Crystallography brackets

Are Miller indices in parentheses or brackets?
The Miller indices when used as face symbols are enclosed in parentheses, as the (111) face for example.
Form symbols are enclosed in braces, as the {111} form for example. Zone symbols are enclosed in brackets, [111] for example and denote a zone axis in the crystal..
What type of brackets should be used to indicate a family of directions?
Angle brackets \x26lt;hkl\x26gt; indicate a family of directions.
A family of directions includes any directions that are equivalent in length and types of atoms encountered.
For example, in a cubic lattice, the [100], [010], and [001] directions all belong to the \x26lt;100\x26gt; family of planes because they are equivalent..
Miller indices are used to specify directions and planes.
These directions and planes could be in lattices or in crystals.
The number of indices will match with the dimension of the lattice or the crystal.
The plane passing through points X and Y (and perpendicular to the page) has axial intercepts 1, ¹/₂, ∞, so its Miller index is (120).
Because all unit cells are equivalent, we know identical (120) planes exist in all the unit cells.

Bracket Conventions. In crystallography there are conventions as to how the indices of planes and directions are written. When referring to a specific plane

Are crystal directions grouped in families?

Crystal directions may be grouped in families

To avoid confusion there exists a convention in the choice of brackets surrounding the three numbers to differentiate a crystal direction from a family of direction

For a direction, square brackets [ hkl] are used to indicate an individual direction

How are crystallographic directions labelled?

Directions in the crystal can be labelled in a similar way

These are effectively vectors written in terms of multiples of the lattice vectors a, b, and c

They are written with "square" brackets: A number of crystallographic directions can also be symmetrically equivalent, in which case a set of directions are written with "triangular" brackets:

How are lattice planes represented in crystallography?

Lattice planes can be represented by showing the trace of the planes on the faces of one or more unit cells

The diagram shows the trace of the (2 1 3) planes on a cubic unit cell

In crystallography there are conventions as to how the indices of planes and directions are written

When referring to a specific plane, "round" brackets are used:

In crystallography there are conventions as to how the indices of planes and directions are written. When referring to a specific plane, "round" brackets are used: (hkl) (2.4.1) (2.4.1) (h k l) When referring to a set of planes related by symmetry, then "curly" brackets are used: {hkl} (2.4.2) (2.4.2) { h k l }

Crystallography brackets

Are Miller indices in parentheses or brackets?

What type of brackets should be used to indicate a family of directions?

Are crystal directions grouped in families?

How are crystallographic directions labelled?

How are lattice planes represented in crystallography?