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The paper provides the Coxeter schemes of all the discrete groups generated by reflections in the faces of simplicial prisms the combinatory type of which is the product of a simplex and a segment in Lobachevskian spaces.

The effect of electron reflection from electrodes and of anisotropy of angular scattering on slow-electron diffusion in a gas is investigated theoretically and experimentally. An analytic expression is obtained for the diffusion currents by means of an approximate solution of the kinetic equation. Two electrode configurations are considered, infinite parallel planes and infinite coaxial cylinders. Measurements performed on an instrument with cylindrical electrodes are compared with results of theoretical calculations.

The reflection coefficients at normal incidence are found for a large class of one-dimensionally inhomogeneous or stratified half-spaces, which contain a homogeneous half-space. The formulation of the problem involves a combination of the classical boundary value technique, and the nonclassical principle of invariant imbedding. Solutions are in closed form and expressible in terms of Bessel functions. All results are given in terms of the ratio of the distance between free space and the homogeneous half-space to the wavelength in vacuo. One special case is that of an arbitrary number of layers lying on a homogeneous half-space where the dielectric constant of each layer has a constant gradient. A number of other special cases, limiting cases, and generalizations are developed including one in which the thickness of the top layer obeys a probability distribution.

The lattice vibrations of AgCl are calculated from an extended shell model where the shell of the Ag-ion has a quadrupolar and a rotational degree of freedom. The model parameters are discussed in connection with the electronic 4d-shell of the Ag-ion. Thermal expansion, infrared reflection, and anharmonic frequency shift are calculated from a simple extension of the harmonic model, and are found to be in good agreement with experimental data. The anharmonic effects are comparable to those of the alkali halides. Die Gitterschwingungsfrequenzen im AgCl werden mit einem erweiterten Schalenmodell berechnet, bei dem die Schale des Ag-Ions einen quadrupolaren und einen rotationsartigen Freiheitsgrad besitzt. Die Modellparameter werden im Zusammenhang mit der 4d-Elektronenschale des Ag-Ions diskutiert. Mit einer einfachen Erweiterung des harmonischen Modells werden thermische Ausdehnung, Infrarot-Reflexion und anharmonische Frequenzverschiebung berechnet; die Ergebnisse sind in guter Ubereinstimmung mit dem Experiment. Die anharmonischen Effekte sind mit denen der Alkali-Halogenide vergleichbar.

Absorption and reflection spectra of β-Ga2O3 are measured with polarized light in the wavelength region near its absorption edge. The crystals of β-Ga2O3 are grown by using a Ga/HCl/O2/Ar vapor reaction system. The platelike crystals of β-Ga2O3 have (100), (010), and (001) surfaces, and the major surface is (100). The energies of the absorption edge are observed to be 4.90 eV for E//b, 4.54 eV for E//c, and 4.56 eV for E⊥b&c at room temperature. The energies for E//b and for E//c at 77 K are larger than those at room temperature by 40 meV and 220 meV, respectively. Reflection minima are observed at 5.06 eV and 5.30 eV for E//b, and at 4.63 eV and 5.30 eV for E//c at room temperature.

The spectra of the fundamental reflectivity of CdxHg1 − xTe solid solution thin films thermally evaporated from raw polycrystalline material onto mica substrates have been investigated in the 1.7−5.5 eV energy range. Measurements of the positions of the reflection maxima as a function of the chemical composition determined by the spectrophotometric method for compositions from x = 0.00 up to x = 0.25 have been carried out. From these investigations a linear dependence of the positions E1 of the reflection maxima on the composition x has been obtained. The results thus obtained are compared with results published in the literature for CdxHg1 − xTe single-crystal solid solutions as well as for amorphous and polycrystalline thin films of some other materials. Finally, the possibility of obtaining a criterion for the degree of crystalline order in a thin film is considered.

A formula, derived for the scattering of the various orders, differs from the results of Eckart and Brekhovskikh in the same way as these results differ from each other—namely, by the term in front of the Bessel function. In our case the term is unity. By deducing a simple geometric formula for the angular distribution of scattered energy in the high‐frequency limit, and by using an asymptotic form for the Bessel function, the three formulations are compared in the high‐frequency limit at various values of height, angle, etc., with the geometric formula. The result is that our formulation agrees best.

A model based on the Mayadas-Shatzkes theory of polycrystalline films is proposed to represent discontinuous films in which island boundaries are considered to be partially reflecting planes, the coefficient of reflection at the boundaries being equivalent to the energy associated with charge transfer from one island to the neighbouring one. The relation between DC resistivity and the thickness of discontinuous films is discussed, and a quantitative picture is presented. The resistivity at radio frequencies, at which islands are effectively AC-shunted, is also considered. The coefficient of reflection at these frequencies is significantly different from that for DC measurements, and its value depends on the nature of the crystallinity of the islands. Thickness-dependent DC and RF resistivities of polycrystalline, discontinuous bismuth films have been studied, and the results are presented. The agreement of the data with our model is quite satisfactory.

It is shown that it is always possible to expand the scattering matrix for an isotropic medium in generalized spherical functions. Additional physical symmetry properties of the scattering process, e.g., time-reversal invariance or reflection invariance, give rise to simple symmetry relations for the expansion coefficents. The expansion in generalized spherical functions naturally leads to decomposition of variables and appears to be the simplest way to include the various symmetry relations for the scattering matrix discussed in the literature.

To improve the accuracy of calculations for the reflection and transmission functions, doubling techniques are in use. The central theme of this method is to derive the total reflection function when two portions of a medium are adjoined together. The synthesis is done by the use of star product techniques which require a knowledge of theS andT functions of both parts of the medium. Infinite series expansion is necessary to compute the total reflection. The method developed in this article splits the total reflected beam into two parts, one relating to that flux which suffers no scattering at all in the first portion of the medium and the second portion that undergoes at least one scattering in the first portion. The first part can be evaluated simply by knowing the reflection function of the second portion of the medium. The other part of the total reflection for variations of the thickness of the first portion of the medium is found to obey a simple Riccati type integro-differential equation with zero initial conditions. Knowledge of theT functions is not necessary and integration has to be performed over the interval corresponding to thickness of the first portion of the medium. Order-of-scattering analysis is also carried out.

The exact expression for A(t), the tth-order Fourier coefficient of an X-ray diffraction line profile in terms of column length distribution, mean thickness, the r.m.s. strain and various mean strain gradients, has been derived and the assumptions involved in the Warren–Averbach method of separating particle size and r.m.s. strain have been critically examined. It has been observed that the Warren–Averbach method gives a r.m.s. value of the pseudo strain 〈ē2〉1/2 which is equal to the true r.m.s. strain 〈e2〉1/2 only at t = 0. It has been further shown that ln J(t), where J(t) is the tth-order Fourier coefficient of the strain profile, is not, as is taken in the Warren–Averbach method, linear in l20 when the given reflection hkl has been converted into a 00l0 reflection by suitable changes of axes. In the Warren–Averbach method, this essentially non-linear curve is taken as linear and a straight line passing through two points on this curve is extended to meet the ln A(t) axis, the intercept on which is supposed to give ln N(t), where N(t) is the tth-order Fourier transform of the particle-size profile. Thus approximate values of the mean particle size 〈T〉 and the r.m.s. pseudo strain 〈ē2〉1/2 are obtained. Based on the exact expression for A(t) a new multiple-order technique for determining not only the particle size and r.m.s. strain but also various strain derivatives has been developed and its limitations examined. It is found that an error introduced in the r.m.s. strain is of an order less than that of the experimental errors. Similarly, the single-line technique of Mitra & Misra [Acta Cryst. (1967), 23, 867–868] has been shown to give correct values of 〈T〉 and 〈e2〉1/2 within experimental error. The single-line technique has been proved to be quite a perfect and useful technique.

The transformation of the parent b.c.c. phase of the TiNi intermetallic to the 9A cubic transition structure was studied by utilizing electron microscopy and diffraction. Very thin domain shaped precipitates are observed to form in samples annealed and slowly cooled from higher temperatures. The precipitate particles were densely distributed within the grains of the parent phase These produced reflections at the 1 3 position of the fundamental reflection of the b.c.c. phase in electron diffraction patterns. In certain orientations of the foil, reflections from the precipitate phase appeared as satellite spots around a diffused main reflection and are analysed to be from four different (111) precipitate habits statistically distributed as a domain structure.

A parametric form of the amplitude of elastic reflection of very low energy electrons is derived. The amplitude expression conforms to the results of an earlier analysis of a simple case of electron reflection called the quasi two-beam case. The parameters in the amplitude expression refer to: (1) the surface states of the crystal; (2) the band structure of the substrate crystal; and (3) absorption (inelastic scattering) in the energy range of the experiment The amplitude expression also includes parameters relating to (4) the behavior of the amplitude at infinity and at negative energy. The amplitude expression is used to parameterize existing experimental results for nickel (001) and for the surface formed by adsorption of sodium on nickel (001) to form the centered (2 × 2) structure. The parameterization employs previously-computed values of parameters relating to the nickel band structure [category (2) above], and parameters in categories (1), (3) and (4) are adjusted to fit the electron-reflection data. In the case of the sodium-covered surface it is shown that the shape of the intensity-energy curve and the general level of intensity relative to that for clean nickel depends critically on the surface-state parameters. Two surface states are needed to fit the intensity data The values of the surface-state parameters are: location relative to vacuum level: 2.5 ± 0.1, 6.9 ± 0.2eV; width: 4.2 ± 0.4, 7.5 ± 1.0eV. The classification and significance of surface-state resonances is discussed briefly.

