Volume 28, Issue 5

A short review is given of plasma phenomena produced in solids by impinging X-rays. The first category refers to bulk plamons due to X-ray photons scattered on solids. They are observed through the appearance of a new component in the spectrum of the scattered radiation. The energy shift increases slightly with scattering angle but eventually the dispersion stops. A second category of phenomena consists in the light emitted by decaying surface plasmons. They are excited by photoelectrons produced in colloidal materials by X-rays. The spectrum shifts with the dielectric constant of the stabilizing medium.

Using the newly developed method of dynamical interference between anomalously transmitted waves in a crystal containing a non-diffracting zone 1 , we have measured the real part of the atomic scattering factor for germanium at the value of sin θ/λ corresponding to the 220 Bragg reflection. The result, f 0 = 23.79 ± 0.08 electron units is in excellent agreement with values obtained in perfect crystal intensity measurements 2,3 and from triple crystal rocking curve studies 4,5 but significantly differs from the value obtained using Pendellösung fringes 3 . Finally, we seek to assess the reliability of each method by comparison with the corresponding results for silicon, concluding that the error probably lies in the Pendellösung result.

Bragg case wavefield beams are generated with MoKα radiation in a uniformly bent silicon crystal. The propagation of the wavefield beams is investigated by measuring their exit locations and intensities. Very good agreement is found with locations and intensities calculated from the Bragg case beam propagation theory formulated by one of the authors 1a some time ago. Both low and high absorption wavefields were investigated.

The dependence of the characteristic X-ray production on electron beam orientation is studied using very thin epitaxially grown single crystals. In crystals of Ag and Pd of thickness ~100 Å the L shell yield can change by more than a factor of 2 for small changes in orientation near the [111] direction. Theoretical analysis of the results shows that the different Bloch waves do not produce X-rays independently but that interference effects occur. The significance of these observations is discussed.

The energy flow of the X-ray wave fields set up by diffraction in a germanium single crystal has been studied by shadow sharpness measurements. The shadow has been produced by an absorbing wire close to the X-ray entrance surface of the crystal. Intensity profiles have been observed in the wavelength range from 1.541 Å to 0.709 Å, including the K absorption edge of germanium at 1.117 Å. It is shown that the angular divergence of the energy flow is almost independent of the wavelength on each side of the absorption edge. The angular divergence is considerably reduced when passing the absorption edge from the low-energy side to the high-energy side, the thickness of the crystal being kept constant.

A description is given of the Borrmann effect associated with a 3- and 4-beam interaction, as observed in the zero beam distribution of a Kossel-Möllenstedt electron diffraction pattern. In the 3-beam interaction which is studied in detail, the contribution to the intensity asymmetry is characterised by the order of the Born process. Considering the inversion symmetry about the central intersection, even order terms contribute an absorption effect, independent of the phase of the structure amplitude, while odd order terms contribute a structure dependen term which to the first order is independent of absorption. Considering the asymmetry across the weak line and parallel to the strong line, the absorption contributes an asymmetry which inverts with the sign of the structure amplitude. This latter property of the Borrmann effect has possible applications in structure analysis.

A brief discussion of G. Molière's generalized dynamical theory is given with respect to the interpretation of the experimental data|χ ⊥ ig /χ i0 |obtained by means of the Borrmann effect. In order to compare theory and experiment photoelectric absorption cross sections for Silicon and Germanium have been calculated over the X-ray energy range from 5 to 25 keV. Linear absorption coefficients measured by us and other authors agree with theory within a few per cent. Taking the Debye-Waller factor into account, the same theoretical data have been used to calculate |χ ⊥ ig /χ i0 | for Ge and Si. The agreement with extensive measurements of the Borrmann effect in Ge is very good in most cases. The experiments presented in this paper confirm the existence of the electric quadrupole transitions within the photoelectric effect.

