For a BaTiO3 crystal at room temperature, its x1 [100], x2 [010], and x3 [001] directions...

     

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For a BaTiO3 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 x = [011], x2= [0] 1], (2.a) find the transformation matrix (a) - the set of direction cosines relating the new axes to the old. [30 0 0 (2.b) If the dielectric property in the original system is given as [5/8]= 0 30 0 find out the dielectric constant 11' along the direction x'//[011]. 0 0 50 30 0 0 (2.b) If the dielectric property in the original system is given as [/s]-0 300 find out the dielectric constant 11' along the direction x1'//[011]. 0 0 50 (2.c) Provide a sketch of the directional dependence of its dielectric property (i.e., &' as a function of 0 and 6) for 0 0 180 degrees. A two-dimensional drawing is fine when proper labels are given. For a BaTiO3 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 x = [011], x2= [0] 1], (2.a) find the transformation matrix (a) - the set of direction cosines relating the new axes to the old. [30 0 0 (2.b) If the dielectric property in the original system is given as [5/8]= 0 30 0 find out the dielectric constant 11' along the direction x'//[011]. 0 0 50 30 0 0 (2.b) If the dielectric property in the original system is given as [/s]-0 300 find out the dielectric constant 11' along the direction x1'//[011]. 0 0 50 (2.c) Provide a sketch of the directional dependence of its dielectric property (i.e., &' as a function of 0 and 6) for 0 0 180 degrees. A two-dimensional drawing is fine when proper labels are given.