Question

Which of the following has face-centered Bravais Lattice?
A. Hexagonal
B. Monoclinic
C. Cubic
D. Orthorhombic

Answer 1

Hint:
Bravais Lattice refers to the \[{{14}}\] distinct three-dimensional structures during which crystal atoms are often arranged. A unit is taken into account the tiniest group of symmetrically arranged atoms that can be replicated in an array to form up the whole crystal.

Complete step by step answer:
Cubic Systems:
In Bravais lattices with cubic systems, the subsequent relationships are often observed.
\[{{A = B = C}}\]
\[{{\alpha = \beta = \nu = 9}}{{{0}}^o}\]
Where \[{{A,B,C}}\] are the length of the cell and \[{{\alpha , \beta ,\nu }}\] are angles of the cell.
There are three possible cubic Bravais lattices –
Primitive (or Simple) Cubic Cell (P)
Body-Centered Cubic Cell (I)
Face-Centered Cubic Cell (F)
Orthorhombic Systems:
The Bravais lattices with orthorhombic systems obey the subsequent equations:
\[{{a}} \ne {{b}} \ne {{c}}\]
\[{{\alpha = \beta = \nu = 9}}{{{0}}^o}\]
Where \[{{a,b,c}}\] are sides of the cell and \[{{\alpha , \beta ,\nu }}\]are angles of the cell.
The four sorts of orthorhombic systems (simple, base centered, face-centered, and body-centered orthorhombic cells)
Monoclinic Systems:
Bravais lattices having monoclinic systems obey the subsequent relations:
\[{{a}} \ne {{b}} \ne {{c}}\]
\[{{\beta = \gamma = 9}}{{{0}}^{{0}}}{{;}}\alpha {{ = 9}}{{{0}}^o}\]
Where \[{{a,b,c}}\]are sides of the cell and \[{{\alpha , \beta ,\nu }}\]are angles of the cell.
The two possible sorts of monoclinic systems are primitive and base centered monoclinic cells.
Hexagonal System;
The only sort of hexagonal space lattice is that of the simple hexagonal cell. it's the subsequent relations between cell sides and angles.
\[{{a = b}} \ne {{c}}\]
\[{{\alpha = \beta = 9}}{{{0}}^{{o}}}{{ ; \gamma = 12}}{{{0}}^{{o}}}\]
Where \[{{a,b,c}}\] are sides of the cell and \[{{\alpha , \beta ,\nu }}\] are angles of the cell.
So, from the above explanation option C and D both are correct.
Hence, the correct options are “C” and “D”.

Additional information:
Bravais lattice is often noted that each one 14 possible Bravais lattices differ in their cell length and angle relationships. it's important to stay in mind that the space lattice isn't always an equivalent because the space lattice. A space lattice can ask one among the 14 differing types of unit cells that a crystal structure is often made from. These lattices are named after the French physicist Auguste Bravais.

Note:Main characteristics of crystal lattice are Each constituent particle is represented by one point during a space lattice. The points referred to as lattice points or lattice sites during a space lattice are joined together by straight lines. By joining the lattice points with straight lines, the geometry of the space lattice is made.