1277
HEATCONTENT OF KzS FROM 298 TO 1260°K containing the dimer but have been assigned to the monomer. The existence of the dimer was known to Carlson4 but he preferred to interpret the spectroscopic data on the ba,sis of a weak association in the chlorine bridge-type bonding between the Nb atoms, in which the molecule retains an approximate D3h structure. Krynauw, e2 ut.,27have used Carlson's frequencies in a vibrational analysis to derive a set of force constants which they considered satisfactory. However, since the frequencies were not measured for the gas and because of the difficulty of these measurements, some low-lying frequencies may have been missed. Since there is still some uncertainty about the value for Xo298(s),we have not calculated the absolute en-
tropies or free energy functions at temperatures above 298°K from the data in Tables I1 and III.32 (32) NOTE ADDEDI N PROOF.After this report was submitted, Werder, et al. (R. D. Werder, R. A. Frey, and Hs. H. Gunthard, J . Chem. Phgs., 47, 4159 (1967)), published the results of spectroscopic studies of niobium pentachloride in the solid state, in organic solvents, and in low-temperature matrices. Frequency assignments for both the monomer and dimer were made. Their frequency assignments are somewhat different from those of Gaunt, et al.,3 and Krynauw, et aZ.,27 and lead to a value of So2ga(gas)for the monomer of 95.82 eu instead of the value we calculated above (91.9 eu) The assignments made by Werder, et al., are clearly to be preferred since they were able to distinguish between monomer and dimer spectra by means of the matrix isolation technique. Using Sozss(gas) = 95.82 and AS'm(sub1) = 45.40, we calculate S02g8(solid) = 50.42 eu (instead of 46.5), which is in agreement with the Latimer estimate. We think this value is sufficiently well substantiated that reliable values of free energy functions can be calculated from it and the data in Tables I1 and 111.
Diffuse Transition and Melting in Fluorite and Anti-Fluorite Type of Compounds: Heat Content of Potassium Sulfide from 298 to 1260"Kl by A. S. Dworkin and M. A. Bredig Chemistrv Division, Oak Ridge hrational Laboratory, Oak Ridge, Tennessee
(Received September $6,1967)
The heat content and entropy of KzS from 298 to 1260°K have been measured by meanr of a copper block drop calorimeter. K2S was found to have the low entropy of fusion of 3.16 eu mole-l, similar to those in CaF2 and SrC12 with which it is anti-isotypic. As in these latter crystals, this is connected with the occurrence of a diffuse transition, with a heat capacity maximum of 45 cal deg-l mole+ at about 780" but extending from about 550" to the melting point at 948O, and involving an entropy change of 4 eu mole+. It is suggested that the occurrence of a diffuse transition is a general characteristic of the substances AB2 of fluorite and anti-fluorite types of crystal structure. It is attributable to the gradual distribution of the 13 ions, with rising temperature, over both the octahedrally and tetrahedrally coordinated lattice positions. This leads to the high rate of diffusion and electrical mobility of the R ions. Heat content data found in the literature for such fluorite type crystals as UOZ,ThOz, and Na20 indicate that diffuse transitions also occur in these compounds although more information is needed in these cases.
Introduction Through our observations on the anomalous heat content of solid strontium dichloride2 which is isotypic in structure with calcium difluoride, we have become interested quite generally in the thermal and structural behavior of the substances possessing either the fluorite (MX2) or the anti-fluorite (MzY) type of structure. The former group (MXJ includes certain halides of divalent metals and oxides of tetravalent metals, such as CaF2 and SrC12,and ZrOz, Tho2, and UOz, while the group M,Y consists mainly of the oxides and other chalcogenides of the alkali metalsa3 The present calorimetric study of potassium sulfide was further motivated, as was the earlier one of strontium chloride, by the need for knowledge of the entropy of fusion in
attempts to extract from the fusion equilibria some information about the nature of the solution of the metal in the molten c ~ m p o u n d . ~
Experimental Section The copper block drop calorimeter used for the present heat content measurements and the experimental procedure were the same as described in detail (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) (a) A . S. Dworkin and M. A. Bredig, J . Phys. Chem., 67, 697 (1963); (b) A. S. Dworkin and M .A. Bredig, J . Chem. Eng. Data, 8,
416 (1963). (3) Cf., e.g., R. W. G. Wykoff, "Crystal Structures," Vol. 1, Interscience Publishers, Inc., New York, N. Y . , 1963, p 239 ff. (4) A . S. Dworkin and M.A. Bredig, J . Phys. Chem., 71, 764 (1967).
Volume 72,Number 4
April 1968
A. S. DWORKIN AND M. A. BREDIG
1278 previously.6 The preparation of the K2S and its analysis (better than 99% KZS) have also been described else~here.~ The defined calorie is equal to 4.184 absolute joules, and the molecular weight of K2S is 110.27.
