scholarly journals Debye?Waller Factors of a-Iron and Sodium. II. Willis's Anharmonic Theory

1975 ◽  
Vol 28 (6) ◽  
pp. 707 ◽  
Author(s):  
LP Pathak ◽  
Jyoti Prakash ◽  
VP Singh ◽  
MP Hemkar
Keyword(s):  
Experimental Data ◽  
Waller Factor ◽  
Experimental Results ◽  
Crystal Potential ◽  
Debye Waller Factor ◽  
Wide Range ◽  
Temperature Parameter

An application of Willis's anharmonic theory has been made to improve the earlier calculations of the Debye-Waller factors of (X-iron and sodium reported in Part I, and to estimate the effect of including anharmonic. terms in the crystal potential. The calculations have been compared with the existing experimental data in terms of the Debye-Waller factor temperature parameter Y. The agreement between the calculated values and the experimental results is now shown to be quite good over a wide range of temperature.

scholarly journals A Temperature Variation of Debye-Waller Factor for Alkali and Noble Metals

1983 ◽  
Vol 38 (5) ◽  
pp. 503-508 ◽  
Author(s):  
A. R. Jani ◽  
V. B. Gohel
Keyword(s):  
Experimental Data ◽  
Temperature Variation ◽  
Phenomenological Model ◽  
Noble Metals ◽  
Experimental Information ◽  
Waller Factor ◽  
Critical Examination ◽  
Debye Waller Factor ◽  
Different Temperatures ◽  
Experimental Findings

Debye-Waller factors at different temperatures of four alkali and three noble metals have been computed on the basis of a screened shell phenomenological model. The theoretical values are compared with existing experimental data. Particularly for lithium and potassium, most recent experimental information has been included. A critical examination of the results reveals a satis­factory agreement between the theoretical and experimental findings.

scholarly journals Symmetry of Terms in the Temperature Factor for Bragg Diffraction of X Rays or Neutrons

1985 ◽  
Vol 38 (3) ◽  
pp. 421
Author(s):  
SL Mair
Keyword(s):  
Point Group ◽  
Waller Factor ◽  
Bragg Diffraction ◽  
Group Symmetry ◽  
X Rays ◽  
Point Group Symmetry ◽  
Many Body ◽  
Crystal Potential ◽  
Debye Waller Factor ◽  
Particle Potential

Terms in the anharmonic Debye-Waller factor, taken as a perturbation about the harmonic case to second order in the van Hove ordering parameter, are classified according to the point-group symmetry of the vibrating atom. The classification is valid for a fully interacting (many-body) crystal potential. It is pointed out that certain terms, which are symmetry-allowed for such a general crystal potential, are excluded if an effective one-particle potential is employed.

Bubble Dynamics for Nucleate Pool Boiling of Electrolyte Solutions

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Seyed Ali Alavi Fazel ◽  
Seyed Baher Shafaee
Keyword(s):  
Experimental Data ◽  
Bubble Dynamics ◽  
Pool Boiling ◽  
Close Relation ◽  
Electrolyte Solutions ◽  
Nucleate Boiling ◽  
Heat Fluxes ◽  
Experimental Results ◽  
Nucleate Pool Boiling ◽  
Wide Range

Bubble dynamics is the most important subphenomenon, which basically affects the nucleate pool boiling heat transfer coefficient. Previous investigations state that the effect of physical properties of liquid and vapor phases on bubble departure diameter are often conflicting. In this article, extensive new experimental data are presented for the bubble departure diameter for various electrolyte aqueous solutions over a wide range of heat fluxes and concentrations. Experimental results show that the bubble detachment diameter increase with increasing either boiling heat flux or electrolyte concentration. Experimental results also present a close relation between the dimensionless capillary and bond numbers. A new model for the prediction of vapor bubble departure diameter in nucleate boiling for the electrolyte solutions is proposed, which predicts the experimental data with a satisfactory accuracy.

Temperature Coefficient of the Refractive Index of H2O and D2O and Proposed Models of Water Structure

1980 ◽  
Vol 35 (11) ◽  
pp. 1171-1177 ◽  
Author(s):  
G. Abbate ◽  
U. Bernini ◽  
E. Ragozzino ◽  
F. Somma
Keyword(s):  
Experimental Data ◽  
Refractive Index ◽  
Temperature Coefficient ◽  
Liquid Water ◽  
Structural Model ◽  
Deuterium Oxide ◽  
Water Structure ◽  
Experimental Results ◽  
Molecular Polarizability ◽  
Wide Range

Abstract The temperature coefficient of the refractive index, (∂n/∂T)p, has been measured for deuterium oxide. The observed values are considered together with those previously obtained for water. The experimental data cannot be explained with the best known models of molecular polarizability, at least in the approximation generally used in these models. Therfore they are discussed on the basis of a different approximation, suggested by a well-known structural model of liquid water. It is shown that the experimental results are very well explained, in a wide range of temperature, with the hypothesis of the existence of "structural voids".

