IGNOU PHE 13 2026 - The values of the elastic stiffness constants for are:

Question

The values of the elastic stiffness constants for $\text{GaAs}$ are:

$C_{11}=1.18\times 10^{11}\\mathrm{N\,m^{-2}},\quad C_{44}=0.59\times 10^{11}\\mathrm{N\,m^{-2}}\quad\text{and}\quad C_{12}=0.54\times 10^{11}\\mathrm{N\,m^{-2}}.$
Given that the density of $\text{GaAs}$ is $5.32\text{ g cm}^{-3}$ , determine the bulk modulus of elasticity and the velocity of the transverse and longitudinal elastic waves in the [100] direction.

29 Jan 2026

Answer :

Word Count : 259

The density of GaAs is given as ( \rho = 5.32~\text{g/cm}^3 = 5.32 \times 10^3~\text{kg/m}^3 ). The elastic stiffness constants are ( C_{11} = 1.18 \times 10^{11}~\text{N/m}^2 ), ( C_{12} = 0.54 \times 10^{11}~\text{N/m}^2 ), and ( C_{44} = 0.59 \times 10^{11}~\text{N/m}^2 ). Step 1: Bulk modulus For a cubic crystal, the bulk modulus ( B ) is given by: [ B = \frac{C_{11} + 2 C_{12}}{3} ] Substitute the values: [ B = \frac{1.18 \times 10^{11} + 2(0.54 \times 10^{11})}{3} = \frac{1.18 \times 10^{11} + 1.08 \times 10^{11}}{3} = \frac{2.26 \times 10^{11}}{3} = 0.753 \times 10^{11}~\text{N/m}^2 ] So, ( B

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