9780073529585, Chapter 1, Problem 14

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Chapter 1, Problem 14 Problem (a) The crystal structure of particular material consists of single atom in the center of cube. The lattice constant is a0 and the diameter of the atom is a0. Determine the volume density of atoms and the surface density of atoms in the (110) plane. (b) Compare the results of part (a) to the results for the case of the simple cubic structure shown in Figure with the same lattice Step-by step solution Step The expression of surface density of atoms can be expressed as number of atoms per lattice plane surface density of atoms area of lattice plane The expression of surface density of atoms can be expressed as number of atoms per unit cell volume density of volume unit cell Step (a) The number of atoms per unit cell in body centered cubic can be calculated as (8 corner atoms) atom 1 enclosed atom atoms The number of atoms per unit cell in body centered cubic is The area of lattice plane is The surface density of atoms can be calculated as follows number of atoms per lattice plane surface density of atoms= area lattice plane Substitute 2 for number of atoms per lattice plane and for area of lattice plane in the expression of surface density of atoms. 2 surface density of atoms= atoms cm⁻² 2 The surface density of atoms in the plane (110)is atoms cm Step The number of atoms per unit cell in body centered cubic can be calculated as (8 corner atoms) atom 1 enclosed atom atoms The number of atoms per unit cell in body centered cubic is 2 The volume of unit cell is The volume density of atoms can be calculated as follows, volume number of atoms per unit cell density of atoms volume of unit cell Substitute 2 for number of atoms per lattice plane and for volume of unit cell in the expression of volume density of atoms volume density of atoms 2 atoms cm 2 The volume density of atoms in the plane (110)is Step Step (b) The number of atoms per unit cell in simple cubic can be calculated as (8 corner atoms) 8 atom The number of atoms per unit cell in simple cubic is The area of lattice plane is The surface density of atoms can be calculated as number of atoms per lattice plane surface density of atoms= area of lattice plane Substitute number of atoms per lattice plane and for area of lattice plane in the expression of surface density of atoms. surface density of atoms atoms cm The surface density of atoms in the plane (110)is atoms cm Step The number of atoms per unit cell in simple cubic can be calculated as (8 corner atoms) atom 8 The number of atoms per unit cell in simple cubic is 2 The volume of unit cell is The volume density of atoms can be calculated as follows, number of atoms per unit cell volume density of atoms volume unit cell Substitute number of atoms per lattice plane and for volume of unit cell in the expression of volume density of volume density of atoms atoms cm -3 Step The volume density of atoms in the plane atoms cm 2 For bcc, the surface density of atoms in the plane (110)is atoms cm The 2 volume density of atoms in the plane atoms cm For simple cubic, the surface density of atoms in the plane (110)is atoms cm The volume density of atoms in the plane (110)is atoms cm