Linear absorption coefficients and transmitted intensities have been calculated for all twelve modes of propagation in one case of 6-beam diffraction of x-rays through germanium. At the 6-beam point the absorption coefficients of four of the modes are less than 1 cm -1 , using CuKα 1 radiation, compared with the “normal” value of 352 cm -1 ; one third of the energy incident on the crystal at the exact 6-beam angle is allocated to these low absorption modes.

A set of linear equations for the Fourier components of the field vectors D 0 (p) (direct waves) and D g (p) (Bragg-reflected waves) is formulated by the Fourier transform of the Maxwell equations. Starting from these equations, the scattering matrix theory and the equation equivalent to the Takagi-Taupin equation are derived systematically. The equivalence of these formulations is concluded. The formal similarity of the Takagi-Taupin equation to the Dirac equation for a relativistic charged particle is pointed out.

The diffraction behaviour of vibrating Cd S crystals was studied by theory and experiment. Vibrations were generated by the acoustoelectric effect. Their amplitudes reached up to 0.15 nm and their wave vectors were of the order of 5·10 6 m -1 . Theoretical analysis of experimental results shows that a single reflection of an ideal crystal transforms into a series of satellite reflections. The intensity of the nth satellite is given by the usual equations 1 replacing χ h by χ h J n (- hu) (J n is the Bessel function of nth order, h a lattice vector, u the vibration amplitude, and χ h the coefficient of the susceptibiliy expansion). With increasing vibration amplitude the number of satellites increases and the over all intensity approaches asymptotically the kinematical value.

The defect structures of large single crystals of lithium formate monohydrate. HCOOLi · H 2 O (space group Pbn2 1 ), have been examined by X-ray topography. Two types of planar defects occur: a) Twin boundaries and twin lamellae parallel to (100). The twinning is produced by a rotation of 180° around the axis [100]. b) Defect planes parallel to (010), which could not fully be characterized. The crystals contain grown-in dislocation lines with Burgers vectors parallel to [100], [010], [001], 〈110〉, and probably also parallel to 〈011〉 and 〈012〉. Many of these lines have moved after crystal growth. Bundles of essentially straight dislocation lines with distinct but not always sharply defined preferred directions occur. These directions are in reasonable agreement with directions calculated by minimizing the elastic dislocation energy per unit growth length. Furthermore, dislocation half loops with a Burgers vector [001] produced by plastic deformation have been observed. Some relations between the relative growth velocities of two neighbouring growth faces and the geometry of the corresponding growth-sector boundary are discussed.

The ray theory of Kato and Kambe for imperfect crystals is derived in a formal way from a general dynamical theory of diffraction. This development together with the results from a previous paper concerning Takagi's equation (the wave theory) helps to clarify the meaning and limits of various phenomenological theories that have been extended to an imperfect crystal from the dynamical diffraction theory for a perfect crystal.

The diffuse scattering from neutron-irradiation-produced defects in copper was measured in anomalous transmission and near the 111 Bragg reflection. The results were related through the theory of Dederichs, and the intensities and forms of the scattering curves obtained from the two measurements were found to be in good agreement over a wide range of defect concentrations and sizes. It was shown that the intercept of a plot of the diffuse scattering intensity I s (q 0 ) vs In (q 0 ) is at q 0 =e 1/2 /R for defects of uniform radius R and at q 0 ≌1/R 0 e for an exponential size distribution of average size R 0 .

Asymmetric dynamical diffractions of X-rays are successively used for multiple crystals arranged in the (n 1 , +n 2 ) setting. Double successive asymetric diffractions of the (n 1 , +n 2 ) arrangement give a beam of peculiar spread in angle and wavelength. Triple successive asymmetric diffractions of the (n, + n, - n) arrangement give a highly parallel and monochromatic beam for some appropriate combination of the asymmetry factors of the three crystals. Possible use of multiple asymmetric diffractions is discussed.

