A Born–von Karman Force Constant Model for Aluminum

1974 ◽  
Vol 52 (17) ◽  
pp. 1714-1715 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Force Constant ◽  
Frequency Distribution ◽  
Brillouin Zone ◽  
Normal Modes ◽  
Frequency Distribution Function ◽  
Von Karman ◽  
Von Kármán ◽  
Good Agreement

A Born–von Karman force constant model of aluminum, fitted to the frequencies of normal modes with wave vectors distributed throughout the Brillouin zone, is described, and the frequency distribution function calculated. The result is in very good agreement with a distribution function calculated directly from the experimental data.

A New Condition of Formation and Stablity of All Crystalline Systems in a Good Agreement with Experimental Data

2015 ◽  
Vol 11 (3) ◽  
pp. 3224-3228
Author(s):  
Tarek El-Ashram
Keyword(s):  
Experimental Data ◽  
Brillouin Zone ◽  
Electron Concentration ◽  
Free Electron ◽  
Lattice Point ◽  
Valence Electron ◽  
Fermi Gas ◽  
Valence Electron Concentration ◽  
Fermi Sphere ◽  
Good Agreement

In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;𝑽𝑭𝑽𝑩= 𝒏𝑽𝑬𝑪𝟐for all crystalline systems (wheren is the number of atoms per lattice point).

Calculating Fundamental Vibrational Frequencies of Rutile by Combining Ab Initio Method with GF Matrix Method

1994 ◽  
Vol 05 (02) ◽  
pp. 299-301
Author(s):  
Lin Libin ◽  
Zheng Xiangyin
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Matrix Method ◽  
Cluster Model ◽  
Normal Modes ◽  
Vibrational Frequencies ◽  
Ab Initio Method ◽  
Environment Factor ◽  
Factor Α ◽  
Good Agreement

Based on cluster model, we have calculated the fundamental vibrational frequencies of rutile by combining ab initio method and Wilson’s GF-matrix method. In the calculation, we have introduced the concept of environment factor α to correct the force field of the cluster model. The results of calculation are in good agreement to the experimental data and the normal modes give us clear physical picture of the crystal vibration.

On the Velocity Distribution of Turbulent Flow in Pipes and Channels of Constant Cross Section

1946 ◽  
Vol 13 (2) ◽  
pp. A85-A90
Author(s):  
Chi-Teh Wang
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Length Distribution ◽  
Critical Examination ◽  
Large Reynolds Number ◽  
Good Picture ◽  
Von Karman ◽  
Von Kármán ◽  
New Formula ◽  
Good Agreement

Abstract This paper follows the Prandtl conception of momentum transport and gives a critical examination of the so-called Prandtl-Nikuradse formula and the von Kármán formula for the velocity distribution of the turbulent flow in tubes or channels at large Reynolds number. It shows that both formulas would not give a good picture of the turbulent flow near the center of the conduit, and indeed they actually do not. A new formula for the velocity distribution is developed from a study of the mixing-length distribution across the section. This new formula checks quite well with the experiments and yields the same skin-friction formula as derived by von Kármán and Prandtl, which itself is in very good agreement with experiments.

THEORY OF THE PRESSURE-INDUCED ROTATIONAL SPECTRUM OF HYDROGEN

1959 ◽  
Vol 37 (10) ◽  
pp. 1187-1198 ◽  
Author(s):  
J. Van Kranendonk ◽  
Z. J. Kiss
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Absorption Coefficient ◽  
Pair Distribution Function ◽  
Wave Functions ◽  
Rotational Line ◽  
Induction Effect ◽  
Rotational Spectrum ◽  
Absorption Coefficients ◽  
Good Agreement

The theory of induced infrared absorption developed previously is applied to the pressure-induced rotational spectrum of hydrogen. The intensity of the rotational band is due mainly to the quadrupolar induction effect, and to a small interference effect between the quadrupolar and overlap moments. From the experimental data on the binary absorption coefficients, values of the angle-dependent overlap moments are obtained for H2–He, H2–H2, H2–Ne, H2–N2, and H2–A. A calculation of the overlap moment for pure H2 is presented. Rosen-type wave functions appear to be inadequate for a calculation of the small angle-dependent rotational as well as vibrational overlap moments. The temperature dependence of the binary absorption coefficient is calculated, taking into account the quantum effects in the pair distribution function, and found to be in good agreement with the experimental data. The dependence on the ortho–para ratio is also discussed. The double rotational line S(1) + S(1) has been observed and its intensity measured.

TABLES OF DEBYE FUNCTIONS

1966 ◽  
Vol 44 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Roger Howard ◽  
J. Grindlay
Keyword(s):  
Heat Capacity ◽  
Distribution Function ◽  
Frequency Distribution ◽  
Phonon Frequency ◽  
Heat Capacity Data ◽  
Frequency Distribution Function ◽  
Capacity Data ◽  
Negative Moments

Tables and asymptotic limits of the Debye functions[Formula: see text]are presented for n = 0.5, 1.0, 1.5, 2.0, 2.5. This information may be used to facilitate the calculation of the negative moments of the phonon frequency distribution function from the heat capacity data of crystals.

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