[Terminologies] M2.2 MatSci

Crystal system

Classification scheme for crystal structures based on unit cell geometry

Lattice parameters

Six values (a, b, c, alpha, beta, gamma) defining unit cell geometry

Cubic

Crystal system with the highest symmetry and one unique parameter

Triclinic

Crystal system with the lowest symmetry and six unique parameters

Cubic

Crystal system to which FCC and BCC structures belong

Hexagonal

Crystal system to which HCP structures belong

Point coordinates

Fractional multiples of edge lengths specifying a lattice position

q r s

Standard notation for point coordinates

Crystallographic direction

Line or vector in a crystal specified by three integer indices

[uvw]

Notation used for a specific crystallographic direction

<uvw>

Notation used for a family of crystallographically equivalent directions

Perpendicular

Geometric relationship between [hkl] and (hkl) in cubic systems

t = -(u+v)

Redundancy formula for the third index 't' in hexagonal notation

Miller indices

Integers specifying the orientation of a crystallographic plane

(hkl)

Notation used for a specific crystallographic plane

{hkl}

Notation used for a family of crystallographically equivalent planes

i = -(h+k)

Redundancy formula for the third index 'i' in hexagonal notation

Move origin

Required action if a crystallographic plane passes through the origin

Atoms on vector / length

Formula for Linear Density (LD)

Atoms on plane / area

Formula for Planar Density (PD)

Slip system

Combination of a specific slip plane and a slip direction

12

Total number of slip systems available in FCC crystals

Highest PD and LD

Geometric conditions for the occurrence of plastic deformation

ABABAB

Close-packed layer stacking sequence for HCP structures

ABCABC

Close-packed layer stacking sequence for FCC structures

0.74

Maximum Atomic Packing Factor (APF) for equal spheres

Grain boundary

Narrow transition region of atomic mismatch between adjacent grains

Texture

Preferential crystallographic orientation of grains in a polycrystal

Anisotropy

Material properties that depend on measurement direction

Isotropy

Material properties independent of measurement direction

Amorphous

Material classification where atoms lack long-range periodic arrangement

Rapid cooling

Cooling condition that favors the formation of an amorphous solid

Bragg's Law

Constructive interference condition for diffracted X-rays

nlambda = 2d*sin(theta)

Mathematical expression for Bragg's Law

Bragg angle

Specific definition of theta in Bragg's Law

Interplanar spacing

Perpendicular distance between adjacent parallel planes

d_hkl = a / sqrt(h^2 + k^2 + l^2)

Formula for interplanar spacing in the cubic system