M-1921
J. Chem. Therm&namics
1986, 18,381-401
Silver(l)
sulfide:
Heat capacity
thermodynamic
transitions
a
FREDRIK
Ag,S
from 5 to 1000 K,
properties,
and
GRONVOLD
Department of Chemistry. University of Oslo.
Blindern, 0315 Oslo 3, Norway,
and EDGAR
F. WESTRUM,
JR.
Department of Chemistry, University of Michigan,
Ann Arbor, Michigan 48109, U.S.A.
(Received 19 August 198s)
The heat capacity of Ag,S has been measured by adiabatic-shield calorimetry from 5 to
1000 K. The heat capacity increases regularly up to about 445 K where the pre-transitional
contribution causes rapidly rising values. The a-to-p transition of Ag,S occurs in the range
449.3 to 451.3 K, depending upon previous history of the sample. The enthalpy of transition
A,,, H, = (4058 k 26) J. mol- I. A slightly decreasing heat capacity is observed for P-Ag,S from
88.1 .l.K-‘,rnol-’
at 460 K to 85.0J~K-‘~mo1-1
at 850K with a minimum of
84.6 J. K ’ mol- ’ at 750 K. The transition of P-Ag,S to y-Ag,S occurs at about 865 K with
Atr6H, = (784 + 5) J. mol- I, Thermodynamic functions have been evaluated and the values of
c 8.m, {Sm(‘F)-Sm(0)), and -{C:(T)-HL(O)j/T
at 298.15 K are 75.31, 142.89, 85.43. and at
loo0 K are 80.57, 253.28, 172.77 J. K - ’ . mol- ‘, respectively. No signs of further transitions
were found, either in the stoichiometric compound, or in a sample with overall composition
Ag,S,,,,,,. Thus, the present work does not support the hypothesis of Perrott and Fletcher
concerning partial disordering of stoichiometric Ag,S around 600 K as opposed to complete
disordering around 450 K in the presence of excess silver or sulfur. Subtraction of the
estimated lattice heat capacity at constant pressure leaves a large transitional heat capacity for
P-Ag,S above 450 K. It is about 11 J K- ’ mol- ’ at 500 K and decreases gradually to about
6 J. K- ’ mol-’ at 850 K. Its origin is discussed.
1. Introduction
The only well characterized solid compound of silver and sulfur is silver(I)
sulfide: Ag,S. It exists under ordinary pressure in three well-defined crystalline
modifications,
usually designated CZ-, b-, and y-Ag,S, with a-Ag,S as the lowtemperature phase. The heat capacity of these silver(I) sulfide phases has been
” This research was supported in part by the Structural Chemistry and Chemical Thermodynamics
Program of the Division of Chemistry of the National Science Foundation under Grant No.
CHE-7710049.
OO?l-9614/86/040381+21
%02.00/O
0 1986 Academic Press Inc. (London) LimIted
382
F. GR0NVOLD
AND
E. F. WESTRUM.
JR
studied repeatedly in recent years, partly with surprising outcome. The results for
ct-Ag,S by Gultyaev and Petrov (I) in the region 80 to 300 K were superseded by
those of higher accuracy from Walsh et al.“’ over the region 10 to 300 K.
Overlapping results were obtained by Jost and KubaschewskiC3’ in the range 200 to
300 K, and the regularly rising trend continued up to 370 K. With further rise in
temperature, an increasing defect-formation contribution to the heat capacity of
cl-Ag,S was observed. The actual a-to-0 transition occurs at about 450 K and the
heat capacity of P-Ag,S was found to decrease from 90 to 88 J. K-l . malli
over
the range 460 to 620 K.
In contrast to the latter result, Perrott and FletcherC4’ observed a rising heat
capacity for stoichiometric P-Ag,S in the same temperature range and a rapid fall to
a constant value of about 92 J. K- ’ . mol- ’ above 620 K. This was interpreted in
terms of structural lattice disordering of the silver atoms. Strangely enough, the
effect occurred only for a stoichiometric sample, while two other samples with an
excess of 0.01 in the mole fraction of either Ag or S failed to show the k-type
transition in the 600 K region. The enthalpy increment of the a-to-p transition was,
however, found to be correspondingly larger in the non-stoichiometric
samples:
A,,,H, = (6.5kO.4) kJ. mol-‘, than in the stoichiometric one: A1,,H, = (4.OkO.4)
kJ.mol-‘.
Perrott and Fletcher’sC4’ claim that their results were consistent with partial
disordering of stoichiometric Ag,S above the a-to-l3 transition temperature was a
consequence of their observation of a monotonically
increasing-and
rather
irreproducible-heat
capacity, culminating in an additional transition at 620 K, in
contrast to the low and essentially constant heat capacities above 450 K for samples
annealed in the presence of excess silver or sulfur.
The authors have repeated and extended the heat-capacity measurements on a
well-characterized silver(I) sulfide sample in order to ascertain whether the peculiar
behavior reported by Perrott and Fletcher “) for stoichiometric
Ag,S could be
confirmed. A sample with some excess of sulfur was also prepared and measured for
comparison.
Information
about compositional differences and extension of the homogeneity
ranges of the three silver(I) sulfide phases is plentiful. Thus, Kracek”’ observed a
1.5 K shift in the cr-to-8 transition temperature from the silver-rich to the sulfur-rich
side. Later studies by Schmalzried and ReyeC6-s’ have shown that for cl-Ag,+,S the
value of 6 is in the range +6 x 10s6 just below the transition temperature (450 K).
For l3-Ag,+,S the variability
is much larger. and is already in the range
0.0001 < 6 < 0.002 close to the same temperature. The 40 K shift for the P-to-y
transition of Ag2+* S around 870 K with the sulfur content, reported by Kracek,ls’
was related by RauC9) to a compositional variation of P-Ag2 +,S from 6 = + 0.005 to
-0.015 in this temperature range. An even larger composition range was derived for
y-Ag2+dS by Rau (9) (c?,,,~,,= -0.020 at 1017 K, S,,, = 0.015 at 1081 K).
Furthermore, the energetics of the transitions need to be related to the structural
changes in the silver(I) sulfides. According to Frueh”“’ and Sadanaga and Sueno”‘)
the monoclinic structure of a-Ag,S, achantite, can be described as a slightly
distorted body-centered cubic structure with two types of silver atoms in equal
HEAT
CAPACITY
OF Ag,S
383
amounts, occupying octahedral and tetrahedral interstices between the sulfur atoms.
The coordination polyhedra are considerably distorted.
