CHEM 548: Materials Chemistry

By the end of this lecture, you should be able to:

1. Explain why real crystals always contain defects, even under equilibrium conditions.
2. Identify and describe the major types of intrinsic point defects:
   • Vacancies
   • Interstitials
   • Substitutions (intrinsic site-mixing)
   • Schottky defects
   • Frenkel defects
   • Color centers
3. Understand how configurational entropy drives the presence of defects in crystals.
4. Relate defects to important material properties (optical, electronic, mechanical).

• Perfect crystals are an idealization; real crystals always contain defects and surfaces.
• Defects can be beneficial: gemstone colors, phosphors in LEDs, semiconductor doping, and improved mechanical properties (steel vs. iron).
• Intrinsic point defects:
  • Vacancy – missing atom.
  • Interstitial – extra atom in normally empty site.
  • Substitution – atom on the “wrong” site.
  • Schottky defect – paired cation + anion vacancies (charge balance).
  • Frenkel defect – ion displaced from lattice site into interstitial.
  • Color centers – trapped electrons at anion sites, responsible for colors in minerals.
• Thermodynamic basis:
  • Formation of defects costs enthalpy (bond breaking).
  • Configurational entropy increases possible arrangements.
  • Equilibrium defect concentration arises from the balance (ΔG = ΔH − TΔS).
  • Defects are always present; concentration grows with higher T and lower ΔH.

• Define and distinguish extrinsic defects from intrinsic defects.
• Differentiate between isovalent substitution (e.g., ruby, emerald, YAG lasers) and alloeovalent substitution.
• Explain how charge balance is maintained in alloeovalent doping:
  • Excess positive charge → anion interstitials or cation vacancies.
  • Deficit of positive charge → cation interstitials or anion vacancies.
• Describe technological importance of doping:
  • Yttria-stabilized zirconia (oxide ion conductor).
  • Semiconductors (donor/electron doping vs. acceptor/hole doping).
  • Transition metal oxides (variable oxidation states, batteries, superconductivity, magnetoresistance).
• Interpret Kröger–Vink notation to describe defect types, sites, and charges.

Substituting with a cation of higher charge

The crystal must compensate for the excess positive charge. If we don’t allow changes in the oxidation states of the ions, there are two charge compensation mechanisms:

1. Anion interstitials

CaF₂  — Substitute Y³⁺ for Ca²⁺ →  Ca_1−xY_xF_2+x

2. Cation vacancies

NaCl  — Substitute Ca²⁺ for Na⁺ →  Na_1−2xCa_x□_xCl  (□ = vacancy)

Substituting with a cation of lower charge

The crystal must compensate for the excess negative charge. If we don’t allow changes in the oxidation states of the ions, there are two charge compensation mechanisms:

1. Cation interstitials

SiO₂  — Substitute Al³⁺ for Si⁴⁺ →  Li_xSi_1−xAl_xO₂

2. Anion vacancies

ZrO₂  — Substitute Y³⁺ for Zr⁴⁺ →  Zr_1−xY_xO_2−x/2□_x/2  (□ = vacancy)

Compounds containing transition metal ions, are very sensitive to the oxidation state of the cation. By doping we can control the oxidation state, thereby controlling the properties.

Doping that leads to oxidation

Cation vacancies
LiCoO₂  — Remove Li⁺ →  Li_1−xCoO₂   [Co⁺³ → Co^+(3+x)]

Anion interstitials
La₂CuO₄  — Add O²⁻ →  La₂CuO_4+x   [Cu⁺² → Cu^+(2+2x)]

Aliovalent doping with lower valent cation
La₂CuO₄  — Sub. Sr²⁺ for La³⁺ →  La_2−xSr_xCuO₄   [Cu⁺² → Cu^+(2+x)]

Compounds containing transition metal ions, are very sensitive to the oxidation state of the cation. By doping we can control the oxidation state, thereby controlling the properties.

Doping that leads to reduction

Cation interstitials
TiS₂  — Insert Li⁺ →  Li_xTiS₂   [Ti⁺⁴ → Ti^+(4−x)]

Anion vacancies
WO₃  — Remove O²⁻ →  WO_3−x   [W⁺⁶ → W^+(6−2x)]

Aliovalent doping with higher valent cation
CaMnO₃  — Sub. La³⁺ for Ca²⁺ →  Ca_1−xLa_xMnO₃   [Mn⁺⁴ → Mn^+(4−x)]

• Extrinsic defects arise from introducing foreign atoms into a lattice.
• Two substitution types:
  • Isovalent substitution: no net charge imbalance.
  • Alloeovalent substitution: different charge, requiring compensating defects.
• Compensation mechanisms include interstitials, vacancies, or oxidation state changes of transition metals.
• Key examples:
  • Ruby/emerald coloration, YAG lasers.
  • Y-stabilized ZrO₂ for oxygen conduction.
  • Semiconductor doping (n-type, p-type).
  • Battery cathodes (LiCoO₂), superconductors (La₂CuO₄), bronzes (WO_3−x), colossal magnetoresistance oxides.
• Kröger–Vink notation provides a systematic language for defect chemistry.