The structure and properties of the stepped surfaces of MgO and NiO

The static lattice computer simulation method has been used to study the structure and properties of high index faces of MgO and NiO. The (10_n) series of faces can be considered as stepped (001) surfaces and have been studied for both materials. In addition, the (403) and (302) faces which can be considered as stepped (101) surfaces have been studied for NiO. The calculated energies for steps on the (001) face are 3.72×10^?10 and 3.62×10^?10 J m^?1 for MgO and NiO respectively. The NiO energy also requires correction for the crystal field splitting. The energy of steps on the (101) surface is at least an order of magnitude lower. The interaction between the steps is repulsive but of short range. The large variation of surface energy with angle indicates that torque terms cannot be neglected in the analysis of thermal grooving experiments. The step structure is modified by substantial ionic displacements leading to an obtuse step angle. The structure is qualitatively similar for both NiO and MgO. The large distortions are likely to modify the step properties from those deduced by consideration of only the ideal geometry.     

A measurement of surface diffusion across steps on a curved surface (Pd on W)

The surface diffusion of palladium on the curved part of a tungsten crystal is studied by field electron microscopy. The variation of the local coverage distribution is measured by a probe-hole device on the stepped surface region around (001). The measured data allow a determination of the mass transport surface diffusion coefficient D of Pd on W across atomic steps as a function of temperature, coverage and step density. D has been found (1) to be constant for a given step density and for coverages lower than about 5 × 10¹⁴ Pd adatoms/cm², (2) to increase for higher coverages, and (3) to increase with increasing step density for a given coverage. The activation energy of the process is nearly constant (about 24 kcal/mol) for all coverages up to about 6 × 10¹⁴ adatoms/cm², while the pre-exponential factor of D increases with increasing step density. Interpretation of the results gives some information on the diffusion mechanism.     

Substrate steps/adsorbed layer interaction; selective effect on the possible epitaxial relationships: Case of the S/Cu ∼ (111) system

The interaction between monoatomic steps on a vicinal ～ (111) copper surface and the adsorbed sulphur monolayer has been investigated by a method involving the existence of two possible structures of the monolayer. The parts of the surface occupied by each structure, which are equal on a perfect (111) crystal plane, and differ on a vicinal surface (selective effect of the steps), have been deduced from LEED intensity measurements. Experiments on a wide range of surfaces have revealed a very strong selective effect of the steps, even for misorientations as small as 4° off the (111) plane. On surfaces with $\text{〈3}\text{2}\text{1}\text{〉}$ steps, only one monolayer structure exists, which appears to fit perfectly the steps. The behaviour of the other surfaces having the same misorientation angle allowed us to devise a model of the step/monolayer interaction, which includes a partial decomposition of a step into the two nearest $\text{〈3}\text{2}\text{1}\text{〉}$ steps (2D “faceting”). A general framework for exploiting experiments of the kind described above, on other adsorption systems, is also outlined.     

Reaction of molecular hydrogen with the 100 face of MoO3: I. Kinetics in the low pressure range (10−8–10−6 Torr) in the presence of platinum particles

Three successive processes are observed when the 100 face of a MoO₃ single crystal covered with a specific density of platinum particles of known diameter is exposed to molecular hydrogen in a pressure (P) domain between 10^?8 and 10^?6 Torr. During the first step, called the activation step, the rate process is a function of the surface area of the Pt particles and it is slightly thermally activated. During this activation step, H₂ dissociatively chemisorbed on the platinum surface and the hydrogen atoms are inserted into the MoO₃ surface layers. The inserted atom is partially ionized, the electrons given to the lattice reducing Mo⁶⁺ into Mo⁵⁺ and Mo⁴⁺. The rate of hydrogen insertion (V_a) in the activation step increases about linearly with time. The activation step is followed by a stationary step where V is independent of the extent of the Pt surface, V = 0.7Z(1?X), where Z is the number of collisions between H₂ and the MoO₃ surface and X the electronically reduced fraction of the surface area. $\text{X =}\text{a}\text{P}\text{(1 + a}\text{P}\text{)}$, where a is a function of the temperature only. In the stationary step, the platinum particles do not play any role and molecular hydrogen is dissociatively chemisorbed on the MoO₃ surface. The stationary step is followed by a deceleration step. The slowing down of the reaction rate is due to the formation of fractures within the crystal. During all these three steps, the surface is self-cleaning, since protons diffuse into the bulk. The final product of the insertion process would be H_1.6MoO₃, the properties of which have been studied in detail elsewhere. The model which is summarized above is very different from that which would result from the classical views on the so-called hydrogen spillover process since the Pt surface producing the H atoms spilling over the surface would operate only during the activation step.     

