Feb. , 1963
THERMOPHYSICAL PROPERTIES
cal. (g.i'.w. Goldstein, et uL14have estimated 36.92 cal. (g.f.w. OK.1-l for this value by assuming tlhe "spin-only" value (2R In 4) is achieved a t 100°K. These authors based their estimate on their measured values of the entropy from 20 to 298.15OK. for lanthanum oxide of 30.28 cal .(g.f.w. OK.)-' and for neodymium oxide of 33.12 cal. (g,f.w. OK.)-'. This investigation yielded 30.22 and 33.03, respectively, over the same range. Extension of thermal data on neodymium(II1) oxide to lower temperatures together with magnetic susceptibility determinations a t low temperatures are olbvious desiderata. Thermodynamics of Formation.-The free energies of formation for these substances can nom De deriwd from available thermodyiiamic data.41-44 The standard entropy of formation of lanthanum oxide is ASfozp8.1s = -70.4
f
0.5 cal. (g.f.m.
OK.)-'
and that for neodymium oxide is (41) E. J. Huber, Jr., and C. E . Holley, Jr., J . Am. Chem. Soc., 76, 3594 (1953) (42) E. J. Huber, Jr., and C. E. Holley, Jr., abzd., 74, 5530 (1952). (43) D. H. Parkinson, F. E. Simon, and F. H. Spedding, Proc. Roy. Soc. (London), Aa07, 137 (1951); H. A. Boorse, A. Berman, R. C. Worley, and M. W. Zemansky, Bull. anst. zntern. froad Anneze, 499 (1955) (44) K. K. Kelley and E. G. King, "Contributions to the Data on Theoretical Metallurgy. XIV. Entropies of the Elements and Inorganic Compounds," Bureau of Nines Bulletin 592. 1961.
OF
LL4NTHANIDEOXIDES
ASfo29815
=
-70.7
=!=
345
0.5 cal. (g.f.w. OK.)-'
based on the entropies of the element^^^^^^ and the entropy values from this work. King, et aZ.,28found -70.0 cal. (g.f.w. OK.)-' for lanthanum oxide. Hence the standard Gibbs energy of formation of lanthanum oxide is
dGfoZs815
=:
-407.6 kcal. (g.f.w.)-l
and that of neodymium oxide is AGfo298.15= -411.1 kcal. (g.f..v\-.)-l based on the respective enthalpies of formation by Huber and H ~ l l e y . ~King, ~ , ~ et~ a l l z 8found the Gibks energy of formation of Laz03 to be -407.7 kcal. (g.f.w.)-l. The corresponding value for neodymium oxide given by Coughlin45as -408.8 kcal. (g.f.w.)-' is based upon an estimated entropy of neodymium oxide. Acknowledgment.-The authors appreciate the cooperation of Dr. Leonard Labowitz in the calorimetric measurements and the loan of a sample of neodymium oxide from and several stimulating discussions with Professor David White. The partial support of the Division of Research of the United States Atorric Energy Commission is acknowledged. (45) J. P. Coughltn, "Contributions to the Data on Theoretical Metallurgy. XII. Heats and Free Energies of Formation of Inorganic Oxides," Bureau of Mines Bulletin 542, 1954.
THERMOYHYSPCAL PROPERTIES OF THE LANTHANIDE OXIDES. 11. HEAT CAPACITIES, THERR_IODYSA3IIC PROPERTIES, AND SOME ENERGY LEVELS OF SAXlARIUM (111), GADOLINIUM (111), AYD YTTERBIUX (HI) OXIDES FROM 10 TO 35OoP(.' BY BRUCEH. JUSTICE AND
EDG-4R
F. WESTRURI, JR.
Department o j Chemistry, University of Michigan, A n n Arbor, Michigan Receiced .4ugust 9, 1961 Resolution of the electronic and lattice contributions to the heat capacities of two cubic lanthanide oxides over the range 10 to 350'K. has been achieved by extraction of a lattice contribution from the measured heat capacities of ytt,erbium(III) oxide below 100'K. and gadolinium( 111) oxide above this temperature. Above 10°K. the magnetic contributions t o the heat capacities are Schottky anomalies characteristic of electronic excitation t o discrete energy levels occasioned by the splitting of the free-ion ground term by the crystalline electric field. Low-lying energy levels have been evaluated, albeit tentatively in some instances. By extrapolation below 10°K. practical entropies (SO)a t 298.15"K. of Smz03, Gda03, and YbgOa have been assigned as 36.1, 36.0, and 31.8 cal. (g.f.w. OK.)-'. The corresponding enthalpy increments ( H o - HI$) have been determined to be 5021, 4424, and 4685 cal. (g.f.w.)+.
Introduction The interesling results from the earlier study of the thermal properties of lanthanum(II1) and neodymium(111) oxides2 provoked a further investigation of the heat capacities of other lanthanide oxides. This paper describes the results of thermal measurements on the C-type cubic isomorphs3 of gadolinium(II1) oxide (Gdz0 3 ) and ytterbium(II1) oxide (Yb203), as well as those for the B-type monoclinic form416 of samarium(I11) (1) This Investigation is a part of a doctoral thesis submitted by B. H. J. to the Horace H. Rackham School of Graduate Studies of the University of Michigan. This work was supported in part by the Division of Research of the United States Atomic Energy Commission and v a s presented a t the Arrowhead Research Conference on Rare Earths, Lake Arrowhead, Californin, October, 1960. (2) B. H. Justice and E. F. Westrum, Jr., J. P h y s . Chem., 67, 339 (19631. (3) L. Pauling and M. D. Shappell, 2.Krist., 75, 128 (1930).
