The effect of ordering on lattice heat capacities ordered and disordered AuCu

j. Chem. Thermodynamics1971, 3, 175-186

The effect of ordering on lattice heat capacities Ordered and disordered AuCut D O N A L D T. H A W K I N S and R A L P H H U L T G R E N

Inorganic Materials Research Division, Lawrence Radiation Laboratory, and Department of Materials Science and Engineering, University of California, Berkeley, California 94720, U.S.A. (Received 19 August 1970) Heat capacities of pure Au and of AuCu in both the ordered and disordered states have been measured between 20 and 298 K by isothermal calorimetry. Values for pure Au agree well with previous results except in the temperature range 70 to 150 K, where they are 0.5 to 1.0 per cent higher. Combination of the heat capacities for AuCu obtained in this study with existing high-temperature values yields the configurational entropy of the disordered state: S°(Au0.~Cu0.5, disordered, T = 0) = (1.195 ± 0.05) cal mol- 1 K - 1. This value is somewhat lower than the theoretical value of 1.38 cal mo1-1 K -1 expected for a completely disordered alloy of this composition. The difference is attributed to shortrange order, the existence of which is confirmed by enthalpy of formation measurements. Ordered and disordered states both show a slight positive deviation from Kopp's law up to about 175 K; then the deviations become slightly negative. The heat capacity of the disordered state is higher than that for the ordered state up to 100 K, above which it becomes slightly lower. In agreement with previous work on AuCua below 4,2 K, little change of C~ on ordering was observed.

1. Introduction The l o w - t e m p e r a t u r e lattice h e a t c a p a c i t y o f b i n a r y metallic alloys has n o t been studied extensively. O f 141 alloy systems p r e s e n t e d in the u n p u b l i s h e d s u p p l e m e n t to the c o m p i l a t i o n by Hultgren, Orr, A n d e r s o n , a n d Kelley, ° ) 63 have l o w - t e m p e r a t u r e heat c a p a c i t y data, b u t only 20 o f these 63 systems have d a t a extending a b o v e 20 K. K o p p ' s law, stating t h a t the h e a t c a p a c i t y o f a n alloy equals the sum o f the h e a t capacities o f the constituent elements, is usually a p p l i e d in the absence o f data. However, large deviations f r o m K o p p ' s law c a n exist, especially in the t e m p e r a t u r e range where Cp is rising rapidly. N o study has b e e n m a d e o f the effect o f o r d e r i n g on the lattice heat c a p a c i t y o f a n alloy. H e a t capacities o f o r d e r e d Cd + M g alloys have been m e a s u r e d ; (z'a) Cp values were very close to K o p p ' s law, b u t n o m e a s u r e ments were m a d e on the d i s o r d e r e d alloys. This study was u n d e r t a k e n to observe the effect o f o r d e r i n g o n the lattice h e a t capacity o f A u C u a n d to a t t e m p t to calculate A S ° ( T = 0), the zero p o i n t e n t r o p y t Paper based on a thesis submitted by Donald T. Hawkins to the University of California, Berkeley, in partial fulfilment of the requirements for the degree Doctor of Philosophy.

176

D.T. HAWKINS AND R. HULTGREN

of the "disordered" alloy. The Au + Cu system was chosen for this work because much previous work at high temperatures has been done on this system, (1~ making the extrapolation of Co to T = 0 less uncertain, and also because preparation of the sample does not pose any special difficulties. The heat capacities o f both the ordered state and the disordered state were measured by isothermal calorimetry. The degree of short-range order remaining in the disordered sample after quenching was estimated by enthalpy of solution measurements. In addition to the measurements on the alloys, the Cp of pure gold also was measured.

