TABLE OF CONTENTS The design of useful materials generally involves the simultaneous optimisation of large numbers of parameters, often in circumstances where the interactions between the parameters are ill-defined. This chapter describes some of the methods by which the task can be enhanced using quantitative models which cover a range of disciplines and which include both rigour and empiricism. From the scientific point of view, modelling can lead to the creation of new theory capable of dealing with complexity; the practical goal is to accelerate the design process and to minimise the use of resources. Each of the following sections is intended to communicate the concepts associated with a particular method; appropriate references are provided where the details can be sought.
A metal is created when the atoms are brought sufficiently close together so that the electrostatic repulsion in transferring a valency electron between adjacent atoms is offset by the gain due to delocalisation of the electron.1 This enables the valency electrons to move within the metal.
The essential characteristics of the metallic state can be understood in terms of a single-electron wave function which in one-dimension ( x) and for the description of stationary states takes the time-independent form:
where k is the wave number, C is a constant. All such wave functions must become zero at the boundaries of the metal so that allowed values of k are discrete, each of which defines a quantum state. The Pauli exclusion principle permits only two...