1,1′Trimethylene-π-dicyclopentadienedichlorozirconium, (CH2)3(C5H4)2- ZrCl2, is orthorthombic, space group Pbca. The unit cell dimensions found were a = 8.277(2), b = 13.922(4), c = 22.568(5), Z = 8. The strucutre was determined from three-dimensional X-ray data (1049 independent reflection) refined to an R facotr of 2.64%. The coordination about the zirconium atom is that of the a distorted tetrahedron comprised of the chlorine atoms and the centroids of the π-cyclopentadienyl rings. The ClsZrCl bond angle is 96.92(7)° and the centroid Zrcentroid angle 129.5°. The ZrCl bond distances found are 2.451(2) and 2.431(2) A which are very close to the sum of the Paulling radii. Zirconiumring centroid distances are 2.192 and 2.193 A and the range of ZrC distances is 2.4772.516 A. The carboncarbon distances within the π-cyclopentadiene rings verage 1.395(10) A and range from 1.363(9) to 1.413(9) A. These values establish the Pentahapto nature of the metalring bonding.

Single crystals of copper were grown which displayed predominantly the (1, 1, 1) plane. The crystals were electropolished and characterized by acid etch patterns, X-ray back reflection orientation and topology techniques and by Auger electron spectroscopy. The crystals having a geometric surface area of 78 cm2 were specially mounted in a bakeable ultrahigh vacuum volumetric adsorption apparatus. Krypton adsorption isotherms were determined on these copper crystals at 78.9°, 91.2°, 98.6°, and 108.0°K. Pressures were measured using an MKS all-welded bakeable capacitance manometer. The isotherm data encompassed the very low coverage region, the monolayer region and for the two lower temperature isotherms a portion of the multilayer region. The low coverage isotherm data were analyzed in terms of the virial approach to physical adsorption. The gas-solid interaction parameter, ϵ 1s ∗ /k , was found to be 1678°K. The virial approach was found to yield reasonably good values of the surface area of the crystals. This is the first application of the virial approach to very small surface area samples. The intermediate coverage region was analyzed in terms of the significant structure theory of adsorption. The analysis yields a value of ϵ 1s ∗ /k of 1654 ± 50°K and a value for the lateral interaction parameter ϵ 1s ∗ /k of 48 ± 7°K. The high value of ϵ 12 ∗ /k and the unusually low value of ϵ 1s ∗ /k are in accord with quantum mechanical theories of many-body interactions involving metal substrates and with the results of the virial analysis of the low coverage data. Isosteric heats of adsorption were determined as a function of coverage. The zero coverage heat, qs10/R, was found to be 1770°K and the slope of the heat versus coverage curve in the monolayer region is about 270°K which is in agreement with the small value of ϵ 12 ∗ /k reported above.

An X-ray topographic study of helical line defects in Czochralski grown Gd3Ga5O12 is described. Both the Lang transmission configuration and the double reflection method have been employed to characterize the strain field in and around the helices. From this study it is concluded that the helix is a dislocation of the prismatic, interstitial type which surrounds a helicoidal region of smaller lattice constant. The topographs also reveal an alignment of the helix loops with the crystal growth striae.

