THEHMOPHYSICAL PROPERTIES OF LANTHAXIDE OXIDES
Feb., 1963
previously reported ?;a2BDS and K2BDS data were reanalyzed including only the points below 2 X molar. TABLE I11 FIXALPARAMETERS Salt
MgBDS
SrBDS CaBDS BaBDS Na2BDS K2BDS
J
AD
113 118 119 122 109 133
17 92 11 92 68 51
8581 8878 8804 8836 1890 2018
a,
(A)
5 5 5 4 4 4
34 22 13 84 90 24
At0
ref 12
53 59 59 63 50 73
06 46 50 64 11 52
A-DBDS
60 59 69 59 59 60
1 5 6 3 6 0
The A-ovalues obtained from the AIgBDS and KzBDS
339
data are 60.1 and 60.0, respectively, while the average of the four other salts is 59.5 f 0.15. I n the case of MgBDS the discrepancy could be tentatively ascribed to the lack of a hydrolysis correction in the work on which the Harned and Owen X+o (Mg+2)is based. The KzBDS discrepancy is not explained. It is hoped that transference number measurements being undertaken will clarify some of the limiting conductance value discrepancies. Acknowledgment.-The authors wish to express their gratitude to the A4rmyResearch Office (Durharn) for project 3417C and to the United States Atomic Energy Commission for Contract AT-(40-1) 2983 for support of various aspects of this work.
THERMOPHYSTCAL PROPERTIES OF THE LANTHANIDE OXIDES. I. HEAT CAPACITIES, THERMODYNAMIC PROPERTIES, AND SOME EXERGY LEVELS OF LANTHANUM(II1) AND NEODY&TIUM(III) OXIDES FROM 5 TO 350"K.l BY BRUCEH. JUSTICE AKD EDGAR F. WESTRUM, JR. Department of Chemistry, University of Michigan, Ann Arbor, Michzgan Received August 7 , 196% Heat capacities of Laz03and NdZO3 were determined from 5 to 350'K. by adiabatic calorimetry. A complex Schottky anomaly with a maximum near 14°K. was resolved from the lattice contribution and shown to rise from doubly degenerate states a t 0, 21, 81, and 400 cm.-l, which are in sharp contrast with the assignment of Penney. The entropy (SO), enthalpy ("I- Hog)),and Gibbs energy iunction ( [ G o - HoO]/T) for La201 at 298.15"K. are 30.43 cal. (g.f.w. OK.)-', 4742 cal. (g.f.w.)-l, and -14.53 cal. (g.f.Fr. The estimated entropy (SO) of Nd203is 37.9 cal. (g.f.w. OK.)-'; the measured entropy increment (SO - SsO) and enthalpy (HO- H s @ are ) 35.05 cal. (g.f.w. OK.)-' and 4989 cal. (g.f.w.)-l, respectively, a t 298.15"K.
Introduction The degeneracy of complex magnetic st'ructures ma,y be lowered in crystalline lattices by either of two different mechanisms. In some substances the magnetic moments couple cooperatively ( e . g . , antiferromagnetically or ferromagnetically) a t suficiently low t'emperatures. Here, the heat capacity typically shows a discontinuity called a "lambda" anomaly. On the other hand, an electric field (e.g., the static charge of the anions around a paramagnetic metal ion) can cause the removal of this degeneracy by creating a set of states of different energies. ,The statistical distribution of electrons over the energy levels created by the potential field results in a continuous heat capacity contribution called a Schottky anomaly.2 These characteristic thermal anomalies, in which a bell-shaped maximum occurs where kT is of the order of the energy difference between two levels, have been observed, for example, in several rare earth ethyl sulfates by Meyer and Smith.3 Here, they are a consequence of the cryst'allineor ligand field which surrounds the paramagnetic ion splitting a degenerate (spin-orbit) state into discrete energy levels. Our initial interest in the thermal properties of rare earth oxides was stimulated by the heat capacity measurements on lanthanum(II1) and neodymium(II1) oxides (La203and Nd2O3) report'ed by Goldstein, et aL14 (1) This investigation is a part of a doctoral thesis submitted by B. H. J. t o the Horace H. Rackham School of Gradnate Studies of the University of Michigan. The work was supported in part b y the Division of Research of the United States Atomic Energy Commission. (2) W. Schottky, Physik. Z., 23, 448 (1922). (3) H. Meyer a n d P. L. Smith, J . Phys. Cham. Solids, 9, 285 (1959). (4) H. W. Goldaitein, E. F. Neiluon, P. N. U'alsh, and B. White, J. P h y s . Chem., 63, 1445 (1959).
