EFFECT OF LATTICE DISTORTION ON THE DEBYE–WALLER FACTOR: II. CRYSTAL SURFACES

1967 ◽  
Vol 45 (8) ◽  
pp. 2661-2670 ◽  
Author(s):  
J. Vail
Keyword(s):  
Lattice Distortion ◽  
Nearest Neighbor ◽  
Waller Factor ◽  
Potential Interaction ◽  
Coupling Constants ◽  
Crystal Surfaces ◽  
Cubic Crystal ◽  
Debye Waller Factor ◽  
Factor Ii ◽  
Cubic Model

The lattice distortion which occurs at the surface of a monatomic metal is investigated by considering a simple cubic model based on a Morse potential interaction between pairs of atoms. Effective nearest-neighbor harmonic coupling constants are estimated for the following cases: (a) an atom in an infinite monatomic cubic crystal; (b) an atom in the surface layer of a semi-infinite monatomic cubic crystal, taking account of lattice distortion, and considering vibrations both parallel and perpendicular to the surface; and (c) an atom cn the surface, vibrating perpendicular to the surface. From these results the relative magnitudes of the Debye–Waller factor are estimated for the various cases. It is found that this model, in contrast to purely harmonic-force models, has the Debye–Waller factor for vibrations parallel to the surface greater than the bulk value. Also, comparison with the results of other models suggests that surface lattice distortion reduces the Debye–Waller factor from the bulk value by about as much as does the creation of a surface itself, ignoring the attendant lattice distortion.

EFFECT OF LATTICE DISTORTION ON THE DEBYE–WALLER FACTOR: I. EXTENDED INTERNAL DEFECTS

1967 ◽  
Vol 45 (8) ◽  
pp. 2651-2660 ◽  
Author(s):  
J. Vail
Keyword(s):  
Nearest Neighbor ◽  
Harmonic Approximation ◽  
Waller Factor ◽  
Potential Interaction ◽  
Coupling Constants ◽  
Extended Defects ◽  
Extended Defect ◽  
Cubic Crystal ◽  
Perfect Lattice ◽  
Debye Waller Factor

A model is introduced in which a Mössbauer atom in an extended internal defect is replaced by a point defect in a perfect lattice, with coupling equal to that in the extended defect. Lattice distortions are considered which are typical for extended defects, with 5 and 10% dilatation and compression, effective coupling constants in nearest-neighbor harmonic approximation are estimated for these cases for a monatomic cubic crystal with Morse potential interaction, and Visscher's data are then used to estimate the fractional change in the Debye–Waller factor, e−2W. Decreases of 14 and 38% are found in e−2W for 5 and 10%, respectively, of lattice dilatation in extended defects, using parameters that are typical of monatomic metals.

THERMAL VIBRATION ANALYSIS OF RuO2 BY EXAFS

2006 ◽  
Vol 20 (25n27) ◽  
pp. 4111-4116 ◽  
Author(s):  
KEI-ICHIRO MURAI ◽  
YASUHIRO AKUNE ◽  
YOHEI SUZUKI ◽  
TOSHIHIRO MORIGA ◽  
ICHIRO NAKABAYASHI
Keyword(s):  
Thermal Expansion ◽  
Nearest Neighbor ◽  
Weak Interactions ◽  
Negative Thermal Expansion ◽  
Pair Potential ◽  
Waller Factor ◽  
Thermal Vibration ◽  
Debye Waller Factor ◽  
Effective Pair Potential ◽  
Effective Pair

Ruthenium dioxide which has a rutile-type structure is an important material in a viewpoint of electronic and magnetic properties. RuO 2 has a negative thermal expansion along c-axis in the high temperature region above room temperature. In this study, we could obtain detailed information about the thermal vibration of atoms by the analysis of EXAFS Debye-Waller factors. EXAFS analysis provides an effective pair potential with temperature dependent shape with Debye-Waller factor. The distance between second-nearest neighbor atoms ( Ru - Ru ) are equal to the length of c-axis in unit cell. It has become apparent that Ru - O bonds in RuO 6 octahedron are much stronger than the interaction between the second-nearest neighbor atoms ( Ru - Ru ) as same as FeF 2 in fluorides. Those results suggest that the negative thermal expansion along c-axis is caused by those weak interactions between second-nearest neighbor atoms ( Ru - Ru ).

