Show that the reciprocal lattice of a bcc lattice with a lattice constant a is a fcc lattice with the side of the cubic cell to be 4π/a. [Hint: Use a symmetric set of vectors for bcc, a= ²/2 (y+z-x), b= ² (z+x−y), c = (x + y − 2) where a is the lattice constant of a conventional primitive cell, and x, y, z are unity vectors of a Cartesian coordinate. For fcc, a= ² (v+z), b=²(x+x), c= (x+y).]
Show that the reciprocal lattice of a bcc lattice with a lattice constant a is a fcc lattice with the side of the cubic cell to be 4π/a. [Hint: Use a symmetric set of vectors for bcc, a= ²/2 (y+z-x), b= ² (z+x−y), c = (x + y − 2) where a is the lattice constant of a conventional primitive cell, and x, y, z are unity vectors of a Cartesian coordinate. For fcc, a= ² (v+z), b=²(x+x), c= (x+y).]
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Transcribed Image Text:6. Show that the reciprocal lattice of a bcc
lattice with a lattice constant a is a fcc
lattice with the side of the cubic cell to
be 47/a. [Hint: Use a symmetric set of
vectors for bcc,
a =
= 2/2 (v+z-x), b= = ² (z+x−y), c = (x + y − 2)
where a is the lattice constant of a
conventional primitive cell, and x,
y, z are unity vectors of a Cartesian
coordinate. For fcc,
a= 2 (v+x), b=²(x+x), c= = (x+;
+y).
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