scholarly journals A quantitative study of the reflexion of X-rays by sylvine

1928 ◽  
Vol 121 (787) ◽  
pp. 155-171 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Theoretical Result ◽  
Zero Point ◽  
Coherent Scattering ◽  
X Rays ◽  
Point Energy ◽  
X Ray ◽  
Quantitative Results ◽  
Theory And Experiment ◽  
Quantitative Treatment

In recent papers on the intensity of reflexion of X-rays from rocksalt crystals it has been shown that, from the temperature of liquid air up to about 500° abs., the dependence of the intensity of reflexion upon temperature is in accord quantitatively with a formula of the type originally deduced by Debye, if the modification suggested later by Waller is introduced, although the decrease of intensity for higher temperatures is much greater than that indicated by the law. In dealing with quantitative results of experiments on reflexion from crystals, it is convenient to consider the quantity usually denoted by F, which is a measure of the scattering power, in a given direction, of an atom for X-rays. In the course of experiments with rocksalt it has been possible to determine F both for Na and Cl, and the values so obtained, when corrected for temperature, agree very closely with the F factors calculated from Hartree’s Schrodinger density-distribution for the ions Cl - and Na + . The calculation is based upon the theoretical result, due to Wentzel and Waller that, to obtain the coherent scattering from an electron in an atom, the electron must be represented by its corresponding Schrodinger charge-density, each element of which must be supposed to scatter classically. In order to get agreement between the calculated and observed F curves, it is necessary to assume the existence of zero-point energy of amount half a quantum per degree of freedom, which is of course required by the new quantum mechanics. The agreement between theory and experiment in the case of rocksalt is extremely interesting, but, in order to place the quantitative treatment of X-ray reflexion on an entirely satisfactory basis, it appears to be of some impor­tance to see whether a similar agreement can be obtained with other crystals. This is not quite so easy as might be supposed.

scholarly journals An investigation into the existence of zero-point energy in the Rock-Salt Lattice by an X-Ray Diffraction Method

1928 ◽  
Vol 118 (779) ◽  
pp. 334-350 ◽  
Keyword(s):  
Rock Salt ◽  
Diffraction Method ◽  
Zero Point ◽  
Temperature Factor ◽  
X Rays ◽  
Zero Point Energy ◽  
Chlorine Atoms ◽  
Point Energy ◽  
X Ray ◽  
State Of Rest

In the present paper we shall attempt to collate the results of four separate lines of research which, taken together, appear to provide some interesting checks between theory and experiment. The investigations to be considered are (1) the discussion by Waller* and by Wentzel,† on the basis of the quantum (wave) mechanics, of the scattering of radiation by an atom ; (2) the calculation by Hartree of the Schrödinger distribution of charge in the atoms of chlorine and sodium ; (3) the measurements of James and Miss Firth‡ of the scattering power of the sodium and chlorine atoms in the rock-salt crystal for X-rays at a series of temperatures extending as low as the temperature of liquid air ; and (4) the theoretical discussion of the temperature factor of X-ray reflexion by Debye§ and by Waller.∥ Application of the laws of scattering to the distribution of charge calculated for the sodium and chlorine atoms, enables us to calculate the coherent atomic scattering for X-radiation, as a function of the angle of scattering and of the wave-length, for these atoms in a state of rest, assuming that the frequency of the X-radiation is higher than, and not too near the frequency of the K - absorption edge for the atom.¶ From the observed scattering power at the temperature of liquid air, and from the measured value of the temperature factor, we can, by applying the theory of the temperature effect, calculate the scattering power at the absolute zero, or rather for the atom reduced to a state of rest. The extrapolation to a state of rest will differ according to whether we assume the existence or absence of zero point energy in the crystal lattice. Hence we may hope, in the first place to test the agreement between the observed scattering power and that calculated from the atomic model, and in the second place to see whether the experimental results indicate the presence of zero-point energy or no.

scholarly journals From Femtoseconds to Hours–Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

2021 ◽  
Vol 11 (13) ◽  
pp. 6179
Author(s):  
Felix Lehmkühler ◽  
Wojciech Roseker ◽  
Gerhard Grübel
Keyword(s):  
Time Scales ◽  
Free Electron Laser ◽  
Photon Correlation Spectroscopy ◽  
Signal To Noise Ratio ◽  
Coherent Scattering ◽  
Correlation Spectroscopy ◽  
X Rays ◽  
Photon Correlation ◽  
X Ray ◽  
Scattering Technique