Magnetic properties of paramagnetically doped crystals Fe3+, Nd3+ and Ho3+ in various compounds

In this work we calculate the energy levels, wave functions and transition probabilities for a number of compounds whose crystal field parameters have been determined. We introduce a convergence criterion in the diagonalization of the Hamilton matrices dependent upon a self consistency test on the eigenvectors. This assures us of numerically accurate wave functions.First we calculated energy level and susceptibility differences in (Nd³⁺)PbMoO₄ dependent on the multiplicative constants θ_n, used with the published A_l^m to determine the crystal field parameters B_l^m, (B_l^m = θ_nA_l^M). Calculated energy levels as a function of external magnetic field strength and orientation are compared with experimental results for three different sets of published crystal field parameters, B_l^m, for (Fe³⁺)TiO₂. The ground state energy levels, and wave functions, have been calculated for the non-Kramers Ho³⁺ ion in the crystals PbMoO₄, LaCl₃ and HoCl₃. Easily distinguishable variations in the temperature dependence of the X_zz component of the susceptibility are found as a function of the host crystal. It is pointed out that susceptibility calculations, based upon measured crystal field parameters, in conjunction with subsequent susceptibility measurements, provide a good check on the validity of the crystal field parameters.     

The vibration-rotation spectrum of methinophosphide: l-Type doubling, l-type resonance and the ν2, 2ν2, and 3ν2 bands of H12CP; The ν1 and ν2 bands of H13CP

The vibration-rotation bands ν₂, 2ν₂, and several “hot” bands of H¹²CP have been recorded and assigned. The states with v₂ = 2, perturbed by l-type resonance and l-type doubling effects have been analyzed on the basis of the existing theory. The energy difference between the 02²0 and the 02⁰0 states was found to be 17.5095 (19) cm^?1. Because of insufficient data, the states with v₂ = 3 could not be corrected for l-type resonance interaction and therefore only an effective l-type doubling constant was obtained. The ν₁ and ν₂ bands of the H¹³CP isotopic molecule (present at natural concentration) were also identified and their spectroscopic constants obtained. The value of I_e for H¹²CP is found to be 25.18793 (26) amu Ų.     

Effect of dislocations on the lattice thermal conductivity of superconducting niobium

Thermal conductivity measurements on single crystal Nb samples in the superconducting state have demonstrated a resonant scattering of thermal phonons at roughly 5 × 10¹⁰Hz. The assumption of a mechanical resonance associated with the dislocation structure accounts for the present data and is consistent with other data found in the literature. The thermalization of phonons at an abraded sample surface, and the attendant failure of the relation l^?1 = ∑_jl_j^?1 for phonon mean free paths, was also observed.     

The evolution of a crystal surface: Analysis of a one-dimensional step train connecting two facets in the ADL regime

We study the evolution of a monotone step train separating two facets of a crystal surface. The model is one-dimensional and we consider only the attachment-detachment-limited regime. Starting with the well-known ODEs for the velocities of the steps, we consider the system of ODEs giving the evolution of the “discrete slopes.” It is the l²-steepest-descent of a certain functional. Using this structure, we prove that the solution exists for all time and is asymptotically self-similar. We also discuss the continuum limit of the discrete self-similar solution, characterizing it variationally, identifying its regularity, and discussing its qualitative behavior. Our approach suggests a PDE for the slope as a function of height and time in the continuum setting. However, existence, uniqueness, and asymptotic self-similarity remain open for the continuum version of the problem.     

