Suppose that a particular crystal has a primitive unit cell that can be described by the following primitive lattice vectors: NOTE: i, j and k are unit vectors. a1 = √2ai + √2aj a2 = (−3a√2)i +( 3a√2)j a3 = −√2ai − √2aj + 2√3ak (a) Determine the crystal system of the crystal. (b) Using the reciprocal lattice, determine an expression for the interplanar spacings of the crystal. (c) Suppose that the constant ? has a value of 0.546 nm and that the interplanar spacing for planes with certain unknown Miller indices was measured to be 0.539 nm. Determine an equation satisfied by the Miller indices of the planes and hence suggest which planes they are.

Suppose that a particular crystal has a primitive unit cell that can be described by the following primitive lattice vectors: NOTE: i, j and k are unit vectors. a1 = √2ai + √2aj a2 = (−3a√2)i +( 3a√2)j a3 = −√2ai − √2aj + 2√3ak (a) Determine the crystal system of the crystal. (b) Using the reciprocal lattice, determine an expression for the interplanar spacings of the crystal. (c) Suppose that the constant ? has a value of 0.546 nm and that the interplanar spacing for planes with certain unknown Miller indices was measured to be 0.539 nm. Determine an equation satisfied by the Miller indices of the planes and hence suggest which planes they are.

Welding: Principles and Applications (MindTap Course List)

8th Edition

ISBN:9781305494695

Author:Larry Jeffus

Publisher:Larry Jeffus

Chapter26: Welding Metallurgy

Section: Chapter Questions

Problem 7R

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Suppose that a particular crystal has a primitive unit cell that can be described by the following primitive lattice vectors: NOTE: i, j and k are unit vectors. a1 = √2ai + √2aja2 = (−3a/√2)i +( 3a/√2)ja3 = −√2ai − √2aj + 2√3ak (a) Determine the crystal system of the crystal. (b) Using the reciprocal lattice, determine an expression for the interplanar spacings of the crystal. (c) Suppose that the constant ? has a value of 0.546 nm and that the interplanar spacing for planes with certain unknown Miller indices was measured to be 0.539 nm. Determine an equation satisfied by the Miller indices of the planes and hence suggest which planes they are.
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