The Nature of Minerals and Rocks as Materials - Materials Science for Structural Geology - page 2

largest and most distinctive class, while the sulfides, of special importance in ore
deposits, form a rather separate class in respect of their properties. The mechanical
properties of minerals are mainly determined by their crystal structure, the nature
of their bonding, and the properties of their crystal defects. The crystal structures
are well known from X-ray diffraction studies and need not be elaborated here
(Bragg and Claringbull 1965 ; Deer et al. 1992 ; Wenk and Bulakh 2004 ). In this
section, we consider crystal bonding and defects (Barrett et al. 1973 , Chap. 2 ;
Frank-Kamenetskaya et al. 2004 ; Hammond 2001 ; Kelly et al. 2000 ; Kittel 1976 ,
Chap. 3 ; Phillips 1975 ; Putnis 1992 ; Rohrer 2001 ; Sands 1969 ; Schmalzried 1995 ).
Bonding is atomic interaction that arises mainly through the valence electrons
and is related to the electron density distribution. The overall strength of bonding
is represented in the cohesive energy, the difference in total energy of the atoms
when separated and when assembled in the crystal structure. The mechanical
properties are sensitive to the nature of the bonding. In minerals, this nature
generally falls somewhere in the continuous range between the limiting cases of
ionic or heteropolar bonding and covalent or homopolar bonding. In ideal ionic
bonding, valence electrons are completely transferred from the more electropos-
itive to the more electronegative atoms and the interaction between them can be
fairly satisfactorily viewed as a classical electrostatic one between spherical ions.
In ideal covalent bonding, in contrast, valence electrons are equally shared
between the atoms and tend to be distributed spatially in such a way as to define
directional bonds; the bonding results from the electrons occupying lower energy
states than when localized on either atom and require a quantum-mechanical
explanation.
The theoretical analysis of bonding may be approached either in terms of
individual atom-atom bonds, as in molecular orbital and valence bond theories, or
in terms of the total assemblage of atoms of the crystal, as in energy band theory
(Adler 1975 ; Coulson 1961 ; Harrison 1980 ; Kittel 2005 ; Madelung 1978 , Chap. 8 ;
Marfunin 1979 , Chaps. 3 and 4 ; Martin 2004 ; Weaire 1975 ). Energy band theory
explains why most minerals are insulators. This property arises from the existence
of a band gap separating the valence band of energy states, fully occupied by the
valence electrons, from the next band of possible but unoccupied energy states
known as the conduction band. For strongly ionic crystals the band gap tends to be
wide (order of 10 eV, kT) but it can be relatively narrow for crystals with a
considerable degree of covalency in the bonding (for example, 3.6 eV for ZnS and
0.3 eV for PbS). Another important property of the electron energy distribution is
the Fermi energy or chemical potential of the electrons, that is, the energy level of
an extra electron in equilibrium with the existing electron population of the crystal;
for the pure insulator, the Fermi energy lies in the middle of the band gap but its
level can be strongly influenced by impurities.
Although the cases of pure covalent bonding (C, Ge, Si) and of highly ionic
bonding (alkali halides) are well characterized, it has proved to be difficult to specify
quantitatively the degree of ionicity in intermediate cases. The initial approach of
Pauling was through electronegativity, that is, the relative ability of an atom to attract
electrons, and various measures of this property have been proposed, most