The long wavelength optical phonons of ionic crystals give rise to dipole-dipole forces, whose long range nature causes the vibrations to depend on the size and shape of the crystal sample. This dependence affects significantly most spectral properties of all crystals whose dimensions are of the order of or shorter than the wavelength of reststrahlen (characteristically several tens of micrometres). In experimental work in which the infrared properties of ionic crystals were examined on small samples, in powder form or in colloidal suspension or in the shape of thin layers, the peculiarities due to size and shape were not always properly recognized. The infrared frequencies of the material which are derived with disregard to these peculiarities may be in error by some tens of wavenumbers. In the experimental section of the review we interpret the general characteristics of the experimental spectra and analyse in detail some representative infrared measurements in the light of the theory. The theory of optical vibrations which takes account of the finiteness of the specimen is formulated firstly in general terms and then by special reference to samples which have one, two or three dimensions short (slab, cylinder and sphere-like geometries). Synthetic spectra are drawn whose characteristic features are interpreted in terms of bulk and surface modes. In the theory retardation effects, i.e. the coupling between lattice and electromagnetic waves, are also included, and the quantized modes are combinations of these, i.e. polaritons. For tiny crystallites of such size that the characteristic infrared radiation wavelength is much larger than the sample size, retardation effects can be neglected. The theory becomes much simpler and the spectrum sharper. Some of the absorption peaks are due to optical surface modes, and their positions are simply related to the characteristic shapes of the crystallites. The theory is so presented as to provide a practical aid in the correlation of spectra with sample shape. The consequences on the spectra of other, less common variables of experiments, for example, the refractive index of the environments, are also calculated. The role of optical surface modes in Raman - and electron - scattering is then discussed. Simple geometrical arrangements of small sized crystals enable the spectra of surface modes to be scanned.

https://iopscience.iop.org/article/10.1088/0034-4885/33/1/304/pdf

Optical phonons of small crystals

Structural Characterization of Nanocrystalline SnO2by X-Ray and Raman Spectroscopy

Structural and morphological analysis of nanocrystalline SnO2 for gas sensor applications were performed at different annealing conditions by using nanopowders and thin nanocrystalline layers. The evolution of the grain size and the morphology of Pt doped tin dioxide nanoparticles with increase of annealing temperature from 450 to 1000°C were analyzed by means of transmission electron microscopy (TEM), X-ray diffraction (XRD), and Fourier transform infrared (FTIR) and micro-Raman spectroscopies. TEM shows that the average particle size increases, the size distribution becomes more spread out, and the grain faceting, as a mechanism of energy minimization, is more evident with increasing temperature. Furthermore, the shape of the particles changes with the annealing temperature, which explains the results of the FTIR spectra using the Theory of the Average Dielectric Constant (TADC). As temperature increases, the Raman spectra are modified in agreement with a reduction of the crystalline defect concentration and a grain size increase. The the tin nanocrystalline SnO2 layers, deposited on α-Al2O3 or on thermally oxidezed Si substrates, have been annealed at 700° C for 8 h under different atmospheres, such as oxygen or synthetic air. TEM proves that the annealing atmosphere has a strong influence on the size and size distribution of the nanoparticles in the thin layer. The main differences are found near the layer-substrate interface and are dependent on the annealing atmosphere as well as the nature of the substrate.

Morphological analysis of nanocrystalline SnO2 for gas sensor applications

Infrared Spectroscopy of Minerals and Related Compounds

The infrared transmission of 0.1 μm crystals of MgO has been measured in the region of fundamental lattice absorption. In particular, the effects of anharmonicity and particle density on the transmission have been observed. These effects have also been calculated using a continuum model applicable to spheres very much smaller than the wavelength of light. In agreement with these calculations, the frequency of the fundamental infrared absorption of small particles was found to decrease with increasing particle density. In addition, it was observed that the frequency dependent damping function of massive MgO must be increased by a factor of about eight in small crystals in order to fit the experimental data.



Schichten von etwa 0,1 μm grosen MgO-Kristallen wurden im Bereich der fundamentalen Gitterschwingungsabsorption im Infraroten gemessen, wobei besondere Effekte der Anharmonizitat und drastische Einflusse der Teilchendichte gefunden werclen. Urn die Infrarot-Durchlassigkeit zu verstehen, mus angenommen werden, das die Dampfungsfunktion kleiner MgO-Kristalle etwa achtmal groser ist, als die von massivem MgO. Auserdem verschiebt sich die fundamentale Absorptionsbande nach niederen Frequenzen mit ansteigender Teilchendichte. Eine Kontinuumstheorie des elektrodynamischen Verhaltens der Kristalle, die als kugelformig und klein gegen die Wellenlange der Strahlung angenommen werden, last dieses Verhalten verstehen.

Infrared Absorption in Small Ionic Crystals

Magnesium oxide powders obtained from three sources exhibit strikingly different infrared absorption spectra. These differences are correlated herein with variations in the size and shape of the particles in the powders, and are interpreted in terms of both Fr\"ohlich-type (surface) modes and classical electromagnetic scattering theory. (1) Reagent-grade MgO powder exhibits a strong and broad absorption centered at 550 ${\mathrm{cm}}^{\ensuremath{-}1}$, the position of which is determined by the Fr\"ohlich-type fundamental frequency for spherical particles that are small compared with the radiation wavelength. The absorption broadening results from variations in particle size and shape. The presence of double particles gives rise to a secondary absorption near 460 ${\mathrm{cm}}^{\ensuremath{-}1}$. (2) MgO smoke in various matrices absorbs strongly at the bulk-mode frequency (401 ${\mathrm{cm}}^{\ensuremath{-}1}$) owing to the presence of both individual large cubical particles and long chains of small cubical particles. A second strong absorption occurs at 490 ${\mathrm{cm}}^{\ensuremath{-}1}$ in Nujol, or at 546 ${\mathrm{cm}}^{\ensuremath{-}1}$ on polyethylene plates; these frequencies represent a surface mode of small MgO cubes. A shoulder at still higher frequencies is ascribed to surface modes of rod-shaped particles. (3) MgO powder obtained from thermally decomposed MgC${\mathrm{O}}_{3}$ absorbs strongly at the bulk-mode frequency (401 ${\mathrm{cm}}^{\ensuremath{-}1}$), because of the presence of large flakelike particles having a very fine grain structure. With increasing grain size, the principal absorption shifts to lower frequencies, and a secondary absorption, near 490 ${\mathrm{cm}}^{\ensuremath{-}1}$ in Nujol, appears as a result of absorption by small MgO particles.

Effect of Particle Size and Shape on the Infrared Absorption of Magnesium Oxide Powders

Correlation of the absorption frequencies of powders of noncubic crystals has been achieved with the substantially different bulk‐mode lattice frequencies. A general Frohlich equation is derived which relates the ir‐absorption frequencies of a powder (consisting of “small” spherical particles embedded in a matrix), to the bulk‐mode lattice frequencies obtained from single‐crystal reflection spectra. This equation is applied to stannic oxide and titanium dioxide (rutile). By means of electromagnetic scattering theory, the transmittance of powdered stannic oxide and rutile is computed with use of the complex refractive index obtained from bulk crystals. The absorption peaks obtained in the scattering calculations compare well with experimental results and are consistent with the generalized Frohlich equation.

Robert Summitt

Papers

Effect of Particle Size and Shape on the Infrared Absorption of Magnesium Oxide Powders

Interpretation of the Infrared Absorption Spectra of Stannic Oxide and Titanium Dioxide (Rutile) Powders

Comment on the infrared spectrum of single crystal, fibrous SiC