Mean Square Amplitudes Of Vibration Research Articles

Effect of mean-square amplitude of atomic vibrations on the creep behaviour of cubic crystals

Correlation between the activation energyQ of high-temperature creep and the Debye-Waller thermal parameterB, which is proportional to the mean-square amplitude of atomic vibrations, has been examined in the case of 17 faced-centred cubic, body-centred cubic and diamond-structure cubic elements. It is observed thatQ is a function ofB, irrespective of the crystal structure;Q decreases asB increases. The correlation is governed by the power-lawQ=Q0(B/B0)M0, whereQ0=0.095eV andM0=−0.62 are numerical constants determined by least-squares fit method, and the constantB0=1 nm2.

Vibrational dynamics in solid α-oxygen: Experimental assessment of spin-phonon couplings

The dynamics of $\ensuremath{\alpha}$-oxygen is investigated by means of high-resolution inelastic neutron scattering. The generalized frequency distribution for vibrational motions is derived from the large-angle spectra. A comparison of spectra on both sides of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\alpha}}}$\ensuremath{\beta} magnetic ordering transition provides a clear indication of the extent of the coupling between the magnetic and lattice degrees of freedom. The specific heat and vibrational mean-square amplitudes are calculated from the spectra and compared with experimental and ab initio results. The latter also aids with the assignment of the spectral features, and to reconcile the present observations with previous measurements.

Symmetry of generalized mean-square vibration amplitudes and their effect on mean and equilibrium bond lengths in benzene, pyridine, and N-oxypyridine

Symmetry properties of generalized mean-square vibration amplitudes for plane six-membered rings belonging to the C2v and D6h symmetry groups are investigated. Corrections to average and equilibrium interatomic distances in benzene, pyridine, and N-oxypyridine are calculated. The character of the corrections in the series of these molecules and their deuterosubstituted analogs is investigated.

Structure and metastability of superheated Al(111)

The high-temperature properties of the Al(111) surface are studied by molecular-dynamics simulation. This surface does not melt below the bulk melting point, but can be superheated. Superheating of metal surfaces has been recently observed in several experiments. A molecular-dynamics study of the structural properties reveals how after going through the superheating regime melting occurs over the whole crystal in a narrow temperature range. The temperature dependence of the surface stress, the mean-square vibrational amplitudes and the anomalous outward expansion of the distance between two top layers are calculated. A transition from superheated to liquid state is analyzed using kinetic description for the formation of liquid nuclei by the Fokker-Planck equation and conservation of heat at the liquid-solid interface.

Premelting on the low-index faces of Palladium

Premelting on the (100), (110) and (111) faces of Pd is investigated by the Molecular Dynamics technique using the semi-empirical potential based on the embedded atom method. Mean-square vibrational amplitudes and the structure factors of the atoms in a plane are used to study the onset of anharmonicity in the three faces as a function of temperature. The premelting temperature is determined by calculating the layer density. The observed order in the surface stability follows the order in the packing density. (110) premelts first at 1300K, followed by (100) and (111) which premelt respectively at 1500K and 1600K. The bulk melting temperature of Pd is found to be (1825±25)K.

Temperature-dependent high-angle electron scattering from a phase-separated amorphous Ge[sbnd]Te thin film

This paper describes the results of experiments and simulations on the thermal diffuse scattering of 200 keV electrons from an amorphous Ge48Te52 thin film using high-angle annular-dark-field (HAADF) imaging in a scanning transmission electron microscope (STEM). This imaging techniques shows that the film is phase separated on a ∼ 10–20 nm length scale into Te-rich and Ge-rich amorphous domains. The average high-angle-scattered intensity increases as the temperature increases from 106 to 300 K. The contrast between the two domains decreases over this same range indicating that, in addition to the atomic-number (Z) effects on contrast for a given temperature, the temperature-dependent vibrational properties and, hence, phonon-scattering behavior are different for the two different elements in this specimen. Simulations of the HAADF intensity based on an Einstein model using a Debye expression for the mean-square vibrational amplitude give qualitative agreement where temperature-dependent contrast variations are due to differences in atomic number, Debye temperature, and atomic-scattering factor.

Short-range order in crystalline, amorphous, liquid, and supercooled germanium probed by x-ray-absorption spectroscopy.