The diffraction contrast produced by 90° ferromagnetic domain walls in X-ray transmission topographs is calculated. Two cases are considered: very low and very high normal absorption. The results indicate that the difference in contrast on walls having opposite signs of lattice tilt is due to the anomalous absorption and depends on the magnitude of normal absorption. These theoretical results are in agreement with the contrast observations in X-ray transmission topographs taken from Fe-3 wt%Si single crystal samples using different plate thickness and different radiations.

The molecular packing of the crystal N-methyl acetamide has been studied, taking into account van der Waals and electrostatic interactions, together with the hydrogen bonds between the molecules. Contact criteria were used to obtain the molecular position in the unit cell approximately, which was then refined using the potential energy functions. This involved three position parameters, consisting of two translations and one rotation of the molecule in the a - c plane. The calculated values of these parameters are in reasonable agreement with the observed values in the crystal structure, particularly if hydrogen atoms are included in making the energy calculations.

Even imperfect thick crystals show consequences of Borrmann effect: 1. A light-dark structure of the tails of transmission-rocking curves can be detected. 2. The integrated intensities change. A theoretical description of these phenomena is given. Experimental results and the information content especially of the tails of transmission curves are discussed in some detail.

High energy C + implantation is used to construct a two crystal monolithic X-ray interferometer. The X-ray interferometer technique is applied to in-situ studies of radiation damage annealing in the interferometer. Volume changes in the crystal due to the transformation of single crystal silicon to amorphous silicon and due to the formation of silicon carbide are measured.

The Pendellösung fringe structure within the Bragg reflection from perfect crystals of germanium has been studied over a wide interference range using full-spectrum incident neutron radiation. After allowing for the effects of residual crystal curvature, the experimental data yield a precision determination of the crystal structure amplitude. The coherent nuclear scattering amplitude for germanium is determined to be 0.81858 (36) x 10 -12 cm.

The charge density distribution in the strongest Bloch waves for a dynamical many-beam diffraction situation was calculated for electrons and positrons. Near the [110] zone axis of MgO there exist three strong Bloch waves for electrons. One Bloch wave is concentrated at the rows of Mg-atoms, a second at the rows of O-atoms and a third one between the atoms. The positron Bloch waves are mainly concentrated between the atom rows and have only small charge density at the positions of the atoms. For an incident beam parallel to the [110] axis there exists only one strong positron Bloch wave while for electrons more than three Bloch waves are strong, explaining the channeling behaviour of positrons and electrons. Strong partial waves of different electron Bloch waves can be identified in the diffraction pattern from a MgO crystal wedge.

An energy loss peak at 2 eV in the energy spectrum of electrons transmitted through thin copper films is observed and the variations of the energy value and of the intensity of the peak with film thickness are studied. The cross section for the surface plasmon excitation is calculated from optical data. The observed variations of the energy value and of the intensity of the peak show quantitative and qualitative agreements, respectively, with calculated values. It is concluded that the peak is mainly due to the surface plasmon which does not emit plasma radiation.

The spherical wave theory of Kato is applied to calculate the intensity field in the moire fringe pattern produced by two perfectly aligned simultaneously reflecting crystals separated by a gap when only anomalously transmitted waves need be taken into account. Under practical experimental conditions the incident wavefront curvature adds significantly to the phase difference between interfering waves. This contribution, together with a previously omitted term involving the ratio of gap width to sum of the crystal thicknesses, should be added to the argument of the trigonometric interference term used by previous workers in deriving structure factors from gap-fringe spacings. Expressed directly in terms of a change in the 220 structure factor, use of our revised interference term would reduce Hart and Milne's measured value for silicon by ½% and Baker, Hart and Helliar's measured value for germanium by 1.3%.

Single crystals of pure silver have been grown by the Czochralski technique and Borrmann X-ray topography has been used to study the perfection of the as-grown crystals. Conditions have been found under which dislocation-free growth takes place and crystals of about 1 cm length and 1 mm diameter have been grown free from dislocations.

