THERMOPHYSICAL PROPERTIES OF THE LANTHANIDE OXIDES. IV. converted to Si-OD groups. This exchange process did not affect the silane speoies A and B. The specimen was then heated in oxygen. The resulting destruction of the silanes led to the formation of Si-OH groups, the spectral changes observed being like those described above; the spectra in the 0-H region were much like those shown in Figure 8A. However, in such oxidation experiments there was no change, or only a small modification, of the intensity and shape of the 2761cm-’ band of Si-OD groups. It is thus concluded that the oxidation led only to the formation of localized hydroxyl groups, water molecules not being formed because exchange was not observed, and also that the interactions producing the new shape of the 3742-cm-1 band were more of an intra- than intermolecular nature, because the hydroxyls already present on the surface were not involved at all. One would expect the oxidation of species A to lead
333
to the formation of geminal hydroxyls, and the above results and conclusions are not at variance with this. On the other hand, it seems surprising that such geminal hydroxyls gave rise to interactions which were so weak that the Si-OH band after the oxidation reaction was not much different from that caused solely by isolated silanols. However, such behavior is congruent with Peri’s conclusion, ‘6 based upon work with ordinary silica, that geminal hydroxyls are probably not hydrogen bonded to their partners because a five-or six-membered ring is normally needed for intramolecular hydrogen bonding.
Acknowledgment. Support by grants from the National Center for Air Pollution Control and the Communicable Disease Center are gratefully acknowledged. We thank Dr. G. Underwood for fruitful discussions and help with the esr experiments.
Thermophysical Properties of the Lanthanide Oxides, IV. Heat Capacities and Thermodynamic Properties of Thulium (111) and Lutetium(111) Oxides. Electronic Energy Levels of Several Lanthanide(111) Ions1 by Bruce IT. Justice, Edgar F. Westrum, Jr.,2 Elfreda Chang, and Ray Radebaugli Department of Chemistry, University of iMichigaia, Ann Arbor, Michigan 48104
(Received June $3, 1968)
The heat capacities of thulium(IT1) and Intetium(TI1) oxides wcrc measured froin A to 350OTC. The elect>roiiicheat capacity associntctl with the Tm(II1) ion is resolved from the total hcnt capacity values for the two oxides nntl that of .gndoliniuin(III) oxide. Several low-lying energy levels for the Tm(II1) ion arising froin crystal field splitting of the ground term ( W g ) of Tm(I11) ion and of relatctl I,.tnthanitle(IIT) ions are A ’ O p , and (Go I i o ~ t ) / T24.32, 26.28, discernible. The observed heat capacity values yield for C,, So and -12.22 cal/(mol O K ) at 298.15OK for Lu& with T’ = O°K and 27.90, 33.15, and -16.41 for Tinz03 with T’ = 10°K. The latter values are extended to a O O K reference point by estimating a magnetic contribution below 1OoK.
-
Introduction This paper extends and broadens the earlier studies3-s on the thermophysical properties of the lanthnnide oxides by providing thermal capacity data on thulium(II1) and lutetium(II1) oxides. Since both oxides crystallize with cubic symmetry as the C-type i s o m ~ r p h ,this ~ ~ ~endeavor supplements knowledge of gradual change in the lattice heat capacity for cubic oxides with increasing atomic number obtained from a combination of the heat capacity curves for gadolinium arid ytterbium oxides, by providing data on diamagnetic lutetium oxide with a ISo ground state. The inter-
-
polated lattice heat capacity results in n rensonable accomit,ing of the electronic heat capacities of the intervening cubic parmnngiietic oxides. Moreover, exten(1) This research was supported in part by the U. S. Atomic Energy Commission. (2) To whom correspondence concerning this paper should be addressed. (3) B. H.Justice and E. F. Westrum, Jr., J. Phus. Chent,, 67, 339 (1963). (4) B. H.Justice and E. F. Westrum, Jr., ibid., 67, 345 (1903). (5) E.F.Westrum, Jr., and R. H. Justice, ibid., 67, 659 (1963). (6) L. Pauling, Z. Krist., 69, 415 (1929). (7) R. S. Roth and S. J. Sohneider, J. Res. Yaf.Bur. S t a i d , 64, 309 (1960). Volume 75, Nuniber B FebruarU 1069
334
BRUCEH. JUSTICE, EDGAR F. WESTRUM,JR.,ELFREDA CHANG,AND RAYRADEBAUGH