2. Experimental APPA RATUS The sample holder (calorimeter), shown in figure 1 is made of copper, 0.38 mm thick, and is 13.3 cm long and 3.8 cm in diameter. A small well, also of copper, for insertion of the calorimeter thermocouple is soldered to the bottom of the can. The upper end 1.27 cm

0.00635 rnm ~ Platinum foil

0.38 mm Copper can

Thermocouplew e l l

~-=~q --3.8cm~-

FIGURE 1. Calorimeter can and top. of the can, and the 1.27 cm diameter "chimney", are made of Monel. The lid is softsoldered into place after insertion of the sample. A small pinhole in the lid allows for evacuation and backfilling with about 1 atm of helium before final sealing. The outer surface of the can is covered with several thin layers of G.E. 7031 Formvar varnish, wound with 612 turns of silk-wrapped No. 40 (B & S) gold wire, and covered with 0.00635 mm platinum foil. The gold wire serves both as a resistance thermometer and heater during the measurements. The entire sample holder is placed in a high-vacuum system, shown in figure 2. The sample holder is surrounded by a heavy copper jacket, into the upper portion of which is cast 2500 g of lead, The jacket serves as a nearly constant temperature

ORDERED AND DISORDERED AuCu

177

3.8 cm diameter s. s. pipe -Cup Thermocouple hole 60/40 Solder joint Linen cord Lead casting Jacket ]~ower

terminal

Linen cord

Liquid N 2 blowout tube

Calorimeter can Outer monel can Pyrex Dewar

-

Evacuation hole

FIGURE 2. Calorimeter can and jacket assembly (high-vacuum system). shield around the calorimeter. The calorimeter-jacket assembly is suspended inside an outer Monel can, which is connected to a diffusion p u m p and mechanical forepump, through a liquid nitrogen trap, A vacuum of better than 5 x 10 - 6 Torr was maintained during the measurements.t Cooling was accomplished by submerging the outer can and jacket assembly in a Pyrex Dewar vessel containing the coolant. Liquid hydrogen, liquid nitrogen, a dry ice + acetone slurry, and an ice + water mixture were used as coolants. A small amount of helium admitted to the high-vacuum system during cooling provided heat exchange between the system and coolant. The helium was pumped out before commencing measurements. t Torr = (101.325/760) kN m-L

178

D. T. HAWKINS AND R. HULTGREN

With this arrangement, measurements could be made between 20 K and room temperature. Facilities were available in the apparatus to reduce the pressure over the liquid hydrogen coolant, thereby making it possible to attain temperatures as low as 15 K, but the extra time and effort needed to gain this small reduction in temperature were judged unnecessary in this study, since the extrapolation of the Cp values to T = 0 introduces only a negligible uncertainty in the entropy. Electrical measurements to the nearest 0.1 IxV were made using a White double potentiometer. Power was supplied to the resistance thermometer by two, 2 V lowdischarge cells connected in series. The thermometer current was maintained at approximately 250 gA. The resistance of the thermometer was determined by measurements of the current through, and the potential drop across, the gold resistance wire. Before a measurement, the temperature of the jacket was adjusted so as to be 1 or 2 K above the temperature of the calorimeter. A small upward, linear, drift in the resistance was observed due to heat transfer. After this drift rate had been satisfactorily established, heating was initiated. During the heating interval, the current from the resistance thermometer battery was directed through a series of "dummy" resistors which had been previously matched to the value of the actual resistance thermometer, thus maintaining a constant, steady discharge of the thermometer battery. During the heating interval, power was supplied to the calorimeter by two 12 V storage batteries connected in series. Measurements of the potential and current were made at intervals during this period, in order to determine the power input to the calorimeter. Heating was continued until the temperature of the calorimeter was approximately 1 or 2 K above that of the jacket. The length of the heating interval was measured by a timer graduated in divisions of 0.001 rain, and connected to a 110 V a.c., 60 Hz tuning fork. The timer was connected in such a way that it was automatically started and stopped simultaneously with the power. After heating ceased, measurements of resistance were made as before the run, until the final drift rate and temperature were established. From measurements of the power input, which was calculated from the potential and current readings by the method described by Gibson and Giauque, (4) and from the temperature rise of the calorimeter, the total heat capacity was calculated. Small corrections were made to the results to account for power losses in the connecting wires, Newton's law heat transfer, and the fact that the surface temperature of the calorimeter, as measured by the resistance thermometer, is slightly higher than the temperature of the sample because heat is not distributed instantaneouslyduring heating. A series of measurements on the empty calorimeter provided values for its heat capacity, which were subtracted from the total measured Cp values, with minor corrections for the Cp of the helium gas in the calorimeter, and the varying amounts of solder used to seal the lid, to obtain the Cp of the sample. During the measurements, the resistance thermometer was routinely calibrated against the copper-to-constantan calorimeter thermocouple, which had been calibrated against a Pt resistance thermometer standardized by the U.S. National Bureau of Standards. A complete description of the calorimeter and the method of operation is given in reference 5, with an earlier description in reference 6.

