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Low-temperature heat capacities and thermodynamic properties of zinc ferrites—III
J. Phys.
Pergamon
Chem. Solids
Press 1959. Vol. 10. pp. x20-125.
LOW-TEMPERATURE DYNAMIC
HEAT CAPACITIES
PROPERTIES
EFFECT
OF ZINC
OF COPPER
EDGAR F. WESTRUM, Department
of Chemistry,
AND THERMO-
SUBSTITUTION
JR.
and D. M. GRIMES
University of Michigan, (Received
FERRITES-III
3 November
Ann Arbor, Michigan
1958)
Abstract-The heat capacities of annealed and quenched samples of Cuo.osZno.soFes.os04 have been determined over the range 5350°K. The Neel temperature is the same as that previously reported for a similar lithium-substituted zinc ferrite. The result is discussed in terms of the sublatticepopulation and molecular-field coefficients. 1. INTRODUCTION
THE low-temperature heat capacity and thermodynamic properties of zinc ferrite and of a solid solution of composition 90 mole per cent zinc ferrite (ZnFesOd) and 10 mole per cent lithium ferrite (Lia.sFes.sO4) have been studied and reported previously.(i) The data were taken on samples which, after forming spinels from the constituent oxides, had been annealed and on similar samples which had been quenched from 1100°C in distilled water. It was found(s) that the annealed samples had X-type anomalies in the vicinity of 9°K. This effect has been associated with an antiferromagnetic-type ordering in zinc ferrite.(a) The heat-capacity curve for the quenched samples showed inflections at about 9”K, but a local maximum did not exist. These effects were explained on the basis of sublattice populations and freezing in the 1400°K population equilibrium by the water quench. Similar experimental data have now been obtained on other samples of quenched and annealed ferrite. The samples were solid solutions of composition 90 mole per cent zinc ferrite and 10 mole per cent copper ferrite (Cus.sFea.sO4). The copper ferrite was prepared in such a way that, according to STIERSTADT,(~) it should be in the univalent state.
place of the ball mill. The results of chemical analyses on the samples for iron and copper are shown in Table 1. Table 1. Analyses of copper-zinc ferrites
Sample treatment
/ I i --___
Percentage Observed’--
~ cu Annealed Quenched
~
1.33 1.29
/
Fe 47.68 47.37
1 ~.~___ ~-~
by weight
i
Theoreticaf Cu 1.32 1.32
Fe 47.60 47.60 --..___~ _
The cryogenic technique was as described previously,(ss) except that calorimeter of laboratory designation W-IO was employed for these measurements. This calorimeter is similar to calorimeter W-9 previously described,@) but has a slightly greater volume and lacks heat-conduction vanes. The masses of the calorimetric samples were 187.486 g of annealed and 166.54 g of quenched Cua.asZna.s0Fea.ss04. The gram-molecular weight was taken to be 240.51 g. 3. RESULTS
The values of heat capacity, corrected for “curvature” and in terms of the defined thermochemical calorie of 4~1840 absolute J, and an ice point of 273~15°K are presented in Table 2. The
2. EXPERIMENTAL The samples were prepared as described previously(2), except that a Szegvari mixer was used in 120
HEAT
CAPACITIES
AND
THERMODYNAMIC
discussion of precision and intrinsic errors of the previous work(r*z) applies 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 Tables 3 and 4. 4. DISCUSSION
The results at temperatures above 20°K are depicted graphically in Fig. 1, as the deviation of
0
PROPERTIES
OF
ZINC
FERRITES
121
A major difference between the copper- and the lithium-containing ferrites is that the copper can migrate between sublattices at the temperature of firing, 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. The slight difference in absolute value of heat capacity between annealed lithium- and copper-
300
200
100 TEMPERATURE,
OK
FIG. 1. The deviation of the heat capacities of copper-zinc and lithium-zinc ferrites from those of annealed zinc ferrite.
the heat capacities of the measured ferrites from those of annealed zinc ferrite. Only the smooth curve for the lithium-zinc ferrites and for the quenched zinc ferrite are shown; the curves for the copper-zinc ferrites are shown with the data points representing the actual determinations. The most striking characteristic of the curves is that, for the quenched samples, the copper-zinc ferrite resembles closely in properties the zinc ferrite itself, while the annealed copper-zinc ferrite more nearly resembles the lithium-zinc ferrite.
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 coppercontaining ferrite, to the presence of divalent copper or to different values of exchange coefficients. Within experimental error, and certainly within O*l”K, the temperature of the anomalous peak is the same in both annealed lithium-containing and in annealed copper-containing ferrites (cf. Fig. 2).
