nothing to say dont waste time, Assignments of Thermodynamics of Materials

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Unit- 1 : Assignment/ Practice Set-5 [on Symmetry] Question 1: Define the symmetry elements present in a hexagonal crystal. Answer:

In the hexagonal groups, the first place is reserved for the defining six-fold symmetry element lying along the unique c-axis, sometimes with a perpendicular mirror, and the second position for symmetry elements lying along the a-axis, the [100] (or equivalent) direction. The third position is allocated to symmetry elements referred to a [120] (or equivalent) direction. This direction is at an angle of 30 degree to the a-axis, (see figure a ). For example, the point group 6mm has a rotation hexad along the c-axis, a mirror with the mirror plane normal in a direction parallel to the a-axis, and a mirror with a normal parallel to the direction [120]. Operation of the hexad generates a set of mirrors, each at an angle of 30degree to its neighbours, (see figure b ). The point group 6/m 2/m 2/m has a hexad along the c-axis, a mirror plane normal parallel to the c-axis, (i.e. a mirror plane normal to the hexad), diads along [100] and [120], and mirror plane normals parallel to these directions, (see Figure c ) See Figures: Symmetry elements present in a hexagonal crystal: (a) directions in a hexagonal lattice; (b) the point group 6mm has a rotation hexad along the c-axis which generates a set of mirrors, each at an angle of 30 degree to its neighbours; (c) the point group 6/m 2/m 2/m has a hexad along the c-axis, a mirror plane normal parallel to the c-axis, diads along [100] and [120], and mirror plane normals parallel to these directions Question 2: Define the symmetry elements present in a tetrahedron and octahedron crystals. Answer : Please refer to class notes and lecture notes, we have already discussed this in class. Question 3: Define the symmetry elements present in the following