ORDERED AND DISORDERED AuCu

179

MATERIALS Au of purity better than 99.999 moles per cent was obtained from Corninco American, Inc., and Cu of similar purity was obtained from American Smelting and Refining Company. For both metals, all impurities were below the 1 p.p.m, level, except that the copper had 2 p.p.m, of Te. After the measurements on pure Au were completed, the AuCu alloy was prepared. The pure metals, weighed to the proper composition, were melted together in 'a graphite crucible under helium in an induction furnace at 1200 °C, then poured into a chilled copper mold to form an ingot 2.5 cm in diameter and 15 cm long. X-ray diffraction showed a single-face-centered-cubic phase with a lattice parameter compatible with the composition Xgu = 0.50. The ingot was slightly cold worked, then sealed into an evacuated quartz tube, homogenized at 590 °C for 12 d, and quenched into an ice+brine bath. After quenching, the ingot was sawed into rods 0.6 cm square and 13 cm long. The rods were given an ordering anneal by resealing them under vacuum into a quartz tube, holding them at 365 °C for 5 d, and then slowly cooling them to about 200 °C over a period of 4 d, reducing the furnace temperature about 25 °C every 12 h. The X-ray diffraction pattern of the rods showed sharp superlattice lines with a welldefined, simple tetragonal structure, indicating that the sample was well ordered. After measuring the Cp of the ordered samples, the rods were again resealed into evacuated quartz tubes. To insure rapidity of quenching, each rod was individually sealed into its own tube. Five small pellets suitable for enthalpy of formation measurements were also prepared and placed into five of the sample tubes, so that the pellets were given the same heat treatment and quench as the rods. All tubes were then heated to 075_+2)°C for 9 d and quenched one by one into an ice+brine bath. The tubes shattered on contact with the brine solution, so that quenching was very rapid. The X-ray pattern of the quenched samples showed no evidence of superlattice lines, indicating the absence of long-range order. However, enthalpy of formation measurements by liquid tin solution calorimetry showed that short-range order was present. For equilibrium alloys of this composition, Orr °°~ found AH~(Auo.sCuo.5,320 K) = - 2150 cal mol- 1 and AH~(Auo.sCu0.5,720 K) = - 1230 cal mol- 1.~. At 320 K the sample is highly ordered; at 720 K it is mainly disordered. The difference between the two AH~ values, 920 cal mol - t , is nearly all due to ordering. For a sample quenched from 873 K, Orr found AH~(Auo.sCuo.5,320 K) = - 1630 cal mol- 1, so that, even though no long-range order was evidenced by the X-ray data, the sample had gained 400 cal tool- ~ of enthalpy during the quench. This enthalpy is attributed to short-range order. t Throughout this paper cal = 4.184 J.