An investigation of the manner in which thickness extinction contours change with the deviation from the Bragg condition of a single non-systematic reflection has been carried out. The particular non-systematic and low order systematic reflections chosen for the study were the 133 and 220 reflections in silicon, respectively. The experimental results obtained were found to be in quantitative agreement with calculations based on the multi-beam dynamical theory while a good qualitative description was obtained from a three beam approximation including the directly transmitted, the 133 and the 220 reflections. The results of the investigation showed that the strongest effects of a non-systematic reflection occur over a narrow range of deviations from the Bragg condition of that reflection. These effects are characterized by a sharp change in extinction distance accompanied by the appearance of intensity profiles which are complex in shape. When the 220 systematic reflection was in its Bragg condition, a single region of complexity, at a positive deviation of the non-systematic reflection from its Bragg condition, was found. However, when the crystal was tilted so that the 220 reflection was no longer in its Bragg condition, there were two regions of complexity. One of these occurred at a positive deviation from the Bragg condition of the non-systematic reflection while the other occurred at a negative deviation. Es wird die Art untersucht, in der sich die Dicken-Extinktionsnrofile mit der Abweichung von der Bragg-Bedingung einer einzelnen nichtsystematischen Reflexion andern. Die speziellen nichtsystematischen und systematischen Reflexionen niedriger Ordnung, die fur die Untersuchung gewahlt wurden, waren die 133- bzw. 220-Reflexionen in Silizium. Es wurde gefunden, das die erhaltenen experimentellen Ergebnisse quantitativ mit Rechnungen auf der Grundlage der dynamischen Vielstrahltheroie ubereinstimmen, wahrend eine gute qualitative Beschreibung mit einer Dreistrahlnaherung unter Einschlus der direkt transmittierten, der 133- und der 220-Reflexionen erhalten wird. Die Ergebnisse der Untersuchung zeigen, das die starksten Einflusse einer nichtsystematischen Reflexion uber einen schmalen Bereich der Abweichung von der Bragg-Bedingung dieser Reflexion auftreten. Diese Einflusse sind durch eine scharfe Anderung im Extinktionsabstand charakterisiert, begleitet vom Auftreten eines Intensitatsprofils mit komplizierter Form. Wenn sich die systematische 220-Reflexion in ihrer Bragg-Bedingung befindet, wird ein einzelner komplexer Bereich bei einer positiven Abweichung der nichtsystematischen Reflexion von ihrer Bragg-Bedingung gefunden. Wenn jedoch der Kristall so gekippt wird, das die 220-Reflexion nicht langer ihre Bragg-Bedingung erfullt, treten zwei komplexe Bereiche auf. Einer von diesen beiden tritt bei einer positiven Abweichung von der Bragg-Bedingung der nichtsystematischen Reflexion auf, wahrend der andere bei einer negativen Abweichung auftritt.

Formulae are derived for the reflection and transmission coeficients of plane elastic waves for a transition layer. Haskell's technique and the so-called delta matrices[5, 7] are used for this purpose. No problems are encountered in deriving the reflections and transmission coefficients from Haskell's matrices[3]. However, in some cases Haskell's matrices do not guarantee the accuracy required. For this reason attention is mainly devoted to deriving the reflection and transmission coefficients from the delta matrices. In deriving the transmission coefficients use is made of the fact that some3×3 subdeterminants of the delta matrices are squares of the3×3 subdeterminants of Haskell's matrices.

With an effective nucleon-nucleon interaction used the Hartree—Fock method is applied for deformed nuclei. No rearrangement term is taken into account which results in a serious lack of binding energy. On the other hand good r.m.s. radii and correct deformations are obtained. In the region covered by the investigations the Hartree—Fock gap has been found to be small.

Some aspects of exciton polariton behaviour in anisotropic crystals are investigated for a specific model of the response function of an exciton split by a uniaxial field. The extraordinary-polariton dispersion scheme shows an additional branch for propagation in a nonprincipal direction appearing in the anomalous dispersion gap of the cubic case. The reflectivity spectrum obtained for this case is in good agreement with measurements performed on the basal plane of the uniaxial crystal PbI2 under oblique incidence. For a consideration of spatial-dispersion effects (finite exciton mass) the theory of Hopfield and Thomas is extended to uniaxial crystals. It is found that three simultaneous waves exist for every frequency and that a sharp extra reflection peak appears for every long-wavelength polariton mode of nonzero frequency. Reflection curves are calculated for different values of the exciton massm and the thicknesst of the Hopfield layer. The experimental normal-incidence «extraordinary” spectrum obtained by Biellmannet al. on the\((10\bar 11)\) of PbI2 which shows two additional sharp peaks can be reproduced by appropriate choice of the parametersm andt.

The structure of the semicoherent interface between grain boundary nucleated M23C6 and the related austenite grain has been studied in a 20%Cr-25%Ni-0.05%C stainless steel. Transmission electron microscope observations of the direction of Moire fringes, as a function of the operative reflection, have shown that for some particles there is a 0.6° twist deviation from the previously reported exact cube/cube orientation relationship. In contrast, other particles have no twist component. Bright field kinematical imaging conditions have revealed, networks of interfacial defects which have been interpreted as dislocations with a 3 〈111〉 Burgers vectors. The spacing and crystallographic directions of these dislocations account well for the precipitate/matrix relationship in both the cube/cube precipitates and those with a twist component.

Polarized specular reflection spectra have been obtained of the antibiotic polyene, amphotericin B, in its monolayers and in those of cholesterol in its expanded-liquid phase. An analysis of the reflectivity of the long wavelength member of the 3 band group observed in these spectra gives both its extinction coefficient and the orientation of its transition moment. In the case of the amphotericin B monolayers, an increase in surface pressure from 9.4 to 15.6 dynes/cm produces a decrease in the molar extinction coefficient from 1.20 · 10 5 to 0.65 · 10 5 and possibly a decrease in the angle which the heptaene transition moment makes with the surface. Accompanying these changes is red-shift of all three bands which shifts the long wavelength band from 4072 to 4150 A. These changes in the molar extinction and wavelength with compression appear to be due to the formation of polyene-polyene complexes. The effect of an expanded-liquid monolayer of cholesterol on the surface interactions of amphotericin B is to increase the polyene orientation from 6° to 35° and shift the 4150 A band to 4190 A without further affecting the extinction coefficient of 0.65 · 10 5 . The values of the wavelengths, extinction coefficients and orientations obtained from the reflection spectra of the two polyene monolayers were in agreement with those obtained from the transmission spectra of similar systems.

