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Draw a fully labelled diagram showing how a polycrystalline material appears under a microscope. Why may different grains within the material have different appeara

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Hi, Can you solve the question please. And can you explain each steps please? This subject is related to Crystallography
The group velocity and the phase velocity both exist in the crystal. How are they related? O a. The group velocity is larger than phase velocity. O b. The group velocity is smaller than phase velocity. O c. The group velocity is equal to phase velocity. O d. They are generally not equal.
How does duality manifest in symmetry operations in crystallography? Provide examples of crystallographic duals.
2- Assuming that the oscillating ionic compound is cesium chloride, if you know the atomic weight of chlorine is 35.5 gm/mol and the atomic weight of cesium is 133 gm/mol, and assuming that Hooke's constant is y=4N/m²? NA = 6.02 x 1023 mol-¹ 1. Calculate the maximum frequency of the optical branch? 2. Calculate the frequency of the optical and acoustic branch at the boundary? 3. Determine the range of the forbidden frequency region? 4. Determine the Debye Temperature? 5. If you know that the lattice constant a = 3.14 Å, draw the first Brillion zone curve with its optical and acoustic branches. 6. If you know that the two atoms have the same mass equal to the mass of the smaller atom, then repeat the previous calculations and redraw the differentiation curve?
Useful Constants: k = 9.00 × 10º Nm² C2 8.85 x 10-12 C² Nm2 %3D e = 1.6 x 10-19 C me = 9.11 x 10 mp = 1.67 × 10-27kg %3D -27 mn = 1.68 x 10 %3D
65 N 45 P 56 N 30% C 60° 52 N P Pearson