Notation

Symbol Meaning
\(\mathbf R_n\), \(\mathbf R_i\), \(\mathbf R\) Direct-lattice or nuclear/ionic position vector
\(\mathbf r_j\), \(\mathbf r_\mu\), \(\mathbf r_{n\mu}\) Electron or basis-atom position
\(\mathbf a_i\) Primitive direct-lattice vector
\(\mathbf b_i\) Primitive reciprocal-lattice vector
\(V_{\mathrm c}\), \(V_{\mathrm{WS}}\) Primitive-cell volume
\(V\) Sample/crystal volume
\(A\) Area or scattering amplitude, depending on context
\(L\) Sample length
\(d_{hkl}\) Interplanar spacing
\(d\) Characteristic sample diameter or boundary length
\(\mathbf G\) Reciprocal-lattice vector
\(\mathbf k\), \(\mathbf k'\) Incident/scattered wave vector
\(\Delta\mathbf k\) Scattering vector \(\mathbf k'-\mathbf k\)
\(\mathbf q\) Phonon wave vector
\(q\) Magnitude/scalar component of \(\mathbf q\)
\(q_D\) Debye wave vector
\(\Omega_{\mathrm{BZ}}\) First-Brillouin-zone volume
\(h,k,l\) Miller/reciprocal-lattice indices
\((hkl)\) Family of lattice planes
\(n_{\mathrm B}\) Bragg diffraction order
\(r'\) Number of atoms in the primitive cell/basis
\(N\) Number of primitive cells, illuminated cells, or electrons
\(N_i\) Number of cells/modes along direction or propagating modes
\(M_k\), \(M_\alpha\), \(M\) Nuclear/atomic mass
\(m_{\mathrm e}\) Electron mass
\(m_{\mathrm s}\) Sample mass
\(\mu\) Reduced mass, absorption coefficient, or chemical potential
\(Z_k\) Nuclear charge number
\(-e\) Electron charge
\(H\), \(H_a\) Hamiltonian / adiabatic Hamiltonian
\(\Psi\), \(\psi_s\), \(\chi_s\) Full, electronic, and nuclear wavefunctions/amplitudes
\(U\) Internal energy or lattice potential energy
\(U_{\mathrm{eq}}\) Static equilibrium lattice energy
\(U_{\mathrm{harm}}\), \(U_{\mathrm{anh}}\) Harmonic/anharmonic potential-energy contributions
\(U_0\) Zero-point vibrational energy
\(U_{\mathrm{th}}\) Thermal vibrational internal energy
\(E\), \(E_F\) Single-electron energy; Fermi energy
\(E_{\mathrm{coh}}\) Cohesive energy
\(E_{12}\) Two-level-system energy splitting
\(F\) Force or Helmholtz free energy, context-dependent
\(S(\mathbf K)\), \(S_{\mathbf G}\) Structure factor
\(S\) Thermopower / Seebeck coefficient
\(T\) Absolute temperature
\(\Theta_D\), \(\Theta_E\) Debye and Einstein temperatures
\(T_F\) Fermi temperature
\(T^\ast\) Crossover temperature
\(\beta\) Inverse thermal energy
\(k_B\) Boltzmann constant
\(\hbar\), \(h\) Reduced Planck constant; Planck constant
\(N_A\) Avogadro constant
\(R\) Gas constant
\(\nu\) Amount of substance
\(C\) Heat capacity of a sample
\(C_V\) Heat capacity at constant volume
\(C_p\) Heat capacity at constant pressure
\(c_m\) Molar heat capacity
\(c_{\mathrm{mass}}\) Heat capacity per mass
\(c_{\mathrm{vol}}\), \(c_V\) Heat capacity per volume
\(c_{V,r}(q)\) Modal contribution to \(c_V\)
\(p\) Pressure
\(B\) Bulk modulus
\(\alpha_L\), \(\alpha_V\) Linear and volume thermal expansion coefficients
\(\kappa\) Thermal conductivity
\(\boldsymbol\kappa\) Thermal-conductivity tensor
\(\rho\) Density field or electrical resistivity
\(\sigma\) Electrical conductivity or scattering cross section
\(\omega\) Angular frequency
\(\omega_0\), \(\omega_E\), \(\omega_D\) Local, Einstein, and Debye angular frequencies
\(\omega_{\mathbf q r}\) Angular frequency of phonon mode \((\mathbf q,r)\)
\(\omega_r(\mathbf q)\) Functional form of phonon branch \(r\)
\(D(\omega)\) Phonon density of states in frequency space
\(D(E)\) Electronic density of states
\(D_{\alpha i}^{\beta j}(\mathbf q)\), \(D(\mathbf q)\) Dynamical matrix
\(\Phi_p\), \(\Phi_1\) Plane-plane force constants
\(K_{\mathrm{bond}}\) Local bond stiffness
\(f\), \(f_j\) Force constant in two-atom chain; atomic form factor
\(\mathbf u\), \(u_n\), \(u_{n\alpha i}\) Atomic displacement field/components
\(A_{\alpha i}(\mathbf q)\) Polarization amplitude
\(r\) Phonon branch/polarization index
\(n\), \(\langle n\rangle\), \(\langle n_{\mathbf q r}\rangle\) Quantum number / phonon occupation
\(f(E)\) Fermi-Dirac occupation probability
\(v_g\), \(v_s\), \(v_i\), \(v_L\), \(v_T\), \(v_F\) Group, sound, branch, longitudinal, transverse, and Fermi velocities
\(\tau\) Relaxation time / phonon lifetime
\(\ell\) Mean free path
\(\lambda\), \(\lambda_{\mathrm{th}}\) Radiation wavelength; thermal phonon wavelength
\(\mathbf J_h\), \(J_{h,x}\) Heat-current density and component
\(\mathbf J_{\mathrm e}\) Electrical current density
\(\mathbf E\) Electric field
\(\varphi_{\mathrm{el}}\) Electric potential
\(\gamma_{\mathbf q r}\), \(\gamma\) Mode and averaged Grüneisen parameter
\(\gamma\) Sommerfeld coefficient
\(L_0\) Lorenz number
\(\mathrm{RRR}\) Residual resistance ratio