Erhard Hayer

Enthalpy of formation of the (Pt–Sn) system

Abstract With a fully automated high temperature calorimeter the enthalpy of formation of the [Pt–Sn] liquid system was determined on the molar fraction range 0 Δ mix H m °=x(1−x)(−123.76−96.27x−119.62x 2 +88.89x 3 +97.58x 4 ) with x=x Pt . The enthalpies are negative over the entire concentration range with a minimum ΔmixHm°=−46.8±2 kJ mol−1 at x=0.554, independent of temperature. The limiting partial molar enthalpy of mixing of platinum is determined as Δ mix h m ° ∞ ( Pt sc , x Pt =0)=−124±5 kJ mol −1 . Enthalpies of formation and fusion of PtSn and Pt3Sn, respectively, have been determined by calorimetric measurements. They show that PtSn exists in an high temperature (H.T.) and a low temperature (L.T.) form, respectively: Δ for H m °( Pt 0.5 Sn 0.5 (L.T.), sol )=−74 kJ mol −1 , Δ for H m °( Pt 0.5 Sn 0.5 (H.T.), sol )=−63.5 kJ mol −1 , Δ for H m °( Pt 0.75 Sn 0.25 , sol )=−55.3 kJ mol −1 . Moreover, some points of the equilibrium phase diagram were obtained by the calorimetric experiments. The integral and limiting partial enthalpies of mixing have been compared with the data previously obtained for other (T.M.–Sn) systems. The energetic effect is caused by sharing 3 electrons from Sn at most with the uppermost bands of Pt.

The PtIn system: Enthalpies of formation of liquid and solid alloys

The integral enthalpies of mixing (ΔmixHmo = f(xPt)] of the Pt + In liquid system were determined using a very high temperature calorimeter in the ranges of temperature and molar fraction 1247 < T(K) < 1467 and 0 < xPt < 0.599 respectively. It can be described by the equation ΔmixHmo(kJ mol−1) = xPt(1 − xPt)[− 113.43 − 257.69xPt + 97.81xPt2 + 255.47xPt3 − 132.08xPt4]. This function is negative with a minimum ΔmixHmo = −48.6 ± 3.0 kJ mol−1 at xPt = 0.516, and is independent of temperature within experimental error. The limiting partial molar enthalpy of supercooled liquid Pt in liquid In deduced from experiments performed at 1170 K is Δmixhm(Pt supercooled liquid in ∞ liq In)o = −113.4 ± 5 kJ mol−1. In contrast, by extrapolation to xPt = 1, the limiting enthalpy of In in supercooled liquid Pt was obtained as Δmixhm(In liquid in ∞ liquid Pt)o = −150 ± 30 kJ mol−1. Moreover, by calorimetric measurements performed at 1320 K, the enthalpy of formation of Pt2In3 and the enthalpy of fusion of this compound were determined: ΔforHmo(Pt2In3(sol)) = −51.2 kJ mol−1; ΔfusHmo(Pt2In3) = +18.9 kJ mol−1. Some points of the liquidus were deduced from the calorimetric experiments: xPt = 0.2 with T = 1255 K, xPt = 0.347 and xPt = 0.442 with T = 1320 K, xPt = 0.53 with T = 1373 K and xPt = 0.594 with T = 1469 K. The enthalpies of mixing were compared with data (i) published on solid alloys, (ii) predicted by Miedemas semi-empirical model, and (iii) measured in the homologous system Pd + In. The strong negative enthalpy of formation is also discussed according to an electron transfer from In to Pt of 2.5 electrons at most.

