CSIR NET Physical Sciences Condensed Matter Physics Syllabus

Condensed Matter Physics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Condensed Matter Physics in CSIR NET Physical Sciences, not a summary of it.

1. 1

   Crystal Structure

   2 topics

   • Bravais Lattices
   • Reciprocal Lattice
2. 2

   Diffraction and Structure Factor

   2 topics

   • Diffraction Patterns
   • Structure Factor
3. 3

   Bonding of Solids

   2 topics

   • Types of Bonds in Solids
   • Bonding Forces
4. 4

   Elastic Properties and Phonons

   2 topics

   • Elastic Modulus
   • Phonons and Lattice Vibrations
5. 5

   Electronic Properties of Solids

   3 topics

   • Free Electron Theory
   • Electronic Specific Heat
   • Band Theory of Solids
     • Metals
     • Insulators
     • Semiconductors
6. 6

   Superconductivity

   3 topics

   • Type-I Superconductors
   • Type-II Superconductors
   • Josephson Junctions
7. 7

   Response and Relaxation Phenomena

   5 topics

   • Drude Model of Electrical Conductivity
   • Drude Model of Thermal Conductivity
   • Hall Effect
   • Thermoelectric Power
   • Electron Motion in Periodic Potential
8. 8

   Defects and Dislocations

   2 topics

   • Crystal Defects
   • Dislocations
9. 9

   Ordered Phases of Matter

   4 topics

   • Translational Order
   • Orientational Order
   • Liquid Crystalline Order
   • Quasicrystals

Condensed Matter Physics flashcards for CSIR NET Physical Sciences

22 of 61 cards from the Condensed Matter Physics deck — real questions with worked answers.

1. What is a Bravais lattice?

   An infinite array of discrete points generated by primitive translation vectors $\vec{R} = n_{1}\vec{a}_{1} + n_{2}\vec{a}_{2} + n_{3}\vec{a}_{3}$ (with integers $n_{i}$), such that the arrangement and orientation appear exactly the same from every lattice point.

2. How many distinct Bravais lattices exist in three dimensions, and how many in two dimensions?

   There are $14$ Bravais lattices in 3D (grouped into 7 crystal systems) and $5$ Bravais lattices in 2D.

3. List the three cubic Bravais lattices and their conventional packing fractions.

   Simple cubic (SC), $\approx 0.52$; body-centered cubic (BCC), $\approx 0.68$; face-centered cubic (FCC), $\approx 0.74$.

4. How many atoms per conventional unit cell are there in SC, BCC, and FCC lattices?

   SC has $1$ atom, BCC has $2$ atoms, and FCC has $4$ atoms per conventional unit cell.

5. What are the coordination numbers of SC, BCC, FCC, and HCP structures?

   SC: $6$; BCC: $8$; FCC: $12$; HCP: $12$.

6. Define the reciprocal lattice in terms of the direct lattice vectors.

   The reciprocal lattice is the set of vectors $\vec{G}$ satisfying $e^{i\vec{G}\cdot\vec{R}} = 1$ for all direct lattice vectors $\vec{R}$. Equivalently $\vec{G} = h\vec{b}_{1} + k\vec{b}_{2} + l\vec{b}_{3}$ with integers $h,k,l$.

7. Write the formula for the primitive reciprocal lattice vector $\vec{b}_{1}$.

   $$\vec{b}_{1} = 2\pi\frac{\vec{a}_{2}\times\vec{a}_{3}}{\vec{a}_{1}\cdot(\vec{a}_{2}\times\vec{a}_{3})}$$ with cyclic permutations for $\vec{b}_{2}$ and $\vec{b}_{3}$.

8. What is the reciprocal lattice of an FCC lattice, and of a BCC lattice?

   The reciprocal lattice of FCC is BCC, and the reciprocal lattice of BCC is FCC.

9. What is the relationship between the reciprocal lattice vector $\vec{G}_{hkl}$ and the lattice planes $(hkl)$?

   $\vec{G}_{hkl}$ is perpendicular to the $(hkl)$ planes, and the interplanar spacing is $d_{hkl} = \dfrac{2\pi}{|\vec{G}_{hkl}|}$.

10. Give the interplanar spacing formula $d_{hkl}$ for a cubic lattice of side $a$.

    $$d_{hkl} = \frac{a}{\sqrt{h^{2}+k^{2}+l^{2}}}$$

11. State Bragg's law of diffraction.

    $$2d\sin\theta = n\lambda$$ where $d$ is the interplanar spacing, $\theta$ the glancing angle, $\lambda$ the wavelength, and $n$ the integer order of diffraction.

12. State the Laue (von Laue) condition for diffraction.

    Constructive interference occurs when the scattering wavevector change equals a reciprocal lattice vector: $\Delta\vec{k} = \vec{k}' - \vec{k} = \vec{G}$, equivalently $2\vec{k}\cdot\vec{G} = G^{2}$.

13. What is the Ewald sphere construction used for?

    It is a geometric construction (a sphere of radius $|\vec{k}| = 2\pi/\lambda$ in reciprocal space) that determines which reciprocal lattice points satisfy the Laue diffraction condition: diffraction occurs wherever the sphere's surface intersects a reciprocal lattice point.

14. Define the geometric structure factor $S_{hkl}$ of a crystal.

    $$S_{hkl} = \sum_{j} f_{j}\, e^{2\pi i (h x_{j} + k y_{j} + l z_{j})}$$ where $f_{j}$ is the atomic form factor and $(x_{j},y_{j},z_{j})$ are the fractional coordinates of atom $j$ in the basis.

15. What are the selection rules (allowed reflections) for a BCC lattice?

    Reflections are present only when $h+k+l$ is even; reflections with $h+k+l$ odd have zero structure factor and are forbidden.

16. What are the selection rules for an FCC lattice?

    Reflections appear only when $h,k,l$ are all even or all odd (unmixed parity); mixed parity reflections vanish.

17. How does the atomic form factor $f$ depend on scattering angle, and what is $f$ in the forward direction?

    $f$ decreases with increasing scattering angle (increasing $\sin\theta/\lambda$) because of destructive interference within the electron cloud. In the forward direction ($\theta = 0$), $f = Z$, the number of electrons in the atom.

18. Name the four main types of bonding in solids.

    Ionic, covalent, metallic, and van der Waals (molecular) bonding. Hydrogen bonding is often listed as a fifth, weaker type.

19. Which type of bond holds together an inert-gas crystal, and what is its origin?

    Van der Waals (London dispersion) bonding, arising from fluctuating induced dipole–induced dipole interactions; the attractive potential varies as $-1/r^{6}$.

20. Write the Lennard-Jones potential and identify its terms.

    $$U(r) = 4\epsilon\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]$$ The $r^{-12}$ term is short-range Pauli repulsion; the $r^{-6}$ term is the attractive van der Waals interaction.

21. What is the Madelung constant?

    A dimensionless geometric factor $\alpha$ that gives the net electrostatic (Coulomb) energy of an ion in an ionic crystal: $U_{Coulomb} = -\dfrac{\alpha q^{2}}{4\pi\epsilon_{0} r}$. For NaCl, $\alpha \approx 1.748$.

22. What characterizes covalent bonding and gives examples?

    Covalent bonding involves shared electron pairs forming strong, highly directional bonds with saturation. Examples: diamond (C), silicon, and germanium, which adopt the tetrahedral diamond structure.

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