الحالة الصلبة – المحاضرة العاشرة
د محمد هاشم مطلوب
العنوان ومقاطع من المحاضرة
Molecular solids and covalent networks
X-ray diffraction studies of solids reveal a huge amount of information, including
interatomic distances, bond angles, stereochemistry, and vibrational parameters.
In this lecture we can do no more than hint at the diversity of types of solids
found when molecules pack together or atoms link together in extended
networks.
In covalent network solids, covalent bonds in a definite spatial orientation link the
atoms in a network extending through the crystal. The demands of directional
bond- ing, which have only a small effect on the structures of many metals, now
override the geometrical problem of packing spheres together, and elaborate and
extensive structures may be formed. Examples include silicon, red phosphorus,
boron nitride, andvery importantly-diamond, graphite, and carbon nanotubes,
which we discuss in detail.
Diamond and graphite are two allotropes of carbon. In diamond each sp3 –
hybridized carbon is bonded tetrahedrally to its four neighbours (Fig. 1). The
network of strong C-C bonds is repeated throughout the crystal and, as a result,
diamond is the hardest known substance.
Fig. A fragment of the structure of diamond. Each C atom is tetrahedrally
bonded to four neighbours. This framework-like structure results in a rigid crystal.
In graphite, a bonds between sp2-hybridized carbon atoms form hexagonal rings
which, when repeated throughout a plane, give rise to sheets (Fig. 2). Because
the sheets can slide against each other when impurities are present, graphite is
used widely as a lubricant.
Fig.2 Graphite consists of flat planes of hexagons of carbon atoms lying above one another. (a) The arrangement of carbon atoms in a sheet; (b) the relative arrangement of neighbouring sheets. When impurities are present, the planes can slide over one another easily.
Molecular solids
Molecular solids are the subject of the overwhelming majority of modern
structural determinations, are held together by van der Waals interactions.
The observed crystal structure is Nature's solution to the problem of condensing
objects of various shapes into an aggregate of minimum energy (actually, for T>
0, ofminimum Gibbs energy). The prediction of the structure is a very difficult
task, but software specifically designed to explore interaction energies can now
make reasonably reliable predictions. The problem is made more complicated by
the role of hydrogen bonds, which in some cases dominate the crystal structure,
as in ice (Fig. 3), but in others (for example, in phenol) distort a structure that is
determined largely by the van der Waals interactions.
Fig. 3 A fragment of the crystal structure of ice (ice-I). Each 0 atom is at the centre
of a tetrahedron of four 0 atoms at a distance of 276 pm. The central 0 atom is
attached by two short 0- H bonds to two H atoms and by two long hydrogen
bonds to the H atoms of two of the neighbouring molecules. Overall, the structure
consists of planes of hexagonal puckered rings of H20 molecules (like the chair
form of cyclohexane).
The properties of solids
In this lecture we consider how the bulk properties of solids, particularly their
mechanical, electrical, optical, and magnetic properties, stem from the properties
of their constituent atoms. The rational fabrication of modern materials depends
crucially on an understanding of this link.
Mechanical properties
The fundamental concepts for the discussion of the mechanical properties of
solids are stress and strain. The stress on an object is the applied force divided
by the area to which it is applied. The strain is the resulting distortion of the
sample. The general field of the relations between stress and strain is called
rheology.
Stress may be applied in a number of different ways. Thus, uniaxial stress is a
simple compression or extension in one direction (Fig. 4); hydrostatic stress is a
stress applied simultaneously in all directions, as in a body immersed in a fluid. A
pure shear is a stress that tends to push opposite faces of the sample in opposite
directions. A sample subjected to a small stress typically undergoes elastic
deformation in the sense that it recovers its original shape when the stress is
removed. For low stresses, the strain is linearly proportional to the stress. The
response becomes nonlinear at high stresses but may remain elastic. Above a
certain threshold, the strain becomes plastic in the sense that recovery does not
occur when the stress is removed. Plastic deformation occurs when bond
breaking takes place and, in pure metals, typically takes place through the
agency of dislocations. Brittle solids, such as ionic solids, exhibit sudden fracture
as the stress focused by cracks causes them to spread catastrophically.
The response of a solid to an applied stress is commonly summarized by a
number of coefficients of proportionality known as 'moduli':
Fig.4 Types of stress applied to a body. (a) Uniaxial stress, (b) shear stress,
(c) hydrostatic pressure.
The typical behaviour of a solid under stress is illustrated in Fig. .5 For small
strains, the stress-strain relation is a Hooke's law of force, with the strain directly
pro- portional to the stress. For larger strains, though, dislocations begin to playa
major role and the strain becomes plastic in the sense that the sample does not
recover its original shape when the stress is removed.
The differing rheological characteristics of metals can be traced to the presence
of slip planes, which are planes of atoms that under stress may slip or slide
relative to one another. The slip planes of a ccp structure are the close-packed
planes, and careful inspection of a unit cell shows that there are eight sets of slip
planes in different directions. As a result, metals with cubic close-packed
structures, like copper, are malleable: they can easily be bent, flattened, or
pounded into shape. In contrast, a hexagonal close-packed structure has only
one set of slip planes; and
Fig. 5 At small strains, a body obeys Hooke's law (stress proportional to strain) and is elastic (recovers its shape when the stress is removed). At high strains, the body is no longer elastic, may yield and become plastic. At even higher strains, the solid fails (at its limiting tensile strength) and finally fractures.