D. T. HAWKINS AND R. HULTGREN

180

E n t h a l p y o f f o r m a t i o n m e a s u r e m e n t s m a d e in the same m a n n e r o n the samples used in this w o r k gave AH~(Au0. 5 Cuo.5, 320 K ) = - 1365 cal tool - 1 , showing them to be highly disordered, b u t still possessing a short-range o r d e r i n g enthalpy of 135 cal tool -1

3. Results Seventy-two runs were m a d e on p u r e A u . T h e e x p e r i m e n t a l results are given in table 1, a n d the s m o o t h e d values in table 3. T h e results are also shown on figure 3, along with the values chosen b y Hultgren, Orr, a n d Kelley. ° ) T h e present results TABLE 1. Experimental heat capacities Cp(Au) of pure gold T K

Cp(Au) cal mo1-1 K -1

T K

Cp(Au) cal tool71 K -£

T K

C~,(Au) cal mo1-1 K - i

T I~

Cp(Au) cal mo1-1 K-~S

19.68 21.61 24.22 27.36 27.50 30.88 31.34 35.48 42.69 49.70 58.75 68.54 73.89 78.45 80.79 82.86 85.32 91.14 96.06

0.656 0.876 1.182 1.602 1.624 2.013 2.035 2.365 2.934 3.446 3.985 4.414 4.616 4.675 4.824 4.878 4.931 5.057 5.125

101.38 106.55 111.61 116.56 121.40 127.02 131.67 136.23 143.29 153.05 158.48 163.78 168.95 176.95 181.89 187.49 191.47 198.57

5.195 5.273 5.323 5.428 5.439 5.474 5.534 5.563 5.627 5.667 5.709 5.732 5.729 5.785 5.753 5.795 5.785 5.818

202.64 202.69 206.74 210.51 210.84 214.31 214.90 215.95 219.81 222.21 223.91 227.61 231.44 232.03 235.06 235.65 238.81 239.49

5.833 5.836 5.811 5.914 5.867 5.879 5.884 5.860 5.848 5.84.1 5.876 5.928 5.886 5.886 5.882 5.912 5.915 5.946

242.55 243.19 246.83 247.06 251.24 252.23 255.35 258.16 264.44 267.96 273.89 277.38 277.76 281.54 284.00 285.74 290.88 295.70

5.889 5.900 5.896 5.993 5.909 5.868 5.969 6.016 5.921 5.959 5.973 5.983 5.977 6.015 5.980 6.013 5.998 6.034

agree well with the previous d a t a o f F r a n z o s i n i , (7) G e b a l l e a n d G i a u q u e , (8) and Clusius a n d H a r t e c k , (9) except in the t e m p e r a t u r e range 70 to 150 K, where the present results are 0.5 to 1.0 p e r cent higher. I n t e g r a t i o n o f the values obtained in this study yields S ° ( A u , 298.15 K ) = 11.397 cal m o l - x K - a ; o f which 0.012 cal tool - x K - x are f r o m the e x t r a p o l a t i o n b e l o w 20 K , a n d {H°(298.15 K ) - H ° ( 0 ) }

= 1440 cal tool - x .

Values f r o m Hultgren, Orr, a n d Kelley (1) for the e n t r o p y a n d e n t h a l p y difference, which are used t h r o u g h o u t this paper, are, respectively, (11.352 + 0.05) cal t o o l - 1 K - 1, a n d 1438 cal tool -x. Very little scatter in the results is evident b e l o w 200 K. A b o v e this temperature, there is a slight increase in the scatter. The precision o f the results is within 0.2 per cent below 200 K, a n d within 0.5 p e r cent thereafter. F o r t y - n i n e runs were m a d e o n the o r d e r e d A u C u sample. F i g u r e 4 shows the e x p e r i m e n t a l values, the s m o o t h e d curve, a n d the K o p p ' s law line for the ordered

