Crystal structure

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Fundamental Concept:

 A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances;  that is, long-range order exists, such that upon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms.

For those that do not crystallize, this long-range atomic order is absent; are called noncrystalline or amorphous materials.

Some of the properties of crystalline solids depend on the crystal structure of the material, the manner in which atoms, ions, or molecules are spatially arranged.

 When describing crystalline structures, atoms (or ions) are thought of as being solid spheres having well-defined diameters. This is termed the atomic hard sphere model in which spheres representing nearest-neighbor atoms touch one another.

 Sometimes the term lattice is used in the context of crystal structures; in this sense “lattice” means a three-dimensional array of points coinciding with atom positions (or sphere centers).

The unit cell geometry is completely defined in terms of six parameters:

the three edge lengths a, b, and c, and the three interaxial angles α,β  and γ ; are sometimes termed the lattice parameters of a crystal structure.

Table From

Materials Science and Engineering William D. Callister, Jr

Metal	Symbol	Crystal Structure	Atomic  Radius (nm)
Aluminum	Al	FCC	0.1431
Cadmium	Cd	HCP	0.1490
Chromium	Cr	BCC	0.1249
Cobalt	Co	HCP	0.1253
Copper	Cu	FCC	0.1278
Gold	Au	FCC	0.1422
Iron(α)	Fe	BCC	0.1241
Lead	Pb	FCC	0.1750
Molybdenum	Mo	BCC	0.1363
Nickel	Ni	FCC	0.1246
Platinum	Pt	FCC	0.1387
Silver	Ag	FCC	0.1445
Tantalum	Ta	BCC	0.1430
Titanium (α)	Ti	HCP	0.1445
Zinc	Zn	HCP	0.1332
Tungsten	W	BCC	0.1371
		FCC= face-centered cubic; HCP =hexagonal close-packed; BCC =body-centered cubic	1 nm=

                                                                                                                               1 nm =10^-9 mt
There are seven crystal system:

Lattice Parameter Relationships and Figures Showing Unit Cell Geometries for the Seven Crystal Systems:

Crystal System	Axial Relation	Interaxial Angel	Space lattic (3+4+1+2+1+2+1=14)	Unit cell Geometry
Cubic	a=b=c	α=β=γ=900	1.Simple cubic 2.BCC 3.FCC
Orthorhombic	a≠b≠c	α=β=γ=900	1.Simple Orthorhombic 2.Body- Centered Orthorhombic 3.Base-Centered Orthorhombic 4.Face-Centered Orthorhombic
Rhombohedral (trigonal)	a=b=c	α=β=γ≠900	1.Simple Rhombohedral
Tetragonal	a=b≠c	α=β=γ=900	1.Simple Tetragonal 2.Body-centered Tetragonal
Hexagonal	a=b≠c	α=β=900,γ=1200	1.Simple Hexagonal
Monoclinic	a≠b≠c	α=γ=900,β≠90	1.Simple monoclinic 2.Base-Centered Orthorhombic
Triclinic	a≠b≠c	α≠β≠γ≠900	1. Simple Triclinic

Some metals, as well as nonmetals, may have more than one crystal structure, a phenomenon known as polymorphism. When found in elemental solids, the condition is often termed allotropy. The prevailing crystal structure depends on both the temperature and the external pressure. One familiar example is found in carbon: graphite is the stable polymorph at ambient conditions, whereas diamond is formed at extremely high pressures. Also, pure iron has a BCC crystal structure at room temperature, which changes to FCC iron at 912⁰ C

 .

Atomic Structure and Interatomic Bonding

It is possible to have interatomic bonds that are partially ionic and partially covalent, and, in fact, very few compounds exhibit pure ionic or covalent bonding. For a compound, the degree of either bond type depends on the relative positions of the constituent atoms in the periodic table  or the difference in their electronegativities. The wider the separation (both horizontally—relative to Group IVA—and vertically) from the lower left to the upper-right-hand corner (i.e., the greater the difference in electronegativity), the more ionic the bond. Conversely, the closer the atoms are together (i.e., the smaller the difference in electronegativity), the greater the degree of covalency. The percentage ionic character of a bond between elements A and B (A being the most electronegative) may be approximated by the expression:

where XA and XB are the electronegativities for the respective elements.
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The periodic table of the elements

The numbers in parentheses are the atomic  weights of the most stable or common isotopes.

 The electronegativity values for the elements.