A Review of some Theoretical Models for Point Defect Calculations

Abstract

A Brief Sketch of Different Models for the Calculation of Defect Parameters in Metals and Alloys, Comparison of Data and Limitations Has Been Reviewed here; Especially Relaxations due to a Vacancy Type of Point Defect, its Formation, Migration, Activation Energies and Related other Parameters Based upon the Present Experimental Status. the Models Reviewed Are the Bond Model, Continuum Model, Semi-Discrete Model, Jellium Model, Thermodynamic Model, Lattice Statics Model, Atomistic Continuum Model and Pseudopotential Model. the Main Thrust Concerns the Last Model. the Taylor, Vashishta and Singwi, Harrison, Kleinmann and King and Kutler Form of Exchange and Correlation Function Are Almost Similar, Give Moderate Results and May Be Trusted for Better Results.

Calculation of Parameter of the Ashcroft Model Potential for Hexagonal Closed Pack (hcp) Crystals

“…A graph shown in Fig. 5 for atomic number and fitted r c for different fcc [1] and hcp cubic crystals satisfies this idea. Thus out of two valence states (1, 2) for beryllium z = 1 has been chosen.…”

“…Here f (q) is the exchange and correlation function (hence forth called ECF). Out of several ECFs only nine such forms are taken into account and the expressions [1] are King and Kutler ECF (abbreviated henceforth as K-K)…”

“…The pseudopotential approach has been tested earlier several times [1][2][3] and in this paper this formalism is applied to twenty two different hexagonal closed pack (hcp) crystals, viz. (1) beryllium (Be), (2) magnesium (Mg), (3) scandium (Sc), (4) titanium (Ti), (5) cobalt (Co), (6) zinc (Zn), (7) yttrium (Y), (8) zirconium (Zr), (9) technetium (Tc), (10) ruthenium (Ru), (11) cadmium (Cd), (12) gadolinium (Gd), (13) terbium (Tb), (14) dysprosium (Dy),(15) holmium (Ho), (16) erbium (Er), (17) thullium (Tm), (18) lutetium (Lu), (19) hafnium (Hf), (20) rhenium (Re), (21) osmium (Os) and (22) thallium (Tl) (arranged according to increasing atomic number).…”