For an inverted spinel all A-sites would be occupied by Fe3+, the B-sites would contain both R2+ and Fe3+. For the normal spinel the molecular field approximation should remain always valid. For the inverted case differences would be manifested near the Curie point. For intermediate cases the situation is not so clear. Intermediate cases can arise for two reasons, (a) the material can be retained in metastable positions by suitable tempering and (b) the bivalent ion could be a mixture of metals forming normal and inverted ferrites. Consider first (a) above. For each R2+ there is an Fe3+ on the other sublattice. Let the potential for the R2' to be on the A sublattice be La, on the B sublattices Lb. Per mole of material there will be N sites available on the A sublattice and 2NT on the B sublattice. Let y be the fraction of the R cations on the A sublattice. The number of ways this can be done is: N(3) (Ny)l [N(l-y)l 2[N(L+y I Upon using Stirling's approximation: in W = const. - N [y in Ny + 2(1-y) in N (l-y) + (l+y) in N (l+y)] The number of filled sites is given by N = yNi + (l-y)N. The total energy is:

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN E = CaysT + Cb(l-y)N. These three conditions must be stable with respect to variations in y. Thus: y(l+y = exp ( ) (1-y) 2 KT (8) AC= Ea b At OOK, for Ae < O, y = 0, the spinel will be normal. Conversely for AC > 0 the spinel will be inverted. This situation would be the final equilibrium state. For materials cooled in a finite time a steady state will be reached depending upon the relative magnitude of the right side of Lq. 8 and the magnitude of the ionic mobility. Studies of the magnetic moment of magnesium ferrite as a function of temper have been carried out by Kriessman, Harrison and Callen.20 They have found that Eq. 8 does not fit their data, but rather an equation similar to it where AC = A o - ey where e is a constant. This would mean that the energy necessary for a cation to go from one sublattice to the other is a function of the sublattice population. Neel considers the series Mn, Fe, Co, Ni, Cu, Zn to be one of decreasing magnitude of AE from Mn (See Fig. 25) to Cu, then becoming positive for Zn. Thus the ferrites most likely to be retained in a metastable condition would be those of Cu and Zn. That the structure insensitive properties of CuFe204 is a function of temper is well known, this case was treated by Neel.13 It has also been reported21 that ZnFe204 can be made magnetic by quenching from 1400oC. A theoretical analysis of possible cations distributions has been carried out by Smart.22 46

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 3.6 Properties of NilxZnxFe204, Experimental and Discussion 3.6.1 The Magnetic Moment. In conjunction with Professor S. Legvold of the Low Temperature Laboratory, Iowa State College, magnetic moment data were taken on samples with x = 0.6, 0.7, 0.3 and 0.9. The data were taken using a Gouy type balance. Fields up to 18,200 oe were used. The temperature range from 200K to room temperature was investigated on two samples, from 800K to room temperature on two other samples. Curves taken for H = 18.2 Koe and H = 12 Koe are shown in Fig. 26. The magnetic moment for the larger values of x increases between H of 12 and 18.5 Koe. From more detailed data, the moment is still rising at the largest value of magnetic field utilized. For large values of x, the o- vs T curves tails slowly toward the axis. Thus the concept of a fairly definite Curie point for the material as a whole cases to exist. On the samples measured,, the moment goes through a definite maximum as a function of temperature. This is not quite in accordance with the paramagnetic data of Neel and Brochet23 which predicts that the material when cooled below its Curie temperature should follow a curve of type Q, Fig. 23. Type Q material should have a monotonic decreasing magnetic moment as a function of temperature. The a-P plane is depicted in Fig. 27 for two values of X/p.. It is seen that a slight shift of the points could move the material from a region predicting type Q to one predicting type P behavior. Type P, see Fig. 23, predicts a maximum in the M-T curve. 3.6.2 The Heat Capacity. Heat capacity data were taken using equipment described in Progress Report No. 1, Task 6, EDG, January, 1953. The heat capacity of the same samples considered in the previous section I7

120 X:.60 110 H=12000 Oe X =.70 ~.. I00 _ — - _ H= 18200 Oe 70 X =.80 Z 0 _ —0-e __ 5~~~~~~ 0 i~~~~: 1 _ _ _ _ ____....... _ _ - " _ _ _ _ o. _ _ 4 0 _ — _ _- _. 30 _ X =.90 2 0_ _ _ _ _ _ _ _ _ 0 20 40 60 80 I 00 120 140 180 200 220 240 260 280 3 0 TEMPERATURE (OK) FIG 26 VARIATION OF MAGNETIC MOMENT WITH TEMPERATURE FOR Nii xZn Fe204