The sulfur-atom arrangement is practically unchanged in the transition to bodycentered cubic l%Ag,S. In the early structural study by Rahlfs(12) the silver ions were
assumed to be randomly distributed over 6 octahedral, 12 tetrahedral, and 24
triangular interstices. According to the single-crystal neutron-diffraction
study by
Cava et a1.‘i3’ in the range 460 to 600 K, the silver ions are confined to the
tetrahedral interstices at 530 K and above, while at temperatures approaching the
lower limit for l%Ag,S, about l/5 of the silver atoms are located in the octahedral
interstices. In the transition of l3-Ag,S to y-Ag,S the structure changes from bodycentered to face-centered cubic according to Djurle’14’ and Frueh.“” and likewise
according to Skinner,‘16’ who inferred that the structure was identical to the f.c.c.
form of Cu,S.
Phenomenological
theories applicable to the transition of a-Ag,S to the fast-ion
conductor l3-Ag,S have been developed in terms of the mean-field approximation
by
Gurevich and Kharkats,(“) and of the single-valued dependence of defect formation
energy and entropy on the crystal volume by Schmalzried.(18’ The transitional heat
capacity of a-Ag,S and l%Ag,S are re-evaluated and compared with these theories.
2. Experimental
SAMPLE
PREPARATION
Silver(I) sulfide was synthesized from high-purity silver and sulfur. The >99.99
mass per cent purity silver shot was from the American Smelting and Refining
Company, N.J.. U.S.A. It was reported to contain the following impurities (mass
fraction x 106): Bi, < 1; Cu. 8; Fe, 3; Pb, < 1. No other elements were detected. The
>99.999 mass per cent purity sulfur from the same source was reported to contain
mass fractions less than 1 x lO-‘j of Cl and Na, while no Ag, Al, Bi, Ca, Cd, Cr. Cu,
Fe, In, Mg, Mn, Ni, Pb, Sb, Si. Sn, or Zn were detected by standard spectrographic
methods.
The mixture of the elements was heated in an evacuated silica-glass tube from 360
to 480 K over a period of 6 d, and was afterwards kept at 590, 670, and 770 K for 3,
1, and 1 d, respectively. It was then cooled to 300 K in the furnace. Duplicate silver
analyses by hydrogen reduction of the shiny black sulfide at 1100 K gave 87.05 and
87.03 mass per cent of Ag (theoretical: 87.06) after a slight adjustment for silver
evaporation.
The stoichiometry
of the sample was changed after completion
of the
measurements by adding 1.074 g of sulfur to 157.80 g of stoichiometric Ag,S in a
sample container of fused silica. The sample was heated at 620 K for 24 h in
sealed condition and then cooled with the furnace.
X-ray photographs of the Ag,S-sample were taken in a Guinier-type camera of
80 mm diameter. Cu (Kcr,) radiation was used with KC1 as a calibration substance
for which a(293 K) = 629.19 pm. (19) The structure of a-Ag,S is monoclinic, and the
orientation by Sadanaga and Sueno (il) is chosen here as it facilitates comparison
with the cubic high-temperature
structure. The orientation corresponds to the
384
F. GRBNVOLD
AND
E. F. WESTRUM,
JR.
standard setting of the space group C&, (P2,/c). while Ramsdell’20’ chose B2,/c and
Frueh”” chose P2,/n. The derived cell dimensions are (the figures in parentheses
indicate one standard deviation in the last digit): a = 423.1(l), b = 692.7(l),
in good agreement with earlier findings by
c = 953.2(2) pm, fl = 125.65(l)“,
Djurle:(r4’ a = 422.5, b = 692.5, c = 953.1 pm, fl = 125.59”, by Frueh:“” a = 423,
b = 691, c = 953 pm, p = 125.52”. by Swanson et u/.:‘~” a = 422.9, b = 693.1,
c = 952.9 pm, p = 125.56”, and by Sadanaga and Sueno:@’ a = 423.1, b = 693.0,
c = 952.6 pm, /? = 125.48”. Only one very weak line at sin28 = 0.10677 on the
X-ray photograph remained unidentified in the range up to sin2fI = 0.28. The lattice
constants of Ag2S,,,,26 were found to be equal to those of Ag,S within the limits of
error.
CALORIMETRIC
TECHNIQUE
5 to 350 K, University of Michigan. Heat-capacity
measurements were made in the
Mark (II) adiabatic cryostat, which has been described previously.‘22’ The sample
was contained in a gold-plated copper calorimeter (laboratory designation W-54)
which incorporated a gold-gasketed seal and gold-plated copper vanes to enhance
conduction. The calorimeter had a mass of 42 g and an internal volume of 80 cm3.
To facilitate rapid thermal equilibration.
a small amount of helium gas was
introduced. The temperature of the calorimeter was measured with a platinum
capsule-type 25 fi (nominal) resistance thermometer (laboratory designation A-5)
inserted into a re-entrant well in the calorimeter.
The sample was loaded into the calorimeter under an atmosphere of nitrogen in a
dry-box. The stainless-steel vessel containing the calorimeter was connected to a
high-vacuum line and after evacuation a small amount of helium gas was admitted
(2.5 kPa at 300 K). The calorimeter was then sealed, placed in the cryostat, and
cooled.
300 to 1000 K, Unioersity of Oslo. The calorimetric
apparatus and measuring
heated and
techniques have been described. (23’ The calorimeter was intermittently
surrounded by electrically heated and electronically controlled adiabatic shields.
The substance was enclosed in an evacuated and sealed silica-glass tube of about
50 cm3 volume, tightly fitted into the silver calorimeter. A central well in the tube
served for the heater and platinum resistance thermometer.
Calibrations. The platinum-resistance
thermometer
for the low-temperature
calorimeter was calibrated by the U.S. National Bureau of Standards, and that for
the high-temperature calorimeter locally, at the ice, steam, tin, zinc, and antimony
points. Temperatures are judged to correspond to IPTS-68 within 0.03 K from 5 to
300 K and within 0.05 K between this temperature and 900 K. The uncertainty rises
to 0.2 K at 1000 K. Resistance, energy, and.mass were measured with reference to
instruments calibrated by the U.S. National
Bureau of Standards. The heat
capacities of the empty calorimeters were determined in separate series of
experiments. The heat capacity of the sample was about 98 per cent of the total in
HEAT
CAPACITY
385
OF Ag2S
the low-temperature calorimeter at 10 K, 83 per cent at 50 K. and 71 per cent above
100 K, and about 40 per cent in the high-temperature calorimeter.
Small corrections were applied for temperature excursions of the shields from the
calorimeter temperature and for “zero drift” of the calorimeter temperature. Further
small corrections were applied for differences in amounts of helium gas and
Apiezon-T grease for the low-temperature calorimeter and for differences in mass of
the silica-glass containers for the high-temperature
calorimeter. The mass of Ag,S
sample used in the calorimeters was about 160 g.
3. Results
The experimental heat capacities for the low- and high-temperature ranges are given
in table 1 and the transitional enthalpy determinations are summarized in table 2.
Since the heat capacities are listed in chronological
sequence, the temperature
increments employed in the determinations
may usually be inferred from the
temperature differences between adjacent determinations.