For x-ray scattering from amorphous media at large sin θ/λ (> 1.00 Å -1 ) momentum and energy is either imparted to a single electron (Compton effect) or to a single atom (Thermal Spike effect). In both cases the impulse approximation provides a convenient method for treating the scattering. Measurements of the ratio of Thermal Spike scattering to Compton scattering were made on paraffin.

The differential equations of Bloch wave type which are used in transmission electron microscopy for the calculation of the diffraction contrast from lattice defects are discussed with special reference to crystals with anomalous absorption (i. e. with a complex crystal potential). anomalous absorption is included, the eigenvalue equation by which the Bloch waves are defined in the perfect reference lattice, becomes non-Hermitian. It is shown that for some particular contrast effects not only the eigenvalues but also the eigenvectors must be corrected for the imaginary part of the crystal potential. As a consequence the orthogonality of the Bloch waves is violated. The correction of the eigenvectors may result in long-range contrast tails of the images of lattice defects (intraband scattering). If, however, only the peak positions of the contrast profiles are considered, it suffices in practical cases to correct only the eigenvalues as is usually assumed for the diffraction in perfect crystals.

An exact possible turbulence for Burger's equation is found. It allows the 2-point distribution function to be calculated in closed form

In the frame of the information theory approach to quantum statistics, we examine the conditions which a given information “Tr(WA) =m” must satisfy in order to determine a unique quantum state with maximum information entropy.

In the present paper a method of calculation of the density matrix in the Schrödinger picture is given, in terms of the known creation and annihiliation operators a + and a. New magnetic operators are given with the help of the coherent states, which depend on two free parameters μ and ν. For the case μ=ν= (e H )/ (2 ħ c), these operators lead to the well-known magnetic operators, as they are given in the current litterature.

For the ground-state and the lower lying excited states of the fluorine-molecule VB -CI calculations with Slater-type orbitals and SCF -CI calculations with contracted Gauß-Lobe functions have been carried out. The SCF -CI method yields a fairly good description of the ground-state. But it is rather difficult to decide whether the SCF -CI calculations of the excited states are accurate or not. The discussion of the potential-curves of some higher excited states leads to the conjecture that the experimentally observed orange band-systems may belong to two transitions 1 Σ g - → 1 Π u and 1 Σ u + → 1 Π g . But this should be checked in further calculations which must include higher orbitals as basis functions.

The rotational Zeeman effect of CH 3 -NO 2 , a molecule with a very low barrier to internal rotation has been studied at field strengths up to 25 kG. From the Zeeman splittings of rotational transitions in excited torsional states the “g-value of the methyl-group” was determined to be g a = +0.347 ± 0.002. This comparatively high value indicates that in nitromethane valence electrons are shifted from the C - H-bond region towards the NO 2 -group, an explanation which is backed by the results of CNDO/2 and INDO-calculations.

Differential cross-sections for the elastic scattering of He + on Ne, Ar, Kr, and Xe were measured at different energies. At energies between 3 eV and several 100 eV, Stueckelberg oscillations could be observed. Between 1 eV and 8 eV rainbow structures were detected, but the rapid oscillations could not be resolved. The measured differential cross-sections were compared with calculated curves. The angular positions of the primary rainbows indicated a very weak interaction in the order of the polarisation energy between the He + -ion and the noble gases. Thus a 12 - 4 potential was used for the calculations since the attractive part of this potential describes the ion induced dipole potential. The depth of the potential well was obtained as < 0.05 eV for He + -Ne, 0.19 eV for He + -Ar, 0.22 eV for He + -Kr and 0.28 eV for He + - Xe. A method is described which allows for correction of the nominal energy of the primary ion beam for contact potentials.

