1959
THERMOPHYSICAL PROPERTIES OF THE LANTHANIDE OXIDES KBr reaction 3 is of minor importance only and reaction 4 predominates, even though the F-center concentration decreases with increasing KBr content. The rapidity with which the maxima and minima are annealed out indicates the high sensitivity of these reactions to thermal conditions. Despite the annealing out of the maxima and minima, the S- yields in general show no particular trend with time of heating at 75". However, at 215" for all compositions there is a maximum in the S- yield. In the samples with low KBr content, the maximum occurs at 6 hr; in samples with higher KBr content, it occurs a t 3 hr. ilt this temperature there is evidently a competition between reactions 3 and 4, with the latter being the faster.
I n summary, the results of this study are quite consistent with the Maddock-Mirsky model. The results can be explained by the existence of S+, So, and S- species in the crystals and by their reactions with oxidizing and reducing defects. However, allowance must be made for the effect of composition on the reactivity of the defects and for competition among the proposed reactions. Acknowledgement. This work was supported in part by research grants ( G P 5443 and GP 8071) from the National Science Foundation. The cooperation of Mr. J. J. O'Connor and the staff of the U. S. Army Materials and Mechanics Research Center Reactor is gratefully acknowledged.
Thermophysical Properties of the Lanthanide Oxides. V. Heat Capacity, Thermodynamic Properties, and Energy Levels of Cerium(II1) Oxide' By Bruce W. Justice and Edgar F. Westrum, Jr.2 Department of Chemistry, University of Michigan, A n n Arbor, Michigan
48104
(Received October 1 5 , 1 9 6 8 )
The thermal capacity of a sample of composition Ce203.02has been determined from 5 to 350°K by adiabatio calorimetry. A cooperative anomaly with maximum a t 8.5"K occurs with AS, = 0.83 cal/ (mol OK). The observed thermal capacity values yield for C,, So - S"~OK, and (Go - H O p ~ ) / values T of 28.05, 32.60, and -15.74 cal/(mol OK) for stoichiometric Ce203 a t 298.15"K. These values are referenced to 0°K with an estimated ordering contribution.
Introduction The measurement and interpretation of the low temperature thermal capacities of the lanthanide (111) 0xides~9~ are here extended to include cerium sesquioxide, Ces03. High temperature enthalpy data for Ce2O3+, have been reported by Pankratz and Kelley5 and by Kuznetsov and Rezukhina.6 Heat capacity data over the range 51-300°K have been obtained by Weller and King.' The present investigation is predicated on a more nearly stoichiometric sample (Ce203.02) and a broader temperature range (4350°K). Thermal capacities for A-type isomorphs of Nd203 and La20s (in which all of the magnetic ions occupy equivalent heptacoordinated sitess) have been supplemented by the spectraQ of Nd(II1) in a hexagonal (A-type) La203 host. Spectra of Nd(II1) ion in a cubic Y203 (C-type) host'O also have become available. These data permit a firm calculation of the lattice heat capacity of hexagonal Nd203. In turn the lattice heat capacity of hexagonal Ce203may be interpolated in a
manner similar to that presented for the paramagnetic C-type isomorphs between Gd20a and L U ~ O ~Such .~ a treatment would permit the resolution of the Schottky contribution for Ce(II1) ion in Ce203from which the two excited levels of the Ce(II1) ion (ground t e r q (1) This research was supported in part by the U. 9. Atomic Energy Commission. (2) To whom correspondence concerning this paper should be addressed. (3) (a) B . H. Justice and E. F. Westrum, Jr., J . P h y s . Chem., 67, 339 (1963);(b) B. H. Justice and E. F. Westrum, Jr., ibid., 67, 345 (1963): (c) E . F. Westrum, Jr., and B. H. Justice, dbid., 67, 643 (1963). (4) B. H.Justice, E. F. Westrum. Jr., E. Chang, and R . Radebaugh, i b i d . , 72, 2438 (1968). (5) L. B . Pankratz and K. K. Kelley, U. 9. Bureau of Mines Report of Investigations 6248 (1963). (6) F. A. Kusnetsov and T. N. Resukhina, Zh. Fia. K h i m . , 3 8 , 956 (1961). (7) W. W. Weller and E. G. King, U. 9. Bureau of Mines Report of Investigations 6245 (1963). ( 8 ) R. M. Douglass and E . Staritzky, A n a l . Chem., 28, 552 (1956). (9) J. R. Henderson, M. Muramoto, and J. B. Gruber, J . Chem. P h y s . , 46, 2515 (1967). (10) N. C. Chang, ibid., 44, 4044 (1966).
