Use the rhombohedral/trigonal metric tensor to show that the relations between the hexagonal (a, c) and rhombohedral (ar, a) lattice parameters are given by the following expressions: a= a√2-2 cos α; c= a√3+6 cos a. a₂ O-GO -1 -2 2a² -a² 0 *-*-*[*][B]-44 a² = \a{ ² = [2 1 1] a² 2a² 0 0 0 a₁-a₂ = a cos a a → -Ar= 3+ a (9) 3 V 18 2a²-a² ***** a a= [2 1 1] -a² 2a² 0 0 0 cos a = 1- 2c² 9 2(c/a)² +6 0 2c² Homework: a = a,√2-2 cos α; c = a√3+6 cos α.

Use the rhombohedral/trigonal metric tensor to show that the relations between the hexagonal (a, c) and rhombohedral (ar, a) lattice parameters are given by the following expressions: a= a√2-2 cos α; c= a√3+6 cos a. a₂ O-GO -1 -2 2a² -a² 0 --[][B]-44 a² = \a{ ² = [2 1 1] a² 2a² 0 0 0 a₁-a₂ = a cos a a → -Ar= 3+ a (9) 3 V 18 2a²-a² ***** a a= [2 1 1] -a² 2a² 0 0 0 cos a = 1- 2c² 9 2(c/a)² +6 0 2c² Homework: a = a,√2-2 cos α; c = a√3+6 cos α.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.3: Solving Trigonometric Equations

Problem 11ECP

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