Miedema's Semi-empirical Model Research Articles

The PtIn system: Enthalpies of formation of liquid and solid alloys

The integral enthalpies of mixing ( Δ mix H m o = f( x Pt)] 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 < x Pt < 0.599 respectively. It can be described by the equation Δ mix H m o ( kJ mol −1) = x Pt(1 − x Pt)[− 113.43 − 257.69 x Pt + 97.81 x Pt 2 + 255.47 x Pt 3 − 132.08 x Pt 4] . This function is negative with a minimum Δ mix H m o = −48.6 ± 3.0 kJ mol −1 at x Pt = 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 Δ mix h m(Pt supercooled liquid in ∞ liq In) o = −113.4 ± 5 kJ mol −1 . In contrast, by extrapolation to x Pt = 1, the limiting enthalpy of In in supercooled liquid Pt was obtained as Δ mix h m(In liquid in ∞ liquid Pt) o = −150 ± 30 kJ mol −1 . Moreover, by calorimetric measurements performed at 1320 K, the enthalpy of formation of Pt 2In 3 and the enthalpy of fusion of this compound were determined: Δ for H m o ( Pt 2 In 3( sol) ) = −51.2 kJ mol −1; Δ fus H m o ( Pt 2 In 3) = +18.9 kJ mol −1 . Some points of the liquidus were deduced from the calorimetric experiments: x Pt = 0.2 with T = 1255 K, x Pt = 0.347 and x Pt = 0.442 with T = 1320 K, x Pt = 0.53 with T = 1373 K and x Pt = 0.594 with T = 1469 K. The enthalpies of mixing were compared with data (i) published on solid alloys, (ii) predicted by Miedema's 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.

Standard enthalpies of formation of some carbides, silicides and germanides of cerium and praseodymium

The standard enthalpies of formation of some congruent-melting compounds in the binary systems ReX, where Re  Ce, Pr or La and X  C, Si or Ge have been determined by direct-synthesis calorimetry at 1473 ± 2 K. The following values of ΔH f o are reported: CeC 2, −25.4 ± 1.4 kJ (mol atom) −1; CeSi 2, −60.5 ± 2.0 kJ (mol atom) −1; CeSi, −71.1 ± 3.3 kJ (mol atom) −1; Ce 5Ge 3, −73.4 ± 2.3 kJ (mol atom) −1; CeGe 1.6, −75.6 ± 1.9 kJ (mol atom) −1; PrC 2, −29.4 ± 1.6 kJ (mol atom) −1; PrSi 2, −61.5 ± 1.7 kJ (mol atom) −1; PrSi, −78.1 ± 1.9 kJ (mol atom) −1; Pr 5Ge 3, −70.4 ± 2.3 kJ (mol atom) −1; PrGe 1.6, −81.7 ± 1.7 kJ (mol atom) −1; LaSi 2, −56.8 ± 2.5 kJ (mol atom) −1. The results are compared with earlier experimental data, with predicted values from Miedema's semiempirical model, and with available data obtained for Sn and Pb compounds by Borzone et al., by Palenzona and by Palenzona and Cirafici.

Standard enthalpies of formation of some borides of Ce, Pr, Nd and Gd by high-temperature reaction calorimetry

The standard enthalpies of formation of five lanthanide borides have been determined calorimetrically at 1473 ± 2 K. The following values of ΔH f 0 are reported: PrB 6, − 51.3 ± 5.7 kJ/g · atom (this value was determined by solute-solvent drop calorimetry); CeB 4, − 53.5 ± 1.5 kJ/g · atom; PrB 4, − 53.1 ± 1.6 kJ/g · atom; NdB 4, − 53.3 ± 1.5 kJ/g · atom; Gd 2B 5, − 43.1 ± 1.4 kJ/g · atom (these four values were all obtained by direct synthesis calorimetry from the elements). The results are compared with earlier experimental data and with values predicted from Miedema's semi-empirical model. Finally, a systematic comparison is presented between the considered boride data and values for compounds of the rare-earth metals with Al, Ga, In and Tl taken from the published literature.

Standard enthalpies of formation of some neodymium and gadolinium carbides, silicides and germanides by high-temperature direct-synthesis calorimetry

The standard enthalpies of formation of some congruent-melting compounds in the binary systems Nd + X and Gd + X (where X = C, Si, Ge) have been determined by direct-synthesis calorimetry at 1473 ± 2 K. The following values of ΔH0f (kJ/g.atom) are reported: NdC2, −29.2 ± 1.4; NdSi2, −62.0 ± 1.9; NdSi, − 78.7 ± 2.5; Nd5Ge3, −72.1 ± 1.6; NdGe1.6, −80.2 ± 1.9; GdC2, −24.8 ± 1.6; Gd5Si3, − 68.0 ± 2.3; GdSi2, −59.0 ± 2.1; Gd5Ge3, −82.0 ± 2.6. The results are compared with some earlier experimental data (all derived from e.m.f. or vapor pressure measurements), with predicted values from Miedema's semi-empirical model, and with earlier calorimetric data for NdX3 and GdX3 (where X = Sn, Pb).