sion of the interpolation scheme to the lattice heat capacity of the hexagonal oxides enhances the correlation between the observed spectrum and the (re)derived electronic heat capacity. Both calorimetric and spectroscopic investigations involved A-type hexagonal isomorphs7~*in which the heptacoordinated magnetic ions occupy equivalent lattice sites. Since thermal measurements on lanthanum(II1) and on neodymium(II1) oxides and deduced crystal field splitting of the ground electronic level of the former were r e p ~ r t e d the , ~ spectrum of Nd(II1) ion in a lanthanum(II1) oxide host has been observed by Henderson, et ala9 They report five crystal field lines for the ground state (%/,) at 0, 23, 84, 253, and 496 cm-l. The first two excited levels are in excellent accord with corresponding values deduced from heat capacity data alone3 (0, 21, 81, and 400 cm-l), and the center of density of the higher levels also corresponds. However, the interpretatiori of the electronic heat capacity data4s5of the cubic gadolinium(III), dysprosiuni(III), holmium(III), and erbium(II1) oxides was hampered by the lack of spectral data. These cubic lattices have two nonequivalent types of cation sites. lo Threequarters of the cations have Cz symmetry and each is surrounded by six anions at the corners of a cube with the two missing anions at the ends of a face diagonal. The remaining cations possess C3( symmetry, in which each cation is similarly surrounded except that the missing anions are at the ends of a body diagonal. The spectra reported for Dy(III),” Er(III),12213 and Tm(III)13 ions with Cz symmetry in yttrium(II1) oxide or in singlc crystal lanthnnide(II1) oxldes together with heat capacity data for Gd~.03,~ Dy&5 Erz03,6 TmZO3, and Lug03 permit derivation of the lattice heat capacity for any of the cubic oxides from Gdz03 to LuZO3and energy levels for the C S ions ~ in Dy208, ErzO3, and Tmz03. Thus, thermal measurements on thulium and lutetium oxides provide correlations of lattice heat capacity contributions for C-type oxides and electronic heat capacity contributions from ions on both types of sites. The measurements on thulium oxide afford a further opportunity for correlation of electronic heat capacity with the highly degenerate Tm(I1I) ion (3H,3) and further insight into the effect of the two-site structure of the C-type oxides on their energy levels. Experimental Section
Thulium(I11) and Lutelium(l11) Oxide Samples. Finely divided (about 300 mesh) samples of the two lanthahide(II1) oxides \yere loaned to us by Professor F. H. Spedding, 1)irector of the Ames Laboratory of Iowa State University. The samples, with reported purities greater than 99.97%, were placed in alundum crucibles and fired in air within a muffle furnace at 900”. After cooling to room temperature, the samples were loaded into the calorimeter in a nitrogen-filled The Journal of Physical Chemistry
drybox. A pressure of about 100 Torr (at 300°K) of helium exchange gas facilitated thermal equilibration. The masses of thulium and lutetium oxide taken for measurement were 124.261 and 127.202 g in vacuo; molecular weights of 385.88 and 397.98 g were used. Powder patterns of the calorimetric samples showed C-type cubic structures with the accepted lattice constants. Cryostat and Calorimeter. Measurements were made in the Mark I1 cryostat, which is similar to that described by Westrum and M c C ~ l l o u g h by , ~ ~use of the quasiadiabatic technique. l6 A capsule-type, platinumresistance thermometer (laboratory designation A-5) calibrated by the National Bureau of Standards (NBS) from 10 to 90°K on their provisional scale and above 90°K on the International Temperature Scale was used. Below 10°K a provisional scalel6 was adopted. Measurements of mass, resistance, potential, and time were made with devices whose calibrations are traceable to standards of NBS. The heat capacity of the gold-plated, copper calorimeter (laboratory designation W-28) was determined in a separate series of measurements. The calorimeter-heater-thermometer assembly contributed about 795 of the total apparent heat capacity a t 1O”K, 50% at 80”K, and decreased gradually to 40% at 350°K for thulium(II1) oxide. Corresponding percentages for the lutetium(II1) oxide are 40, 56, and 45. Corrections were made for slight differences in amounts of helium, grease, and solder between the calibration determination and the measurements on the samples. Crystallographic densities” of 8.84 and 9.30 g/cc for TrnzO3and Luz03, respectively, were used in making buoyancy corrections.
Results and Discussion Heat Capacities and Theymal Functions j o y Thulium and Lutetium Oxides. The observed heat capacities for thulium and lutetium oxides are presented in Table I in chronological order so that temperature increments of the individual points can usually be inferred froin (8) R. M. Douglass and E. Staritzky, Anal. Chem., 28, 552 (1956). (9) J. R. Henderson, M. Muramoto, and J. B. Gruber, J. Chem. Phys., 46, 2515 (1967). (10) L. Pauling and M, D. Shappell, Z.Krist., 75, 128 (1930). (11) J. R. Henderson, M. Muramoto, T. M. Henderson, and J. B Gruber, J. C h e w Phus., 47, 5097 (1967). (12) P. Kisliuk, W.E’. Kruplce, and J. B. Gruber, ibid., 40, 3606 (1964). (13) J. B. Gruber, 7.V. F. Xrupke, and J. M. Poindexter, ibid., 41, 3363 (1964). (14) E. F. Westrum, Jr., G. T. Furukawa, and J. P. McCullough,
“Adiabatic Low-Temperature Calorimetry,” in “Experimental Thermodynamics,” J. P. McCullough and D. W. Scott, Ed., Butterworth and Go., Ltd., London, 1968. (15) E. F. Westrum, Jr., J. B. Hatcher, and D. W. Osborne. J . Chem. Phys., 21, 419 (1953). (16) H. J, Hoge and F. G. Brickwedde, J. Res. Nut. Bur. Stand., 22, 351 (1939). (17) D. H. Templeton and C. H. Dauben, J. Amer. Chem. Soc., 76, 5237 (1954).
