Crystal Structures and Defects in Materials Science

HCP Directions

Convert [UVW] to [uvtw] using equations.

HCP Planes

Identify plane intersections with a1, a2, c.

Cubic Planes

Reciprocal of (hkl) gives plane orientation.

Anisotropy

Properties vary with direction in materials.

Isotropy

Properties remain constant in all directions.

Crystalline Structures

Long range order with repeated atomic patterns.

Amorphous Structures

Random atomic distributions with short range order.

Linear Density

Atoms per unit length in crystallographic direction.

Planar Density

Atoms per area on a 2D crystallographic plane.

FCC Unit Cell

Edge length = 2R√(2), 1 atom per cell.

BCC Unit Cell

Edge length = 4R/√(3), 2 atoms per cell.

X-ray Diffraction

Constructive interference from parallel crystal planes.

Bragg's Law

nλ = 2d(hkl)sinθ for diffraction conditions.

Interplanar Spacing

Distance between atomic planes, computed via θ.

Point Defects

Lattice irregularities like vacancies and solutes.

Line Defects

Dislocations causing one-dimensional lattice irregularities.

Area Defects

Grain boundaries and free surfaces in crystals.

Grain Boundaries

Regions between different crystal grains.

Atomic Plane Spacing

Calculated using Bragg's law for crystal structures.

Vacancies

Vacant atomic sites in a crystal structure.

Self-Interstitials

Host atoms in interstitial positions between atoms.

Equilibrium Vacancy Concentration

N(v)/N=exp(-Q(v)/k(b)*T) formula.

Hume-Rothery Rule

Criteria for substitutional solid solutions.

Line Defects

One-dimensional defects causing atomic misalignment.

Dislocations

Defects where atoms are misaligned in crystals.

Edge Dislocations

Extra half-plane of atoms, stress state complex.

Screw Dislocations

Spiral planar ramp due to shear deformation.

Burgers Vector

Measure of lattice distortion along dislocation line.

Simple Dislocation Loop

Closed loop-shaped dislocation disrupting lattice.

Planar Defects

Disruptions along two-dimensional planes in crystals.

Twin Boundaries

Mirror reflections of atom positions across twin plane.

Stacking Faults

Errors in planar stacking sequence of atoms.

Fick's First Law

J=Flux=(Mass transport)/(Area*Time) formula.

Diffusion Coefficient

D=D(0)exp(-Q(d)/(RT)) relationship.

Factors Affecting Diffusion

Temperature influences diffusion rates significantly.

Interstitial Diffusion

Faster than vacancy diffusion due to smaller atoms.

Vacancy Diffusion

Atomic motion from lattice site to adjacent vacancy.

Activation Energy (Q(v))

Energy required to create vacancies in a lattice.

Boltzmann Constant (k(b))

Constant relating temperature to energy in statistical mechanics.

Self-diffusion

Atomic motion within a pure material.

Interstitial diffusion

Atomic movement between interstitial sites.

Short-Circuit Diffusion

Diffusion along dislocations and grain boundaries.

Fick's second law

Describes concentration change over time and space.

C(x,t)

Concentration at position x and time t.

Error function (erf)

Mathematical function used in diffusion calculations.

Solubility limit

Maximum solute concentration before phase change.

Components

Elements or compounds forming a solution.

Phase

Distinct chemically and structurally defined material region.

Degrees of freedom

Controllable variables like temperature and pressure.

Microconstituent

Identifiable structure element in microstructure.

Unary phase diagram

Single component with multiple phases (e.g., water).

Binary phase diagram

Two components interacting (e.g., Cu and Ni).

Ternary phase diagram

Three components interacting in a system.

Allotrope

Distinct crystal structure form of an element.

Allotropy

Change in crystal structure of an element.

Polymorph

Distinct crystal structure form of a material.

Polymorphism

Change in crystal structure of a material.

Isomorphous

Complete miscibility without structural change.

Miscibility gap

Region where components form multiple phases.

Gibbs phase rule

P + F = C + N relationship.

Eutectic transformation

Liquid transforms into two solid phases.

Eutectoid transformation

One solid phase transforms into two solid phases.

Peritectic transformation

Liquid and one solid phase form a second solid.