Find Debye Temp of GaAs: E,v,rho Given

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To find the Debye temperature of gallium arsenide (GaAs) using Young's modulus (E), Poisson's ratio (v), and density (rho), the elastic constants c11 and c12 are first calculated. The bulk modulus (K) and shear modulus (G) are derived from these constants, which are then used to determine the longitudinal (ul) and transverse (ut) sound velocities. The Debye temperature formula incorporates these velocities and other constants, leading to a calculated value. In this case, the calculated Debye temperature was 295K, while the expected value is 360K, indicating a discrepancy likely due to the values of c11 and c12 derived from E and v. Accurate measurements of these parameters are crucial for obtaining the correct Debye temperature.
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If the young's modulus(E), poisson's ratio(v) and density(rho) of gallium arsenide is given how to find its debye temperature

K=c11+c12/2
G=c11-c12/3

Debye temp = (h/k)*(9N/4*3.14*V)^(1÷3)*(2/ut^3+1/ul^3)^(-1/3)

Using E and rho i found out the c11 and c12 and then found out bulk modulus(G) and shear modulus(K) and then the longitudinal velocity(ul) and transverse velocity(ut).. using all these data my value of debye temperature came upto 295K but the actual value should be 360K
 
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c11 and c12 are found using E and v.
 
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