331HW2Solution

331HW2Solution - Homework 2 Solution Winter 2011...

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Unformatted text preview: Homework 2 Solution Winter 2011 Prof.Ringel 3.41 Determine the Miller indices for the planes shown in the following unit cell: Solution For plane A we will leave the origin at the unit cell as shown; this is a (403) plane, as summarized below. x y z Intercepts a 2 ∞ b 2c 3 Intercepts in terms of a , b , and c 1 2 ∞ 2 3 Reciprocals of intercepts 2 0 3 2 Reduction 4 0 3 Enclosure (403) For plane B we will move the origin of the unit cell one unit cell distance to the right along the y axis, and one unit cell distance parallel to the x axis; thus, this is a ( 1 1 2) plane, as summarized below. x y z Intercepts – a – b c 2 Intercepts in terms of a , b , and c – 1 – 1 1 2 Reciprocals of intercepts – 1 – 1 2 Reduction (not necessary) Enclosure ( 1 1 2) Homework 2 Solution Winter 2011 Prof.Ringel 3.43 Determine the Miller indices for the planes shown in the following unit cell: Solution For plane A since the plane passes through the origin of the coordinate system as shown, we will move the origin of the coordinate system one unit cell distance to the right along the y axis; thus, this is a (3 2 4) plane, as summarized below. x y z Intercepts 2 a 3 – b c 2 Intercepts in terms of a , b , and c 2 3 – 1 1 2 Reciprocals of intercepts 3 2 – 1 2 Reduction 3 – 2 4 Enclosure (3 2 4) For plane B we will leave the origin at the unit cell as shown; this is a (221) plane, as summarized below. x y z Intercepts a 2 b 2 c Intercepts in terms of a , b , and c 1 2 1 2 1 Reciprocals of intercepts 2 2 1 Reduction not necessary Enclosure (221) Homework 2 Solution Winter 2011 Prof.Ringel 3.43 Determine the Miller indices for the planes shown in the following unit cell: Solution For plane A since the plane passes through the origin of the coordinate system as shown, we will move the origin of the coordinate system one unit cell distance to the right along the y axis; thus, this is a (3 2 4) plane, as summarized below. x y z Intercepts 2 a 3 – b c 2 Intercepts in terms of a , b , and c 2 3 – 1 1 2 Reciprocals of intercepts 3 2 – 1 2 Reduction 3 – 2 4 Enclosure (3 2 4) For plane B we will leave the origin at the unit cell as shown; this is a (221) plane, as summarized below....
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This note was uploaded on 04/30/2011 for the course ECE 331 taught by Professor Rajan during the Spring '09 term at Ohio State.

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331HW2Solution - Homework 2 Solution Winter 2011...

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