The results are shown
together with some earlier low-temperature results in figure 1, while earlier results at
higher temperatures are incorporated in figure 2.
T/K
300
400
500
800
900
loo0
P
40- /i/--20 -
0
0
FIGURE
+ , Gultyaev
I
50
I
I
100
150
1. Heat capacity
of Ag,S. 0.
and Petrov;”
n . Walsh et al.“’
20
10
0
I
200
I
250
- 0
T/K
Present
results
U of M;
0.
Present
results,
U of 0:
TABLE
gJ
cl?,,
K
J.K-‘.mol-’
University
145.66
150.29
155.69
161.02
166.29
144.72
152.43
160.18
168.04
<T,
K
Series I
Series II
427.62
82.92
434.06
85.81
440.44
87.12
AH Detn. D
457.45
88.32
69.099
69.894
70.592
71.274
71.843
72.408
72.952
73.438
74.166
Series III
4.951
5.457
6.151
6.867
7.709
8.699
9.895
11.155
12.378
0.724
0.971
1.431
1.946
2.711
3.728
5.146
6.619
8.205
Ag,S,
<T,
K
= 247.80
and of Ag2.0526S
cp.,
J.K-‘.mol
g. mol-
13.642
14.997
16.553
18.345
20.289
22.414
24.672
27.049
29.591
33.031
35.830
38.898
42.305
46.468
51.437
56.787
58.282
64.671
71.270
75.032
CT)
K
C,.,
J.K-‘~mol-’
r
9.958
11.845
13.870
16.180
18.506
20.841
23.414
25.573
27.769
30.476
32.401
34.275
36.116
38.204
40.413
42.555
44.011
45.526
47.760
49.020
82.625
52.103
89.886
53.329
99.207
56.890
110.69
59.132
121.59
61.191
132.37
63.024
143.20
64.567
AH Detn. A
AH Detn. B
276.19
74.203
285.82
74.793
295.71
75.212
306.02
75.659
316.35
76.111
326.71
76.626
337.42
77.312
346.18
77.224
Series IV
303.26
75.63
318.40
76.23
333.58
76.59
348.72
77.34
363.81
78.09
378.85
78.96
390.33
79.98
405.30
80.88
420.13
82.53
434.94
84.96
444.15
86.76
AH Detn. F
456.02
88.08
459.72
87.69
Series V
430.07
83.91
439.20
85.44
442.83
85.83
446.46
87.33
AH Detn. G
455.13
88.38
Series VI
Series III
441.24
85.41
442.68
86.04
444.11
87.00
445.52
89.28
446.94
90.51
AH Detn. E
450.92
88.32
452.32
88.44
453.12
88.23
sulfide.
c,.,
M(Ag,S)
187.25
197.78
208.19
218.50
228.75
238.9 1
248.98
258.98
273.91
of Oslo
319.94
76.41
333.23
76.98
346.46
77.73
359.63
78.36
372.74
78.87
385.81
79.56
398.84
80.28
411.81
81.66
424.72
83.10
437.53
85.77
AH Detn. C
481.05
87.55
493.88
87.42
506.75
87.36
of silver(I)
J,K-‘.mol-’
of Michigan
Series J
64.848
64.823
66.078
66.659
67.182
64.743
64.865
66.551
67.392
Series 11
109.71
58.969
117.48
60.47 1
127.1 I
62.174
137.15
63.710
147.45
65.065
155.84
66.082
165.79
67.166
176.60
68.191
University
1. Heat capacity
436.37
85. f I
443.64
86.73
AH Detn. H
455.25
87.42
458.89
87.99
Series VII
437.46
85.38
444.37
87.09
AH Detn. I
Series VIII
444.25
86.88
AH Detn. J
453.27
88.20
456.85
88.02
460.42
88.23
467.00
88.25
Series IX
504.26
515.53
526.88
538.08
549.52
561.01
572.54
584.13
595.76
607.48
619.28
631.13
643.05
655.06
666.59
678.68
690.87
703.12
7 15.43
727.80
740.23
87.36
86.85
86.64
86.70
86.82
86.66
86.61
86.40
86.31
85.86
85.35
85.50
85.26
84.99
85.32
85.20
84.75
84.69
84.90
84.90
84.84
Series X
788.18
84.66
801.11
84.78
814.08
84.60
827.07
85.08
840.04
84.78
853.03
85.08
AH Detn. K
875.67
82.98
888.96
81.12
902.39
80.43
915.92
79.86
929.58
79.74
945.22
80.22
959.00
79.77
972.85
79.98
986.81
80.31
1000.90
80.58
810.90
823.84
836.66
Series XI
84.54
84.69
84.90
AH Detn. L
885.25
80.82
899.02
80.67
AH Detn. M
AH Detn. N
Series
747.00
159.24
771.54
783.88
XII
84.54
84.51
84.24
R4.69
HEAT
CAPACITY
TABLE
CT)
K
University
c,.,
J.K-‘.mol-’
K
of Oslo
Series I
467.22
90.76
477.95
90.22
488.72
499.54
510.40
521.32
532.30
543.34
(0
90.21
89.96
89.65
89.22
88.90
88.68
l--continued
c,,rn
(0
J.K-i.mol-’
M(Ag2S,,0526)
554.43
565.56
88.61
88.24
576.92
588.19
599.40
611.04
622.78
Series II
87.65
86.88
87.08
86.75
87.11
387
OF Ag,S
K
= 249.48
634.52
646.30
C,,,
J.K-*.mol-’
g. mol-
(0
K
c,.m
J,K-‘.mol-’
’
87.03
86.54
Series III
85.13
86.86
87.51
AH Detn. 0
454.94
90.88
424.30
435.73
443.35
458.74
462.55
466.37
91.58
90.26
90.38
Series IV *
384.76
388.49
392.22
” Heat capacities adjusted for the presence of 0.047 mol of S, but not for its enthalpy
’ AT = 3.5255 K; A,,.H/Ar,,H,
= 81.3 J/1717 J,mol-’
4 0.0474 mol of S.
19.44
102.8 *
80.08
of fusion.
10 OotJ
1000
loo
T/K
FIGURE
2. Heat capacity
of Ag,S.
0, Present
results U of M; 0, present results U of 0;
+. Gultyaev
and Petrov;“)
n , Walsh et a/.; (”
., Jost and Kubaschewski;r3i
@---a.
Perrott
and
Fletcher’4’
with spread indicated
by I; - - -. Thompson
and Flengas;‘30’
-. -, estimated
nontransitional
lattice heat capacity at constant pressure.
388
F. GRBNVOLD
TABLE
CT>
AT
K
K
transition
AH Detn.
E. F. WESTRUM,
2. Fractional
C P.m
J.Km’.mo]-l
enthalpies
C,,,(n.t.)