oxide (SrnzO3). Insofar as possible, the heat capacities of these isomorphs were studied in an endeavor to rlesolve them into their lattice and electronic contributions as was done in the case of neodymium oxide. The results for gadolinium oxide and ytterbium oxide, as discussed below, provide an approximation to the lattice heat capacity of the cubic phase and thereby aid in the resolution of the thermal contributions. Unfortunately, the results on samarium oxide can be interpreted only qualitatively in the absence of a more secure knowledge of the lattice heat capacity curve. Experimental Samarium(III), Gadolinium(III), and Ytterbium(II1) Oxide Samples.-Finely-divided oxide samples obtained from Michigan (4) R. M. Douelass and E. Staritzky, Anal. Chem., 88, 552 (1956). (5) D. T. Cromer, J. Phys. Chem.. 61, 753 (1957).
BRUCEH. JUSTICE Ah'D EDGAR F. WESTRUM, JR.
346
TEMPERATURE,
0
100
-
200
TABLE I
"K.
DETAILSCONCERNING THE CALORIMETRIC SAMPLES
300
Sample masses,
Substance SmzOa, sample I SmzOa, sample I1 GdaOa
Sme03
Yb208
0 IO TE M PER ATU RE, Fig. 1.-Heat
20
Vol. 67
30
O K ,
capacities of Sni203,Gd2O3, and Yb2O3.
Chemical Company were rrported to have a purity in excess of 99.9% and to contain less than the stated amounts of impurities indicated in Table I together with other details concerning the various samples. Sample I and sample I1 are designations used to distinguish between two separate loadings of samarium oxide occasioned by the loss of helium conduction gas, subsequent refiring, and reloading of the calorimetric sample. l17ith the exception of YbzOa, the oxides were pelleted in a hard steel die approximately 1 cm. in diam. under pressures varying between 150 and 300 kg. cm.-2 to provide a somewhat improved thermal diffusivity within the sample and to increase the packing density of the original powder. The samples were fired to constant weight in air a t about 1170°K. With the exception of ytterbium, which was fired in a pure alumina crucible, the oxides were fired in a platinum vessel. After firing, the samples were loaded immediately into the calorimeter in the anhydrous nitrogen atmosphere of a drybox. Powder X-ray diffraction of the pelleted, heattreated materials revealed only the presence of the R-type structure for the samarium oxide samples and the C-type structure for gadolinium and ytterbium samples. Cryostat and Calorimeter.-Measurements were made in the Mark I calorimetric cryostat which is similar in most respects to one already described6 and employs the adiabatic technique. A capsule-type, platinum resistance thermometer (laboratory designation A-3) was employed for these measurements. This thermometer was calibrated at the National Bureau of Standards on the international temperature scale above 90°K. and against the Bureau's scale' from 10 to 90OK. The temperature scale is considered to be reliable t o within 0.03"K. from 10 to 90°K. and to within 0.04"K. a t higher temperatures. All measurements of mass, potential, resistance, and time were also calibrated against devices certified by the Xational Bureau of Standards. A copper calorimeter (laboratory designation 'Mi-16) described in the preceding paper of this series2was employed for measurements on all three samples. The heat capacity of the thermometer-heatercalorimeter assembly was determined in a separate experiment and represented a contribution of between 10 and 40% of the heat capacity over most of the temperature range. Small adjustments were applied where necessary for the small measured differences of helium, solder, and grease employed; buoyancy corrections on the samples were made on the basis of calculated densities indicated in Table I. (6) E. F. Westrum, Jr.. J. B. Hatcher, and D. W. Osborne, J . C h ~ m . Phys., 21, 419 (1953). (7) H. J. Hoge and F. G. Brickwedde, J . Res. SatE Bur. Std., 22, 351 (1939).
Impurities, ppm. Eu-100, Si-200, Ca-360 Eu-100, 51-200, Ca-350 Y-450, Eu-75, Si-200, Ca-100 Lu-500, Si-100, Ca-100
Gram formula in vacuo wt. 136.9046 348.70 138.4672
Densities, g . cm.-a 7.74
152.3403 362.52 183.3216 394.08
7.78 9.23
g.,
Results and Discussion Heat Capacity Measurements.-The observed values of the heat capacities of the samarium, gadolinium, and ytterbium oxides are presented in Table I1 in chronological sequence, to facilitate estimation of the temperature increments employed in the individual determinations from the adjacent meail temperatures. These data have been adjusted by a small amount proportional to the second derivative of the apparent heat capacity with respect to temperature, to correct for the finite temperature increments employed in the measurements. The data are presented in terms of an ice point of 273.15OK., the defined thermochemical calorie of 4.1840 abs. j., and the gram formula weights shown in Table I. The heat capacity data are presented graphically in Fig. 1 and values from the least squaresfitted, smoothed curve a t selected temperatures are listed in Table 111. As a further test of the integration procedure and the precision of the data, an enthalpytype increment was made between temperatures of 15.77 and 35.93OK. on samarium oxide, sample I. The resultant enthalpy increment of 43.38 cal. (g.f.w.)-l is in excellent accord with the integral of the measured heat capacity over this region, which yields 43.37 cal. (g.f.w.) -l. Absorption of the conduction helium precluded measurements on the finely divided powders commercially available a t temperatures below those indicated in Table 11. The heat capacity values in Table I11 are considered to have a probable error less than 0.1% above 25OK., increasing to about 1% a t 1OoK., and to somewhat larger values a t still lower temperatures as a consequence of decreased sensitivity of the resistance thermometer, the provisional nature of the temperature scale below loOK., and the thermal effects associated with the absorption of the conduction helium. Resolution of Electronic Heat Capacity Contributions.-The lattice heat capacity contribution for the cubic oxides of this paper is achieved from the two cubic oxides themselves. Ideally, the lattice heat capacity contribution might be better approximated by thermal data on the diamagnetic lutetium oxide (the L u + ~ion has a completed 4f shell and a Hund ground term of ISo) over the entire temperature range. Moreover, other considerations noted in the previous paper2 suggest that the lattice entropy contribution may be a significant function of the position within the lanthanide series and that it may differ by several tenths of a per cent between adjacent elements. For the present purposes, however, it should be noted that the Gd+8 ion has seven unpaired electrons (4f7), has a ground term of sSi/z, and consequently has a spin-only susceptibility. Group theory predicts that a cubic field will tend to remove the degeneracy of the ground term for a free Sstate ion, but the exact mechanism of this phenomenon
THERMOPHYSICAL PROPERTIES
Feb., 1963
O F LANTHANIDE OXIDEX
347
TABLE I1 HEAT CAPACITIESo F SAMARIUM( 111), GADOLINIUM( 111), [In cal. (g.f.w. "K.)-l] T, O K .