27.29 28.03 28.83 29.56 30.31 30.93
Series III 6.46 6.49 6.67 6.96 j, 7.16 /
0.67 0.69 0.84 1.30 2.01
Series II 131.9 Y / 17.56 137.3 18.36 143.72 i 19.30 150.86 i 20.30 21.33 158.54 167.02 22.44 175.75 23.53 184.33 24.52 193.49 25.52 202.80 26.49 211.90 27.36 27.07 208.95 217.89 27.90 226.90 28.71 235.95 29.47 245.10 30.20 254.46 30.85 263.88 31.55 273.13 32.15 282.23 32.70 33.22 291.36 300.67 33.71 310.12 34.23 319.62 34.65 329.21 35.04 338.90 35.50 347.53 35.87
211.01 219.18 228.15 237.29 246.28 255.09
Se ries I
5.24 5.78 6.20 6.69 7.13 7.38 7.76 17.19 18.64 20.80 23.32 25.88 28.42 31.07 33.76 36.45
Series V
Series IV ) 5.53 6.01 6.63 , 7.09 ; ~ 7.69 8.10 ; 8.65 9.46 10.08 1 10.53 11.18 11.97 12.78
0.34 0.47 0.67 0.86 1.82 3.05 3.33 1.964 1.889 1.826 1.821 1.879 1.994 2.173 2402 2.673
0.35 0.46 0.80 1.50 3.42 2.90 2.65 2.60 2.550 2.495 2,454 2.350 2,297
Series III (cont.) 2.70 7.34 , 3.33 7.72 2.96 8.03 2.86 8.23 2.83 8.39 2.74 8.53 2.72 8.66 2.71 8.81 2.66 8.96 2.64 9.14 0.34 0.43 0.53 0.62 0.71 1.13 2.63 3.02 2.96 2.69 2.631 2.571 2.502 2.460 2.419 2.332 2.262 2.168 2.086 1.994 1.921 1.870
Series VII 79.46 ! 9.130 85.46 I 10.144 91.50 11.133 97.88 12.161 104.90 13.343 112.02 / 14449 119-26 127.28
Series VI 5.33 I 5.84 6.20 ( 6.50 6.62 6.88 7.46 ~ 7.82 ~ 8.09 ) 8.64 ~ 9.23 9.87 , 10.52 11.12 11.58 12.25 13.22 ’ 14.22 I 15.40 ’ 16.67 17.95 i 19:17 ~
Series V (:cont.) 39.26 2.990 42.38 3.374 46.18 3.888 51.17 4.607 5 460 56.68 62.28 6.337 7.239 67.90 8.178 73.75 9.246 SO.15
Annealed Cuo.osZno.goFez.os04
/:i-
I
=
4.82 13.18 14.24 15.68 4.57 4.68 5.04 5.71 6.67 7.83 9.07 44.10 47.32
93.82 99.48 106.98 115.57 124.36 133.17 142.05 151.03
TW I
0.28 1.56 1.59 1.62 0.19 0.22 0.38 0.72 1 .Ol 1.21 1.36 4’193 4.682
12-I-02 13.356 14.539 15.91 17.31 18.66 19.96 21.22
S0-l ‘es II
stis
Table 2. Heat capacities of copper-zinc ferrites in cal(deg.
1 j i
:
I / 1
1 G
-
L
152.30 161.81 171.34 180.63 189.73 195.16 203.90 212.90 222.17 231.74 241.26 250.88 260.78 270.55 28048 29044 30044 310.47 32028 329.06 336.67 345.33
series III 7.23 1.12 10.34 1.43 11.75 1.518 13.31 1.569 14.99 1.608 16.71 1.64-O 18.45 1.685 20.29 1.739 1.836 22.31 24.37 1.957 26.39 2.098 28.73 2.291 31.35 2.547 34.15 2.860 37.25 3.247 40.49 3.681 43.95 4.177 56.27 6.108 61.73 7.015 67.27 7.942 8.943 73.38 79.84 10.047
,... _
86-43 93.32
Series II (cont.) 51.49 5.333 56.42 6.147
(cont.) 11.183 12.320
c,,
-.
-
.