-I II /f3 — G -2 M FIG 27 PLOT OF THE a-: PLANE FOR DIFFERENT VALUES OF. -— =.176 X _.250 4I

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN in addition to one with x = 1 was measured from T = 5~K to 3000K. The results are depicted in Figs. 28 and 29. Obviously, there is a maximum in the curves at T - 9.30K. This takes the form of a sharp spike for x = 1.0, and is more spread out as xo decreases. The effect is still obvious for x = 0.6. It is to be noted that the sharpness of this effect is in direct contradiction with the results of Friedberg, et. al. According to Corliss and Hastings24 below the transistion temperature there is some type of antiferromagnetic ordering on the B sublattice. Above that temperature all ions are oriented paramagnetically. These points will be expanded in the next section. Perhaps an equally important though negative result is the absence of any irregularities in the heat capacity curve other than the 9.30 one. 3.6.3 Discussion. From the experimental results of the two previous sections we seek answers to the questions of the type of B sublattice ordering present below 9.30K, if one can find experimental confirmation of Yafet and nittel'sl8 predictions, what produces the measured variance of the 9.30 peak with nickel content, and how is this related to the observed magnetic properties? Further, can an understanding of these phenomena in any way aid the interpretation of the magnetic effects described in the other sections? First, let us consider the question of the type of magnetic ordering found on the B sublattice below about 9.30~K. Yafet and Kittell18 have shown that the lowest energy arrangement is the same for the B sublattice subdivided into two sublattices as when it is subdivided into four sublattices in the absence of anisotropy. dannier has shown that a simple antiferromagnetic ordering cannot exist in a planar triangular lattice. Thus some more complicated ordering structure must be involved. A simple calculation shows that for minimum energy, a configuration similar to that shown in Fig. 30a would be present. 5o

99-tZ-9 MO 6~1-99-( Z9ZZ I0 9 8 I7 I,A W m: -J 6. 0 LL 45 a: FIG. 28 3 - ~~~ ~~~~~~LOW TEMPERATURE HEAT CAPACITY OF NilixZnxFezO,4 X 0.9 -j~~~~~~-0 4 a. FIG. 28 LOW TEMPERATURE HEAT CAPACITY OF Ni,.xZnFe2O4 2 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 TEMPERATURE OK

NICKEL ZINC FERRITE I 36 32 - x 28 7 I / H~~~~~~~~~~~~~~~~~~~~ 24 3r, O Is <~~~~~ 12 0 X=0.7 U-o / X=0.8 X r~~~~~~~~~ X=0.9 _ X=O. 0 50 100 150 200 250 300 T, K FIG 29 HEAT CAPACITY OF Ni1..,ZnFe204

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN (a) FOUR Fe3+ CATIONS (b) THREE Fe3 CATIONS FIG 30 POSSIBLE B SUBLATTICE ORDERING MECHANISM If this is the type of ordering, then the presence of a Ni2+ cation carrying a spin of 1 on a B site with a nearest neighbor A site Fe3+ (for local electrical neutrality) would surely strongly alter the molecular field coefficients and thus either strongly alter or eliminate any such transistion. It would also effect second nearest neighbor molecular field coefficients. To qualitatively account for this effect, assume the magnetic heat capacity of pure ZnFe204 to be a delta function with the spike at 9.30K, the presence of Ni is assumed to eliminate the contribution to the spike from all its nearest neighbors. On the basis of this model one proceeds to calculate the height of the specific heat curve at the transistion temperature. For ease in calculation we count the fraction of groups of four B site cations composed of four Fe3+ cations and surrounded by its ten nearest neighbor A site cations all of Zn2+. If the nickel is randomally oriented on the B sites, and the zinc is wholly on the A sublattice the probability of a specified group of four B site cations to be Fe3+ is given by [(l+x)/2)]4 The probability that the ten nearest neighbor A sites to this group of four B sites be occupied by Zn2 is x10. If local electric neutrality is required the probability goes to x8. Thus, the probability of a specified group of four B site cations to be all Fe3+ and surrounded by ten nearest neighbor A

