Phonon Interaction-Solid State Physics-Lecture Slides, Slides of Solid State Physics

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In The Name of ALLAH

Photon-Phonon Interaction

 The interaction of photon to phonon may result in the creation

or absorption of phonon.

 Inelastic scattering phenomenon

 This interaction occurs due to change in local concentration of

atoms and refractive index of the crystal

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 Let this photon interacts with a phonon  As a result, the wave vector and frequency of the photon change to k´ and ν´  A new phonon having wave vector K and angular frequency ω is created in this process  The conservation of energy and momentum gives us

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 ħωph = ħω´ph + ħω for energy  ħk = ħk´ + ħK for momentum  If we take vs is the velocity of phonon and assume it constant  Then, ω = vsk  Comparing ω = vsk with ωph = ck/n or ωph = ck  The wavelength of the emitted phonon is comparable to the wavelength of incident photon

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 Where φ is angle b/w k and k´

 The equation shows that a phonon is produced when a photon

is elastically scattered at an angle

 The frequency of phonon will be ω = vsK or

 or

Specific Heat

 The heat required to raise the temperature of one gram molecule of the substance through 1oC or 1k  C = dQ/dT  The amount of heat required to increase the temperature of a body is different under different conditions  e.g. the specific heat at constant pressure Cp is different from specific heat at constant volume Cv

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 If the system expands against a constant pressure, then the 1st

law can be written as; dQ = dE + pdV

 If the heat is added at constant volume, then the 2nd^ term in

above equation vanishes and specific heat may be written as;

 Cv = (dQ/dT)v = (∂E/∂T)v

 Cp = (dQ/dT)p

Conclusion

 In gases, there is a large difference b/w Cp and Cv  However, in solids, Cp and Cv are almost same due to small change in volume, particularly at very low temperature  So, the term ‘specific heat of solid’ is commonly used in case of solids.  Thus, in case of solid, mostly heat supplied is used to up in increasing the internal energy

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 First contribution due to atomic vibration and often called ‘lattice specific heat’  Second contribution due to electronic contribution and is relatively small contribution

 In general, the specific heat of solid may be expressed as;

 Csolid = Clat + Celec

Assignment No. 4

 Q. No. 1

 Describe the Classical Theory of lattice heat capacity

 Q. No. 2

 Describe the Einstein model of lattice heat capacity

 The last date to submit Assignment No. 4 is;

 April 27, 2012 on Friday