A detailed experimental investigation of the short-range structural properties in condensed phases of germanium is presented. X-ray-absorption measurements at the Ge K edge have been collected in a wide temperature range for different samples. Polycrystalline c-Ge was measured at 77, 296, 450, 620, 782, 920, and 1110 K, close to the Ge melting-point temperature ${\mathit{T}}_{\mathit{m}}$=1210.4 K. Evaporated amorphous Ge was measured at 297 K. Eight independent measurements for liquid germanium have been collected from about 950 K in highly supercooled conditions up to about 1600 K. The spectra show a remarkable temperature trend. By comparison, previous diffraction measurements on l-Ge were limited to two narrow temperature regions only, either above ${\mathit{T}}_{\mathit{m}}$ or around 1500 K, and no measurements in the supercooled liquid region existed. Data analysis has been performed with the GNXAS approach and account has been taken for the presence of double-excitation channels involving 3d and 3p electrons in addition to the 1s. The c-Ge structural results are found in excellent agreement with the known properties. The expansion of the average bond length R is in agreement with thermal expansion data. Mean-square vibrational amplitudes are in excellent agreement with both previous measurements and calculations in the harmonic approximation. The analysis of the signal in liquid Ge has been performed using a technique that allows to extract information on the radial distribution function g(r) directly comparable with molecular dynamics (MD) simulations or previous diffraction determinations.A regular trend is observed in the intensity of the first g(r) peak that decreases from 2.3 to 950 K to about 1.8 at 1610 K. At the same time a widening of the peak and a shift of the rising short distance edge is clearly detected. The data are in excellent agreement with diffraction measurements and recent ab initio MD results by Kresse and Hafner [Phys. Rev. B 49, 14 251 (1994)]. The general relevance of these findings, in connection with the possibility to obtain structural information for liquid systems complementary to that contained in diffraction measurements, is addressed.

Thermal relaxation of Ag(111)

We present the results of an embedded-atom-method molecular-dynamics simulation of the thermal relaxation of Ag(111). Contrary to recent medium-energy ion-scattering experiments [P. Statiris et al., Phys. Rev. Lett. 72, 3574 (1994)], which find that a change in the sign of the surface relaxation takes place upon heating above 750 K (from contraction to expansion), we find the surface layer to relax inwards at all temperatures. The calculated mean-square amplitudes of vibration, on the other hand, agree quite well with experiment. The model, in addition, shows evidence of premelting at a temperature of about 1000 K.

Surface anharmonicities and disordering on Ni(100) and Ni(110).

Recent observations on various low-index metallic surfaces of an extraordinary thermal attenuation of diffracted peak intensities suggest that anharmonic effects are important at high temperatures, though such observations have also been interpreted in terms of disordering processes (premelting and roughening). In order to address this problem, we have carried out an extensive molecular-dynamics investigation of the evolution in temperature of the (100) and (110) surfaces of Ni, with the interactions between atoms described using embedded-atom method potentials. We observe both surfaces to suffer an anomalously large thermal expansion, with a concomitant rapid increase of the mean-square amplitudes of vibration; the latter are found in both cases to be larger in the plane of the surface than out of the plane. An analysis of our simulated low-energy electron-diffraction intensities supports the experimental interpretation of the measured ones in terms of enhanced mean-square displacements. Indeed, anharmonicities are found to appear at temperatures well below the onset of disordering, which occurs at 1200 and 1000 K for the (100) and (110) surfaces, respectively (via in-plane diffusion and adatom-vacancy formation). The onset of disordering proceeds differently on the two surfaces: while it involves essentially only the outermost layer on the (100) surface, both the first and second layer participate in the process on the (110) surface. We also calculate the phonon spectra at high-symmetry points of the surface Brillouin zone, which we find to be in good agreement with experimental values at room temperature. We predict, further, that the temperature-dependent frequency shifts are not significantly softened in comparison with bulk phonons, which suggests that surface phonons are affected by anharmonicity in a nontrivial way. Several of the observed properties can be understood in terms of the larger displacements that surface atoms can afford, because of their reduced coordination compared to bulk atoms.