On the Debye-Waller Factor and Debye Temperature of Dendrite-Shaped PbTe

2013 ◽  
Vol 678 ◽  
pp. 17-21
Author(s):  
R. Karunamoorthi ◽  
P. Indra Devi ◽  
K. Ramachandran
Keyword(s):  
Dispersion Curve ◽  
Shell Model ◽  
Debye Temperature ◽  
Phonon Dispersion ◽  
Lead Telluride ◽  
Waller Factor ◽  
Phonon Dispersion Curve ◽  
Thermal Parameters ◽  
Experimental Results ◽  
Debye Waller Factor

In this study, the phonon dispersion curve of dendrite-shaped lead telluride (PbTe), a nano structured material is obtained by shell model and the thermal parameters are calculated and compared with experimental results.

Numerical Study of Turbulent Helical Pipe Flow With Comparison to the Experimental Results

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Anup Kumer Datta ◽  
Yasutaka Hayamizu ◽  
Toshinori Kouchi ◽  
Yasunori Nagata ◽  
Kyoji Yamamoto ◽  
...  
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Pipe Flow ◽  
Numerical Study ◽  
Circular Cross Section ◽  
Turbulence Models ◽  
Experimental Results ◽  
Helical Pipe ◽  
Wide Range

Turbulent flow through helical pipes with circular cross section is numerically investigated comparing with the experimental results obtained by our team. Numerical calculations are carried out for two helical circular pipes having different pitches and the same nondimensional curvature δ (=0.1) over a wide range of the Reynolds number from 3000 to 21,000 for torsion parameter β (=torsion /2δ  = 0.02 and 0.45). We numerically obtained the secondary flow, the axial flow and the intensity of the turbulent kinetic energy by use of three turbulence models incorporated in OpenFOAM. We found that the change to fully developed turbulence is identified by comparing experimental data with the results of numerical simulations using turbulence models. We also found that renormalization group (RNG) k−ε turbulence model can predict excellently the fully developed turbulent flow with comparison to the experimental data. It is found that the momentum transfer due to turbulence dominates the secondary flow pattern of the turbulent helical pipe flow. It is interesting that torsion effect is more remarkable for turbulent flows than laminar flows.

Debye Waller Factors of fee Metals by the Modified Angular Force Model

1977 ◽  
Vol 32 (6) ◽  
pp. 570-576 ◽  
Author(s):  
Hira Lai Kharoo ◽  
O. P. Gupta ◽  
M. P. Hemkar
Keyword(s):  
Characteristic Temperature ◽  
Mean Square Displacement ◽  
Waller Factor ◽  
Force Model ◽  
Debye Waller Factor ◽  
Different Temperatures ◽  
Temperature Parameter ◽  
The Mean ◽  
Experimental Values ◽  
Theoretical Results

Abstract A modified form of the non-central force model which takes account of the electron-ion inter­ action term of the Kreb's model in the Clark, Gazis and Wallis type angular forces is considered to calculate the Debye-Waller exponents at different temperatures for five fee metals: copper, silver, gold, aluminium and nickel. The results are compared with the available x-ray measurements in terms of the temperature parameter Y of the Debye-Waller factor, the Debye characteristic temperature ΘM and the mean square displacement of the atoms. The theoretical results are found to be in reasonably satisfactory agreement with the experimental values.

Lattice Dynamical Properties of Nickel

1973 ◽  
Vol 51 (17) ◽  
pp. 1869-1873 ◽  
Author(s):  
Satya Pal
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Frequency Spectrum ◽  
Reasonable Agreement ◽  
Sampling Technique ◽  
Waller Factor ◽  
Characteristic Temperatures ◽  
Debye Waller Factor ◽  
Root Sampling ◽  
Theoretical Results

The frequency spectrum of nickel has been calculated on the basis of the lattice dynamical model of Sharma and Joshi. The frequency spectrum has been computed with the help of Blackman's root sampling technique for a discrete subdivision in the reciprocal space. The computed frequency distribution has been employed for the calculation of the specific heat and the temperature variation of the Debye–Waller factor of nickel. The theoretically computed values of specific heat are compared with the experimental data in terms of the Debye characteristic temperatures. The theoretical results are in reasonable agreement with the experimental data.

Lattice Dynamics of Molybdenum and Chromium

1980 ◽  
Vol 35 (2) ◽  
pp. 230-235
Author(s):  
B. P. Singh ◽  
L. P. Pathak ◽  
M. P. Hemkar
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Lattice Dynamics ◽  
Waller Factor ◽  
Mean Square ◽  
Frequency Wave ◽  
Debye Waller Factor ◽  
Nearest Neighbours ◽  
The Mean ◽  
First Time

Abstract The frequency-wave vector dispersion relations, the frequency spectrum, the Debye temperature, the temperature dependence of the Debye-Waller factor and the mean square displacements of the atoms molybdenum and chromium, the metals for which long range forces are also important, have been computed on the basis of the extended improved Fielek model for BCC transition metals. The model considers, for the first time the d shell-d shell central interactions upto next-nearest-neighbours. The calculated results show a satisfactory agreement with the available experimental data.

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).

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