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN site cations of Zn2+ is, if local electrical neutrality is required, given by: P(x) = [(l+x)/2)}4 x 8 Table 5 lists P(x) as a function of x. TABLE 5 TABULAR VALUES OF P(x) x P(x) 1 1.000 0.9.351 0.8.110 0.7.030 0, o.6.007 To compare with experiment, it would be desirable to normallize the experimental height of the peak for x = 1 to one, then compare the results with Table 5. Unfortunately, the height of the peak, if there is one, cannot be determined. We therefore compare by normallizing the experimental value for x =.9 to be.351. The measured heat capacities at 9.3 K were corrected for the lattice contribution by extrapolating from the K. K. Kelly phamphlets. The values are given in Table 6. It is observed that P(x) drops faster than experiment below x =.9, but is too weak a function of x above. At least the curves vary in the same way. TABLE 6 COMPARATIVE ANOMALY HEIGHTS x C9.30K1 C1 Cm P'(x) P(x) 1.0 8.070 8 1.99 1.000.9 1.657.069 1.588.351.351.8.784.068.716.158.110.7.432.067.365.o081.030.6.201.066.135.030.007 26 It is known, that lithium ferrites contains an ordered face centered cubic array of Li+l cations on the B sublattice. Further, Li+l carries no unpaire

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN electrons. Thus if it be assumed that small amounts of Li also form f.c.c. structures, the effect upon the local molecular fields should be considerably different from Ni+2. One possible sublattice arrangement would be for the spins of the remaining three ferric ions to be oriented as shown in Fig. 30b.* For the case x =.9 above the A sublattice contains, assuming ZnFe204 to be completely normal and NiFe204 inverted, (.9 Zn2+ +.1 Fe3+) cations, the B sublattice contains (1.9 Fe3+ and.1 Ni2+) cations. If now a lithium-zinc ferrite were made which had the same cations on the A sublattice, the B sublattice would contain (1.95 Fe3+ +.05 Li l) cations. If the Li+l1 were randomally distributed, heat capacity results similar to the nickel zinc ferrite would be expected. If, however, the Li+l were ordered in some manner this would be expected to alter the "averaged" local fields and thus the transition temperature as well as its magnitude. Such a sample was prepared and measured. The results are shown in Figs. 31a and 31b. The transition temperature has indeed been altered and stands at about 7.20K. Since the height of the heat capacity curve for zinc ferrite is, according to the statistical arguments, very dependent upon any inversion the sample was made with considerable care. Weighed quantities of dried ZnO and Fe203 were milled for six hours in a hardened steel ball mill using a dilute acetone slurry. After passing the slurry through a magnetic separator, the bulk of the acetone was decanted and the remainder evaporated. Fifty gram slugs were pressed, the surface layer removed, and the slugs fired for 14 hours in air at 11000C. After furnace cooling, the slugs were broken in a hardened steel * This was originally proposed by Dr. B. A. Calhoun, Westinghouse Research Laboratories, during a private discussion.

35 32 C) 28 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~24 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ w 24 0 Ld Lu rY 6 (- 16 0 Lu U) CL W~~ w cr CO LU 8 3 2 0 10 20 30 40 50 60 100 150 200 250 300 350' 0 12S~TEMPERATURE (DEGREES K) FIG 31a HEAT CAPACITY OF LITHIUM FERRITE I 1~~~~~~~~ 0 ~, _ _ 1 __ 1 _ 0 10 2030)40 5060 I00 5~0 200 250 300 350' 400 TEMPERATURE (DEGREES K) FIG 31a HEAT CAPACITY OF LITHIUM FERRITE

GSS-Z -L:i:d ~e1-99-V g9ZZ 4.25 - - 4.0 3.5 3.0 -J 0 2.5 - w (9 0. 0 ~.5 a. 1.0 0.5 0 5 10 15 20 25 30 35 40 45 50 55 (T OK) FIG 31b HEAT CAPACITY OF LITHIUM FERRITE (Li 0o.sZno0.9Fe2.o504)

