The Raman effect in crystals

A review is given of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years. Attention is given to the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering. In particular the phenomena observed in the Raman scattering from crystals which lack a centre of inversion are related to the theory. The angular variations of the scattering by any type of lattice vibration in a crystal having any symmetry can be easily calculated using a complete tabulation of the Raman tensor. Recent measurements of first-order lattice vibration spectra are listed. A discussion of Brillouin scattering is included. The relation of second-order Raman spectra to critical points in the lattice vibration density of states is discussed, and measurements of the second-order spectra of diamond and the alkali halides are reviewed. The theory and experimental results for Raman scattering by electroni...

[1]  R. S. Krishnan,et al.  Intensity ratio of the Raman lines in diamond , 1950 .

[2]  S. Bhagavantam,et al.  Raman effect in relation to crystal structure , 1939 .

[3]  T. M. Nedungadi Effect of temperature on the raman spectrum of quartz , 1940 .

[4]  W. Kaiser,et al.  Absorption and Fluorescence of Sm2+ in CaF2, SrF2, and BaF2 , 1962 .

[5]  V. Chandrasekharan Scattering matrix for Raman effect in cubic crystals , 1963 .

[6]  R. S. Krishnan Raman and Infra-red Spectra of Rock-salt , 1945, Nature.

[7]  T. S. Krishnan Raman spectrum of strontianite (SrCO3) , 1956 .

[8]  E. Gross Change of Wave-length of Light due to Elastic Heat Waves at Scattering in Liquids. , 1930, Nature.

[9]  P. Narayanan The distribution of intensity in the Raman spectrum of diamond , 1951 .

[10]  E. I. Blount Formalisms of Band Theory , 1962 .

[11]  A. Maradudin,et al.  On the Evaluation of Phonon Widths and Shifts , 1962, 1962.

[12]  R. S. Krishnan The scattering of light in diamond and its Raman spectrum , 1947 .

[13]  R. Loudon,et al.  The possible observation of electronic Raman transitions in crystals , 1963 .

[14]  Helen M. J. Smith The theory of the vibrations and the Raman spectrum of the diamond lattice , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[15]  H. Poulet,et al.  Spectre de vibration des cristaux piézoélectriques : VI. Etude des vibrations dégénérées du sulfate de béryllium hydraté et du phosphate monoammonique , 1956 .

[16]  R. S. Krishnan The theory of the vibrations and the Raman spectrum of the diamond lattice , 1948 .

[17]  R. S. Krishnan,et al.  Elastic constants of crystals from light scattering measurements , 1955 .

[18]  R. S. Krishnan The second order Raman spectrum of diamond , 1946 .

[19]  J. Hougen,et al.  Electronic Raman Effect in Pr 3+ Ions in Single Crystals of PrCl 3 , 1963 .

[20]  K. D. Gupta CHARACTERISTIC MODIFIED X-RAY SCATTERING , 1962 .

[21]  S. Porto,et al.  Ruby Optical Maser as a Raman Source , 1962 .

[22]  D. Pines,et al.  Electron Interaction in Solids. Collective Approach to the Dielectric Constant , 1958 .

[23]  P. Narayanan Raman spectrum of cesium bromide , 1955 .

[24]  A. Maradudin,et al.  SCATTERING OF NEUTRONS BY AN ANHARMONIC CRYSTAL , 1962 .

[25]  C. Darwin The Refractive Index of an Ionized Medium , 1934 .

[26]  D. Krishnamurti The raman spectrum of calcite and its interpretation , 1957 .

[27]  J. Mathieu,et al.  Spectres de Raman et structure des cristaux de chlorure de cuivre et de chlorures doubles de cuivre et de métaux alcalins , 1953 .

[28]  R. Cowley The theory of Raman scattering from crystals , 1964 .

[29]  J. Mathieu,et al.  Étude du spectre de diffusion de l’anglésite , 1958 .

[30]  E. Wigner,et al.  Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals , 1936 .

[31]  O. Theimer SELECTION RULES AND TEMPERATURE DEPENDENCE OF THE FIRST-ORDER RAMAN EFFECT IN CRYSTALS , 1956 .

[32]  C. Raman The physics of crystals , 1956 .

[33]  O. Theimer Règles de sélection pour la diffusion Raman; Cas de la calcite , 1955 .

[34]  S. Khambata Raman Spectrum of Magnesium Oxide , 1956 .

[35]  W. Cochran,et al.  LATTICE DYNAMICS OF ALKALI HALIDE CRYSTALS. II. EXPERIMENTAL STUDIES OF KBr AND NaI , 1963 .

[36]  O. Theimer The First Order Raman Effect in Crystals, particularly in Diamond , 1951 .

[37]  R. Loudon Theory of Stimulated Raman Scattering from Lattice Vibrations , 1963 .

[38]  R. S. Krishnan Temperature variations of the Raman frequencies in diamond , 1946 .

[39]  H. L. Welsh,et al.  Raman Spectrum of Rocksalt , 1949, Nature.

[40]  P. Narayanaswamy Influence of temperature on the Raman spectra of crystals , 1947 .

[41]  H. W. Thompson Infra-Red and Raman Spectra of Polyatomic Molecules , 1946, Nature.

[42]  D. Hornig,et al.  Vibrational Spectra of Molecules and Complex Ions in Crystals VII. The Raman Spectrum of Crystalline Ammonia and 3‐Deutero‐Ammonia , 1954 .