Excitation of CO molecules into the lowest vibrational level of the B 1 Σ + electronic state by absorption of the (B 1 Σ + υ′=0 →X 1 Σ + , υ′′=0) resonance band at 1150 Å has been studied under various experimental conditions by observing the steady state fluorescence of the (B 1 Σ + →A 1 Π ) Angstrom bands. Stern-Volmer plots of the fluorescence intensities at the addition of various foreign gases yielded straight lines whose slopes k̃ q м = k q м · τ eff were strongly dependent on the CO sample pressure. This effect was found to be due to changes of the effective radiative lifetime of the B 1 Σ + υ′=0 because of resonance trapping of the (0,0) band of the (B → X) fluorescence. The CO(B 1 Σ + υ′=0) molecules are found to be quenched by He, Ne, Ar, H 2 and D 2 with effective collision cross sections of 0.23, 0.48, 22.4, 10.7, and 11.4 Å 2 , respectively, at 298 °K. In addition, an approximate value for the ratio A BA / (A BA +A BX )of the radiative transition probabilities of the (B → A) and (B → X) transitions could be derived from the measurements.

Metastable O (3s 5 S 0 ) atoms were produced by rare gas sensitized decomposition of various oxygen containing compounds. The quenching rate constants of H 2 , N 2 , O 2 , NO, N 2 O, N 2 O 4 /NO 2 , CO, CO 2 , SO 2 , SO 3 , H 2 O and the noble gases for the 0 ( 5 S) have been measured by absorption spectroscopy. The noble gases, except xenon, deactivate the metastable oxygen atom with low collision efficiency. Xenon and molecular gases, except hydrogen, deactivate this species efficiently, the cross section being of the order of gas kinetic cross sections.

The microwave spectra of the two chlorine isotopic species of 2-chlorothiophene have been measured in the region 26 500 - 40 000 MHz. For both isotopic species, the rotational constants of the ground state and one vibrationally excited state were determined, as well as the centrifugal distortion coefficients of the ground state. From the hyperfine splitting of the rotational lines, the nuclear quadrupole coupling constants were calculated. The values in MHz are for 35 Cl: and for 37 Cl: χ aa = -74.77 ±0.05, χ bb =37.51 ± 0.17, χ cc =37.25 ± 0.18 χ aa = -58.98 ±0.09, χ bb =29.55 ± 0.26, χ cc =29.43 ± 0.28 in the principal-axes system of the molecule.

We have investigated the internal vibrations of metal hydrate complexes in ionic single crystals and their interactions with the phonon system of the lattice, by observing the Raman spectra and infrared reflection spectra with polarized light at different temperatures T(2 K ≦ T ≦ 300 K). As special systems the octahedral nickel hydrate complexes in NiSnCl 6 · 6 H 2 O, NiSnCl 6· 6 D 2 O and in NiSO 4 · 6H 2 O. NiSO 4 · 6D 2 O have been chosen. For NiSnCl 6 ·6 aqu a complete interpretation of the spectra is given, starting from the assumption of isolated metal hydrate complexes and SnCl 6 -- -ions as structural units. The discussion of the spectra of the sulfate crystal is based on the corresponding assumption. However, here an unambiguous assignment of all lines observed was not possible. The most prominent feature of all spectra is the strong temperature dependence of the line widths which is much more pronounced than in anhydrous crystals in the same temperature interval. This effect is qualitatively explained in terms of the anharmonicity of the potential by which the water molecules are bound in the crystal lattice. Simple models for this potential are discussed.

An analysis of the rotational spectra in torsional excited states is given for propane, dimethylsilane and dimethylsulfide. The analysis is based on the Hamiltonian for the quasi-rigid model. The potential barrier V 3 and one additional potential coefficient V′ 12 were determined. The splitting within the multipletts could be reproduced, but not the spacing between them.

The Barkhausen spectra, i. e. the pulse height distribution of pulses induced in a coil by spontaneous magnetization changes, have been measured for two Fe samples. Particular emphasis was given to the effect of the instrumental time constant compared to the Barkhausen time constant and to a low instrumental cut-off (3.5 x 10 -8 magnetic cgs units). No maximum was found in the Barkhausen spectra.

