Crystal Defect, Non-stoichiometry, and Solid Solution
From: ‘Basic Solid State Chemistry’, by Anthony West, 2nd edition, 1999, John Wiley & Sons; Chapter 5.
Driving force of defect: Increase of entropy of the material.
H is enthalpy
T is temperature
S is entropy
G is Gibbs free energy
S is configurational entropy
k is boltzmann’s constant
W is probability of the configuration
Point defects: defect at atomic scale.
Schottky defect: A pair of ions is missing
Frenkel defect: a ion (usually cation) is moved to an interstitial site.
Kroger-Vink notation: an easy way for representing different kinds of point defect.
V is vacant site
A dot superscript is a +1 charge
A prime superscript is a -1 charge
x is a zero charge.
i is interstitial site
Examples:
From G = -RTlnK
Thermodynamics of Schottky defect:
Equilibrium constant for the equation:
Therefore,
But,
Therefore,
, as
, we get:
Thermodynamics of Frenkel defect:
Arhenius Equation: showing dependence of defect concentration and temperature.
For most structure:
Colour centers: (or F-center) Electron is trapped in an anion vacancy, giving rise
to color due to adsorption characteristic of its energy level.
Other kinds of color center:
H-center
Cl- is trapped to an anion site
V-center
Cl- is trapped to two anion sites
Intrinsic vs Extrinsic defects
Intricsic defect is due to thermal activation, occurs naturally from thermodynamic
consideration.
Order-Disorder phenomena
Ex: Dissolution of Zn in Cu in brass. Zn tends to occupy body-center site
(ordered structure), instead of random distribution (disorder structure) as in
general solid solution. This occurs at temperature below 450oC.
Extrinsic is due to charge balance requirement, when there are impurities atoms
(dopants) in the ionic material.
Ex: NaCl doped with CaCl2, we get
Wustite:
Solid Solution: random mixing of more than two kinds of atoms in solid phase.
1. Substitutional solid solution: solute atoms substitute solvent site in the
crystal structure.
2. Interstitial solid solution: solute atoms is at interstitial sites in the crystal
structure of the solvent.
Substitutional solid solution:
Ex: Al2O3-Cr2O3 : Cr substitutes Al site.
- can be written as (Al2-xCrx)O3
- complete range of solid solution is possible
For a large range of dissolution to be possible:
1. The solute must have the same charge.
2. Similar size, usually less than 15 percent.
3. Same crystal structure.
4. High temperature promotes solid solution. TS term has big influence.
Examples of limited solid solution:
Mg2-xZnxSiO4, Zn2-xMgxSiO4, LiCr1-xAlxO2,, AgCl1-xBrx
Interstitial solid solution.
Usually, small atoms such as H, C, B, N can dissolute in metals, occupying
interstitial site in the host metal crystal structure.
Ex: C in Fe become ‘steel’
- dissolution at large percentage is possible when Fe is in FCC structure
(-Fe) at temperature greater than 910oC.
- with rapid cooling to room temperature C atoms are trapped, and the
usual BCC structure of Fe is distorted to a structure called ‘Martesite’.
Ex: H in steel
- dissolution of H in liquid steel is high.
- cooling to solid phase traps dissoluted H atoms
- combination of H atoms forms H2 gas, and cause embrittlement of steel.
Homovalent vs Heterovalent (or aliovalent) substitution.
Homovalent substitution: substitution by atom of the same charge.
Ex: Al2O3-Cr2O3
Heterovalent (or aliovalent) substitution: substitution by atom of different charge.
Ex: NaCl-CaCl2
- Charge compensation (Ionic or Electronic) is necessary to maintain
charge neutrality.
Ionic charge compensation mechanism: insulator
1. Creating cation vacancy: when the substitute atom has a higher charge than
the host atom. Ca replaces Na, requires formation of VNa.
2. Creating interstitial anions: when the substitute atom has a higher charge
than the host atom.
Ex: Y3+ substitute Ca2+ in CaF2 (dissolution of YF3 in CaF2), interstitial
F is created.
Ex: Mixture of U4+ and U6+ in UO2. Interstitial of O is created.
3. Creating anion vacancy: when the substitute atom has a lower charge than
the host atom.
Ex: Ca2+ substitute Zr4+ in ZrO2 (dissolution of CaO in ZrO2), vacancy of
O is created.
4. Creating interstitial cations: when the substitute atom has a lower charge than
the host atom, interstitial cation is required to maintain charge balance.
Ex: Al3+ substitute Si4+ in SiO2, Li+ interstitial is required.
Double substitution: substitution can be made at more than one site.
Ex: Mg2SiO4:
Ex: Solid solution of AgBr and NaCl
Summary:
Ex: Solid solution of CaAl2Si2O8 and NaAlSi3O8
Ex: Sialon, which is system of Si-Al-O-N
Electronic compensation mechanism: metals, semiconductor, superconductor.
3. Loss of oxygen by reduction at high temperature. e- enter the structure.
1. Cation vacancy:
Ex: LiCoO2 and LiMn2O4 in Li battery. Substitution of Co3+ by Co4+
require removal of Li+
Ex:
After the transition, the material become more metallic.
Ex: Absorption of O2 by NiO. This requires removal of Ni
4. Interstitial of one cation and mixed valency of another cation. It is the reverse
process of 1.
Ex: Interstitial of Li in MnO2, Li in WO3.
2. Creation of mixed valency cations, due to interstitial anions.
Ex: YBa2Cu3O. (or YBCA, Y123).  is 6 to 7, and Cu is 1+ to 3+
Change occurs as temperature is lowered. The material changes from
insulating to semiconducting to superconducting at temperature lower than
90 K, when  is 7, and Cu is oxidized to Cu3+.
5. Half of double substitution mechanism.
Ex: Ba-doped La2CuO4
Ex: K-doped BaBiO3