Table I : Measured Heat Contents of K2S Run no.
23
Results and Discussion The measured heat contents of KzS are given in Table I. The "run number" indicates the order in which the measurements were made. The following equations were obtained by the method of least squares for HT - H298.1b (cal mole-').
HT -
Hzg8.15
- Hzg8.16
=
19 20 21 24 22 25 9 29 10 11 26 12 13 27 14 30 15 16 28 17 4
+ 16.78T +
= -5230
2.370 X 10-aT2(*0.5%) HT
18
(298420°K)
+ 34.02T(h0.05%)
-18,370
(1100-1 22 1OK) AHfusion =
HT -
H298.16
=
* 40 cal mole-l
3860 -2440
(1221°K)
+ 24.13T(k0.05%) (1221-1260°K)
Figure 1illustrates the occurrence of a diffuse transition beginning at about 820°K and continuing to the melting point at 1221°K after showing a sharp specific heat
5 6 31 7 8 32
q . 2
0
200
400
600
800
1000
1200
4400
3 33 2
35
1 a
HT T,OK
- H288.16,
koa1 mole-'
Solid 384.4 452.5 516.3 575.9 634.8 667.8 686,6 717.4 741.6 745.7 789.3 835.8 864.4 882.5 929.5 959.6 975.9 1000.7 1016.9 1045.2 1054.6 1073,9 1103.8 1126.3 1150.2 1163.7 1172.6 1194,9 1208.3
15.59 16.81 17.24 18,09 19.19 19.93 20.76 21.22 21.50 22,29 22,91"
Liquid 1228.7 1237.5 1243.7 1260.4
27.20 27.43 27.56 27.97
1.55 2.84 4.03 5.22 6.39 7.08 7.44 8.03 8.44 8.61 9.46 10,47 11.13 11.59 12.73 13.56 14,07 15,00
Premelting.
maximum at about 1050°K. The smoothed heat content values in the temperature range 820-1100°K which appear in Table I1 were obtained from the curve since no equation was used for the temperature range of transition. The entropy values in Table I1 were calculated from the heat content data by the method suggested by Kelleya6 The premelting effect evident in H, - HZe8at 1208.3"K is small because the suspected impurities (KzO, K) are likely to be soluble in solid K,S.4 The diffuse transition as well as the low heat of fusion (3.86 kcal mole-l at 1221°K corresponding to an entropy of 3.16 eu mole-') is analogous to that in SrClgZband CaFq to which K2S is structurally antiisotypic. The specific heat maximum of about 45 cal 400
600
800
1000 "K
1200
4400
Figure 1. Heat content and molar heat capacity of K2S compared with SrC12, CaF2, and MgF2. The Journal of Physical Chemistry
1600
1
(5) A. S. Dworkin and M.A . Bredig, J . Phya. Chem., 64, 269 (1960). (6) K. K. Kelley, U. S. Bureau of Mines Bulletin 584, U. S.Government Printing Office, WaBhington, D. C., 1960, p 8. (7) B. F. Naylor, J . A m . Chem. SOC.,67, 150 (1945).
1279
HEATCONTENIT OF I12SFROM 298 TO 1260°K
Table I1 : Smoothed Values of Heat Content and Ent'ropy for :K,S
T ,OK
400 500 600 700 800 850 900 950 1000 1050 1100 1150 1200 1221 (S) 1221 (L) 1250
-
kea1 mole-1
ST 8288.15, cal deg-1 mole-'
1.86 3.75 5.69 7.67 9.71 10.80 11.97 13.27 14.92 17.02 19.05 20.76 22.45 23.16 27.02 27.72
5.37 9.54 13.08 16.13 18.85 20.17 21.51 22.92 24.61 26.65 28.55 30,07 31.50 32.09 35.25 35.82
HT
- H298.11,
deg-' mole-' at about 1050°K corresponds to those found earlier in CaF2 and SrC12 at 1423 and 993°K (Figure 1). The transition is believed to reflect the gradual disordering of the potassium cation sublattice analogous to the disordering of the anion sublattice observed by X-ray diffraction in SrClzSand also assumed in CaF2.9 I n all these cases, the B ions which are the anions in the fluorite type and the cations in the antifluorite type of compounds AB2 become distributed increasingly with increasing temperature over two sets of positions between the A ions, the latter being arranged on a face-centered cubic lattice. I n the first set of positions numbering eight per unit cell, the B ions (eight per unit cell) are tetrahedrally surrounded by four A ions. This is the set occupied by the B ions at low temperature. I n the other set of positions of which there are also eight per unit cell, half of them, however, occupied permanently by the A ions, the B ions are octahedrally surrounded by six A ions. At the melting point the eight B ions of the unit cell may be assumed to be randomly distributed and freely moving over the total of 12 positions of both these sets of B ion positions. The high hea,t capacity (C, = 34 cal deg-l mole-') in the temperature region 1100-1221 OK, which compares with the almost equally high values of 28.5 for SrClz and 30 for CaF2 below their melting points, indicates that the transition, Le., the particular process of disordering, continues all the way up to the melting point. For comparison, the heat content of MgF, which has the tetragonal rutile rather than the cubic fluorite type of structure is included in Figure 1 as an example for "normal" behavior (C,(solid) = 21 cal deg-l mole-'). I n this case, all the disordering occurs on melting (ALL, = 9.1 eu mole-'). To estimate the entropy involved in the K,S tran-