Quantum effects on the step interaction energy and the equilibrium shape of crystals

This paper shows that, due to quantum effects associated with surface states forming standing waves at steps surfaces, the leading term of the surface steps interaction energy near to a facet goes like p², where p is the surface slope. This term dominates over the p³ contribution of the existing theoretical model predictions and therefore the equilibrium shape of the crystal near the flat surface of size x₀ is not singular but goes like (x − x₀)².     

Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

Thermal desorption and surface lifetimes of bromine and iodine adsorbed on an ionizer of LaB6

Thermal desorption of bromine and iodine from an ionizer surface made of cold pressed and sintered LaB₆ powder has been studien in the temperature interval 800–1300°C. A new technique, where the extraction field is accelerating only during short intervals, has been developed to monitor separately the neutral desorption of readily ionized elements. The technique has been combined with the modulated beam and the modulated voltage methods for measurements of residence times and ionization efficiencies. It has also been combined with the temperature programmed desorption method used for determination of the Arrhenius parameters of desorption. The following values were obtained for l_? and l₀, the activation energies of ionic and neutral desorption, and for the corresponding pre-exponential factors C and D (D = 4C) for halogens): Bromine: l_? = 3.8 eV, l₀ = 4.3 eV, C = 2.0 × 10¹³ s^?1; Iodine: l_? = 3.4 eV, l₀ = 3.7 eV, C = 1.1 × 10¹³ s^?1. The ionization efficiencies measured at 1100°C, 0.95 for bromine and 0.7 for iodine, correspond well to what is given by the Saha-Langmuie equation using a work function of 2.7 eV. All measurements were performed with the number of adsorbed particles well below 10¹⁷ atoms/m². For higher coverages l_? was found to increase linearly by about 0.15 eV for an adsorption of 10¹⁸ atoms/m².     

New analysis of the Coriolis-interacting v2 and v5 bands of CH3Br and CH3Br

The and fundamental bands of CH₃⁷⁹Br and CH₃⁸¹Br have been studied by Fourier transform infrared spectroscopy with an unapodized resolution of 0.004 cm⁻¹, corresponding to an improvement of one order of magnitude compared to previous studies. For both isotopomers, some 2427 (2239) lines were newly assigned for the parallel and the perpendicular bands and, in addition, 80 perturbation-allowed transitions were also added. The ground-state axial rotational constants A₀ were redetermined from allowed and perturbation-allowed infrared transitions observed in the v₂ and v₅ bands around the local crossing. The A₀ values obtained for both isotopomers are more accurate but fully compatible with those obtained previously. Using those results, and the variation of the rotational constants with vibration, new accurate equilibrium constants A_e and B_e have been also determined for CH₃⁷⁹Br and CH₃⁸¹Br. The excited states v₂=1 and v₅=1 are coupled by Coriolis-type interactions (Δl=±1,ΔK=±1) and (Δl=?1,ΔK=±2), while the l₅=±1 levels of v₅ interact also through “l(2,2)”-type interaction (Δl=±2,ΔK=±2). The Coriolis coupling term was determined to be for CH₃⁷⁹Br and for CH₃⁸¹Br. All interaction parameters have been determined with higher accuracy, compared to previous studies. A total of 4213 (3704) line positions with J?68(64) and K?16(11) including all available data was fitted using 20 (18) parameters with a root-mean-square deviation of 0.0007 (0.0006) cm⁻¹ for CH₃⁷⁹Br and CH₃⁸¹Br, respectively. Two different but equivalent forms of reduced Hamiltonians with two different sets of constrained constants were successfully applied according to Lobodenko's reduction [J. Mol. Spectrosc. 126 (1987) 159]. The ratio of the transition moments, |d₂/d₅|=1.65, and a positive sign of the Coriolis intensity perturbation d₂×ζ₂₅×d₅ were determined. Therefore, it has been possible to generate an accurate prediction of the whole spectrum between 1200 and 1650 cm⁻¹, including Q branches.     