Anharmonic non-Gaussian contribution to the Debye–Waller factor. II. KCl

1973 ◽  
Vol 29 (3) ◽  
pp. 228-231 ◽  
Author(s):  
G. Solt ◽  
N. M. Butt ◽  
D. A. O'Connor
Keyword(s):  
Waller Factor ◽  
Debye Waller Factor ◽  
Factor Ii ◽  
Non Gaussian

EELFS AND EXFAS ELECTRON SPECTROSCOPIES: A COMBINED STRUCTURAL INVESTIGATION

1995 ◽  
Vol 02 (02) ◽  
pp. 255-268 ◽  
Author(s):  
L. LOZZI ◽  
M. PASSACANTANDO ◽  
P. PICOZZI ◽  
S. SANTUCCI ◽  
M. DE CRESCENZI
Keyword(s):  
Fine Structure ◽  
Nearest Neighbor ◽  
Structural Information ◽  
Mean Free Path ◽  
Waller Factor ◽  
Auger Transition ◽  
X Ray ◽  
Debye Waller Factor ◽  
Electron Energy Loss ◽  
X Ray Absorption

Detailed extended oscillating features above the Cu M2,3VV Auger transition, recently named EXFAS (Extended Fine Auger Structure), and above the Cu M2,3 core edge, named EELFS (Electron Energy-Loss Fine Structure), on the polycrystalline Cu surface have been compared to assess the short-range nature of the EXFAS features. To obtain the structural information in terms of Debye-Waller factor, interatomic distance, anharmonic effects, backscattering amplitude, and phase-shift functions, the data analysis has been performed following the EXAFS (Extended X-ray Absorption Fine Structure) procedure. The intensity of the extended structures decreases strongly when the temperature increases. In both cases no difference, as a function of temperature, in the nearest-neighbor distance was observed but a sizeable increase of the Debye-Waller factor was observed. The Debye-Waller factor has been fitted, as a function of temperature, to obtain the Debye temperature. The main result shows that the EELFS spectroscopy mainly investigates the bulk properties because of the high mean free path of the analyzed electrons. On the contrary, the Debye-Waller factor obtained from the analysis on the EXFAS structures, which are due to the first 2–4 atomic layers, is greater than that obtained from the EELFS analysis because of the greater movement of the surface atoms with respect to the bulk atoms. The close analogy between the EELFS and EXFAS structural results confirms that the extended features above the Auger transition are dominated by a genuine autoionization effect rather than by a diffraction process and/or a density-of-state effects which modulate the background of the secondary emitted electrons. Our interpretation is confirmed by the complete lack of the extended Auger features in the electron yield spectrum, N(E), when a monochromatic X-ray source is used.

Exafs characterisation of amorphous GaAs

1998 ◽  
Vol 524 ◽  
Author(s):  
M. C. Ridgway ◽  
C. J. Glover ◽  
G. J. Foran ◽  
K. M. Yu
Keyword(s):  
Chemical Etching ◽  
Nearest Neighbor ◽  
Structural Parameters ◽  
Amorphous Material ◽  
Waller Factor ◽  
X Ray ◽  
Coordination Numbers ◽  
Debye Waller Factor ◽  
Selective Chemical ◽  
X Ray Absorption

ABSTRACTThe structural parameters of stoichiometric, amorphous GaAs have been determined with extended x-ray absorption fine structure (EXAFS) measurements performed in transmission mode at 10K. Amorphous GaAs samples were fabricated with a combination of epitaxial growth, ion implantation and selective chemical etching. Relative to a crystalline sample, the nearest-neighbor bond length and Debye-Waller factor both increased for amorphous material. In contrast, the coordination numbers about both Ga and As atoms in the amorphous phase decreased to ˜3.85 atoms from the crystalline value of four. All structural parameters were independent of implantation conditions and as a consequence, were considered representative of intrinsic, amorphous GaAs as opposed to an implantation-induced extrinsic structure.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

Electronic and Vibrational Properties of Single Crystal Surfaces of NiAl

1986 ◽  
Vol 83 ◽  
Author(s):  
S.-C. Lui ◽  
J. M. Mundenar ◽  
E. W. Plummer ◽  
M. E. Mostoller ◽  
R. M. Nicklow ◽  
...  
Keyword(s):  
Photoelectron Spectroscopy ◽  
Nearest Neighbor ◽  
Surface States ◽  
Active Surface ◽  
Atomic Displacement ◽  
Inelastic Electron ◽  
Crystal Surfaces ◽  
Single Crystal Surfaces ◽  
Nial Alloy ◽  
Bulk Surface

ABSTRACTSurface and bulk electronic structure of the ordered NiAl alloy were measured using angle resolved photoelectron spectroscopy. The measured bulk d-bands (Ni like) were observed to be narrower than theoretically calculated d band widths which are 20 to 40% wider (depending upon what is used as a measure of the width). At least two surface states were observed on both the (110) and (111) surfaces. The nature of these surface states and their relationship to the bulk band structure is discussed. Dispersion of bulk phonons was measured by neutron scattering and fitted with a fourth nearest neighbor Born-von Karman model. Dipole active surface phonons on the (110) and (111) surfaces were observed by inelastic electron scattering and the frequencies also calculated assuming a truncated bulk surface. The calculated surface modes present a qualitative picture of the atomic displacement at each surface and also show that the surface phonon energy and intensity depends upon the structure of the surface.

Anharmonic contributions to the Debye-Waller factor of aluminium

1989 ◽  
Vol 72 (11) ◽  
pp. 1135-1140 ◽  
Author(s):  
R.C. Shukla ◽  
H. Hübschle
Keyword(s):  
Waller Factor ◽  
Debye Waller Factor
Sign in / Sign up

Export Citation Format

Share Document