Crystallography and Unit Cells

Flashcards covering key concepts, equations, and definitions related to crystallography, unit cells (especially FCC), and calculations involving atomic properties and density.

FCC (Face Centered Cubic) structure

A type of crystal structure where atoms are located at each of the corners and the center of all the cube faces. For FCC, the coordination number is 12 and there are 4 atoms per unit cell (Z-value).

Coordination Number (for FCC)

The number of nearest neighbors for an atom in a crystal structure. For an FCC structure, it is 12.

Z-value (for FCC)

The number of atoms (or formula units) effectively contained within a unit cell. For an FCC structure, it is 4.

Relationship between 'a' and 'r' in FCC

The relationship between the edge length 'a' of the unit cell and the atomic radius 'r' in an FCC structure is r = a / Square root of 8 (or a = r * Square root of 8).

Angstrom

A unit of length equal to 10^-10 meters, commonly used to express atomic radii and interatomic distances.

Picometer

A unit of length equal to 10^-12 meters, also used for very small distances in atomic structures.

Density Equation

An equation used to relate mass and volume, typically expressed as Density = Mass / Volume.

Molar Mass

The mass in grams of one mole of a substance (e.g., 197.0 grams/mole for Gold).

Avogadro's Number

The number of constituent particles (atoms, molecules, ions, etc.) per mole of a substance, equal to approximately 6.022 x 10^23 particles/mole.

Volume of a Cubic Unit Cell

Calculated as the cube of the edge length 'a', i.e., V = a^3.

Packing Efficiency (Percent Packing)

A measure of how efficiently identical spheres are packed in a crystal structure, calculated as (Volume occupied by atoms / Volume of unit cell) * 100%. For FCC, it is 74%.

Volume of a Sphere (Atom)

The formula for the volume of a single spherical atom is (4/3) * pi * r^3, where 'r' is the atomic radius.