THERMOPHYSICAL PROPERTIES OF THE LANTHANIDE OXIDES.IV. T, 'ii 0
100 I
I
200 I
I
Table I: Heat Capacities of Lutetium(II1)
300 I
I
335
I
and Thulium( 111) Oxides"
30 T , OK
CD
6.03 5.77 6.61 7.80 8.85 9.68 10.42 11.20 12.10 13.18 14.49 16.10 17 87 19.67 21.53 23.41 25.39 27.57 30.02 32.75
0.019 0.016 0.025 0.041 0.060 0.078 0.098 0.119 0.143 0.172 0.210 0.267 0.351 0.465 0.613 0.788 0.997 1.254 1.564 1.934
T,OK
CP
T , OK
CP
Lutetium(II1) Oxide (Lun03)
- 20 F E
i
tl.
3 u
3 10
I
0
Figure 1. Heat capacities of TmzOaand LuzOa.
35.59 39.51 43.97 48.84 54.08 60.12 63.46 68.93 74.37 79.86 86.04 92.86 99.91 107.53 115.90 124.54 133.00 141.60 150.46 159.36
2.343 2.908 3.552 4.254 4.979 5.799 6.249 6.923 7.559 8.250 9.018 9.782 10.545 11.381 12.294 13.221 14.102 14.956 15.793 16.58
168.18 178.62 189.02 197.26 206.20 215.17 224.10 233.03 242.05 251.11 260.13 269.18 278.22 287.32 296.53 305.83 315.34 325.96 337.75 347.35
17.33 18.15 18.92 19.46 20.07 20.61 21,12 21.62 22 09 22.51 22.87 23.24 23.63 23.95 24,27 24,58 24.89 25.19 25 54 25.70 I
I
Thulium(II1) Oxide (TmgOa) Series I
differences in adjacent mean temperatures. The observed apparent heat capacities have been adjusted for curvature with a Taylor series expansion of the true heat capacity about the mean temperature (T)of the measurement.I8 The curvature adjustment is then given by
If it is assumed that the temperature derivatives of C, and A H / A T are equal, the derivatives in the infinite sum can be easily calculated from an analytical formulation of the apparent heat capacity. These adjustments were always considerably smaller than experimental precision. The data are given in terms of the defined thermochemical calorie (4.1840 J) and ice point (273.15"K). Heat capacities for both compounds are displayed in Figure 1. The heat capacities and derived thermodynamic functions at selected temperatures are presented in Table 11. The probable error in the heat capacity is less than 0.1% above 30°K; that in the other functions is about 0.1% above 100°K. Below these temperatures the error increases somewhat due to the decreasing sensitivity of the thermometer and adiabatic shield thermocouples. Resolution of the Electronic Heat Capacities in Lanthanide(III) Oxides. Electronic heat capacities, Gel, are here derived by procedures used formerly2 except that the lattice heat capacity contribution is interpolated linearly in terms of atomic number between
300.10 308.91 318.17 327.46 836.58
17.40 19.48 21.43 23.18 24.87 26.67 28.69 31.02 33.58 36.41
27.94 28.26 28.53 28.74 28.90
Series I1 254.71 263.59 272.70 281.75 290.76 299.82 308.96 318.10 327.22 336.31 345.39
26.31 26.68 27.03 27.38 27.67 27.93 28.18 28.44 28.63 28.87 29.07
Series I V
4
Series I11 6.94 8.07 8.87 9.75 10.61 11.59 12.76 14.11 15.58 a
0.32 0.46 0.61 0.76 0.91 1.03 1.21 1.391 1.549
Units: cal, mol,
1.728 1.926 2.120 2.306 2.498 2.709 2.962 3.260 3.609 4.013
5.26 6.21 7.24 8.31 9.23 10.14 11.18 12.38 13.73 15.21 16.88 18.65 20.49 20.47 22.54 24.77 27 43 30.36 33.24 36.23 I
0.12 0.20 0.34 0.50 0.67 0.85 0,980 1,147 1.339 1.497 1.671 1.843 2.028 2.024 2.240 2.486 2.806 3.173 3.567 3.983
39.66 43.42 47.42 51.98 57.24
4.466 4.997 5.567 6.234 6.970
Series V 55.05 60.80 67.17 74.17 81.46 89.20 07.46 105.63 113.46 121.48 129.69 137.88 146.32 155.01 163.76 172.47 181.18 189.87 198.70 207.53 216.63 225.79 235.04 244.36 253.63
6.664 7.494 8.393 9.324 10.351 11.429 12.470 13.522 14.517 15.522 16.515 17,478 18.40 19.31 20.17 20.97 21.71 22.41 23.07 23.69 24.27 24.82 25.36 25.79 26.23
OK.
