Rare Gas Crystals Research Articles

Systematic calculations of the band structures of the rare-gas crystals neon, argon, krypton, and xenon.

Scalar relativistic self-consistent calculations of the band structure of Ne, Ar, Kr, and Xe have been performed with the augmented-plane-wave method using the Hedin-Lundqvist local-density (LD) expression for exchange and correlation. The trends with increasing atomic number in this inert-gas solid series are presented for the valence-band width, LD band gap, and for low-lying conduction-band eigenvalues. A simplified form of self-energy correction that accounts for dynamical exchange and correlation processes to the single-particle excitations is included. Comparisons are made with previous studies using different methods. The present approach is most reliable for valence-band properties and gives semiquantitative agreement with experimental values of the band-gap and conduction-band separations.

Growth and roughening transition of rare gas crystals

The crystals of krypton and xenon were grown from the vapor on a Cu substrate in a temperature range from 85 K to their melting point (Kr 115.8 K, Xe 161.4 K) and at low supersaturations below 1%. Faceted crystals grew at lower temperatures, but the facets (111) and (100) disappeared completely and the crystals became rounded at ≈ 93 K for Kr and ≈ 129 K for Xe. The transition temperatures were identified as respective roughening temperatures. The addition of He gas as impurity had no influence on the roughening temperature. Closer to their melting point (within ≈ 5 K below it), the crystals grew in a completely rounded shape. The results are compared with theories, computer simulations and other experiments.

Self-consistent LDA approach for closed-shell atomic liquids

Abstract A simple local density scheme, suitable for closed-shell systems, is used to calculate the polarizability of rare-gas liquids. To assess its accuracy the scheme is first applied to the calculation of the total energy of rare-gas crystals, which is then analysed in terms of Lennard-Jones parameters. The accuracy is comparable to that obtained in Xα band calculations. The environmental potential in the liquid phase is constructed using published molecular-dynamics results for the pair correlation function of a Lennard-Jones fluid. The calculated liquid polarizabilities are of the typical LDA quality. The comparison between the isolated atom and the liquid phase shows in all cases a small decrease in polarizability in accord with simple considerations of compression effects in the condensed phase.

High density excitation of rare gas crystals for stimulated emission

Excimer densities of 5X10 18 cm -3 and a light output of 10 7 W at 172, 145 and 128 nm is obtained from electron beam excited rare gas crystals.

Observation of intense two-beam positron diffraction and the precise determination of the positron band gap in rare-gas crystals.

We have measured the energy dependence of the elastic specular reflection of positrons from the (111) surfaces of solid rare-gas crystals. For each sample we observe an intense first-order Bragg peak with a profile closely resembling the ideal ''top-hat shaped'' profile first derived by Darwin. The well-defined width and center of the peak enables us to determine the positron-energy gap and inner potential as a sensitive test of the positron--gas-atom interaction in the solid.

On an adiabatic theory of multielectron systems

An adiabatic approximation is constructed for the outer atomic electron using its weak bond as compared to other electrons. The adiabatic approach is well-grounded for a helium atom and is extended to other atoms and crystals of rare gases, a functional dependence being established between electron properties of crystals and free atom constants.

Up-conversion by V-E transfer in rare gas crystals doped with molecular defects

Electronic emission from the a 1Δ g, b 1Σ + g and C 3▵ u states of 16O 2 and 18O 2 induced by IR excitation o f 13C 18O has been observed in rare gas crystals doped with oxygen and carbon monoxide. The concentration dependence, the influence of O 2 isotopic substitution, the matrix effects and the time development of the various emissions have been investigated. The results suggest that upconversion results from intermolecular V-V transfer between CO and O 2 followed by intramolecular intersystem crossing and internal conversion in O 2.

Evaluation of brillouin scattering intensities from rare gas crystals

Corrections to the dipole-induced-dipole theory coming from both electronic overlaps and dispersion-force effects are introduced into the self-consistent equation for the effective atomic polarizability and applied to the case of rare-gas crystals. We show that the one-phonon expansion for Brillouin-scattered intensities can be rigorously solved, with the difference from a pure dipole-induced-dipole theory that Brillouin intensities now contain three microscopic quantities of the system. In the case of krypton crystals these quantities, which are related to the corrections to elasto-optic coefficients, are estimated by using experimental data. A comparison with theoretical predictions and experimental results is discussed. In the case of neon, argon and xenon available experimental data are not sufficient to estimate the three quantities, so just the rates of the elasto-optic coefficients are discussed. A slight discrepancy might be due to an overestimate of the anisotropic short-range contribution coming...