in 1959. A t the lowest temperature of their experiment (16'K.) the heat capacity of neodymium sesquioxide was reported to be 1.99 cal. (g.f.157. whereas lanthanum oxide-a diamagnetic, isostructural anallog of neodymium oxide-was reported to have a heat capacity of 0.43 cal. (g.f.w. The paramagnetic 4f3 configuration of trivalent neodymium is presumed to be the cause of the large excess heat capacity, and a thermal anomaly is to be expected in neodymium oxide below 16OK. Heat capacity determinations made over the range 4 to 16'K. to elucidate the nature of the thermal anomaly indicated that it is occasioned by a complex Schottky effect. filoreover, the cryogenic calorimetric approach offered an unusually rich yield of data concerning tlhe energy levels of the trivalent ions in the rare earth sesquioxides, as single crystal samples have not long been available for absorption spectroscopy or for paramagnetic resonance experiments. Although such techniques may yield energy levels directly and more precisely, low temperature heat capacity determinations provide a quantitative estimate of the magnitude of these levels and their degeneracies. However, even if such spectroscopic data were extant, thermal measurements would provide both a thermodynamic test of the level scheme and chemical thermodynamic data of permanent worth. Insome instances heat capacity measurements yield more direct information than do magnetic measurements. At lorn temperatures the heat capacity contribution of the Schottky anomaly may exceed that of the lattice. The oxides are especially favorable in this respect to even higher temperatures than usual
because of the relatively small proportion of atoms not contributing to the eleqtronic phenomenon (as compared, for example, to a hydrated organic sulfate). Magnetic susceptibility determinations on neodymium(II1) sulfates5-' arid oxides8-I4 reveal that the free-ion momelit is mrasurable down to tlic temperature of liquid nitrogen. At this point, marked deviations clue to the unequal population of the various St,ark lcvels caused by the crystal ficld splitting of the ground begin to appear. t'crm 41q/2 The first attempts t~oexplain t,he deviations from the Curie--M'eiss law a t low tempcratures were made by I'eriiiey and Schlapp.15+16They found that the susceptibilities of powdered samples of neodymium sulfate octahydrate [Ndp(S0.,)3.81-I,0] measured by Gorter and De Haas5 could be explained by assuming that a crystalline poteiitial with cubic symmetry was caused by the static electrical effect of eight oxide ions a t the corners of an oct,ahedron surrounding the centrally located metal ioii. 'l'wo quartet Ievcls above the ground doublet &t292 and 834 cm.-l gave agreement between the theoretical and expcrimental suscept,ibility for the neodymium salt. J,ater Spedding, ct U Z . , ~ ~ observed , ~ ~ t,hc optical absorption spectra and reported levels a t 0, 77, and 260 em.-*. Adjusthg the over-all splitting of the theoretical levels to that of the Spedding data gives exccllerit agreement with the level a t 77 em.-'. In 1937, Ahlberg, Blanchard, and I,undberglg measured the heat capacity from 3 to 40OIC. to verify thc existence of the energy level a t 77 em.-'. The data are not inconsistent with the existence of a I c . i ~ lin the region 40 to 80 em.-', but arc hardly conclusive. Single cryst,al susceptibilitymeasurements by .ICrishnan and Rlookherj i6 and by Jackson7 disclosed ail 11% anisot,ropy in the susceptibility a t 300OK. in both experiments and a 70% anisotropy a t 14'K.' lteasuremcnts of thc absorption spectra by Satten and Young20led to the discovery of levels a t 0, 7 6 , 226, 263, and 301 em.-] and axial crystal field symmetry. l'enney21 calculated crystal field splittings in neodymium oxide on the assumption that the field symmetry was rhombic by basing his calculations on the susccptibility data of S ~ c k s m i t t iand ' ~ of Cabrera and Dupcrier'2 (of which only Sucksmith's data extend as lowas O O O K . ) . IIis computed levels for neodymium oxide were doublrts at. 0, 4112, 1476, 2952, aiid 4920 cm.-'.
Experimental Lanthanum(II1) and Neodymium(II1) Oxide Samples.-Both oxides wcrc obtained from the Lindsay Chemical Go. Lanthanum (A) C . J. Gorter and W. J . De Maas, Proc. Acad. Sci. Amsterdam, 34, 12 L3 ( 193 1).
(6) K. S. ICrishntrn nnd A. Mookhcrji, Phil. Trans. R o y . SOC.London, A237, 135 (1038). (7) L. C. .Jackson, Proc. Roy. Soc. (London). A170, 2FF (1939).