Volume 7% Number 6 June 1.968
1960
BRUCEH. JUSTICE AND EDGAR F. WESTRUM,JR.
Table I: Thermal Capacity of Cerium(II1) Oxide, Cez03a
-
-
CP,
cal/(mol
T , OK
OK)
Series I 71.73 78.06 84.99 93.33 102.64 111.55 120.27 129,28 138.54 147.84 157.21 166.42 175.53 184.85 194.42 204.14
8.967 10.069 11.205 12.482 13.816 15.042 16.18 17.29 18.35 19.33 20.24 21 -06 21.83 22.55 23.23 23.87
Series I1 AH Detn
199.89 209.50 219.09 228.70 238.36 248.05 257.73 267.40 277.10 286.86 296.61 306.42 316.30 326.10 335.82
A 23.59 24.20 24.77 25.29 25.79 26.25 26.66 27.05 27.41 27.77 28.11 28.28 28.53 28.79 29.04
c,,
CP,
T , OK
cal/(mol
345.48
29.26
OK)
Series I11 6.05 6.83 8.21 9.23 11.11 13.54 15.78 17.69 19.42 21.24 23.22 25.26 27.30 29.33 31.44 33.64 35.99 38.57 41.31 44.32 47.67 51.47 55.78 60.08 64. SO 70.30 75.86 81.44
0.421 0.653 0.832 0.740 0.491 0.468 0.511 0.588 0.690 0.831 1.015 1,239 1.488 1,758 2.062 2.397 2.765 3.183 3.639 4.150 4.739 5.404 6.163 6.934 7.777 8.711 9.645 10.589
Series IV 5.44 5.77
0.405 0.450
F,OK
cal/(mol OK)
6.05 6.54 7.11 7.63 8.04 8.40 8.63 8.95 9.52 10.18 10.89 11.64 12.41 13.16 13.59 14.60 15.27 15.91 16.52 17.20 17.95 18.64 19.34
0.579 0.466 0.506 0.711 0.772 0.901 2.164 0.654 0.584 0.545 0.496 0.468 0.462 0.465 0.472 0.450 0.496 0.519 0.532 0.562 0,599 0.637 0.682 Series V
A l f t Detn B
12.85
0.461
Series VI A H t Detn
C
Series VI1 A H t Detn D
12.55
0.461
Values adjusted for impurities as described in text.
2Fa,z) may be deduced. These results would yield broader knowledge, albeit empirical, of the crystal fields and lattice forces operative in the lanthanide (111) oxides. Experimental Section Cryogenic Calorimetric Technique. Thermal capacity measurements were made in the Mark I1 cryostat in calorimeter W-28 using thermometer A-5 and an intermittent heating, adiabatic p r o ~ e d u r e . ~ Characterization of the Sample. The finely divided sample of Cez03.0zwas provided by Dr. T. A. Henrie of the Reno Metallurgy Research Center of the U. S. Bureau of Mines. It was prepared by carbon reduction of pure cerium dioxide and was reported to analyze as follows (in wt %): oxygen (by activation analysis) 14.7 =t0.02 (theoretical = 14.62), carbon 0.18, calcium 8.1, iron 0.006, magnesium 0.007, and silicon 0.008. Although other interpretation is possible (as noted in The Journal of Physical Chemistry
the Discussion) , the proximate analysis of the olive green sample was taken as (in wt %): 96.6 CezOa, 3.1 CeOl, and 0.2 C. X-Ray diffraction patterns on samples thus prepared show only lines for the (111) and (IV) oxides.' The 209.38-g calorimetric sample was handled only in a nitrogen-filled drybox. It had a density of 6.86 g/cm* and was assigned a molecular weight of 328.24. The heat capacity of the sample varied from 96% of the total at 10°K to a minimum of 65% a t 70°K.
Results The heat capacity results are presented graphically in Figure 1 and also in Table I in chronological sequence so that the temperature increments employed may usually be inferred from differences in the mean temperatures. The results are expressed in defined calories equal to 4.1840 J and temperatures based upon an ice point of 273.15"K. These data have been adjusted for
1961
THERMOPHYSICAL PROPERTIES OF THE LANTHANIDE OXIDES
Z OK
0
10
"
20
7; OK Figure 1. Heat capacity of CezOs.00from data on CezOa.oz adjusted by procedure described in the text.
