scholarly journals An X-ray study of the heat motions of the atoms in a rock-salt crystal

1927 ◽  
Vol 117 (776) ◽  
pp. 62-87 ◽  
Keyword(s):  
Fourier Analysis ◽  
Rock Salt ◽  
Low Temperatures ◽  
X Rays ◽  
Salt Crystal ◽  
X Ray ◽  
Salt Crystals ◽  
Different Temperatures ◽  
Atomic Scattering ◽  
Actual Amplitude

1. The present paper may be divided into two parts. In the first, some experiments on the intensity of reflexion of X-rays by rock-salt crystals at low temperatures are described. The results of these experiments, when combined with data obtained previously at high temperatures, are compared with the theoretical formulæ of Debye and Waller for the temperature factor of X-ray reflexion. In the second part of the paper we have attempted to get some idea of the actual amplitude of the heat-motions of the atoms in the rock-salt lattice, by analysing the F curves, or curves showing the variation of the atomic scattering power with angle of scattering, using the method of Fourier analysis introduced by Duane and Havighurst, so as to obtain the distribution of electrons in the crystal unit at different temperatures. In connection with this work a new set of absolute determinations of intensity of reflexion has been made, and, from these, the F factors at different temperatures have been calculated, using the results of the experiments described in the first part of the paper.

A focusing X-ray telescope for use in the study of extraterrestrial X-ray sources in the energy range 20–140 keV

1968 ◽  
Vol 46 (10) ◽  
pp. S1103-S1106 ◽  
Author(s):  
T. R. Llndquist ◽  
W. R. Webber
Keyword(s):  
Energy Range ◽  
Rock Salt ◽  
Angular Resolution ◽  
X Rays ◽  
Effective Energy ◽  
Optimum Thickness ◽  
Bragg Condition ◽  
X Ray ◽  
Area Efficiency ◽  
Salt Crystals

We have designed and tested a focusing X-ray telescope with an angular resolution (FWHM) of 1.0° for the study of extraterrestrial X-ray sources in the energy range 20–140 keV. The telescope's lens is an array of rock salt crystals (each of which is approximately one inch square), mounted on a 6-ft-diameter paraboloidal frame. The lens is located 9.5 ft above a 2-in.-diameter NaI crystal and PM tube (which measures the energy of the incident X ray). X rays passing through the salt crystals undergo a 2θ deflection if the Bragg condition for reflection, nλ = 2d sin θ, is approximately satisfied. Optimum thickness and effective energy bandwidths for such reflections have been determined for energies in the telescope's operating range. The area-efficiency product of the lens is approximately 8 times the NaI crystal area from 20 to 40 keV, giving a real improvement in the signal-to-background ratio. Crystals more nearly perfect than rock salt offer the possibility of increased gain over narrow energy intervals. Polarization measurements of the incident X rays may also be made.

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.

X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

X-ray Scattering Factors of Ions in Crystals

1979 ◽  
Vol 34 (12) ◽  
pp. 1471-1481 ◽  
Author(s):  
P. C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Gaseous Phase ◽  
Form Factors ◽  
Negative Ions ◽  
X Rays ◽  
Charged Sphere ◽  
Sphere Model ◽  
X Ray ◽  
Hartree Fock ◽  
X Ray Scattering ◽  
Atomic Scattering

AbstractThe atomic scattering factors for X - Rays are given for the ions Li⊕, Be2⊕, B3⊕, C4⊕, N5⊕, N3⊖, O2⊖, F⊖, Na⊕, Mg2⊕, Al3⊕, S2⊖, Cl⊖, K⊕, Ca2⊕, Sc3⊕, Ti4⊕, V5⊕, Ni, Cu⊕, Zn2⊕, Ga3⊕, Se2⊖, Br⊖, Rb⊕, Sr2⊕, Y3⊕, Pd, Ag⊕, Cd2⊕, I⊖, Cs⊕, and Ba2⊕ in the crystal. The crystal potential is simulated by a hollow charged sphere (Watson sphere model). The Hartree-Fock-Roothaan-method was used for the calculation. The crystal field affects most strongly the atomic form factors of the negative ions, especially the twofold and threefold ionized negative ions, which are unstable in the gaseous phase.

Measurement of L X-ray production cross sections and relative intensities of some lanthanide compounds depending on the temperature

2020 ◽  
Vol 108 (5) ◽  
pp. 415-423
Author(s):  
Esra Cinan ◽  
Bünyamin Aygün ◽  
M. I. Sayyed ◽  
Yüksel Özdemir
Keyword(s):  
Cross Sections ◽  
Full Width Half Maximum ◽  
Production Cross ◽  
Emission Spectra ◽  
X Rays ◽  
X Ray ◽  
Different Temperatures ◽  
Intensity Ratios ◽  
Annular Source

AbstractL X-ray intensity ratios for CeO2, Sm2(SO4)3, Ho2O3, and Yb2O3 compounds were experimentally investigated. The measurements were gauged following excitation by 59.54 keV γ-rays from a 100 mCi 241Am radioactive annular source at different temperatures in situ. Temperature change occurred between 50 °C and 400 °C. L X-ray emission spectra were obtained by using a solid-state Si(Li) X-ray detector. L X-ray production cross sections, intensity ratios, and full-width half maximum (FWHM) values for the compounds were determined by evaluating the emission spectra varying with the temperature. According to the results obtained, it was observed that Lβ1 X-rays were less influenced in comparison with Lα X-rays while Lα X-rays were also less influenced in comparison with Lβ2 X-rays.

