Thermodynamic study of sulphur-silver-gold solid solutions

Scripta METALLURGICA T H E R M O D Y N ~ I C V o l . 21, pp. 7 3 9 - 7 4 2 , 1 9 8 7 P r i n t e d in t h e U . S . A . STUDY SOLID OF SULPHUR Pergamon Journals, Ltd. All rights reserved --SILVER--GOLD SOLUTIONS Mathilde DELHOUME-DEBREU, Nisso BARBOUTH and Jacques 0UDAR Laboratoire de Physico-Chimie des Surfaces Equipe de Recherche associ4e au CNRS - UA 425 ii, rue Pierre et Marie Curie - 75005 PARIS (Received January 27, 1986) ( R e v i s e d A p r i l 13, 1987) The solubility of sulphur, in various metals and alloys has been extensively studied in this laboratory (1-4). All studies were carried out in the following way. I- the concentration of dissolved sulphur was determined with a radiochemical method based on the use of~- radiations emitter35S. 2- The sulphur solubility was plotted at various temperatures with respect to the composition of H2S/H 2 atmosphere. These measurements enable one to obtain the enthalpy of dissolution of sulphur, in relation to the state of hydrogen sulfide. A method based on thermodynamique statistics has been developped by McLellan (5) and transposed to the case of dissolved sulphur in copper (6), then in various other metals and alloys. It allows us to determine the energy and entropy of dissolution of sulphur, in relation to the state of atomic gaseous sulphur, at 0 K. In this article, we propose to extend the same thermodynamic treatment to the results recently obtained by Delhoume and Barbouth (7) for sulphur dissolved in silver-gold alloys. The results obtained by these authors are given in table i. (C is given in 10 -6 = 0.0001% in weight). TABLE 1 Metal or alloy Temperature range log C~ppm=f(PH2S/pH 2 . T) Ag (i) 600°C to 900°C log PH2S/pH 2 + 6.2 - 3060 T Ag-2%Au 600°C to 900°C Ag-10%Au 600°C to 900°C Ag-18%Au 600°C to 900°C Ag-26%Au 600°C to 9000C log PH2S/pH 2 + 5,6 - 2510 T log PH2S/pH 2 + 5.9 - 2924 T log PH2S/pH 2 + 6.3 - 3588 T log PH2S/pH 2 + 8,2 - 5883 T As in the other sulphur-metal or sulphur-alloy systems previously studied, the concentration of dissolved sulphur was found to be proportional to the PH2S/pH 2 ratio in the whole composition range, according to Sievert's law. One can conclude that the interaction between solute atoms are negligible. Then, the McLellan method can be applied and the equation of solubility can be written as : @ _ A (i0 #$2)I/2. e ~s /k -(Es + E~)kT T 714 " ' . e in which : 8 is the solubility expressed as an atomic fraction, ~ is the number of possible locations for one atom of the lattice, pS 2 is the vapor pressure of the S 2 molecules expressed in Pa~ g~ is the partial entropy related to the dissolution of sulphur (vibrational contribution), E~ is the enthalpy of dissociation of the S 2 molecule at O K (2.2eV at I-I), (8), E s is the partial energy related to the dissolution of sulphur, that is to say, the difference between the energy of one atom still in the gas and the energy of one atom in solution in the 0036-9748/87 Copyright (c) 1 9 8 7 739 $ 3 . 0 0 + .00 Pergamon Journals Ltd. 740 THERMODYNAMICS OF S O L U T I O N S Vol. 21, No. 6 metalland A is a coefficient representing the entropy of S 2 gaseous molecules and can be easily calculated from the spectroscopy data (8). It has been shown that this equation, established for interstitial solutions (9), still remains valid for sulphur which is in a substitutional position (6). The curves 8 T7/4 log = (PS2)i/2 A f(1/T) have been plotted for different alloys (figure 1). ~I T - 7 S S V I / / / / \ o~,-~A, i~ &Ag-I%Au +, ,o ,s I'~'~ Figure i : Graphical determination of the partial entropy and energy of sulphur in silver-gold alloys. From these curves the partial entropy and the partial energy of sulphur shown in Table 2 were determined. TABLE 2 Metal or alloy g~s/K ~s(kj/at.g ) +n_(~s+Z~)_Tkl/4 A H with A H with between ref-state ref-state 600°C & 900°C of H2S of I/2 S 2 (kJ/mol) (kJ/mol) Ag 12.0 - 226.8 - 31.5 to 34.3 58.5 - 31.6 Ag-27~u 10.7 - 237.4 - 38.0 to 42.6 48.2 - 42.2 Ag-10£Au 11.5 - 229.3 - 30.1 to 34.3 56.2 - 33.9 Ag-18XAu 12.4 - 216.6 - 17.1 to 21.7 69.0 - 21.3 Ag-26ZAu 16.9 - 172.6 22.1 to 26.3 113.1 23.0 (.Es+E~) - 7/4kT represents the enthalpy of dissolution of sulphur from the state of S 2 molecules according to 1/2 S2~--=-~Smeta I. Vol. 21, No. 6 THERMODYNAMICS OF SOLUTIONS 741 One notes that these values are in good agreement with the mean values calculated by direc t application of the Van't Hoff relation, taking into account