= 247.80
JR.
of transition
Aklh
min
J.K-‘.mo]-’
M(Ag,S)
a-to-p
AND
AH,, rrc
J-mol-’
T find,
K
g.moI-’
of Ag,S
C
446.609
449.745
456.068
5.418
0.855
11.790
361.2
2917
101.9
87.4
88.0
88.2
80
65
64
1483
2418
162
449.318
450.173
461.963
4063
AH Detn.
D
446.215
449.100
449.417
451.872
5.201
0.568
0.066
4.844
123.2
2111
38050
138.7
87.3
88.0
88.1
88.3
259
164
416
343
186
1149
2505
244
448.816
449.384
449.450
450.294
4084
AH Detn.
E
448.246
449.052
449.271
449.300
449.332
449.366
449.400
449.443
449.493
449.552
449.602
449.633
449.672
449.717
449.991
1.2028
0.4100
0.0280
0.0285
0.0363
0.03 11
0.037 I
0.0503
0.0492
0.0674
0.0327
0.0296
0.0487
0.0793
0.4314
126.9
635
10870
10700
8337
9927
8085
6018
6162
4464
9273
9645
6180
3723
582.3
87.8
87.9
88.0
88.0
88.0
88.0
88.0
88.0
88.0
88.1
88.1
88.1
88.1
88.1
88.’
48
156
158
158
149
301
158
159
163
81
165
73
166
209
I20
47
224
302
302
299
306
297
298
299
295
300
283
297
288
213
448.847
449.257
449.285
449.314
449.350
449.381
449.418
449.469
449.518
449.585
449.618
449.648
449.696
449.775
450.207
4050
AH Detn.
F
447.548
449.328
449.929
450.530
450.775
450.983
452.673
AH Detn.
3.108
0.453
0.750
0.453
0.036
0.381
2.999
126.1
1932
919
1583
26140
1935
140.9
87.6
88.0
88.2
88.3
88.4
88.4
88.4
66
1156
163
120
1255
181
58
120
835
623
677
938
704
157
4054
449.102
449.554
450.304
450.757
450.793
451.174
453.173
87.9
88.0
88.1
88.35
1136
130
156
319
510
691
2837
29
4067
449.132
449.340
449.946
453.354
G
448.697
449.236
449.643
45 1.650
0.869
0.208
0.606
3.408
674.3
3411
4770
96.95
TABLE
(T)
AT
K
K
AH Detn.
Cn m
J.K-‘.mol-l
2--continued
C,.,(n.t.)
J.K-‘.moj-’
At\tah
._
min
I AH, erc
J.mol-’
128
157
936
55
2535
737
743
22
T rim,
K
H
448.354
449.472
449.711
451.666
2.152
0.084
0.395
3.514
1266
8865
1970
94.47
87.8
88.0
88.1
88.35
449.430
449.514
449.909
453.423
4037
AH Detn.
I
448.354
449.570
450.314
1.829
0.160
1.330
1505
4635
629.4
87.8
88.1
88.3
107
148
42
2592
728
720
449.490
449.650
450.979
4040
AH Detn.
J
441.485
449.139
449.541
449.950
450.825
2.866
0.438
0.363
0.454
1.307
149.6
1571
3966
3150
448.2
87.6
88.0
88.1
88.2
88.4
38
175
130
68
85
149
650
1408
1390
470
448.91X
449.355
449.71X
450.17’
45 I -479
4067
4058 i: 26
P-to-y
transition
AH Detn.
853.035
864.302
AH Detn.
of Ag2S
K
12.9983
9.5351
85.08
166.0
84.98
84.8
41
49
4
774
-778
859.534
X69.06’,
12.7196
9.4412
13.1591
85.38
165.6
85.00
84.96
85.0
83.45
73
73
67
8
761
20
855.807
865.24X
X78.407
L
849.417
860.527
871.828
789
AH Detn.
M
863.127
864.184
864.43 I
865.08 1
866.2 19
867.555
868.917
AH Detn.
1.9312
0.1764
0.3173
0.9815
1.2949
1.3774
I .3474
159.1
1662
863
186.1
93.15
86.37
84.72
85.0
85.0
85.0
85.0
84.65
84.40
84.00
27
37
71
33
53
33
54
144
278
247
99
11
3
I
-783
864.096
864.273
864.590
865.571
866.867
868.244
869.591
9.3285
0.533 1
0.1725
0.4386
1.1035
1.3619
1.4222
91.68
450.6
1525
551.7
142.8
93.72
84.42
84.98
85.0
85.0
85.0
85.0
84.55
84.5
32
39
36
44
35
29
‘6
63
195
248
705
64
12
0
863.552
864.086
864.258
864.696
865.800
X67.162
X6X.584
N
858.888
863.819
864.171
864.477
865.248
866.48 1
867.874
787
A,r.Hm:
784,5
390
F. GRBNVOLD
AND
TABLE
CT)
AT
K
J,K-l,mo~-l
.transition
AH Detn.
447.126
450.068
451.132
451.174
451.241
452.164
in A@,
0526 sample
At slab
min
C,,,(n.t.)
J,K-l,mol-'
M(Ag,S,
a-to-p
JR.
2-continued
c P. m
~__
K
~-.
E. F. WESTRUM,
o,,5) = 24?.96
with sulfur
T final
K
g’mol-’
excess subtracted
0
3.1529
2.1129
0.029
0.056
0.078
I .7668
89.88
256.5
56128
14538
10408
332.4
87.5
88.3
88.4
88.4
88.4
88.4
44
52
204
I28
I31
45
AtrsHm:
9
356
1625
809
805
431
449.004
451.117
451.146
45 I .202
45 I .280
453.047
4035
The estimated standard deviation of a single measurement in the low-temperature
determinations is about 5 per cent at 10 K and 0.08 per cent over the region 30 to
350 K. The corresponding value for the high-temperature determinations is 0.25 per
cent. The experimental heat capacities for the low- and high-temperature
regions
were fitted to polynomials in temperature by the method of least squares. The fitting
and especially the joins between fitted segments were checked by inspection of a plot
of dC,/dT against T. At the lowest temperatures the heat capacities were smoothed
with the aid of a plot of C,/T against T2 and the thermodynamic
functions
extrapolated by this linear relation. From this plot the electronic heat-capacity
coefficient was found to be zero within the experimental error limits.
To evaluate and compare the different determinations
through the transition
regions (compare table 2) non-transitional-or
rather reference-heat capacities had
to be derived. For this purpose the least-squares-fitted polynomial expressions for
the heat capacity of b-Ag,S were extrapolated to give 88.4 J. K- ’ mol- ’ at 451.3
and 85.0 J. K-’ mol-’ at 865.0 K. In the cc-Ag,S region the heat capacity was
extrapolated linearly from 87.0 J. K-’ mole1 at 445 K to the same value as for
p-Ag,S at 451.3 K. Considerable pre- and post-transitional contributions which are
not included in the results of table 2 will be considered later.
