Electro-optic ceramics

5.10.5 Electro-optic ceramics

Certain special ceramics combine electrical and optical properties in a unique manner. Lead lan- thanum zirconium titanate, known as PLZT, is a highly transparent ceramic which becomes optically birefringent when electrically charged. This phenomenon is utilized as a switching mechanism in arc-welding goggles, giving protection against flash blindness. The PLZT plate is located between two ‘crossed’ sheets of polarizing material. A small impressed d.c. voltage on the PLZT plate causes it to split the incident light into two rays vibrating in different planes. One of these rays can pass through the inner polar sheet and enter the eye. A sudden flash of light will activate photodiodes in the goggles, reduce the impressed voltage and cause rapid darkening of the goggles.

Problems

5.1 Assuming that the vacancy concentration of a close packed metal is 10 −4 at its melting point and that D 0 = 10 −4 m 2 s −1 , where D =D 0 exp ( −E D /kT ) and D is the self-diffusion coefficient, answer questions (i)–(vi), which relate to diffusion by a vacancy mechanism in a close-packed metal:

(i) What are the vacancy concentrations at 1 4 , 1 2 and 3 4 T m (in K)? (ii) Estimate the diffusion coefficient of the vacancies at 1 4 , 1 2 and 3 4 T m . (iii) Estimate the self-diffusion coefficient for the metal at 1 4 , 1 2 3 and 4 T m . (iv) How far does a vacancy diffuse at T m / 2 in 1 hour? (v) How far does an atom diffuse at T m / 2 in 1 hour?

(vi) If copper melts at 1065 ◦

C, estimate E f . (Boltzmann’s constant k = 8.6 × 10 −5 eV K −1 . )

5.2 The diffusivity of lithium in silicon is 10 −9 m 2 s −1 at 1376 K and 10 −10 m 2 s −1 at 968 K. What are the values of E D and D 0 for diffusion of lithium in silicon? (E D is the activation energy for diffusion in J mol −1 and R = 8.314 J mol −1 K −1 .)

5.3 The melting endotherm of a sample of an impure material has been analyzed to determine the fraction, f , of sample melted at each temperature T s :

f 0.099 0.122 0.164 0.244 0.435 T s (K) 426.0 426.5 427.0 427.5 428.0

288 Physical Metallurgy and Advanced Materials The fraction, f , of the sample melted at temperature T s is given by

T s =T 0

= (T 0 −T m ), T 0 is the melting point of the pure and T m the impure sample. The van’t Hoff equation,

RT 2

−1 mol −1 ),

H f is the enthalpy of fusion and x 2 the mole fraction of impurity.

If the enthalpy of fusion of the pure material is 25.5 kJ mol −1 , use the above data to determine graphically the lowering of the melting point and hence determine the mole fraction of impurity present in the sample.

5.4 The resistivity of intrinsic germanium is 0.028 m at 385 K and 2.74 × 10 −4 m at 714 K. Assume that the hole and electron mobilities both vary as T −3/2 .

(a) Determine the band-gap energy E g . (b) At what wavelength would you expect the onset of optical absorption?

5.5 The magnetic susceptibility (χ) of iron is temperature dependent according to χ ∝ 1/(T − T c ),

C, χ has a value of 2.5 × 10 −4 .T c for iron is 770 ◦ C. Determine the susceptibility at 800 ◦ C.

where T c is the Curie temperature. At 900 ◦

5.6 The current flowing around a superconducting loop of wire decays according to i(t) R t = i(0)e −

where R = resistance and L = self-inductance. What is the largest resistance a 1 m diameter loop of superconducting wire, 1 mm 2 cross-sectional area, can sustain if it is to maintain a current flow of 1 A for one year without appreciable loss (<1%)? (Given: a loop with diameter 2a and " wire thickness 2r has a self-inductance L

8a 7 #

=μ o a ln r − 4 , where μ 0 = 4π × 10 −7 .)

Further reading

Anderson, J. C., Leaver, K. D., Rawlins, R. D. and Alexander, J. M. (1990). Materials Science. Chapman & Hall, London. Braithwaite, N. and Weaver, G. (eds) (1990). Open University Materials in Action Series. Butterworths, London. Cullity, B. D. (1972). Introduction to Magnetic Materials. Addison-Wesley, Wokingham. Hume-Rothery, W. and Coles, B. R. (1946, 1969). Atomic Theory for Students of Metallurgy. Institute of

Metals, London. Porter, D. A. and Easterling, K. E. (1992). Phase Transformations in Metals and Alloys, 2nd edn. Van Nostrand Reinhold, Wokingham. Raynor, G. V. (1947, 1988). Introduction to Electron Theory of Metals. Institute of Metals, London. Shewmon, P. G. (1989). Diffusion in Solids. Minerals, Metals and Materials Soc., Warrendale, USA. Swalin, R. A. (1972). Thermodynamics of Solids. Wiley, Chichester.

Warn, J. R. W. (1969). Concise Chemical Thermodynamics. Van Nostrand, New York.

Chapter 6

Mechanical properties I