(a) What is the angle, in degrees, between the [110] direction and the following directions? (100] [010] [001] [100] i [010] i [001] i (b) What are the cosines of these angles? [110]-[100] cosine i [110]-[010] cosine i [110]-[001] cosine i

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(a) What is the angle, in degrees, between the [110] direction and the following directions?
[100]
[010]
[001]
[100]
i
[010]
i
[001]
i
(b) What are the cosines of these angles?
[110]-[100] cosine
i
[110]-[010] cosine
i
[110]-[001] cosine
Transcribed Image Text:(a) What is the angle, in degrees, between the [110] direction and the following directions? [100] [010] [001] [100] i [010] i [001] i (b) What are the cosines of these angles? [110]-[100] cosine i [110]-[010] cosine i [110]-[001] cosine
As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic; that is, they are dependent
on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a
general [uvw] direction, Euvw, is described by the relationship
1
1
1
1
- 3
E100)
E10) E11)
)م م و ( )
Euww
where E(100) and E(111) are the moduli of elasticity in [100] and [111] directions, respectively; a, ß, and y are the cosines of the
angles between [uvw] and the respective [100], [010], and [001] directions. Verify that the E(110) values for aluminum, copper, and
iron in Table 3.4 are correct.
Transcribed Image Text:As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic; that is, they are dependent on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general [uvw] direction, Euvw, is described by the relationship 1 1 1 1 - 3 E100) E10) E11) )م م و ( ) Euww where E(100) and E(111) are the moduli of elasticity in [100] and [111] directions, respectively; a, ß, and y are the cosines of the angles between [uvw] and the respective [100], [010], and [001] directions. Verify that the E(110) values for aluminum, copper, and iron in Table 3.4 are correct.
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