Smoothed values of the heat capacity C,,,, entropy (S:(T)--S$(O)),
enthalpy
are given for selected
{K,(T) - KXO)), and the function - [{G:(T)-HG(O)}/T]
temperatures in table 3. Up to 350 K the heat capacity is judged to be precise within
+ 0.2 per cent and the other thermodynamic functions within + 0.15 per cent, values
which correspond to twice the standard deviation in the results. In the highertemperature region the corresponding precision indices are 0.4 and 0.3 per cent,
respectively.
4. Discussion
The present heat-capacity
results are about 1 per cent lower than those by Walsh
et al.“’ in the 250 to 300 K region while the differences become more erratic in the
HEAT
TABLE
T
K
0
5
CAPACITY
3. Thermodynamic
properties
of silver(I)
M(Ag,S)
= 247.80 g’mol-’
C.
J.K-‘P.;O,-I
SZ(T) - %&O)
J,K-‘,mol-’
0
0
IO
I5
20
25
30
40
50
60
70
80
90
100
120
140
160
180
200
220
240
260
280
298.15
300
320
350
400
450
451.30
0.745
5.216
11.795
18.18
23.63
28.14
34.89
39.75
43.81
47.50
50.90
53.99
56.72
61.05
64.14
66.50
68.46
70.11
71.43
72.47
73.42
74.44
75.31
75.39
76.32
77.66
80.47
(88.11)”
(88.40)
0.167
1.842
5.178
9.466
14.127
18.85
27.93
36.26
43.87
50.91
57.48
63.65
69.49
80.23
89.89
98.61
106.56
113.86
120.61
126.87
132.71
138.18
142.89
143.35
148.24
155.14
165.67
(175.52)
(175.77)
451.30
500
550
600
850
700
750
800
850
865.00
(88.40)
87.26
86.65
86.03
85.35
84.80
84.56
84.69
84.97
(85.00)
865.00
900
950
1000
(85.00)
80.38
79.91
80.57
a-Ag,S
to P-A@
to y-Ag,S
H;(T)-H;(O)
0
-(C(T)-wm(o)j,T
J.K-‘.mo]-’
0
0.626
13.982
56.24
131.52
236.46
366.23
683.6
1057.8
1476.0
1932.8
2425.0
2949.8
3503.7
4683.8
5937
7245
8595
9981
11397
12836
14295
15773
17132
17271
18789
21098
25044
(29225)
(29339)
0.041
0.444
1.429
2.890
4.668
6.638
10.840
15.10
19.27
23.30
27.16
30.88
34.45
41.20
47.48
53.33
58.81
63.96
68.80
73.39
77.73
81.85
85.43
85.78
89.53
94.86
103.07
(110.57)
(110.76)
(33397)
37670
42017
46335
50620
54872
59104
63334
67576
(68852)
110.80
118.45
125.68
132.37
138.57
144.37
149.79
154.89
159.70
(161.09)
(69636)
72506
76506
80512
161.09
164.28
168.64
172.77
transition
transition
(241.59)
244.84
249.17
253.28
are predicated
sulfide.
J,mol-’
(184.80)
193.79
202.08
* 209.59
216.45
222.75
228.59
234.05
239.20
(240.68)
p-Ag,S
’ The values in parentheses
3Y1
UF Ag,S
on the assumption
that the transition
is isothermal.
392
F. GRBNVOLD
TABLE
Ttrs
K
4,s Hm
kJ,mol-’
AND
4. Enthalpies
M(Ag,S)
E. F. WESTRUM.
of transitions
of silver(l)
= 247.80 g.mol-’
JR
sulfide
Method
a-Ag,S
Authors
Year
Bellati and Lussana””
Kapustinskii
and Veselovskil’“’
Roy et ~1.‘~”
Perrott and Fletcher”’
Perrott and Fletcher”’
Thompson
and Flengas’3”’
Mamedov
et ‘11.‘~”
This work
1889
1938
1959
1969
1969
1971
1980
Thompson
This work
1971
to P-A@
448
452
449
450
450
449
441to 453
449.3 to 451.3
3.98iO.04
4.39kO.08
6.38jy1.76
3.98"+0.42
6.49 bf0.42
3.93kO.20
4.31&?
4.06iO.03
Bunsen-type
Metal block
Clapeyron
ice-calorimeter
859
865
0.50+0.54
0.784iO.005
Drop calorimeter
Adiabatic
C,
CP
CD
Drop calorimeter
d.t.a.
Adiabatic
C,
P-Ag2S
to y-Ag,S
and Flengas’30’
’ Stoichiometric
sample.
* Non-stoichiometric
samples
lower-temperature range. The results by Gultyaev and Petrov”’ were again about
2 per cent lower than the present values in the 200 to 300 K region and showed a
rather large spread. The good correspondence between the values of Walsh et u/.‘~’
and of Jost and KubaschewskiC3’ over the common region made us recheck the
composition of our sample by determination of its silver content (see section 2). It
corresponded to the sample composition Ag 2,003S, which we consider to represent
exact stoichiometry within the limit of error of the analysis. The derived standard
entropy: Sm(298.15 K) = (142.89kO.44) J. K-l * mol- l, is 0.4 per cent lower than
that found by Walsh et ~1.‘~’ and 1.3 per cent higher than that obtained by Mills’24’
by integration of the results by Gultyaev and Petrov. (I) Electrochemical-cell
results
by Goates et ~1.,(~~’ Kimura,‘26’ and Kiukkola and WagnerC2” were also evaluated
by Mills,‘24’ who selected the value Sk(298.15 K) = (143.5 + 1.2) J. K- ’ . mol- ‘.
The present heat-capacity results are systematically about I per cent lower than
those shown in the plot by Jost and Kubaschewski’3’ until the cc-to-p transition is
approached. This is true also for the decreasing heat capacity in the P-Ag,S region
up to 620 K. Kapustinskii and Veselovskii(28’ reported a much higher average heat
capacity (92.0 J. K-l +mol- ‘) over the range 452 to 843 K. as did Bellati and
Lussana’29’ over the range 452 to 594 K. The enthalpy equation derived by
Thompson and Flengas (30) from their drop-calorimetric
experiments indicated a
much lower and slightly rising heat capacity (82.7 J. K- * . mol-’
at 450 K to
83.8 J. K-l . mole1 at 860 K). These determinations and earlier ones referred to by
Kapustinskii and Veslovskii’28’ are considered as superseded by the present results.
It is remarkable, however. that the enthalpy results by Thompson and Flengas,‘30’
which agree so well with the present results to just above the a-to-p transition,
become about 1 kJ . mol- ’ lower both at 850 and 1000 K.
