AQOSR-TN-58-980 ASTiA Document N o AD 205 877 T H E E' N I Vi E R S O T' - 0 F M': C H- I G A N (COL4LEtCE O:F ENi.L,-EEB.'ELNCJ Department c.f Electrical Engineeri.ng Solid State Laboratories Techn:Lcal Report NOc 6 LOW-TEMPERA'1TURE PFEA'-,APAOZTIES AND THERMOD'! NAMIC PROPERTES OCF Z-INC FERF TES -: -LI EFFECMT' )F COPPER StB'BST.Z':J iON DM,M Grimes Edgar'F. est.rlm. Jr., Mi:$R p Project 21495 under contract wi th., AIR FOR.E:OFI -E O SCIEN'i:.F-lU RESEARC.Kji' AiR RESEARFH 1 AND DEVELOPMENT1' COCMMAND SOLID SlT'ATE SCIENCE DIVISiON COI'"TRA^':' SCNO. AF 18( 63 ) - admini. stere- _-: yTHE U"NVERSITZY OF MI-CH: IAN RESEARCH. INSTL;7I'KE ANN AR? OR Jani,.ary, 19.5

ABS TIAI CT The heat capacities of annealed and quenched sampnles of CuO QoZnO. 90Fe2 0)01 have been determined over the range 5-3500Ko The Nlel temperature is the same as previously reported for a similar lithium-substituted zinc ferrite. The result is discussed in terms of sublattice popluation and molecular field coefficients~

1! INTRODUCTION The low-teimperature heat capacity and -thermodynamic oroperties of zinc ferrite and of a solid solution of comDosition S0 mole oercent zinc ferrite (Zn~'e20~) and 10 mole:!ercent lit-hl.ium ferrite (Lio0 e2 5~l) have been studied and reported -previouslyi The data TwJere taken on samples which, after forming sninels from the constituent oxides, had been annealed and on similar samples which had been quenched from 1100~C in distilled water. It was found2 that the annealed sam-iies had — t},pe anomalies in the vicinity of 9OK. This effect has been associated with an anti'ferromagnetic-type ordering in zinc ferrite)3 The heat-,capacity curve for the couenched samlples slowed inflections at about 9~K, but a local maximrLum did not exist. These effects were explained on the basis of sublattice popuu. lations and freezing in the 11000~K po-ulation equilibriujm by the Tw.ater cuench. Similar experim lental data have now been obtained on other samples of quenched and annealed ferrites, The samples were solid solutions of comrnosition c90 mole p-ertcent zinc ferrite and 10 mole oercent copnoer ferrite (CUc F;e2 O0L) o The copper ferrite was ore'oared in such a way that according to Stierstadth it would be in the univalent state~ 2. EXPERiL - -iTAL The samples were prepared as described previously,2 except that a Szegvari mixer was used in olace of the ball milli The results of chemical analyses on the samples for iron and copprer are shown in Table i.

Table 1, Analyses of Copper-zinc ferrites Sample Percent by weight Treatment Observed Theoretical Cu F'e Cu Fe Annealed 1 33 47068 1 32 L7 ~60 Quenched lo29 70 37 1 32 47 060 The cryogenic technique was as described previously, 2' except that calorimeter of laboratory designation W10 was employed for these measurements, This calorimeter is similar to calorimeter W-9 previously described,2 but has a slightly greater volume and lacks heat conduction vaneso The masses of the calorimetric samples were 1970ktP6 g of annealed and l66,54 g of quenched Cu0O0 ZnO090Fe2 o05o The gram molecular weight was taken to be 2410,51 go 3 _ RESULTS The values of heat capacity, corrected for "curvature" and in terms of the defined thermochemical calorie of o184LO absolute J, and an ice point of' 2730150K are presented in Table 2e The discussion of precision and intrinsic errors of the previous workl2 apply equally to the present results, Values of the heat capacity at selected temperatures, together with the standard entropy increment and enthalpy function, are presented for the two samples in Table 3 and 4h