CP
%,
CP
OK.
T , OK.
CP
Samarium oxide (Smz03,sample I) Series I 20.34 1.196 12.23 0.391 22.35 1.497 13.47 0.483 4.99 0.052 24.56 1.852 14.84 0.587 AH Run 5.42 .128 27.03 2.276 6.09 ,299 29.73 2.776 38.03 4.355 7.34 .310 32.62 3.316 42.28 5.142 8.91 .287 35.85 3.939 46.67 5.987 10.04 .312 39.49 4.625 50.31 6.578 10.94 ,325 55.74 7.487 Series I1 61.72 8.457 11.99 .376 13.03 ,443 68.27 9.464 14.05 .526 7.90 0.284 74.75 10.396 15.27 .630 8.90 0.280 81.63 11.411 16.73 .763 9.88 0.309 11.01 0.331 18.44 .960 Samarium oxide ( SmzOa, sample 11) Series I 73.12 80.20 86.96 94.11 101.74 109.47 116.82 124.56 132.79 141.07 149.55
10.176 11.210 12.181 13.096 14.032 14.961 15.82 16.89 17.56 18.37 19.16
158.36 167.07 176.42 186.08 195.45
19.93 20.66 21.36 22.04 22.65
Series I1 201.42 210.67 219.84 228.80 237.73
23.01 23.54 24.05 24.51 24.95
Gadolinium oxide (Gd203) 13.18 0.736 14.53 0.735 139.94 15.86 16.00 0.733 148.25 16.67 17.63 0.757 156.97 17.48 19.32 0.816 165.89 18.25 21.14 0.916 23.11 1.064 Series I1 25.48 1.284 7.28 1.305 28.58 1.627 8.48 1.187 Series I11 8.98 1.110 Series I
10.21 11.71
0.950 0.819
8.45 9.52
1.171 1.066
246.47 255.24 264.07 272.87 281.01 291.40 300.76 310,13 319.56 329.07 338.52 346.78
10.56 11.56 12.52 13.50 14.48 15.45 16.56 17.77 19.03 20.45 22.04 23.92 26.34
25.38 25.75 26.18 26.47 26.80 27.14 27.461 27.76 28.05 28.32 28.55 28.77
0.92,7 0.824 0.775 0.749 0.735 0.730 0.738 0.761 0.804 0.875 0.979 1.134 1.374
still is not well explained. Van Vleck and Penneys suggest that the splitting of a "spin-only" ion is caused by a second-order interaction of the crystal field and t b e spin orbit coupling vector. Thus they explain the very low-lying Stark levels observed in several trivalent gadolinium compounds which show splittings varying from 0.1 to 10 cm.-l. ,4lthough gadolinium oxide has ti pronounced thermal anomaly below 10'K., as shown in Fig. 1, this anomaly probably contributes less than 0.02 cal. (g.f.w. a t 50°K., and certainly the heat capacity of gadolinium oxide may be used with confidence to approximate the lattice heat capacity of the cubic oxides from 100 to 350'K. The ground term for the singbe unpaired electron of the Yb+3ion (4f13)is 2F,/2. Experimentally, the heat capacity of ytterbium oxide differs ( 8 ) J.
H.Van Vlrck and W.G. Penney, Phd. X a g . , 17, 961 (1934).
AND
YTTERBIUM( 111) OXIDES
T,OK. CP T , OK. c, Gadolinium oxide (GdzOa) (contd.) Series IV Series VI Series VI1 196.38 20.51 27.01 1.448 79.21 8.628 205.30 21.08 29.80 1.774 86.08 9.571 214.55 21.63 32.71 2.153 93.33 10.460 223.70 22.13 35.95 2.599 101.12 11.417 232.62 22.59 39.52 3.103 109.02 12.396 241.46 23.05 43.30 3.644 116.95 13.337 250.54 23.45 47.34 4.231 125 30 14.293 259.86 23.85 51.97 4.897 134 35 15.27 269.20 24.22 57.25 5.637 143.89 16.24 278.61 24.58 63.11 6.468 153.66 17.17 288.05 24.89 163.29 18.03 297.72 26.21 Series V 172.50 18.79 307.61 25.51 181.55 19.49 317.42 25.79 6.198 190.55 20.13 327.16 26.04 61.16 336.80 26.28 67.27 7.033 73,10 7.811 346.08 26.48 T,OK.