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN "diamond mortar" to pass a 30 mesh screen. These granules were again formed into slugs and refired at 11000C for 12 hours with an intervening hour at 12000C. The refiring was done in air within a closed furnace with ZnO slugs present. After gradual cooling of the furnace, the accompanying zinc oxide slugs were still white. The resulting ferrite granules were of a uniform brownish color throughout. Two chemical and spectrographic analysis of the ZnFe2O04 by the Detroit Testing Laboratories gave the following results| Chemical analysis Test No. 1 Test No. 2 Percentage by weight Zn 27.35 Zn 27.00 Fe 46.24 Fe 46.2h Ideal 1/1 mole ratio Zn 27.12 Fe 46.33 Spectrographic Analysis.01 -.1 percent.001 -.01 percent Al Ca, Cu, Mg Mn Ni, Si It is believed that at least some of the difference between our results and those of I'riedburg is due to differences in manufacturing techniques for the two samples. However, the difference may also be due to the extended periods necessary for thermal equilibrium to be established (up to 42 hours) below the transition temperature. Another sample prepared in the same fashion has been sent Dr. Hastins -of the Brookhaven National Laboratories for neutron diffraction me a sureme nt s. According to Yafet and Kittel,l1 one test for experimental confirmation of their theory would be the resence of irregularities in the specific heat curve for the, composition wTe have called x = 0.3. No such irregularities exist.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN However, using the statistical arguments it would be expected that the any such transition should only be local in effect. Thus, any contribution would be very broad and as such probably not possible to measure. Thus, no conclusions can be drawn. We now turn to a consideration of the magnetic saturation data. From the shape of the x = 0.9 curve it is apparant that the definition of a Curie point would be rather nebulous. This, too, is to be expected from the standpoint of fluctuations in the local field, for each region would carry its own Curie point. An item of note is the difference in value of a, (see Fig. 26) as a function of applied field for large values of H. Three plausible explanations are: (1) The small volumes of ferrimagnetic regions surrounded by antiferromagnetic regions have their magnetic moment oriented in the field direction quite analogous to a paramagnetism. (2) The local field is increased by the external field, thus inducing a larger fraction of the material to be below its Curie point than in the absence of the field. (3) Angles of the type proposed by Yafet and Kittel exist locally and are decreased by the action of the applied field. Items (2) and (3) both yield a term too small to account for the increase in M. As shown by brown,27 item (1) should yield a term proportional to 1/H. xpoerimentally, we find closer agreement with a term proportional to H. However, neither the theory nor the experimental data are believed good enough to allow a definite statement of behaviour, and the theoretical magnitude can be made large enough to account for the change observed. Therefore, explanation (1) above seems the most plausible. In summary, it is believed that the behaviour of nickel-zinc ferrite can be qualitatively explained on the basis of a random distribution on nickel cations on the B sublattice. This model can be extended to include materials now being

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - used for their large permeability. It is obvious that any attempt to produce locally zero magnetostrictive constants or arisotropy would be abortive, but local regions containing opposites signs would be possible, and thus a macroscopic zero would be possible. Further the permeability dispersion curve cannot be fitted to a simple differential equation with constant coefficients. However, quite good agreement can be obtained by averaging the coefficients over a given 28,29 range. The model proposed above would require such a variation in coefficients. Therefore, if sharp resonances are desired simple type ferrites must be used. 3.7 Temperature Effect on L-Q for Differing Ferrous Iron Contents In conjunction with the studies reported in Section 3.2 of this report, it was desired to know how much of the magnetic properties could be directly linked to the ferrous iron content in the material. A step in this direction was to measure the magnetic properties as a function of temperature. The apparatus used had been built previously. It is shown schematically in Figure 32. The temperature of the test chamber is adjusted by controlling the energy input into the heating coils. The Q-meter reading have to be corrected for losses due to the length of lead used. No correction were made for the extra capacitance introduced. The results are shown for cores A-532-1 and A-507-1. A-532 had a stoichiometric composition, core A-507-1 was composition five (See Sec. 3.2). Figs. 33a and 33b show the results on two material types. The real part of the permeability is quite temperature dependent for A-532-1, but the phase angle is not temperature dependent. Just the inverse is true for A-507-1. Although the phase angle undergoes a considerable change in A-507-1 between -40~ and 0 C the permeability remains fairly constant. Also, the order of the frequency points change between these two temperatures. 60o

GIASKE CANNON PLUG 20- 29 P GASKET LIQUID N2 LEVEL LEADS TO TEST COILS, HEATER, 8: THERMOMETER DEWAR FLASK CO02 "SANTOCEL" INSULATION MONEL TERMINAL STRIP HEATER COIL LATINUM THERMOMETER COPPER WOUND CORES.. TO BE TESTED 1 FIG 32 NITROGEN CRYOSTAT

cj-6Z-L 3OH St1-99-V Z9ZZ 400 300 o 50 KILOCYCLES a 100 300 A 700A 200 A-532-1 -_ 100 A- 507-1 -200 -160 -120 -80 -40 0 40 TEMPERATURE (~C) FIG 33a UL VS TEMPERATURE 62