the enthalpy of dissociation of H2S (last column of Table 2). As can be observed from the values in table 2, the enthalpy Es and the entropy ~s of sulphur dissolution do not vary monotonously as a function of the Au content. Surprisingly, a minimum occurs at a Au content of 2Z,both for ~s and ~s- For an explanation of such an anomaly the influence of the dissolved hydrogen has been systematically studied. Hydrogen, the major species in the gas phase during the experiments on sulphur solubility, is known to be soluble in some extent in silver(10)so that we could not exclude some complex interaction with the bulk sulphur. In order to check this assumption we have measured the bulk sulphur content in absence of hydrogen for various equilibrium between the metal and the bulk Ag2S. The sulfide was formed on the metal by direct reaction with elementary sulphur. Then the sulfide covered sample was treated in vacuum in a silica cell at various temperatures for a period of time sufficient to saturate the metal with sulphur. After rapid cooling to room temperature, the residual sulfide was removed and the bulk sulphur content was measured by the radiochemical technique. The values so obtained correspond to the PH2S/pH 2 equilibrium values for the sulfidation of the metal into Ag2S. For the alloys these values were obtained by using the following relationship. pH2S l PH2 I alloy ~pH2S l = ~P--~-2] A g l Xa--~Ag Here aAg is the activity of silver in the alloy. To determine aAg we have used the values determined at 800K in (Ii) and assumed that these values depend on the temperature. I t has been shown that the Ag-Au solid solutions behave roughly ~s a regular solution. As a consequence the relation between the activity coefficient YAg given by YAg = aAg NA and the interaction parameters Ln y Ag - k is given by X (I-NAg) 2 RT (kJ) -225 111 where NAg is the molar fraction of Ag in the alloy, i -- I -250 i9 ; i -27,j ~7 Fig. 2 : Variation of E s and Ss/k versus the Au content of silver-gold alloys. -30( - Ag - ,b ~ 3!5 weight per cent Au If now we assume that the solubility is proportional to the PH2S/pH 2 ratio, A H, E and s ~s can be determined as above from the slopes of the curves at various temperatures of the solubility to the PH2S/pH 2 ratio. Results are shown in Table 3 and figure 2. We observe that now the anomaly in the variation of Es and ~s/k as a function of the Au content does not exist any more. The comparison with values obtained in the presence of hydrogen illustrates the strong influence of hydrogen on the sulphur solubility. Hydrogen increases the enthalpy of dissolution by about 30 to 60 kj mol -I indicating strong attractive interactions with dissolved sulphur. These interactions may play an important role in the well known synergetic effect of sulphur in hydrogen embrittlement of metals. 742 THERMODYNAMICS TABLE : : Metal or a l l o y : 900°C : Ag : : : Ag-18%Au : Ag-26%Au : : : 80U °C : 1,000 : : : : 1,000 : : : 700°C : : 600°C .................. : : 900°C : :PH'2S 800°C : - - e q 700°C 0,988 : 0,988 : : : : 0,873 : : 0,795 : . : : : : : 0,219 : : : 0,224 : : : : : : : limit 700°C : 191 : : : 0,229 0,236 : : 0,245 : 185 : : : 0,255 0,263 135 : 114 : 90 : : 25 : : 25,5 :~ •.~S : : -265 i T/k :: : : : : 0,272 : 174 : : : : 0,790 0,340 : 0,303 : 0,351 : --- : : : 0,365 : --101 : : : 61 : : : 128 : : 67 : 50 : i0 : : : 32,7 : : 42,5 : : 58,3 : : -244 : : : : : -263,5 • : -254 : : : :: 7,8 :: : : 0,383 : i00 : : : 120 : : : 0,315 : • : : : 6,8 0,292 : 148 : : : : : 0,285 : : 165 : : : 162 6,8 0,249 : : : : : : 229 • : 0,224 0,870 : • : 900°C H2S 0,799 : : : : ~. .............. : : Solubility : at the : :AH : kJ/mole 0,875 : 0,936 " .~ ........... : 600°C : 0,802 ? ........... : 0,239 : : : • : 0,937 • : 0,876 : 600°C : 0,937 : 0,988 : : ~. .......... : 800°C 0,938 : ": : 1,000 : : 6 .~ ........ : 0,231 : 0,988 • : :PH2 : NO. 3 : : Ag 21, : Ag-10%Au : a Vol. : : 1,000 : SOLUTIONS : Ag-2%Au : : OF : 8,7 :: : -229 : : 9,9 :: .-......... ......... : ........ : . . . . . . . . . . : . . . . . . . . . . . .-. . . . . . . . . . . : . . . . . . . . . . . . . . : A c o m p l e t e a n a l y s i s of the t h e r m o d y n a m i c d a t a on the t e r n a r y A g - A u - H s y s t e m w o u l d r e q u i r e us to s t u d y the s u l p h u r s o l u b i l i t y at v a r i o u s h y d r o g e n p r e s s u r e s and to s i m u l t a n e o u s l y measure the bulk h y d r o g e n content. 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