Elastic electron reflection at crystal surfaces for electron energies below the threshold of the first diffracted beam (≲ 10eV for most surfaces, near normal incidence) is studied in the framework of the dynamical theory of diffraction. The model considered is an idealized substrate crystal with selvedge (surface region) consisting, e.g., of an ordered layer of adsorbed atoms. The indirect effect of inelastic scattering (absorption) is included phenomenologically by going to complex values of the electron energy or propagation vector. A description of the amplitude of reflection as a function of energy is developed in detail for the quasi two-beam case; the quasi two-beam case is defined by the requirement that the totally-symmetric part of the relevant substrate and vacuum band-structure sections be the same as in the two-beam (one-dimensional) form of the dynamical theory, except for the presence of evanescent waves. It is shown that in the absence of a selvedge, the reflection amplitude function possesses branch points deriving from the substrate band structure but does not possess any finite poles or zeros. In the presence of a selvedge, the reflection amplitude may be expressed as the product of a “background” function representing the substrate band structure and having no poles or zeros, and a factor having poles and zeros symmetrically located relative to the real-energy axis. The poles are identified with surface-state resonances of the crystal, and the conjugate zeros with conditions of destructive interference in surface multiple scattering. It is shown that the surface-state resonances, acting through the associated conditions of destructive interference, can have a dominant effect in very low energy electron reflection.

A system is described for determining spectral positions from high resolution infrared spectra which have been recorded in digital form on magnetic tape. The system employs a minicomputer located in the laboratory and line centers are determined by an interactive procedure in which the operator makes judgments based on information displayed on the CRT screen of the computer. This information consists of the spectrum, a reflection of a local section of the spectrum at a vertical line through the center of the screen, a plot of the difference between the spectrum and its reflection, and the square of the area under the difference curve. Very high accuracy is demonstrated for locating the centers of single lines as well as the centers of the components of incompletely resolved double lines. Determinations of spectral positions (wavenumber calibration) parallel operations that were previously performed as batch jobs by a much larger computer. Spectral positions are determined by standard methods of calibration of interference fringes and interpolation.

RHEED-diagrams of vacuum deposited GaAs-films with high density of structural defects often show splitting of matrix reflections into satellites. It can be shown by simple models, for example of {111}-oriented films, that this phenomenon is originated by formation of stacking faults perpendicular to 〈ĪĪĪ〉-B growth directions of the films. The conditions for 〈110〉 and 〈211〉 azimuths are discussed. In RHEED-Diagrammen defektreicher GaAs-Aufdampfschichten wird haufig eine Aufspaltung der Matrixreflexe zu Satelliten beobachtet. Auf Grund einfacher Uberlegungen wird am Beispiel von {111}-orientierten Schichten nachgewiesen, das diese Erscheinung durch in der Schicht auftretende Stapelfehlerbildung senkrecht zu 〈ĪĪĪ〉-B-Wachstumsrichtungen verursacht wird. Die Verhaltnisse werden fur den 〈110〉- und 〈211〉-Azimut diskutiert.

It is well known that reflection from metal films in the visible and infrared spectrum (region of the anomalous skin effect) depends on the parameters determining the scattering of the conduction electrons at the sample surface, which are extremely sensitive to the structure of the films and the surface quality. We started by considering two kinds of structure: coarse-crystalline condensates with a small number of defects and highly dispersed condensates; in samples of these two kinds the dimensions of the structural inhomogeneities were either much larger or much smaller than the light wavelength. We tried to arrange the experiments so as to be able to study a wide range of crystallite sizes, while keeping the other physical parameters of the films as constant as possible, and to determine the influence of the surface relief imparted by the structure of the condensates on the reflecting power.

The reflection curve for the Laue case of diffraction by a bicrystal composed of two plane-parallel parts of different thickness and slightly different lattice constants is investigated theoretically using the plane wave dynamical theory of X-ray diffraction. As one can see from the numerical calculations performed for the (220) reflection of a silicon bicrystal, the reflection curve is asymmetrical and the location of its maximum is shifted with respect to the ideal crystal case. Die Laue-Reflexionskurven fur Interferenzen an einem aus zwei planparallelen Teilen verschiedener Gitterkonstante zusammengesetzten Bikristall wurden mit Hilfe der dynamischen Theorie fur ebene Wellen untersucht. Aus numerischen Berechnungen fur die Interferenz-Ordnung (220) eines Si-Bikristalles wurde festgestellt, das die Reflexionskurve in diesem Fall asymmetrisch ist und ihr Maximum eine Verschiebung gegenuber dem fur den Idealkristall aufweist.

