Debye temperatures op cubic crystals estimated from measured phonon frequencies by means of a frequency sum rule

1984 ◽  
Vol 34 (8) ◽  
pp. 883-886 ◽  
Author(s):  
V. Frei ◽  
M. Polčík
Keyword(s):  
Sum Rule ◽  
Cubic Crystals ◽  
Debye Temperatures

CHARACTERISTIC TEMPERATURES OF CUBIC METALS

1957 ◽  
Vol 35 (5) ◽  
pp. 507-511 ◽  
Author(s):  
E. E. Budzinski ◽  
H. Schiff
Keyword(s):  
Cubic Crystals ◽  
Cubic Metals ◽  
Characteristic Temperatures ◽  
Debye Temperatures

An approximation is developed for the determination of the characteristic Debye temperatures of cubic crystals. This method yields results more accurate than those obtained by Bhatia and Tauber using Houston's three-term formula and slightly more accurate than those obtained with the more recent six-term formula of Betts, Bhatia, and Wyman, and also provides a means of estimating the accuracy of these formulae.

scholarly journals INTERATOMIC FORCES, PHONONS, THE FOREMAN–LOMER THEOREM AND THE BLACKMAN SUM RULE

2001 ◽  
Vol 15 (26) ◽  
pp. 3439-3452 ◽  
Author(s):  
A. M. STEWART
Keyword(s):  
Phonon Dispersion ◽  
Dispersion Relations ◽  
Force Constants ◽  
Sum Rule ◽  
Cubic Crystals ◽  
Hexagonal Close Packed ◽  
Atomic Force ◽  
Principal Directions ◽  
General Relations ◽  
Phonon Dispersion Relations

Foreman and Lomer proposed in 1957 a method of estimating the harmonic forces between parallel planes of atoms of primitive cubic crystals by Fourier transforming the squared frequencies of phonons propagating along principal directions. A generalized form of this theorem is derived in this paper and it is shown that it is more appropriate to apply the method to certain combinations of the phonon dispersion relations rather than to individual dispersion relations themselves. Further, it is also shown how the method may be extended to the hexagonal close packed and diamond lattices. Explicit, exact and general relations in terms of atomic force constants are found for deviations from the Blackman sum rule which itself is shown to be derived from the generalized Foreman–Lomer theorem.

Measurement of the Displacement Across a Coincidence Grain Boundary

1977 ◽  
Vol 35 ◽  
pp. 124-125
Author(s):  
J. W. Matthews ◽  
W. M. Stobbs
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Stacking Fault ◽  
The Other ◽  
Measuring Technique ◽  
High Angle ◽  
Twin Boundaries ◽  
Rigid Displacement ◽  
Cubic Crystals ◽  
Lattice Displacement

Many high-angle grain boundaries in cubic crystals are thought to be either coincidence boundaries (1) or coincidence boundaries to which grain boundary dislocations have been added (1,2). Calculations of the arrangement of atoms inside coincidence boundaries suggest that the coincidence lattice will usually not be continuous across a coincidence boundary (3). There will usually be a rigid displacement of the lattice on one side of the boundary relative to that on the other. This displacement gives rise to a stacking fault in the coincidence lattice.Recently, Pond (4) and Smith (5) have measured the lattice displacement at coincidence boundaries in aluminum. We have developed (6) an alternative to the measuring technique used by them, and have used it to find two of the three components of the displacement at {112} lateral twin boundaries in gold. This paper describes our method and presents a brief account of the results we have obtained.