(8) C. II. I,a,Rlanchetais, J . rech. centre natl. rcch. sci.. Xo. 29, 103 (1954). (9) C. J. Rodden, J . A m . C h e m . Soc.. 56, 6 4 8 (1934). (10) W.Klemm and A. Rocsy, Z. anorg. allgem. Chem., 233, 84 (1037). (11) P. W.Sel~vood,J . A m . Chem. Soc.. 55, 3161 (1933). ( 1 2 ) B. Cabrera a n d A. Diiperier. Compt. rend., 188, 1040 (1929). (19) IV. Sucktimitli, Phil. MOO.,[7] 14, 111.5 (1932). (14) E. 11. \Villiams. Phys. Reo.. 12, 158 (1918). ( I n ) W,G , Penncy a n d R. Schlapp. ibid., 41, 194 (1932). ( I n ) R. Schlapp and W'. G. Pcnney, ihid.. 42, 606 (1932). (17) F. II. Sp&ding, €1. F. IIarnIin, and Q. C . Nutting, J . Chem. ~ h v s .6, . 191 (1937). (18) 1'. 1-1. Sprdding, J. P. IIowe, and W.1-1. IG?ller. ibid., 6 , 410 (1937). (19) 6 . E. Ahlbery. E. R. Blanchard, and W. 0. Lundbrrg, ibid., 5, 5 j 2 (1 937).
(20) R. A. Satten and D. J. Young, ibid., 23, 404 (1955).
oxide wns claimed t o hnvc a purity of 99.997(;;,, and neodymium !Ic% : m i to contain less oxido was rcptirtd to have a purity of than 0.1C;, of l'r mid Sin comhincd as osidc.2' 1,c:ss than 3 p.p.rii. of Fc was dotect.c.das :in impurity in eithrr. Tho oxidvs wrre prlletcd without :L binder in h:irtlencd dim into cylinders of 1-ctn. diameter and 1-cm. lcngth, Just prior t,o loading into tho calorimcter, they were hcatcd to con8t:int weight in a pltttiririni dish at 900" in air to clocornposr: m y hydroxide Or c:trbonatr prwerit. Tr:msfcr of thc: pollets to the caloririirtor w:ts tlonct in tho anhydrous nitrogen atmosphrre of a drybox. l'owdrr X-ray tliffraction of both pelletrd hc:tt-trezttc.tl niatcrinls slio\ved only the '4-typc sesqriioxitfe strurturc.22-21 Cryostat and Calorimeter.-;\le:iurrmelits wrre m;dc in thc: Mark I ctdorimetric cryostat using an adiahntic tcchniquo. This cryostat i s similar in most rcsprcts to onc alrcndy drscribrd.26 .4 capsule-type, platinum rosistance thcrmomrtrr (1:d)or:ttory designatiop A-3) was employed. This tlicrmometor wtts Calibrated by tho National Burctau of Stttndards on tlic internation:d tempcraturc scttlc above OODK.and against tlict Rurc!su's scnle2fi from 10 to 00°K. The tcniperaturo sc:tlc was cstahlishetf provisionally below 10"IC. from tho value of the rrsist:incc%,62, a t 10°K. arid at the helium boiling point, and from tlii/tl7' tit 10°K. utilizing thc relationship proposed hy IIogc and F3rickwetidc>.26 Tho tcmperature scale is considrrrd t o hr rdiablc to 0.0j"IC. hrlow 10"1C., t o 0.03OIi. from 10 to 9O"K., arid t o 0.04"K. a t higher temperatures. .4n ttutocalibratwi White potentiomrtrr, 3338 c:dibratcd registnncos and stJandard cclls, and tirncrs operated by un electrically-driven tuning fork ciilibrated agttirist signals from N13S station JV\Vl- wcre used in energy arid tcniperature dctcrmiqations. A copper calorimeter (li4bortttory designation W-16) was employed for measurements on both samples. This calorirrictcr, originally designed for use with cylindrical samples 2.0 cm. in diam., w,w rather simi1:rr to a caloriinctcr previously ciescribrdz7 except that the entrant hcater-well mas eccentric t o thc! vertical cylindric41 axis and the portion housing the glass se:tI on the therxnometcr projected about 2 . 