(18) N. 8. Osborn, H. F. Stimson, T. S.Sligh, Jr., and C. S. Cragoe, Nat. Bur. Stand. Sci. Papers, 20, 65 (1924). Volurns YS, Number R Februarv 1960
BRUCEH. JUSTICE, EDGAR F. WESTRUM,JR., ELFREDA CHANG,AND RAYRADEBAUGH
336
Table 11: Thermodynamic Functions of Lutelium(II1) and Thulium (111) Oxidesa
-
-(Go H0iood/T
- Hoa
-(Go Hoa)/T
T
5 10 15 20 25
Lutetium(II1) Oxide (Lu203) 0.014 0.011 0 003 0.172 0 022 0.077 0.906 0.080 0.225 0.176 2.614 0 489 0.332 6.147 0.955
0.000 0.005 0.019 0.046 0.086
10 15 20 25 30
Thulium(II1) Oxide (TmOa) 0.804 otooo 0.000 1 480 0.462 5.816 1.976 0.958 14.490 2.515 25.68 1.455 3.128 39.75 1.967
0.000 0.075 0.234 0.428 0.642
30 35 40 45 50
1.563 2.257 2.980 3.704 4.416
0.558 0.850 1.199 1.592 2,019
0.145 0,224 0.324 0.442 0.578
35 40 45 50 55
3.810 4.514 5.226 5.942 6.658
2.499 3.046 3.619 4.207 4.807
57.07 77.58 101.93 129 85 161.35
0.869 1.107 1.354 1.610 1.873
60 70 80 90 100
5 780 7,064 8.280 9 * 444 10.569
2,946 3,934 4.958 6.001 7.054
0.895 1.258 1.656 2.081 2.525
60 70 80 90 100
7.371 8.778 10,153 11.496 12.808
5.417 6.659 7.921 9.195 10.474
196.4 277.2 371.9 480.2 601.7
2,143 2.699 3.273 3.860 4 * 457
110 120 130 140 150
11.666 12.739 13,787 14.798 15.761
8.113 9.174 10.236 11.295 12,349
564 1 686.1 818.8 961.7 1114.6
2.985 3 457 3.937 4.425 4.918
110 120 130 140 150
14.091 15,341 16.549 17.704 18.793
11.755 13.035 14.311 15.580 16.839
736.2 883.4 1042.9 1214,2 1396.8
5.063 5.674 6.289 6.908 7.528
160 170 180 190 200
16.66 17.50 18 27 18.99 19.65
13.395 14,431 15.453 16.460 17,452
1276 8 1447.6 1626.6 1812.9 2006.1
5.415 5.915 6.417 6.919 7.421
160 170 180 190 200
19.81 20,75 21.62 22.42 23.16
18.085 19,315 20.526 21.716 22.885
1590 1793 2005 2225 2453
8.149 8.769 9.389 10.007 10.621
210 220 230 240 250
20.29 20.89 21.45 21.98 22.47
18,426 19,384 20,325 21.249 22,156
2206 2412 2623 2841 3063
7.922 8.421 8.918 9.413 9.904
210 220 230 240 250
23.84 24,48 25.06 25.60 26.09
24.032 25,156 26.257 27.336 28.390
2688 2929 3177 3431 3689
11.233 11.840 12,443 13.041 13.634
260 270 273.15 280 290
22.91 23.31 23.43 23.68 24.04
23.046 23.918 24.190 24 * 773 25.610
3290 3521 3595 3756 3995
10.393 10.878 11.030 11.359 11.836
260 270 273.15 280 290
26.53 26.93 27.05 27.30 27 64
29.42 30.43 30.74 31.42 32.38
3952 4220 4305 449 1 4765
14.22 14.80 14.99 15.38 15.95
298.15 300 310 320 330
24,32 24.39 24 72 25,03 25 30
26.281 26,431 27.236 28 026 28.801
4192 4237 4482 4731 4983
12,222 12,309 12.777 13 242 13.701
298.15 300 310 320 330
27.90 27.95 28.25 28.52 28.75
33.15 33.32 34.24 35.15 36,03
4992 5043 5324 5608 5895
16.41 16,51 17.07 17.62 18.16
340 350
25.54 25.76
29.560 30,303
5237 5494
14.157 14.607
340 350
28.96 29.16
36.89 37.73
6183 6474
18.70 19.23
T
CP
SO
He
I
I
I
I
I
I
I
I
12.395 21.92 35.01 51.72 72.03 123.08 187.4 264.1 352.8 452.9 I
I
I
I
Cp
So
- S0loo~cH o - Ho1oaic
I
I
I
Units: cal, mol, OK,
Gdz03and LutOa. The two assumptions (a) that the electronic levels reported for Gd(II1) ion in cubic Gdz03*represent the electronic heat capacity of Gdz03 and (b) that the Cz and CS(ions have identical levels with an overall splitting of about 10 cm-l are still inherent. The latter is a reasonable consequence of the small second-order interaction of the crystal field with “spin only” ions of the ground state. However, the discussion of Abraham, et aZ.,19 who cite Wybourne’s20discouraging endeavor to derive a theoretThe Joumal of Physical Chemisfry
ical description of the splitting of S-state ions should be noted. This procedure results in substantially identical lattice heat capacities for Gdz03and L u z O from ~ 5 to 10°K. A further implicit assumption is that the variation of the increment, C, - C,, is compensated across the series; hence, subtracting the lattice con(19) M. M.Abraham, L. A. Boatner, C. B. Finch, E. J. Lee, and R. A. Weeks, J , Phys. Chem. Solids, 28, 81 (1967). (20) B. G. Wybourne, Phys. Rev., 148, 317 (1966).
337
THERMOPHYSICAL PROPERTIES OF THE LANTHAXIDE OXIDES. IV. 1
2.0 I
v
0
100
200
T,
300
OK
1.0 I
Y
r
Table 111: Experimental Electronic Heat Capacities for Lanthanide( 111)Ions and Lanthanide(II1) Oxides" T
Nd(II1)
DYW)
Er(II1)
Tm(II1)
5 10 25 50 100
0,202 0,783 0.817 0.675 0.544
0.056 0.128 0 598 0,874 0.986
0.032 0 494 1.407 1.430 0.882
0.048 0.360 0.764 0.742 1.018
150 200 250 300 350
0.560 0.58 0.53 0.50 0.49
1.258 1.44 1.47 1.40 1.30
0.720 0.69 0.65 0.60 0.54
1 360 1.60 1.67 1.65 1.58
a
Units:
I
I
I
ca1, mol, OK.
