Crystals and Their Properties Quiz

A type of crystal lattice where the unit cells are arranged in a square pattern.

A type of crystal lattice where the unit cells are arranged in a hexagonal pattern.

A type of crystal lattice where the unit cell has one lattice point at each corner.

A type of crystal lattice where the unit cell has one lattice point at each corner and one lattice point at the center of the cell.

A type of crystal lattice where the unit cell has one lattice point at each corner and one lattice point at the center of each face.

In crystallography, replacing atoms with geometric points at their stable positions creates a geometric structure representing the crystal's properties.

The repeating pattern of atoms in a material extends over a large distance.

A geometric structure formed by representing each atom in a crystal with a point placed at its stable position.

Materials with long-range order, meaning atoms are arranged in a repeating pattern.

The stable configuration of an atom within a crystal lattice.

Materials with short-range order; their atoms lack a repeating pattern.

The geometric properties of a crystal, such as its shape, symmetry, and unit cell, are maintained in its geometric structure of points.

A common example of a crystalline material with a regular, repeating arrangement of sodium and chlorine atoms.

The stable position of each atom in a crystal lattice is determined by factors such as interatomic forces and electrostatic interactions.

A very hard, crystalline material composed of carbon atoms arranged in a tetrahedral structure.

The distance between two nearest atoms in a face-centered cubic (FCC) lattice is half the length of the face diagonal.

The relationship between the radius (r) of an atom and the lattice constant (a) in an FCC lattice is given by √2a = 4r, where a is the length of the edge of the unit cell.

The volume of the primitive cell of a face-centered cubic (FCC) lattice is 1/4 the volume of the conventional unit cell.

The filling factor (or packing factor) is the ratio of the volume occupied by atoms to the total volume of the unit cell.

The vectors that define the edges of the primitive unit cell in a face-centered cubic (FCC) lattice are a/2(i+j), a/2(j+k), and a/2(i+k), where a is the lattice constant.

The Miller indices represent a set of three numbers that define the orientation of a crystal plane.

To find the Miller indices of a crystal surface, take the inverse of the coordinates of the intersection with the axes, multiply by the least common multiple, and simplify to the smallest possible integers.

When a crystal surface intersects an axis at infinity, the Miller index for that axis is zero.

The Miller indices help us understand the geometry of a crystal and predict properties like cleavage and growth patterns.

A negative sign in a Miller index indicates that the plane cuts the corresponding axis on the negative side of the origin.

The direction of a crystal, representing a common direction along which a group of intersecting surfaces share. This signifies that these surfaces belong to the same domain.

A group of surfaces sharing a common direction or band axis. They are considered part of the same domain within a crystal.

A notation used to represent directions in crystals. It uses angle brackets and three numbers, like this: . Each number represents the direction along a specific crystallographic axis. For example, <110> means all directions equivalent to [101], [101], [011], etc.

Crystallographic axes are imaginary lines used as references within a crystal structure. They define the orientation of a crystal lattice and help describe directions and planes within the crystal.

The formula represents directions within a crystal structure. It effectively describes a set of equivalent directions because crystals are often symmetrical. So, <110> includes all directions that are equivalent to [101],[101],[011],[011],[110],[101],[011], etc.