5 cm. below the bottom of t,tie cylinder. In place of radial vanes, a single, Rplit cylindcr of perforitted copper foil (2.6 cm. in diam.) wtts used. The cover was soldcred in place with Ccrroseal (50-50 Sn-In solder), :md a hIonrl stud with a 0.3-mm. dialn. hole scaled with soldrr was used for addition of helium gits (ca. 10 cm. at 300°K.) in the sample space t.o provide thermal coiitact with t h s sample. Inadequate thcrnial contact (noted in a continuing study of eight other lanthanide( HI) oxides t o be dcscribcd in subsequent papers) between the suniple and the helium guy in the sample spacc below about 8°K. was riot present in measurements on lanthanum and ncodymiuni(II1) oxides. The present samplcs (from a dif'fcrcnt supplier) are presumed to have less spccific surface and hence nt)sort) 8 smallcr fr:ict,ion of the conduction helium than did the 1 2 ~used to cnsure that hcatcr and other oxide samples. A ~ ~ 0 0 u-as ttiermometer leads were constrairicd t o the calorimcter surfaco tcmporaturc. Apiozon-T grease wits used to provide thermal contixt between the t,hrrmomoter, heater, and ca1orimc:tor. Small corrwtiong were applied where necessary for the sm:dl (weighcd) diffcrcnccs of helium, solder, anti grease employed. The hcat capacity of the thermoinetcr-hentc,r-c:tlorimcter t i s somhly, tlctcrniincd in a separate set of measiircnicnts, rcprcscntetl a contribqtion varying gradually from 4(djof t,he total hcat capacity when loaded with neoti,ymium oxidc at 10°K. t o 50(,;6 a t 60°K. and t o 45(>;, a t higher temperature. When loaded with lanthanum oxide, the assembly contributed 35 to 45Y0 of the total ovcr thc entire rttnge. The citlorimctric samples of ncodymiuni oxide and lanthanum oxide wcighed (in vacuo) 87.549 and 118 .,589 g., respcct,ively. I3uoyancy corrections were mado on tho bwis of densities of 6.51 and 7.28 g. cm.?, respectively, ctilculatod from X-ray diffraction d&L. (21) W. C . I'ennay. Phys. Res.. 43, 485 (1933). (22) R. R. Roth and S. J. Schnpidrr, .I. Res. A ' d . Bur. Std., 64, 309 (1960). , Stnritaky, Atinl. Chem.. 2 8 , ,552 (1956). ruyat. and (;. X I . Vyrinic. Sirtional Rureari of
ndard X-ray 1)iffraction Powder Patterns," (2,5) 15. 14'. \\"estrum, ,Jr., J. l3. IIutcher. and I). 1 %'. Osbornc. J . Chcm. P ~ ~ Wa. i. , 419 (19x3). ( 2 0 ) II. J. IIoye a n d 1:. G. Brickwedde. .I. Iies. Nall. Bur. Sld., 22, 351 (1939). (27) D. W. Osborno and E. F. Westrum, Jr., J . Chem. PhYS.. 21, 1881 (1953).
l+"eb.,19G3
34 1 TABLE 1 HEAT CAPACITIESOF LAXTIIANUM(III) A N D NEODYMIUM(III) OXIDES
T,OK.
CP
T,O K .
CP
Lanthanum oxide (La203) 20.82 0.758 Series I 22.74 0.978 24.73 1 ,227 5 30 0.007 213.82 1.516 6 . 38 .015 29.19 1 ,868 7.45 ,026 31.84 2.282 8.3) .052 34.i 9 2.764 10.14 ,084 38.27 3.341 11.51 .128 12.82 .178 Series I11 14.07 . 236 15.41) .311 31 48 2 711 17.04 ,415 38 81 3 349 18.74 ,552 42 ?J3 4 024 20.54 .728 46 93 4.$05 22.42 9 38 52 20 5 696 24.41 1.186 57.54 6.581 6'2 92 7 47G Series I1 G8 40 8.337 7 i 05 0 192 1,G!) 0,004 80 14 10 127 5 .!)O ,013 87 07 11 . I 8 0 7.17 .024 8.34 .04l Series IV 0.44 , OG5 10.G .loo 83 51 10 017 11.82 .140 90 51 11 G56 12.05 ,184 !)7 X2 12 606 14.26 .244 105 58 18 567 15.70 . :325 118 35 14 459 17.29 ,134 121 18 15 47 18.99 .5i3
T,OK.
