Electronic Properties of Materials: Structure and Bonding in Materials


Covalent bond: A bond formed by sharing a pair of valence electrons between two atoms.
Crystal: A three-dimensional array of atoms, molecules, or ions arranged in a periodic manner.
Diffusion: Time and temperature dependent mass transport phenomenon in atomic level.
Electronegativity: The ability of an atom to attract the electrons toward itself to form a bond.
Ionic bond: A bond formed by the transfer of electrons between a metal and a non-metal. Please note that pure ionic bonding does not exist.
Ionization: To remove the outermost electron(s) of a neutral atom. The energy required to ionize a neutral atom is called as ionization energy.
Lattice energy: The energy released when one mole of a crystalline compound is assembled at a temperature of zero kelvin from its infinitely separated components.
Metallic bond: A bond formed due to the attraction between the positive metal ions and the mobile valence electrons.
Polymorphism: The ability of a material to exist in more than one crystalline form.
Secondary bond: A weak bond formed between two molecules due to the existence of dipoles.
Unit cell: The smallest arrangement of atoms which when repeated in three dimensions produces the structure of a crystal.
Valence electrons: The electrons in the outermost shell of an atom.


overline{E}=overline{KE}+overline{PE} and overline(KE}={{-1}/2}overline{PE} (Virial theorem)
PE = {{Q_1}{Q_2}}/{4{pi}{{epsilon}_0}{r_0}}={-e^2}/{4{pi}{{epsilon}_0}{r_0}} and KE = {1/2}{m_e}{v^2}
{F_net} = {F_attraction} + {F_repulsion} [In equilibrium Fnet = 0, and it gives the bond length and the bond energy]
% Ionic character = 1 - exp({{{{-}Delta}{{chi}^2}}/4}) x 100%, where {Delta}{chi} is the difference in the electronegativities. [Henry Smith formula]

{E_dispersion} = {-C_ij}{{r_ij}^{-6}}
{E_repulsion} = {B_ij}{e^{-{alpha}{r_ij}}}
{E_coulomb} = {1/{{4}{pi}{{epsilon}_0}}}{Sigma}{{q_i}{q_j}({e^2}/{r_ij})} or {E_coulomb} = {{-e^2}/{4{pi}{{epsilon}_0}{R}}}{A} [A is the Madelung constant]
{E_{zero-point}} = {9/8}{h}{{nu}_max}
{E_lattice} = [{Sigma}({E_dispersion}+{E_repulsion}+{E_coulomb}+{E_{zero-point}})]{N_avo}

SystemAxial lengths and anglesBravais latticeLattice symbol
Cubic Three equal axes at right angles
{a = b = c}
{{alpha} = {beta} = {gamma} = {90^o}}
simple
body centered
face centered
P
I
F
Tetragonal Three axes at right angles, two equal lengths
{a = b <> c}
{{alpha} = {beta} = {gamma} = {90^o}}
simple
body centered
P
I
Orthorhombic Three unequal axes at right angles
{a <> b <> c}
{{alpha} = {beta} = {gamma} = {90^o}}
simple
body centered
base centered
face centered
P
I
C
F
Rhombohedral
(or Trigonal)
Three equal axes, equally inclined
{a = b = c}
{{alpha} = {beta} = {gamma} <> {90^o}}
simple P (R)
Hexagonal Two equal coplanar axes at 120o, third axis at right angles
{a = b <> c}
{{alpha} = {beta} = {90^o}, {gamma} = {120^o} }
simple P
Monoclinic Three unequal axes, one pair not at right angles
{a <> b <> c}
{{alpha} = {gamma} = {90^o}} <> {beta}
simple
base centered
P
C
Triclinic Three unequal axes, unequally inclined and none at right angles
{a <> b <> c}
{{alpha} <> {beta} <> {gamma} <> {90^o}}
simple P (R)

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