ORDERED

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181

AuCu

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182

D. T. HAWKINS AND R. HULTGREN

alloy. The values of Cp were smoothed by drawing a smooth curve on the AC~ plot, and were extrapolated by extrapolating the ACp curve to T = 0. Integration of the smoothed values gave, for ordered Auo.sCuo.s,{S°(298.15K)-S°(O)}=9.791 cal mo1-1 K -1, and {H°(298.15 K ) - H ° ( 0 ) } = 1325 cal mo1-1. Forty-nine runs were made on,the disordered AuCu sample. The Cv results, the smoothed curve, and the Kopp's law line are shown on figure 5. Extrapolation to 7 --

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t

150

200

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t --z-

7 r~ t

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50

100

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1

250

300

T/K FIGURE 5. Heat capacity Cp of disordered Auo.sCuo.5.

T = 0 was done in the same manner as for the ordered alloy. Integration of the smooth curve gave, for disordered Auo.5 Cuo.5, {S°(298.15 K)-S°(0)} = 9.886 cal tool -1 K - I , and {H°(298.15 K)-H°(0)} = 1323 cal tool- 1. Experimental results for both ordered and disordered AuCu are given in table 2. Smoothed Cp values, along with the deviations from Kopp's law, expressed as ACp values, are given in table 3. With the aid of high-temperature data, the zero point entropy of AuCu can now be calculated. Combination of e.m.f, and entropy of formation measurements at 800 K (1) yields AS~(Auo. s Cu0.s, 800 K) = 1.448 cal mo1-1 K -1. In the absence of other data, it was assumed that the disordered alloy obeys Kopp's law down to 298,15 K~ so that this same AS~ value applies at that temperature. As shown in table 4,

ORDERED AND DISORDERED AuCu

183

TABLE 2. Experimental heat capacities C,(Auo.sCuo.8) of AuCu T

C,(Auo.BCuo.5) calmol-lK-1

T K

C~(Auo.sCuo.5) T calmol-lK-1 " K

25.08 26.97 30.22 33.63 40.36 44.06 48.20 52.05 57.49 64.25 69.59 75.40 80.74

0.784 0.921 1.216 1.462 1.898 2.146 2.450 2.672 2.995 3.379 3.619 3.861 4.083

85.50 94.65 100.60 106.60 112.75 118.81 124.64 133.05 138.74 144.72 150.92 156.87 162.75

4.249 4.456 4.579 4.695 4.733 4.916 4.982 5.090 5.182 5.247 5.313 5.325 5.357

24.66 26.31 28.42 31.43 35.12 40.08 46.73 51.49 55.41 60.20 65.83 71.91 77.75

0.678 0.837 1.025 1.248 1.507 1.719 2.264 2.608 2.843 3.114 3.410 3.652 3.947

80.30 84.42 91.84 97.94 103.76 109.77 115.77 122.09 128.30 134.03 140.01 145.94 152.04

3.992 4.179 4.264 4.371 4.643 4.775 4.911 4.951 5.059 5.185 5.279 5.271 5.342

Cv(Auo.sCuo.5) calmol-lK- ~

T K

Cp(Auo.BCuo.5) calmol-lK-1

Disordered 168.79 174.81 181.55 187.10 193.09 197.93 203.94 209.91 216.37 220.05 227.87 233.96 240.08

5.478 5.427 5.487 5.511 5.586 5.538 5.578 5.654 5.653 5.693 5.736 5.751 5.721

246.00 251.87 258.02 263.77 269.87 274.76 279.89 285.80 291.52 303.60

5.779 5.775 5.765 5.825 5.849 5.815 5.786 5.889 5.843 5.913

Ordered 157.87 163.88 170.28 176.13 187.92 194.15 199.87 203.94 207.82 212.79 216.75 220.97 233.11