From crystal steps to continuum laws: Behavior near large facets in one dimension

The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by explicit computations the emergence from step motion laws of continuum-scale power series expansions for the slope near the edges of large, flat surface regions (facets). We consider surface diffusion kinetics via the Burton, Cabrera and Frank (BCF) model by which adsorbed atoms diffuse on terraces and attach-detach at steps. Nearest-neighbor step interactions are included. The setting is a monotone train of N steps separating two semi-infinite facets at fixed heights. We show how boundary conditions for the continuum slope and flux, and expansions in the height variable near facets, may emerge from the algebraic structure of discrete schemes as N→∞. Our technique relies on the use of self-similar discrete slopes, conversion of discrete schemes to sum equations, and their reduction to nonlinear integral equations for the continuum-scale slope. Approximate solutions to the continuum equations near facet edges are constructed formally by direct iterations. For elastic-dipole and multipole step interactions, the continuum slope is found in agreement with a previous hypothesis of ‘local equilibrium’.     

Long life potential resonances in 16O12C scattering from an l-dependent absorptive potential

A semiclassical theory is applied to elucidating essential features of ¹⁶O¹²C scattering from an l-dependent absorptive potential. Long life potential resonances do occur for surface partial waves and cause an enhanced backangle differential cross section and a typical interference pattern at intermediate angles. The almost constant frequency of the backangle oscillation is, however, essentially due to the narrow l-window characteristic of surface transparent potentials.     

Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems

From measurements of the decrease in the heat (enthalpy) of transition in the solid phase using differential scanning calorimetry, the apparent molar heats of solution, slope ΔH_t/x, the partial molar heats of solution at infinite dilution, χ, and the heats of solution, ΔH_s^°, of Tl⁺ in CsNO₃ crystal and Cs⁺ in TlNO₃ crystal and Rb⁺ in CsNO₃ crystal and Cs⁺ in RbNO₃ crystal along with their recovered lattice energies, ΔH_L^°, are reported. ΔH_s^° of Tl⁺ and Rb⁺ in CsNO₃ crystal are each found to be negligible or zero representing an ideal solid solution, i.e. ΔH_mix=0. The complete phase diagrams of the TlNO₃-CsNO₃ and RbNO₃-CsNO₃ systems with details of the sub-solidus regions are included. The properties of Tl_(1−x)Cs_xNO₃ and Rb_(1−x)Cs_xNO₃ compositions are discussed in terms of a ‘mixed crystal’ or ‘crystalline solid solution’ in relation to parallel compositions of Tl_(1−x)Rb_xNO₃.     

Elastic scattering of deuterons by 14C from Ed = 4 to 10 MeV

Angular distributions for the elastic scattering of deuterons by ¹⁴C were measured at nine energies between E_d = 4.2 and 10 MeV. Excitation functions were taken in 50 keV steps from E_d = 4 to 10 MeV. A resonance was observed at E_d = 4.5 MeV, which corresponds to an excitation energy of 14.41 MeV in ¹⁶N. An analysis using an optical model plus a single-level formula derived from the R-matrix formalism yields an l-value assignment of l = 4 for this resonance. Of the three J^π values allowed for l = 4 (J^π = 3⁺, 4⁺, 5⁺), the value of J_π = 3⁺ is found to be slightly preferred. Possible identification of this resonance with an analog in ¹⁶O is discussed. The angular distributions measured at off-resonance energies were analyzed with an optical-model potential which has a surface-peaked imaginary well. The energy dependence of the real and imaginary well depths are explicitly determined in the present work for E_d = 4 to 10 MeV. The best-fit optical-model parameters obtained from the present study are compared to those from the ¹⁴N(d, d)¹⁴N work.     

Higher overtones of the bending vibrations of the ground states of 12CS2 and 13CS2

Large numbers of ‘hot’ bands in the first electronic absorption systems of ¹²CS₂ and ¹³CS₂ have been analyzed from plates taken at high dispersion, and accurate rotational constants have been obtained for the overtones of the ground state bending vibration up to v₂ = 6 and l = 3 for ¹²CS₂ and v₂ = 4, l = 2 for ¹³CS₂. The energy differences between the various levels with the same l value have been determined to an accuracy of about ±0.006 cm^?1, but (because of the parallel polarization of the electronic transition) the absolute energies of levels with l > 0 cannot be obtained.     