)40 DTISCUSSTOJ The results at temperatures above 200K are depicted graphically in tIigo 1, as the deviation of -the heat capacities of the measured ferri.tes from those of' annealed zinc ferrite~ Only the smooth curve for the lithiurmzinc ferrites and for the quenched zinc ferrite are shown; the curves for the copper-z-inc ferrites are shown with the data points renresenting the actual determinations, The most striking characteri-st-i.c of the curves is that for the ouenchied sam ples, the copper-zinc ferrite resembles closely the Droperties of zinc ferrite itself, while the annealed copper-zinc ferrite more nearly resembles the lithium-zinc ferrite, Table 2. HIeat Capacities of Copper-Zinc Ferrites in cal(deg g mole)-' T(OK) Cp T(~K) Cp T(OK) Cp (Annealed) Cuo 05 Zn0 o 90Fe2 2o05 Series I 7 16 2,01 39026 2.990 7.34 2.70 42o38 3,374 211o01 272?9 7.72 3~33 46o18 3.888 219.18 28~03 8.03 2. 6 51.17 4,o607 22 3. 15 28,83 8.23 2 e;36 56,68 5o,460 237,29 29o56 8,39 2.83 62,28 6.337 246.28 3Co31 8,53 2,74 67o90 70239 255.09 30093,.66 2.72 73075 8,178 8.81 2o7i 80o,15 9246 Series II 3o,96 2o66 9.14 2o64 Series VI 131.98 17.56 137o 33 18, 36 Series IV 5,33 0o34 14 3 o 72 19, 30 5, o 84 o043 150.36 20o30 5.53 0.35 6,20 0.53 158,54 21o33 6.ol o,46 6,50 0.62 167,02 22,o. 6. 63 0. 80 662 0o 71 175 75 23653 7 09 1.50 6, 8 lo,13 184,'33 24o.52 7,69 3.42 70L6 2k63

Table 2 (continued) 193.L49 25o52 8,1.0 2.90 7, o2 3~02 202.90 26,49 8.65 2.65 8.09 2.96 211.90 27036 9o46 2.60 8,6)4 2.69 208.95 27~07 10.08 2.550 9.23 2.631 217.89 27090 10o53 2o,95 9.87 26571 226,90 28,71 11o 18 20 Lh 10652 26502 235o95 29047 11.97 2.350 11.12 2.h60 245,10 30,20 12.78 2.297 11.58 2,19 254o46 30.85 Series V 12.25 2.332 263088 31655 13.22 2.262 273.13 32o15 5.o2 0o,-3 14.22 2,168 282.23 32070 5.78 0oh7 15040 2,086 291.36 33.22 6.20 0,67 16.67 1.994 300~67 33071 6.69 0.86 17095 1.921 310,12 3o423 7o13 1.82 19,17 10870 319062 34,65 7038 3.05 329.21 350)4 7076 3,33 Series VII 338090 35$50 17 e19 1o 964 347o53 35.87 18o6), 16819 79.6 9.130 20, 80 1.826 85$.6 101oh44 Series III 23032 1.o21 91650 11,133 25.3 8 1,879 970,8 12.161 6,.46 0,67 28~942 1 o 994 10lo4.90 13.343 64s9 0,69 31o07 2.173 112.02 1h.449 6067 0,h4 33076 2.o402 119.26 15.60 6,96 1o30 36. )5 20673 127,28 16.85 T(~K) Cp T(~K) Cp T(OK) C, Quenched CUO Q05Zno 901Fe2o 050h Series I 51.49 50333 86o)43 11,183 56 4h2 6o.147 93032 12,320 93.82 12h402 99,48 13.356 Series III Series IV 106,98 14o539 115057 15.91 7.23 1,12 152,30 21,39 124o 36 17.31 10o.3 1. 43 161.81 22.66 133.17 18,66 11.75 1o518 17103)4 23.86 142o05 19.96 13.31 1.569 180,63 2h.95 151003 21.22 14.99 1.608 189073 25.96 16.71 1.6ho 195o16 26.52 Series II 183 45 1. 635 203.90 27.42 20.29 1.739 212,90 28.26.82 0.28 22,31 1, o 36 222.17 29.09 13018 1,56 2)4~37 10957 231.74 29,90 1)o2) 1o$9 26.39 2,098 2l1,26 30066

