※ 引述《boudi (boudi)》之銘言：
: [領域] (題目相關領域)
: 固態物理
: [來源] (課本習題、考古題、參考書...)
: 考古題
: [題目]
: For a bcc lattice the primitive lattice vector are
: b1=2π/a(y+z)
: b2=2π/a(x+z)
: b3=2π/a(x+y)
: where a is the lattice constant and x,y,z are unit vector in the x,y,z
: dierctions.
: For a fcc lattice the primitive lattice vector are
: b1=2π/a(-x+y+z)
: b2=2π/a(x-y+z)
: b3=2π/a(x+y-z)
: (a)calculate the spacing d between two neighboring (111) lattice planes of a
: sc lattice in terms of a lattice constant a
b1=2πx/a
b2=2πy/a
b3=2πz/a
=> d(111) = 2π / |b1+b2+b3|
= a / sqrt(1^2+1^2+1^2)
= a / sqrt(3)
: (b)repeat (a) for a bcc lattice
b1=2π/a(y+z)
b2=2π/a(x+z)
b3=2π/a(x+y)
=> |b1+b2+b3| = 2π/a * sqrt(2^2+2^2+2^2) = sqrt(3) * 4π/a
=> d(111) = 2π/ |b1+b2+b3|
= a / (2*sqrt(3))
: (c)repeat (a) for a fcc lattice
|b1+b2+b3| = sqrt(3) * 2π/a
=> d(111) = a / sqrt(3)
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