curvature4 and then for the thermal capacities of the CeOZl1and C12 impurities. The composition adjustments aggregate about 3y0 at 10°K and 0.5(r, above 100°K. After consideration of all factors, the present data above 10°K have a probable error of f 0 . 3 % . The calculated thermal capacities for stoichiometric CezOs do not agree well over the common range of determination with the adjusted data of Weller and King7 whose sample contained about 50 mol yo of CezOa. Their data are 15% higher at 55"K, 0% a t 210"K, and 2% lower at 295"K, but give an entropy increment 3% higher over the common range. The most prominent feature of the diagram is the cooperative transition with a sharp maximum a t 8.5"K. In addition to the usual thermal capacity determinations to delineate the shape of the anomaly, four Table 11: Measured Enthalpy Increments of
Cerium(II1) Oxidea Determination designation A B C D
No. o f
- H Ti?
determinations
T I , OK
T x ,OK
cal/mol
1 1 1 2
157.51 3.964 5.324 4.087
195.09 11.841 14.101 11.936
820.9 6.331 6.150 6.287
TZ
a The corresponding integral along the smooth heat capacity curve is 821.3.
enthalpy increment determinations over larger portions of the transition region were taken and are also indicated in Figure 1 and in Table 11. The thermodynamic functions evaluated by digital computer are summarized at a few selected temperatures in Table 111. The extrapolation below 5°K is unfortunately arbitrary. The internal consistency of Table I is typically better than O.l'%; however, the probable error of the functions is estimated at 0.2% above 100°K. The accuracy could be significantly poorer than the precision for stoichiometric Ce20aas the subsequent Discussion indicates. The experimentally evaluated entropy from 5 to 298.15"K plus a small Debye-like extrapolation to 0°K aggregates 33.47 cal/ (mol OK), However, the Kramers' degeneracy contribution of 2R In 2 has not been totally accounted for in the cooperative transition. Presumably the remainder [( So5- Soo)w 1.9 cal/(mol OK) and (Hob - Hoa)< 10 cal/mol] is removed below 5°K since the absence of a high-temperature tail on the 85°K transition (evidenced by the accord of the lattice and measured heat capacities between 20 and 70°K) argues against the presence of Kramers' ordering at higher temperatures. The excess C,I between 70 and 220°K has not been accounted for but appears to have a counterpart in Y b ~ 0 3 . On ~ ~ this basis the appropriate .15'K, for chemical thermodynamic purentropy, So298 poses would be 35.4 cal/(mol OK). This is to be compared with the value 36.0 cal/(mol OK) given by Weller and King.'
Discussion The electronic thermal capacity, Gel, presented in Figure 2 has been calculated from the data given in Table 111, and a lattice thermal capacity evaluated from those of Laz03and NdzOa9&in the following manner. The lattice contribution of Kd203 was taken as the residual between its apparent thermal capacity less the C,I calculated in the usual manneraafrom the energy levels of the ground term given by Henderson, et al.," and of the excited states of the ground multiplet given by Chang.l0 The column designated C, (lattice) in Table I11 is the result of interpolating (tabularly) to one-third of the decrement between C, for LanOaand C,(lattice) for Ndz03. The plotted points of Figure 2 represent the increments between C, and C, (lattice) for Ce01.5. Figure 2 depicts the Schottky transition resulting from the presence of two doublets with an average energy at about 550 cm-l and a cooperative transition with a maximum near 8.5"K to remove the ground-state degeneracy. The entropy increment of this transition is about 0.83 cal/(mol OK) and is considerably less than the ordering entropy expected for two (11) E. F. Westrum, 65, 353 (1961).
Jr., and A . F. Beale, Jr., J. P h y s .
Chem..
(12) R. Hultgren, R . L. Orr, P. D. Anderson, and K . K . Kelley. "Selected Values o f Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York. N. Y.,1963. Volume Y3. Number 6 June 1889
1962
BRUCEH. JUSTICE AND EDGAR F. WESTRUM,JR.