5.379 5.358 5.443 5.503 5.579 5.583 5.633 5.628 5.642 5.663 5.684 5.715 5.765

238.85 245.04 251.50 256.14 262.35 268.04 280.18 286.07 292.10 295.98

5.748 5.829 5.825 5.802 5.824 5.831 5.882 5.899 5.905 5.926

AS~(Au0.sCuo.5, T = 0) can t h e n be calculated, a n d is f o u n d to e q u a l 1.195 c a l m o 1 - 1 K -1. A small negative c o r r e c t i o n ( - 0 . 0 0 5 c a l m o 1 - 1 K - 1 ) m u s t be a p p l i e d to AS? to a c c o u n t for the fact t h a t K o p p ' s law is o b e y e d only to 400 K , rather t h a n to 298.15 K , (see table 3). One can also calculate AS~ f r o m t h e r m a l d a t a f o r the e q u i l i b r i u m alloy. M e a s u r e ments o f AH~ as a function o f t e m p e r a t u r e b y Orr, L u c i a t - L a b r y , a n d H u l t g r e n , ( ~ and also b y H e r t z (12~ show a c o n s t a n t AH~ f r o m 298.15 to 560 K , f o l l o w e d b y a c o n t i n u o u s increase in AH~ f r o m 560 to 683 K , followed b y a first-order t r a n s f o r m a tion a t 683 K , a n d then a n o t h e r slow increase in AH~ to 800 K, a b o v e w h i c h AH~ is constant. T h e c o n s t a n t regions a r e a n excellent c o n f i r m a t i o n o f K o p p ' s l a w at those temperatures. The increase in AH~ b e l o w the t r a n s f o r m a t i o n t e m p e r a t u r e is a t t r i b u t e d to the onset o f disordering, while t h a t a b o v e the t r a n s f o r m a t i o n is a t t r i b u t e d to the d i s a p p e a r a n c e o f s h o r t - r a n g e order. Slopes o f the AH~ against T curve were t a k e n , yielding ACp values, which were then i n t e g r a t e d to give entropies. A s s u m i n g t h a t the o r d e r e d alloy is c o m p l e t e l y o r d e r e d a t T = 0, i.e. t h a t AS~(ordered, T = 0) = 0, the value AS~(Au0.sCuo,5, 800 K ) = 1.445 c a l m o 1 - 1 K - t can be calculated f r o m the 13

184

D. T. HAWKINS AND R. H U L T G R E N TABLE 3. Smoothed values Pure Au T /~ 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300

Disordered AuCu

Ordered AuCu

C~(Au) Cp(Auo.~Cuo,5)ACp(Auo.sCuo.~) C~(Auo.sCuo.5) AC~(Auo.~Cuo.5) cal mol - 1 K - 1 cal m o l - ~ K - 1 cal tool - 1 K - 1 cal m o l - 1 K " 1 cal tool - ~ K - z 0.700 1.230 1.781 2.273 2.712 3.119 3.474 3.783 4.056 4.287 4.481 4.646 4.784 4.902 5.008 5.100 5.181 5.317 5.425 5.513 5.588 5.649 5.701 5.746 5.782 5.813 5.839 5.861 5.882 5.900 5.919 5.937 :5.955 5.973 5.993 6.012 6.027 6.029

0.496 0.817 1.173 1.535 1.896 2.231 2.554 2.858 3.142 3.413 3.650 3.852 4.030 4.184 4.325 4.455 4.570 4.762 4.927 5.071 5.180 5.276 5.356 5.424 5.485 5.540 5.585 5.632 5.673 5.712 5.743 5.774 5.801 5.828 5.854 5.879 5.895 5.903

0.073 0.078 0.087 0.096 0.092 0.085 0.084 0.088 0.105 0.130 0.145 0.142 0.131 0.115 0.101 0.090 0.080 0.060 0.042 0.025 0.011 --0.004 --0.015 --0.026 --0.034 --0.040 --0.045 --0.049 --0.052 --0.054 --0.055 --0.056 --0.055 --0.052 --0.049 --0.046 --0.044 --0.042

