scholarly journals Melting Criterion for Cubic Metals Based on a Modified Angular Force Model

1974 ◽  
Vol 27 (1) ◽  
pp. 129 ◽  
Author(s):  
Jyoti Prakash ◽  
MP Hemkar
Keyword(s):  
Melting Point ◽  
Periodic Table ◽  
Lattice Dynamics ◽  
Force Model ◽  
Mean Square ◽  
Interatomic Spacing ◽  
Cubic Metals ◽  
The Mean ◽  
Thermal Vibrations

A modified angular force model for the lattice dynamics of metals is used to test Lindemann's melting criterion by computing the ratio Ym of the mean square amplitude of thermal vibrations to the square of the interatomic spacing at the melting point for a number of cubic metals belonging to different groups in the periodic table.

Krebs's model and Lindemann's melting law

1968 ◽  
Vol 46 (15) ◽  
pp. 1677-1679 ◽  
Author(s):  
A. K. Singh ◽  
P. K. Sharma
Keyword(s):  
Melting Temperature ◽  
Periodic Table ◽  
Lattice Dynamics ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Interatomic Spacing ◽  
Cubic Metals ◽  
The Mean ◽  
Thermal Vibrations

Lindemann's melting criterion for cubic metals is examined using Krebs's model for the lattice dynamics of metals by computing the ratio, xm, of the mean square displacement of thermal vibrations and the square of interatomic spacing at the melting temperature for a number of cubic metals belonging to different groups of the periodic table. This ratio has nearly the same value for elements of one particular group, but exhibits wide variation from one group to another. It is concluded that Lindemann's melting law is inadequate.

Noncentral force model for the lattice dynamics of cubic metals

1979 ◽  
Vol 19 (4) ◽  
pp. 1963-1971 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Awasthi
Keyword(s):  
Lattice Dynamics ◽  
Force Model ◽  
Cubic Metals

Mean square displacements of atoms in cubic metals at melting point

1968 ◽  
Vol 18 (11) ◽  
pp. 1413-1415 ◽  
Author(s):  
S. K. Sangal ◽  
P. K. Sharma
Keyword(s):  
Melting Point ◽  
Mean Square ◽  
Cubic Metals

Predicting some Effects of Lattice Vibrations on Proton Scattering Patterns

1970 ◽  
Vol 14 ◽  
pp. 1-10
Author(s):  
C. S. Barrett
Keyword(s):  
Temperature Factor ◽  
Lattice Vibrations ◽  
Proton Scattering ◽  
Mean Square ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Integrated Intensity ◽  
The Mean ◽  
Thermal Vibrations

AbstractA method of predicting the approximate relative intensities of lines in proton blocking patterns recently proposed, which is based on summing the squares of structure factors for the various orders of reflection of a plane, is found to predict certain effects of lattice vibrations on the lines in some recently reported patterns. The mean square amplitude of vibration enters the calculations through a Debye-Waller temperature factor like that used in X-ray diffraction. When patterns are compared for groups of crystals that are nearly identical except for this temperature factor, the qualitative predictions by this method agree with the observations. If it is also arbitrarily assumed that the integrated intensity dip at a spot where lines intersect is approximated by summing the calculated Integrated intensity dips for all of the lines crossing at the spot, one has a simple and convenient method of predicting relative spot intensities. Such calculations have been successful in establishing the order of decreasing intensity for most of the spots along a given line, with several different kinds of crystals. This method also serves to predict qualitatively how prominent the spots appear relative to the lines, in general, in patterns of crystals that differ appreciably only in the amplitude of the thermal vibrations.

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.

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