Cohesive energy, properties, and formation energy of transition metal alloys

Abstract

The cohesive energy of transition metals and its contributions related to the s-and d-electrons are calculated. The correlation of interatomic bonding strength, molar volume, and compressibility of transition metals with cohesion energy and corresponding contributions to it is shown. It is demonstrated that the s-electrons play an important part in the cohesion of transition metals. The main contributions to the formation energy of disordered alloys of copper with transition metals are calculated using the tightbinding approach. The results obtained are in qualitative agreement with experimental data on the thermodynamic properties of Cu-3d-metal systems.In condensed state, atoms are held together by cohesive forces, which are the total forces exerted by an atom on its nearest neighbors. In most cases, it is very difficult to measure these forces because ultimate strength and elastic limit depend on the imperfection of samples in mechanical tests. Therefore, various physical properties associated with the cohesive forces and characterizing, in a way, the strength of interatomic bonds in a crystal are used as measures of these forces among atoms in a crystal lattice. These characteristics include various thermodynamic, elastic, and thermal constants of which the most important are sublimation heat, atomization energy, melting point, elastic modulus, Debye characteristic temperature, and thermal expansion coefficients [1].Since elucidating the physical and chemical nature of interatomic interaction and cohesive forces in transition metals and their alloys is of great importance for developing the theory of condensed phases and modern physical metallurgy, it appears expedient to try to asses their cohesive energy within the available chemical binding models. COHESIVE ENERGY AND PROPERTIES OF TRANSITION METALSIt was shown in [2−4] that the cohesive energy of transition metals is high due to the band energy of d-electrons and that the change of the energy along transition series may be associated with increased filling of the d-band. According to [2,4,5], the tight-binding model uses simple summation of one-electron cohesive energies to calculate the cohesive energy of a transition metal due to overlapping of d-electrons:where E d is the cohesive energy due to d-electrons; E f is the Fermi energy reckoned from the conduction-band bottom; E d is the energy of the atomic d-level spreading into a band of finite width W d ; B d is the energy of the d-band bottom; and n d (E) is the density of electron states in the d-band.Thus, to calculate the cohesive energy of transition metals and their alloys, it is necessary to know the density of electronic states n d (E) in the d-band. In the general case, the function n d (E) has a complicated form (there are minima Donbass State Mechanical Engineering Academy, Kramatorsk.

Shape‐Controlled Synthesis of Colloidal Metal Nanocrystals by Replicating the Surface Atomic Structure on the Seed

“…However, it still remains a grand challenge to achieve the same level of shape control for most of the platinum‐group metals (PGMs), including Pt, Ir, Rh, and Ru. The difficulty is likely related to the relatively high cohesive energies and/or the high specific surface free energies associated with PGMs, as these parameters have a direct impact on the nucleation and growth of nanocrystals …”

Electron microscopy studies of electron‐beam sensitive PbTe‐based nanostructures

“…The inner structure of these core/shell nanocrystals was also peculiar. Instead of carrying a single large Au domain inside, as for the structures displayed in Figures 4 and 5, and which should be expected given the large cohesive energy of gold (Turchanin et al, 2008), each nanocrystal contained many small (1–4 nm) high contrast domains, and in some cases even 10 of them. Again these inner domains, as revealed by HRTEM, had lattice parameters that could be up to 4–5% larger than that of fcc gold.…”

Atomically resolved tomography to directly inform simulations for structure–property relationships

“…To demonstrate this concept, we have carried out DFT simulations to calculate 'local cohesive energy', 'local Fermi energy' and 'local elastic moduli' within regions of the specimen. The cohesive energy is closely correlated with many properties, including interatomic bonding strength, molar volume and compressibility 32 , while the Fermi energy is critically important for the electrical and thermal properties of solids 33 .…”