The Vibrational Spectra of Molecules and Complex Ions in Crystals III. Ammonium Chloride and Deutero‐Ammonium Chloride
TL;DR: In this paper, the infra-red spectra of thin non-scattering films of NH4Cl and ND4Cl were obtained at 28°, −78° and −190°C.
Abstract: The infra‐red spectra of thin non‐scattering films of NH4Cl and ND4Cl were obtained at 28°, −78° and −190°C. A convenient low temperature transmission type cell usable for such films is described. No indication of fine structure due to free rotation of the NH4+ ions was found. Instead, evidence is presented for the existence, both above and below the λ‐point, of a torsional lattice mode involving the NH4+ ions. The limiting frequencies of the torsional oscillations were observed at about 390 and 280 cm−1 for NH4Cl and ND4Cl, respectively. These values agree quite well with the frequencies calculated on the basis of a purely electrostatic potential function. The spectra of the low temperature modifications indicate strongly that the structures belong to the space group Td1 in which the NH4+ ion symmetry is Td. Of the eight observed bands, two are assigned to the triply degenerate fundamentals ν3 and ν4, one to the overtone 2ν4, one to the combination ν2+ν4 which resonates strongly with ν3, one to the combi...
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TL;DR: In this article, the infrared spectra of 7 ferrites of the formula $M{\mathrm{Fe}}{2}{\mathrm {O}}_{4}, where $M$ designates a divalent metal, are presented and analyzed.
Abstract: The infrared spectra of 7 ferrites of the formula $M{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$, where $M$ designates a divalent metal, are presented and analyzed. Electronic absorption was observed in the visible and near-infrared regions. Two absorption bands arising from interatomic vibrations were measured and force constants calculated for the stretching of bonds between octahedral or tetrahedral metal ions and oxide ions. These force constants are in agreement with the elastic and thermodynamic properties of these compounds and are sensitive to distribution of metal ions between the alternate sites. The integrated vibrational band intensities were measured: they are compatible with predominantly ionic bonding for these structures.
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TL;DR: The No. 10123 1quart "Success" can as discussed by the authors dispenses solvent by finger pressure on the valve, which then closes upon release of the pressure, as indicated in the accompanying figure.
Abstract: use and allows it to dispense no more solvent than is needed when the swab-stick is dipped into it like a pen into an inkwell. Available in 4 oz., 6 oz., and 8 oz. sizes, the price ranges from $3. 50 to $3. 75. This same company also advertises a model No. 10123 1quart "Success" can which dispenses solvent by finger pressure on the valve, which then closes upon release of the pressure, as indicated in the accompanying figure. There is also a plunger can of I-pint size that dispenses solvent by pressure on the plunger. Price for the first type of can is about $8, for the second, about $7.
1,518 citations
TL;DR: In this article, the experimental studies of displacive phase transitions in solids are summarized, focusing on inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized.
Abstract: This paper reviews the experimental studies of displacive phase transitions in solids. Primary emphasis is upon inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized. Several prototype structures are considered in detail: (1) the rocksalt IV-VI semiconductors PbTe, SnTe, and GeTe; (2) the ferroelectric perovskites exemplified by PbTi${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$; (3) perovskites which exhibit cell-doubling transitions, such as LaAl${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$; (4) crystals having the $\ensuremath{\alpha}$-quartz structure, including Ge${\mathrm{O}}_{2}$, Si${\mathrm{O}}_{2}$, and AlP${\mathrm{O}}_{4}$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$ and ${\mathrm{Tb}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$; (6) the V-VI-VII semiconductors typified by SbSI; (7) the hydrogen-bonded ferroelectrics of the K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ family; (8) Jahn-Teller systems such as DyV${\mathrm{O}}_{4}$ and RbCo${\mathrm{F}}_{3}$, in which structural distortions occur as secondary effects; (9) order-disorder systems such as NaN${\mathrm{O}}_{2}$ and the ammonium halides (N${\mathrm{H}}_{4}$Cl, N${\mathrm{H}}_{4}$Br), in which no "soft mode" occurs in the spectral region ($\ensuremath{\omega}g{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\ensuremath{\beta}$-tungsten ($A\ensuremath{-}15$) structures such as ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, which exhibit high-temperature superconductivity. These crystal categories are used to illustrate several phenomena of current physical interest: Specifically, we discuss harmonic and anharmonic mode coupling; "critical exponents" $\ensuremath{\beta}$ differing from one-half in the temperature dependences of the order parameter $\ensuremath{\phi}(T)={\ensuremath{\phi}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$ and of the soft-mode frequency $\ensuremath{\omega}(T)={\ensuremath{\omega}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$; and the recently discovered "central" modes centered at zero frequency, which grow in intensity as the transition temperature ${T}_{0}$ is approached from above or below. The review covers the period 1940-1972. A few 1973 works are mentioned for which the author had preprints in 1972 or very early 1973. This review is in no sense a comprehensive survey of ferroelectricity. Readers are referred to the following earlier reviews on that subject: Silverman (1966, 1969), Cochran and Cowley (1967), Blinc (1968), Murzin et al. (1968), Nettleton (1970), and Blinc and Zaks (1972).
