Umklapp collisions and thermal conductivity

2021 ◽  
pp. 309-321
Author(s):  
Geoffrey Brooker
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Flow ◽  
Group Velocity ◽  
Thermodynamic Equilibrium ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Momentum Balance ◽  
Lattice Vector ◽  
Phonon Group Velocity

“Umklapp collisions and thermal conductivity” deals with heat conduction in a dielectric solid. Collisions of phonons are divided into Umklapp and normal according as a reciprocal lattice vector is or is not involved in the phonon momentum balance. A local temperature is defined by appeal to local thermodynamic equilibrium. An equilibrium phonon distribution can be off-centred, yet non-decaying, if the only collisions are “normal”, conserving the total phonon momentum. Then heat flow does not decay, even if a representative collision reverses the phonon group velocity. Conversely, in an Umklapp collision it is the non-conservation of phonon momentum that causes heat flow to decay.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 540-541
Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov
Keyword(s):  
Reciprocal Lattice ◽  
Unit Cell ◽  
Reciprocal Lattice Vector ◽  
Unit Cell Parameters ◽  
Lattice Vector ◽  
Cell Parameters ◽  
Accuracy Of Measurements ◽  
The Difference ◽  
Image Position ◽  
Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

Angle calculations for a three-circle goniostat

2006 ◽  
Vol 39 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen ◽  
Jon Are Beukes
Keyword(s):  
General Procedure ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Laboratory System ◽  
Lattice Vector ◽  
New Approach ◽  
Rotation Matrices ◽  
Rotation Axes ◽  
Vector Description

A general procedure for angle calculations for a three-circle goniostat has been developed. This new approach is based on a vector description of the transformation of a reciprocal-lattice vector under the action of a rotation shaft. It does not invoke the use of rotation matrices and applies equally well to cases where the directions of the rotation axes do not conform with coordinate axes of the laboratory system adopted for the analysis.

The effect of diffuse scattering on the dark-field contrast from precipitates

1978 ◽  
Vol 11 (3) ◽  
pp. 190-192 ◽  
Author(s):  
J. Gjønnes ◽  
J. K. Solberg
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Dark Field ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Field Technique

Precipitate contrast due to Bragg interactions in the diffuse scattering has been studied. Both ordinary dark-field contrast and moiré contrast were found to be preserved at quite large distances from the Bragg spots, especially along the direction normal to the reciprocal lattice vector. The effects, which are similar to those seen in thickness fringe contrast from perfect crystals, may be disturbing in the search for faint precipitate reflections with the dark-field technique, especially in thicker parts of the crystal.

Thermal Characterization of High-Density Interconnects in the Form of Equivalent Thermal Conductivity

2009 ◽  
Author(s):  
Wataru Nakayama ◽  
Katsuhiro Koizumi ◽  
Takashi Fukue ◽  
Masaru Ishizuka ◽  
Tatsuya Nakajima ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Flow ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Thermal Characterization ◽  
High Density ◽  
Cooperative Effort ◽  
Equivalent Thermal Conductivity ◽  
Metal Pattern

The issue addressed in the present study is how to model wiring substrates to perform heat conduction analysis on moderate computational resource. Equivalent thermal conductivity is a convenient measure in thermal modeling. However, its notion needs re-examination where higher accuracy of heat conduction analysis is pursued. Proposed is a scheme where the indexed volumetric metal contents are used to estimate the equivalent conductivity of representative volume element (RVE). The index is designed to reflect the effect of metal pattern on heat flow through RVE. In order to illustrate the core concept we report the analysis performed on template models of high-density interconnect (HDI) substrates. The element of HDI contains copper in several forms; through-via, continuous plane, and cross wires. Five heat flow directions are assumed; two are linear and three are right-angled turn. From combinations of the metal pattern and the heat flow direction twenty five templates are created, then, they are subjected to detailed numerical analysis. The values of equivalent thermal conductivity derived from the numerical solutions reveal that the gross volumetric metal content is totally inadequate as a parameter of thermal characterization. The paper also outlines the overall organization of our analysis system which is being developed in an industry-academia cooperative effort under the auspices of JSME.

On The Visibility of Supported Metallic Particles

1980 ◽  
Vol 38 ◽  
pp. 404-405
Author(s):  
D. Romeu ◽  
A. Gómez ◽  
José M. Yacamán ◽  
J.M. Domínguez
Keyword(s):  
Infinite Number ◽  
Reciprocal Lattice ◽  
Computing Time ◽  
Reciprocal Lattice Vector ◽  
Special Treatment ◽  
Twin Boundaries ◽  
Lattice Vector ◽  
Metallic Particles ◽  
Beam Approximation

Several methods have been presented for the calculation of diffraction intensities in the case of twin boundaries and other two-crystal systems in the N-beam approximation (1,2,3). It has been realized that when two or more beams diffracted by the top crystal differ by a reciprocal lattice vector of the bottom crystal, the beams become coupled and the problem requires special treatment. It has been pointed out (3) that the methods described in references (2) and (3) are formally equivalent for an infinite number of beams but the method described by Gomez et al (3) requires less computing time.