Er2 3'
Table IV : Lattice Heat Capacity Contribution for Some Lanthanide(II1) Oxides"
I
200
I
I
600
1000
T,
I
I
I
1400
O K
Figure 2. Schottky anomalies for Er(II1) ion in Ergo$. In Figure 2a the circles represent data from this laboratory.6 The dashed curves represent the calculated electronic heat capacity of the CZions based on the spectroscopic data of Kisliuk, et aZ.,12 and Gruber, et d ; 1 3 the dotted curve shows total electronic heat capacity by adding the contribution for the Cadlevels in Table V. In Figure 2b the circles represent heat capacities from enthalpy increment determinations of Pankratz and KingjZaand the curves have the same significance.
T
NdiOs
DyiO3
En03
TmrOs
5 10 25 50 100
0.005 0.076 1.213 5.255 12.593
0.011 0.083 1 039 4.530 11.084
0.011 0.080 1.006 4.484 10.878
0.011 0.079 0.989 4.461 10,775
150 200 250 300 350
17.94 21.56 23.98 25,67 26.93
16.525 20.44 23.15 25.03 26.35
16,219 20.12 22 88 24 77 26.13
16.066 19.96 22.75 24.64 26.02
a
Units:
I
I
I
cal, mol, OK.
Table V : Electronic Levels for Cai Ions in Lanthanide(II1) Oxide"
tribution from the apparent heat capacity yields the true C,l at constant volume as shown in Figure 2 . The Electronic Heat Capacity of Er(III) Ion. Contributions to Cel based on spectroscopic levels reported for the C2-type ions in erbium(II1) o ~ i d e , ' ~ aconsisting '~ of doublets at 0, 39, 76, 89, 158, 258, 495, and 500 cm-I, are represented by dashed curves in Figure 2. Figure 2a depicts Cel for the low-temperature region. These values summarized in Table I11 were derived by subtracting the lattice contribution given in Table IV from the apparent heat capacities. The C,I remaining after removal of the contributions from the C2 ions is attributed to the levels in the Cst ions. The levels and their degeneracies (shown in Table V) are deduced in part from the position and magnitude of the Schottky peaks in the observed C,I (for separations of less than 100 cm-l) and in part from the splittings of the groundstate term by fourth- and sixth-order terms of cubic crystal fields.21 The levels thus derived are doublets at 0, 12, 50, 55, 150, and 450 cni-l and a quartet at 550 cm-l. These correspond most closely to the levels in a
Dy(II1):
0(2), 42(2), 200(2), 450(2), 600(2), 700(2), 950(4), [3700](14)," [6100](12)," [7700](lo)," (81001(12),11 [9200](8),11[9300]
Er(II1):
0(2), 12(2), 50(2), 55(2), 150(2), 450(2), 550(4), [6660](14),1z113 [103001(l2)l2'l3 O(l), 600(3), 1050(2), 2500(7),13 [6500](9)13
Tm(II1):
' Degeneracies are indicated in parentheses; values in cin-l. Values in square brackets are mean values selected to represent other Russell-Saunders states of the ground multiplet.
cubic field with a ratio of sixth- to fourth-order terms (V6/V4)of -0.25. The I's level is split to 12 and 50 (or 55) em-', and the second I's level is split to 150 and 450 em-'. The C,I data require levels a t 12,50, and 55 cm-I (*lo% of A E ) . The uncertainties in the upper levels can probably reach 20% due to the re1at)ive magnitude of the lattice heat capacity and the consequent insensitivity of the electronic heat capacity at temperatures corresponding to levels above 100 cin-'. (21) J. A. White, J. Phus. Chem. Solids, 23, 1787 (1962). Volume 76, Number
,O
Febmaru IQGD
338
BRUCEH. JUSTICE, EDGAR F. WESTRUM,JR., ELFREDA CI-IANG, A N D RAYRADEBAUGH
It is interesting, but not surprising, that C S flevels are quite similar to C2 levels. Concern4 about the magnitude of error introduced by adsorption of helium exchange gas on the samples below 10°K was probably overly conservative. Effects associated with the onset of antiferromagnetismz2 and poor thermal equilibration may have been mistakenly attributed to helium adsorption in view of the present excellent accord of the known spectral data and the derived lattice heat capacity. The only significant deviation of theoretical and observed electronic heat capacities is found below 35°K. This is probably associated with the removal of the ISramers degeneracy of the Er(II1) ion by ordering. The measured entropy increment from 10 to 298.15"K5 of 33.81 cal/(mol O K ) correlates well with the value of 33.71 cal/(mol OK) calculated from the energy levels plus the lattice contribution. Moreover, the electronic heat capacity of the Er(II1) ion, derived from hightemperature enthalpy data for 3r203,23Gdz08,24and Luz03 25 using a treatment similar to that employed for the low temperatures, gives excellent agreement with the heat capacity calculated from the observed spectra and proposed levels as shown in Figure 2b. The practical entropy of Er203 at 298.15"K is calculated as 37.2 rt 0.1 cal/(mol OK) using the lattice entropy extrapolated below 1O"K, the given levels, and the 2R In 2 entropy units removed by antiferromagnetic ordering. This compares with 36.6 cal/(mol O K ) reported previously.6 The ElectTonic Heat