Metals elastic constants

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

Mehl M J and Papaconstantopoulos D A 1996 Applications of a tight-binding total-energy method for transition and noble metals Elastic constants, vacancies and surfaces of monatomic metals Phys. Rev. B 54 4519... 

In table 2 and 3 we present our results for the elastic constants and bulk moduli of the above metals and compare with experiment and first-principles calculations. The elastic constants are calculated by imposing an external strain on the crystal, relaxing any internal parameters (case of hep crystals) to obtain the energy as a function of the strain[8]. These calculations are also an output of onr TB approach, and especially for the hep materials, they would be very costly to be performed from first-principles. For the cubic materials the elastic constants are consistent with the LAPW values and are to within 1.5% of experiment. This is the accepted standard of comparison between first-principles calculations and experiment. An exception is Sr which has a very soft lattice and the accurate determination of elastic constants is problematic. For the hep materials our results are less accurate and specifically in Zr the is seriously underestimated. ... 

Kim, J.O., Achenbach, J.D., Mirkarimi, P.O., Shinn, M. and Barnett, S.A, (1992), Elastic constants of single-crystal transition-metal nitride, films measured by line-focus scoustic microscopy , Journal of Applied Physics, Vol. 72 5, 1805-1811. 

Steinle-Neumann G. and Stixrude L. (1999) First-principles elastic constants for the hep transition metals Fe, Co and Re at high pressure. Phys. Rev. B 60, 791-799. 

The anomalous temperature dependence of elastic constants found from the CJTE calculations is shown for transition metal compounds of the NiCr204 and CuCr204 type crystals on the Fig. 4. As in this case the soft acoustic mode is double degenerate there is a splitting of the high symmetry modulus of elasticity Ci of the cubic crystal phase in C2 and C3 constants of the tetragonal phase. 

Timgsten has been of keen theoretical interest for electron band-structure calculations [1.14-1.25], not only because of its important technical use but also because it exhibits many interesting properties. Density functional theory [1.11], based on the at initio (nonempirical) principle, was used to determine the electronic part of the total energy of the metal and its cohesive energy on a strict quantitative level. It provides information on structural and elastic properties of the metal, such as the lattice parameter, the equilibrium volume, the bulk modulus, and the elastic constants. Investigations have been performed for both the stable (bcc) as well as hypothetical lattice configurations (fee, hep, tetragonal distortion). 

FIGURE 1.10. Shear modulus G, bulk modulus K, Young s modulus E, and Poisson s ratio v of tungsten vs. temperature, as calculated fium single-crystal elastic constants (Gj, E, and v ) [1.31], and from measurements on polyciystalline tungsten (G, K, E, and Vj). [1.30] Taken from Metals Handbook [1.40]. o... 

Mehl M. J. and Papaconstantopoulos D. A., Apphcations of a Tight-Binding Total-Energy Method for Transition and Noble Metals Elastic Constants, Vacancies and Surfaces of Monatomic Metals, Phys. Rev. B54, 4519 (1996). 

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