128 88 137 20 146 UG 154 72 160 14 168 82 177 41 186 16 195 26 204 56 213 89 223 06 230 45 240 01
[Ih CUI. (g.f.w. OR.)-'] T,"IC. Cp CP
16 17 18 18 19
3% 20 05 82
71 . 00 77.4G
!I ,853 10.655
26
10 95
20 58 21 18 21 76 22 29 2'2 79 28 24 23 59 24 03
Series V
2:35 , 7 1 245 . : 3 3 254.00 263. G2 272.54 281.47 290.35 209.17 308.12 3 1 7.20 320.30 355.51 :345.12
Series I
23 . 8 2 24.23 24,5!3 24,92 25.23 25.51 25.78 26.03 26.27 26.48 26.69 2G. 88 2 7 . on
Results and Discussion Heat Capacity Measurements.--The expcrimcntal heat capacity values for lanthanum and Iirodymium oxidcs arc prcscntcd in chroriological sequcncc in Tablc I so that the approximate tempcraturc increments employed usually may bc estimated by differencing the adjacent mcaii tcnipcrstures. These data are based up011 gram formula weights of 323.83 g. for lanthanum oxidc and 336.54 g. for Iicodymium oxidc, thc defiticd 1Eicrmoclicmical calorie equal to 4.1840 abs. j ., and ai1 ice poiiit of 273.15OIC. Tlie data have hccii adjusted for curvature, ie., for thc fiiiitc tcmperaturc increments employed in the measurements. This adjustment is lcss than 0.1% above l 3 O K Thc hcat capacity mcasurcments in thc transition region wcre sitbmitted to an cntltalpy test in which a single irtcrcmciit from 4.62 to 20.31 O K . requircd 25.81 cai. g.f.w.-', whcreas the inttgral of thc smoothed heat capacity curve indicated an cnthalpy increment of 2.7.99 ral. (g.f.w.)-l. The agrecmrnt is excellent in vicw of tlic rclativc insensitivity of tlic platinum resistaricc tlicrmomctcr at tlic lower elid of thc tcmpcraturc ratigc. Values of the molal hcat capacity at selcctcd tcmperatures froma smooth curw through thccxperimental data points are presented in Table 11. These values arc cotisidcred to have a probable error of lcss than 0.1 yoabovr 2jo1C., iricrcnsing to 104 at IOOTi., and to 5% at thr lowest trmperaturcs as a coiisequcnw of tlic dccreascd sciisitivity of t h r rcsistaiice thcrmomrter a i d tlic pro-
Series I1
5.29
0.4G3
Series 111 4.84 5.59 6.60 7.87 9.10
0.398 0.494 0.736 1.115 1.435
Series IV
4.83 5.72 6.8!) 7.94 8.81) 9.08 11 .3!) 12.88 11.27 15.56 16.78 18.05 19.47 21.03 2 2 . G9 24.54
26.66 29.07 31 .!)5 35.14 38.5!) 42.45 4 7 , 0%
0.380 0.533 0,815 1 .113 1.387 1 . 670 1.752 1.871 1 .!I71 2.044 2,130 2.185 2,300 2.421 2.587 2.791 3 , 057 3 . :392 3 . 805 4.2!)8 4 . 833 5.426 G . 139
Series V
4 73 5.65
0 344 0.541
T,OK. CP T,OK. CP Neodymium oxide ( Nd203) G .8:3 0.803 Series VI11 5.82 1 .OG!) 42 54 5 440 8.61 1,287 !I .30 1.510 46.67 6 085 51 11 6 'iij 9 . 93 1.029 10.51 l.Mi 56 13 7 536 61 :13 8 345 11.08 1.745 11 . G 3 1. i G 2 Series IX 12.17 1.814 12.69 1.854 52 04 6 91 1 13.50 1.935 57 15 7 693 AH Run 82 66 8 540 69 0:3 9 461 Series VI 75 60 10 381 82 55 11 401 5 08 0 411 89 96 12 429 6 06 0.602 97 40 1 3 341 7.19 0 891 105 32 14 320 8.16 1.196 113 45 15 29 9 14 1 485 121 56 1G 23 !I 47 1 589 129 !)1 17 10 9 79 1 570 139 08 18 0fj 10 10 1 034 138 21 17 98 10 31) 1 677 146 85 18 80 10 G!) 1 671 155 G6 19 56 10 98 1 710 164 47 20 20 12 20 1 810 173 55 20 98 13 83 1 !I41 182 78 21 6.3 15 03 2 017 191 i!) 22 22 16.41 2 101 200 81 22 77 209 $12 23 24 Series VI1 218 !)8 23 70 227 i 5 24 11 4.5!) 0 406 226 66 24 07 5 58 0 522 235 82 24 45 G 76 0 772 244 88 24 86 7 81 1 Oil 253 83 25 19 8 06 1 3 15 263 04 25 $4 0 37 1 535 272 47 25 86 10 90 1 730 281 77 2G 14 12 11 1 792 291 02 26 12 l:$ 39 1 916 300 1 3 26 68 14 71 2 001 30!) I G 20 00 16 1 1 2 OG!) 318 44 27 1:s I7 G!) 2 171 327 !):3 27 Xi l!) :30 2 286 21 21 2 447 337 34 2T 57 346 43 27 78
visional nature of the tcmpcrature scale bclow IOOK. 'l'hc hcat capacity data of Tablc I also arc plotted in l'ig. 1. The dcviations of the ncodymium oxide data of Goldstein, et u Z . , ~ from the smoothed curve of the present investigation over the common range of mcasurcment are shown in I:ig. 2 . Uccausc of thc significant disagreement hetmeeii the two scts of data arid the fact that thc values of Goldstcin, et aZ., extcridcd only to 1G"I-L and presented an unecrtain basis for extrapolation, it was considered desirable to redetcrmine the heat capacity of diamagnetic lanthanum oxide. Subscqucntly publishcd data on lanthanum oxidc from the I3urcau of Alincs 1,aboratory a t BcrkclcyZxincluded (28) 15 K i n g , W \V Wf Ilrr. a n d I,. B I'rrnkrata, Biircau of Mirirs livport uf Inwaligationb 38,;i I W i I ( 7
BRUCFH. JUSTICE AKD EDGAR F. WESTRUM, Jiz.
