1. Which of these properties of a crystal may be anisotropic?

   Yes	No	a	Density
   Yes	No	b	Young's modulus
   Yes	No	c	Surface energy
   Yes	No	d	Refractive index
   Yes	No	e	Electrical conductivity
   Yes	No	f	Thermal conductivity
   Yes	No	g	Heat capacity
   Yes	No	h	Melting point
   Yes	No	i	Coefficient of thermal expansion

2. Two similar transparent uniaxial crystals show the same (principal) extraordinary refractive index, n_e. However one is optically positive, and the other is optically negative. In which will the light travel faster along the optic axis?

3. Which of these could not induce anisotropy in an initially isotropic material?

   	a	Application of a stress
   	b	Application of an electric field
   	c	Application of a magnetic field
   	d	Application of a high temperature

4. Below 0°C a particular material has a crystal structure that gives rise to anisotropic thermal conductivity. At room temperature the thermal conductivity of a sample of this material is found to be isotropic. In what circumstances would the following hypotheses explain this observation?

   	a	The sample is polycrystalline
   	b	The sample has undergone a phase transition when brought up to room temperature
   	c	The principal values of thermal conductivity have changed with temperature

5. Which of these materials will show isotropy in its mechanical properties?

   	a	Wood
   	b	Carbon fibre reinforced polymer
   	c	Window glass
   	d	Extruded polyethylene

6. An olivine crystal has the following diffusion constants for Ni at a certain temperature:

   D_x = 6 x 10^-18 m²s^-1,
   D_y = 4 x 10^-18 m²s^-1
   D_z = 120 x 10^-18 m²s^-1.

   The unit cell dimensions are as follows:

   a = 0.5 nm
   b = 1.0 nm
   c = 0.6 nm

   By considering the representation surface, what will the diffusion constant be when the concentration gradient lies along the [101] direction?

7. A certain orthorhombic crystal has the following principal values of thermal conductivity:

   k_x = 6.25 Wm^-1K^-1
   k_y = 1.00 Wm^-1K^-1
   k_z = 1.75 Wm^-1K^-1

   (where the subscripts represent conductivity parallel to the x, y, and z axes respectively).

   The unit cell dimensions are: a = 0.8 nm, b = 0.6 nm, c = 0.10 nm.

   Calculate the thermal conductivity along the [111] direction.

8. Explain how anisotropy is involved in the operation of the following devices:

   1. a liquid crystal display
   2. a fuel cell that uses a sold state electrolyte
   3. a pyroelectric intruder alarm

9. Suggest ways of distinguishing between the answers to Question 4.

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