9S 6Z-ZL:) 9 1FI-99-V z9aZ 280 i 240 - 0 50 KILOCYCLES A-532-1 ISOI /~~~I 160 __ I0 I / 120 o, / I _ __ _ / / _ 60. A-5-,/ / -200 -160 -1 20 -80 -40 0 40 TEMPERATURE (DEGREES C) FIG 33b Q vs TEMPERATURE

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 4. CONCLUSIONS 4.1 Q-Meter Measurements It has been possible to account for the variation of the permeability spectrum as a function of the number of turns wound on the specimen. This in turn imposes quite serious limitations on the Q-meter measurement as a method of obtaining accurate results. The important points are the variation in size of the applied AH with frequency, the capacitive effects of the windings, and the effective wire resistance. 4.2 Iron-Rich Nickel Zinc Ferrites Since a technical report includn- this subject is to be issued shortly, the results have not been described in detail in this report. The important points are the variation of L and Q with quenching and annealing, the variation of ~ and Q with ferrous iron content, the variation of ferrous iron with time and temperature, and thus its apparently important role in the spinel formation. The equilibrium value of ferrous iron as a function of nickel-zinc content and temperature was not previously known. This provides an opportunity for study of materials with controlled ferrous iron content. (See Sec. 3.7). 4.3 Effect of Grain Size on iagnetic Properties Aside from the preliminary data discussed in Task 6 Quarterly Progress Report No. 8, Section 3.3, the important points to date arise from the difficulties involved. First, the difficulty of the decreasing permeability with time has emphasized the problems of zinc volatility and zinc cation placement. This would result in intraspecimen variations. To circumvent this difficulty, V20O was added to the mix. It has been found that this decreases the necessary firing temperature up to hOOC. This 61,

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN constitutes proof that mineralizers or fluxes exist which augment the spinel formation reaction. Since this is the case, small quantities will greatly effect the resulting properties, whether added accidentally or purposefully. What other agents act in this manner (3203, CrO3 and MoO3 do not) is not known but it can be immediately predicted that raw materials containing V205 as an impurity will produce quite different cores than those made without this impurityl The proper firing temperature is a function of the amount of V205 present. 4.4 Cobalt, Iron Nickel, Zinc F'errites The-analysis of the curves presented in Section 3.4 has not as yet been carried out in satisfactory manner, if indeed it is possible to do so. The only conclusion drawn at the moment is that it is possible to obtain dramatic changes in the variation of,u and Q with biasing fields with the proper choice of cations and firing conditions. 4.5 Structure and Properties of Nil_ ZnxFe204 There is a thermal anamoly at about 9.5~K in ZnFe204. This is carried over to specimens containing some nickel. It is believed that this is due to a transition from the paramagnetic to the antiferromagnetic state as the temperature decreases. Just what type of ferromagnetic ordering is involved is not understood at present. Magnetic moment measurements and the statistical model of the variation of the local fields indicates that thie concept of Curie Temperatures losses significance as the percentage of nickel decreases. Instead there would be localized regions carrying aligned magnetic moments. The size and number of these regions decreases as the temperature increases. No indication of a Yafet and?littel y type transition in a nickel zinc

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN ferrite was found. Because of the small percentages of nickel present when the result was predicted it is believed that localized variations would cause differing temperatures at which these changes in magnetization would occur. The result would, therefore, be spread out and probably not observable. 5. PROGfVi1d FOR TEE; NEXT IJTERVAL 5.1 Q-Meter Measurements It is hoped that curves showing the variation in permeability with the size of the AH field as a function of frequency can be obtained during the next period. 5.2 Iron-Rich Nickel Zinc Ferrites The future program here has not been decided at present, and will be held pending until the forthcoming technical report is completed. 5.3 Effect of Grain Size on Magnetic Properties It is expected that four batches of cores will be made, with two different mean permeabilities. For each permeability, one batch will be treated by a fairly high firing temperature and a short firing time —the other by a long firing time and a lower temperature. (Both times and temperatures to be long enough for the spinel formation to be completed.) The grain sizes in these mixtures will be determined. The material is purposefully not prefired and ground to a specified grain size since maximum intergranular contact is to be desired. 5.h Effect of Fluxes It is expected that the effect of differing q antities of V205 will be determined. An effort will be made to understand the role of the flux. 66

