The intermetallic compound LiAg crystallizes in a cubic lattice in which both lithium and silver atoms have coordination number of eight. To what crystal class does the unit cell belong ?a)Simple cubic [1997]b)Face-centred cubicc)Body-centred cubicd)NoneCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

A solid centroid cube explanation .a body centroid cubic unit cell consisted of 8 atom at the corners and one atom at the center

Answer

Correct option (c) body-centred cube

Explanation : A body centred cubic unit cell consists of 8 atoms at the corners and one atom at the centre.

Answer

Explanation:

In order to determine the crystal class of a unit cell, we need to consider the coordination number and the arrangement of atoms within the lattice.

Coordination Number:
The coordination number is the number of nearest neighboring atoms or ions that surround a central atom or ion in a crystal lattice. In this case, both lithium and silver atoms have a coordination number of eight, which means that each atom is surrounded by eight nearest neighboring atoms.

Arrangement of Atoms:
Based on the given information, the intermetallic compound LiAg crystallizes in a cubic lattice. This means that the arrangement of atoms within the unit cell follows a cubic symmetry.

Crystal Class:
The crystal class is determined by the combination of the symmetry elements present in the lattice. There are seven crystal systems, namely cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and rhombohedral.

Based on the coordination number of eight and the cubic symmetry of the lattice, we can determine the crystal class of the unit cell.

Cubic Crystal System:
The cubic crystal system is characterized by a three-fold rotational symmetry along each of the three crystallographic axes (a, b, and c). There are three types of cubic lattices: simple cubic, body-centered cubic, and face-centered cubic.

Simple Cubic:
In a simple cubic lattice, the atoms are located only at the corners of the unit cell. Each atom has a coordination number of six, as it is surrounded by six nearest neighboring atoms. This is not the case in the given intermetallic compound LiAg, as both lithium and silver atoms have a coordination number of eight.

Face-Centered Cubic:
In a face-centered cubic lattice, the atoms are located at the corners and the center of each face of the unit cell. Each atom has a coordination number of twelve, as it is surrounded by twelve nearest neighboring atoms. This is also not the case in the given intermetallic compound LiAg, as both lithium and silver atoms have a coordination number of eight.

Body-Centered Cubic:
In a body-centered cubic lattice, the atoms are located at the corners and at the center of the unit cell. Each atom has a coordination number of eight, as it is surrounded by eight nearest neighboring atoms. This matches the given coordination number of both lithium and silver in the intermetallic compound LiAg.

Therefore, the unit cell of the intermetallic compound LiAg belongs to the body-centered cubic crystal class.

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