Crystal Structure Imperfections: Defects, Polymorphism, and Material Properties

Polymorphism and Allotropy in Materials

Polymorphism and Allotropy: A single element or compound can exist in more than one crystalline state under different conditions of pressure (P) and temperature (T).

Example: Diamond vs. Graphite

• Diamond: Possesses a 3D covalent structure, resulting in extreme hardness, transparency, and insulating properties.
• Graphite: Possesses a laminar structure with secondary bonds between layers, resulting in softness, opacity, and electrical conductivity.

Understanding Crystal Defects

Defects are deviations from the perfect periodic arrangement of atoms in a crystal lattice. They significantly influence material properties.

Point Defects

Point defects are localized imperfections involving one or two atomic positions.

• Vacancy: The lack of an atom in a position where it should be located in the crystal lattice.
• Interstitial: An atom occupies an interstitial site (a position normally unoccupied, typically less abundant).

Origin of Point Defects: Defects occur during solidification processes (due to impurities or alloying), particle bombardment, plastic deformation, or thermal vibrations (increasing exponentially with temperature).

Specific Point Defects in Ionic Crystals and Alloys

• Schottky Defect: A pair of vacancies (anionic and cationic) appearing in an ionic crystal to maintain overall electroneutrality.
• Frenkel Defect: An ion migrates from its normal lattice position into an interstitial position (a combined vacancy-interstitial pair).
• Antistructural Disorder: An order-disorder phenomenon, common in alloys, where atoms occupy positions corresponding to the wrong sublattice (occurs in solids with elements of similar electronegativity).

Linear Defects (Dislocations)

Dislocations are defects that cause a distortion of the crystal lattice centered around a line.

Key Features of Dislocations

• They can be moved inside the crystal with relatively low effort.
• They produce the complete displacement of crystal planes.

Significance: Dislocations explain why the theoretical strength (based on Young's modulus) is much greater than the experimental strength ($ ext{E}_{ ext{theoretical}} > ext{E}_{ ext{experimental}}$). They are fundamental to understanding plastic deformation in metals (malleability and ductility).

Formation: Dislocations form during solidification, plastic or permanent deformation of the crystal, condensation of vacancies, or in atomic solid solutions.

Types: Edge (wedge or Taylor), Screw (propeller or Burgers), and Mixed dislocations.

Planar Defects

Planar defects are imperfections that extend over a two-dimensional surface.

Grain Boundaries

Grain boundaries separate crystals (grains) of different crystallographic orientation.

• Formation: Occurs during solidification as distinct crystals formed from distinct nuclei grow simultaneously.
• Effect: They limit the movement of dislocations in the material. Generally, decreasing grain size increases mechanical strength ($ ext{R}_{ ext{mecánica}}$).

Surface

The surface is the end of the crystal structure or grain. Atoms at the surface have a lower coordination number and higher energy compared to atoms in the interior ($ ext{E}_{ ext{surface}} > ext{E}_{ ext{interior}}$).

Stacking Faults

A stacking fault occurs when a crystal plane does not follow the ideal stacking pattern (e.g., ABCABC vs. ABCABA).

Twin Boundaries (Macla)

A twin boundary separates two parts of a grain that are mirror images of each other across the boundary plane (the reflection plane).

• Formation: Deformation processes or heat treatment.
• Effect: They increase mechanical resistance ($ ext{R}_{ ext{mecánica}}$) by hindering the glide of dislocations.