Lattice-dynamical functions of solids at very high pressures

Abstract Vibrational spectra of face-centered cubical (f.c.c.) solids are investigated at the pressure region, where the quantum-statistical model for the electron energy is applicable. Phonon dispersion curves are obtained for different values of the specific volume. The integration of the phonon spectra over the Brillouin zone yields the zero-point vibrational energy, the Debye temperature, the Gruneisen coefficient, mean-square amplitude of zero-point and thermal vibration, the melting temperature. All quantities under consideration are calculated from the universal functions of the reduced volume, using the scaling relations for given atomic number 2.

Determination of the molecular structure of gaseous dichloromethylvinylsilane, CH2CHSiMeCl2, by electron diffraction

Abstract The molecular structure and conformation of dichloromethylvinylsilane in the gas phase have been determined by electtron diffraction. A force-field, which reproduced experimental vibrational frequencies, was used to calculate mean-square amplitudes of vibration and shrinkage corrections, so that the r α structure could be determined. At room temperature, 67(19)% of the molecules were in a gauche conformation in which the CCSiC dihedral angle was 104(5)°, while the remaining molecules adopted a conformation in which this angle was 0°. The principal refined parameters were r (CC) 131.9(7) pm, r (SiCl) 204.8(2) pm, ∠CSiCl 108.4(4)° and ∠CSiC 115.6(13)°. The SiC(methyl) and SiC(vinyl) distances were refined as a single parameter, with the difference between them being fixed at 2.3 pm. The SiC(methyl) distance was then 186.0(3) pm. The SiCC angle refined to 124.3(13)° in the gauche conformer, with the angle in the other conformer fixed at 1.2° larger than this.

Debye temperature and mean-square amplitudes of vibration of Ti3Al alloys

The meagre experimental data on the physical properties of titanium aluminides, in particular on the alloys belonging to the Ti3Al phase, has prompted the authors to undertake a detailed study of these alloys. In this paper, Debye temperatures and mean-square amplitudes of vibration of four single-phase Ti3Al alloys of composition 22.5, 25.0, 30.0 and 33.0% aluminium are presented. The root-mean-square amplitudes of vibration of stoichiometric Ti3Al are compared with those of other metals having hexagonal-close-packed structures. The variation of the Debye temperature with the percentage of aluminium is also discussed.

Structural disorder within computer-simulated crystalline clusters of alkali halides.

The method of molecular-dynamics (MD) simulation of alkali halides and computer code cluster were developed. The method was applied to calculate structural and kinetic characteristics of small clusters of RbBr, NaBr, NaI, NaCl, KI, and KCl from 10 K to their assumed melting points (${\mathit{T}}_{\mathit{m}}$). The temperature dependence of relative mean-square vibrational amplitudes has a universal character and satisfies the Lindemann criterion of melting in the vicinity of ${\mathit{T}}_{\mathit{m}}$. In spite of the size effect the values of ${\mathit{T}}_{\mathit{m}}$ for all the salts except NaI agree within the error bars of about 100 K with the bulk melting temperatures. The anomalous behavior of NaI at about 200 K below its experimental melting point is interpreted in terms of enhanced mobility of ${\mathrm{Na}}^{+}$ ions linked to the anomalous enhancement of conductivity observed previously for this salt.

Relation of flow stress to the mean-square amplitude of atomic vibrations in cubic metals.

The critical resolved shear stress (CRSS) of 14 face-centered- and body-cubic elements in the temperature range 0 to 300 K has been examined as a function of the mean-square amplitude of atomic vibration measured at room temperature. It is found that the CRSS of elements with a given crystals structure is a unique fonction of . For a given temperature and crystal structure, the CRSS decreases as increases. The dislocation lines composed of atoms with large value have low line tension, and are easy to move in the slip plane of the crystal, resulting in a low CRSS value

Anharmonic effects at the Ni(100) surface.

Using molecular dynamics with embedded-atom potentials, we investigate the role of anharmonicities at the (100) surface of Ni. In accord with recent low-energy electron diffraction (LEED) measurements [Y. Cao and E. Conrad, Phys. Rev. Lett. 65, 2808 (1990)], we observe an anomalously large thermal expansion of the surface, with a concomitant rapid increase of the mean-square amplitudes of vibration, and an extraordinary attenuation of the LEED intensities. These anomalies appear at a temperature of about 900 K, well below the onset of disordering. We find no evidence of anomalous softening of the surface phonons. Our results suggest that the observed anharmonic behavior results solely from enhanced vibrational motion.