-
Series IV 21.39 22.66 23.86 24.95 25-96 26.52 27.42 28.26 29.09 29.90 30-66 31.37 32.04 32.67 33.25 33.80 34.34 34-82 35.28 35.64 35.96 36.31
seriesIII
1 T(“K) 1
Quenched Cuo.osZno.soFe2.o&4
T(“K)
mole)-1
-
-
-
HEAT
CAPACITIES
AND
THERMODYNAMIC
Table 3. MOM thermodymmic
c,
so-So”
(caljdeg. mole)
(caljdeg. mole)
TIO
JOY
OF ZINC
FERRITES
annealed copper-x&c ferrite (Cuo.osZno.soFea.osO4)
(cal~mole)
at
H”--HO”
(cal/deg. mole}
WW
123
H” -Ho0
CD
H”-Ho”
I[caljmole)
(cal~eg.
mole)
l-437 l-568 I.620 I.676
170 180 190 200 210
---22.82 24.03 25.15 26.20 27.18
61.75 75.70 42.66 113.0 165.0
1.764 I.893 2-059 2.260 2,749
220 230 240 250 260
28.09 28.97 29.79 30.53 31.25
26.455 27.724 28.974 30.206 31.417
3068.3 3353-7 3647.5 3949.2 4258.1
13.947 14*581 15.198 15,797 16.377
7-109 8.227 9407 IO.635 II-901
232.7 316.6 419-s 536.2 669-2
3-324 3.957 4.661 5.362 6,083
270 280 290 300 350
31.94 32.57 33.17 33.73 35.98
32.609 33.783 34.936 36.070 41449
4574.0 4896.6 5225.3 5559.8 7305.8
16,941 17.488 18.018 18.533 20.874
13.198 14.516 IS.850 17-193 18-538
818-2 983.1 1163.2 1357.9 1.566-3
6.819 7.562 8.308 9.052 9.790
273.15
32.14
32.981
4674.4
17.113
298.15
33.63
35,861
5497.6
18.439
-_
--
~-
10 15 20 25 30
2.554 2.121 l-844 l-852 2.094
I.297 2.245 2.810 3,218 3.573
35 40 4.5 50 60
2,522 3.077 3-720 4.429 5.978
3-927 4.299 4-697 5.126 6.069
70 80 90 100 110
7,569 9.218 IO.85 12.49 14.10
120 130 140 150 160
15.71 17.25 18.76 20.17 21.52
-
functions
PROPERTIES
9.954 21.56 31.36 40.49 50.27
0.995
___-__....
.--_ -_-_
--
21.221 22.551 23.868 25.170
1788.1 2022.4 2268.3 2525.1 2792.0
10.518 11.235 11.938 12.625 13.295
19.882
~_
4
However, the transition temperature is lower in the lithium-cont~ning ferrite than in a nickelcontaining zinc ferrite.(a) One of the differences noted was that annealed lithium ferrite without zinc forms an ordered array of lithium ions on the B sublattice. Such is not the case for copper ferrite, yet the transition temperature is the same in copper- as in lithium-containing zinc ferrite. Therefore, it is concluded that the decrease in transition temperature is not due to intrasublattice 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 course, ferric iron. Both divalent copper and divalent iron ions possess permanent magnetic moments, as does divalent nickel. The fact that the annealed coppercontaining sample has a transition similar to the lithium-containing sample in both anomaly shape and temperature and not to the nickel-containing
-
L
0” 22 -i
4 c
u” 1
‘C %os”o.aoFe2.*504a
- - Lio*o 5 zno~oFe2.0504m I
0 0
20 IO TEMPERATURE, OK
30
FIG. 2. The heat capacities of zinc ferrites at low temperatures.
124
EDGAR
F.
WESTRUM,
JR.
and
D.
M.
GRIMES
Table 4. Molal thermodynamic functions for quenched copper-zinc ferrite (Cuo.osZno.soFes.os04) selected temperatures
_.~. __.. -__
T(“K)
