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Reciprocal lattice

About: Reciprocal lattice is a(n) research topic. Over the lifetime, 4980 publication(s) have been published within this topic receiving 112649 citation(s). The topic is also known as: reciprocal lattice vector.

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Journal ArticleDOI: 10.1107/S0567739468000707
Abstract: An extension of Furnas's method is described. The variation of intensity of an axial reflection as the crystal is rotated about the goniometer axis is used to give a curve of relative transmission T against azimuthal angle ϕ for the corresponding reciprocal lattice level. Transmission coefficients for any general reflexion hkl are then given approximately by T(hkl) = [T(ϕinc) + T(ϕret)]/2 where ϕinc and ϕret are the azimuthal angles of the incident and reflected beams. Equations are derived for (ϕinc and ϕret and the accuracy of the method is discussed.

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6,855 Citations


Journal ArticleDOI: 10.1107/S0108767383000252
Abstract: Absorption effects usually present the most serious source of systematic error in the determination of structure factors from single-crystal X-ray diffraction measurements if the crystal is not ground to a sphere or cylinder. A novel method is proposed for the correction of these effects for data collected on a diffractometer. The method works from the premise that the manifestation of systematic errors due to absorption, unlike most other sources of systematic error, will not be evenly distributed through reciprocal space, but will be localized. A Fourier series in the polar angles of the incident and diffracted beam paths is used to model an absorption surface for the difference between the observed and calculated structure factors. Knowledge of crystal dimensions or linear absorption coefficient is not required, and the method does not necessitate the measurement of azimuthal scans or any extra data beyond the unique set. Moreover, application of the correction is not dependent upon the Laue symmetry of the crystal or the geometry of the diffractometer. The method is compared with other commonly used corrections and results are presented which demonstrate its potential.

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4,913 Citations


Journal ArticleDOI: 10.1063/1.1704269
Abstract: Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points.The number of distinct points visited after n steps on a k‐dimensional lattice (with k ≥ 3) when n is large is a1n + a2n½ + a3 + a4n−½ + …. The constants a1 − a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 are given for simple and face‐centered cubic lattices. Formulas have also been obtained for the number of points visited r times in n steps as well as the average number of times a given point has been visited.The probability F(c) that a walker on a one‐dimensional lattice returns to his starting point before being trapped on a lattice of trap concentration c is F(c) = 1 + [c/(1 − c)] log c.Most of the results in this paper have been derived by the method of Green's functions.

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Topics: Integer lattice (64%), Reciprocal lattice (59%), Lattice plane (57%) ...read more

2,144 Citations


Journal ArticleDOI: 10.1063/1.331665
Abstract: This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...

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Topics: Thermal conduction (57%), Brillouin zone (57%), Debye model (56%) ...read more

1,998 Citations


Journal ArticleDOI: 10.1006/JCPH.1996.5612
Abstract: A quasi-Newton method is used to simultaneously relax the internal coordinates and lattice parameters of crystals under pressure. The symmetry of the crystal structure is preserved during the relaxation. From the inverse of the Hessian matrix, elastic properties, and some optical phonon frequencies at the Brillouin zone center can be estimated. The efficiency of the method is demonstrated for silicon test systems.

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Topics: Brillouin zone (58%), Quasi-Newton method (57%), Nearly free electron model (55%) ...read more

1,858 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202155
202085
201976
201884
2017120

Top Attributes

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Topic's top 5 most impactful authors

G. Bauer

17 papers, 510 citations

AA Anton Darhuber

16 papers, 245 citations

Gerrit E. W. Bauer

15 papers, 239 citations

Vasily I. Punegov

12 papers, 109 citations

Václav Holý

11 papers, 157 citations

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