The real part of the bound-atom coherent neutron scattering length of $^{3}\mathrm{He}$ has been measured by comparing the reflectivities of quartz-liquid-$^{3}\mathrm{He}$ and quartz-liquid-$^{4}\mathrm{He}$ interfaces and has been found to have the value (6.1 \ifmmode\pm\else\textpm\fi{} 0.6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}\phantom{\rule{0ex}{0ex}}13}$ cm.

The optical constants in the photon energy range between 4 and 10.5 eV for E ⌈ b on (001) and E ⌈ L and E ⊥ L on the (010) plane are discussed. In particular the influence of macroscopic fields on the optical properties of anisotropic crystals is considered. For E ⌈ a on the (001) plane reflection spectra have been measured at various angles of incidence. These data and results obtained recently by Hymowitz and Clark for several artificially prepared crystal faces are discussed on the basis of the frequency dependend dielectric functions. New information on the directional dispersion of exciton bands is thus obtained.

We present the results of a combined x-ray and neutron diffraction study of the temperature dependence of the "forbidden" (222) reflection in germanium. Integrated intensities were measured from room temperature to 850\ifmmode^\circ\else\textdegree\fi{}C with x rays and to 904\ifmmode^\circ\else\textdegree\fi{}C with neutrons. In addition, an earlier x-ray study of the silicon (222) reflection has been improved and extended to 800\ifmmode^\circ\else\textdegree\fi{}C and a correction has been made in the corresponding neutron results. The germanium and silicon data are interpreted in terms of anharmonic atomic vibrations and anticentrosymmetric valence-charge distributions. Contrary to our previous reports, the temperature dependence of the scattering from the bonding electrons is found to be similar to that from the core electrons.

Neu dargestellt wurden Cs2TlFeF6 (a = 9,211 A), Cs2KFeF6 (a = 9,041 A), Rb2KFeF6 (a = 8,868 A) und Rb2NaFeF6 (a = 8,464 A) alle kubische Elpasolith-Vertreter, sowie Cs2NaFeF6 (Cs2NaCrF6−Typ, hexagonal mit a = 6,281, c = 30,532 A) als farblose Pulver. Cs2KFeF6 wurde magnetisch vermessen (70 bis 297,2 K). Das Reflexionspektrum von FeF3 wurde gemessen (9000 bis 36000 cm−1). Der Madelunganteil der Gitterenergie, MAPLE, wird berechnet und diskutiert. On Hexafluoroferrates(III): Cs2TlFeF6, Cs2KFeF6, Rb2KFeF6, Rb2NaFeF6, and Cs2NaFeF6 New prepared are the compounds Cs2TlFeF6 (a = 9.211 A), Cs2KFeF6 (a = 9.041 A), Rb2KFeF6 (a = 8.868 A) and Rb2NaFeF6 (a = 8.46 4A) all cubic Elpasolithes as well as Cs2NaFeF6 (Cs2NaCrF6−type, hexagonal with a = 6.281, c = 30.532 A), all colourless. Cs2KFeF6 was measured magnetically (70–297,2 K). The spectra of reflection were measured (9000–36000 cm−1). The Madelung Part of Lattice Energy, MAPLE, is calculated and discussed.

In this paper various diffraction formulae deseribing elastie scattering of spinless uncharged particles are analysed. Expressions for thel-dependence of theS-matrix elements of boundary condition models are derived and compared with directS-matrix models. Some incompatibility between the two different approaches, which are supposed to describe the same phenomenon, are found. In the derivation of Kirchhoff’s diffraction formula there exists an incompatibility of the boundary conditions. Namely, for its derivation one should know both the values of the wave function and the normal component of the gradient of the wave function on the absorbing sphere. The solutions to bo both boundary problems are separately presented. The reflection from the absorbing sphere is treated and new formulae are derived. The differential and total cross-sections of the described models are analysed.

It is predicted theoretically and justified experimentally that infrared reflectances are proportional to the concentrations of the vibrational species causing them. In the binary Li2O-, Na2O-, and K2O-SiO2glasses used in this study, the reflection peaks have been assigned to vibrations of single silicon-oxygen tetrahedra in different symmetry environments caused by the presence of alkali ions. Care has been taken here in recording the spectra of high alkali glasses to prevent chemical reactions with water vapor in the atmosphere. The influence of phase separation on reflection spectra is also discussed.

