A gold (Au) crystal forms an FCC crystal with the lattice constant 4.1 10-10 m...

 

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A gold (Au) crystal forms an FCC crystal with the lattice constant 4.1 × 10-10 m and the atomic weight is 197. The elastic stiffness constants of Au are C₁1 = 1.9 × 10¹2 dyn/cm², C₁2 = 1.6 × 10¹2 dyn/cm² and C44 = 0.42 x 1012 dyn/cm². Q1: Does the Au crystal have an optical mode phonon dispersion? Q2: Calculate the longitudinal sound velocity c. Use the unit of m/s. Q3: Calculate the Debye angular frequency w in the Debye model. Use the unit of rad/s. Q4: Calculate the maximum angular frequency from the w-k dispersion relation. Use the theoretical w of a monatomic 1D crystal model and the unit of rad/s. Assume that interatomic spring constant a is equal to E-Ro, here Eis the Young's modulus and Ro is the interatomic distance at the equilibrium. Q5: Experimental Debye angular frequency is about 2.3 × 10¹3 rad/s. Show whether all phonon angular frequencies are expected to work at the room temperature (300 K). A gold (Au) crystal forms an FCC crystal with the lattice constant 4.1 × 10-10 m and the atomic weight is 197. The elastic stiffness constants of Au are C₁1 = 1.9 × 10¹2 dyn/cm², C₁2 = 1.6 × 10¹2 dyn/cm² and C44 = 0.42 x 1012 dyn/cm². Q1: Does the Au crystal have an optical mode phonon dispersion? Q2: Calculate the longitudinal sound velocity c. Use the unit of m/s. Q3: Calculate the Debye angular frequency w in the Debye model. Use the unit of rad/s. Q4: Calculate the maximum angular frequency from the w-k dispersion relation. Use the theoretical w of a monatomic 1D crystal model and the unit of rad/s. Assume that interatomic spring constant a is equal to E-Ro, here Eis the Young's modulus and Ro is the interatomic distance at the equilibrium. Q5: Experimental Debye angular frequency is about 2.3 × 10¹3 rad/s. Show whether all phonon angular frequencies are expected to work at the room temperature (300 K).

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Given Lattice constant a 41 1010 m Atomic weight M 197 Elastic stiffness constants C11 19 1012 dyncm C12 16 1012 dyncm C44 042 1012 dyncm Experimental ... View the full answer