Thermodynamics of nickel-tin liquid alloys

Copyright (c) 1996 Elsevier Science B.V. All rights reserved. An automated very high temperature calorimeter has been used to investigate the partial and integral enthalpies of mixing of liquid nickel+tin alloys in the temperature and molar fraction range 867<T/K<1579 and 0<x Ni <0.80 respectively. The enthalpies of mixing, D mix H° m =f(x Ni r are exothermic over the entire concentration range. They are represented by the following equation for temperatures between 1530 and 1580K: D mix H° m /kJmol −1 =x(1−xr(−46.01−6.788x−209.616x 2 +203.879x 3 −20.145x 4 r where x=x Ni . The coordinates of the minimum are D mix H° m =−20.2p0.6kJmol −1 at x Ni =0.60. The limiting partial molar enthalpy of Ni in liquid tin, referred to liquid Ni, was determined to be h° m (Ni (l& rpar; in ∞ Sn (l& rpar;r/kJmol −1 =−36.48−12960/T over the entire temperature range scanned. The change in Fermi enthalpy on alloying indicates a restricted number of electrons transferred from Sn to Ni for alloys with x Sn ?0.75. Higher tin concentrations do not change the number of electrons accepted by Ni.

The Fermi energy and the enthalpy of mixing

Abstract In this paper we describe a new function to determine the number of electrons transferred by alloying. H F , the new function proposed, is given by the difference of the partial enthalpies of the two constituents, i.e. H F = h ( i ) - h ( j ) - h ( i ) o and is called the Fermi enthalpy. It is retrieved from data calorimetrically measured. In some way, it describes the change in the enthalpic part of the Fermi energy on alloying. This function is determined for Pd + Ga, Pd + In, Ni + Ga, Ni + In, Pt + In, Au + Al and Ag + Al. The corresponding number of electrons transferred is calculated on stoichiometric considerations.

Enthalpies of formation of liquid and solid (gallium + palladium) alloys

The enthalpies of formation of liquid (Ga + Pd) alloys were determined by direct reaction calorimetry in the temperature range 1322 <T/K < 1761 and the molar fraction range 0 <xPd < 0.87. The enthalpies are very negative with a minimum ΔmixHm = −70.4 ± 3.0 kJ mol-1 atxPd = 0.6, independent of the temperature. Limiting partial molar enthalpies of palladium and gallium were calculated as Δhm (Ga liquid in ∞liquid Pd) = −265 ± 10 kJ mol−1 and Δhm (Pd liquid in ∞liquid Ga) = -144 ± 5 kJ mol−1. The integral molar enthalpy is given by ΔmixHm =x(1-x) (-143.73 -232.47x + 985.77x2-4457.8.x3 + 6161.1x4 + 2577.4x5), wherex = xPd. Moreover, values for the enthalpies of formation and fusion of PdGa, Pd2Ga, and the solid solution (withxPd = 0.8571) have been proposed. These results have been discussed taking into account the equilibrium phase diagram.

[Pd−Sn] system: enthalpies of formation of the liquid [Pd+Sn] and heat capacities of PdSn, PdSn2, PdSn3 and PdSn4 compounds

Abstract Using high temperature calorimeters, the molar enthalpies of formation of some [Pd−Sn] liquid alloys have been measured at 952, 1058, 1108, 1184, 1193, 1208, 1240, 1292 and 1372 K. The coordinates of the extremum of the Δ mix H m °= f ( x Pd ) have been estimated (Δ mix H m °=−73 kJ mol −1 with x Pd =0.71). Besides, the limiting molar partial enthalpies of liquid tin was extrapolated (Δ mix h m °(Pd liq. in ∞ liquid Sn)=−120±6 kJ mol −1 ) and some points of the liquidus were determined. With another technique, differential scanning calorimetry, the molar heat capacity of four solid alloys (PdSn, PdSn 2 , PdSn 3 and PdSn 4 ) have been measured.