Standard enthalpy of formation of Cu 3As and heats of mixing in the liquid systems CuAs and FeAs by direct combination high temperature drop calorimetry

The standard enthalpy of formation of the congruent melting compound Cu 3As (m.p. 1000 K) was determined by high temperature direct synthesis drop calorimetry in fused silica capsules at 1113 K. We found ΔH f o (298 K) = −14.6 ± 3.8 kJ mol −1. Using our measured values of the heats of reaction of the process aAs(s)+ bCu(s) → cCu 1− x As x (1) at 1113 K, we calculated the liquid-liquid enthalpies of mixing for three alloy compositions in Cu 1− x As x : x=0.235, 0.26 and 0.375. We carried out similar measurements at 1123 K for the eutectic alloy Fe 1− x As x (1) at x = 0.24. The calorimetric results for the solid and liquid alloys are compared with predicted values from Miedema's semiempirical model.

Standard enthalpies of formation of some rare earth carbides by direct synthesis calorimetry

The standard enthalpies of formation of carbides in the binary systems Sc-C, Y-C and La-C have been determined by direct synthesis calorimetry at 1473 ± 2 K. The following values are reported: ΔH f 0(Sc 2C) = −45.5 ± 1.6 kJ (g atom) −1; ΔH f 0(Y 2C) = −31.8 ± 1.3 kJ (g atom) −1 and ΔH f 0 (LaC 2) = −27.2 ± 1.4 kJ (g atom) −1. The results are compared with earlier experimental data and with values predicted from Miedema's semi-empirical model. The enthalpies of formation for the carbides considered are also compared with the corresponding data for silicides and germanides.

Phase transformations in the NbAu system by ball milling and the study of the metastable phases

A detailed study on the NbAu binary alloy system upon ball milling is reported. An analysis of the energy levels of the NbAu alloy reveals that the solid solution has a lower enthalpy than the amorphous state for all compositions. The ball milling experiments were performed on five compositions of the NbAu alloys. All five alloys transformed to solid solutions after 40h of grinding. The structures of these solid solutions are different depending on the composition of the starting material. In further experiments, the properties of the metastable phases obtained by ball milling were studied. The lattice parameter of the solid solutions turns out to obey Vegard's law. The exothermic heat of the phase restoration appears to be approximately proportional to the enthalpy as predicted by Miedema's semi-empirical model. The magnitude of the peak temperatures and the activation energies follows the same trend as the melting temperaures. Examination of particle size and shape for two composition gives more insight in the milling process. Finally, the results for prolonged milling are presented.

Thermochemistry of Binary and Ternary Noble Metal Alloys: the Systems Cu-Ce, Ag-Ce, Au-Ce, Cu-Ag-Au, and Ce-Ag-Au

The enthalpies of mixing of the liquid alloys in the binary systems Cu-Ce, Ag-Ce, Au-Ce and in the ternary liquid systems Cu-Ag-Au and Ce-Ag-Au have been measured by high-temperature calorimetry at 1473 ± 2 K. The standard enthalpies of formation of congruently melting inter- metallic compounds in the considered binary systems have also been determined. The results obtained for the solid alloys are compared with predicted values from Miedema's semiempirical model. Interpretation of the data for the two ternary liquid alloy systems has been based on a model which includes contributions from two-body and three-body interactions which occur in the solutions.

Standard enthalpies of formation of 5d aluminides by high-temperature direct synthesis calorimetry

The standard enthalpies of formation of aluminides in the binary systems La-Al, Hf-Al, Ta-Al, W-Al, Re-Al and Pt-Al were determined by direct synthesis calorimetry at 1473 ± 2 K. The results are compared with earlier experimental data and with predicted values from Miedema's semi-empirical model. In systematic plots the enthalpies of formation of 5d aluminides are compared with similar data for the 3d and 4d aluminides, and with enthalpy data for the 5d borides, germanides and silicides.

EXAFS study of chemical short-range order in amorphous Ni xTi 1−x alloys

Extended X-ray absorption fine structure (EXAFS) measurements of amorphous Ni xTi 1- x alloys produced by planar magnetron sputtering were obtained using the transmission detection technique at both Ti and Ni absorption K edges. The local environment was determined around the two atomic species by fitting the filtered EXAFS functions. The result reflects the presence of chemical short-range order (CSRO) which favours unlike atomic bonds. Using Miedema's semi-empirical model, the CSRO in amorphous Ni x Ti 1- x is found to be intermediate between that of a random alloy and that of an ordered crystalline alloy. The results are compared with those of other amorphous alloy systems.

Mechanically-induced phase transformation and magnetic properties of σ-CrFe

A phase transformation of σ-CrFe to the bcc solid solution during high-energy ball milling was monitored by X-ray diffraction, AC susceptibility and high-field magnetization measurements. The saturation magnetization shows a maximum as a function of milling time. The increase is ascribed to the phase transformation, the decrease during further milling to the generation of nanocrystalline material. The phase transformation from the σ-phase to the solid solution is discussed in terms of Miedema's semi-empirical model.