Triplet states of CO trapped in rare gas crystals

Vibrational progressions due to the a 3Π, a′ 3Σ+, d 3Δ, and e 3Σ− states of CO in Ar, Kr, and Xe crystals are observed in absorption. Two groups of phonon sidebands separated from the zero phonon lines by about 4 and 8 meV for the a′ 3Σ+ and d 3Δ states are attributed to librations and to localized phonons. The broad absorption bands, the even broader emission bands, and the large Stoke shift of the a 3Π transition are treated in terms of a configuration coordinate model by a momentum analysis. A quadratic coupling has to be invoked with relaxation energies in the excited states increasing from 14 meV for Ar to 95 meV for Xe and with relaxation energies in the ground state increasing from 29 meV for Ar up to 1278 meV for Xe. The changes of the configuration coordinate of 0.2 to 1.5 Å are also discussed with the help of two pair potential models.

Vibrational states of surface crystal atoms

AbstractThe momenta–time correlation functions and their spectral densities are studied for rare gas crystal atoms at the (100) and (110) surfaces. Their characteristics essentially differ from the bulk behaviour for particles lying in the surface plane, but already in the third subsurface atomic plane the differences from the bulk crystal spectrum are only slight. Distinct quasi‐resonance peaks observed in the spectral densities may be an information source for experimental analysis of the surfaces.

Nonlinear Excitation of Pure and Doped Rare Gas Crystals

AbstractThe power dependence up to the destruction limit and the coefficient of two photon absorption in Xe and Kr crystals are derived from transmission and luminescence experiments. A temperature dependent reduction of the quantum efficiency for luminescence at high power densities due to exciton—exciton annihilation is observed.

Photoelectron spin-polarization spectroscopy: A new method in adsorbate physics

Energy-, angle-, and spin-resolved photoemission results from adsorbates are discussed. The measurements employed circularly polarized synchrotron radiation from BESSY, a special photoelectron spectrometer, and a Mott detector for electron spin-polarization (ESP) analysis. It is demonstrated by the example of physisorbed Xe, Kr, and Ar atoms how this method provides independent information complementary to intensity spectroscopy. Almost complete ESP parallel or antiparallel to the photon spin measured at certain conditions allowed a direct assignment of symmetries of electronic states. Sharp photon-inducednp→ n's resonances (ΔE<80 meV) have been observed, which show only small relaxation shifts compared to the gas phase. The ESP provided an unambiguous quantum-number labelling of the transitions and revealed an additional line splitting due to symmetry lowering on the surface. Photo-ESP spectroscopy is further demonstrated as to increase spectral resolution, to gain an insight into dynamical relaxation mechanisms of electronically excited adsorbates, and to be a sensitive probe of the “local” symmetry. A detailed discussion is given of line positions and ESP when going from a commensurate overlayer via an incommensurate monolayer and multilayers of different thickness onto a 3D rare-gas crystal.

Self-consistent calculations of the dynamic and thermodynamic properties of rare gas solids

On the basis of the reduced second order self-consistent phonon approximation the dynamic and thermodynamic functions of rare-gas crystals are computed and compared with experimental and other theoretical data in the low and high temperature limits. The instability and critical parameters are calculated also. The system of self-consistent equations is solved for the Morse, Rydberg and Varshni models of interatomic interactions.

Average square atomic displacement: A comparison of the lattice-dynamics, molecular-dynamics, and Monte Carlo results.