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Quantitative Determination of Carbon in Solid Hydrocarbons Using the Intensity Ratio of Incoherent to Coherent Scattering of X-Rays

1964 ◽  
Vol 18 (6) ◽  
pp. 171-174 ◽  
Author(s):  
C. J. Toussaint ◽  
G. Vos
Keyword(s):  
Intensity Ratio ◽  
Coherent Scattering ◽  
X Rays ◽  
Ray Method ◽  
Sample Weight ◽  
X Ray ◽  
Carbon Determination ◽  
Solid Hydrocarbons ◽  
Good Agreement

A method is presented for the determination of carbon in solid hydrocarbons using the intensity ratio of incoherent to coherent scattering of x-rays. The method is very rapid with precision at the 95% confidence level of about ±0.3%. The minimum sample weight necessary is 0 2 g. Analysis of samples by the x-ray method shows good agreement with values obtained by microcombustion. Finally a general comparison between different methods for carbon determination in solid hydrocarbons is discussed.

X-Ray Investigation of the Amorphous State of Rubber

1955 ◽  
Vol 28 (3) ◽  
pp. 728-731 ◽  
Author(s):  
V. I. Kasatochkin ◽  
B. V. Lukin
Keyword(s):  
Diffraction Pattern ◽  
Amorphous State ◽  
Coherent Scattering ◽  
X Rays ◽  
X Ray Diffraction ◽  
Molecular Liquids ◽  
X Ray ◽  
Large Molecules ◽  
Molecular Substances ◽  
High Degree

Abstract The x-ray diffraction pattern of amorphous rubber, which is an amorphous ring, resembles the pattern of low-molecular liquids. In our previous work, it was established that the diffraction pattern observed is due to the coherent scattering of only those segments of the molecular chains in which the aggregation is analogous to that of low-molecular liquids, and is determined by the presence of a pseudo-order. A large part of the links of the molecular chains, owing to the prevailing disorder, scatters the x-rays incoherently, like scattering by a gas. For one component of amorphous rubber, the concept of “liquid phase” was introduced, and, for the other, that of “gaseous phase”, thereby subdividing them according to the type of scattering of x-rays. Amorphous rubber, according to our data, contains a large number of chair segments which are characterized by a high degree of disorder. The presence of such a disordered molecular phase is a general and characteristic property of high-molecular substances, and is caused by natural obstacles in the dense packing of the large molecules. This characteristic of molecular aggregation is undoubtedly reflected in the physical-mechanical properties of polymers.

scholarly journals A quantitative study of the reflexion of X-rays from crystals of aluminium

1929 ◽  
Vol 125 (798) ◽  
pp. 401-419 ◽  
Keyword(s):  
Single Crystals ◽  
Quantitative Study ◽  
Rock Salt ◽  
Zero Point ◽  
X Rays ◽  
Point Energy ◽  
Absolute Intensities ◽  
Metallic Element ◽  
Atomic Scattering ◽  
Direct Confirmation

1. It has already been shown that the observed variations with temperature of the intensity of reflexion of X-rays from crystals of rock-salt and sylvine agree closely with those predicted by the theory of Debye as modified by Waller, from the lowest temperature at which experiments have been made, that of liquid air, up to about 500° abs. Moreover, the absolute intensities of reflexion agree closely with those calculated theoretically, if the atomic scattering factors, F, are calculated from the Schrödinger charge-distributions for the atoms, obtained by the method due to Hartree. To obtain agreement, it is necessary to assume the existence of zero-point energy of an amount half a quantum for each degree of freedom, and the experiments may perhaps do considered as furnishing direct confirmation of such energy, since the differences between the intensities calculated with and without it are considerable. The work to do described in this paper was undertaken with a view to extending the investigations to a crystal of a metallic element. Aluminium at ones suggested itself as suitable for this purpose, since it can do obtained in largo single crystals, and since its coefficient of adsorption for the X-rays employed in the experiments, Mo K a , is small.