CP
Ytterbium oxide (YbzOa) 147.00 17.18 18.57 0.494 155.54 18.12 164.30 19.03 87.12 9.676 Series IV 173.23 19.91 95.08 10.701 182.45 20.77 103.01 11.725 19.55 0.556 191.73 21.59 111.08 12.778 21.18 0.880 200.86 22.32 119.48 13.885 23.05 0,849 209.88 23.010 25.27 1.082 Series I1 27.94 1.400 Series VI 30.88 1.786 2.206 33.89 5.32 0.183 214.95 23.38 2.706 37.32 5.85 ,221 224.22 23.99 3.287 41.28 6.80 .372 233.32 24.58 3.891 45.37 7.97 .366 242.54 25.14 4.460 49.26 9.27 ,317 251.72 25.59 5.039 53.34 10.76 ,278 255.06 25.7'9 5,698 57.98 26.21D 263.89 6.412 63.08 Series I11 26.61 272.94 7.136 68.45 26.98 281.98 7.961 74.68 8.21 0.393 27.31 291.15 8,919 81.67 9.22 ,319 300.41 27.65 10.29 .285 27.95 Series V 309.84 11.29 ,274 319.34 28.2'2 12.15 .274 123.56 14.357 328.76 28.4'7 13.07 .290 14.17 .326 130.85 15.27 338.09 28.69 15.55 .356 138.66 16.21 346.72 28.91 17.03 ,413 Series I
from that of gadolinium oxide by less than 0.02 cal. (g.f.w. OK.)-' over the range 50 to 100'K. Moreover, the electronic heat capacity of ytterbium oxide a t temperatures in excess of 10O'K. is used later to argue the absence of Schottky contributions to the heat capacity below this temperature. Specifically, it is coiisidered that the heat capacity of ytterbium oxide ma,y represent the cubic lattice contribution from 20 to 100'K. Below 20'K. the heat capacity of ytterbium oxide no longer reliably approximates the lattice contribution because of the onset of antiferromagnetism at 2.5°K.9 Moreover, the absorption of the helium conduction gas below 10'K. occasioned experimental difficulties in the heat capacity measurements. Hence the heat capacity of ytterbium oxide was extrapolated below 20'K. by (9)
W.E. Henry, Phys. REV.,98, 226 (1955).
BRUCE H. JUSTICE AND EDGAR F. WESTRUM,JR.
348
Vol. 67
TABLE I11 THERMODYNAMIC FUKCTIOXS OF SAMARIUM(III), GADOLINIUM(III), AND YTTERBIUM( 111)OXIDES (In cal., g.f.w., OK.) -----Samarium
T
CP
oxide (SmpOs)-------.
so - siQQ HO
...
- Hiom
...
,---Gadolinium
CP
10 15 20 25 30
0.306 0.603 1.151 1.928 2.829
0.168 0.412 0.749 1.178
2.12 6.43 14.05 25.90
0.991 0.730 0.848 1.237 1.801
35 40 45 50 60
3.776 4.720 5.636 6.518 8.180
1.686 2.252 2.861 3.500 4.838
42.41 63.66 89.56 119.96 193.56
2.462 3.169 3.893 4.615 6.033
70 80 90 100 110
9.727 11.178 12.545 13.831 15.04
6.216 7.611 9.007 10,396 11.772
283.18 387.78 506.5 638.4 782.8
120 130 I40 150 160
16.18 17.26 18.26 19.21 20.08
13,130 14.468 15.784 17.077 18.344
170 180 190 200 210
20.89 21.62 22.30 22.92 23.51
220 230 240 250 260
oxide (GdzOs)-----.
so - slQQ EQ - HioQ
...
...
-----Ytterbium
CP
oxide (YbzOs)--
so - slQQ
...
FIQ
- HiaQ
...