Table 2 (continued) 15,68 1.62 28.73 2 291 250o28 31037 L4,57 0 O19 310 35 2,5)47 260,78 32,0)4 )h 69 0,22 3)4,15 2 860 270,55 32,67 5 04 o, 38 37~25 3o2147 28,o)8 33o25 5,71 0,72 4o.049 3 oR 290I[4) 33o,~0 6,67 1,01 )43.95 ho177 300o44h 3)o3)4 7083 1,21 56,27 6o108 310 o.47 3. 82 9e07 1,36 61073 7,015 320,38 35.28 )4. lto 4 o,193 67.27 7 o942 329,06 35 6)4 L47.32 14, 6.82 7 3~ 38,o 943 336,67 35o96 79.14 10o,047 345033 36,31 Table 30 liolal thermodynamlic functions for (annealed) copper-zinc ferrite (Cu0o. oZno.90ie2 05()) ) at selected temperatures T(OK) Cp So~ s H~~Ho 0-H 0 0 T (cal/dego (cal/deg. (cal/ (cal/deg. mnole) mole) mole) mole) 10 255)4 1 o 2 7 9,954 0 o,995 15 2o121 2.2)t5 21,56 1, 437 20 1 8)44 2,810 31 036 1,568 25 1, 352 3o218 40. i9 1, 6o20 30 2,09)4 3,573 50,27 1.676 35 2, 522 3,927 61,75 1076)4 4o 30077 )4o299 75o70 1o893 L45 3,720 4o 697 92.66 2o 059 50 4o429 5,126 113,0 2,260 60 5o978 6,069 165o0 2.749 70 70569 70109 232.7 3o324 80 90218 8,227 316.6 3,957 90 10o 85 90407 419.5 4,o 661 o00 12 )49 100635 536,2 5 362 110 14,10 11,901 66902 6,083 120 15,71 130198 818,2 6,819 130 17,25 1) o516 98 3 ol 7 562 140 18,76 15,35 1163,2 8o 308 150 20,17 17 193 1357,9 9,052 160 21o52 13,538 1566,3 9~790

Tablle 3 (continued) 170 22,82 19,882 178.1 10,518 1,30 2ho03 21.221 2022,)4 11,?35 190 25,15 22.551 2268,3 11,938 200 26,20 23.868 2525,1 12,625 210 27.18 25,170 2792,0 13.295 220 28.o09 26 o455 3068 3 1309)47 230 28,97 27 724 3353,7 14ol581 240 29079 28o974 36)4705 15,198 250 30o53 30,206 39L49.2 15o797 260 31o25 31 o17 425801 16,377 270 31o94 32,609 4571 o0 16o,941 2 0 32057 33,783 48996.6 17 ol88 290 33017 34, 936 5225.3 1,e018 300 33073 36,070 5559.8 18s,533 350 35 98 41049 7305,8 20.774 273,15 32,1l4 32.9"1 )467)4.4l 17 113 298150 33~63 35 861 5497 6 18 0,39 Table 4. Molal thermodynamic functions for quenched copper-zinc ferrite (Cu0 05Zn0 90Fe2 o0 0L) at selected termperatures T( K) Cp so-s8 HO-HO i-HO' 0 0 0 T (cal/dego (cal/deg. (cal/ (cal/deg. mole) mole) mole) mole) 10 1,428 0o834 5.873 0,587 15 1o607 1.LS5 13.55 0,903 20 1,730 1.932 21,86 1,093 25 1,98 0 2,344 31.13 1,245 30 24 o10 2o.743 l42,08 1oLo03 35 2, 964 3.155 55.)47 1.585 40 3,612 3o592 71.88 1o797 4L5 L-,329 4,0058 91.70 2.038 50o 5o098 ).oF55 115,3 2,305 60 6,o 728 5,626 17.3 2o905

