Solution Found!
As noted in Section 3.15, for single crystals of some
Chapter 6, Problem 6.12(choose chapter or problem)
As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic that is, they depend 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 Euvw = 1 E81009 - 3a 1 E81009 - 1 E81119 b (a2 b2 + b2 g2 + g2 a2 ) (6.30) where E81009 and E81119 are the moduli of elasticity in the [100] and [111] directions, respectively; a, b, and g are the cosines of the angles between [uvw] and the respective [100], [010], and [001] directions. Verify that the E81109 values for aluminum, copper, and iron in Table 3.4 are correct.
Questions & Answers
QUESTION:
As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic that is, they depend 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 Euvw = 1 E81009 - 3a 1 E81009 - 1 E81119 b (a2 b2 + b2 g2 + g2 a2 ) (6.30) where E81009 and E81119 are the moduli of elasticity in the [100] and [111] directions, respectively; a, b, and g are the cosines of the angles between [uvw] and the respective [100], [010], and [001] directions. Verify that the E81109 values for aluminum, copper, and iron in Table 3.4 are correct.
ANSWER:Step 1 of 5
First we must set up our equation based upon the known angles of 45,45 , and 90 which translate to:
We can now write the equation in the problem as:
