Structure of Crystalline
Solid Materials
 Contain atoms that are regularly arranged with respect to each other and may
be classified according to their crystal structure
Solid Solution
 A solution in the solid state the consists of two kinds of atoms combined in one
type of space lattice; the two elements are soluble in each other
Crystal Structure
 The manner in which atoms, ions, or molecules are spatially arranged
Crystalline
 Refers to the orderly geometric arrangement of the atoms (fixed locations)
 Long-range order exists
Amorphous
 Refers to the random distribution of atoms (disorder)
 Absence of long-range order
Atomic Hard-sphere
 Atoms are thought of as being solid spheres having well-defined diameters
 Spheres representing nearest neighbor atoms touch one another
Lattice
 A three-dimensional array of points coinciding with atom positions (or sphere
centers)
Unit Cells
 Basic structural unit or building block of a crystal structure
 Repeating entities in crystal structure which are in the form of parallelepipeds or
prisms three sets of parallel faces
Characteristics of Crystal Structure
Coordination Number
 number of nearest neighbor or touching atoms
Atomic Packing Factor (APF)
 the fraction of the solid sphere volume in a unit cell
APF
 volume of atoms in a unit cell / total unit cell volume = Vs / Vc
Metallic Crystal Structures
Face-Centered Cubic Crystal (FCC)
 Has a unit cell of cubic geometry, with atoms located at each of the corners and
the centers of all the cube faces
 Al, Cu, Au, Pb, Ni, Pt, Ag
 a = 2 R  2
a = cube edge length
R = atomic radius
 CN = 12
 APF = 0.74
 No. of atoms in a unit cell = 4
 1/8 each of the corner atoms and 1/2 each of the six face atoms = 4
Body-Centered Cubic Crystal (BCC)
 Also has a cubic unit cell with atoms located at all eight corners and a single
atom at the cube center
 Cr, Fe, Mo, Ta, W
 a = 4R/ 3
a = cube edge length
R = atomic radius
 CN = 8
 APF = 0.68
 No. of atoms in a unit cell = 2.
 1 center atom and 1/8 each of the corner atoms
 8 Corner atoms
Hexagonal, Close-Packed (HCP)
 With hexagonal unit cell and atoms are located at all the corners, single atom
each at the center of the top and bottom planes and another three atoms
contained in a plane between the top and the bottom planes
 c/a = 1.633
(ideal)
 CN = 12
 APF = 0.74
 No. of atoms in a unit cell = 6
 Cd, Co, Ti, Zn
Density Computations
 Theoretical density:
 = nA / VcNA
  = theoretical density (g/cm3)
 n = number of atoms associated with each unit cell
 A = atomic weight
 Vc = volume of the unit cell
 NA = Avogadro’s Number = 6.022 x 1023atoms/mol
Polymorphism
 having more than one crystal structure; in elemental solids, the term used is
allotropy
 Pure Iron is BCC at room temperature
 FCC at 912oC
Lattice parameters
 The unit cell geometry is defined in terms of six parameters: three edge lengths
a, b, c and three interaxial angles lengths , , 
Crystal System
 based on the different possible combinations of the lattice parameters (7 crystal
systems).
Cubic Crystal System
 Diamond, Garnet, Rhodolite, Spinel
Hexagonal Crystal System
 Aquamarine, Bentonite, Beryl, Emerald, Heliodor, Morganite
Tetragonal
 Zircon
Trigonal
 Amethyst, Citrine, Curundum, Ruby, Sapphire, Tourmaline, Eudialyte, Quartz
Orthorhombic Crystal System
 Alexandrite, Andalusite, Chrysoberyl, Iolite, Peridot, Tanzanite, Topaz, Varisite
Monoclinic Crystal System
 Azurite, Diopside, Feldspar, Kunzite, Nephrite
Triclinic Crystal System
 Turquoise
Single Crystals
 Periodic and repeated arrangement of atoms is perfect or extends throughout
the entirety of the specimen without interruption
 Exist in nature but may be produced artificially
 Grows in a carefully controlled environment
Polycrystalline Materials

Composed of a collection of many small crystals or grains
Grain boundary
 the region where two grains meet
Anisotropy
 Associated with the variance of atomic or ionic spacing with crystallographic
direction
 The extent and magnitude of anisotropic effects in crystalline materials are
functions of the symmetry of the crystal structure
Isotropic
 Substance in which measured properties are independent of the direction of
measurement
Amorphous Materials
 “without form”
 also called supercooled liquids
 characterized by atomic or molecular structures that are relatively complex and
become ordered only with some difficulty
 rapid cooling through the freezing temperature favors the formation of
noncrystalline solids
 metals and some ceramics (normally crystalline), polymers (noncrystalline or
semi-crystalline)