342
TEMPERATURE, IO0 200
0
10 20 TEMPERATURE,
0 Fig. 1.-Heat 0.2 0. I
’ K. 3 00
30 O K ,
capacities of La203 and SdzOa.
r:-. . . L
I
y 0.5% Deviufion
I
.. _-.
I--
-I
*
-F
o
I
3
-0.1
0 V
- 0.2 I-
*
I
Vol. 67
deviations (beyond the combined estimated precision indices of the respective measurements) also occur in this substance. Although the failure of different laboratories to reproduce heat capacity curves over the low temperature region is not uncommon, confidence in the data of this research is predicated on the fact that the heat capacity of a Calorimetry Conference sample of benzoic acid measured in the Mark I helium cryostat mas in good accord with the data of other established cryogenic l a b o r a t o r i e ~ . ~ ~ Resolution of the Electronic Heat Capacity of Neodymium Oxide.--Separation of the lattice and magnetic contributions to the heat capacity of neodymium oxide is achieved by using the heat capacity of diamagnetic, isostructural lanthanum oxide as the representation of the lattice contribution in neodymium oxide. Because of the small fractional deviations in the atomic weights of the cations and the lattice constants of the two substances, the approximation probably is relatively good. However, comparison with presently available data30 on laiithaiium and lutetium oxides suggests that the lattice entropy contribution may decrease across the entire lanthanide series by as at 298.15OK. If the much as 2.2 cal. (g.f.w. decrease is considered proportional to the decrease in the radius of the cation, the unadjusted estimate based on lanthanum actually may represent 3 to 5% more than the true lattice contribution of neodymium oxide.30 An adjustment for this would involve only slight changes in the numerical values presented subsequently in this paper. The electronic heat capacity of the neodymium ion in the oxide as determined from this smooth curve through the lanthanum oxide data is presented in Fig. 3. It is immediately evident from this curve that the magnetic heat capacity of neodymium oxide is characterized by the type of excitation of electronic states discussed by Schottky.? The Schottky Heat Capacity.-An equation for the Schottky heat capacity can be developed from the methods of statistical mechanics. Using the partition function, Q, for a general system of n energy levels of energies, E,, and degeneracies, g1 n
V I
Q
0.1
c
c ._ 0
=
c
g1 exp(--EJRT)
2=0
and taking Eo = 0, the average energy of such a system is given by
o “ 0
V
-0.1 -0
I
IO
I
I
I I 50
I l l 1
I
“1
I
100 200 TEMPE R ATU R E, O K .
I
*
1-0 P 1
l
l
300
E
=
&-I
5 giE, exp(-E,/RT)
a=O
Hence, the electronic heat capacity is given by
Fig. 2.-Deviation plot of heat capacities of Lad& and xdd& from the respective smoothed curves of this research. Experimental points from this research are depicted by 0, those of Goldstein, et by arid Lhose of King, et a1.,28by
*,
.
values only to approximately 5OOK. and hence would have provided an even less secure extrapolation. For resolving the electronic contribution, the advantage of having both compounds determined in the same apparatus is obvious. The deviations of all three sets of data on lanthanum oxide from those of the smoothed curve of the present series of measurements also are represented in Fig. 2 . It is to be noted that significant
(29) G. T. Furukawa, R. E. McCoskey, and G. J. King, J. Res. Natl. Bur. Std., 47, 256 (1951). (30) E. F. Westrum, Jr., a n d F. Grznvold, paper presented a t the International Atomic Energy Agency Symposium on Thermodynamics of Nuclear Materials, Vienna, Austria, May. 1962; B. H. Justice, “Thermodynamic Properties and Electronic Energy Levels of Eight Rare Earth Sesquioxides,” Ph.D. Dissertation, University of Michigan, U. S.Atomic Energy Commission Report TID-12722, 1961; E. F. Westrum, Jr., unpublished data.
