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# Structure.homework__2-answer - MTLE-2100 Structure of...

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MTLE-2100 Structure of Engineering Materials , Homework #2 - Answer 1. calculate the theoretical density of the following materials: (a) SiO 2 β-Quartz (hexagonal, a = 4.989Å, c = 5.446Å) Unit cell contains 3 SiO 2 . Its volume is a 2 c sin(60)= a 2 c( 3/2). Atomic weight Si = 29.09; O = 16. d= 3 (28.09 + 2x16)/ a 2 c ( 3/2)N A = 3x60.09/[(4.989x10 -8 ) 2 x 5.446x10 -8 x( 3/2)x6.02x10 23 ]= 180.27/70.669 = 2.55g/cm 3 (b) SiO 2 β-Cristobalite (cubic, a = 7.03Å) 8 SiO 2 in unit cell. d = 8x(28.09 + 2x16)/ a 3 N A = 8 x 60.09/[(7.03x10 -8 ) 3 x 6.02x10 23 ] = 480.72/209.15 = 2.30 g/cm 3 (c) BaTiO 3 , perovskite (cubic, a = 4.01Å) d = (137.3 + 47.88 + 3x16) /a 3 N A = 233.18/(4.01x10 -8 ) 3 x 6.02x10 23 = 233.18/38.818 = 6.01 g/cm 3 (d) Diamond, (cubic, a= 3.56Å) There are 8 C atoms in unit cell. d = 8x12/a 3 N A = 96/(3.56x10 -8 ) 3 x 6.02x10 23 = 96/27.16 = 3.54 g/cm 3 2. BaTiO 3 (perovskite structure) transforms from cubic (high temperature form, a=4.009Å) to tetragonal (low

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