A.R. Miedema

Cohesion in alloys — fundamentals of a semi-empirical model

Abstract A semi-empirical model of alloy cohesion involving two material constants for each element is introduced by means of the physical ideas underlying the scheme. The resulting expressions for the heat of formation of binary alloys are presented and their applicability in various extreme situations is discussed. The model is shown to reproduce a vast amount of experimental information on the sign of heats of formation. Detailed comparison with experiment for particular classes of alloys will be presented in the sequels to this paper.

On the heat of formation of solid alloys

Abstract We demonstrated recently that the available experimental data on the heat of formation of solid alloys of transition metals can be accounted for by means of a cellular model. The energy effect is derived from two contributions; a negative one, arising from the difference in chemical potential, ϑ∗, for electrons at the two types of atomic cells, and a second term, which reflects the discontinuity in the density of electrons, n ws , at the boundary between dissimilar atomic cells. Expressed as a formula, ΔH ~ [-Pe(Δϑ∗) 2 + Q(Δn ws ) 2 ] . In this paper we demonstrate that the second term is preferably to be written as Q 0 (Δn 1 3 ws ) 2 . Values for P and Q 0 can be derived from basic arguments. The advantage of this alteration is that the values for P and Q 0 are now nearly the same for widely different alloy systems (i.e., as different as intermetallic compounds of two transition metals, and liquid alloys of two non-transition metals). It is demonstrated that the description (and hence the predictions) for heats of formation of alloys of transition metals is sufficiently accurate to be of practical interest. The present model conflicts strongly with descriptions of heats of formation of transition metal alloys in terms of the Engel-Brewer theory.

The electronegativity parameter for transition metals: Heat of formation and charge transfer in alloys

It is demonstrated that a cellular model gives an excellent account of the heat of formation of binary alloys of 27 transition metals. The energy effects are described by two terms, the first representing the difference in electronegativity between the two types of atoms in an alloy and the second term reflecting the discontinuity in the density of electrons at the boundary between dissimilar Wigner-Seitz atomic cells. The electronegativity is expressed in a scale which closely resembles that of the experimental work functions of pure metallic elements. The use of this scale also gives a clear insight into the heat effects which accompany the alloying of transition metals with non-transition metals. If the latter have p-electrons a negative term adds up to the heat of formation which apparently does not depend on the particular metals considered. As a result, simple rules for the alloying behaviour of transition metals are formulated which have an accuracy between 96 and 100%; the electronegativity concept is shown to apply also for hydrogen in metals. The relation between the charge transferred per atom, ΔZa, and the difference in electronegativity, Δφ∗, is discussed quantitatively. As an example, the result for solid solutions of two transition metals is ΔZa = 1.2 (1 − ca)Δφ∗, where ca is the concentration of metal A. Our analysis supports the idea that the work function of a metal is, in principle, proportional to the chemical potential for electrons in Wigner-Seitz atomic cells; the proportionality factor is found to be about 1·4.

On the heat of formation of solid alloys. II

Abstract In Part I of this paper [1] it has been shown that a relatively simple atomic model does account for the sign of the heat of formation, ΔH, in a wide variety of alloy systems. Here we consider numerical values of ΔH for solid alloys; a quite satisfactory agreement is obtained for the heat of formation of intermetallic compounds of transition metals, including their borides, carbides and nitrides. Transition metal suicides, germanides, carbides, and nitrides, can be treated in the same way as the other compounds if one allows for an additional positive energy contribution required to convert elementary Si, Ge, C or N2 into a metal (8, 6, 24 and 57 kcal per gram-atom of these four elements, respectively). As an example, predictions for heats of formation of binary intermetallic compounds containing a rare-earth element have been tabulated.

Hydrogen absorption in LaNi5 and related compounds: Experimental observations and their explanation

Results are given of a study of the change in hydrogen sorption properties caused by partly replacing La or Ni in LaNi5 by other metals. Desorption isotherms at 40 deg C were measured for or Cu, and for La0.8R0.2Ni5, where represents Nd, Gd, Y, and Er, also Th and Zr. Equilibrium hydrogen pressures in the two-phase region can be explained qualitatively by assuming that the more stable the original RNi5 compound, the weaker is the tendency to form a RNi5--hydride, i.e., the higher the equilibrium pressure obtained for the hydride. This assumption which connects the stability of ternary hydrides with the heat of formation of the original compounds can also be formulated in a more quantitative way. This leads to a fair description of the experimental observations for the compounds having the CaCu5 type of structure.

Which intermetallic compounds of transition metals form stable hydrides

Abstract The stability of ternary hydrides with respect to their decomposed state ( i.e. , to a transition metal intermetallic compound and hydrogen gas) is discussed in terms of a model that predicts the enthalpy of formation of a ternary hydride from a knowledge of ΔH values for the corresponding binary hydrides and binary intermetallic compounds. We present predictions for the stability of hydrides formed from compounds AB n ( n ⩾ 1), where A is one of the metals Sc, Y, Gd, La, Ti, Zr, Hf, Th, U or Pu, and B is one of the transition metals.

Enthalpies of formation of liquid and solid binary alloys based on 3d metals

Abstract Model predictions are presented for heats of formation of binary intermetallic compounds of Sc, Ti or V with arbitrary metal partners, and for heats of mixing and solution of the corresponding liquid alloy systems. Predicted values are compared with the existing experimental data as well as with qualitative information derived from phase diagram information. A complete set of binary phase diagrams based on Sc, Ti or V is presented in schematic form. Differences between experimental and calculated enthalpy values are discussed.

Hydrogen absorption in intermetallic compounds of thorium

Abstract The formation of ternary hydrides has been studied for 15 intermetallic compounds of thorium, (five compounds in each of the systems Th-Ni, Th-Co and Th-Fe). With the exception of the compounds richest in 3 d -metal, they all form hydrides by reaction with hydrogen gas at room temperature. The hydrides prepared include the compounds ThCoH 4 , ThNi 2 H 5 and Th 7 Ni 3 H 28 - Some compounds (Th 2 Co 7 H 4 , Th 2 Fe 7 H 5 ) have equilibrium hydrogen pressures near to 1 atmosphere at 300 K. The results are discussed in terms of a model that predicts the enthalpy of formation of a ternary hydride from the knowledge of ΔH for the corresponding binary hydrides and binary intermetallic compounds. In addition we discuss experimental results on hydrogen absorption in LaNi 5 and related compounds, published earlier. The agreement between model predictions and experiment is quite convincing.

On the valence state of europium in alloys

Abstract As a pure metal, the element europium is divalent; it is more like Ca than it is like the other rare-earth metals. In alloys, Eu can also be trivalent. Using Gschneidners [1] result that the energy difference between divalent and trivalent metallic Eu is equal to 23 kcal/g-at., and the model calculations for the enthalpy of formation of transition metal alloys that we presented in a recent paper [2, 3], we are able to account for the experimental data on the valence state of Eu in intermetallic compounds. We also give predictions for those binary systems of Eu with a transition metal, on which experimental information is lacking.

Thermal expansion anomalies of rare earth-cobalt compounds

Determinations have been made of the thermal expansion of the compounds SmCo5, Sm2Co7, SmCo3, Gd2Co17, GdCo5, Gd2Co7, GdCo3 and GdCo2 in the range from room temperature to 700 °C. With the exception of Gd2Co17 all compounds show an abnormal thermal expansion below the Curie temperature. These results are in keeping with the pressure dependence of the Curie temperature observed for the rare earth-cobalt compounds.