No enthalpy of transition was given by Jost and Kubaschewski.‘3’ Results
HEAT
CAPACITY
OF Ag,S
393
obtained by other investigators are given in table 4. The values by Bellati and
Lussana,(29) Thompson
and Flengas, (30) Kapustinskii
and Veselovski,‘28’ and
Mamedov et ~1.‘~~’ agree reasonably well with the present one. That by Roy
et ~1.‘~~’ and those by Perrott and Fletcher (4) for their non-stoichiometric
samples
exceed the present value by more than 50 per cent. Application of the Clapeyron
equation, using the more recent (d7’/dp),+p value 16 x 10m9 K. Pa-’ by Clark and
Rapoport (33’ together with At,, V, = 0.16 x 10e6 rn3. mol-’ by Kimura,‘26’ leads to
Alr,H, = (4.5 +0.5) kJ * mol- ‘. The apparently closely corresponding transitional
enthalpy increment for the stoichiometric
Ag,S of Perrott and Fletcherf4’ is,
however, hardly comparable as it is followed by another one amounting
to
(2.5OkO.42) kJ. mol-’ in a region where we find no transition.
Since there was no sign of the extra transition reported by Perrott and Fletcher”’
for stoichiometric Ag,S, we decided to change the composition of our sample to see
how excess sulfur affects its thermodynamic behavior. Heat-capacity measurements
on a sample with overall composition Ag2S1,0526 were first performed in the 450 to
650 K range. The observed values decreased from about 91 J. K - ’ . mol- ’ at the
former temperature to about 86.5 J. K- ’ . mol-’
at the latter. This decrease is
somewhat steeper than for the stoichiometric sample. The 2.5 to 1.3 J. K-’ . mol. ’
higher heat-capacity values are in reasonable agreement with the presence of about
0.05 mol of S in the sample, in view of the pronounced heat-capacity changes which
occur in liquid sulfur in this temperature range and also the increasing solubihty of
sulfur in Ag,S with temperature.
One evaluation
of the a-to-p transition
enthalpy,
see table 2, gave
A,,,H, = 4035 J.mol-‘,
within the range of uncertainty for the stoichiometric
compound. The sample was then cooled overnight to about 370 K before the excess
sulfur in it was determined from its enthalpy of fusion: AfusH, = 17 17 J . mol - ’ for
S according to West.‘34’ The enthalpy increment corresponded to the presence of
0.047 mol of S and thus to the composition Ag,S,,,,,
for the coexisting r-Ag,S.
Whether this apparent sulfur excess is real or possibly caused by impurities remains
to be investigated.
The extra transition reported by Perrott and Fletchert4’ was not observed, but it
might possibly be associated with the presence of another phase. Thus. Jeannot’“s’
reported the compound Ag,S and found that it decomposed-presumably
into
(Ag+Ag,S)-in
vacuum (2 1 Pa) at (587+20) K.
The fractional enthalpy determinations of the a-to-b transition show that it does
not occur at a well-defined temperature, but covers a variable range depending upon
the previous history of the sample. In the three first series of determinations (C, D.
and E). the measurements were begun without any extended equilibration below the
z-to-a transition
temperature,
and under these conditions
the transition
is
practically complete at (450.1 *O. 1) K. Afterwards the sample was tempered at
420 K for 2 a and the low-temperature measurements were than completed. In the
next determination
through the transition region (F), the transition is only about
l/3 completed at 450.3 K; and it extends to above 45 1.2 K. Repeated measurements
without extended tempering of the sample indicate practical completion of the
transition at 450.0 K (G, H, and I). The sample was finally tempered for 14 d at
394
F. GR0NVOLD
AND
E. F. WESTRUM.
JR.
420 K and the last series of runs in the transition region (J) again show an extension
of the transition to higher temperatures, but not as pronounced as that after 2 a of
tempering.
The slowness of the transition is in keeping with the results by Bonnecaze et a/.(36)
who found that about 150 d of tempering below 450 K were needed to obtain stable
coulometric titrations, i.e. a very long time compared with the relaxation time for
point defects in cl-Ag,S. It resulted in a decrease in width of the homogeneity range
by a factor of about 10 from the results by ValverdeC3” at 420 K. The results by
Bonnecaze et a1.‘36’ were largely confirmed by Reye and Schmalzried(38’ on
a-Ag,+,S crystals prepared below the transition temperature and lead to a
homogeneity range with A6 of about 1 x 10m5 at 440 K. The behavior was found to
be in accordance with ideal point-defect thermodynamics.
Just above the transition temperature a lOOO-fold widening of the homogeneity
range occurs, and this is towards increasing silver content only. Wagner’39’ in his
pioneering study found the limits to be Ag,.,,2S and close to Ag2,&
at 470 K.
Later calculations and experimental results (see Schmalzried and Reye)“’ place the
silver-rich limit at Ag Z,OoZOSand the sulfur-rich limit at Agz.ctoozS at 450 K. The
resulting phase relations are shown in figure 3.
The interval melting observed for stoichiometric Ag,S in the present study might
448
a-Ag$
+ S(I)
f
I
Q
400
Ag + a-AgzS
7
,
2
,
1
i
I
1
-1
0
10’6 for
FIGURE
3. (Silver + sulfur)
phase
diagram
0.020 > 6 z -0.025.
Phase boundaries
at saturation
Rall.‘9’
,
1
I
-2
Ag, +,,S
in the composition
range
Ag,+$.
where
pressures are mainly results of the calculations
by
HEAT CAPACITY
OF AgzS
395
thus arise from a very slight silver excess (6 3 +0.0002), and the continuous and
broad transition of the fully transformed sample (see table 2, Detn. E) support this
view. Incomplete equilibration
below 450 K might lead to the formation of ;I
(slightly non-stoichiometric?)
cl’-AgzS phase, which reverts back to l%Ag?S on
heating to about 449.3 K. The presence of such an intermediate metastable phase
has been reported by Mamedov ef ~1.t~~’ and Boettcher rt ~1.“‘) In either case. on
tempering below the transition temperature the l3- or cr’-Ag,S slowly converts to the
stable stoichiometric a-Ag,S phase with a slightly higher transition temperature.
Sulfur excess (see table 2, Detn. 0) is seen to largely prevent non-isothermal
transition behavior, even after a short equilibration time. and the major part of the
transitional enthalpy is taken up between 45 1.O and 45 1.3 K.
The presence of a further solid-state transition in Ag,S was reported by
Urazova.‘41’ A change in transition temperature from 849 K on the silver-rich side
to 865 K on the sulfur-rich side was related to a variable composition of the b- and
y-Ag,S phases from 12.52 to 13.07 mass per cent of sulfur, i.e. from Ag,,,-S
to
Ag,,,,,S.
Somewhat different results were obtained by Kracek,“’ who gave the
composition range as Ag,.,, S to Ag,.,,S with transition temperature increasing
from 859 to 894 K. A much narrower composition range was inferred by Rat+“’
from sulfur-fugacity measurements on Agz +dS and defect-model calculations. The
resulting phase boundaries are indicated in figure 3. A calorimetric determination of
the small enthalpy change associated with the transition was made by Thompson
and Flengas,‘30’ but the uncertainty was as large as the observed value, see table 4.