0.331 0.550 0.778 1.051
4.03 7.86 12.99 20.54
0.291 0.337 0.558 1.052 1.671
1.377 2.167 2.615 3.582
31.17 45.23 62.89 84.16 137.44
2.368 3.098 3.833 4.562 5.980
0.976 1.339 1.746 2.188 3.146
25.54 38.20 55.52 76.52 129.27
7.405 8.738 10.037 11.300 12.521
4.616 5.692 6.796 7.919 9.054
204.66 285.40 379.30 486.01 605.2
7.353 8.697 10.025 11.342 12.643
4.172 5.241 6.342 7.467 8.609
195.97 276.24 369.85 476.69 596.6
939.0 1106.3 1283.9 1471.3 1667.8
13.691 14.804 15.85 16.83 17.75
10.194 11.334 12.470 13.598 14.714
736.3 878.8 1032.1 1195.6 1368.6
13.922 15.17 16.36 17.51 18.59
9.764 10.928 12.096 13.264 14.429
729.5 875.0 1032.6 1202.1 1382.6
19.586 20.801 21.989 23.149 24.282
1872.7 2085.3 2305.0 2531.1 2763.3
18.59 19.37 20.09 20.75 21.36
15,815 16.900 17.967 19.015 20.042
1550.3 1740.2 1937.6 2141.8 2352.4
19.60 20.55 21.43 22.25 23.02
15,587 16.735 17.870 18.990 20.095
1573.6 1774.5 1984.5 2203.0 2429.4
24.06 24.58 25.07 25.53 25.96
25.388 26.469 27.525 28.558 29.568
3001.2 3244.4 3492.6 3745.6 4003.1
21.93 22.47 22.96 23.43 23.86
21.049 22.036 23.003 23.950 23.878
2568.9 2791 .O 3018.1 3250.1 3486.6
23.72 24.37 24.97 25.52 26.03
21.182 22,251 23.301 24.332 25.343
2663.1 2903.6 3150.4 3402.9 3660.7
270 280 290 300
26.36 26.73 27.09 27.43
30.555 31.520 32.465 33.389
4264.7 4530.2 4799.3 5071.9
24.26 24.62 24.96 25.28
25.786 26.674 27.544 28.396
3727.3 3971.7 4219.6 4470.8
26.48 26.90 27.28 27.63
26.334 27,305 28.255 29.186
3923.3 4190.2 4461.1 4735.7
I. 752
0.118 0.244 0.422 0.666
1.46 3.68 7.71 14.46
350
28.84
37.73
6481
26.57
32.40
5769
29.02
33.55
6153
273.15
26.48
50.86
4348
24.38
26.07
3804
26.62
26.64
4007
298.15
27.37
33.22
5021
25.22
28.24
4424
27.57
29.02
4685
using a Debye 0 of 3 1 5 O K . based upon the heat capacity over the range 18 to 2 3 O K . which is approximately proportional to T 3 . The electronic contributions to the heat capacities of these oxides are shown in Fig. 2 . These curves were obtained by deducting the lattice contributions (as evaluated above) from the total heat capacities. Crystal Field Levels of Gadolinium Oxide.-As discussed by Pauling and Shappell,3 the oxide ions surround the gadolinium ion in the C-type oxide at six of the eight corners of a cube. Hence, as the first approximation, the crystalline electric field around the gadolinium ion probably is of nearly cubic symmetry with a relatively small correction for the potential of the two missing oxide ions. The crystal field levels would be expected to be similar to those of the trivalent gadolinium ion in the calcium fluoride lattice.1° Moreover, they would be anticipated to be the inverse of early predictions (based on the presumption that the field about the gadolinium ion has cubic symmetry with sixfold octahedral coordination) for the octahydrated ~ u l f a t e . l ~ - ~According 3 to Bethel4 an ion with J = (10) W. Low, Phys. Rev., 109, 265 (1958).
7 / 2 should be split into a quartet level flanked by a doublet on either side. The ratio of the interlevel spacing should be 3 :5 or 5 : 3 depending on the sign of the over-all splitting parameter as discussed by Low. The present data fit the 3 :5 ratio better than the inverted system. As a consequence of the two vacancies in the cubic crystal field, the quartet level probably is split into two doublets with a center of gravity at roughly 40y0 of the over-all splitting. This mould occasion a Schottky heat capacity curve with only a slightly lowered peak. The absorption of the helium conduction gas hindered accurate measurements below 9°K. so that, as may be seen in Fig. 2 , only the high temperature tail of the Schottky anomaly was experimentally observed in these measurements. Although a maximum Schottky heat capacity of approximately 1.9 cal. (g. ion was anticipated, this was approached a t 7.28"K. only to (11) H. van Dijk and W.U. Auer, Phglsica, 9, 785 (1942). (12) H. van Dijk, tbzd., 12, 371 (1946). (13) R. J. Benaie and A. H. Cooke, Proc. Phys. Soc., 63A, 213 (19.50). (14) H. Bethe, Ann. P h y s i k , [i] 3, 133 (1929). (15) W. Low, "Solid State Physics," Suppl. 2, Academic Press, Iiew Pork, K. Y . , 1960.
THERMOPHYSICAL PROPERTIES OF LANTHANIDE OXIDES
Feb., 1963
349
the extent of 0.6 cal. (g. ion This point is probably slightly low because of slow thermal equilibrium, but the higher points are reliable. The available data are well accounted for by levels at 0, 5.9, and 9.5 cm.-'l with respective statistical weights of 2,4, and 2 based on the eightfold degeneracy of the ground term of the free trivalent gadolinium ion. The theoretical curve employing these levels is developed by the equation2 ACel = Q-2R-'T-z {Q
2 giEi2 exp(-Ei/RT)
i=l
-
5 [giEi exp(-Ei/RT)
i=l
1.1
and is represented by the dashed curve of Fig. 2. The electronic entropy calculated from the above equation and the level assignment over the range 10 to which is in 298.15OK. yields 0.50 cal. (g.f.w. excellent agreement with the experimental value of 0.52 cal. (g.f.w. OK.)-l. The presence of a lower temperature thermal anomaly, which removes the entropy (222 In 2) associated with the ground state degeneracy, is evidenced by the decrease in the magnetic susceptibility with increasing magnetic field strength observed at 1.5OK. by Giauque and Stout.16 Gdz(SOa)a.8H20 has a cooperative anomaly a t about 0.250K.12 which probably removes the degeneracy of the ground doublet. The total entropy of the Schottky anomaly described above together with the ground state degeneracy (222 In 2) plus the observed heat capacity of gadolinium oxide, with the exception of the 0.52 cal. (g.f.w. OK.)-* as a mentioned above, yields 36.0 cal. (g.f.w. reliable value of the practical entropy of gadolinium oxide in the cubic phase at 298.ldOK. Corroborative evidence for the correctness of the interpretation expressed here has recently appeared jn measurements of gadolinium metal samples vtiith O . l l > 0.12, and 0.22% by weight oxygen content by Crane." Two anomalies observed below 4OK. were attributed t o the oxide impurity and provide confirmatory evidence for the heat capacity rise herein interpreted as a Schottky effect and for a low temperature cooperative transition. Lounasmaal* reported similar data on gadolinium metal with 0.54% by weight of oxygen present and interproted the residue after subtraction of the estimated heat, capacity of the metal as the heat capacity of the sesqrxioxide. Again, two peaks observed a t 1.3 and a t 3.8OK. appear to be cooperative and Schottky anomalies, respectively. Although differences exist in both the apparent heat capacity of the oxide and in that estimated for the metal by these a u t h o r ~ , ~they ~J* both obtain the theoretical entropy increment of 2R In 8. The data of Lounasmaa just below 4OK. accord very well with the data of the present series above 6OK. and yield a total entropy of 7.6 f 0.8 cal. (g.f.w. OK.)-L, which also agrees well with our estimated electronic entropy of 2R In 8 = 8.26 cal. (g.f.w. OK.) -l for gadolinium oxide. Due reserve in accepting such an identification is, of course, appropriate until the phase equilibria in the gadolinium-oxygen system are more fully studied and the situation concerning the existence of solid solutions iiq elucidated. (16) W. F. Giauqus and J. W. Stout, J. Am. Chenz. Soc., 61, 1384 (1939). (17) L. T. Crane. J . Chem. Phys., 36, 10 (1962). (18) 0. V. Lounasmaa, Phys. Rev., in presa.