Coherent and incoherent scattering of low-energy X-ray photons in the atomic region 13 ≤ Z ≤ 82

1996 ◽  
Vol 74 (1-2) ◽  
pp. 10-16 ◽  
Author(s):  
D. V. Rao ◽  
R. Cesareo ◽  
G. E. Gigante ◽  
D. V. Rao ◽  
G. E. Gigante
Keyword(s):  
Cross Sections ◽  
Detection System ◽  
Form Factors ◽  
Coherent Scattering ◽  
Incoherent Scattering ◽  
X Rays ◽  
Bremsstrahlung Radiation ◽  
X Ray ◽  
Scattering Cross ◽  
Scattering Cross Sections

Coherent- and incoherent-scattering cross sections for the elements Al, Cu, Y, In, Au, and Pb were measured using nearly monoenergetic unpolarized 35.86 and 39.96 keV X-ray beams with high-resolution Si (Li) detectors. Bremsstrahlung radiation from an X-ray tube was used to excite nearly monoenergetic X-rays in secondary targets. To improve the efficiency of the detection system the excitation source, detector, and the target assembly were placed in a vacuum chamber and a pressure of 10−2 mbar was maintained throughout the measurements. This system considerably reduced the background and scattering effects and improved the monochromacy. Experimental coherent-scattering cross sections are compared with the normalized integrated coherent-scattering cross sections calculated using the relativistic, nonrelativistic, and relativistic-modified form factors. Experimental incoherent-scattering cross sections are compared with the theoretical values, calculated using the nonrelativistic incoherent-scattering function. Good correspondence is observed between experimental and theoretical values in the given energy region.

scholarly journals Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser Facility

2021 ◽  
Vol 28 (2) ◽  
pp. 637-649
Author(s):  
A. Madsen ◽  
J. Hallmann ◽  
G. Ansaldi ◽  
T. Roth ◽  
W. Lu ◽  
...  
Keyword(s):  
Free Electron ◽  
Free Electron Laser ◽  
Condensed Matter ◽  
Coherent Scattering ◽  
X Rays ◽  
Structured Materials ◽  
X Ray ◽  
Structure And Dynamics ◽  
Laser Facility

The Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser (EuXFEL) facility is described. EuXFEL is the first hard X-ray free-electron laser operating in the MHz repetition range which provides novel science opportunities. The aim of MID is to enable studies of nano-structured materials, liquids, and soft- and hard-condensed matter using the bright X-ray beams generated by EuXFEL. Particular emphasis is on studies of structure and dynamics in materials by coherent scattering and imaging using hard X-rays. Commission of MID started at the end of 2018 and first experiments were performed in 2019.

Quantum mechanics under X-rays in the Gran Sasso underground laboratory

2017 ◽  
Vol 15 (08) ◽  
pp. 1740004 ◽  
Author(s):  
Catalina Curceanu ◽  
Diana Sirghi ◽  
Florin Sirghi ◽  
Sergio Bartalucci ◽  
Massimiliano Bazzi ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Pauli Exclusion Principle ◽  
Underground Laboratory ◽  
Exclusion Principle ◽  
X Rays ◽  
X Ray ◽  
Localization Model ◽  
Continuous Spontaneous Localization ◽  
Broad Region

By performing X-ray measurements in the “cosmic silence” of the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: the Pauli Exclusion Principle (PEP) for electrons. We present the achieved results of the VIP experiment and the ongoing VIP2 measurement aiming to gain two orders of magnitude improvement in testing PEP. X-ray emission can also be used to put strong constraints on the parameters of the Continuous Spontaneous Localization Model, which was introduced as a possible solution to the measurement problem in Quantum Mechanics. A Bayesian analysis of the data collected by IGEX will be presented, which allows to exclude a broad region of the parameter space which characterizes this model.

Interface characterization of B4C-based multilayers by X-ray grazing-incidence reflectivity and diffuse scattering

2013 ◽  
Vol 20 (3) ◽  
pp. 449-454 ◽  
Author(s):  
Hui Jiang ◽  
Zhanshan Wang ◽  
Jingtao Zhu
Keyword(s):  
Diffuse Scattering ◽  
Aging Process ◽  
Grazing Incidence ◽  
X Rays ◽  
X Ray ◽  
Interface Characterization ◽  
Quantitative Results ◽  
Fabrication And Characterization ◽  
Stable Structures

B4C-based multilayers have important applications for soft to hard X-rays. In this paper, X-ray grazing-incidence reflectivity and diffuse scattering, combining various analysis methods, were used to characterize the structure of B4C-based multilayers including layer thickness, density, interfacial roughness, interdiffusion, correlation length,etc.Quantitative results for W/B4C, Mo/B4C and La/B4C multilayers were compared. W/B4C multilayers show the sharpest interfaces and most stable structures. The roughness replications of La/B4C and Mo/B4C multilayers are not strong, and oxidations and structure expansions are found in the aging process. This work provides guidance for future fabrication and characterization of B4C-based multilayers.

Sign in / Sign up

Export Citation Format

Share Document