Table 111: Thermodynamic Functions of Cerium(II1) Oxide Cm T,
C,(lattice), cal/(mol O K )
cal/(mol OK)
OK
sa - SaaoK, cal/(mol OK)
H e - HosOKv cal /mol
- H05'K)/T, cal/(mol OK)
-(Go
5 10 2.5 35 50
0.276 0.542 1.208 2.607 5.145
0.005 0.076 1.228 2.748 5.261
0 0.566 1.139 1.755 3.103
100
200 250 300
13.458 19.53 23.60 26.33 28.14
12.727 18.19 21.84 24.25 25.91
9.318 15.998 22,218 27.795 32.77
563.5 1397.5 2484 3736 5101
3.683 6.681 9.801 12.852 15.77
350
29.36
27.11
37.20
6539
18.52
298.15
28.00
25.86
32.60
5049
15.66
150
spin-only Ce (111) ions [2R In 2 = 2.76 cal/ (mol "K)]. Closer examination of Figure 2 shows that C,1 is slightly negative between 20 and 50°K. This anomaly may be a consequence of some of the following factors: (a) inexactness in adjustment of impurity corrections due to the uncertainty of the oxygen analysis; (b) consequent uncertainties in oxidation state, stoichiometry, etc. ; (e) assumptions about the proximate composition of the sample (Cez03,CeOz, graphite) ; and (d) effect of lattice defects on C, and, hence, on the experimental C,l. The complex phase behavior of Ce0z-Ce20813-16 would suggest that the Ce20a.02 sample in the presence of carbon may not he described best as a mixture of CeOz and Cez08. In summary, the characterization of the sample does not permit as reliable an interpretation as has been hitherto possible3p4 for other sesquioxides. Measurements on a sample of unambiguous stoichiometry and crystallinity extending to still lower temperatures is a desideratum.
0 4.449 14.55 33.26 91.05
0
0.121 0.557 0.805 1.282
Gibbs Energy of Formation The Gibbs energy of formation at 298.15'K can be derived from existing thermodynamic data and the entropy of Ce2O3(c) reported here. The entropy of Ce(c) has been reviewed16 and the value of 16.66 cal/(mol "K) selected is based on data reported by Lounasmaa,l' Parkinson and Roberts,ls and Parkinson, et al.lB The entropy of Oz(g) taken from Wagmanz0is 49.003 cal/(mol OK). The value of AS? derived is -71.46 cal/(mol "K) . A similarly selected valuel6 of AHr" for Cez08(c)is -434.92 f 0.01 kcal/mol and is based upon calorimetry reported by Kuznetsov, et U Z . , ~ ~and Gerassimov, et ~ 1 The . ~ value ~ calculated for the Gibbs energy of formation ( A G f ~ s s . 1 6 0 ~ )is -4 13.6 kcal/m01.~~ Acknowledgment. The authors appreciate the financial support of the U. S. Atomic Energy Commission and the generous provison of the sample by the Reno Metallurgy Research Center of the U. S Bureau of Mines. (13) G. Brauer, K. A. Gingerich, and U. Holtschmidt, J . Inorg. Nucl. Chem., 17, 16 (1960). (14) D.J. M. Bevan and J. Kordis, i b i d . , 16, 1509 (1960). (15) P. Kofstad and A. 2.Hed, J. Amer. Ceram. Soc., 50, 681 (1967). (16)E. F. Westrum, Jr., "Lanthanide-Actinide Chemistry," Advances in Chemistry Series, No. 71, American Chemical Society, Washington, D. C., 1967, pp 25-50. (17) 0. V. Lounasmaa, Phys. Rev., 133A, 502 (1964). (18) D. H. Parkinson and L. M. Roberts, Proc. Phys. Soc., B70,
I
0
I
I
I
I
200
100
I
I
300
7;% Figure 2. Electronic heat capacity contribution of Ce(II1) ion in CezOs. The dashed curve is the C,! derived from the levels discussed in the text. The experimental points are calculated from the original heat capacity data and the lattice contribution as described in the text. The Journal of Physical Chemistry
I
471 (1957). (19) D. H. Parkinson, F. E. Simon, and F. H. Spedding, Proc. Roy. Soc., Ser. A , 207, 137 (1951). (20) D. D. Wagman, et al., U. S. National Bureau of Standards Technical Note 270-3 (1967). (21) F. A. Kuznetsov, T. N . Rezukhina, and A. N. Golubenko, Zh. Fiz. K h i m . , 34, 2129 (1960). (22) Ya. I. Gerassimov, V. L. Lavrent, F. A. Kuznetsov, and T. N. Rezukhina in "Symposium on Chemical and Thermodynamic Properties a t High Temperatures" (XVIIIth International Congress of Pure and Applied Chemistry, Montreal, Canada), National Bureau of Standards, Washington, D. C., 1961, p 117. (23) NOTEADDEDIN PROOF,F. B. Baker and C. E. Holley [J. Chem. Eng. Data, 13, 405 (1968)l review thermal and equilibrium measurements and report a new determination of the enthalpy of oxidation of cerium sesquioxide to the dioxide. Their new value Of Afff02s8.16"KO f -429.31 & 0.68 kcal/mol corresponds to a AGf02~s.l6"K of -408.0 & 1.2 kcal/mol and is to be preferred.
