Question

(5) A platinum (Pt) crystal forms a FCC crystal with the lattice constant 3.9 ~ 10-10 m and the atomic weight is 195. The elastic stiffness constants of Pt are C11 = 3.6 × 1012 dyn/cm², C12 = 2.5* 1012 dyn/cm2 and C44 = 7.7 * 1011 dyn/cm2. Q1: Does the Pt crystal have an optical mode phonon dispersion ? Q2: Calculate the Young's modulus and the Poisson's ratio of the Pt metal. Don't forget to give an unit, if it is necessary. Q3: Estimate the longitudinal sound velocity c Use the unit of m/s. Q4: Estimate the Debye angular frequency wp in the Debye model. Use the unit of rad/s.

Answer 1

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Azu bzy (167) ~ It Exxteyyit zz - but tyytz &= vw v on the othe way mass of unit cell = yas congitudinal compression (Young's Modulus) a Cas= 195X4 ધા Gx Na carregado numas) 19584 Naa² 42 Young's modules - poisson's ratio 3.6 8 10 12 dynlem transverse strain axial stonin 195x4 longitudinal relocitys us all Na.a3 2.5x101 pobye frequeney wp- 672 p v3 3.6 8 10 25 36 CL longitudinal relocity Р Feie erystal y density of the material (unit cell total no. of atting a 8** +6x 4 mass of 195 mess of 6.023X1023 no. of pt atoms a las gno 4 atom - nole - 195 6023X1023 4 atoms a 195 x4 6:02 5x1023