0.453 0.779 1.140 1.508 1.854 2.185 2.507 2.815 3.100 3.361 3.600 3.807 3.992 4.158 4.309 4.446 4.566 4.770 4.944 5.090 5.211 5.315 5.397 5.466 5.527 5.579 5.620 5.664 5.700 5.735 5.766 5.797 5.825 5.851 5.877 5.902 5.920 5.929

0.030 0.040 0.054 0.069 0.050 0.039 0.037 0.045 0.063 0.078 0.095 0.097 0.093 0.089 0.085 0.081 0.076 0.068 0.059 0.050 0.042 0.035 0.026 0.016 0.008 --0.001 --0.010 --0.017 --0.025 --0.029 --0.032 --0.033 --0.031 --0.029 --0.026 --0.023 --0.019 --0.016

TABLE 4. Calculation of AS~(Auo.~Cuo.~, disordered, T = 0) AS°/cal mol- 1 K - 1 0.5Au(298 K) + 0.5Cu(298 K) Auo.sCuo.5(disordered, 298 K) 0.5Cu(T = 0) 0.5Au(T = 0)

= = = =

Auo.5 Cuo.B(disordered, 298 K); Auo.~ Cuo.~(disordered, T = 0); 0.5Cu(298 K); 0.5Au(298 K);

1.443 --9.886 3.962 5.676

0.5Au(T = 0) + 0.5Cu(T----- 0) = Auo.sCuo.~(disordered, T---- 0);

1,195

I" Includes correction of --0.005 for Auo.6Cuo.s(disordered) between 298 and 400 K (see text),

ORDERED AND DISORDERED AuCu

185

TABLE 5. Calculation of ASf°(Auo.8Cuo.8,disordered, 800 K), using enthalpies of formation

0.5Au(T = 0) + 0.5Cu(T = 0) = Auo.5Cuo.8(ordered, T = 0) = Auo.5Cu0.8(ordered, 298 K) = Auo.sCuo.8(ordered, 683 K) = Auo.sCu0.8(disordered, 683 K) = 0.5Au(800 K) = 0.5Cu(800 K) =

Auo.sCuo.5(ordered, T = 0); Auo .5Cuo.8(ordered, 298 K); Auo.5Cuo.8(ordered, 683 K); Auo.sCuo.5(disordered, 683 K); Auo.sCuo.8(disordered, 800 K) 0.5Au(T = 0); 0.5Cu(T = 0);

AS°/cal mo1-1 K-~ 0 9.791 5.758 t 0.490 1.191 --8.770 --7.015

0.5Au(800 K) + 0,5Cu(800 K) = Auo.5Cuo.5(disordered, 800 K); Experimental value:

1.445 1.448

Difference:

--0.003

"~Includes correction of --0.001 for Auo.sCuo.5(ordered) between 298 and 400 K (see text).

Cp values, as shown in table 5. This value is only 0.003 cal m o l - ~ K - ~ lower than that obtained from the high-temperature AG~ and AH~ measurements, which is an excellent confirmation of the present results, the high-temperature measurements, and the assumption that the sample was nearly completely ordered. The u n c e r t a i n t y in AS~ is estimated to be +__0.05 cal m o l - 1 K - 1 . Converting the AS~(T= 0) value to 298.15 K using the Cp values measured in this work gives: Au o.5Cuo. 5(ordered) = Auo. 5Cuo.5 (disordered); AS~(298.15 K) --- (1.290+__0.05) cal mo1-1 K -1.

