List of frequently used symbols and abbreviations; conversion factors 1. Symbols
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I List of frequently used symbols and abbreviations; conversion factors 1. Symbols Symbol Unit a activity oxygen activity Å, nm lattice parameters absorbance electron-hole mobility ratio T, G magnetic induction internal magnetic induction Nernst coefficient cm2 K−1s−1 Pa, bar, N m−2 bulk modulus (adiabatic, isothermal) Pa, dyn cm−2 elastic moduli (stiffnesses) J mol−1 K−1, cal mol−1 K−1, heat capacity heat capacity at constant pressure magnetic heat capacity specific heat capacity J g−1 K−1 emu K mol−1 = Curie constant per mole cm3 K mol−1 g cm−3 density X-ray density thickness, (interatomic) distance, bond length µm, Å, nm optical density (log I0/I) diffusion coefficient cm2 s−1 diffusion coefficient for electrons (holes) eV crystal field splitting parameter polarization vector C elementary charge e (transverse) effective ionic charge Pa, bar Young's modulus Young´s modulus measured in[hkl] direction electric field strength V cm−1, V m−1 eV, Ry, J energy ionization energies of acceptors (donors), energy of acceptor (donor) state activation energy (mostly of conductivity) binding energy binding energy of bound multiexcitons carbon donor level band edge of conduction (valence) band critical point energy Fermi energy energy gap, band gap energy gap extrapolated to 0 K (thermal energy gap) direct (indirect) energy gap kinetic (photoelectron) energy aO2 a, b, c A b B Bi B B0, (BS, BT) clm C Cp Cm c Cm d dX d dopt D Dn(p) Dq e e e*(T) E E[hkl] E E Ea(d) EA Eb Ebmc EC EC(V) Ecrit EF Eg Eg,th Eg,dir (ind) Ekin Property II Symbol Unit Ep Epl(pc), Epeak Er Etot Et Ethr E0,1,2,.., E(Γ6).. ∆E f f f g Hz kg g|| g⊥ gc, gn g v , gp g(E) gc(v) gV G G[hkl] G ∆G0f ∆Gtr h h hν H HB,V,K H HA Hcr Hext H(p-p) HT ∆Hf (0) ∆Htr i I Iph I Ilum IR J J k various units J Pa, bar J mol−1, cal mol−1 J mol−1 J mol−1 Å eV Pa, N m−2, kg mm−2 Oe, A m−1 Oe, A m−1 J mol−1 J mol−1, cal mol−1, J g-atom−1 J mol−1 A cm−2 A various units eV Property primary electron energy (in ELS) photoluminescence (photoconductivity) peak energy relative energy total energy trapping energy of charge carrier photoelectric threshold energy energies of critical points in optical spectra (see also Ecrit energy of band edge of type Γ6 ... energy loss frequency oscillator strength frictional force spectroscopic splitting factor longitudinal g-factor transverse g-factor g-factor of conduction electrons g-factor of holes density of states (also N(E) or DOS is used) density of conduction (valence) band states Gibbs energy of formation of a neutral cation vacancy shear modulus shear modulus measured in[hkl] direction free energy standard free energy of formation Gibbs energy of phase transition Planck constant height (of icosahedron) photon energy hardness, microhardness hardness (Brinell, Vickers, Knoop) magnetic field (strength), also given as µ0H in tesla (T)) applied magnetic field critical magnetic field external magnetic field (peak to peak) linewidth of resonance spectrum enthalpy at temperature T (standard) heat of formation heat of transformation current density electric current photocurrent intensity luminescence intensity Raman intensity total orbital angular momentum quantum number exchange interaction energy (J/kB in K) extinction coefficient (absorption index) III Symbol Unit Property k k Å−1, nm−1 dyn Å−1 wavevector of