In the present work the transition appeared well-behaved and reproducible but was
not sharp. The enthalpy and entropy of transition are A,rFH,,, = (784 + 6) J molt ’
and A,,,&,, = (0.907f0.003)
J. K-l mol-‘. The transition occurs in the range 863
to 866 K and calls for a narrower (l3 + y)-Ag,S diphasic range at the stoichiometric
composition than is indicated in figure 3. Possibly. the transition is continuous and
does not involve a two-phase region.
In the y-Ag2S region the heat capacity decreases to a minimum
of about
80 J. K-l mall’
at 950 K. It then rises again as the melting temperature is
approached:
T, = (1109 + 6) K.‘5.30*42.43’ The drop-calorimetric
results by
Thompson and Flengas (30) also led to a lower heat capacity for y-Ag,S than for
b-Ag,S, but not as low as found here. In fact, the subtraction of a normal dilational
heat-capacity contribution in the 900 to 1000 K range results in a constant-volume
heat capacity for y-Ag,S considerably below the classical limit.
The non-transitional
heat capacity of the Ag,S phases. which form the basis for
the derived enthalpies and entropies of transition in table 4, was chosen on the
assumption that the transitions were almost isothermal. This assumption is clearly
unwarranted, as evidenced by the high heat-capacity values at considerable
distances from the temperature of the maximum. Constant-volume
lattice heatcapacity values C,,(l), which take the grossly anharmonic vibrations of the silver
atoms into account, have not yet been derived. Approximate values for C,..,(l) can
be obtained by applying the Nernst-Lindemann
relation outside the transition
regions:
C,(d) = Cp.m-CC:m = AC,‘,,(T/T,),
396
F. GRBNVOLD
AND
E. F. WESTRUM.
JR
where C,(d) is the dilational heat capacity, A = 0.0017 1 J- ’ . K . mol for 3 atoms,
and
T,
the
melting
temperature:
1109 K.
At
1000 K
then,
c V.m-- 70.5 J. K-’ . mol-’
or 94.3 per cent of the value in the harmonic
approximation.
Application of the Nernst-Lindemann
relation to the heat capacity
of sc-Ag,S in the 100 to 200 K region, in combination with the Debye heat-capacity
model, leads to a maximum 0, = 258 K at 160 K. This Debye temperature is used
for calculating
the harmonic
C,,(l)
in the higher-temperature
region.
Anharmonicity
contributions
are subtracted for fl- and y-Ag,S on the rough
assumption of proportionality
with T. Addition of the Nernst-Lindemann
dilation
contribution then leads to the non-transitional
C,., values shown in figure 2 and to
the A,,, C,. ,,, values shown in figure 4.
The dilational heat capacity can also be calculated using the thermodynamic
relation:
C,(d) = (a’/k-) V, T.
where c( is the isobaric expansivity, x the isothermal compressibility. and V, the
molar volume. Room-temperature
experimental values are: tl = 39 x lO-‘j K-’ (303
to 348 K);(44) 45.6 x 1O-6 K-l
(300 to 448 K);‘45’ 126 x 1O-6 K-’
(293 to
393 K);(32)
140 x 1O-6 K-’
(303 to 363 K);(“j)
ti = 32 x lo-l2 Pa-‘;‘44’
120x lo-l2 Pa-‘;(47’
V, = 34.3 x lop6 m3.mol-‘.(46’
More definite values for
expansivity and compressibility are needed in order to derive a useful value in this
way. By way of its general nature the expression also includes the transitional
200
400
600
TIK
800
1OOO
FIGURE
4. Estimated
transitional
heat capacities for Ag,S. - ~ -, Present results; .-‘. results below
450 K by Jost and Kubaschewski;
‘s) .-. ., estimate above 450 K by Schmalzried;“”
- -,
calculated
curve for P-Ag,S, fitted to the Schmalzried(“’
equation
at 500 K;
. . calculated
Schottky
heat capacity
for 2Ag with go/g, = l/2 and AE/hc = 685 cm-‘:
+ - +. calculated
Schottky
heat capacity
for
go/y, = l/5.74 and AElhc = 570 cm-‘.
HEAT
CAPACITY
397
OF AgzS
component of the dilation contribution and might thus be larger than the NernstLindemann value derived in the previous paragraph.
Around 550 K the isobaric expansivity for g-Ag,S is 113 x 10e6 K-’ (458 to
558 K) according to Lehovec(45) and about 90 x 10m6 K-l according to Glazov and
Makhdumova.‘46’
The four lattice-constant determinations by Cava et ~1.‘~~) in the
range 459 to 598 K lead to a = 115 x 1O-6 K-i, while the three determinations by
Djurle’14’ in the range 462 to 773 K indicate a somewhat lower value:
a = 75 x 1O-6 K-l.
Thus, the experimental
expansivities around 550 K are
consistently about 110 x 10m6 K-l. The compressibility
of P-Ag,S is unknown.
however, and Schmalzried”*’
used x = 50 x lo- ‘* Pa-’
at 450 K in his
calculations. The resulting dilation contribution is then 9.7 J. K-l .moll’.
or about
twice as high as the Nernst-Lindemann
estimate used here. It would thus diminish
the transitional heat capacity in figure 4 to about 5 J. K-l . mol-’ at 550 K. but
this value is still four times larger than that used in the calculations by
Schmalzried.’ 18’
The earlier transitional
heat-capacity estimate for cx-Ag,S by Jost and
Kubaschewski’3J was apparently a result of extrapolation of the practically linearly
rising total heat capacity in the range 250 to 380 K and of using it as the lattice heat
capacity at constant pressure. The excess heat capacity was analyzed in terms of
Frenkel defects among the silver cations by the expression derived earlier by Jost:‘3n’
AC,, mT2 = (exp(AS,/2R)J(AH~/2R)exp(
- AH,$RT).
by plotting log(AC,,, T2) against l/T, see figure 5. Our choice of
capacity at constant pressure does not lead to a strictly linear relation.
approximation
over the range 300 to 430 K gives AH,,, z 35 kJ
AS,,, z 13 J. K- ’ . mol- ‘. The defect-formation enthalpy value derived
lattice heat
but such an
mol ~’ and
here is only
FIGURE
5. Plot for deriving
enthalpy
of defect formation
in P-Ag2S. - - -, Present results:
..
corresponds
to AH,,, = 35 kJ,mol-’
and Ag+ ions, and AS, = 13 J.K-’
‘mole’:
.-..
results below
450 K by Jost and Kubaschewski;
(3’ -. . . estimate above 450 K by Schmalzried
‘I *’
398
F. GR0NVOLD
AND
E. F. WESTRUM.
JR
a fraction of that claimed by Jost and Kubaschewski:‘“’
AH, = 138 kJ mol-’
for W&S.