4. Conclusion The value of the zero point entropy of A u C u is less than the theoretical value of R In 2 for a completely disordered (random) alloy with XAu = 0.5, showing that some short-range order exists, although there is no evidence of order from the X-ray data. More rapid cooling rates, such as would be obtained by splat cooling methods, would probably yield a value of AS°(T = 0) closer to the theoretical value. Ordering had little effect on the heat capacities. At low temperatures, the Cp of the disordered state is slightly higher than that for the ordered state, while at higher temperatures (above approximately 175 K for AuCu), Cp of the ordered state is slightly higher. The maximum Cp difference between the two states of Auo.5 Cuo.5 is less than 0.05 cal tool-1 K - 1 . The s a m e general behavior has been observed in recent measurements on AuCuaJ TM One would expect Cp(disordered) to be higher at low temperatures because in a disordered sample, with a less perfect lattice, there is a greater opportunity for low-frequency lattice vibrations to occur, thereby lowering the Debye temperature and raising the heat capacity. Previous work on AuCu3 O4,15) below 4.2 K also revealed little effect of ordering on Cp, while work on NiaMn (16) and CuPt, (17) also below 4.2 K, showed a large effect. It may be that in systems in which a large effect is observed, other causes, such as magnetic effects, may be respon-

186

D . T . HAWKINS AND R. HULTGREN

sible. All these studies, however, confirmed the fact that C v for the ordered state is lower than C v for the disordered state. At higher temperatures one would also expect the C v of the ordered state to be higher, since as the temperature increases, the ordered state releases enthalpy. However, the crossover of Cp(ordered) over Cp(disordered) cannot be attributed to the onset of disordering, since at the low temperatures of this study, diffusion rates of atoms in the alloy are so small as to be negligible. Enthalpy of formation measurements have shown that the disordering does not begin until the temperature is above 560 K.

Mr Stanley E. Ross and M r Hong-il Y o o n gave valuable assistance in the measurements. This work was conducted under the auspices of the U.S. Atomic Energy Commission.

REFERENCES 1. Unpublished supplement to Hultgren, R.; Orr, R. L.; Anderson, P. D.; Kelley, K. K. Selected Values of the Thermodynamic Properties of Metals and Alloys. Wiley: New York. 1963. 2. Satterthwaite, C. B.; Craig, R. S.; Wallace, W. E. J. Amer. Chem. Soc. 1954, 76, 232. 3. Coffer, L. W.; Craig, R. S.; Krier, C. A.; Wallace, W. E. J. Amer. Chem. Soc. 1954, 76, 241. 4. Gibson, G. E.; Giauque, W. F. J. Amer. Chem. Soe. 1923, 45, 93. 5. Hawkins, D. T. USAEC Report UCRL-19125 (Ph.D. Thesis). 1970. 6. Huffstutler, M. C., Jr. Ph.D. Thesis. University of California, Berkeley. 1961. 7. Franzosini, P. Ric. ScL Rend. 1963, A3, 365. 8. Geballe, T. H.; Giauque, W. F. J. Amer. Chem. Soc. 1952, 74, 2368. 9. Clusius, K.; Harteck, P. Z. Physik. Chem. 1928, 134, 243. 10. Orr, R. L. Acta Met. 1960, 8, 489. 11. Orr, R. L.; Luciat-Labry, J.; Hultgren, R. Acta Met. 1960, 8, 431. 12. Hertz, J. Ph.D. Thesis. University of Nancy, France. 1967. 13. Yoon, H. Private communication. 1970. 14. Rayne, J. A. Phys. Rev. 1957, 108, 649. 15. Martin, D. L. Can. J. Phys. 1968, 49, 923. 16. Goldman, J. E. Rev. Mod. Phys. 1968. 25, 108. 17. Rocssler, B.; Rayne, J. A. Proc. Low-Temp. Phys. LT9, 1965, 1074.

N o t e added in proof. Martin and Waterhouse, (is) in an exhaustive investigation of the Cp of AuCu below 3 K, report that disordered A u C u is unstable at r o o m temperature and slowly becomes ordered. The transformation is stated to be a function of either time or thermal cycling between r o o m temperature and liquid helium temperatures. At r o o m temperature, this spontaneous transformation should have little effect on the present results due to the slow diffusion of atoms at and below r o o m temperature.

REFERENCE 18. Martin, D. L.; Waterhouse, N. Can. J. Phys. 1970, 48, 1217.