a 0 -0 21 cj w
20
60
40
?, -I
a u io u 0 I
0 0
100 200 TEMPERATURE,
300 K.
Fig. 2.-Electronic heat capacities of SmaOa, Gd203, and YbzOs on a gram ion basis. The circles represent the experimental values and the dashed curves indicate the Schottky effects calculated from the energy level schemes proposed. The curves for SmzOs are explained in the text; the dotted curve on the GdzOs plot shows the data of Lounasmaa.18
Schottky Function and Energy Levels of Ytterbium Oxide.-The eightfold degenerate ground term of trivalent ytterbium provides a maximum of four crystal field terms because of the Kramers degeneracy. The resolution of the electronic contribution is shown in Fig. 2, and it is immediately evident that the peak of the Schottky anomaly has not been reached a t the highest temperature of the present measurements. Assignment of energy levels must therefore remain ap proximate and tentative until higher temperature measurements are available. The first two of the doubly degenerate excited levels are assigned values of 500 and 1000 cm.-l. The difference between the assumed l a b tice heat capacity and the actual heat capacity measured from 10 to 20OK. is not detailed in this figure. The Stark levels for trivalent ytterbium in a crystal-. line field of cubic symmetry with sixfold octahedral coordination have been calculated by Kynch.lg If, as a first approximation, the ytterbium ion in the C-type oxide is considered to be in a crystalline field of eight-. fold cubic coordination, then three levels would be expected with relative spacings of 5 :3 and degeneracies of 2, 4, and 2 . However, this does not accord with the experimental data, as the first level above the doublet ground state also appears to be a doublet from the present measurements. Uncertainties in the resolution of the lattice contribution a t these temperatures preclude a firm judgment. If the third excited level should (19) G. J. Kynch, Trans. Fayeday &e.,
33, 1402 (1937).
350
BRUCE
H. JCSTICE
A S D EDGAB
prove to be a t about 1200 crn.-l, then it might be concluded that the crystalline field is largely of cubic symmetry for the following reason. Since the center of gravity of the proposed levels a t 500 and 1000 cm.-I is a t 750 cm.-', the presence of a doublet level a t 1200 cm.-l would give the cubic separation ratio of 5 :3 with respect to the center of gravity of the inner two doublets observed in this investigation. The crystalline field levels present in ytterbium oxide were calculated by PenneyzOas doublets a t 0, 860, 2580, and 5160 cm.-l from the susceptibility data of Cabrera and Duperier21 and of Sucksmith.22 These diverge significantly from the present values possibly because of the relative insensitivity of the energy level scheme to the high temperature magnetic susceptibility data. In the oxide, the trivalent ytterbium ion is apparently in its ground state at 2OoK., for if there were another doublet between the ground state and the first observed excited state, the ground state would represent effectively a quartet level at the region of the observed Schottky anomaly in these measurements. (To have escaped experimental detection in the present measurements, such a postulated state would have to exist below approximately 10 cm.-l.) A doubling of the statistical weights of the excited levels observed would be required to explain the experimental electronic heat capacity, leading to the paradoxical conclusion that the ground state of the free ion has a degeneracy greater than eight. The electronic entropy calculated for ytterbium oxide from 100 to 298.16OK. is 1.26 cal. (g.f.w. OK.)-l, in good agreement with the observed value of 1.12 cal. (g.f.w. The proposed lattice heat capacity gives an excess entropy for the ytterbium ion of 0.06 cal. (g.f.w.'K.)-l from 10 to 20°K., which is probably associated with the antiferromagnetic ordering found in ytterbium oxide a t 2.5OK. by Henryeg Again one could presume this to be a transition removing the entropy (2R In 2) caused by the Kramers degeneracy of the ground state. By adding 2R In 2 and the lattice entropy at 1O0K. to the tabulated value, it is estimated that the practical entropy of the C-type ytterbium oxide a t 298.15OK. is 31.8 cal. (g.f.m. OK.)-'. Electronic Energy of Samarium Oxide.-Although the experimental data represented by both figures clearly reveal the presence of st Schottky anomaly with a peak in the range 50 to 15OoK.,adequate knowledge of the lattice contribution precludes a complete analysis a t the present time. The plotted points on the lower curve of samarium oxide in Fig, 2 are obtained on the assumption that the lattice heat capacity of hexagonal lanthanum oxide represents that of the lattice of the monoclinic B-type samarium oxide and those points of the upper curve by utilizing the cubic lattice heat capacity contribution previously described. Probably neither of these approximations is of quantitative significance, but, from the qualitative aspects of either curve, it is evident that monoclinic samarium oxide does have a Schottky anomaly. The plot also shows evidence for the existence of an excited level of the ground multiplet (6H7,,)above 12OOK. I n a crystal field of low symmetry, as in the monoclinic oxide, the samarium ion would be expected to (20) W. G. Penney, Phw. Reo., 43, 486 (1933). (21) B. Cabrera and A. Duperier, Compt. rend., 188, 1640 (1929). (22) W. S;urhnlith, P h i l Mag., 14, 1116 (1932).