Modification of Cd1−xMnxTe crystal surface layers by nanopulsed laser irradiation

The surface modification of Cd_1−xMn_xTe (x = 0-0.3) crystal wafers under pulsed laser irradiation has been studied. The samples were irradiated by a Q-switched ruby laser with pulse duration of 80 ns. Optical diagnostics of laser-induced thermal processes were carried out by means of time-resolved reflectivity measurements at wavelengths 0.53 and 1.06 μm. Laser irradiation energy density, E varied in the range of 0.1-0.6 J/cm². Morphology of irradiated surface was studied using scanning electron microscopy. The energy density whereby the sample surface starts to melt, depends on Mn content and is equal to 0.12-0.14 J/cm² for x ≤ 0.2, in the case of x = 0.3 this value is about 0.35 J/cm². The higher Mn content leads to higher melt duration. The morphology of laser irradiated surface changes from a weakly modified surface to a single crystal strained one, with an increase in E. Under irradiation with E in the range of 0.21-0.25 J/cm², the oriented filamentary crystallization is observed. The Te inclusions on the surface are revealed after the irradiation of samples with small content of Mn.     

The vibration-rotation spectrum of D12CP in the region of the ν2 band: The spectroscopic constants for the states 0000, 0110, 0200, and 0220 and the bond lengths of the molecule

The vibration-rotation spectrum of DCP has been recorded with a resolution of 0.004 cm^?1 in the spectral region extending from 575 to 475 cm^?1. The fundamental band ν₂ and the “hot” bands from the vibrational level (01¹0) to the levels (02⁰0) and (02²0) have been identified and analyzed. A total of 347 infrared transitions have been measured and their wavenumbers together with 13 microwave or millimeter-wave frequencies have been fit simultaneously to obtain 15 spectroscopic constants including those arising from l-type doubling and l-type resonance. The agreement between the calculated and measured wavenumbers of nonblended lines is usually within 1 × 10^?4 cm^?1. These constants, used in conjunction with the ones previously obtained for the molecule, allow the calculation of the anharmonicity constants x₂₂ and g₂₂ and of the second-order vibration-rotation interaction constants γ₂₂ and γ₁₁. Although many of the γ's are still missing because an insufficient number of bands have been analyzed, the equilibrium bond lengths for the molecule have been recalculated using the improved set of first-order vibration-rotation interaction constants: r_e(CH) = 1.06596(11)Å and r_e(CP) = 1.540452(18)Å.     

Scaling and universality in models of step bunching: the “C<Superscript>+</Superscript>–C<Superscript>-</Superscript>” model

We recently introduced a novel model of step flow crystal growth – the so-called “C⁺–C^-” model [B. Ranguelov et al., C.R. Acad. Bulgare Sci. 60, 389 (2007)]. In this paper we aim to develop a complete picture of the model’s behaviour in the framework of the notion of universality classes. The basic assumption of the model is that the reference (“equilibrium”) densities used to compute the supersaturation might be different on either side of a step, so C_L/C_R ≠ 1 (L/R stands for left/right in a step train descending from left to right), and that this will eventually cause destabilization of the regular step train. Linear stability analysis considering perturbation of the whole step train shows that the vicinal is always unstable when the condition C_L /C_R >1 is fulfilled. Numerical integration of the equations of step motion combined with an original monitoring scheme(s) results in obtaining the exact size- and time- scaling of the step bunches in the limit of long times (including the numerical prefactors). Over a broad range of parameters the surface morphology is characterized by the appearance of the minimal interstep distance at the beginning of the bunches (at the trailing edge of the bunch) and may be described by a single universality class, different from those already generated by continuum theories [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002), J. Krug et al., Phys. Rev. B 71, 045412 (2005)]. In particular, the scaling of the minimal interstep distance l_min in the new universality class is shown to be l_min = (S_n /N)^1/(n+1), where N is the number of steps in the bunch, n is the exponent in the step-step repulsion law U ~ 1/d₀ ⁿ for two steps placed a distance d₀ apart and S_n is a combination of the model parameters. It is also shown that N scales with time with universal exponent 1/2 independent of n. For the regime of slow diffusion it is obtained for the first time that the time scaling depends only on the destabilization parameter C_L/C_R. The bunching outside the parameter region where the above scaling exists cannot be assigned to a specific universality class and thus should be considered non-universal.