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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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 a;
c = a√3+6 cos a.
0-G400
a² = |a₁|²
aa = a co a
2
=
1 1]
→ar =
cos α = 1
a
3 V
18
2a²-a²
1² 2a²
0
0
3+
2a² -a²
***
a a [21 -a² 2a² 0
0 0 2c²
20-$+$
=
9
2(c/a)² +6
2c²
0
Homework:
9
a = a√2-2 cosa;
c = a√3+6 cos a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ae13a06-229f-45d1-95f4-ee2e7a608e61%2Fba4822fc-33c4-4a19-bef2-847582a06730%2Fr9j34q4_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 a;
c = a√3+6 cos a.
0-G400
a² = |a₁|²
aa = a co a
2
=
1 1]
→ar =
cos α = 1
a
3 V
18
2a²-a²
1² 2a²
0
0
3+
2a² -a²
***
a a [21 -a² 2a² 0
0 0 2c²
20-$+$
=
9
2(c/a)² +6
2c²
0
Homework:
9
a = a√2-2 cosa;
c = a√3+6 cos a.
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