Advanced Solid-State Physics Vocabulary

Key vocabulary terms and definitions extracted from the lecture covering diffraction, reciprocal space, electronic bands, phonons, magnetism, and thermal properties.

Bragg’s Law

Condition for constructive X-ray interference in a crystal: nλ = 2d sin θ.

Reciprocal Lattice

A lattice in Fourier (k) space whose vectors are normals to real-space crystal planes and inversely proportional to their spacing.

Interplanar Spacing (d₍ₕₖₗ₎)

Distance between successive parallel crystal planes identified by Miller indices (h k l).

Ewald Sphere

Geometric construction that shows which reciprocal-lattice points satisfy the diffraction condition for a given X-ray wavelength.

Scattering Vector (Δk)

Difference between incident and scattered wave vectors; equals a reciprocal-lattice vector at diffraction.

Fourier Series

Expansion of a periodic function as a sum of sinusoidal terms with discrete reciprocal-lattice frequencies.

Structure Factor (F₍ₕₖₗ₎)

Complex amplitude that combines atomic positions and form factors to determine intensity of a diffracted beam.

Atomic Form Factor (f)

Efficiency of an atom in scattering X-rays, depending on electron distribution and scattering angle.

Reciprocal-Lattice Vector (G)

Vector h a* + k b* + l c* that labels sets of parallel planes and enters diffraction conditions.

Brillouin Zone

Wigner-Seitz primitive cell of the reciprocal lattice; contains all unique k-vectors.

First Brillouin Zone

Central cell in reciprocal space bounded by perpendicular bisectors of the shortest reciprocal vectors.

Density of States (g(E))

Number of allowed quantum states per energy interval per unit volume.

Fermi Energy (E_F)

Highest occupied electron energy at absolute zero in a metal.

Fermi–Dirac Distribution

Probability f(E)=1/[exp((E–E_F)/kT)+1] that a fermion state of energy E is occupied at temperature T.

Effective Mass (m*)

Apparent mass of an electron responding to forces in a crystal, m* = ħ²/(d²E/dk²).

Band Gap (E_g)

Energy difference between conduction-band minimum and valence-band maximum in a semiconductor or insulator.

Conduction Band

Set of electron states above the band gap that contribute to electrical conduction when occupied.

Valence Band

Highest filled electron band at 0 K; electrons must be excited out of it to conduct.

Acoustic Branch

Low-frequency phonon branch where neighboring atoms oscillate in phase; ω∝k at small k.

Optical Branch

Higher-frequency phonon branch in diatomic lattices where neighboring atoms oscillate out of phase.

Umklapp Process

Phonon–phonon scattering in which momentum is conserved up to a reciprocal-lattice vector, leading to thermal resistance.

Normal (N) Process

Phonon scattering event conserving total phonon momentum within the first Brillouin zone.

Magnon

Quantized spin wave; carries ħω energy and ħk crystal momentum.

Bloch Wall

Transition layer separating magnetic domains with different magnetization directions.

Domain

Region inside a ferromagnet where magnetization is uniformly aligned.

Coercivity (H_c)

Reverse magnetic field required to reduce induction or magnetization to zero.

Saturation Magnetization (M_s)

Maximum magnetization when all magnetic moments are aligned with the field.

Curie Temperature (T_C)

Temperature above which a ferromagnet becomes paramagnetic.

Néel Temperature (T_N)

Temperature above which an antiferromagnet becomes paramagnetic.

Ferromagnetism

Magnetic order with parallel alignment of neighboring spins, giving a spontaneous magnetization.

Antiferromagnetism

Magnetic order with antiparallel neighboring spins, leading to zero net magnetization.

Ferrimagnetism

Magnetic order with unequal opposing sublattice moments, yielding non-zero net magnetization.

Paramagnetism

Magnetic behavior where unpaired spins align weakly with an external field; χ ∝ 1/T.

Diamagnetism

Universal, weak negative susceptibility arising from field-induced changes in electronic orbits.

Exchange Interaction (J)

Quantum mechanical coupling between spins; positive J favors ferromagnetic, negative J antiferromagnetic alignment.

Spin Wave

Collective precession of spins in a magnet; classical precursor of magnons.

Brillouin Function (B_J)

Function describing magnetization of a paramagnet: B_J(x) = [(2J+1)/(2J)] coth[(2J+1)x/2J] – (1/2J) coth(x/2J).

