Crystalline Structures in Materials Science

This set of vocabulary flashcards covers the fundamentals of crystalline structures, lattice systems, Miller indices, and material characterization properties as presented in the lecture.

Crystalline

A solid body with a regular arrangement of atoms on both micro and macro scales, consisting of chains of atoms or molecules that repeat periodically with characteristic symmetry.

Amorphous

A solid state (e.g., glass) where there is an irregular distribution of atoms on the micro scale and little order, similar to the liquid state.

Semi-crystalline

Materials like certain thermoplasts that exhibit a regular arrangement on a sub-micro scale but irregular distribution overall.

Unit Cell

The smallest structural unit characterized by lattice parameters ($a_0, b_0, c_0$ and angles $\alpha, \beta, \gamma$) that defines a crystal.

Bragg’s equation

Proposed in 1914 by William Henry Bragg and William Lawrence Bragg, this allows for the quantitative determination of atomic distances in crystals.

Bravais lattices

A set of $14$ distinct lattice types that represent all possible crystal symmetries.

Simple Cubic Lattice

The simplest crystal case where $a_0 = b_0 = c_0$ and $\alpha = \beta = \gamma = 90^\circ$.

Triclinic Lattice

The most complicated crystal case where $a_0 \neq b_0 \neq c_0$ and $\alpha \neq \beta \neq \gamma \neq 90^\circ$.

BCC (Body-Centred Cubic)

A cubic lattice type (I) characterized by atoms at the corners and one atom at the center; examples include ferrite, tungsten, and vanadium.

FCC (Face-Centred Cubic)

A cubic lattice type (F) with atoms at the corners and the centers of each face; examples include austenite, aluminium, and nickel.

HDP (Hexagonal Dense Packed)

A hexagonal lattice structure with high relevance for metals like magnesium and titanium, characterized by parameters $a_0 = b_0 \neq c_0$, $\alpha = \beta = 90^\circ$, and $\gamma = 120^\circ$.

Lattice Directions [u v w]

Straight lines in a lattice containing atoms, defined by integer indices; negative indices are marked with an overbar, such as $[11\bar{1}]$.

Miller Indices (hkl)

A nomenclature used to definitely describe lattice planes by taking the relatively prime reciprocals of the plane intercepts with the coordinate axes.

Family of Planes {hkl}

A grouping of all equivalent planes in a lattice, such as the cube faces represented by ${100}$.

Coordination Number (CN)

The number of the nearest equidistant neighboring atoms; for the FCC lattice, $CN = 12$, and for BCC, $CN = 8$.

Density Ratio (DR)

The percentage of unit cell volume occupied by atoms, calculated as $\text{DR} = \frac{V_{atoms}}{V_{unit cell}} \times 100\%$. FCC has a DR of $74\%$ while BCC has $68\%$.

Octahedral Site

A non-occupied site located in the center of the cube and at the centers of the cube edges in the FCC lattice; there are $4$ per unit cell.

Tetrahedral Site

A non-occupied site located within tetrahedral bodies in the lattice; FCC has $8$ per unit cell with a radius of $0.225r$.

Slip System

A combination of a slip plane (defined tracks for plastic deformation) and a slip direction; FCC has $12$ slip systems of type ${111}<110>$.

Allotropy

The phenomenon where an element can exist in different lattice modifications depending on temperature; for example, Iron is BCC ($\alpha$) below $911^\circ C$ and FCC ($\gamma$) between $911^\circ C$ and $1392^\circ C$.

Intermetallic Compounds

Phases involving two or more metallic/semi-metallic elements that exhibit metallic properties and specific stoichiometric compositions like $MgZn_2$.