The electronic Debye - Waller factor for X - ray scattering

1993 ◽  
Vol 87 (7) ◽  
pp. 631-633
Author(s):  
B.N. Kodess ◽  
S.Ya. Rakhmanov
1974 ◽  
Vol 52 (22) ◽  
pp. 2281-2298 ◽  
Author(s):  
H. R. Glyde

The properties of interference between the one and multiphonon contributions to the dynamic and static scattering functions, S(Q, ω) and S(Q), first considered by Ambegaokar et al., are discussed in detail for b.c.c 3He and 4He for comparison with recent neutron and proposed X ray scattering experiments. Calculations of interference for Na and of the Debye temperature appropriate to the Debye–Waller factor in b.c.c 3He are also presented. In all cases the on shell interference term which alters the one phonon scattering intensity is found to be more important than the off shell term which alters the one phonon line shape. This is characteristic of systems in which anharmonic effects produce a large phonon frequency shift but in which the phonon lifetimes remain long. The difficulty in establishing the one phonon sum rules experimentally in the presence of interference is emphasized. As noted by Horner, existing unusual variations of scattering intensity observed in solid 4He can be satisfactorily explained by taking account of interference and this difficulty without introducing an anomolous Debye–Waller factor. Comparisons with liquid 4He suggest a similar difficulty in establishing the sum rules there.


1962 ◽  
Vol 6 ◽  
pp. 136-141
Author(s):  
F. R. L. Schoening ◽  
F. Witt

AbstractOxygen was introduced into a single crystal of titanium in successive stages. The intensities of the h00 and 00l reflections were measured with a single-crystal diffractometer. The observed variation of the intensities with oxygen concentration was attributed to three factors: (1) the additional scattering from the oxygen atoms, (2) a change in the Debye-Waller factor, and (3) an exponential factor originating from the distortion around the oxygen atom. The theory of X-ray scattering from crystals containing centers of distortion was applied to the hexagonal titanium containing interstitial oxygen atoms. Using the variation of the lattice constant with oxygen concentration, it was possible to predict the intensity reduction due to lattice strains. It was concluded that it would have been possible to obtain an estimate of the defect concentration from the X-ray measurements of lattice expansion and intensity reduction.


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

2002 ◽  
Vol 12 (6) ◽  
pp. 385-390 ◽  
Author(s):  
J.-F. Bérar ◽  
L. Blanquart ◽  
N. Boudet ◽  
P. Breugnon ◽  
B. Caillot ◽  
...  

2007 ◽  
Vol 2007 (suppl_26) ◽  
pp. 247-252
Author(s):  
R. Kužel ◽  
L. Nichtová ◽  
Z. Matěj ◽  
D. Heřman ◽  
J. Šicha ◽  
...  

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