Anisotropy in the reciprocal lattice space of critical X-ray scattering in TGS

1973 ◽  
Vol 43 (3) ◽  
pp. 217-218 ◽  
Author(s):  
B. Pura ◽  
J. Przedmojski
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
V. V. Lizunov

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.


The broadening of X-ray line profiles is usually described by the kinematical scattering theory. In this chapter, the basic concepts and equations of the kinematical X-ray scattering are presented in order to better understand the theory of line profile analysis. The correlation between the crystal structure and the diffracted intensity distribution is shown. The scattering angles of the diffracted peak maxima are given by the Ewald construction in the reciprocal space. The correspondence between the reciprocal lattice vectors and the lattice planes is also presented, and the relationship between the scattering angle and the lattice plane spacing is given by Bragg’s law.


1990 ◽  
Vol 68 (11) ◽  
pp. 1279-1290
Author(s):  
W. Mayr ◽  
G. Fritsch ◽  
E. Lüscher

We report on experimental results for the thermal diffuse X-ray-scattering cross section from Na single crystals. Data are presented for the [100], [110], and [111] directions taken in the temperature range from 38 K to the melting point. In addition we present a numerical calculation of the harmonic diffuse-scattering cross section including all orders of multiphonon contributions using a realistic phonon-dispersion relation. The results of this model are compared with a simpler approximation for the higher order multiphonon terms. The differences between the calculations and the experimental data show a distinct asymmetrical behaviour with respect to the reciprocal lattice points. Owing to this fact and their temperature dependence they can be related to anharmonic scattering. The contributions of the four lowest order terms are derived from the data. The lowest order antisymmetric contribution agrees quite well with available theoretical calculations.


One-body potential theory, which includes the effect of exchange and correlation forces, is used to calculate the change in the electron density due to small displacements of the ions. The final result contains a Dirac density matrix for the perfect crystal, the diagonal element being the exact ground state density ρ 0 ( r ). The basic quantity R ( r ) determining the electronic contribution to the dynamical matrix is such that the gradient of ρ 0 ( r ) is obtained by superposition of R ( r - l ) on each lattice site l . An integral equation is obtained which gives R ( r ) uniquely once the exchange and correlation energy is known. The Fourier transform R k of R ( r ) is given in term s of the Fourier components ρ K n of the charge density, which are known from X-ray scattering, by R K n = i ρKn K n the reciprocal lattice vectors K n . This is the same result as the rigid-ion model at the K n 's, which makes the assumption that this is true for all k . Deviations from rigid ions can be evaluated quantitatively from the integral equation obtained here. Such deviations reflect the role of many-body forces in lattice dynamics and the present theory provides a systematic basis for their calculation.


Author(s):  
Eva-Maria Mandelkow ◽  
Eckhard Mandelkow ◽  
Joan Bordas

When a solution of microtubule protein is changed from non-polymerising to polymerising conditions (e.g. by temperature jump or mixing with GTP) there is a series of structural transitions preceding microtubule growth. These have been detected by time-resolved X-ray scattering using synchrotron radiation, and they may be classified into pre-nucleation and nucleation events. X-ray patterns are good indicators for the average behavior of the particles in solution, but they are difficult to interpret unless additional information on their structure is available. We therefore studied the assembly process by electron microscopy under conditions approaching those of the X-ray experiment. There are two difficulties in the EM approach: One is that the particles important for assembly are usually small and not very regular and therefore tend to be overlooked. Secondly EM specimens require low concentrations which favor disassembly of the particles one wants to observe since there is a dynamic equilibrium between polymers and subunits.


Author(s):  
Eva-Maria Mandelkow ◽  
Ron Milligan

Microtubules form part of the cytoskeleton of eukaryotic cells. They are hollow libers of about 25 nm diameter made up of 13 protofilaments, each of which consists of a chain of heterodimers of α-and β-tubulin. Microtubules can be assembled in vitro at 37°C in the presence of GTP which is hydrolyzed during the reaction, and they are disassembled at 4°C. In contrast to most other polymers microtubules show the behavior of “dynamic instability”, i.e. they can switch between phases of growth and phases of shrinkage, even at an overall steady state [1]. In certain conditions an entire solution can be synchronized, leading to autonomous oscillations in the degree of assembly which can be observed by X-ray scattering (Fig. 1), light scattering, or electron microscopy [2-5]. In addition such solutions are capable of generating spontaneous spatial patterns [6].In an earlier study we have analyzed the structure of microtubules and their cold-induced disassembly by cryo-EM [7]. One result was that disassembly takes place by loss of protofilament fragments (tubulin oligomers) which fray apart at the microtubule ends. We also looked at microtubule oscillations by time-resolved X-ray scattering and proposed a reaction scheme [4] which involves a cyclic interconversion of tubulin, microtubules, and oligomers (Fig. 2). The present study was undertaken to answer two questions: (a) What is the nature of the oscillations as seen by time-resolved cryo-EM? (b) Do microtubules disassemble by fraying protofilament fragments during oscillations at 37°C?


1992 ◽  
Vol 2 (6) ◽  
pp. 899-913 ◽  
Author(s):  
Patrick Davidson ◽  
Elisabeth Dubois-Violette ◽  
Anne-Marie Levelut ◽  
Brigitte Pansu

1996 ◽  
Vol 6 (8) ◽  
pp. 1085-1094 ◽  
Author(s):  
A. Gibaud ◽  
J. Wang ◽  
M. Tolan ◽  
G. Vignaud ◽  
S. K. Sinha

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