The cobalt-indium system: enthalpy of formation and phase diagram

With a fully automated, high-temperature calorimeter, the molar enthalpy of formation of the [Co + In] liquid system was determined in the region 1080 K < T < 1765 K over a large mole fraction range. The molar enthalpy of formation of [Co + In] liquid alloys corresponding to the reaction, aCo(liq.) + bIn(liq.) = CoxIn1−x(liq.), with x = a/(a + b), is positive for all concentrations and may be expressed as: ΔmixHmo = xCo(1 − xCo)[28.11 + 46.73xCo − 121.04xCo2 + 63.91xCo3] in kJ mol−1. The values of the partial molar enthalpies of cobalt and indium were determined and the limiting values were calculated as Δhmo(Coliq. in ∞Inliq.) = + 28.1 ± 2.0 kJ mol−1 and Δhmo(Inliq. in ∞Coliq.) = + 17.7 ± 5.0 kJ mol−1. The shape of the graph ΔmixHmo = f(xCo) obtained in the region 1528 K < T < 1765 K confirms the existence of a liquid miscibility gap. A new position of the miscibility gap and the liquidus line on the In-rich side of the phase diagram is proposed: the coordinates of the critical point are located at 0.40 < xIn(cr) < 0.45 and Tcr = 1770 ± 5 K.

The limiting molar partial enthalpies of mixing of iron, cobalt, nickel, palladium and platinum in liquid gallium and indium

Gallium and indium have been used as solvents for the determination of the molar partial enthalpy of mixing Δmixhmo(TM, Ga or In) (denoting liquid transition metal (TM) in infinite liquid gallium or indium) of the pure liquid transition metals Fe, Co, Ni, Pd and Pt by direct reaction calorimetry between 1000 K and 1500 K with the exception of Δmixhmo(Fe, In) (because of the shape of its equilibrium phase diagram). All the limiting enthalpies listed below refer to the liquid state. With pure gallium as solvent, they correspond to the reaction TM(liq) − nGa(liq) → TM1Gan(liq) at the experimental temperature Te, with n ⪢ 1. 1. (i) Δmixhmo in gallium is found for Fe, Co, Ni, Pd and Pt to be −2, −44, −82, −144 and −155 kJ mol−1. 2. (ii) Δmixhmo in indium is found for Co, Ni, Pd and Pt to be +28, −25, −127 and −114 kJ mol−1. In both solvents, these limiting enthalpies vary with a similar trend. This observation makes it possible to predict the limiting molar partial enthalpy Δmixhmo(Fe, In) of mixing of iron in indium as +70 kJ mol−1. The results have been compared with the data proposed by Miedema and co-workers.

Fine structure of the melting process in pure CdTe and in CdTe with 2 mol% of Ge or Sn

Abstract The melting process of pure CdTe as well as of CdTe+2 mol% Ge and CdTe+2 mol% Sn was investigated experimentally by means of differential thermal analyses. The samples were heated above their respective melting temperatures T m and annealed at various defined temperatures before continuation of heating. Volume fractions of clusters, remaining in the melt even above the melting point, were derived from the area of the corresponding thermal effects. It was confirmed that the melt consists in all cases of two types of structures: clusters (with a short-range order close to the crystalline substance) within an amorphous matrix. The size of the clusters was estimated from the activation energies of the crystallization process; they were found to consist of about 66 to 98 atoms in pure molten CdTe. For two cases, pure CdTe and CdTe+2 mol% Ge, ‘hot crystallization’ was observed, i.e. after a given heat treatment the melt crystallized at temperatures above T m .

Chemical interaction in the liquid (Co + Ga), (Co + In), (Ni + Ga), and (Ni + In) systems

Abstract Although Co and Ni have very similar physical and chemical properties, the four binary systems with Ga and In reveal strong, medium, and weak interactions leading to a miscibility gap in (Co + In). Starting from high temperature calorimetric measurements on the liquid alloys, the chemical interaction of four systems is discussed. The energetic interactions are characterized by the respective integral and partial thermodynamic functions. χ-functions and the partial enthalpies show deviations from a subregular behaviour for (Ni + Ga), (Ni + In) and (Co + Ga) revealing strong association in the liquid alloys. Short range order parameters were calculated and different models discussed.