THERMOPHYSICAL PIZOPERTIES
Feb., 1963
'TABLE
343
O F LAK'THANIDE O X I D E S
11
THERMODYSAYIC FCSCTIONS OF LSXTHAKUM(111)
.4ND
NEODYMIUM(
111)OXIDES
[Units: cal., g.f.w., and OK.] T 5 10 15 20 25 30 35 40 45 50 60 70 80 90
100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 350 273.15 298.15
Lanthanum oxide ( La203) H Q - HoQ SQ 0 0057 (0.002) (0.01) ,021 0.16 080 1.01 .087 ,284 ,216 3.30 ,672 .426 8.07 1,265 0,720 16.18 1.995 1.087 28.13 2.796 1.514 3.630 44.18 1.991 64.44 4,477 2.506 88.94 5.324 150.54 3.625 6.990 228.52 4.823 8.595 6.071 322.15 10.120 7.347 430.59 11.557 8.635 553.0 12.903 14.163 9.924 688.4 11.208 835.9 15.34 12,479 16,44 994.8 1164.4 17.45 13.735 18.40 1343.7 14.972 19.26 1532.0 16.187 20.05 1728.6 17.379 20.77 1932.8 18.546 2143.8 21.43 19.686 2361.1 20.801 22.03 2584.2 22.58 21.889 23.09 2812.6 22,952 23.57 3045.9 23.989 24.01 3283 . 9 25.001 24.42 25.990 3526.1 24.79 26.955 3772.1 4021.8 25 14 27.897 28.817 4274.9 25 46 29,716 25 77 4531.0 26.05 30.595 4790.2 34.70 27.20 6122 25.24 28.19 4101 30.43 26.00 4742 CP
-(Go
- HoO)l'-'
(0.000) ,005 ,020 ,051 ,104 0.181 ,283 ,410 559 .727 1.116 1,559 2,044 2.563 3.106 3.667 4,242 4.827 5.418 6.014 6.612 7.210 7.808 8.403 8.995 9.583 10.167 10. 746 11.318 11.886 12.447 13.002 13.550 14,092 14.628 17.21 13.18 14.53
I
I
I
The difference between the mean square energy and the square of the mean energy is often called the fluctuation in the energy. I n its expanded form this equation is especially useful for the evaluation of the electronic heat capacity of multilevel systems. The Schottky heat capacity for a system with a single energy level above the ground state has a maximum value of 0.87 cal. (g. ion OK.) -l a t
T
-
AX,1 = R In Q
io 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 350 273 15 298.15
-
+- E / T
(2) n
which approaches R In go a t 0°K. and R In
gi a t int=O
finite temperature. In addition to the Schottky contribution to the
H o - Hso
.. 5.04 14.31 25.11 38.04 53.93 73.37 96.64 123.82 154.91 228.61 317.27 420.39 537.4 667.8 810.8 965.7 1131.7 1308.1 1494.2 1689.2 1892.5 2103.5 2321.4 2545.5 2775.4 3010.5 3250. :i 3494.7 3743.2 3995.6 4251.7 4511.1 4773.5 5038.8 6403 4333 4989
I.2
A E fcm-!,
A
I
400
z 1.0
0
E
0.0
a w
Q
c
0.6
_1
0
if the degeneracies of the two stantes are equal. In general, the maximum heat capacity for a simple twolevel system will be given approximately by (gl /go)(0.87). For a more complex system of levels, the shape as well as the maximum heat capacity will depend on the spacing and degeneracies of the several levels, However, the electronic entropy will be given by
-
5 10 15 20 25 30 33 40 45 50 60
a
0.42(E1/ R )
Seodymium oxide ( Nd203) CP so sjo 0.409 ... 1.642 0.648 2,014 1.394 2.344 2.013 2.846 2.588 3.520 3.166 4.266 3.764 5.044 4.384 6.828 5,023 6 ,605 5.67'7 8.126 7.017 9.597 8.381 11.081 9.7% 12.383 11.133 13.682 12.505 14,908 13.867 16.06 15,214 17.13 16.542 18.13 17.849 19.07 19.132 19.93 20.391 20.72 21.623 21.45 22.829 22.11 24.007 22.71 25.156 23.25 26.278 2 3 . 75 2i.3T1 21.22 28.437 24.65 29.477 25.05 39.492 25,43 31.482 25.78 32.448 26.09 33.3Y2 26.39 34.312 26.66 35.2112 P i ' . 90 39.42 25.88 32.75 26.61 35.05
1'
0.4
a 0 Q
0.2 O
0
k
'
20
I
40
I
60
1
I
100
00
TEMPERATURE,
Fig. 3.--Schottky
1
200
300
O K .
anomaly of the Xd+3 ion in XdzOa with electronic energy level scheme.
magnetic and hence to the thermal properties of paramagnetic ions, other terms in the spin Hamiltonian,31 such as the effect of the interaction between the nuclear spin of the paramagnetic ion and the electrons, the di(31) Cf. B. Bleaney and K. (1953).