Cupacity of Dij(III) Ion. The contributions of the levels reported for the (3%ions in dysprosium(II1) oxide" consisting of doublets at 0, 74, 261, 335, 505, 602, 746, and 1080 cm-' are shown as dashed curves in Figure 3. Again thc excess C,I (cj. Table 111) obtained by thc same procedure described for erbium(IT1) ion is ascribed to the Cat ions. The levels which best fit these data arc doublets at 0, 42, 200, 450, 600, and 700 cm-I and a quartet at 900 c1n-l. The level at 42 cm-l is readilv apparent in the C1, data of Figure 3. If the first four proposed states of the ion are froni splitting two quartets at about 125 and 525 cm-I in a slightly perturbed cubic field, then the model given by Whitez1 with a potential ratio (V,/T74) of - 0.30 most nearly applies. Uncertainties in the levels would be similar to those given for Er(II1) ion. Here, too, the adsorption of helium exchange gas may not have been a significant contribution in the values published below 1O"Ii. The only significnrit deviation of the theoretical C,1 from the calorimetric value occurs below 25°K. This is probably a consequence of the tail of the antiferromagnetic26 transition removing 2R In 2 units of entropy associated with the Krsmers degeneracy of the ground crystal field state in dysprosium(II1) oxide, The high temperature C,1 of the Dy(II1) ion derived from enthalpy data25 for this oxide does not agree as well with the calculated heat capacity as does that of Er (111)ion, but the agreement is still within the The Journal of Physical Chemistry
I . "
I
1
DY2
43
2.0 1 I
C,; ions
-- -- 4-__. ---
0
0
100
200
300
'1: ''I( Figure 3. Schottky anomalies far the Dy(III), Tm(III), and Nd(II1) ions in LnnOa. The dashed curve is the electronic heat rapacity of CZions derived from the levels discussed in the text. The dotted curve is the total electronic heat capacity, ie., the sum of the C,L contributions from the CSand Cgi ions. The points are calculated from the original heat capacity data and the appropriate lattice heat capacity curve RS described in the text.
experimental error of the heat capacity derived from tlic enthalpy increment data. The observed entropy increment from 10 to 298.15"K was reported as 33.06 cal/ (mol OK) while the sum of lattice and electronic en(22) M. K. Wilkinson, W. C. Koehler, E. 0. Wollan, and J. W. Cable, Bull. Am. Phys. Soc., 2, 127 (1957). (23) L. B. Panltratz and E. G. King, U. S. Bureau of Mines, Report of Investigations No. 6175, U. S. Department of the Interior, Mines Bureau, Pittsburgh, Pa., 1963. (24) L. B. Pankratz, E. G. King, and K. K. Kelley, U. S. Bureau of Mines, Report of Investigations Xo. 6033, U. S. Department of the Interior, Mines Bureau, Pittsburgh, Pa., 1962. (25) L. B. Panltratz and K. K. Kelley, U. 8. Bureau of Mines, Report of Investigations No. 6248, U. S. Department of the Interior, Mines Bureau, Pittsburgh, Pa., 1963. (26) H. Bonrath, K. H. I-Iellwege, K. Nicolay, and G. Webre, Phys. Kondensierten Mat., 4 ( 5 ) , 382 (1966).
TIIERMOPHYSICAL PROPERTIES OF THE LAKTHAXIDE OXIDES. IV. tropies gives 32.99 cal/(mol O K ) . This work therefore confirms the previously reported value of 35.8 f 0.1 cal/(mol OK) lor the practical entropy at 298.15"K. The Electronic Heat Capacity of T m ( I I I ) Ion. The levels given by Gruber, et al.,I3 for the Cz ions (3/4 of the total cations present in Tmz03) are singlets at 0, 30.7, 89.3, 219.0, 230.3, 340.0, 382.4, 435.7, 488.4, (680.1)) 692.3, 788.5, and 769,9 cm-I. These generate, perhaps fortuitously, a Cel equal to the total C,I observed below 110°K within experimental error (which is probably more reliable than Celderived by subtracting the lattice heat capacity from the measured values). The data of Table V are consistent with a triplet at 600 cm-l, a doublet at 1050 ern-', and seven levels near 2500 cm-l. This fits White'sz1 potential term ratio (v6/v4) of -0.20. The sensitivity of this analysis is not high because of relatively high energies of the CSi levels. Some credibility is lent to the unexpectedly high levels by the high-temperature enthalpy data on thulium(II1) oxide of Pankrantz and Kingz3although the correlation is not as good as fqr erbium(II1) ion. The existence of the C3(levels so far removed from the CZ levels is further authenticated by K a I v i u ~ AIOss'~~ bauer spectra of thulium(II1) oxide. He found the energy of electric interaction of the nuclear spin levels with 4f electrons in the Czions to be 8 X lo-' eV and that for the CSlions to be 1.9 X 10-6 eV and implied that the CBI4f electrons are about twice as energetic as the Cz 4f electrons. The entropy increment observed from 10 to 298.15"K is 33.15 cal/(mol "K) while that calculated from the interpolated lattice curve and the deduced levels is 33.18 cal/(mol OK). The practical entropy of Tmz03at 298.15OK is calculated as 33.4 f 0.1 cal/(mol OK) by