F. 'CVZSTRCM, JR.
TTol. 67
split into three doublet levels. The broad peak and maximum of approximately 1 caI. (g. ion OK.)-' in the Cel curves qualitatively accord with this scheme. By magnetic susceptibility determinations, the next level of the ground multiplet in samarium oxide has been estimated by Borovik-Romanov and Kreinesz3to be at 1020 cm.-l. The statistical weight of this level is 8; as can be seen from Fig. 2, the contribution a t 120OK. is considerable and will peak a t about 600OK. Despite the complex magnetic structure occasioned by the low symmetry of the crystal, theyz3 assigned three Stark levels (0, 20, and 150 cm.-l) for the ground term with free-ion magnetic moments to obtain agreement with their susceptibility data. These energy levels are not entirely compatible with the present heat capacity determinations although the level a t 150 cm.-l is not excluded by the present measurements. A level a t 20 cm. -l would have caused an obvious Schottky anomaly peaking at 12OK., and the total heat capacity curve would have resembled that of neodymium oxide.z The entropy of the monoclinic form of samarium oxide a t 298.15'K. can be estimated in the same manner as for the previous two cubic oxides. From the qualitative appearance of the curves in Fig. 2 the entropy a t 1OOK. apparently is due to the Debye T 3extrapolation of the lattice contribution plus 2R In 2 for ordering the doubly degenerate ground state. The value of the entropy from these considerations is 36 cal. (g.f.w. OK.)-l a t 298.15OK. T o experimental evidence exists for the presence of an anomaly to remove the degeneracy of the ground state. Possibly, a portion of this entropy is present in the heat capacity above loOK., but compared with the other oxides this contribution would be anticipated to be less than about 0.25 cal. (g.f.m. Thermodynamic Functions.-The thermodynamic functions for samarium, gadolinium, and ytterbium oxides are also presented in Table I11 relative to 10°K. These functions were obtained by the exact integration of an analytical expression through the experimental points by an IBM 704 computer programz4 and are considered to have less than 0.1% probable error above 100°K. They are referred to 10°K. (near the lowest temperature of measurement) because of the as yet unexplored heat capacity below this point. Gibbs Energies of Formation.-The Gibbs energies of formation for these substances can now be derived from available thermodynamic data. Using the enthalpies of formation of Huber and co-workers,26 entropies of the metals from Westrum and Gr$nvoldZ6 based on the heat capacities by various authors,27 (23) A. 8. Borovik-Romanov a n d N. M. Xreines, Sosiet Phys. J E T P , 2, 657 (1956). (24) B. H. Justice, "Calculation of Heat Capacities and Derived Thermodynamic Functions from Thermal Data with a Digital Computer," Appendix to Ph.D. Dissertation. University of Michigan: United States Atomic Energy Commission Report TID-12722, 1961. (26) Sm208: E. J. Huber, Jr., C. 0. Matthews, and C. E. IIolley, Jr., J . A n . Chem. Soe., 7 7 , 6493 (1955); GdzOa: E. J. Huber, J r . , and C. E. Holley, Jr., ibid., 77, 1444 (1955): and Ybz08: E. J. Huber, Jr., E. L. Head. and C. E. Holley, Jr., J . Phys. C h e n . , 60, 1457 (1956). (26) E. F. West,rum, Jr., a n d F. Gr@nvold, "Proceedings of the IAEA Symposium on Thermodynamics of Nuclear Materials," Vienna, Sustria, 1962, p. 3. (27) Sm: L. D. Jennings, E. D. Hill, and F. H. Spedding, J . C h e n . Phys., 31, 1240 (1969); Gd: M. Griffel, R. E. Skochdopole, and F. H. Spedding, Phys: Reo., 9S, 657 (1954): a n d Yb: D. R. Stull and G. C. Sinke, "Thermodynamic Properties of the Elements," American Chemical Society, Washington, D. C,, 196&
Feb., 1963
TABLE IV FORMATIOX VALUES
FOR AT
THREE LANTHANIDE
OXIDES
298.15'K.
[In cal., g.f.w., OK.]