[43]  K. D. Gupta SMEKAL-RAMAN TYPE MODIFIED X-RAY SCATTERING , 1959 .

[44]  R. Srinivasan Temperature variation of the Raman spectrum of topaz , 1953 .

[45]  M. Born,et al.  The theory of the Raman effect in crystals, in particular rock-salt , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[46]  H. Kogelnik,et al.  Continuous Helium–Neon Red Laser as a Raman Source , 1963 .

[47]  J. Fahrenfort,et al.  Directional Variation of Frequency in the Infrared Spectrum of Crystals , 1952 .

[48]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[49]  P. Richards,et al.  Far-Infrared Energy Gap Measurements in Bulk Superconducting In, Sn, Hg, Ta, V, Pb, and Nb , 1960 .

[50]  D. A. Kleinman,et al.  Infrared Properties of Cubic Silicon Carbide Films , 1959 .

[51]  J. Birman Simplified LCAO Method for Zincblende, Wurtzite, and Mixed Crystal Structures , 1959 .

[52]  B. Dayal The vibration spectrum of Rutile , 1950 .

[53]  R. H. Lyddane,et al.  On the Polar Vibrations of Alkali Halides , 1941 .

[54]  C. Townes,et al.  Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves , 1964 .

[55]  R. Cowley Temperature Dependence of a Transverse Optic Mode in Strontium Titanate , 1962 .

[56]  D. Hornig,et al.  Calculation of Dipole Derivatives from Infrared Reflection Spectra or Raman Spectra of Crystals , 1957 .

[57]  D. Krishnamurti,et al.  The raman spectrum of quartz and its interpretation , 1958 .

[58]  W. Geiger,et al.  Brillouinstreuung an künstlichen quarzgläsern , 1960 .

[59]  W. Cochran,et al.  Dielectric constants and lattice vibrations , 1962 .

[60]  L. Hove,et al.  The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal , 1953 .

[61]  J. Axe Two-Photon Processes in Complex Atoms , 1964 .

[62]  F. A. Johnson,et al.  Critical-point analysis of the phonon spectra of diamond, silicon and germanium , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[63]  K. Vedam,et al.  Raman spectrum of strontium titanate , 1961 .

[64]  D. Krishnamurti Raman spectrum of magnesite , 1956 .

[65]  E. V. Appleton,et al.  Optics and spectroscopy: An english translation of the russian , 1960 .

[66]  K. Viswanathan TEMPERATURE EFFECT ON LIGHT SCATTERING IN CRYSTALS , 1963 .

[67]  P. Narayanan Raman spectrum of rutile , 1953 .

[68]  R. Peierls,et al.  Quantum theory of solids , 1956 .

[69]  Robert Bruce Lindsay,et al.  Physical Properties of Crystals , 1957 .

[70]  S. S. Mitra Vibration Spectra of Solids , 1962 .

[71]  D. A. Kleinman,et al.  Infrared Lattice Bands of Quartz , 1961 .

[72]  S. D. Smith,et al.  Two-phonon infra-red lattice absorption in diamond , 1961 .

[73]  R. S. Krishnan The scattering of light in fused quartz and its Raman spectrum , 1953 .

[74]  B. P. Stoicheff,et al.  Angular Dependence of Maser-Stimulated Raman Radiation in Calcite , 1964 .

[75]  R. Loudon Theory of the first-order Raman effect in crystals , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[76]  D. A. Kleinman,et al.  Infrared Properties of Hexagonal Silicon Carbide , 1959 .

[77]  D. Krishnamurti The Raman spectrum of rutile , 1962 .

[78]  J. Hardy,et al.  Lattice vibrations of sodium chloride: Experimental and theoretical heat capacity data , 1960 .

[79]  V. Heine Group theory in quantum mechanics , 1960 .

[80]  H. Ehrenreich Electron scattering in InSb , 1957 .

[81]  L. Couture,et al.  Spectre de vibration des cristaux piézoélectriques. - V. Sulfate de lithium et de potassium , 1955 .

[82]  L. Brillouin Diffusion de la lumière et des rayons X par un corps transparent homogène - Influence de l'agitation thermique , 1922 .

[83]  W. Heitler,et al.  The quantum theory of radiation , 1936 .

[84]  M. Geller,et al.  STIMULATED EMISSION OF STOKES AND ANTI‐STOKES RAMAN LINES FROM DIAMOND, CALCITE, AND α‐SULFUR SINGLE CRYSTALS , 1963 .

[85]  B. Saksena Raman effect and crystal symmetry , 1940 .

[86]  W. Spitzer,et al.  Theory of the Optical Properties of Quartz in the Infrared , 1962 .

[87]  M. Lax,et al.  Infrared Lattice Absorption in Ionic and Homopolar Crystals , 1955 .

[88]  B. Stoicheff,et al.  The low-temperature heat capacity and the Raman and Brillouin spectra of vitreous silica , 1959 .

[89]  D. Krishnamurti The Raman spectrum of diamond , 1954 .

[90]  A. A. Maradudin,et al.  Thermal Expansion and Phonon Frequency Shifts , 1962, 1962.

[91]  S. Ikegami Raman Spectrum of BaTiO3 , 1964 .

[92]  R. S. Krishnan Thermal Scattering of Light in Diamond , 1947, Nature.

[93]  A. Menzies Raman effect in solids , 1953 .