Lecture # 3 

Defects (Imperfections) of Crystal Structure 

Only ideal crystals have perfect structure. All real materials contain defects of structure

Our world is imperfect

Defects (imperfections) are classified by geometrical criterions

Classification of defects (imperfections) in real metal:

• Point Defects (zero-dimensional or 0D) 
  (Точечные дефекты)
• Line Defects (one-dimensional or 1D) 
  (Линейный дефекты)
• Plane (area) Defects (two-dimensional or 2D) (Поверхностные дефекты)
• Volume Defects (three-dimensional or 3D) 
  (Объемные дефекты)

Point Defects

Point Defects – are essentially “zero-dimensional” imperfections, such as vacancies, that are located typically at one (in some cases a few) sites in the crystal.

Vacancy – An atom or ion missing from its regular crystallographic site

(Вакансия – свободный узел кристаллической решетки)

Fig. 3.1. Vacancy in crystal lattice

Vacancy forms as a result of separation of atom from surface atomic layer due to temperature-induced lattice vibration. This vacancy can be filled by another atom from deeper atomic layer – migration of vacancies. Also “free” (or homeless) atoms can be absorbed by grain boundaries.

Fig.3.2. Generation of a vacancy by the diffusion of an atom to the surface and the subsequent diffusion of the vacancy into the bulk.

Interstitial defect - A point defect produced when an atom is placed into the crystal at a site that is normally not a lattice point (узел кристаллической решетки). Also it can be an “alien” atom in one of the interstitials in a structure.

Atoms can be self-interstitial (same atoms A-A) (межузельные атомы) or just “interstitial” (different atoms A-B, Fe-C) (атомы внедрения)

Fig.3.2. Interstitial atom (not self-interstitial)

Substitutional defect - A point defect produced when an atom (A) is removed from a regular lattice point (узел кристаллической решетки) and replaced with a different atom (B), usually of a different size.

Atoms B can have as greater as smaller diameter in comparison with A diameter.

Fig.3.3 Substitutional atom (D_A>D_B)

Fig.3.4 Substitutional atom (D_A<D_B) 

Why do we have POINT DEFECTS ?

• Vacancies: 
  -Vacant atomic sites in a structure

• Self-interstitials:

      -"extra" atoms positioned between atomic sites.

Surely, distortion of planes (искажение кристаллической решетки) means excess elastic energy (упругой энергии), things in nature – when left alone system – it always goes to states of lowest energy, so how come point defects are here to stay?

Any closed system tends to minimal energy state.

G = E – TS + pV

Minimization of Gibbs free energy (G) decided which structures are stable,

E is internal energy, if there are point defects this term is higher

S is entropy: a measure for the disorder in a system, if there are point defects, entropy is higher

T is temperature

P is pressure

V is volume

So G is smaller for a certain concentration of point defect at a certain temperature, when the increase in the second term outweighs the increase in the first term 

At any temperature equilibrium concentration (равновесная концентрация) of point defects exists. 

how to get the Activation Energy?

Slope – tg угла наклона прямой, угловой коэффициент.

Point defects in alloys

It can be two outcomes if impurity atoms (B) add to host lattice (A) 

Fig. 3.5. Ordering of the solid solution in the AuCu₃. (a) Above 390⁰C, there is a random distribution of Au and Cu atoms among FCC sites. (b) Below 390⁰C the Au atoms preferentially occupy the corner positions in the unit cell, giving a simple cubic Bravais lattice.