___~_. ~_..
at
S”-SO”
G
(caljdeg. mole)
(cal/deg. mole)
s”--so” (cal/deg. mole)
WW
H” -Ho” (Cal/mole)
Ho -Ho” T (cal/deg. mole)
mole)
.IO 15 20 25 30
I .428 I.607 1,730 I.998 2.410
0.834 1.455 1.932 2,344 2.743
5.873 13.55 21.86 31.13 42.08
0.587 0.903 I.093 1.245 1.403
170 180 190 200 210
23.69 24.88 25.98 27.02 27.99
20.363 21.751 23.126 24,486 25.828
1893.6 2136.5 2390.8 2655.9 2931.0
11.139 II-869 12.583 13.279 13.957
35 40 45 50 60
2.664 3.612 4.329 5,098 6.728
3.155 3,592 4.058 4.554 5.626
55.47 71.88 91 a70 115.3 174.3
I.585 I.797 2.038 2.305 2.905
220
/ 230 / 240 / 250
28.90 29.76 30.56 31.30 31‘99
27.151 28.455 29.738 31 .OOI 32-242
3215.5 3508.8 3810.4 4119.8 4436.3
14.616 15.256 15.877 16.479 17.063
70 80 90 100 110
8.386 IO.08 II.78 13.43 IS.04
6.788 8.017 9.302 10.630 Il.984
249.9 342.2 45lfl 577.6 719.9
3.570 4.277 5.017 5.776 6.544
280 290 300 3.50
32.62 33.22 33.78 34.31 36.48
33.461 34.659 35.835 36.989 42.448
4759.4 5088.6 5423.6 5764.0 7536.2
17.627 18.174 18.702 19.213 21.532
120 130 140 150 160
16.64 18.18 19.67 21.08 22.43
13-361 14.754 16.156 17.562 18.965
878.3 1052.4 1241.6 1445.4 1662.9
7.319 8.095 8.869 9.636 IO.393
273.15
32.82
34.841
4862.4
17,80X
298.15
34.21
36.777
5700.6
19-120
I/ 260
’ 270
,I
I
/ sample indicates further that the copper is monovalent. The ferritic compound is considered as Me,Znr_e,Fes+,O~ where Me represents a univalent nonmagnetic ion such as those of Li or Cu. The ferrite is assumed to consist of two B sublattices, Bf and B-, and a single A sublattice. For annealed samples the Me ions are assumed to be randomly distributed on the 3 sublattice. The governing equations in the nonordered state are (by an extension of the treatment of TACHIKI and YUSIDA(~)):
--
_-..
tions (1) exists when H = 0 is that the determinant of the coefficients of the IM’s be zero. The resulting cubic equation contains the root,
which is independent of the magnitudes of ,3 and X. If the moments on the A sublattice are considered to be resolved into two sublattices, the treatment of YAFET and KITTEL(~) is applicable. Their result for the antiferromagnetic ordering
TMB+ = [l-(x/Z)]C~+[li-(cr/2)MB+-aMB---/IMA] TMB-
= [l-(x/2)]Cs-[H-nMs+-(cc/2)MB---/IMA]
I
TMA
= ~xCA[H-/~M~+-/~MB--~MA].
i
It will be assumed that the Lande g-factors are equal, i.e. gs+ = gs- = g_& so CBL = cB- = c,.$. The condition that a nontrivial solution of equa-
(1) 1 I !
temperature on the 3 sublattice, rca, reduces to equation (2) above, For the ferrites measured, x = 0.05, so the ratio
HEAT
CAPACITIES
AND
THERMODYNAMIC
Table 5. ~d~~lix~d ~~Zatt~ce ~op~~~t~o~ ___~~~~~~~~
Annealed A
B
samples
R* Fe
1 .oo 0
0.90 0.10
R
0 2.00
0.05 1.95
I Fe
’
0.90 0.10 0.05 1.95
Quenched samples
-._. .~~. -__-~--.-_ --_____~ * R = ions with zero intrinsic moment.
PROPERTIES
FERRITES
125
The magnetic moments of the quenched samples 0°K are, ideally, the moments of 0.667, 0.660 and 0.684 ferric ions per formula for zinc, mixed lithium-zinc and mixed copper-zinc ferrites, respectively. Since the dependence of the magnetic moment upon temperature is not known as a function of X, it is not possible to correlate the moments with the heat-capacity curve at present.
at
Acknowledgements-The authors acknowledge with gratitude the contribution of NORMAN E. LEVITIN, who collaborated in the calorimetric measurements on the samples, and of LVSANDERASHLOCK, who collaborated in the preparation and analysis of the samples.
*. 2. 3.
of NCel temperatures in the mixed ferrites to that in the zinc ferrite, for constant M, is 0.975. The measured ratio was 0.8. 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+l (radius of 0.78 A) and Cu+l (radius of 0*96*&.
OF ZINC
4.
5. 6 ’ 7.
REFERENCES
WIZ~TRUME. F., J%. and GRIMES D. M., J. Phys. Chem. Solids 3, 44 (1957). W~TRUM E. F., Jr. and GRIME D. M., J. Phys. Chem. Solids 6, 280 (1958). HASTINGSJ. M. and CORLISS L. M., Phys. Rev. 102, 1460 (1956). STIER~TADTK., 2. Phys. 146, 169 (1956). BENJAMXNSE. and WFSTRUM E. F., Jr., J. Amer. Chem. Sot. 79, 287 (1957). TACHIKI M. and YOSIDA K., Progr. Tkeor. Phys. 17, 223 (1957). YAFET Y. and KITTEL C., Phys. RN. 87, 292 (1952)
Pergamon
Chem. Solids
Press 1959. Vol. 10. pp. x20-125.