639 citations
TL;DR: A survey of the relation between four physical properties of crystals and their structural characters is given in this paper, where the properties discussed are the magnetic, optical, piezoelectric and elastic.
Abstract: A survey is given of the relation between four physical properties of crystals and their structural characters. The properties discussed are the magnetic, optical, piezoelectric and elastic. The well-established relations between (a) diamagnetic anisotropy and molecular orientation and (b) paramagnetic anisotropy and the environment of complex ions are briefly reviewed. The more recent study of paramagnetic resonance absorption at high frequencies in a magnetic field is also included. The work on antiferromagnetic crystals is discussed in connection with the spinels. The study of optical activity and Raman spectra are considered under the heading of optical properties. The experimental confirmation by X-rays of the original convention concerning atomic configurations and the sign of optical activity in a molecule are described and also the connection between special features of the structures of tartrates, of sodium chlorate and of quartz and the handedness of the rotatory power is analysed. The piezoelectric properties of zinc blende, quartz, tourmaline, Rochelle salt and potassium dihydrogen phosphate are considered in relation to their structures. In the study of quartz and tourmaline the origin of the piezoelectric charge is attributed to tetrahedra of SiO4 stressed in a direction from one corner to the opposite face. The spontaneous electric polarization of Rochelle salt and KH2PO4 is attributed to cooperative movements of hydrogen ions. Broad generalizations concerning the relation between elastic constants and the crystal structure are given. It is shown that the hardness increases in a regular way with the elastic constant c11 (or an average of c11, c22, c33) and also that there is a close connection between directions of strong interatomic bonds and a large value of the corresponding elastic constant.
365 citations
TL;DR: In this paper, various optical, caloric, dielectric, elastic, and microwave investigations have been used to study the tunneling states connected with the motion of atomic and molecular impurities in alkali halides.
Abstract: The various optical, caloric, dielectric, elastic, and microwave investigations which have been used to study the tunneling states connected with the motion of atomic and molecular impurities in alkali halides are reviewed.
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TL;DR: In this paper, it was shown that the wave equation for a diatomic molecule in a crystal that the motion of the molecule in its dependence on the polar angles θ and φ may approach either one of two limiting cases, oscillation and rotation.
Abstract: It is shown by the discussion of the wave equation for a diatomic molecule in a crystal that the motion of the molecule in its dependence on the polar angles θ and φ may approach either one of two limiting cases, oscillation and rotation. If the intermolecular forces are large and the moment of inertia of the molecule is large (as in I2, for example), the eigenfunctions and energy levels approach those corresponding to oscillation about certain equilibrium orientations; if they are small (as in H2), the eigenfunctions and energy levels may approximate those for the free molecule, even in the lowest quantum state.
It is found in this way that crystalline hydrogen at temperatures somewhat below the melting point is a nearly perfect solid solution of symmetric and antisymmetric molecules, the latter retaining the quantum weight 3 for the state with j=1 as well as the spin quantum weight 3. This leads to the expression S=-nARlognA-(1-nA)Rlog(1-nA)+nARlog9+Str, in which Str is the translational entropy, for the entropy of the solid at these temperatures. At lower temperatures (around 5°K) the solid solution becomes unstable relative to phases of definite composition, and the entropy falls to S=nARlog3+Str, the entropy of mixing and of the quantum weight 3 for j=1 being lost at the same time. Only at temperatures of about 0.001°K will the spin quantum weight entropy be lost.
