# The Structure of Crystalline Solids (Chapter 3, Callister by vyo46383

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```									The Structure of Crystalline Solids (Chapter 3, Callister)

- solids can be classified into two general categories, according to the regularity with
which atoms or ions are arranged w.r.t. one another in 3-D space:

i) crystalline materials:

ii) non-crystalline (or amorphous) materials:

- in this course (and in the text), the atomic hard sphere model is employed to study
crystal structures – atoms (or ions) are represented by solid spheres, of known diameter,
in contact with their nearest-neighbours

- we will also use the term lattice to describe the 3-D network of points that coincide with
atom centres in a crystalline solid

- given that crystalline solids possess long-range order (ie. have a regular repeating
pattern of atoms), a unit cell can be defined to denote the smallest repeating entity within
the crystal structure, i.e. unit cells are the building block that can be stacked side by side
in any direction to produce a crystal lattice of any given size

- the 3 common crystal structures in metals and their alloys are:

i) face-centred cubic (FCC) – eg. Al, Cu, Au, Pb, Ni, Ag

- the atomic packing factor (APF) is 0.74 for the atomic hard sphere model, where
APF = volume of atoms in the unit cell/total volume of the unit cell
- an APF of 0.74 is the maximum possible for solid spheres of equal size

ii) body-centred cubic (BCC) – eg. α-Fe, Cr, Mo, Ta, W

- APF = 0.68, i.e. less densely packed than FCC, which is very important in terms
of plastic deformation behaviour (more on that later!)

iii) hexagonal close-packed (HCP) – eg. α-Ti, Zn, Co

- APF = 0.74, provided that c/a = 1.633
NOTES:     1. A metal’s crystal structure has a profound effect on the way it deforms
plastically.

2. Some metals (and non-metals too) can have more than one crystal
structure, a phenomenon known as polymorphism – when exhibited by an
elemental solid, this behaviour is also called allotropy
eg. at ambient temperatures and pressures, pure carbon takes the form
of graphite, whereas at very high pressures, pure carbon can form
into diamond

3. There are many different crystal structures in addition to the 3 mentioned
above – refer to Table 3.2 in the Callister text for several less common
examples.

- to study crystalline materials, it is necessary to establish a notation for identifying both
crystallographic directions and planes w.r.t. to a given unit cell axis system (eg. Cartesian
for cubic, non-orthogonal for hexagonal) – this naming system is called Miller indices

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