The Ge(001) (2 × 1) reconstruction: asymmetric dimers and multilayer relaxation observed by grazing incidence X-ray diffraction

Grazing incidence X-ray diffraction has been used to analyze in detail the atomic structure of the (2 × 1) reconstruction of the Ge(001) surface involving far reaching subsurface relaxations. Two kinds of disorder models, a statistical and a dynamical were taken into account for the data analysis, both indicating substantial disorder along the surface normal. This can only be correlated to asymmetric dimers. Considering a statistical disorder model assuming randomly oriented dimers the analysis of 13 symmetrically independent in-plane fractional order reflections and of four fractional order reciprocal lattice rods up to the maximum attainable momentum transfer q z = 3c ∗ ( c ∗ = 1.77 × 10 −1 A ̊ −1 ) indicates the formation of asymmetric dimers characterized by R> D = 2.46(5) A ̊ as compared to the bulk bonding length of R = 2.45 A ̊ . The dimer height of Δ z = 0.74(15) A ̊ corresponds to a dimer buckling angle of 17(4)°. The data refinement using anisotropic thermal parameters leads to a bonding length of R D = 2.44(4) A ̊ and to a large anisotropy of the root mean-square vibration amplitudes of the dimer atoms ( 〈u 11 2〉) 1 2 = 0.25 A ̊ , ( 〈u 22 2〉) 1 2 = 0.14 A ̊ , ( 〈u 33 2〉) 1 2 = 0.50 A ̊ ). We have evidence for lateral and vertical disp tenth layer below the surface.

An investigation of the adiabatic potential energy surface of a Pseudo-Jahn-Teller complex using X-ray diffraction

X-ray diffraction combined with theoretical results obtained for isolated molecules can reveal many topologic features of the adiabatic potential energy surface (APS) of pseudo-Jahn-Teller Cu(II) complexes. Single-crystal x-ray results of acetatobis (1,10-phenanthroline)copper(II) perchlorate from 10 to 351 K are presented. The observed Cu-O bond length changes of 0.26 and 0.38 A are rationalized in terms of a one-dimensional APS with two nonequivalent minima. The Silver and Getz model of vibronic coupling applied to the temperature variation of the Cu-O bond lengths is not obeyed. The actual structures of the conformers associated with the energy minima were determined from the x-ray data. A means of estimating the pseudo-Jahn-Teller radius using mean-square vibrational amplitudes along the Cu-O bonds is also discussed.

Anharmonic Effects at the (100) and (110) Surfaces of Ni

ABSTRACTWe present the results of a detailed molecular-dynamics investigation of anharmonic effects at the (100) and (110) surfaces of Ni, with the interactions between atoms described using embedded-atom potentials. We find both surfaces to suffer an anomalously large thermal expansion, with a concomitant rapid increase of the mean-square amplitudes of vibration. For the (100) surface, our results for the surface expansion can be directly compared to the low-energy electron diffraction (LEED) measurements of Cao and Conrad;1 the agreement is excellent. The anomalies appear at a temperature of about 900 K for the (100) surface, well below the onset of disordering, thereby confirming that the observed anomalies indeed arise from anharmonicities. Our simulated LEED intensities are found to reproduce well the observed intensities. The phonon spectra in the anharmonic regime will be discussed, and a detailed comparison between the two surfaces will be established.

Iron motion in a five-coordinated heme model

It is shown that the iron motion in a five-coordinated heme model is controlled mainly by the γ 9 out-of-plane vibration in which the iron atom and the axial ligand move like a rigid unit with respect to the rest of the heme, so the heme domes in-phase with the rigid collective motion of the Fe—L unit. A simple model is presented which accounts for the observed strongly anharmonic behaviour of the mean-square vibrational amplitude of the iron atom as a function of temperature.

Ultrafast Laser Superheating of Metal Surfaces

ABSTRACTReflection high-energy electron diffraction with ∼200-ps temporal resolution is used to study the structural dynamics of the closed-packed surfaces of single crystals of lead and bismuth subjected to ultrafast laser heating. By monitoring the temporal evolution of the diffraction streak intensity, information is obtained on the mean-square vibrational amplitude of the surface atoms and the structural integrity of the surface. Pb(lll) is observed to superheat by ∼120 k above the bulk melting point. With increased heating laser intensity, melting is observed to occur subsequent to superheating. Superheating of Bi(0001) by ∼85 K was also observed.