LOW-TEMPERATURE DYNAMIC
HEAT CAPACITIES
PROPERTIES
EFFECT
OF ZINC
OF COPPER
EDGAR F. WESTRUM, Department
of Chemistry,
AND THERMO-
SUBSTITUTION
JR.
and D. M. GRIMES
University of Michigan, (Received
FERRITES-III
3 November
Ann Arbor, Michigan
1958)
Abstract-The heat capacities of annealed and quenched samples of Cuo.osZno.soFes.os04 have been determined over the range 5350°K. The Neel temperature is the same as that previously reported for a similar lithium-substituted zinc ferrite. The result is discussed in terms of the sublatticepopulation and molecular-field coefficients. 1. INTRODUCTION
THE low-temperature heat capacity and thermodynamic properties of zinc ferrite and of a solid solution of composition 90 mole per cent zinc ferrite (ZnFesOd) and 10 mole per cent lithium ferrite (Lia.sFes.sO4) have been studied and reported previously.(i) The data were taken on samples which, after forming spinels from the constituent oxides, had been annealed and on similar samples which had been quenched from 1100°C in distilled water. It was found(s) that the annealed samples had X-type anomalies in the vicinity of 9°K. This effect has been associated with an antiferromagnetic-type ordering in zinc ferrite.(a) The heat-capacity curve for the quenched samples showed inflections at about 9”K, but a local maximum did not exist. These effects were explained on the basis of sublattice populations and freezing in the 1400°K population equilibrium by the water quench. Similar experimental data have now been obtained on other samples of quenched and annealed ferrite. The samples were solid solutions of composition 90 mole per cent zinc ferrite and 10 mole per cent copper ferrite (Cus.sFea.sO4). The copper ferrite was prepared in such a way that, according to STIERSTADT,(~) it should be in the univalent state.
place of the ball mill. The results of chemical analyses on the samples for iron and copper are shown in Table 1. Table 1. Analyses of copper-zinc ferrites
Sample treatment
/ I i --___
Percentage Observed’--
~ cu Annealed Quenched
~
1.33 1.29
/
Fe 47.68 47.37
1 ~.~___ ~-~
by weight
i
Theoreticaf Cu 1.32 1.32
Fe 47.60 47.60 --..___~ _
The cryogenic technique was as described previously,(ss) except that calorimeter of laboratory designation W-IO was employed for these measurements. This calorimeter is similar to calorimeter W-9 previously described,@) but has a slightly greater volume and lacks heat-conduction vanes. The masses of the calorimetric samples were 187.486 g of annealed and 166.54 g of quenched Cua.asZna.s0Fea.ss04. The gram-molecular weight was taken to be 240.51 g. 3. RESULTS
The values of heat capacity, corrected for “curvature” and in terms of the defined thermochemical calorie of 4~1840 absolute J, and an ice point of 273~15°K are presented in Table 2. The
2. EXPERIMENTAL The samples were prepared as described previously(2), except that a Szegvari mixer was used in 120
HEAT
CAPACITIES
AND
THERMODYNAMIC
discussion of precision and intrinsic errors of the previous work(r*z) applies 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 Tables 3 and 4. 4. DISCUSSION
The results at temperatures above 20°K are depicted graphically in Fig. 1, as the deviation of
0
PROPERTIES
OF
ZINC
FERRITES
121
A major difference between the copper- and the lithium-containing ferrites is that the copper can migrate between sublattices at the temperature of firing, 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. The slight difference in absolute value of heat capacity between annealed lithium- and copper-
300
200
100 TEMPERATURE,
OK
FIG. 1. The deviation of the heat capacities of copper-zinc and lithium-zinc ferrites from those of annealed zinc ferrite.
the heat capacities of the measured ferrites from those of annealed zinc ferrite. Only the smooth curve for the lithium-zinc ferrites and for the quenched zinc ferrite are shown; the curves for the copper-zinc ferrites are shown with the data points representing the actual determinations. The most striking characteristic of the curves is that, for the quenched samples, the copper-zinc ferrite resembles closely in properties the zinc ferrite itself, while the annealed copper-zinc ferrite more nearly resembles the lithium-zinc ferrite.
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 coppercontaining ferrite, to the presence of divalent copper or to different values of exchange coefficients. Within experimental error, and certainly within O*l”K, the temperature of the anomalous peak is the same in both annealed lithium-containing and in annealed copper-containing ferrites (cf. Fig. 2).
