Transition metals, cohesion

The trend in the f-pressure is almost parabolic with band filling and this is typical for a transition metal (with d replaced by f). The physical basis was given by the Friedel who assumed that a rectangular density of states was being filled monotonically and thus was able to reproduce the parabolic trend in transition metal cohesive energies analytically. Pettifor has shown that the pressure formula can similarly be integrated analytically. 

Fig. 2. Calculated properties of the 3d and 4d transition metals-cohesive energy, lattice constant, and bulk modulus- compared with experiment (crosses). This represents a milestone in the development of the methods to calculate with sufficient accuracy to find these quantities. (From refs. 25 and 123, figure courtesy of V. MoruzzO... 

F. R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema and A.K. Niessen. Cohesion in Metals (Transition metal alloys). North-Holland, Amsterdam (1988). 

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

One of the reasons for my having attacked this problem in 1938 was that I was thoroughly dissatisfied with the claim of some physicists that only the s electrons were involved in the cohesion of the transition metals the observed magnetic properties were said to show that the bonding in Ni involves 0.61 s electrons per atom, that in Co involves 0.71, that in Fe involves 0.22, and that in Cu involves 1 (the d shell for copper having its full complement of 10 electrons). The physical properties of these 297 0022-4596/84 3.00... 

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

Considering other families of similar compounds, the contributions given by Guillermet and Frisk (1992), Guillermet and Grimvall (1991) (cohesive and thermodynamic properties, atomic average volumes, etc. of nitrides, borides, etc. of transition metals) are other examples of systematic descriptions of selected groups of phases and of the use of special interpolation and extrapolation procedures to predict specific properties. 

Nevertheless, the inspection of other transition metal series shows that, just as atomic volumes, there are regular variations of cohesive energies when the metal valence changes. Thus, a general increase of about 45 Kcal/mol is found when a metal transforms from a trivalent to a tetravalent state. 

In Fig. 7 the results of the model for the cohesive energy are given, and compared with the experimental values and with the results of band calculations. The agreement is satisfactory (at least of the same order as for similar models for d-transition metals). For americium, the simple model yields too low a value, and one needs spin-polarized full band calculations (dashed curve in Fig. 7) to have agreement with the experimental value. 

The trends in several ground state properties of transition metals have been shown in Figs. 2, 3 and 15 of Chap. A and Fig. 7 of Chap. C. The parabolic trend in the atomic volume for the 3-6 periods of the periodic table plus the actinides is shown in Fig. 3 of Chap. A. We note that the trend for the actinides is regular only as far as plutonium and that it is also broken by several 3 d metals, all of which are magnetic. Similar anomalies for the actinides would probably be found in Fig. 15 of Chap. A - the bulk modulus - and Fig. 7 of Chap. C - the cohesive energy if more measurements had been made for the heavy actinides. 

Fig. 7.11 The contributions to the cohesive energy of the 3d and 4d transition metals. (After Gelatt et al. (1977).)...

The parabolic variation in the cohesive energy across the 4d series is driven by the d-bond contribution alone, as is clearly demonstrated by Fig. 7.11. The sizeable drop in the cohesive energy towards the middle of the 3d series is a free-atom phenomenon, resulting from the special stability of Cr and Mn atoms with their half-full d shells. The simplest model for describing the bonding of transition metals is, therefore, to write the binding energy per atom as... 

The cohesive energy, equilibrium atomic volume, and bulk modulus across a transition metal series may now be evaluated by choosing the following simple exponential forms for ( and h(R), namely... 

Fig. 7.12 The theoretical ( ) and experimental (x) values of the equilibrium band width, Wigner-Seitz radius, cohesive energy, and bulk modulus of the 4d transition metals. (From Pettifbr (1987).)...

The nature of these two phases helps to throw light on the metal-nonmetal transition. For example there has been much speculation that hydrogen molecules at sufficiently high pressure, such as those occurring on the planet Jupiter, might undergo a transition to un alkali metal The fundamental transition is one of a dramatic change of the van der Waals interactions of H, molecules into metallic cohesion. ... 

Table 1.2 compares the melting points of transition metals with those of the carbides and nitrides. The trends in these values were already discussed in connection with the electronic properties of the compounds. Here, note is made of the elevated temperatures of the carbides and nitrides compared to the pure metals. They are among the highest for any type of material, and are more akin to those of the ceramic materials. The melting points are indicative of the high cohesive strengths in the materials. 

The precise nature of the electronic interactions between centers must obviously change dramatically at the NM-M transition, e.g., from van der Waals type interaction to metallic cohesion (112). These gross changes in electronic properties at the transition are sufficient to noticeably influence the thermodynamic features of the system (86,87). The conditions therefore appear highly conducive for a thermodynamic phase transition to accompany the electronic transition at the critical density. In fact, the transition to the metallic state in metal-ammonia solutions is accompanied by a decrease in both enthalpy and entropy (146, 149), and it has been argued convincingly (124, 125) that the phase separation in supercritical alkali metals and metal solutions is... 

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