extrapolating the lattice and electronic heat capacity functions to 0°K. This extrapolation assumes that the ground states for all ions are singlets. Some support for this is provided by magnetic susceptibility data given by Brown and HubbardZNover the range 1.3 to 4.2"K. They assert that no ordering occurs in Tmz03, DyzO3, and Gd2O3. I n the case of Dyz0325 and Gdz03 28 this appears contrary to other evidence. Revaluation of N e o d y m i u m ( I I I ) Oxide Electronic Heat Capacity. The success of the foregoing treatment of cubic oxides suggests that the linear extrapolation scheme may be extended with a somewhat looser approximation to the hexagonal (A-type) oxides. The lattice heat capacity of neodymium(II1) oxide is now approximated by adjusting that of lanthanum(II1) oxide by "7 of the increment between the cubic gadolinium(II1) and lutetium(1I.I) oxides. This new lattice heat capacity for neodymium(II1) oxide is shown in Table IV, together with that derived for the other oxides treated in this paper. Until other evidence for the variation in heat capacity with atomic numbers can be obtained for A-type oxides, the value for neody-
339
mium(II1) oxide must be somewhat provisional, but better than the original estimate of using lanthanum(111) oxide without adjustment. The resulting C,I of n'd(II1) ion is given in Table I11 and shown in Figure 3 as points based at the mean temperatures of the experimental determinations on lanthanum(II1) oxide. The theoretical curve is in this instance based on the , ~ agrees spectroscopic levels of Henderson, et ~ l . and well with hhe thermal value, but trends below the data points near 350°K as a consequence of the fact that Henderson, et al.,do not report levels for the other 411s,2, 41161J. states of the ground multiplet (4111/2, Above 300"K, C,1 would have contributions from these levels which probably range from 2000 to 6000 cm-', if the spectral data of Chang30for the Kd(II1) ion in an yttrium(II1) oxide host are indicative. The practical entropy of Sdz03 at 298.15OK remains at 37.9 cal/ mol "IC) as reported earlier.3 Gibbs E'nei4gy of Formation of T h u l i u m ( I I I ) and Lutet i u m ( I I I ) Oxides. The enthalpies of formation for thulium(II1) oxide3I and lutetium(II1) oxide32 are reported from static oxygen combustion experiments leading to values of -451.4 f 1.4 and -448.9 f 1.4 kcal/mol. Holley, et a1.,33 have reviewed the heat capacity determinations of thulium and lutetium metals and found S O 2 9 8 values of 17.80 f 0.05 and 12.18 i 0.05 cal/(g-atom O K ) . The entropy derived by these authors is based on work by L o u n a ~ m a a Dreyfus, ,~~ et Lounasmaa and Su~idstrOm,~~ and by Jeiinings, et al.37 Similarly, the tabulated entropy for lutetium is based on measurements by Lounasmaa38 and Jennings, et aE.3g The entropy of Oz(g) at 298.13 'IC is taken from the tabulation of Wagman, et al.,40 and is 48.996 cal/(mol OK). From these data one obtains (27) M. Kalvius, 2. Naturfursch., 17a, 248 (1962). (28) R. E. Brown and W.M. Hubbard, U. S.Department of Commerce Clearing House, Technical Information AD 627224, 1965, p p 31-42 [cf. Chem. Abstr., 65, l6lb (1966) 1. (29) W. F. Giauque and J. W. Stout, J . Amer. Chem. Soc., 61, 1342 (1939). (30) N. C. Chang, J . Chem. Phys., 44, 4044 (1966). (31) E. J. Huber, Jr., E. L. Head, and C. E. Holley, Jr., J . Phys. Chem., 64, 379 (1960). (32) E. J. Huber, Jr., E. L. Head, and C. E. Holley, Jr., ibid., 64, 1768 (1960). (33) C. E. Holley, Jr., E. J. Huber, Jr., and F. B. Baker in "Progress in the Science and Technology of the Rare Earths," L. Eyring, Ed., Pergamon Press, London, 1968. (34) 0. V. Lounasmaa, Phys. Rev., 134A,,160(1964). (36) B. Dreyfus, B. B. Goodman, A. Lacaze, and G. Trolliet, Cumpt. Rend., 253, 1764 (1961). (36) 0. V. Lounasmaa and L. J. Sundstrom, Phys. Rev., 150, 399 (1966). (37) L. D. Jennings, E. Hill, and F. H. Spedding, J . Chem. Phys., 34, 2082 (1961). (38) 0. V. Lounasmaa, Phys. Rev., 133, 219 (1964). (39) L. D. Jennings, R. E. Miller, and F. H. Spedding, J . Chem. Phys., 33, 1849 (1960). (40) D. D. Wagman, W.H. Evans, I. Halow, J. B. Parker, S. M. Bailey, and R. H. Sohumm, U. S. National Bureau of Standards Technical Note 270-1, "Selected Values of Chemical Thermodynamic Properties," U. s. Government Printing House, Washington, D. C. 20402, 1965. Volume 73, Number d Februarg 1969
F. J. SMENTOWSKI AND GERALD R. STEVENSON
340 AGfOZgs.15 of Tm20a(c)to be -428.8 AGfOzgs.lsfor Luz03(c)to be -427.6
f
1.5 kcal/mol and 1.5 kcal/mol.
f
Acknowledgment. The authors are grateful for the partial support of the United States Atomic Energy
Commission and to Professor F. H. Spedding and the Ames Laboratory of Iowa State University for the loan of calorimetric samples of both oxides. They further acknowledge the technical assistance of Dr. John C. Trowbridge in making the measurements.
