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Problem 2. Structure-Property Relations: Tensor and Matrix Operations in Describing Materials Properties For a BaTiO; crystal at room temperature, its x₁ [100], x2 [010], and x3 [001] directions constitute a set of orthogonal right-handed axes. To transform this set of axes system to a new right-handed axes system with direction x₁= [011], x₂= [011], (2.a) find the transformation matrix (a) - the set of direction cosines relating the new axes to the old.

Problem 2. Structure-Property Relations: Tensor and Matrix Operations in Describing Materials Properties For a BaTiO; crystal at room temperature, its x₁ [100], x2 [010], and x3 [001] directions constitute a set of orthogonal right-handed axes. To transform this set of axes system to a new right-handed axes system with direction x₁= [011], x₂= [011], (2.a) find the transformation matrix (a) - the set of direction cosines relating the new axes to the old.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Problem 2. Structure-Property Relations: Tensor and Matrix Operations in Describing Materials Properties For a BaTiO; crystal at room temperature, its x1 [100], x2 [010], and x3 [001] directions constitute a set of orthogonal right-handed axes. To transform this set of axes system to a new right-handed axes system with direction x1'= [011], x2'= [0 ī1]. (2.a) find the transfomation matrix (a) - the set of direction cosines relating the new axes to the old. [30 (2.b) If the dielectric property in the original system is given as le, /ɛ]=|0 30 0 0 0 50 find out the dielectric constant ɛ11' along the direction x1'/[011]. (2.c) Provide a sketch of the directional dependence of its dielectric property (i.e., e' as a function of e and 4) for 0s 0 < 180 degrees. A two-dimensional drawing is fine when proper labels are given.
Transcribed Image Text:Problem 2. Structure-Property Relations: Tensor and Matrix Operations in Describing Materials Properties For a BaTiO; crystal at room temperature, its x1 [100], x2 [010], and x3 [001] directions constitute a set of orthogonal right-handed axes. To transform this set of axes system to a new right-handed axes system with direction x1'= [011], x2'= [0 ī1]. (2.a) find the transfomation matrix (a) - the set of direction cosines relating the new axes to the old. [30 (2.b) If the dielectric property in the original system is given as le, /ɛ]=|0 30 0 0 0 50 find out the dielectric constant ɛ11' along the direction x1'/[011]. (2.c) Provide a sketch of the directional dependence of its dielectric property (i.e., e' as a function of e and 4) for 0s 0 < 180 degrees. A two-dimensional drawing is fine when proper labels are given.
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