In the phenomenological
theory by Gurevich and Kharkats””
the defect
formation energy W, the interaction constant i., the changed oscillator frequency
factor v, and the ratio N’/N of interstitial to normal lattice sites, are related for a
“strong” transition by the equation:
AC,< mT2 = vLf2(12X2/2R)exp( - iXJ2RT),
(T < IT;,,).
AC,,,T2
(T > T,;,,),
and
= v-‘(i2(X-
1)2/R}exp{ -A(1 -X)/RT),
where X = W/i. and v = xN’JN. Application of this expression to AgzS leads, as
above, to W 2 35 kJ mol-’ for T < 7;,,. The pre-exponential factor corresponds to
v z 5. Combination of the results below and above 450 K results in a large value for
the interaction constant 1.. This indicates that the transition is not “strong” and calls
for a better delineated model.
The thermodynamic approach by Schmalzried ‘l*) is devoid of physical modeling,
but relates the transitional heat capacity to tangible physical quantities, some of
which unfortunately have not yet been determined. The large uncertainty in the
presently derived values-mainly
through lack of knowledge about the lattice heat
capacity-precludes
consideration of the behavior of sl-Ag,S. The equation derived
by Schmalzried ‘18) for the high-temperature tail of the transition is
AC,., = (RI2)(4T,,,/T)‘exp(
- 2T,,,/T)exp
[ -(AS,*, + R In :)/2R].
He chose AC,,, = 1.25 J.K-‘.mol-’
at T,,, z 7;,, = 450 K for @Ag,S as an
illustration. These assumptions lead to (AS: + R In 2) = 33 J . K- ’ molt ‘. where
AS: is the molar entropy of defect formation and z is the number of equivalent
interstitial sites per elementary unit. The resulting curve. see figure 4. shows a
transitional heat capacity 6 to 10 times smaller than obtained by us. The present
values can be fitted
to Schmalzried’s
equation
with T’,, = 160 K and
(AS:+ R In Z) = 51 J. K-I. mol-‘. The physical implication of these values is not
yet clear.
According to the structural work by Cava rt N/.(‘~’ the four silver atoms in the
unit cell are in a 12-fold position at 600 K. tetrahedrally coordinated to sulfur. and
have restrictions regarding simultaneous occupation of neighboring sites, see below.
Complete randomization
of the silver atoms would correspond to a structural
disorder entropy:
AS,, = tiR(O.333 In 0.333+0.667
In 0.667) = 31.7 J.K-‘-mol-‘.
If the randomization
of silver atoms involves excitation to one higher energy level
only, the heat-capacity behavior might be approximated by a Boltzmann excitation
of the silver atoms from a non-degenerate ground level to a level with degeneracy
leading to the same entropy increment as above, ix.
AS, = 2R In{@, +gO)/gO) = 2R In 6.74.
HEAT
CAPACITY
399
OF Ag,S
The high-temperature tail of the corresponding heat-capacity curve, adjusted to the
experimental curve at 500 K, is shown in figure 4. The decline is steeper than
observed. but this is not unexpected, since the nearest-neighbor tetrahedral sites are
too close (171 pm) for simultaneous occupation by silver atoms. In fact. even
second-nearest neighbors are barely one Ag’-diameter apart (243 pm against 228 pm
for four-coordinated Ag ’). ‘49) The resulting jumping restrictions have been thought
to favor a caterpillar-like
movement of the silver atoms. Diffuse X-ray-scattering
studies by Cava and McWhan (50) indicated that the mobile silver atoms are highly
correlated in cylindrical domains, one unit cell in diameter and between three and
four unit cells long. The correlated motion is thus not confined to a string. but
rather to a cylinder, and involves as many as 25 silver atoms at temperatures just
above the cl-to-p transition for Ag,S.
A lower limit to the structural disorder entropy is
AS, = 2R In 3 = 18.3 J.K-’
.mol-‘,
as result of the random distribution of each silver atom on three positions. The
related Schottky-type heat-capacity curve is shown in figure 4, again adjusted to the
experimental curve at 500 K. The decline in the B-Ag,S region is surprisingly close
to that observed. and so is the entropy increase, see figure 6. A lowering of the
excitation wavenumber from 685 to 600 cm-’ would give complete correspondence
with the observed entropy values for p-Ag,S but is not warranted in view of the
approximations made.
The structure of y-Ag,S is not yet known in detail. It is remarkable, however, that
FIGURE
6. Transitional
type transition
for 2Ag
AEJhc = 593 cm-‘.
entropy for Ag,S. --,
with go/g, = l/2 and
Present results; - ‘, entropy acquired in a SchottkyAE/hc = 685 cm-‘;
.“..
same for gO;‘g, = I!3 and
400
F. GRBNVOLD
AND
E. F. WESTRUM,
JR.
the assumption of antifluorite structure with lattice constant a = 634 pm at 923 K
according to Frueh, (i5) leads to unreasonably long Ag-S tetrahedral bond distances
(275 pm), just as in b-Ag,S. Displacement of the silver atoms from the tetrahedral
interstice to one of the four surrounding trigonal interstices would result in a more
reasonable bond distance (256 pm). Moreover, structural disorder of the silver
atoms is presumably retained in y-Ag,S.
Finally, a brief comment is needed on the work by Perrott and FletcherC4’ whose
peculiar results provided much of the motivation for this study. As already noted,
they found a rapidly increasing-albeit
reproducible only to f 10 per cent-heat
capacity, culminating
in a transition at 620 K for their stoichiometric
sample.
Samples with excess silver or sulfur, however, revealed smaller heat capacities,
readily reproducible and approximately
constant above 450 K. Moreover, the
excess disordering enthalpy of the stoichiometric
sample was balanced by a
correspondingly
larger transitional enthalpy around 450 K in the samples with
excess of one of the components. Detailed experimental results were not provided by
these authors so it is impossible to judge the strength of this assertion. However, this
claim was consistent with their earlier reportC5” of similar behavior in silver(I)
iodide, and a theory’52,53’ was developed to quantify and model the mechanism for
gradual disordering of the stoichiometric compound with temperature, as opposed
to complete disordering at one temperature for compositions deviating from exact
stoichiometry.
We find no support for a significant difference either in the magnitudes of heat
capacity or of the cl-to-p transitional enthalpy of Ag,S between the stoichiometric
sample and that with excess sulfur. We therefore conclude that the Perrott-Fletcher
model is inapplicable and consider it important to provide further study on the
related substance AgI.
The assistance of Bjsrn Lyng Nielsen with the preparation of the samples and in the
higher-temperature
calorimetric measurements is gratefully acknowledged, as is the
assistance of John P. Sutter in the low-temperature measurements.
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