Temperature-Dependent Electron Spin Resonance Studies.
11.’
Cyclooctatetraene Anion Radical
by F. J, Smentowski and Gerald R. Stevenson Department of Chemistry, Texas A & M University, College Station, Texas 77849 (Received April $6,1968)
The cyclooctatetraene (COT) anion radical (I) has been formed by the alkali metal reduction of COT in liquid ammonia. Ion pairing affects the esr spectra of the anion radical I, influencing the line widths of the individual hyperfine splittings, the activation energy of the line-broadening process, and the spin concentration. The dependence of the hyperfine line width of the cyclooctatetraenide salts is Li+ > Na+ > K+, the reverse order of that found in ether solvents. For the COT-”3-K system, the radical(s) observed are dependent upon the ratio of COT to its dianion (11). Equilibrium constants for the disproportionation (eq 3) in liquid ammonia have been measured. Factors affecting the direction of reaction 3 are considered.
Introduction Ion pairing has been found to play a predominant role in solution Current developments hnvc h e n stimulated hy C S ~ , ” ~conduct,anceJGand opticalGstudics. Much of the esr work on ion-pairing phenomena has recently bcen reviewed.’ Studies8fe of the cyclooctatetraene (COT) anion radical (I) in
I
I1
tetrahydrofuran (THF) and 1,2-dimethoxycthane (DME) have given some insight into ion pairing on these systems. Since details of the preparation of anion radicals in liquid ammonia are now available,’O it was of interest to study the system COT-”3metal. Anion radicals of various organic substrates have been prepared by electrolytic reduction in liquid arnmonia.l1 COT has been reduced electrolytically in liquid ammonia, giving nine lines with aH = 3.28 G.”
Experimental Section Adequate safety precautions must be considered, since the esr sample tubes of these ammonia systems are at approximately 11 atm at 30”. COT was purchased from Chemical Procurement The Journal of Physical Chemistry
Laboratories, Inc. and was degassed and distilled under high vacuum before use. The anion radicals were pre(1) Part I : I?. J. Smentowski and G. R. Stevenson, J . Amer. Chem. Roc., 89, 5120 (1967). The present article is d s o part I1 of the
series Anion Radicals in Liquid Ammonia (Part I : I?, ,J. Smentowski and 0.R. Stevenson, ibid., 90, 4661 (1968)). (2) (a) E. Grunwald, Anal. Chem., 26, 1696 (1954); (b) S.Winstein, E. Clippinger, A. H. Fainberg, and G. C. Robinson, J . Amer. Chem. Soc., 7 6 , 2697 (1954); (c) S. Winstein and 0. C. Robinson, ibid., 80, 169 (1958). (3) (a) N. M. Atherton and 5. I. Weissman, J . Amer. Chem. SOC.,83, 1330 (1961); (b) P. J. Zandstra and S. I. Weissman, ibid., 84, 4408 (1962); (c) F. C. Adam and 8. I. Weissman, ibid., 80, 1518 (1958). (4) (a) A. H. Reddoch, J . Chem. Phys., 43, 225 (1965); (b) N. Hirota and R. Kreilick, J. Amer. Chem. SOC.,88, 614 (1966); (c) R. Chang and C. 8. Johnson, ibid., 88, 2238 (1966); (d) N. Hirota, ibid., 90,3603 (1968); (e) N. Hirota, R. Carraway, and W. Schook, ibid., 90, 3611 (1968); A. M. Hermann, A. Rembaum, and W.R. Carper, J . Phys. Chem., 71, 2661 (1967). (5) (a) P. Chang, R. V. Slates, and M. Sewarc, J . Phys. Chem., 70, 3180 (1966); D. N. Bhattacharyya, C. L. Lee, J. Smid, and XI, Sswarc, ibid., 69, 112 (1965); (c) C. Carvajal, K. J. Tolle, J. Smid, and M. Sswarc, J . Amer. Chem. SOC.,87, 6548 (1965). (6) (a) T. E. Hogen-Esch and J. Smid, ibid., 88, 307, 318 (1966); (b) T. E, Hogen-Esch and J. Smid, ibid., 87, 669 (1965); ( e ) J. Smid, ibid., 87, 665 (1965). (7) (a) N. Hirota, J . Phys. Chem., 71, 127 (1967); (b) M. C. R. Symons, ibid., 71, 172 (1967); ( 0 ) N. Hirota, J . Amer. Chem. Soc., 89, 32 (1967).
(8) F. J. Smentowski and G . R. Stevenson, J . Amer. Chem. Soc., 89, 6120 (1967). (9) H. L. Strauss, T. J. Kats, and G. K. Fraenkel, ibid., 85, 2360 (1963). (10) (a) F. J. Smentowski and G. R. Stevenson, ibid., 90, 4661 (1968); (b) H. J. Chen and M. Bersohn, Mol. Phy6. 13, 573 (1967). (11) (a) D. H. Levy, Ph.D. Thesis, University of California. 1965; (b) D. H. Levy and R. Myers, J. Chem. Phys. 41, 1062 (1964); 42, 3731 (1965); 43, 3063 (1965); 44, 4177 (1966).
