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Chapter#5: Thermal Properties: Phonon-II

All short questions of BS Physics book Solid State Physics – I’s Chapter#5: Thermal Properties: Phonon-II for the students.

Q.5.1 Consider the equation of Fick’s law J_n=-DgradN   . Express it in words and state on what factors D depends upon.

Answer: The net flux ‘J’ of one species is related to gradient of concentration ‘N’ of this species by Fick’s law,

    \[J_n=-DgradN\]

 is number of atoms crossing unit area in unit time.

D called diffusion coefficient depends upon:

  • Nature of diffusion species
  • The medium in which it is diffusing and
  • The temperature

Q.5.2 A steel tank contains nitrogen at a constant pressure of 10atm, with a vacuum outside. The concentration at inner surface of tank is equal to 10 . The diffusion coefficient of nitrogen in steel at room temperature is  Find rate at which nitrogen escapes through the wall of tank, which has a thickness of 10mm.

Answer: Using Fick’s law,

    \[J={10}^{-19}\times\frac{10}{10\times{10}^{-3}}={10}^{-16}kgm^{-2}s^{-1}\]

Q.5.3 What are types of imperfections?

Answer: Different types of imperfections are:

  • Point imperfections
  • Line imperfections
  • Planar imperfections

Point imperfections (defects) are further classified as: vacancy, interstitial atom, color centers,

Q.5.4 Write Einstein equation for diffusion constant D by explaining all the terms used. Also define jump frequency.

Answer: According to Einstein relation for diffusion constant, mobility is related to it by relation,

    \[\mu k_BT=qD\]

q is charge on defect or atom whose diffusion may be under study. In diffusion process, the probability per second or number of times the atom actually crosses the barrier in one second is called jump frequency given by relation,

    \[v=v_0e^{-\frac{E_a}{k_BT}}\]

Q.5.5 Differentiate between Schottky and Frenkel defects

Answer: A normal lattice site from where the atom or ion is missing is known as defect. An atom located at a position that is not a normal lattice site is known as defect.

Q.5.6 Define color center, excitons and polarons

Answer: A bound system results from a change compensation mechanism. This bound system, known as color center, has a quantized scheme of energy levels and absorbs visible light in some crystals. These crystals thus show colors which are otherwise colorless.

  • Quantized electron-hole pairs are called
  • A quantized polarization wave consist of

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