Calculation‐ of Some Defect Parameters in F.C.C. Metals

Abstract

The lattice statics model together with the atomistic continuum model is used for the calculation of relaxation due to a vacancy, the vacancy formation energy and divacancy binding energy in the case of some f.c.c. metals whose phonon dispersion curves are available. Using the measured phonon dispersion relations and the elastic constants as constraints the dynamical matrix is derived considering interactions up to the eighth nearest neighbouring shell. The calculation shows that in all the cases the first twelve nearest neighbours relax towards the vacancy and the magnitude of the displacements of the distant neighbours decreases systematically. The available experimental values of the monovacancy formation energy and divacancy binding energy whereever available, show fairly good agreement. Relations among monovacancy formation energy, melting temperature, and activation energy for selfdiffusion are proposed.Das statische Gittermodell zusammen mit dem atomistischen Kontinuumsmodell werden fur die Berechnung der Relaxation, die eine Leerstelle hervorruft, benutzt sowie fur die Leerstellenbildungsenergie und die Doppelleerstellenbindungsenergie fur den Fall einiger k.f.z.-Metalle, deren Phonondispersionskurven zur Verfugung stehen. Mit den gemessenen Phonondispersionsbeziehungen und den elastischen Konstanten als Zwangsbedingung wird die dynamische Matrix unter Beriicksichtigung der Wechselwirkungen bis zu den acht nichsten Nachbarschalen abgeleitet. Die Berechnung zeigt, daD in allen Fallen die ersten zwolf nachsten Nachbarn in Richtung der Leerstelle relaxiieren und die GroDe der Verschiebungen der entfernteren Nachbarn systematisch abnimmt. Die zur Verfugung stehenden experimentellen Werte der Monoleerstellenbildungsenergie und Doppelleerstellenbindungsenergie zeigen ziemlich gute Ubereinstimmung. Beziehungen zwischen Monoleerstellenbildungsenergie, Schmelztemperatur und Aktivierungsenergie fur die Selbstdiffusion werden vorgeschlagen.

Density functional calculations of the formation and migration enthalpies of monovacancies in Ni: Comparison of local and nonlocal approaches

“…Theoretically, many various approaches are also available. They can be partitioned into two groups corresponding to first-principles local spin density approximation ͑LSDA͒ [18][19][20][21]26,27 or generalized gradient approximation ͑GGA͒ 26,27 approaches and various semi-empirical methods [21][22][23][24][25] as molecular statics and dynamics calculations, 28,29 lattice statics model, 30 or embedded atoms methods ͑EAM and MEAM͒. 31,32 LDA or LSDA calculations lead to values ranging from 1.77 to 1.81 eV.…”

The Vacancy Energy in Metals: Cu, Ag, Ni, Pt, Au, Pd, Ir and Rh

“…4 shows that the embedding function goes through the appropriate range of electron densities and the characteristics curves tends to group: Cu, Pd with Au and also Pt with Rh. [20]; e [21]; g [39]; h [24] i ; [25] ; j [26] ; l [27]; l* [28] ; m [29]; n [30] ; p [31] ; q [32] r [33]; t [34] [20]) ; f [22] ; g [23] ; * Computed using equation (8) [37] ; v [38] ; y [16]) Fig. 1.…”

“…Here, is the equilibrium electron density of a-type atoms, Ω is the atomic volume of a -type atoms and Ω is the atomic volume of b -type atoms. [20]; e [21]; f [22]; g [23]; h [24]; i [25]; j [26]…”

Perspectives on the Theory of Defects

“…In this situation, theoretical estimates of the vacancy formation energy have become an increasingly attractive alternative. The early theoretical attempts were based on purely elastic considerations (Kornblit, 1981;Krause et al, 1989;Ghorai, 1991) or on calculations based on empirical interatomic potentials (Harder and Bacon, 1986;Ackland et al, 1987;Rosato et al, 1989). In the early 1990's, ab-initio codes based on densityfunctional theory became powerful enough to allow electronic structure calculations of vacancy formation energies in simple metals such as Al and Li (Beuerle et al, 1991;Mehl and Klein, 1991;Benedek et al, 1992).…”