Crystallography family of directions

What are crystal directions defined as?
Crystal planes are defined as some imaginary planes inside a crystal in which large concentration of atoms are present.
Inside the crystal, there exists certain directions along which large concentration of atoms exists.
These directions are called crystal directions..
What is the family of directions in crystal structure?
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._{Aug 28, 2022}.
What is the family of directions in the FCC?
The equivalent family of directions in the FCC structure are the \x26lt; 110 \x26gt; directions. \x26lt; 110 \x26gt; represents the directions [110], [110], [101], [101], [011], [011 ] and their negative [ 1 10], etc.
The close-packed directions in bcc are the directions \x26lt; 111 \x26gt; (body diagonal of the unit cell)..
What is the 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: \x26lt;u v w\x26gt;..
Given any plane in a lattice, there is a infinite set of parallel lattice planes (or family of planes) that are equally spaced from each other.
One of the planes in any family always passes through the origin.
The equivalent family of directions in the FCC structure are the \x26lt; 110 \x26gt; directions. \x26lt; 110 \x26gt; represents the directions [110], [110], [101], [101], [011], [011 ] and their negative [ 1 10], etc.
The close-packed directions in bcc are the directions \x26lt; 111 \x26gt; (body diagonal of the unit cell).

May 26, 2020Families of Crystallographic Directions and Planes are explained in this video explicitly
Duration: 12:26
Posted: May 26, 2020

Angled brackets denote a family of crystallographic directions. Similarly for other equivalent directions Symmetry operation can generate all the directions

How do you draw a vector with a crystallographic point?

Choose a point for the origin of your vector

Simple directions, such as those shown in Figure 2a, are easy to draw using the 000 crystallographic point as the origin

For more complicated directions (see Figure 2b), it is more convenient to translate (add or subtract) or scale (mul- tiply or divide) the indices of the direction

Dense arrangement of congruent spheres in an infinite, regular arrangement

Crystallography family of directions

What are crystal directions defined as?

What is the family of directions in crystal structure?

What is the family of directions in the FCC?

What is the family of directions?

How do you draw a vector with a crystallographic point?