27.29 28.03 28.83 29.56 30.31 30.93
Series III 6.46 6.49 6.67 6.96 j, 7.16 /
0.67 0.69 0.84 1.30 2.01
Series II 131.9 Y / 17.56 137.3 18.36 143.72 i 19.30 150.86 i 20.30 21.33 158.54 167.02 22.44 175.75 23.53 184.33 24.52 193.49 25.52 202.80 26.49 211.90 27.36 27.07 208.95 217.89 27.90 226.90 28.71 235.95 29.47 245.10 30.20 254.46 30.85 263.88 31.55 273.13 32.15 282.23 32.70 33.22 291.36 300.67 33.71 310.12 34.23 319.62 34.65 329.21 35.04 338.90 35.50 347.53 35.87
211.01 219.18 228.15 237.29 246.28 255.09
Se ries I
5.24 5.78 6.20 6.69 7.13 7.38 7.76 17.19 18.64 20.80 23.32 25.88 28.42 31.07 33.76 36.45
Series V
Series IV ) 5.53 6.01 6.63 , 7.09 ; ~ 7.69 8.10 ; 8.65 9.46 10.08 1 10.53 11.18 11.97 12.78
0.34 0.47 0.67 0.86 1.82 3.05 3.33 1.964 1.889 1.826 1.821 1.879 1.994 2.173 2402 2.673
0.35 0.46 0.80 1.50 3.42 2.90 2.65 2.60 2.550 2.495 2,454 2.350 2,297
Series III (cont.) 2.70 7.34 , 3.33 7.72 2.96 8.03 2.86 8.23 2.83 8.39 2.74 8.53 2.72 8.66 2.71 8.81 2.66 8.96 2.64 9.14 0.34 0.43 0.53 0.62 0.71 1.13 2.63 3.02 2.96 2.69 2.631 2.571 2.502 2.460 2.419 2.332 2.262 2.168 2.086 1.994 1.921 1.870
Series VII 79.46 ! 9.130 85.46 I 10.144 91.50 11.133 97.88 12.161 104.90 13.343 112.02 / 14449 119-26 127.28
Series VI 5.33 I 5.84 6.20 ( 6.50 6.62 6.88 7.46 ~ 7.82 ~ 8.09 ) 8.64 ~ 9.23 9.87 , 10.52 11.12 11.58 12.25 13.22 ’ 14.22 I 15.40 ’ 16.67 17.95 i 19:17 ~
Series V (:cont.) 39.26 2.990 42.38 3.374 46.18 3.888 51.17 4.607 5 460 56.68 62.28 6.337 7.239 67.90 8.178 73.75 9.246 SO.15
Annealed Cuo.osZno.goFez.os04
/:i-
I
=
4.82 13.18 14.24 15.68 4.57 4.68 5.04 5.71 6.67 7.83 9.07 44.10 47.32
93.82 99.48 106.98 115.57 124.36 133.17 142.05 151.03
TW I
0.28 1.56 1.59 1.62 0.19 0.22 0.38 0.72 1 .Ol 1.21 1.36 4’193 4.682
12-I-02 13.356 14.539 15.91 17.31 18.66 19.96 21.22
S0-l ‘es II
stis
Table 2. Heat capacities of copper-zinc ferrites in cal(deg.
1 j i
:
I / 1
1 G
-
L
152.30 161.81 171.34 180.63 189.73 195.16 203.90 212.90 222.17 231.74 241.26 250.88 260.78 270.55 28048 29044 30044 310.47 32028 329.06 336.67 345.33
series III 7.23 1.12 10.34 1.43 11.75 1.518 13.31 1.569 14.99 1.608 16.71 1.64-O 18.45 1.685 20.29 1.739 1.836 22.31 24.37 1.957 26.39 2.098 28.73 2.291 31.35 2.547 34.15 2.860 37.25 3.247 40.49 3.681 43.95 4.177 56.27 6.108 61.73 7.015 67.27 7.942 8.943 73.38 79.84 10.047
,... _
86-43 93.32
Series II (cont.) 51.49 5.333 56.42 6.147
(cont.) 11.183 12.320
c,,
-.
-
.