Determination by high-resolution X-ray diffraction of shape, size and lateral separation of buried empty channels in silicon-on-nothing architectures

2007 ◽  
Vol 40 (2) ◽  
pp. 338-343 ◽  
Author(s):  
Marco Servidori
Keyword(s):  
High Resolution ◽  
Lattice Point ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
X Ray Diffraction ◽  
Lattice Vector ◽  
Reciprocal Lattice Point ◽  
One Dimensional ◽  
X Ray ◽  
Planar Array

High-resolution multi-crystal X-ray diffraction was employed to characterize silicon-on-nothing samples made by a one-dimensional periodic planar array of buried empty channels. When the channels are normal to the scattering plane, under the constraint of lattice continuity from the perfect substrate to the surface, this periodic array gives rise to a well defined Fraunhofer diffraction in a scan crossing a selected reciprocal lattice point and normal to the reciprocal lattice vector (transverse or ω scan). In a longitudinal scan (ω/2θ scan crossing the reciprocal lattice point and parallel to the reciprocal lattice vector) interference fringes are observed. By analysis of the ω scan and numerical fit of the ω/2θ scan, the period of the buried empty channels and their shape, size and lateral gap were easily determined, thanks to the high-resolution optics used for the measurements.

Angle calculations for a six-circle κ diffractometer

1999 ◽  
Vol 32 (5) ◽  
pp. 943-950 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Ragnvald H. Mathiesen ◽  
Helge B. Larsen
Keyword(s):  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Rotation Axes

By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a κ diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed six-circle diffractometer.

THE EFFECT OF SPONTANEOUS AND PIEZOELECTRIC POLARIZATION ON THERMAL CONDUCTIVITY OF InN

2013 ◽  
Vol 27 (09) ◽  
pp. 1350031 ◽  
Author(s):  
BIJAYA KUMAR SAHOO ◽  
SUSANT KUMAR SAHOO ◽  
SUKDEV SAHOO
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Group Velocity ◽  
Room Temperature ◽  
Phonon Scattering ◽  
Polarization Property ◽  
Optical And Electrical Properties ◽  
High Quality ◽  
Phonon Group Velocity ◽  
Debye Frequency

The spontaneous (SP) and piezoelectric (PZ) polarization present in the wurtzite III nitrides influence the optical and electrical properties of these materials. The effects of SP and PZ polarization on thermal properties of III nitrides have yet to be investigated. Here we have investigated the SP and PZ effects on thermal conductivity of InN . Inclusion of polarization property modifies the group velocity of phonons. The combined phonon scattering rates and thermal conductivity k of InN are calculated using modified phonon group velocity, Debye frequency and Debye temperature. Without SP and PZ polarization, the room temperature thermal conductivity of InN is found to be 132.55 W/m.K. Inclusion of SP and PZ polarization property enhances the room temperature thermal conductivity from 132.55 to 134.32 W/m.K. Our predicted thermal conductivity values are closer to the recent experimental value 120 W/m.K measured by Levander et al. for a high quality irradiated InN films at room temperature.

Lattice Dynamics Study of Anisotropic Heat Conduction in Superlattices

2000 ◽  
Vol 626 ◽  
Author(s):  
B. Yang ◽  
G. Chen
Keyword(s):  
Thermal Conductivity ◽  
Group Velocity ◽  
Lattice Dynamics ◽  
Phonon Scattering ◽  
Diffuse Interface ◽  
Phonon Confinement ◽  
Dynamics Model ◽  
Phonon Group Velocity ◽  
Anisotropic Heat Conduction ◽  
The Cross

ABSTRACTPast studies on the thermal conductivity suggest that phonon confinement and the associated group velocity reduction are the causes of the observed drop in the cross-plane thermal conductivity of semiconductor superlattices. In this work, we investigate the contribution of phonon confinement to the in-plane thermal conductivity of superlattices and the anisotropic effects of phonon confinement on the thermal conductivity in different directions, using a lattice dynamics model. We find that the reduced phonon group velocity due to phonon confinement may account for the dramatic reduction in the cross-plane thermal conductivity, but the in-plane thermal conductivity drop, caused by the reduced group velocity, is much less than the reported experimental results. This suggests that the reduced relaxation time due to diffuse interface phonon scattering, dislocation scattering, etc, should make major contribution to the in-plane thermal conductivity reduction.

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