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Unformatted text preview: 2.1 The concept of ordering When attempting to classify a material it is useful to decide whether it is crystalline (conventional metals and alloys), non-crystalline (glasses) or a mixture of these two types of structure. The critical distinction between the crystalline and non-crystalline states of matter can be made by applying the concept of ordering. Figure 2.1a shows a symmetrical two- dimensional arrangement of two different types of atom. A basic feature of this aggregate is the nesting of a small atom within the triangular group of three much larger atoms. This geometrical condition is called short-range ordering. Furthermore, these triangular groups are regularly arranged relative to each other so that if the aggregate were to be extended, we could confidently predict the locations of any added atoms. In effect, we are taking advantage of the long- range ordering characteristic of this array. The array of Figure 2.1a exhibits both short- and long-range Chapter 2 Atomic arrangements in materials Figure 2.1 Atomic ordering in (a) crystals and (b) glasses of the same composition (from Kingery, Bowen and Uhlmann, 1976; by permission ofWiley-Interscience). ordering and is typical of a single crystal. In the other array of Figure 2.1b, short-range order is discernible but long-range order is clearly absent. This second type of atomic arrangement is typical of the glassy state. 1 It is possible for certain substances to exist in either crystalline or glassy forms (e.g. silica). From Figure 2.1 we can deduce that, for such a substance, the glassy state will have the lower bulk density. Furthermore, in comparing the two degrees of ordering of Figures 2.1a and 2.1b, one can appreciate why the structures of comparatively highly-ordered crystalline substances, such as chemical compounds, minerals and metals, have tended to be more amenable to scientific investigation than glasses. 2.2 Crystal lattices and structures We can rationalize the geometry of the simple repre- sentation of a crystal structure shown in Figure 2.1a by adding a two-dimensional frame of reference, or space lattice, with line intersections at atom centres. Extending this process to three dimensions, we can construct a similar imaginary space lattice in which triple intersections of three families of parallel equidis- tant lines mark the positions of atoms (Figure 2.2a). In this simple case, three reference axes (*, y, z) are oriented at 90 to each other and atoms are 'shrunk', for convenience. The orthogonal lattice of Figure 2.2a defines eight unit cells, each having a shared atom at every corner. It follows from our recognition of the inherent order of the lattice that we can express the 1 ThC terms glassy, non-crystalline, vitreous and amorphous are synonymous....
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- Fall '11