electrons force constant force constant between B atoms Boltzmann constant absorption coefficient (sometimes α is used) Knight shift fracture toughness length linear thermal elongation electron mass effective mass of electrons (holes) effective cyclotron resonance mass effective plasma frequency mass effective mass polaronic mass transverse, longitudinal effective mass (saturation) magnetization per unit volume (linear) refractive index refractive index in a, b, c direction birefringence electron concentration (n also carrier concentration in general) acceptor (donor) concentration effective number of electrons per FU, per atom (contributing to opt. properties) Hall density intrinsic carrier concentration spin density density of trapping levels count rate, number of electrons density of states (see also g(E)) hydrostatic pressure (phase) transition pressure magnetic moment effective (paramagnetic) moment magnetic moment per formula unit magnetic moment per ion M, per atom A magnetic moment per rare earth atom saturation magnetic moment hole concentration spontaneous polarization Mulliken effective charge wavevector of phonons wavevector (frequently reciprocal vector component for neutron scattering) internal friction radius (of atom M) reflectivity, reflectance resistance gas constant normal Hall coefficient kBB, kB-B k, kB K K, KB KC L, l ∆l/l m0 mn(p) mωc mωp m* m** m⊥, || M(s) n na,b,c n n, ne J K−1 cm−1 N m−3/2 cm g m0 m0 m0 m0 m0 m0 G g−1,atom−1, unit cell−1,cm−3 na(d) neff ,Neff nH ni nS nt N N(E) p ptr p peff pFU, pm pM,, pA pRE ps p P q q Q Q-1 r(M) R R R RH various units Pa, bar µB cm−3 C m−2 e Å−1, nm−1 Å−1 cm, nm, Å Ω J K−1 mol−1, cal mol−1 K−1 m3 C−1, cm3 C−1 IV Symbol Unit Property Rs S S m3 C−1, cm3 C−1 anomalous Hall coefficient spin quantum number entropy Sf0 Str S S(Q,E) t ti T T Tc TC Tdec , Tdecomp Tg Tm TN Tperit Tprep TQ Ts Ttr TV Tα T0 u U J mol−1 K−1, cal mol−1 K−1 J mol−1 K−1 J mol−1 K−1 mV K−1, µV K−1 barn eV−1 sr−1 atom−1 s, min, h, d, yr K, °C V UH Ui U Uij υ υ V eV Å2 Uiso Uequiv υb υl(L), υt(T) υs Vm W x, y, z x Xik Xk Y z Z cm s−1 Å3, nm3 cm3 (mol−1) eV bar bar K-1 entropy of formation entropy of phase transition Seebeck coefficient (thermoelectric power) INS response function time transport numbers (t+, t− : for cations, anions) transmission, transmittance temperature superconductor transition temperature Curie temperature decomposition temperature glass transition temperature melting temperature Néel temperature peritectic (decomposition) temperature preparation temperature antiferroquadrupolar temperature substrate temperature, spin flip temperature crystallographic transition temperature Verwey temperature critical temperature for cluster formation characteristic temperature in Mott´s law of variable range hopping position parameter voltage (also V is used) Hall voltage induced voltage Hubbard self-energy, electrostatic correlation energy temperature factors isotropic temperature factor equivalent temperature factor velocity, sound velocity bulk velocity longitudinal, transverse sound velocity shear sound velocity valence volume molar volume width of valence or conduction bands fractional coordinates of atoms in the unit cell concentration stress tensor (6×6) (in the literature often labeled Tij) stress vector (6-component) yield of electrons, photoemissive yield figure of merit (z = S2σ/κ) atomic number, coordination number V Symbol α (αF) α α αa,b,c α, β, γ β γ , γG γ γ γ γ γ Γ Γ δ δ tanδ ∆cf ∆el ∆ex ε0 ε = ε1 − i ε2 ε∞ εo ε(0), εo ε1, ε2 εL εe Im ε-1 ∆ε ζ Θ , Θp Θa ΘD ΘE κ κ λ Λ κL κV κe κL λL Unit cm−1 K−1 deg K−1 cm−1 Hz T−1, Hz Oe−1 J mol−1 K−2 Hz Oe, Å−1 cm−1 ppm eV eV eV F cm−1 deg K K K K cm2 dyn−1,m2 N−1, Pa−1 W cm−1 K−1, W m−1 K−1, W mol−1 K−1 nm, µm cm Property Fröhlich polaron coupling constant absorption coefficient linear thermal expansion coefficient lin. thermal expansion coefficient in a, b, c direction unit cell angles volume thermal expansion coefficient Grüneisen constant microbrittleness damping constant nuclear gyromagnetic ratio coefficient of electronic heat capacity hopping rate linewidth (e.g. of nuclear Bragg reflection, in ESR) linewidth (e.g. of phonon wavenumber) chemical shift Anderson-Grüneisen constant dielectric loss tangent (ε2/ε1) CEF splitting energy electronic stabilization energy exchange splitting energy permittivity of free space dielectric constant high frequency limit of dielectric constant static dielectric constant low frequency limit of dielectric constant real, imaginary part of dielectric constants lattice part of dielectric constant contribution of free electron to ε energy loss function oscillator strength reduced wavevector coordinate diffraction angle paramagnetic Curie temperature, characteristic temperature asymptotic Curie temperature Debye temperature Einstein temperature compressibility (= 1/bulk modulus) linear compressibility volume compressibility thermal conductivity charge carrier contribution to κ lattice contribution to κ wavelength wavelength of laser light phonon mean free path VI Symbol Unit Property µ cm2 V−1 s−1 mobility of charge carriers mobility in a, b, c direction drift mobility Hall mobility electron (hole) mobility Bohr magneton frequency plasma frequency Raman frequency photon energy Poisson’s ratio wavenumber piezoresistance coefficient Peltier energy resistivity resistivity in a, b, c direction magnetoresistance microstrength magnetic moment per unit mass = specific magnetization magnetic moment per mole = molar magnetization µB v µa,b,c µdr µH µn, µp νp νR hν v ν , ν/c πik Π ρ ρ a,b,c ∆ρ/ρ0 σ σ σm σ σ a,b,c σd σi σn(p) σph J T−1 Hz eV cm−1 cm2 dyn−1 eV Ω cm, Ω m Pa emu g−1= G cm3 g−1, A m2 kg−1 emu mol−1= G cm3 mol−1 Ω−1cm−1 σopt τ Ω−1cm−1, s-1 s Φ eV Φ χ χg , χm χv ω ω Φe eV emu g−1 = cm3 g−1, emu mol−1 = cm3 mol−1 ωp s−1 eV electrical conductivity conductivity in a, b, c direction dark conductivity intrinsic conductivity conductivity of electrons (holes) photoconductivity optical conductivity relaxation time, rise or decay time, lifetime of carriers work function work function of electrons inner lattice potential magnetic susceptibility magnetic susceptibility per gram magnetic susceptibility per mole magnetic volume susceptibility angular (circular) frequency plasma resonance frequency photon energy VII 2. Abbreviations A a a ac AES AF, AFM AFQ APB APW arb av bcc bct BZ c calc CB CCDW cr, crit CS cub CVD d, D dc dhcp dHvA DFT dir DOS DTA e EDC eff ELNES ELS, EELS EMF EPMA EPR, epr ESCA ESR, esr EXELFS exp fcc F FIR, fir FLAPW FT FWHM h hcp hex actinoid element acceptor amorphous alternating current atomic emisssion spectroscopy antiferromagnetic antiferroquadrupolar antiphase boundary augmented plane wave (method) arbitrary average body centered cubic body centered tetragonal Brillouin zone mostly as subscript: cubic, critical or conduction band calculated conduction band commensurate charge