scholarly journals Interplay of force constants in the lattice dynamics of disordered alloys: Anab initiostudy

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Rajiv K. Chouhan ◽  
Aftab Alam ◽  
Subhradip Ghosh ◽  
Abhijit Mookerjee
Keyword(s):  
Lattice Dynamics ◽  
Force Constants ◽  
Disordered Alloys

scholarly journals Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

1967 ◽  
Vol 20 (5) ◽  
pp. 495 ◽  
Author(s):  
J Oitmaa
Keyword(s):  
Dipole Moment ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Higher Order ◽  
Force Constants ◽  
Dynamical Equations ◽  
Normal Coordinates ◽  
Shell Models ◽  
Rigid Ion Model ◽  
Explicit Expressions

The lattice dynamics of harmonic and anharmonic shell models are reviewed. It is shown that the various dynamical equations for the shell model can be expressed in the same form as those for the rigid ion model, but with modified force constants. The anharmonic shell model leads to higher order contributions to the dipole moment, quadratic and cubic in the normal coordinates, for which explicit expressions are obtained.

ON THE THERMAL EXPANSION OF METALS AT LOW TEMPERATURES

1961 ◽  
Vol 39 (2) ◽  
pp. 263-271 ◽  
Author(s):  
G. K. Horton
Keyword(s):  
Thermal Expansion ◽  
Elastic Constants ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Force Constants ◽  
Central Force ◽  
Force Model ◽  
Lattice Thermal Expansion ◽  
Interionic Potential ◽  
The Ideal

A theory is developed which correlates the thermal expansion of crystals to the anharmonicity introduced into Born's lattice dynamics by allowing the force constants of the crystal to vary with volume. This is achieved by identifying the force constants with the elastic constants of the crystal by the method of long waves. It is then assumed that it is primarily the volume dependence of the elastic constants that give rise to their temperature variation. A central force nearest and next-nearest neighbor force model analogous to Leighton's is applied to copper. The values of the lattice thermal expansion coefficient and of Grüneisen's parameter are given as a function of the temperature and found to agree quite well with the latest experimental results. It is pointed out that the description of the interionic potential in metals by a two-body central force is certainly a serious oversimplification and that the theory is likely to be more realistic for, say, the ideal inert solid gases, as soon as the experimental data becomes available.

scholarly journals The theory of the vibrations and the Raman spectrum of the diamond lattice

1948 ◽  
Vol 241 (829) ◽  
pp. 105-145 ◽  
Keyword(s):  
Raman Spectrum ◽  
Vibrational Spectrum ◽  
Frequency Shift ◽  
Raman Line ◽  
Elastic Constants ◽  
Lattice Dynamics ◽  
Ultra Violet ◽  
Force Constants ◽  
X Ray ◽  
Infra Red

The crystal structure of diamond was first determined by Bragg in 1913 from X-ray photographs; the carbon atoms are arranged at the apices and median points of interlinked tetrahedra. Born (1914) derived expressions for the three elastic constants of diamond in terms of two force constants related to the valency bonds between neighbouring atoms. But, at that time, the only experimental data available were the compressibility and the Debye characteristic temperature 0, and precise determination of the valence force constants was not possible. Meanwhile, investigation of the optical properties of diamond had produced evidence for the existence of two distinct types, one with an absorption band at 8 [i in the infra-red, the other transparent at this point. Robertson, Fox & Martin (1934) took up this problem and found that absorption in the infra-red is associated with absorption in the ultra-violet; diamonds transparent at 8y transmit much farther into the ultra-violet. Both types of diamond have Bragg’s tetrahedral structure, the same refractive index, specific gravity, dielectric constant and electron diffraction. Their infra-red spectra are identical up to 7y, and the frequency shift of the principal Raman line is the same. The derivation of the elastic constants was again considered by Nagendra Nath (1934). He extended the theory to include central forces between second neighbours in the lattice. He also suggested that the frequency shift of the principal Raman line corresponds to the relative vibration of the two carbon atoms in the unit cell, along the line joining their nuclei. Raman and his collaborators have recently (1941) put forward a new theory of lattice dynamics according to which the vibrational spectrum of a crystal consists of a few discrete lines. This is in direct contradiction to the quasi-continuous vibrational spectrum predicted by classical or quantum mechanics. On this new theory there are eight fundamental frequencies of vibration for diamond; the values of these frequencies are deduced from the observed specific heat, ultra-violet absorption and Raman spectrum, which, it is claimed, cannot be explained by ‘orthodox’ lattice dynamics. Raman (1944) has suggested that there are, not two, but four types of diamond, two with tetrahedral symmetry and two with octahedral symmetry depending on the electronic configurations, but X-ray analysis gives no indication of this and the attempts of his school to explain the observed infra-red spectra on the basis of their new lattice theory have been, up to now, unsuccessful.

LATTICE DYNAMICS OF NICKEL

1967 ◽  
Vol 45 (5) ◽  
pp. 1655-1660 ◽  
Author(s):  
S. P. Singh
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Debye Temperature ◽  
Density Of States ◽  
Elastic Constants ◽  
Lattice Dynamics ◽  
Vibration Spectrum ◽  
Force Constants ◽  
Effective Force ◽  
Good Agreement

The vibration spectrum of the nickel lattice has been calculated using the simple de Launay method with values for the effective force constants determined from published experimental data for the elastic constants. The density-of-states curve reproduces the same general features found by Birgeneau et al. (1964) using a fourth-neighbor model. The Debye temperature at 0 °K is found to be 474 °K in good agreement with the experimental value of 468 °K, and the calculated variation of the Debye temperature with temperature agrees quite well with that deduced from measurements of the specific heat.

SOLUTION HARDENING IN DISORDERED ALLOYS : A LATTICE DYNAMICS APPROACH

1987 ◽  
Vol 48 (C8) ◽  
pp. C8-359-C8-364
Author(s):  
S. RAMOS DE DEBIAGGI ◽  
A. CARO
Keyword(s):  
Lattice Dynamics ◽  
Solution Hardening ◽  
Disordered Alloys

scholarly journals Lattice Dynamics of CrW Dilute Alloy Using Modified Embedded Atom Method Potential

2021 ◽  
Vol 16 (2) ◽  
Author(s):  
Manesh Chand ◽  
P D Semalty
Keyword(s):  
Density Of States ◽  
Lattice Dynamics ◽  
Force Constants ◽  
Embedded Atom Method ◽  
Substitutional Impurity ◽  
Vibrational Density Of States ◽  
Embedded Atom ◽  
Modified Embedded Atom Method ◽  
Dilute Alloy ◽  
Vibrational Density

A modified embedded atom method (MEAM) has been used to study the lattice dynamics and vibrational properties of CrW alloy. Using the MEAM potential the force-constants up to second neighbours for pure Cr and its dilute alloy with small concentration of W as substitutional impurity are calculated. The Phonon dispersions for dilute CrW alloy at 0.3%, 0.8% and 1.6 % concentration of W substitutional impurity have been computed and the obtained results are compared with the available experimental data. We have obtained a very good agreement with the experimentally measured results of phonon dispersions. With the application of obtained force-constants from MEAM potential, the local vibrational density of states in ideal crystal and its alloys using Green’s function method has been calculated. On the basis of the results of local vibrational density of states, the condition of resonance modes has been investigated. Using the calculated vibrational local density of states, the mean square thermal displacements of impurity atoms in CrW alloys are also calculated.

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