Spectral absorption measurements involving pure nitrous oxide were performed with the aid of a commercial grating spectrophotometer. A multiple reflection cell with a path length of 1.25 m was used in the investigation. The tests were conducted at pressures in the range from 5 to 8 atm. The obtained data were used to determine the apparent spectral absorption coefficients. Questions regarding the validity of a line approximation relation are discussed.

In preceding papers (cf. Bellman et al.(1,2,3,), integral recurrence for the finite-order scattering and transmission functions have been given in connection with integral recurrence relations for the finite order X- and Y-functions with the aid of an initial-value method. In the present paper, it is shown how to find algebraic recurrence relations for the finite-order scattering and transmission functions in terms of finite-order X- and Y-functions without referring to an initial-value method. These recurrence relations are suitable for the numerical computation of the finite-order scattering and transmission functions by use of a digital computer. Furthermore, in Tables 1–3, a numerical example of the finite-order reflection functions for optical thickness 0·2 with albedo = 1 is listed. Table 4 furnishes an example of the cumulative reflection functions for optical thickness 0·2 with three different albedos.

The optical constants $n$ and $k$ were determined for some transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Pd) from reflection and transmission measurements on vacuum-evaporated polycrystalline thin films at room temperature, in the spectral range 0.5-6.5 eV. Three optical measurements were inverted to determine the film thickness $d$ as well as $n$ and $k$. The estimated error in $d$ was \ifmmode\pm\else\textpm\fi{}2 \AA{} and that in $n$, $k$ was less than \ifmmode\pm\else\textpm\fi{}2% over most of the spectral range. Transmission measurements were made on films in the thickness range 200-500 \AA{}. Many transition metals oxidize rapidly in the air and so measurements on those samples were performed in a nitrogen atmosphere. A detailed analysis of the effect of oxidation on the measured quantities indicates that it is small. The effects on the optical constants of the film thickness and the evaporation rate are discussed. Some recent theoretical calculations of the interband optical conductivity are compared with the results for V, Cr, and Ni. In addition, some other recent experiments are compared with our results.

Infrared reflection spectra of anodic aluminum oxide films prepared in boric acid and natural oxide films on aluminum show a common absorption band in the 900–1000 cm-1 range. This band is shown to be due to the longitudinal mode of the Al-O stretching vibration. In transmission spectra this absorption band is absent; instead one observes the corresponding transverse mode centered around 650 cm-1.

Scattering by extruded polyethylene films has been used to analyze in detail the small-angle scattering of x-rays by strained spherulitic samples. It is shown that the basic small-angle patterns in spherulitic specimens can be obtained by summing small-angle reflections from films drawn both parallel and normal to the direction of extrusion. The representation of a complex pattern by superposition of simpler reflection makes it possible to calculate local strains in various regions of spherulites in bulk specimens.

Summary A direct analysis of phagocytical substances in the alveolar macrophages in semi-thin sections of experimental silicosis of the guinea pig and of human biopsy material, is described. The observation of semi-thin sections in scanning transmission enables a good orientation of the section to be made. Using a large solid angle detector for backscattered electrons, the sections can be observed in the reflection mode of the scanning electron microscope (SEM) with good contrast similar to that of the scanning transmission electron microscopic-mode (STEM). Under these conditions phagocytic substances can be exactly localized in the cell and diagnosed by energy dispersive X-ray analysis.

A simple application of theB3,0 formula is described. This formula is used mainly to avoid inconsistent Σ2-interactions in standard symbolic-addition or multiple-solution techniques. Computer time is reduced by a reflection selection procedure based upon the use of theB2,0 formula. The solution of a centrosymmetric structure is described. This compound, a photodimerization product ofo-distyrylbenzene, is 5,6,11,12-tetraphenyl-dibenzo[2–3,8–9] tricyclo[8,2,0,04,7] dodecadiene-2,8, C44H36. The compound crystallizes in the monoclinic space groupC2/c, with unit cell parametersa = 28.047,b = 9.504,c= 12.600 A and β = 103.4 °. A rather poor set of data was collected by an automatic diffractometer. Structural parameters were refined by full-matrix least-squares methods to anR-value of 0.06 for 970 non-zero reflections. The molecule is situated on a twofold rotation axis. It containscis-, trans-, cis-substituted puckered cyclobutane rings. The dihedral angle between the benzo-groups is 61.5 °.