Table 4. (continued) 70 8 386 6.788 2L499 30570 80 10o03 8,017 342,2 4o,277 90 11078 9.302 L51i5 5.017 100 13043 o10630 57706 5,776 110 15 Olt 11,989 719.9 60544 120 16,64 13o 361 878.3 70319 130 1L.18 17SL54 1052L 8.0o95 1i0 19,67 16o156 12h1,6 $,S69 150 21.08 17 o562 144So. 9,636 160 22,o3 18o965 1662,c 100393 170 23,69 20~363 1893,6 11,139 180 2)4.88 210751 2136.5 11o869 190 25,98 23.126 2390,8 12,583 200 27.02 2 oL)486 2655;o9 130279 210 27,99 25S828 2931,0 130957 220 28.90 27,151 3215.5 1 o.616 230 29,6 29,7 2)55 3508o 1o5256 2)40 30. 6 29 738 3810 o 1o5,877 250 31.30 31,o001 4119.8 16.479 260 31.99 32.242 44W36,3 17o063 270 32.62 33,L61 L759.4 17,627'80 33.22 3ho659 5088,,6 18,174 290 33.78 35 835 5h23o6 18o702 300 3L.31 36,9 c39 5761, 0 19,213 350 36,4)8 )42 0 It48 7536 2 21.532 273.15 32 82 314 o L 84l 4c82 2L. 17 801 298,15 3.o 21 36,777 5700~6 19.120 A major difference between the coppemr and the li thium-containrng errites is that the copper can mi;rate between sublattices at the telmperature of firi ng, while the lithium cannot, Moreover, the mass of the copper is much greater than that of the lithium, Table 5 shows the idealized sublattice populations in terms of the ferric ions and the closed shell ions,'7

Table 5o Idealized Sublattice Populations Sublattice Ion Zn Ferrite Li-Zn Ferrite Cu-Zn Ferrite Annealed Samples A R' 1 00 0 o o090 Fe 0 0o10 0. 10 B R 0 0o05 0o05 Fe 20O0 1oS5 lo95 Quenched Samples A R 0 333 0o30. 0o 317 Fe 0e667 0o695 0o63' B R 0o667 0.645 0633 Fe 1o333 lo355 1,367:R = ions with zero intrinsic moment0 The slight difference in absolute value of heat capacity between annealed lithiumi- and copper-containing ferrites is not explicable on the basis of the idealized sublattice populations~ It might be due, however, to differences in the lattice heat capacity, to imperfect ordering of the copper-containing ferrite, to the presence of divalent copper, or to different values of exchange coefficients0 Within experimental error, and certainly within 0O10K, the temperature of the anomalous peak is the same in both annealed lithiumcontaining and in annealed copper-containing ferrites (cf. Fig0 2)o However the transition t empe'ature is lower in the lithium-containing ferrite than in a nickel-containing zinc ferrite02 One of the Cifferences array of lithium ions on the B sublatticeo Such is not the case for copper

ferrite, yet the transition temperature is the same in copper- as in lithiumcontaining zinc ferrite0 Therefore, it is concluded that the decrease in transition ternperature is not due to intrasul0attice ionic ordering' The presence of divalent copper would require a change in oxidation state in some other ferrite constituent for a fixed oxygen content, The most probable ion to change oxidation state is, of coulrse, ferric iron. Both divalent copper and divalent iron ions possess permanent magnetic moments, as does divalent ni.ckel, The fact that the annealed copper-containing samrle has a transition similar to the lithiuoo-coritai ni ntJ sampile in both anomaly shape and temrlerature and not to the ni.ckel-containing samnle indicates further that the copper is monovalent. The ferritic compround i.s considered as,lexZnl 2xIe2+xO where lie represents a univalent nonmagnetic ion such as those of Li or Cu The ferrite is assumred to consist of two B sublattices, B+ and B,, and a single A sublattice, i orn annealed sam'lrles the fie ions are assuned to be randornly distributed on the B suor)lattijce, The g:overning equ.-tions in the nonordered state are (by an extension of the treotment of Tach!i1i ard Yosida6): 2 (12 — s( TMB_= (1- x) CG O.Fip + - M T2p~ 2 HB — i (1I) TMA X=CA CH Pi3MB* - i3MB~- ~>kI] It will be assumed that the Lande g-factors are equal, ioeo, gB+ g A so CB+ = C_ = 0CA. The condition that a nontrivial solution of equations (1) exists when H = 0 is that the determinant of the coefficients of the II's be zero. The resul-ting cubic equation contains'the rootT = aC (1 x 9, (2) which is independent of the magr itudes of f3 and yo