Microtwinning Evidence For The Apparent Five-Fold Symmetry in T2(Al6Li3Cu)

1987 ◽  
Vol 45 ◽  
pp. 24-25
Author(s):  
Kenneth S. Vecchio ◽  
David B. Williams
Keyword(s):  
Stable Equilibrium ◽  
Equilibrium Phase ◽  
Convergent Beam Electron Diffraction ◽  
Icosahedral Structure ◽  
Cubic Crystals ◽  
Icosahedral Phases ◽  
Heat Treated ◽  
Zero Layer ◽  
Convergent Beam ◽  
Zr Alloy

Since the discovery in 1984 by Shechtman et al. of crystals which display apparent five-fold symmetry, extensive effort has been given to establishing a theoretical basis for the existence of icosahedral phases (eg.2.). Several other investigations have been centered on explaining these observations based on twinning of cubic crystals (eg.3.). Recently, the existence of a stable, equilibrium phase T2Al6 Li3Cu) possessing an icosahedral structure has been reported in the Al-Li-Cu system(4-6).In the present study an Al-2.6wt.%Li-l.5wt.%Cu-0.lwt.%Zr alloy was heat treated at 300°C for 100hrs. to produce large T2 precipitates. Convergent Beam Electron Diffraction (CBED) patterns were obtained from two-fold, three-fold, and apparent five-fold axes of T2 particles. Figure 1 shows the five-fold symmetric zero layer CBED pattern obtained from T2 particles.

MISORIENTATION DISTRIBUTION FUNCTION FOR CUBIC CRYSTALS

2019 ◽  
Vol 85 (5) ◽  
pp. 28-32
Author(s):  
A. S. Kolyanova ◽  
Y. N. Yaltsev
Keyword(s):  
Distribution Function ◽  
Grain Boundaries ◽  
Orientation Distribution ◽  
Recrystallization Annealing ◽  
Misorientation Distribution ◽  
Cubic Crystals ◽  
Special Boundaries ◽  
Pole Figures ◽  
Two Samples ◽  
Euler Space

A calculation method for obtaining the misorientation distribution function (MDF) for cubic crystals which can be used to estimate the presence or absence of special boundaries in the materials is presented. The calculation was carried out for two samples of Al-Mg-Si alloy subjected to various mechanical and thermal treatments: the first sample is subjected to rolling; the second sample is subjected to recrystallization annealing. MDF is calculated for each sample; the results are presented in the Euler space and in the angle-axis space. The novelty of the method consists in the possibility of gaining data on the grain boundaries from X-ray texture analysis without using electron microscopy. A calculation involving only mathematical operations on matrices was performed on the basis of the orientation distribution function restored from incomplete pole figures. It is shown that no special boundaries are observed in the deformed sample, whereas in the recrystallized alloy, special boundaries are detected at Ʃ = 23, 13, and 17. The shortcoming of the proposed method can be attributed to the lack of accurate data on grain boundaries, since all possible orientation in the polycrystal should be taken into account in MDF calculation.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

scholarly journals Study on the Phase Selection and Debye Temperature of Hyper-Peritectic Al-Ni Alloy under High Pressure

Metals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 84
Author(s):  
Xiaohong Wang ◽  
Zhipeng Chen ◽  
Duo Dong ◽  
Dongdong Zhu ◽  
Hongwei Wang ◽  
...  
Keyword(s):  
High Pressure ◽  
Ambient Pressure ◽  
Competitive Growth ◽  
Phase Selection ◽  
Debye Temperatures ◽  
Ni Alloy ◽  
Temperature Heat ◽  
Low Temperature Heat Capacity ◽  
New Phase ◽  
Selection Of

The phase selection of hyper-peritectic Al-47wt.%Ni alloy solidified under different pressures was investigated. The results show that Al3Ni2 and Al3Ni phases coexist at ambient pressure, while another new phase α-Al exists simultaneously when solidified at high pressure. Based on the competitive growth theory of dendrite, a kinetic stabilization of metastable peritectic phases with respect to stable ones is predicted for different solidification pressures. It demonstrates that Al3Ni2 phase nucleates and grows directly from the undercooled liquid. Meanwhile, the Debye temperatures of Al-47wt.%Ni alloy that fabricated at different pressures were also calculated using the low temperature heat capacity curve.

Sign in / Sign up

Export Citation Format

Share Document