A theoretical and experimental study of the application of x-ray-photoelectron angular distribution measurements to quantitative surface characterizations is presented. The basic theoretical model that has been used previously to analyze such angular distributions from flat surfaces in the absence of electron-diffraction (channeling) effects is discussed, including certain new generalizations and special cases pertinent to surface analysis. Previous experimental work is reviewed. The predictions of this model are also found to be consistent with new experimental data obtained from gold specimens with carbon-containing surface layers and from aluminum specimens with successive oxide- and carbon-containing layers. An order of magnitude increase in surface-layer relative intensities is observed at low electron escape angles relative to the surface. Also, effects due to x-ray refraction and reflection are found for very low angles of incidence, and these lead to approximately a four-fold increase in surface-layer relative intensities. Extensions of the theory to include the effects of non-uniform x-ray flux, a more realistic spectrometer acceptance function, non-uniformity of surface layers, and surface roughness are also considered, and numerical calculations for the specific case of a sinusoidally rough surface are presented. It is shown that rough-surface intensities will equal flat-surface intensities provided that both surfaces are clean and that no x-ray shading occurs. If surface layers are present, however, rough-surface angular distributions are predicted to deviate markedly from flat-surface distributions. By means of angular distribution measurements, it thus appears possible to selectively enhance near-surface contributions to photoelectron spectra, as well as to obtain information concerning electron mean free paths, surface layer thicknesses and uniformity, and perhaps surface roughnesses.

The NQR Zeeman effect of 127 I (± 1 2 ←→ ± 3 2 transition) for the LiIO 3 crystal of hexagonal modification has been investigated, and the EFTG asymmetry parameter for nuclei of 127 I determined. Measurements of optical properties of the z -cut crystal in polarized light within the region of stretching vibrations and their overtones for IO − 3 revealed that transmission (reflection) depends on the direction of the incident light wave electric vector. The results obtained indicate that crystals of LiIO 3 grown from aqueous solutions show anomalous biaxiality.

Crystals of 4-cyanopyridine-N-oxide crystallize in space groupP21/c (No. 14). There are four molecules per unit cell, witha = 7.88(2),b = 6.10(2),c =11.61(3) A and β =101.4(4) °. Data for 838 unique reflections were recorded using the multiple-film technique and visually estimated intensities. A three-dimensional least-squares refinement of the structure was carried out to a final conventionalR of 0.098. It was found that the molecule was planar, as expected, and that the centrosymmetric pairs were stacked parallel to each other, as viewed down thea-axis. Bond distances and angles are in agreement with those from comparable molecules.

In computing the total reflection function for two media of given scattering properties adjoined together, the usual techniques require a knowledge of reflection and transmission functions of both the media. An alternate method developed here depends only on solving a Riccati equation with suitable initial conditions. By following this procedure, we are able to calculate the reflection function of a given finite order, for a particle that has suffered a specified number of scatterings in the two portions of the total medium. Such calculations may be useful in radiation dosimetry problems where the body to be irradiated is placed on reflecting materials.

It has been reported that there is a special side chain—side chain interaction between the right-handed and left-handed α-helices in the racemic mixture of poly(γ-benzyl glutamate). In this paper physical properties of mixtures of poly(γ-benzyl-L-glutamate) and poly(γ-benzyl-D-glutamate) are studied. From X-ray diffraction measurements, the reflection characteristic of the regular arrangement of the benzyl group at the end of the side chain was shown to disappear on heating at 97°C and to appear on cooling at 73°C. This reversible change was also observed in viscoelastic, thermal and dilatometric measurements and was ascribed to the breakdown and formation of stacks of benzene rings. In the case of samples cast from benzene solution, it was found that the formation of stacks is hampered by the preferable super helix formation.

Experimental infrared emission and reflection measurements were made from 20-1000 cm-1 at temperatures 1115K and 1175K for LiF (melting point 1143K) and analysed by a combined classical oscillator and Kramers-Kronig procedure. The calculated optical and dielectric constants of molten LiF are presented; the shift in the frequency of maximum absorption reverses the trend exhibited by the solid as the temperature is raised. Comparison of the solid and molten far infrared emission spectra suggests the onset of low frequency transparency at approximately 120 cm-1 in the melt.

On the basis of a theory presented earlier [1] diffraction phenomena in CdS crystals with acoustoelectrically generated lattice vibrations are analyzed. Evidence for the generation of a second harmonic is given. Wave vectors and amplitudes of first and second harmonics are calculated from measured changes of reflection curves. The increase of the integrated intensities in dependence on the vibration amplitudes is evaluated, and a model for the transition from dynamical to kinematical diffraction behaviour is discussed. Auf der Grundlage einer kurzlich veroffentlichten Theorie [1] werden Beugungsphanomene an CdS-Kristallen mit akustoelektrisch angeregten Gitterschwingungen analysiert. Das Auftreten einer zweiten Harmonischen wird nachgewiesen. Wellenvektoren und Amplituden der ersten und zweiten Harmonischen werden aus gemessenen Anderungen der Reflexionskurven berechnet. Die Zunahme der Integralintensitat in Abhangigkeit von der Schwingungsamplitude wird ausgewertet und einModell fur den Ubergang vom dynamischen zum kinematischen Reflexionsvermogen diskutiert.