Gradual transitions covering a range of temperatures and often unaccompanied by a change in crystal structure, reported for CH4, HCl, the ammonium halides, and other substances, are interpreted as changes from the state in which most of the molecules are oscillating to that in which most of them are rotating. The significance of molecular rotation in the interpretation of other phenomena is also discussed.
366 citations
TL;DR: In this paper, it was shown that if a crystal is approximated as a harmonic oscillator, only a very small number of vibrational modes may be active in the infra-red or Raman spectra.
Abstract: It is shown that if a crystal is approximated as a harmonic oscillator, only a very small number of vibrational modes may be active in the infra‐red or Raman spectra. These modes are all totally symmetric with respect to translation. They must also have proper symmetry with respect to the factor group of the space group which we have called the unit cell group. The active frequencies may be calculated from a single unit cell. It is shown further that the number and symmetry type of vibrational modes may be correctly calculated from the local symmetry (site group) of the center of gravity of each kind of molecule. In the harmonic approximation the spectrum should consist of very sharp lines. The wide bands obtained experimentally are probably due to combination lines with lattice vibrations and indicate anharmonic coupling between molecular and lattice modes. Such combinations may cause apparent violations of selection rules for internal vibrations. The symmetry basis for obtaining selection rules in this case is given. The importance of obtaining spectra over a wide temperature range and particularly at very low temperatures is emphasized. In cases where all internal modes have a frequency great compared to the frequency of lattice modes the problem is examined from the point of view of the Born‐Oppenheimer approximation. It is shown that for some symmetries perturbations linear in the lattice displacement may occur. In these cases considerable splitting of degenerate molecular vibration modes is possible. Groups for which first‐order splitting is not expected are listed. Symmetry species of other groups are classified into those which may and which may not be split in this approximation, and the lattice modes responsible for splitting are classified as rotations or translations and by symmetry type.
282 citations
TL;DR: In this paper, Herzberg's new monograph on polyatomic molecules, like that on diatomic molecules preceding it, is an admirable one and it is important to understand just what this book sets out to cover, since in spite of its very great value it cannot, taken alone, be regarded as a manual for new workers in the field.
Abstract: IT is now becoming more widely realized that infrared spectroscopy has grown into a powerful new method for analysis and structural diagnosis, and as such it must be used by many who have hitherto had little knowledge of either the relevant theory or the experimental technique. To this extent any new book on the subject will be studied with interest. Prof. Herzberg's new monograph on polyatomic molecules, like that on diatomic molecules preceding it, is an admirable one. It is important, however, to understand just what this book sets out to cover, since in spite of its very great value it cannot, taken alone, be regarded as a manual for new workers in the field. Infra-Red and Raman Spectra of Polyatomic Molecules By Prof. Gerhard Herzberg. (Molecular Spectra and Molecular Structure, Vol. 2.) Pp. xiii + 632. (New York: D. Van Nostrand Co., Inc., 1945.) 9.50 dollars.
161 citations
TL;DR: The results show that lattice dynamics can account quantitatively for the Raman effect in crystals and that Raman’s attacks against the theory are unfounded.
Abstract: The Raman effect in crystals is treated in this paper with the help of Placzek's approximation. It consists of contributions of different orders with respect to the amplitudes of the vibrations; the first-order effect is a line spectrum depending only on the vibrations of infinite wave-length, the second-order effect is a continuous spectrum depending on combination frequencies of all pairs of branches of the lattice vibrations, each pair taken for the same wave vector. In highly symmetrical crystals like rock-salt the first-order effect is zero. The second-order effect can be calculated for rock-salt with the help of the tables of the lattice frequencies published by Kellermann. It consists of thirty-six peaks, each belonging to a combination frequency. The superposition of these allows us to determine without any arbitrary assumption about the coupling constants, the frequency of the observable maxima in fair agreement with Krishnan's measurements. By adapting three coupling constants one can also determine the relative intensities of the most prominent peaks and obtain a curve which in its main features agrees with the observed one. The results show that lattice dynamics can account quantitatively for the Raman effect in crystals and that Raman's attacks against the theory are unfounded.
54 citations