The intensity distribution function P(I) for the incoherent superposition of interacting stationary waves far from thermal equilibrium and coupled to many other waves e. g. in active photon and phonon systems is determined analytically for a specific interaction model. The model consists of Nm ⪢ 1 equivalent waves concentrated in a small frequency band which interact through their intensities alone. P{I) refers to N m ′′＜ N m of these waves. The remaining Nm′=Nm-Nm′′ waves then act as a reservoir. P(l) is shown to be asymptotically given by a Beta-distribution for N m ′⪢ 1. It is found that the interactions thermalize each individual wave which otherwise would be laser like concerning its statistical properties. The photon counting distribution associated with P(l) is also discussed. For N m ′′ comparable to N m , it can differ significantly from the photon counting distribution of Nm′′ independent thermal waves.

This paper contains further applications on symmetrical liquid mixtures of the molecular thermodynamic theory which has been developped in part I of this series. The essential feature of this theory is the superposition of "chemical" and “random” exchange equilibria between “complexes” formed by a given molecule and its z nearest neighbours, thus allowing a unified treatment of the thermodynamic phenomena in binary liquid mixtures using the equilibrium constant K of the ideal law of mass action and the energy w of pair interactions as parameters. The temperature and pressure dependences of K and the evaluation of experimental excess enthalpy and excess volume data are treated. Formulas and examples for the calculation of K and w from isothermal and non-isothermal vapour-liquid equilibrium data are given. The conditions for azeotropy with minimum or maximum vapour pressure, resp., are derived. Melting curves for a symmetric eutectic system with superposed miscibility gap are discussed. Further models for partially miscible liquids with competing self-association and complex-formation are treated showing the phenomenon of two separated miscibility gaps.

The Structure of Hexamethyl-tetracarbahexaborane(6) has been investigated by gas electron diffraction. The resulting structure parameters are given.

A method is described which permits a rapid determination of the electron density in plasmas from the spectral line Hα broadened by combined Stark and Zeeman effect.

Measurements of dye laser output power vs. oxygen content of the dye solution are reported and compared with a simple theoretical model. The triplet lifetime of rhodamine 6G in oxygen-free methanol at room temperature is seen to lie between 1 and 100 μsec, with 2 μsec giving the best fit of the experimental data.

Cross sections for collisionally induced disorientation of of the Na (3 2 S½) sublevels have been measured for the C 1 - C 4 saturated hydrocarbons. The strong increase of the cross sections with the number of buffer gas electrons can be explained by using the model of spin-orbit-relaxation.

The formation of N 2 O + (Ã 2 Σ + ) from N 2 O by photons is strongly influenced by the Rydberg states 3pπ and 4pπ converging to Ĉ 2 Σ + .N (3s 4 P) can be formed by partial photo dissociation of N 2 O only together with metastable NO.

A relation between CH stretching frequencies and s characters of the corresponding bonds is obtained, using the data of CH, CHD and CHD 2 , groups in hydrocarbons and the maximum overlap approximation [MOA] method. A relationship between dissociation energies and overlap integrals of CH bonds is also found. A new formula for calculating bond energies in hydrocarbons is proposed.

In a binary system of a nematic and a cholesteric liquid crystal an inversion of the helix - sense has been observed at a definite composition x n by measurements of circular dichroism and optical rotatory power. The inversion is accompanied by a decrease of the helical twisting power approaching zero at x n .

Quenching of POPOP fiuorecsence by nitrobenzene follows a diffusion controlled dynamic mechanisme. The characteristic halve value concentration is linearly depending on the viscosity of the used benzene-paraffinoil mixtures. Inclination and axis intersection of this linear correlation give information on the effective quenching radius (a ≈ 17.4 x 10 -8 cm) and on the quenching probability per collision (γ≈ 0.7).

The decomposition of ammonia by second order kinetics in a wire to cylinder type electric discharge has been studied at different initial pressures in the range of 50 - 200 mm Hg at various applied voltages and various discharge currents. Even though the initial pressures are different, yet, in every case the application of the same multiple of the respective starting voltage ensures that the decomposition occurs with the same specific rate.