Molecular-dynamics (MD) and Monte Carlo (MC) calculations of the mean-square displacement (MSD) have been carried out for a fcc nearest-neighbor Lennard-Jones model for a wide range of temperatures and lattice spacings. The lattice-dynamics (LD) calculations of the harmonic and the lowest-order anharmonic (cubic and quartic) contributions to the mean-square displacement were performed for the same potential model as in the MD and MC calculations. The dependence of MSD on sample size (N) has been examined in detail in MC calculations and the results are presented for a 256-atom sample as well as the extrapolated sample of the infinite size. The MD results are given only for the 256-atom sample size. The LD results for the harmonic and quartic contributions to MSD were obtained for almost completely converged Brillouin-zone (BZ) sums, whereas the cubic BZ sums were uncertain by 2%. It is estimated that the N=256 sample size used in MD calculations produces a result which is somewhere between 10% and 20% smaller than the value converged with respect to N. However, the general temperature dependence of MSD is the same in MD, MC, and LD results for all temperatures at the highest lattice spacings examined, while at higher volumes and high temperatures the results differ. This indicates the importance of higher-order (e.g., ${\ensuremath{\lambda}}^{4}$) perturbation-theory contributions in these cases. These results represent the best picture yet obtained for the MSD from the first such calculation for a rare-gas crystal by the MD, MC, and LD methods.

Adequacy of lattice dynamics for high-temperature point-defect properties.

Comparison with existing Monte Carlo and molecular-dynamics data of novel quasiharmonic lattice-dynamics (LD) calculations for formation and migration of lattice vacancies in rare-gas crystals at melting shows that the effect of residual anharmonicity on atomic diffusion is not large. Inclusion of vibrational contributions to the free energy and pressure ensures, for the first time, thermodynamic consistency between LD results at constant volume, pressure, and lattice spacing. Lattice-statics predictions are badly in error. Constant-volume defect entropies are negative and surprisingly large.

The migration of point defects on bcc surfaces using a metallic pair potential

An ab initio ion-ion pair potential derived from the theory of metals for bulk Na is employed to investigate point defect jump dynamics on bcc (211), (110) and (100) surfaces using molecular dynamics. This pair potential produces bcc slabs that are stable to shear, as opposed to pair potentials modeling rare gas interactions. On the channeled bcc (211) surface adatoms undergo a cross-channel exchange mechanism akin to that observed on the fcc (110) surface of the Lennard-Jones (LJ) crystal. Adatom migration parallel to the channels is much enhanced if compared to the latter case, parallel jump events being more frequent than cross-channel exchanges. These results are in accord with experimental FIM findings in metallic crystals of the two structures. The consequences of the softer repulsion of the metallic interaction (i.e., versus LJ) on point defect properties are most apparent on the compact bcc (110) face. Results for this face are reminiscent of the loosely packed fcc (100) LJ surface rather than of the close packed fcc (111) one. The mobilities of adatoms on bcc (211) and (110) surfaces are comparable. On the bcc (100) the adatom mobility is much lower instead, in accord with experiment. On the latter face adatoms are seen to migrate by an exchange mechanism, in addition to performing direct jumps between lattice sites above the surface. This is the first observation of adatom migration via exchanges involving an atom of the surface layer on isotropic surfaces. Surface vacancies are mobile on all three faces. Their mobility on the surfaces of bcc Na is overall higher than on those of fcc rare gas (LJ) crystals. The reverse is true in general for adatoms, with the noteworthy exception of channel diffusion on bcc (211) versus fcc (110). This behaviour is interpreted in terms of structure, surface packing and repulsion stiffness in the interatomic potential.

Average phonon decay rate in anharmonic insulators.