Standard enthalpies of formation of 4d aluminides by direct synthesis calorimetry

The standard enthalpies of formation of aluminides in the binary systems Y+Al, Zr+Al, Nb+Al, Mo+Al and I'd + Al have been determined by direct synthesis calorimetry at 1473 ± 2 K. The results are compared with earlier experimental data and with predicted values from Miedema's semi-empirical model. In systematic graphs the enthalpies of formation of the 4d-aluminides are compared with enthalpy data for the corresponding borides, germanides and silicides.

Standard enthalpies of formation of some refractory borides of 4d and 5d elements from high-temperature direct synthesis calorimetry

The standard enthalpies of formation of YB2, TaB2, and W2B5 have been determined by direct synthesis calorimetry at 1473 ± 2 K. The following values are reported: [math] (YB2) = -35.7 ± 2.6 kJ/g.atom; [math] (TaB2) = -53.3 ± 2.0 kj/g.atom; [math](W2B5) = -17.5 ± 1.1 kJ/g.atom. Two new techniques which facilitate completeness of reactions at the calorimeter temperature are discussed. The results are compared with available thermodynamic data from the Literature and with predicted values from Miedema's semi-empirical model.

THERMAL STABILITY OF REACTIONS OF TRANSITION METALS WITH GaAa

In this paper, the formation enthalpies of the final phases presented in annealed contacts composed of transition metals (Pd, Pt, Ni, Ir, Rh, Co, Ti, Cr, V, Zr) and GaAs are calculated by using Miedema's semi-empirical model. Furthermore, the free energies of reaction both for the formations of the final phases and for the decompositions of the final phases containing As are calculated. These calculated results are compared with the experimental values. We reach the conclusion that for most of the above systems, the free energies of reaction can be adopted to assess the formation temperatures and the stabilities for the final phases.

Standard enthalpies of formation of Me 5Ge 3( Me ≡ Sc, Y, La) by high-temperature calorimetry

The standard enthalpies of formation of the germanides Me 5Ge 3( Me ≡ Sc, Y, La) were determined by high-temperature calorimetry at 1473 ± 2 K. The following values are reported: ΔH f o ( Sc 5 Ge 3) = − 747.3 ± 30.8 kJ mol − 1 and ΔH f o ( Y 5 Ge 3) = − 718.2 ± 39.9 kJ mol − 1, measured by solute-solvent drop calorimetry, and ΔH o f ( La 5 Ge 3) = − 543.9 ± 8.0 kJ mol − 1, measured by the direct synthesis method. The results are compared with estimated values from Miedema's semi-empirical model.

Construction of free-energy diagrams of amorphous alloys

Free-energy diagrams of amorphous alloys are constructed using Miedema's semiempirical model of heats of formation. These diagrams account for the experimental glass-forming concentration range in binary alloys of transition metals. One of the main factors controlling glass formation is the elastic contribution to the heat of mixing of the solid solution phase. Free-energy diagrams of this kind are also useful for interpreting some characteristic processes occurring in amorphous systems, such as the spontaneous vitrification observed by Von Allmen and coworkers in several Ti-based and Nb-based alloys.

Application of the Miedema model to formation enthalpies and crystallisation temperatures of amorphous alloys

The function fBA-which defines the degree by which an A atom is surrounded by neighbours of B atoms in Miedema's semi-empirical model and is used for the calculation of the formation enthalpy of crystalline alloys-is modified for amorphous alloys. For the five alloy systems considered, the fBA function turns out to be well described by fBA=cBs(1+5(cAscBs)2). This fBA also reflects the existence of chemical short-range order. In addition, Buschow's prediction for the crystallisation temperature of amorphous alloys is modified using this fBA, resulting in the relation Tx=5 Delta Hhs+275, where Delta Hhs represents the formation enthalpy of a hole of the same size as the smaller atom.

Magnetic properties and 151Eu Mössbauer effect studied in Eu-Ga and Eu-Sn intermetallic compounds

An investigation of the magnetic properties of various intermetallic Eu-Ga and Eu-Sn compounds is reported. It is shown that in the paramagnetic regime the magnetic properties behave in accordance with the Curie-Weiss law and the effective moments are close to the value expected for europium in the divalent state. All these compounds give rise to antiferromagnetic ordering at low temperatures. Metamagnetic behaviour was found in Eu 3 Ga 8 and in the low-temperature phase of EuGa 2 . From the lattice constants determined for all compounds investigated values were derived for the volume contraction associated with compound formation. These volume contractions are discussed in terms of Miedema's semi-empirical model. The values of the 151 Eu isomer shift were analysed by means of the Miedema and Van der Woude model after applying a correction term related to the volume contraction. For all Eu-Ga compounds the 151 Eu hyperfine fields at 4.2 K were determined.

Liquidus Curves of Eutectic NaK and NaCs Systems

The Conformal Solution and Flory's expressions for the free energy of mixing ΔGM of a binary liquid alloy have been modified by using a form for the enthalpy of mixing ΔHM which incorporates the concentration dependence given by Miedema's semiempirical model. This model emphasizes the importance of the atomic cell-surface area concentration in evaluating ΔHM. The modified forms of ΔGM have been used to construct the liquidus curves of NaCs and NaK.