Exchange Field (B_e)

Effective internal field acting on a spin due to exchange interaction with neighbors.

Magnetocrystalline Anisotropy

Dependence of magnetic energy on magnetization direction relative to crystal axes.

Crystal Field Splitting

Energy separation of degenerate d or f orbitals due to surrounding ligand charges.

Domain Wall Energy

Total exchange and anisotropy energy per unit area associated with a magnetic boundary.

Wiedemann–Franz Law

Ratio k/σT ≈ L (Lorenz number) linking thermal and electrical conductivity of metals.

Relaxation Time (τ)

Average time between momentum-randomizing collisions for charge carriers or phonons.

Mean Free Path (ℓ)

Average distance a particle travels between scattering events.

Debye Temperature (θ_D)

Characteristic temperature separating low-T T³ and high-T constant specific-heat behavior of a solid.

Einstein Model

Specific-heat model treating each atom as an independent harmonic oscillator of one frequency.

Debye Model

Specific-heat model treating vibrations as a continuum of acoustic modes up to a cut-off (θ_D).

Lattice Specific Heat

Heat capacity contribution from phonons; ∝T³ at low temperatures (Debye).

Spin-Orbit Coupling

Interaction between an electron’s spin and its orbital motion, leading to energy splitting and anisotropy.

Quasicrystal

Aperiodic structure with long-range order and non-crystallographic rotational symmetry (e.g., icosahedral).

Order Parameter

Quantity that is zero in one phase and non-zero in an ordered phase, characterizing phase transitions.

Nematic Phase

Liquid-crystal phase with long-range orientational order but no positional order.

Superparamagnetism

Behavior of single-domain nanoparticles that fluctuate thermally, showing paramagnetic-like response with large moment.

Bloch Theorem

Wave functions in a periodic potential can be written ψk(r)=uk(r)e^{ik·r} with u_k periodic.

Wave Vector (k)

Vector characterizing phase change per unit length of a wave; in crystals confined to Brillouin zones.

Reciprocal Space

Vector space of k describing periodicity; useful for diffraction and band theory.

(hkl) Planes

Set of crystal planes indexed by Miller indices (h k l).

Screw Axis

Symmetry element combining rotation with translation along the rotation axis.

Glide Plane

Symmetry element combining reflection with translation parallel to the plane.

Point Group

Set of symmetry operations leaving at least one point fixed; classifies crystal shapes.

Space Group

Complete set of symmetry operations (rotations, reflections, translations) describing a 3D crystal lattice.

Effective Bohr Magneton (p_eff)

Experimental magnetic moment per ion: peff = g√[J(J+1)] μB.

Umclapp (U) Process

Phonon scattering that transfers crystal momentum to the lattice, limiting thermal conductivity.

Normal (N) Process

Momentum-conserving phonon scattering within the first Brillouin zone.

Curie–Weiss Law

Paramagnetic susceptibility χ = C/(T–Θ), accounting for internal molecular field Θ.

Lande g-Factor

Spectroscopic splitting factor g = 1 + [J(J+1)+S(S+1)–L(L+1)]/[2J(J+1)].

Spinel Structure

AB₂O₄ lattice with cations in tetrahedral (A) and octahedral (B) sites; many ferrites adopt it.

Magnetic Anisotropy Energy

Energy required to rotate magnetization away from an easy axis.

Coherent Scattering

Wave scattering that preserves phase relationships, producing interference patterns (e.g., Bragg peaks).

Helmholtz Free Energy

Thermodynamic potential F = U–TS; minimization governs equilibrium including magnetic ordering.

Phonon Mean Free Path

Average distance a phonon travels before scattering; limits lattice thermal conductivity.

Langevin Function

L(x)=coth x–1/x; describes magnetization of classical paramagnets.

Superfluidity

Frictionless flow of a quantum fluid (e.g., helium-4 below λ point).

Screw Dislocation

Line defect in a crystal where lattice planes form a helical structure around the dislocation line.

Glide Plane Symmetry

Reflection plus translation symmetry operation in crystals.

Debye Frequency

Maximum phonon frequency in the Debye model, associated with θ_D.

Quantum Hall Effect

Quantized transverse conductance in 2D electron gas under strong magnetic field (note: mentioned contextually).

Lorenz Number (L)

Constant ~2.45×10⁻⁸ W Ω K⁻² in Wiedemann–Franz law for metals.