-
Oxide
Smp08 Gdz08 YbzO8
35 1
MERCURY-SESSITIZED DECOMPOSITIOX OF MERCURY DIMETHYL
&netslo
8oxtdeO
-ASf@
AHfo X 10-3
- AGfo X 10 -3
16.64 15.77 (15.0)
36.1 36.0 31.8
70.6 69.0 71.7
433.90 433.94 433.68
412.85 413.37 412.31
and that of oxygen from Kelley and - the valu.es given in TablecV result. Acknowledgment.-The authors are grateful to the United States Atomic Energy Commission for the patrtial support of this investigation. They acknowledge with thanks the assistance-of Dr. Shu-Sing Chang in the measurements 011 samarium oxide. (28) K. K. Kelley and E. G. King, "Contributions to the Data on Theoretical &Ietallurgy. XIV. Entropic$ of the Elements and Inorganic Compounds," Bureau of l\lines Bulletin 592, 1961.
T H E MERCURY-SENSITIZED DECOXPOSITIOS OF MERCURY DIMETHYL AT LOW PRESSURE BY P. KEBARLE Department of Chemistry, University of Alberta, Edmonton, Alberta Received August 10, 196#
+
The mercury sensitized decomposition of mercury dimethyl is shown t o proceed by the reaction: Hg* HgCH?)-+ Hg Hg 2CH;. A rate constant for methyl radical recombination equal (CH3)2-+ (Hg HgCHa ~ was determined. It is shown that the kinetics in the flow system used to k = 8 x 10-11 molecule-' C M .sec.-l can be treated qualitatively. Failure t o detect the cross recombination product CH3HgCDs in a decomposition of ordinary and deuterated mercury dimethyl is considered in connection with the lifetime of the methylmercury radical.
+
+
+
+
Lossing and co-workers1 have used mercury dimethyl as % methyl radical source in a number of investigations concerned with primary reactions in mercury-photosensitized photolysis. The primary decomposition of mercury dimethyl should therefore proceed to a considerable extent by the reaction
It is of interest tlo establish whether this is the oidy primary process. For instance, t'he occurrence of a primary C-H split as observed with the paraffins cannot be excluded a priori. The investigation to be described deals with the primary reactions and also attempts to treat the secondary processes, occurring in the flow system used, in a more quantitative manner. Experimental The apparatus used is shown in Fig. 1. It is based on a similar system designed by Lossing.2 Lossing's apparatus consisted of B flow reaction syst,em for mercury photosensitization attached directly to a mass spectrometer ion source, such that free radicals formed in the reaction can be detected with the mass spectrometer. The reactant, a t a few microns of pressure, is added to the helium carrier gas (8 mm.) acd the stream saturated with mercury a t 55". The stream then is irradiated by a mercury resonance lamp. Immediately below the lamp is a pinhole allowing a minute fraction of the reaction mixture to bleed into the mass spectrometer. The present apparatus follows the above outlined features very closely and so no further details on them will be given here, but a few of the departures and modificationci will be mentioned instead. The provision of a saturator, kept a,t 65', and a glass ring packed stripper, kept a t 55", allomed a complete mercury saturation. I t is of importance to ensure saturation and thus corn-. parable conditions in rum where the pressure of the carrier gas is varied. Without an efficient saturator and packed stripper it was observed that the partial pressure of the mercury (as monitored with the mas8 spectrometer) varied in a complex manner. The effects were traced to cooling of the saturator by (1) An apiilication of the methyl radical techniqrir and rrfeiences are t o be found in the following paper, J . Phus. Chem., 67, 354 (1963). ( 2 ) (a) F. P. Lossing, D. G. H. Marsden, and J. B Farmer. Can. J . Chem.. 34, 701 (1956); (b) I?. Kebarle and F. P. Lossing. tbzd., 37, 389 (1959).
carrier gas and t o formation of mercury aerosols in the stripper m hich in the absence of packing were carried downstream and reevaporated by the heater (Fig. 1). In order to be able to study the downstream decay of free radicals, the resonance lamp could be moved within a long water jacket. The water jacket itself also was movable so as t o allow larger displacements of the lamp. Changing the position of the lamp proved advantageous not only when radical downstream decay was measured for rate studies, but also as a help in the positive identification of a radical. Thus a mass peak identified as due to a radical should decrease and finally disappear as the lamp is moved away from the pinhole. A good vacuum seal could be obtained for the connection o f the silica tube to the mass spectrometer by means of a Teflon washer (Fig. l ) , or better, by compressing indium wire3 in the washer seat. The reactant gases, instead of being pumped out, could be condensed a t liquid nitrogen temperature for subsequent gas chromatographic analysis. With this procedure the sensitivity of detection of stable products easily can be increased by two orders of magnitude. The mass spectrometer used was of the Graham, Harkness, and Thode4design incorporating the open ion source of Lossing.zb The open ion source allows the reaction stream to be blown in as a molecular beam into the ionizing region. Shortening the pumping leads, in the present irstrument, allowed an increase of puniping speed a t the ion source to about 12 l./sec. Ope can calculate that even a t this speed the majority of the ionized particles have suffered collisions with the ion source container walls. Kevei*theless the number of collisions is much reduced and thus radicals which could survive only a few impacts with the wall still should be detectable with the present instrument.
Results and Discussion (a) Reaction Products and Primary Decomposition -The products from a typical run are given in Table I . Siiice ethane is by far the most abundant product, the other compounds are expressed per 100 molecules of ethane. The products, other than methane, add up to only 2%. The presence of methyl radicals could be detected directly with the mass spectrometer. As is showii in the subsequent section, the formation of ethane can be consistently explained as due to methyl (3) Consolidated S'aouum Corporation. (4) R . L. Graham, A. L. Harkness. and H. Q. Tbode. Rev. 8 c i . In&., '24, 119 (1947).