The rate ${\ensuremath{\Gamma}}_{\mathrm{Qj}}$ for a phonon to decay by lowest-order anharmonic processes is proportional to T for Tg${\ensuremath{\Theta}}_{D}$. The Brillouin-zone average \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} of ${\ensuremath{\Gamma}}_{\mathrm{Qj}}$ is discussed in detail. An approximate formula for \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} is found which agrees accurately with an explicit calculation for an fcc crystal with nearest-neighbor Lennard-Jones interactions. The Brillouin-zone-average squared anharmonic matrix element is contained in a parameter called ${A}_{3}$ which is the sum of the squares of all third-order force constants. The other important parameter is ${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}, the mean-square frequency which is the trace of the dynamical matrix, or the sum of all diagonal (${K}_{\ensuremath{\alpha}\ensuremath{\alpha}}$(l,l)) second-order force constants.The result is a formula \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}/(${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{1/2}$=${\mathrm{CA}}_{3}$${k}_{B}$T (${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{3}$, where c is (3\ensuremath{\pi}/8)(${d}_{3}$/${f}_{4}$) and ${d}_{3}$ and ${f}_{4}$ are complicated averages over the harmonic frequency spectrum. To an accuracy of \ensuremath{\approxeq}30%, C can be replaced by 1. Thus \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} can be very easily estimated when second- and third-order force constants are known. An ``anharmonicity temperature'' ${\ensuremath{\Theta}}_{A}$ is defined by the formula \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}/(${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{1/2}$=T/${\ensuremath{\Theta}}_{A}$. When T=${\ensuremath{\Theta}}_{A}$, the broadening of the phonons is predicted to be as large on average as the frequency, a signal that perturbation theory is no longer valid.The theory is applied to fcc crystals with Lennard-Jones potentials, and rocksalt-structure crystals with Born-Mayer plus Coulomb potentials describing anharmonic interactions, but a shell model describing harmonic properties. In all cases ${\ensuremath{\Theta}}_{A}$ is found to be only 1 to 2 times greater than the melting temperature. This is compatible with experiment for rare-gas crystals but may overestimate the anharmonic strength in rocksalt-structure ionic materials by as much as a factor of 2. An average decay rate ${\ensuremath{\Gamma}}^{(\ensuremath{\kappa})}$ extracted from experimental thermal conductivity is typically an order-of-magnitude less than \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}.

Thermodynamics (with an emphasis on surface problems)

An elementary presentation of basic thermodynamic notions is given. It is followed by a discussion of the second virial coefficient. This coefficient, although assigned here to gases and vapours in their adsorbed state, receives a much wider significance than the one based on the non-ideality of these gases and vapours. Thus it is shown that space charge effects can be described by means of second virial coefficients. A brief survey of statistical thermodynamics serves to contribute to the solution of such problems as that of the efficiency of lasers and of the temperature dependence (and of the non-additivity) of London-Van der Waals forces. Again the second virial coefficient is made use of, and its relation to the mean field approximation is pointed out. After a concise discussion of the mean field approximation, the problem of the (2 × 1) → (7 × 7) transition of the silicon (111) surface is dealt with, and considerable attention is given to various aspects of surface segregation. These include the segregation at the surface of an alloy A 1+ s B 1− s , in which an order-disorder transition is allowed to take place and in which s is a variable composition parameter. Another aspect is that of the kinetics of the segregation. Starting from irreversible thermodynamics, a simple equation is derived for the diffusion, which is consistent with the mean field approximation. An outline of the thermodynamics of strained solids is given, resulting in a discussion of the physical meaning of the product of the heat of vaporization per unit volume, and the compressibility of cubic crystals. This product, a dimensionless number, varies from 0.1 (rare gas crystals) to 0.6 (alkali metals). As an application, the deformation of the surface region of the (111) surface of silicon crystals obtained by cleavage, is discussed and a reasonable insight is obtained on the basis of the thermodynamics of strained solids.

Summary Abstract: Surface dynamics of rare gas crystals

Summary Abstract: Surface dynamics of rare gas crystals

Estimation of properties of rare-gas solids from compression characteristics of closed-shell ions

The authors present a unified approach to repulsion in ionic and van der Waals solids based on a compressible-ion/atom model. Earlier studies have shown that repulsion in ionic crystals can be viewed as arising from the compression energy of ions, described by two parameters per ion. Here they obtain the compression parameters of the rare-gas atoms Ne, Ar, Kr and Xe by interpolation using the known parameters of related equi-electronic ions (e.g. Ar from S2-, Cl-, K+ and Ca2-). These parameters fit the experimental zero-temperature interatomic distances and compressibilities of the rare-gas crystals satisfactorily. At high-temperature equation of state based on an Einstein model of thermal motions is used to calculate the thermal expansivities, compressibilities and their temperature derivatives for Ar, Kr and Xe. It is argued that an instability at higher temperatures represents the limit to which the solid can be superheated, beyond which sublimation must occur.