density wave mostly as subscript: critical crystallographic shear (plane) cubic chemical vapour deposition donor direct current double hexagonal close-packed de Haas van Alphen oscillations (method) density functional theory direct density of states differential thermal analysis electron electron (intensity) distribution curve effective energy loss near edge structure electron energy loss spectrum electromotive force electron probe microanalysis electron paramagnetic resonance electron spectroscopy for chemical analysis electron spin resonance electron-loss fine structure experimental face centered cubic ferromagnetic far infrared full potential linearized augmented plane wave (method) Fourier transform full width at half maximum hole hexagonal close-packed hexagonal VIII HIP HT I i ICDW ind INDO ion IR, ir KKR L, l L, l, liq LA LCAO LMTO Ln LO LSD LT LTO m M, Me, M´ magn MAS min (max) MO Mn.Mn MSC MVFF NMR obs oct Od opt OPW p P PC PDOS PE PEELS ph PM PVD R, RE, REE R R rel res RF rh RPA hot isostatic pressing high temperature T >300 K insulator intrinsic; sometimes used for interstitial incommensurate charge density wave indirect intermediate neglect of differential overlap ionic, ionization infrared, irradiation Kohn-Korringa-Rostoker method mostly as subscript: longitudinal or lattice liquid longitudinal acoustic linear combination of atomic orbitals linearized muffin-tin orbital ((linear combination of muffin-tin orbitals (method)) lanthanide longitudinal optical local spin density method low temperature, mainly < 10 K longitudinal and transverse optical monoclinic (mostly subscript) metal mostly as subscript: magnetic magic-angle spinning minimum (maximum) molecular orbit Mn ion on Mn site, positively charged magnetically stimulated current modified valence force field nuclear magnetic resonance observed octahedral oxygen deficiency (concentration of deficient oxygen atoms) optical orthogonalized plane wave hole paramagnetic point contact partial density of states photoelectron spectrum parallel electron energy-loss spectra as subscript: photon, phonon, photoparamagnetic physical vapor deposition rare earth element rutile (mostly subscript) as subscript: Raman relative resolution radio frequency rhombohedral random phase approximation IX RT s SC SCF SICF SMT SXS T, TM t, T TA TDOS TEM tetr TG th theor TIP TO tot tr UPS, UPE uv, UV v vac VB VCA VGa... V'Mn VT X XANES XCS XPS, XPE XRD ⊥, || room temperature surface semiconductor self consistant field single ion in a crystal field semiconductor-metal transition soft X-ray spectrum transition element as subscripts or supersripts: transverse transverse acoustic total density of states transmission electron microscopy mostly as subscripts: tetragonal thermal gravimetry thermal, sometimes for theoretical theoretical temperature independent paramagnetism transverse optical mostly as subscript: total transition (subscript for phase transition prameters) UV photoemission spectroscopy ultraviolet mostly as subscript: valence band vacuum, sometimes for vacancy valence band, as subscript v is used virtual crystal approximation vacancy on Ga... site Mn vacancy, negatively charged vapor transport anion (e.g.S, Se, Te) X-ray absorption near edge structural spectra X-ray chemical shift X-ray photoelectron spectroscopy X-ray diffraction perpendicular, parallel to a crystallographic axis X 3. Conversion tables A. Conversion factors from the SIU system to the CGS-esu and the CGS-emu systems. Quantities Symbols SIU CGS-esu (non-rationalized) CGS-emu bulk modulus magnetic induction B B 10 dyn cm–2 10–6/3 esu 10 dyn cm–2 104 G molar heat capacity at const. pressure elastic moduli (stiffnesses) density Cp Pa ( = N m–2) T ( = Wb m–2) = Vs m–2 J K–1 mol –1 clm d N m–2 ( = Pa) kg m–3 107 erg K–1 mol–1 (=0.239cal K–1 mol–1) 10 dyn cm–2 10–3 g cm–3 107 erg K–1 mol–1 (=0.239cal K–1 mol–1) 10 dyn cm–2 10–3 g cm–3 piezoelectric strain coefficient strain tensor dik 3 . 