If the moments on the A sublattice are considered to be resolved.rnto two sublattices, the treatment of" Yaf'et ncd V.`ittel7 is a-.i ahble. Their result for tie antiCerromagnetic ordering temperature on the B sublattice, 0C2, reduces to Eq. (2) above. For the ferrites measured, x =.05, so the ratio of NTel temperatures in the mixed ferrites to that in the zinc ferrite, for constant ca, is 0.9750 The measured ratio was 0.o8 If the difference is attributed to variations of a with x, it should be noted that the shift in a is the same for Li+1 (radius of 0.71:T A) and Cu+1 (radius of 0,96 A). The magnnetic moments of the quenched samples at 00~K are, ideally, the moments of 0.667, 0o660, and 0.68i ferric ions per formula for zinc, mixed lithium-zinc, and mixed copper-zinc ferrites, respectively. Since the dependence of the ima?;n, tic moment unon terlerature is not kno7,m as a function of x, it is not possible to correlate the moments with the heatcan acity curve at resent, A CKNiJLEPD GNENTS The authors acknow,Tledge wit- grati tude the contribution of NTorman E. Levitin wlho collaborated in the calorimetric measurements on the samples and of Lysander A-shlock in the )reparation and analysis o I he samples. -10

ItEli'ERENCES 1. ifestrumy, 9.1. Jr. and Grimes, D.I1. J. Phys. (C'Temo Solids 3, W4 (1957). 2. Wiestrum, 1h.P,. Jr. and Grimes, 1.1ii. J. Phys. Chem. Solids 6, 290 (19SFR)o 3. H:astinms, Jon. and,orliss, L.h.. Phys. R1ev, 1 02, 160 (1956) h, Stierstadt, K. Z,.lir [(Physik ih:6, 169 (1956). 5. Beniamins, E. and'ilrestrum, Ei.t Jr. J. Amrer. Cheri. Soc. 79, 297 (19/57). 6. 1achiki, IJ. and Yosida, K. Prog. Theoo: hysics (Osaka) 17, 223 (1c57)8 7. Yafet, Y. and Kittel, C. GPhys.!1ev.'37, 292 (1952)4 -11

1.6 i_ _ ~ QUENCHED o313 00 5 ~~C Cuo.osZno.90F@ 5.0oo al r QUENCHED T Z n Fe2.0oo04.00 * 1.2 / - / QUENCHED - -- ~/ ~Li~ Zn~~~ Fe 0 ~< L so os~0.0 0.90 F2.05 4.00 U 0.8 — |_ I Cuo, u.Zn o.oo Fe. 04.oo 0- 0 0 0, L io.0 Zno. 9Oge.0504. C~. d 2 7. DEVIATION rite.?la a. Fi.1 h dvaino teha aacte fcD/rzn n

4 Cu Zn Fe 0.I 30 0.0o5 0.90 2.05 4.00 I bOJ I o I U'~ C Zn Fe 0 - <~U0.05 0.90 2.05 4.00 Li5 Zno9 Fe2o5 0 10 20 30 TEMPERATURE, K Fig. 2. The heat capacities of zinc ferrites at low temperatures. 1lb

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