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 5.5 Cobalt, Nickel, Iron, Zinc Ferrites The type of data presented in Section 3.4 will be obtained at higher frequencies. Parallel field data at 500 kc will also be obtained. Further manufacture awaits these results. A theoretical interpretation of the variation of pu, Q with the internal magnetization values will be attempted. 5.6 Magnetization Mechanisms The precise conditions under which magnetization by wall movement, and magnetization by rotation, occurs have never been shown. The question is whether or not magnetization occurs by rotation when the material has been initially fired, then gradually shades to wall movement as the firing time or temperature increase and the resulting grain size increases. In order to study the question, a detailed analysis of the frequency spectra of nickel-zinc ferrites fired various lengths of time will be made. This is currently well underway but it is too early to quote results. If the spectra seems similar for all cores such that one could conclude magnetization by rotation in the manner shown by Park, then it is planned to study material with a higher anisotropy constant, i.e., either a magnesium or a cobalt series. 67

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN REFERENCES 1. Grimes, D. M. and Martin, D. W., "Reversible Susceptibility in Ferromagnetic Materials," Technical Report No. 24, EDG, University of Michigan, June, 1954. 2. Terman, F. E. and Pettit, J. M., Electronic Measurements, 624-625, McGrawHill, 1952. 3. Reference Data for Radio Engineers, 3rd Edition, p. 86-87, Federal Telephone and Radio Corporation, 1949. 4. Kittel, C., "Physical Theory of Ferromagnetic Domains," Rev. Mod. Phys., 21, p. 557, 1949. 5. Akulov, N., Zeits. f. Physik., 66, p. 533, 1930. 6. Bozorth, R. M., NOL Conference on Ferrimagnetism, October, 1954. 7. Wyckoff, R. W. G., Crystal Structures, 2, p. 41, Interscience Publishers, New York, 1951. 8. Barth, T. F. W. and Posnjak, E., Zeit. f. Krist., 82, p. 325, 1932. 9. Verwey, E. J. W. and Heilmann, E. L., J. Chem. Phys., 15, p. 174-180, 1947. 10. Goodenough, J. B. and Loeb, A. L., Phys. Rev., 98, p. 391-408, 1955. 11. Snoek, J. L., New Developments in Ferromagnetic Materials, Elsevier, Amsterdam, 1949, 2nd Edition. 12. Braun, P B., Nature, 170, p 1123, 1952. DeBoer F.; van Santen, J. H., and Verwey, E. J. W., J. Chem. Phys., 18, p. 1032-103, 1950. 13. Neel, L., Ann.de Phys., 3, p. 137-198, 1948. 14. Shull and Smart, Phys. Rev., 76, p. 1256, 1949. Schull, C. G.; Wollan, E. 0.; Koehler, W. C., Phys. Rev., 8V, p. 912-921, 1951. 15. Hastings, J. M. and Corliss, L.,. Rev. Mod. Phys., 25, p. 114-119, 1953. Wilson, V. C. and Kasper, J. S., Phys Rev., 95p. 1108-1411, 1954. 16. Anderson, P. W., Phys. Rev., 86, p. 694, 1952. 17. van Wiergingen, J. S.,P hys. Rev., 90, p. 488, 1953. McGuire, T. R. Phys. Rev., 91, p. 206A, 1953. Wangness, R. K., Phys. Rev., 95, p. 339-35,-7154. 18. Yafet, Y. and Kittel, C., Phys. Rev., 87, p. 290-294, 1952. 19. Ne'el, L., Ann. l'Inst. Fourier, 1, p. 163, 1950. 20. Kriessman, Harrison and Callen, Bull. Am. Phys. Soc., 30, No. 2, p. 39, 1955. 68

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 21. Brockman, F. G., Phys. Rev., 77, p. 841, 1950* 22. Smart, J. S., Phys. Rev., 94, p. 847-850, 1954. 23. Ne'el and Brochet, Compt. Rend., 230, p. 280-282, 1950. 24. Carliss, L. M. and Hastings, J. M., NOL Conference on Ferrimagnetism, October, 1954. 25. Wannier, G. H., P Rev., 79, p. 357, 1950. 26. Braun, P. B., Nature, 170, p. 1123, 1952. 27. Brown, W. F., Jr., Phys. Rev., 58, p. 736, 1940. 28. University of Michigan, EDG, Quarterly Progress Report No. 8, Task 6, Sec. 3.6, September, 1954. 29. Park, D., Phys, Rev., 95, p. 652, 1954. 69

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