合金计算

Ab-Initio Thermodynamics of Metal Alloys: From the Atomic to the Mesoscopic Scale

Stefan M¨u ller

Universit¨a t Erlangen-N¨u rnberg,Lehrstuhl f¨u r Festk¨o rperphysik

Staudtstr.7,91058Erlangen,Germany

Abstract.Density functional theory(DFT)based calculations allow us to study a number of metal alloy properties,as e.g.formation enthalpies,or electronic and elastic properties of intermetallic compounds.However,such so-called ab-initio cal-culations can only be applied as long as the alloy structure requires only small unit cells for the crystallographic description.It will be demonstrated how this limitation can be overcome without giving up the accuracy of DFT calculations by combin-ing them with so-called Cluster Expansion(CE)methods and Monte-Carlo(MC) simulations.This concept gives access to systems containing more than a million of atoms and therefore,permits to treat alloy properties which possess a delicate temperature-dependence.As examples,we discuss mixing enthalpies,short-range order,and precipitation without any empirical parameters as input,but with an accuracy that allows for the quantitative prediction of experimental results.

1Introduction

The increasing interest in metal alloys comes from their widefield of techni-cal applications ranging from lightweight cars and aircraft turbine blades to protective coatings in corrosive environments and magnetic devices.Beside experimental studies which are sometimes connected with a tremendousfi-nancial effort,more and more computer based approaches attract attention by many research groups.The set of all such theoretical methods forms a new discipline known as“computational materials science”.Indeed,this expres-sion includes a large number of different approaches reaching from contin-uum theory and semi-empirical accesses to so-calledfirst-principles methods, mostly based on density functional theory[1,2].Since the latter is strictly based on quantum-mechanical rules,it has a real predictive power,and–from a physical point of view–seems to be the most elegant solution to treat alloy problems.One should,however,keep in mind that we are already confronted with a many-body problem on a atomic scale and now,have tofind a way, how such calculations may be used to describe properties which are directly connected to the phase stability of an alloy,as e.g.short-range ordering.In principle,this demands to solve the following three problems:

(i)The problem of bridging length scales:Many material properties take place on a mesoscopic or even macroscopic scale,i.e.model systems consisting of millions of atoms are necessary–a number far beyond the capacity of today’s computers.

B.Kramer(Ed.):Adv.in Solid State Phys.44,415–426(2004)

c Springer-Verlag Berlin Heidelberg2004