-
Series IV 21.39 22.66 23.86 24.95 25-96 26.52 27.42 28.26 29.09 29.90 30-66 31.37 32.04 32.67 33.25 33.80 34.34 34-82 35.28 35.64 35.96 36.31
seriesIII
1 T(“K) 1
Quenched Cuo.osZno.soFe2.o&4
T(“K)
mole)-1
-
-
-
HEAT
CAPACITIES
AND
THERMODYNAMIC
Table 3. MOM thermodymmic
c,
so-So”
(caljdeg. mole)
(caljdeg. mole)
TIO
JOY
OF ZINC
FERRITES
annealed copper-x&c ferrite (Cuo.osZno.soFea.osO4)
(cal~mole)
at
H”--HO”
(cal/deg. mole}
WW
123
H” -Ho0
CD
H”-Ho”
I[caljmole)
(cal~eg.
mole)
l-437 l-568 I.620 I.676
170 180 190 200 210
---22.82 24.03 25.15 26.20 27.18
61.75 75.70 42.66 113.0 165.0
1.764 I.893 2-059 2.260 2,749
220 230 240 250 260
28.09 28.97 29.79 30.53 31.25
26.455 27.724 28.974 30.206 31.417
3068.3 3353-7 3647.5 3949.2 4258.1
13.947 14*581 15.198 15,797 16.377
7-109 8.227 9407 IO.635 II-901
232.7 316.6 419-s 536.2 669-2
3-324 3.957 4.661 5.362 6,083
270 280 290 300 350
31.94 32.57 33.17 33.73 35.98
32.609 33.783 34.936 36.070 41449
4574.0 4896.6 5225.3 5559.8 7305.8
16,941 17.488 18.018 18.533 20.874
13.198 14.516 IS.850 17-193 18-538
818-2 983.1 1163.2 1357.9 1.566-3
6.819 7.562 8.308 9.052 9.790
273.15
32.14
32.981
4674.4
17.113
298.15
33.63
35,861
5497.6
18.439
-_
--
~-
10 15 20 25 30
2.554 2.121 l-844 l-852 2.094
I.297 2.245 2.810 3,218 3.573
35 40 4.5 50 60
2,522 3.077 3-720 4.429 5.978
3-927 4.299 4-697 5.126 6.069
70 80 90 100 110
7,569 9.218 IO.85 12.49 14.10
120 130 140 150 160
15.71 17.25 18.76 20.17 21.52
-
functions
PROPERTIES
9.954 21.56 31.36 40.49 50.27
0.995
___-__....
.--_ -_-_
--
21.221 22.551 23.868 25.170
1788.1 2022.4 2268.3 2525.1 2792.0
10.518 11.235 11.938 12.625 13.295
19.882
~_
4
However, the transition temperature is lower in the lithium-cont~ning ferrite than in a nickelcontaining zinc ferrite.(a) One of the differences noted was that annealed lithium ferrite without zinc forms an ordered array of lithium ions on the B sublattice. Such is not the case for copper ferrite, yet the transition temperature is the same in copper- as in lithium-containing zinc ferrite. Therefore, it is concluded that the decrease in transition temperature is not due to intrasublattice 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 course, ferric iron. Both divalent copper and divalent iron ions possess permanent magnetic moments, as does divalent nickel. The fact that the annealed coppercontaining sample has a transition similar to the lithium-containing sample in both anomaly shape and temperature and not to the nickel-containing
-
L
0” 22 -i
4 c
u” 1
‘C %os”o.aoFe2.*504a
- - Lio*o 5 zno~oFe2.0504m I
0 0
20 IO TEMPERATURE, OK
30
FIG. 2. The heat capacities of zinc ferrites at low temperatures.
124
EDGAR
F.
WESTRUM,
JR.
and
D.
M.
GRIMES
Table 4. Molal thermodynamic functions for quenched copper-zinc ferrite (Cuo.osZno.soFes.os04) selected temperatures
_.~. __.. -__
T(“K)
