How are crystallographic points directions and planes specified?

How are crystallographic points directions and planes specified?

Indices of crystallographic points, directions, and planes are given in terms of the lattice constants of the unit cell. For points and directions, you can consider the indices to be coefficients of the lattice constants. Remember that you only need to invert the indices for planes.

What is Weiss zone law?

Weiss zone law, also known as Weiss zone rule, states that a lattice direction with indices [uvw] is contained in a lattice plane with Miller indices (hkl) if the following condition is satisfied: hu + kv + lw = 0.

What is the difference between lattice and crystal?

What is the difference between Lattice and Crystal? Lattice describes the structure of crystals. When a group of molecules tends to arrange each unit repeatedly at a lattice point, a crystal is made. In a crystal structure, there is a pattern of arranging the atoms or units.

How do represent a family of directions?

A set of directions related by symmetry operations of the lattice or the crystal is called a family of directions. A family is a symmetry related set. A family of directions is represented (Miller Index notation) as: .

What is crystallographic zone?

A zone is defined as a group of crystal faces that intersect in parallel edges. Since the edges will all be parallel to a line, we can define that the direction of the line using a notation similar to Miller Indices. This notation is called the zone symbol.

What is zone and zone axis in crystallography?

Zone axis, a term sometimes used to refer to “high-symmetry” orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices.

What is lattice point in physics?

A Lattice point is the position in the unit cell or in a crystal where the probability of finding an atom or an ion is the highest. In other words, the atoms or ions occupy the lattice points in a crystalline solid.

What are the crystallographic directions of a hexagonal crystal?

of crystallographic directions hexagonal crystal The hexagon edge (X-direction) is parallel to the translation vector a 1, That is r= a 1, hence is along the [100] – direction. For Y – direction r= a 1 + 2 a 2 that is [120]-direction The system is based on four translation vectors, three of them being in the hexagon plane (i.e. a 1, a 2, a s

How do you find the direction of Crystallography?

13. 13 A crystallographic direction is defined as a line between two points or a vector. The following steps are utilized in the determination of the three directional indices: 3. These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values.

What are the equivalent directions of a crystallographic plane?

As a convenience, equivalent directions are grouped together into a family of directions, which are enclosed in angle brackets, thus: <100>. 16. 3. Crystallographic planes 3.1 Definition Crystallographic planes are specified by three Miller indices as (h k l).

How many indices of crystallography are enclosed in square brackets?

4. The three indices, not separated by commas, are enclosed in square brackets, thus: [u v w]. 2. Crystallographic directions 2.1 Definition Example of a crystallographic direction.