Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors (see figure) a* = 2pi b x c / a . (b x c), b* = 2pi c x a/ a . (b x c), c* = 2pi a x b/ a . (b x c) are such that a. a* = 2pi, a.b* = 0 Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors2πb x c2πα x ba. (bx c)'.(bx c)are such thata₂ =b₂=2пс хаa. . (bx c)'a.a₂ = 2π,C₂a. b. = 0.

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Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors 2πα x b 2πb x c a. (bxc)' a. (bx c) are such that a₂ = b₂ 2πε χα a. (bx c)' a. a₁ = = 2π, C₂ a. b. = 0.

Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors 2πα x b 2πb x c a. (bxc)' a. (bx c) are such that a₂ = b₂ 2πε χα a. (bx c)' a. a₁ = = 2π, C₂ a. b. = 0.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter12: The Solid State

Section: Chapter Questions

Problem 20P

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Question

Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors (see figure) a_* = 2pi b x c / a . (b x c), b* = 2pi c x a/ a . (b x c), c_* = 2pi a x b/ a . (b x c) are such that a. a_*= 2pi, a.b_*= 0

Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors
2πb x c
2πα x b
a. (bx c)'
.(bx c)
are such that
a₂ =
b₂
=
2пс ха
a. . (bx c)'
a.a₂ = 2π,
C₂
a. b. = 0.

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