Classification of Solids

Classification of Solids

• Crystalline materials feature atoms packed in periodic, 3D arrays.
• Metals, many ceramics, and some polymers are typical examples of crystalline materials.
• Noncrystalline materials do not have atoms with periodic packing.
• Complex structure or rapid cooling can result in noncrystalline structures.
• Noncrystalline materials are also known as "Amorphous".

Key Definitions

• Unit cell is the basic repeating structural unit of crystalline solid.
• Lattice point is each sphere that represents an atom, ion, or molecule.

Types of Crystalline Solids

• Ionic crystals are ionic compounds like NaCl and KCl.
• Ionic crystals typically have high melting and boiling points.
• Ionic crystals do not conduct electricity unless dissolved in water.
• Covalent crystals feature atoms bonded by strong covalent bonds.
• Diamond and graphite are examples of covalent crystals.
• Molecular crystals have molecules held by dipole-dipole, dipole-induced dipole, and hydrogen bonding.
• Molecular crystals exhibit weak forces and have low melting and boiling points.
• Molecular crystals are poor conductors of heat and electricity.
• Metallic crystals have atoms of the same metal as the principal constituent particles.
• Metals atoms are closely packed with a strong attractive force, making them ductile, malleable, lustrous, and dense, and have high melting points.
• Silver, copper, chromium, and tungsten are examples of metallic crystals.

Atomic Packing Factor (APF)

• APF is the ratio of the volume of atoms in a unit cell to the volume of the unit cell.
• APF assumes hard spheres.
• Packing efficiency is obtained by multiplying the APF by 100%.
• Packing efficiency represents the percentage of space occupied in a given arrangement.

Crystalline Lattices

• Crystal lattices are differentiated by the number of atoms per unit cell and the coordination number.
• Atoms in the corners of the unit cell contribute 1/8 of an atom.
• Atoms on a face contribute 1/2 of an atom.
• Atoms in the center count as a full atom.
• Coordination number is the number of atoms immediately adjacent to any given atom.
• Higher coordination numbers enable each atom in the lattice to interact with more nearest neighbor atoms.
• Attractive forces in crystal lattices hold the crystal together.

Simple Cubic Structure (SC)

• Simple Cubic (SC) structures are rare due to low packing density; only Polonium (Po) has SC structure.
• Close-packed directions are cube edges.
• Simple Cubic (SC) has a coordination number of 6, which is the number of nearest neighbors.
• The APF for a simple cubic structure is 0.52.

Body-Centered Cubic Structure (BCC)

• In Body-Centered Cubic (BCC) structures, atoms touch each other along cube diagonals.
• BCC structures feature atoms that are identical, but the center atom is shaded differently for ease of viewing.
• Chromium (Cr), Tungsten (W), Iron (Fe(α)), Tantalum, and Molybdenum are examples Body-Centered Cubic (BCC) structures.
• Body-Centered Cubic (BCC) has a coordination number of 8.
• BCC structures have 2 atoms per unit cell: 1 center + 8 corners x 1/8.
• The APF for base-centered cubic structure is 0.68.

Face-Centered Cubic Structure (FCC)

• In Face-Centered Cubic (FCC) structures, atoms touch each other along face diagonals.
• FCC structures feature atoms that are identical; the face-centered atoms are shaded differently for ease of viewing.
• Aluminum (Al), Copper (Cu), Gold (Au), Lead (Pb), Nickel (Ni), Platinum (Pt), and Silver (Ag) are examples Face-Centered Cubic (FCC) structures.
• Face-Centered Cubic (FCC) has a coordination number of 12.
• FCC structures have 4 atoms per unit cell: 6 face x 1/2 + 8 corners x 1/8.
• The APF for face-centered cubic structure is 0.74, which is the maximum achievable APF.

FCC Stacking Sequence

• FCC structures exhibit an ABCABC... Stacking Sequence.

Hexagonal Close Packed Structure (HCP)

• Hexagonal Close Packed (HCP) structures exhibit an ABAB... Stacking Sequence.
• Hexagonal Close Packed (HCP) has a coordination number of 12.
• The APF is 0.74 for HCP Structures.
• The c/a ratio = 1.6333 for HCP Structures.
• Cadmium (Cd), Magnesium (Mg), Titanium (Ti), and Zinc (Zn) are examples of materials with HCP structure, which has 6 atoms per unit cell.

X-Ray Diffraction (XRD)

• Diffraction gratings should have spacings comparable to the wavelength of diffracted radiation.
• Spacings less than the wavelength cannot be resolved.
• Spacing is the distance between parallel planes of atoms.
• X-ray diffraction pattern for polycrystalline α-iron (BCC)

Summary Points

• Atoms assemble into crystalline or amorphous structures.
• Common metallic crystal structures are FCC, BCC, and HCP.
• Coordination number and atomic packing factor are the same for both FCC and HCP crystal structures.
• The density of a material can be predicted if the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP) are known.
• Crystallographic points, directions, and planes are specified using indexing schemes.
• Crystallographic directions and planes relate to atomic linear densities and planar densities.
• Materials can be single crystals or polycrystalline.
• Material properties vary with single crystal orientation (anisotropic) but are generally non-directional (isotropic) in polycrystals with randomly oriented grains.
• Some materials can have more than one crystal structure, which is called polymorphism or allotropy.
• X-ray diffraction is used for crystal structure and interplanar spacing determinations.