sition, the least-squares curve for the heat content below the transition was extrapolated to the melting point. The difference between the entropy calculated from the measured curve and that from the extrapolated curve is about 4 eu mole-'. This value is a good estimate of the entropy of transition and accounts for the unusually low value for the entropy of fusion. The entropy of transition for SrC12 calculated in the above manner is 2.3 eu mole-'. Our earlier valuezbof 1.65 eu mole-' was a rough estimate obtained by treating the transition as if itJwere first order and extrapolating the heat contents to the temperature of maximum heat capacity. It is interesting to note that thermal analysis (both cooling and heating) runs on KzS failed to detect the diffuse transition even though the apparatus was found by us to be capable of detecting isothermal transition heats of less than a few hundred calories per mole. Thermal analysis runs for SrClz and CaF2 gave the same results as with KzS, Le., no transition halt. Thermal analysis, then, may be used in conjunction with heat content measurements to aid in distinguishing between a first-order transition and a diffuse transition with a sharp heat capacity maximum. This test is pertinent to the case of SrC12where a first-order transition (AHt, = 650 cal/mole) has been claimed.'O For CaF2, an isothermal heat of transition of 1140 cal/mole is reported'," although the original paper' clearly states that "The heat content curve shows no discernible discontinuity," and the heat of transition was obtained by treating the transition as if it were first order. No change in over-all symmetry from the low-temperature face-centered cubic structure to a "cubic" one as has been suggested'o is indicated for the fluorite and anti-fluorite type of substances AB2. The transition is wholly attributable to the disordering of the B ions, with the A ions retaining the face-centered-cubic arrangement. The process is very likely to occur in dioxides of this structure type also, e. g. in U02 or ThOz, and has been discussed by h(IObi~s~ in connection with ionic (02-)conduction in ZrOz in terms of the geometry of the lattice and the relative ease of escape of the two kinds of ions through their first shells of coordination of oppositely charged neighbors. The heat contents of U02 and Tho2 have been reported', but only in the solid up to temperatures well below the melting points. The heat content and heat capacity curves shown in Figure 2 indicate the beginning of what may be the diffuse transitions in these two compounds. The heat capacity increases after (8) U. Croatto and M. Bruno, Gam. Chim. Ital., 76, 246 (1946) (9) H. H. Mobius, 2. Chem., 2, 100 (1962). (10) G. J. Jan?;, F. J. Kelly, and J. F. I'erano, Trans. Faradau Soc., 59, 2718 (1963).
(11) See ref 6, p 39. (12) T. G. Godfrey, J. A. Wooley, and J. M. Leitnaker, ORNL-TM1596, 1966. Volume '73, Number 4
April 1968
A. S. DWORKIN AND R4. A. BREDIG
1280
9
"C 600 1000 1400 i8CO 2200 2600 I ' I ' I ' I ' I ' I
1
3000 3400 I ' 1 1 ' 1
P 400
800
1200
1600
2000 2400 'K
2800
3200
3600
4000
Figure 2.
Heitt content and molar heat capacity of NatO, UO,,and Thoz.
remaining constant over a rather large temperature range. The increase is much more rapid for UO, as the measurements extend much closer to the melting point than do those for Tho2. I n neither case, however, has the temperature of maximum heat capacity been reached and further measurements will be necessary to demonstrate whether or not these transitions are similar to those shown in Figure 1. Of the anti-fluorite type compounds not already discussed, there are some heat content data in the literature for solid NazS,13 Naz0,14and LiZO.l5 Unfortunately, the presence of a rather large impurity (4.2%, either wt or mole?) in the SazS caused an obvious premelting effect obscuring the indications of a diffuse transition beginning at about lOOO"K, about 450" below the melting point. The heat content and heat capacity curves for NazO shown in Figure 2 were derived directly from the measurements of Grimley and R/Iargrave14rather than from their equations. The equations give a much poorer fit (e.g., -13% in the heat content at 1100°K) than the data seem to justify and obscure the fact that C, turns up sharply at about 800°K after having remained essentially constant for more than 300". By analogy with the isomorphous I