___~_. ~_..
at
S”-SO”
G
(caljdeg. mole)
(cal/deg. mole)
s”--so” (cal/deg. mole)
WW
H” -Ho” (Cal/mole)
Ho -Ho” T (cal/deg. mole)
mole)
.IO 15 20 25 30
I .428 I.607 1,730 I.998 2.410
0.834 1.455 1.932 2,344 2.743
5.873 13.55 21.86 31.13 42.08
0.587 0.903 I.093 1.245 1.403
170 180 190 200 210
23.69 24.88 25.98 27.02 27.99
20.363 21.751 23.126 24,486 25.828
1893.6 2136.5 2390.8 2655.9 2931.0
11.139 II-869 12.583 13.279 13.957
35 40 45 50 60
2.664 3.612 4.329 5,098 6.728
3.155 3,592 4.058 4.554 5.626
55.47 71.88 91 a70 115.3 174.3
I.585 I.797 2.038 2.305 2.905
220
/ 230 / 240 / 250
28.90 29.76 30.56 31.30 31‘99
27.151 28.455 29.738 31 .OOI 32-242
3215.5 3508.8 3810.4 4119.8 4436.3
14.616 15.256 15.877 16.479 17.063
70 80 90 100 110
8.386 IO.08 II.78 13.43 IS.04
6.788 8.017 9.302 10.630 Il.984
249.9 342.2 45lfl 577.6 719.9
3.570 4.277 5.017 5.776 6.544
280 290 300 3.50
32.62 33.22 33.78 34.31 36.48
33.461 34.659 35.835 36.989 42.448
4759.4 5088.6 5423.6 5764.0 7536.2
17.627 18.174 18.702 19.213 21.532
120 130 140 150 160
16.64 18.18 19.67 21.08 22.43
13-361 14.754 16.156 17.562 18.965
878.3 1052.4 1241.6 1445.4 1662.9
7.319 8.095 8.869 9.636 IO.393
273.15
32.82
34.841
4862.4
17,80X
298.15
34.21
36.777
5700.6
19-120
I/ 260
’ 270
,I
I
/ sample indicates further that the copper is monovalent. The ferritic compound is considered as Me,Znr_e,Fes+,O~ where Me represents a univalent nonmagnetic ion such as those of Li or Cu. The ferrite is assumed to consist of two B sublattices, Bf and B-, and a single A sublattice. For annealed samples the Me ions are assumed to be randomly distributed on the 3 sublattice. The governing equations in the nonordered state are (by an extension of the treatment of TACHIKI and YUSIDA(~)):
--
_-..
tions (1) exists when H = 0 is that the determinant of the coefficients of the IM’s be zero. The resulting cubic equation contains the root,
which is independent of the magnitudes of ,3 and X. If the moments on the A sublattice are considered to be resolved into two sublattices, the treatment of YAFET and KITTEL(~) is applicable. Their result for the antiferromagnetic ordering
TMB+ = [l-(x/Z)]C~+[li-(cr/2)MB+-aMB---/IMA] TMB-
= [l-(x/2)]Cs-[H-nMs+-(cc/2)MB---/IMA]
I
TMA
= ~xCA[H-/~M~+-/~MB--~MA].
i
It will be assumed that the Lande g-factors are equal, i.e. gs+ = gs- = g_& so CBL = cB- = c,.$. The condition that a nontrivial solution of equa-
(1) 1 I !
temperature on the 3 sublattice, rca, reduces to equation (2) above, For the ferrites measured, x = 0.05, so the ratio
HEAT
CAPACITIES
AND
THERMODYNAMIC
Table 5. ~d~~lix~d ~~Zatt~ce ~op~~~t~o~ ___~~~~~~~~
Annealed A
B
samples
R* Fe
1 .oo 0
0.90 0.10
R
0 2.00
0.05 1.95
I Fe
’
0.90 0.10 0.05 1.95
Quenched samples
-._. .~~. -__-~--.-_ --_____~ * R = ions with zero intrinsic moment.
PROPERTIES
FERRITES
125
The magnetic moments of the quenched samples 0°K are, ideally, the moments of 0.667, 0.660 and 0.684 ferric ions per formula for zinc, mixed lithium-zinc and mixed copper-zinc ferrites, respectively. Since the dependence of the magnetic moment upon temperature is not known as a function of X, it is not possible to correlate the moments with the heat-capacity curve at present.
at
Acknowledgements-The authors acknowledge with gratitude the contribution of NORMAN E. LEVITIN, who collaborated in the calorimetric measurements on the samples, and of LVSANDERASHLOCK, who collaborated in the preparation and analysis of the samples.
*. 2. 3.
of NCel temperatures in the mixed ferrites to that in the zinc ferrite, for constant M, is 0.975. The measured ratio was 0.8. 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+l (radius of 0.78 A) and Cu+l (radius of 0*96*&.
OF ZINC
4.
5. 6 ’ 7.
REFERENCES
WIZ~TRUME. F., J%. and GRIMES D. M., J. Phys. Chem. Solids 3, 44 (1957). W~TRUM E. F., Jr. and GRIME D. M., J. Phys. Chem. Solids 6, 280 (1958). HASTINGSJ. M. and CORLISS L. M., Phys. Rev. 102, 1460 (1956). STIER~TADTK., 2. Phys. 146, 169 (1956). BENJAMXNSE. and WFSTRUM E. F., Jr., J. Amer. Chem. Sot. 79, 287 (1957). TACHIKI M. and YOSIDA K., Progr. Tkeor. Phys. 17, 223 (1957). YAFET Y. and KITTEL C., Phys. RN. 87, 292 (1952)