W. €1. Stcvens,
R e p l . l'rogr.
Phgs., 16, 108
UILUCEH. JCSTICE ASD EDC.\R I:. WESTRUM, ,lit.
344
polar interactiori between thesc ions, arid possible othcr types of coupling between the lanthanidc ions, may be present. Such contributions may be obtained from either paramagnetic resonance or paramagnetic rclaxation studies but would be expected to be small above 5OK. The increment in (el)- C,) is cxpceted to be very slight across an isostructural lanthanide series and hence will practically canccl in the above rcsolutioii. Siiice all compounds wcre measured in the same apparatus, systematic errors are minimal. Experimental Electronic Energy Levels.--The cncrgy levels which appear to fit the experimental data best by successive approximations made on a digital Computer arc prcsented in Table 111 togcthcr with the levels from I'ciincy's calculatioiis.z 1 TABLE I11 EXICRGY LEVELSFOR S~mYaiIu\i(III)OXIDE [Cnits: c ~ n . - ~ ] Lex cl
1)egeneracy
0
2 2 2 2 2
1 2
3
4
Tliis uork
0 21 s1 400
..
l'enneyzl
0 492 1476
2032 4!)20
The Schottky function generated by these levels is represented by the solid curve in Fig. 3 . The existelice of a level m a r 21 cm.-l is obvious even from the total heat capacity data and is the major contribution to the maximum near 1 4 O I i . The shouldcr in thc Cel curve near %OK. is attributed to a level at 81 cm.-I. The level at about 400 crn.-' also is apparent from the Ce1 data at 20OoK.; the data of Goldstein, ct aZ.,4 also show a peak at about 180OK. That the theoretical curve is higher by about O.O(i cal. (g. ion O K . ) -I than the cxperimental points from 100 to 300°K. may be attributed partly to a slight iincertainty in a calibration factor used in calculating the heater current on this sample, partly to thc relatively small size of thc sample, but mainly to the approximation involved in the lattice hcat cgpacity. These uncertaiiitirs in the lattice heat capacity contribution can affect significantly 01113' the the lattice hcat assigrimeiit of tkic highest l c ~ d sitice s capacity represents so small a fraction of the tot,al a t lo^ temperatures. Thc assumptions made by l'cn~icy*~ about t,lw nature of the crystal ficld in neodymium oxidc lack expcrimental justification. By using a rhombic ficld and the free-ioii splittiiig factor, he was able to explain thc SUSccptibility data of Cabrcra and I I ~ p c r i c rarid ~ ~ of S u ~ k s m i t lfrom i ~ ~ 90 to G i O 0 K . by doublets a t 0, 492, 1470, 2952, and 4920 cm.-'. T h c crystal ficld is undoubtedly complcx because of tlic lorn axial symmetry, so the splitting factors and the strciigths of the components need to bc measured i n order to arrive a t the correct cncrgy leids. ?'hc Stark Ic\ds postulated by Pentley at 2952 and -2920 em.-' arc probably in error because thc first excited term of the ground multiplet (4111,J is about 2000 cm.-l and 4116/2about GO00 cm.-l above the ground t ~ r m . ~ Since ? , ~ ~the cryst'al fields i n rarc earth compounds are essentially a perturbation of Russell-Saundcrs coupling, they are of smnllcr magnit.ude than this iritcraction. (32) E, Carlaon unci G .
IT. Divkr, J . Chem. I'hus.. 29, 229 (1958). (3X) 1:. Varsanyi ant1 G. 11. Diekc, ibid.. 53, 1610 (1900).
'5'01.
67
The threefold axial symmetry around the neodymium ion in hexagonal neodymium oxid# is similar to that in many of its compounds, including the enneahydrated The ethyl sulfatc and the enncahydrated optical absorption spectrum of the latter has been observed by SattenS6to have five doublets a t 0, 115, 184, 303, and 382 cm.-'. Optical studies on the ethyl sulfate by Dickc atid I - T e r ~ u xrevealed ~~ one level a t 150 em.-', but Elliott and S t e v e ~ iwere s ~ ~ able to find levels at 0, 130, 170, 340, and 350 em.-l from paramagnetic resonance mcasurements of the crystal ficld paramcters. Thc highest level in the oxide may be difficult to resolve calorimetrically bccausc the next level of the ground multiplet (4111/2)begins to contribute significaritly to the heat capacity iiear 30OoI