104 esu 10–6 emu eik C N–1 ( = m V–1) dimensionless 1 (dimensionless) 1 (dimensionless) eik C m–2 3 . 105 esu 10–5 emu E N m–2 ( = Pa) 10 dyn cm–2 10 dyn cm–2 E gik V m–1 m2 C–1 10–4/3 esu 10–5/3 esu 106 emu 105 emu ∆G 107 erg mol–1 J mol–1 –1 ( = 0.239 cal mol ) ( = 0.239 cal mol–1) V m–1 (= N C–1) 10–4/3 esu 107 erg mol–1 10 dyn cm–2 4π · 10–3 Oe 107 erg mol–1 piezoelectric stress coefficients Young's modulus electric field strength piezoelectric strain coefficients molar free energy change piezoelectric stress coefficient hardness magnetic field strength molar enthalpy change hik H H ∆H current density elastoresistance coefficients pressure i mik p N m–2 ( = Pa) A m–1 J mol–1 ( = 0.239 cal mol–1) A m–2 dimensionless Pa (= 10–5 bar) dielectric polarization pyroelectric coefficient elastooptic constant (in cubic crystals) piezooptic constant (in cubic crystals) Hall coefficient linear electrooptic constant elastic compliances molar entropy change P pi pij 106 emu C m–2 C m–2 K–1 dimensionless 10 dyn cm–2 12π · 107 esu 107 erg mol–1 ( = 0.239 cal mol–1) 3 . 105 esu 1 (dimensionless) 10 dyn cm–2 (=1.019 · 10–5 kg cm–2 =7.5 · 10–3 Torr) 3 · 105 esu 3 · 105 esu K–1 1 (dimensionless) 10–5 emu 1 (dimensionless) 10 dyn cm–2 (=1.019 · 10–5 kg cm–2 =7.5 · 10–3 Torr) 10–5 emu 10–5 emu K–1 1 (dimensionless) qij dimensionless 1 (dimensionless) 1 (dimensionless) RH rij sml ∆S m3 C–1 m V–1 m2 N–1 J K–1 mol–1 stress tensor thermal conductivity Xij κ 107 emu 10–6 emu 10–1 cm2 dyn–1 107 erg K–1 mol–1 ( = 0.239 cal mol–1) 10 dyn cm–2 105 erg cm–1 s–1 K–1 dielectric constant ε N m–2 (= Pa) W m–1 K–1 (= J m–1 s–1 K–1) dimensionless 10–3/3 esu 3 · 104 esu 10–1 cm2 dyn–1 107 erg K–1 mol–1 ( = 0.239 cal mol–1) 10 dyn cm–2 105 erg cm–1 s–1 K–1 1 (dimensionless) 1 (dimensionless) XI Quantities Symbols SIU CGS-esu (non-rationalized) CGS-emu piezoresistance tensor coefficients piezooptic constant (in cubic crystals) resistivity conductivity magnetic volume susceptibility magnetic mass susceptiblity πik m2 N–1 10–1 cm2 dyn–1 10–1 cm2 dyn–1 πik m2 N–1 10–1 cm2 dyn–1 10–1 cm2 dyn–1 ρ σ χv Ωm Ω–1 m–1 dimensionless 10–9/9 esu 9 · 109 esu 1/4π (dimensionless) 10–11 emu 10–11 emu 1/4π (dimensionless) χg m3 kg–1 103/4π esu cm3 g–1 103/4π emu g–1 (= 103/4π cm3 g–1) magnetic molar susceptibility χm m3 mol–1 106/4π esu cm3 mol–1 106/4π emu mol–1 (= 106/4π cm3 mol–1) Conversion factors (cont.) Energy conversion Energy: E = e V = h v = h c ν Energy and equivalent quantities 1J 1V 1s–1 (= l Hz) l cm–1 1 V As = 1 J = 107 erg = 2.38845 . 10–4 kcal E V v ν [J] [V] [Hz, s–1] [cm–1] = = = 1 6.2415 . 1018 . –19 1.60219 10 1 6.62619 . 10–34 4.13550 . 10–15 1.50916 . 1033 2.41797 . 1014 1 5.03403 . 1022 8.06547 . 103 3.33564 . 10–11 = 1.98648 . 10–23 1.23979 . 10–4 2.99792 . 1010 1 Error: Experimental errors are frequently given in parentheses referring to the last decimal places. For example, 1.352(12) stands for 1.352 ± 0.012 and 342.5(21) stands for 342.5 ± 2.1.
