Question

Statement: The maximum number of Bravais lattices is shown by tetragonal type crystals.
State whether the given statement is true or false.
A. True
B. False

Answer 1

Hint: In crystallography, the Bravais lattice concept of an infinite array of discrete points is expanded using the concept of a unit cell which includes the space in between the discrete lattice points as well as any atoms in that space. There are two main types of unit cells: primitive unit cells and non-primitive unit cells.

Complete step by step answer:
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a).
There are two tetragonal Bravais lattices: the simple tetragonal (from stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the face-centered or the body-centered cubic lattice). One might suppose stretching face-centered cubic would result in face-centered tetragonal, but the face-centered tetragonal is equivalent to the body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more fundamental, and therefore this is the standard terminology.
The tetragonal crystal system can have a total of two Bravais lattices and they are primitive and face-centered. In the case of an orthorhombic crystal system, there are 4 Bravais lattices (primitive, face centered, body centered and end centered). Thus, the statement which says that the maximum number of Bravais lattices shown by tetragonal type crystals is false.
Thus, the correct option is B. False.

Note:
A primitive unit cell for a given Bravais lattice can be chosen in more than one way (each way having a different shape), but each way will have the same volume and each way will have the property that a one-to-one correspondence can be established between the primitive unit cells and the discrete lattice points. The obvious primitive cell to associate with a particular choice of primitive vectors is the parallelepiped formed by them.