Theory of Detection of X-Rays by Superconductors

1997 ◽  
Vol 11 (19) ◽  
pp. 849-859 ◽  
Author(s):  
N. Murali Krishna ◽  
Lydia S. Lingam ◽  
Keshav N. Shrivastava
Keyword(s):  
Low Temperatures ◽  
Cooper Pair ◽  
Single Electron ◽  
Superconducting Film ◽  
Pair Breaking ◽  
X Rays ◽  
X Ray ◽  
Electron Process

Two new processes occur in a superconducting film when it is used as a detector of X-rays. One of these processes is the scattering of the X-ray by a single electron which gives rise to the broadening of the X-ray line. Another process describes the breaking of a Cooper pair by the X-ray which also contributes to the width of the X-ray. The line arising from the single electron process depends on T4 whereas that arising from the pair breaking process varies almost as T6 at low temperatures. Lines occur at ℏωq ± 2Δ, and at ℏωq where ℏωq is the energy of the X-ray and 2Δ is the gap of the superconductor.

scholarly journals V4046 Sgr: X-rays from accretion shock

2013 ◽  
Vol 9 (S302) ◽  
pp. 46-47
Author(s):  
C. Argiroffi ◽  
A. Maggio ◽  
T. Montmerle ◽  
D. Huenemoerder ◽  
E. Alecian ◽  
...  
Keyword(s):  
Tauri Star ◽  
X Rays ◽  
X Ray ◽  
Accretion Flows ◽  
T Tauri ◽  
Different Temperatures ◽  
Sgr A ◽  
Star Binary ◽  
Accretion Shock ◽  
Density Plasma

AbstractWe present results of the X-ray monitoring of V4046 Sgr, a close classical T Tauri star binary, with both components accreting material. The 360 ks long XMM observation allowed us to measure the plasma densities at different temperatures, and to check whether and how the density varies with time. We find that plasma at temperatures of 1–4 MK has high densities, and we observe correlated and simultaneous density variations of plasma, probed by O VII and Ne IX triplets. These results strongly indicate that all the inspected He-like triplets are produced by high-density plasma heated in accretion shocks, and located at the base of accretion flows.

Masquerade: removing non-sample scattering from integrated reflection intensities

2012 ◽  
Vol 45 (2) ◽  
pp. 292-298 ◽  
Author(s):  
J. A. Coome ◽  
A. E. Goeta ◽  
J. A. K. Howard ◽  
M. R. Probert
Keyword(s):  
Data Collection ◽  
Diffraction Data ◽  
Low Temperatures ◽  
Test Case ◽  
X Rays ◽  
Atmospheric Conditions ◽  
X Ray Diffraction ◽  
New Approach ◽  
X Ray ◽  
Internal Agreement

X-ray diffraction experiments at very low temperatures require samples to be isolated from atmospheric conditions and held under vacuum. These conditions are usually maintainedviathe use of beryllium chambers, which also scatter X-rays, causing unwanted contamination of the sample's diffraction pattern. The removal of this contamination requires novel data-collection and processing procedures to be employed. Herein a new approach is described, which utilizes the differences in origin of scattering vectors from the sample and the beryllium to eliminate non-sample scattering. The programMasqueradehas been written to remove contaminated regions of the diffraction data from the processing programs. Coupled with experiments at different detector distances, it allows for the acquisition of decontaminated data. Studies of several single crystals have shown that this approach increases data quality, highlighted by the improvement in internal agreement factor with the test case of cytidine presented herein.

Optical and Dimensional Changes Which Accompany the Freezing and Melting of Hevea Rubber

1939 ◽  
Vol 12 (1) ◽  
pp. 18-30 ◽  
Author(s):  
W. Harold Smith ◽  
Charles Proffer Saylor
Keyword(s):  
Optical Properties ◽  
Low Temperatures ◽  
Heat Content ◽  
Uniaxial Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Dimensional Changes ◽  
Ether Yield ◽  
The Individual

Abstract At suitable, low temperatures, unvulcanized rubber loses its elasticity and becomes hard and opaque. Similar changes frequently occur in baled rubber which has been tightly compressed before shipment. It is said to be frozen or “boardy.” The phenomenon has been studied by many investigators who have determined changes of volume, softening temperatures, the effects of increasing time of storage at low temperatures, the influence of pressure during freezing, and changes in heat capacity and entropy. These effects have generally been ascribed to a form of crystallization, and x-ray diffraction powder patterns indicate that crystals are present in frozen rubber. When total rubber is stretched, there are changes of volume and of heat content such as attend crystallization. With x-rays a crystal fiber pattern is obtained. It and the powder pattern obtained with frozen, compact rubber have been shown to indicate similar spacings and are assumed to be caused by the same type of crystal, the differences being ascribed to conditions of orientation. Dilute solutions of rubber hydrocarbon in ethyl ether yield small crystals of the hydrocarbon when they are subjected to temperatures between −35° and − 60° C. for several hours. The optical properties and melting points of these crystals and their x-ray diffraction patterns indicate their identity with the crystals in stretched and frozen rubber. Under the best conditions the crystals appear in spherulitic groupings, the individual needles in each spherulite having optical properties that closely approach those of a uniaxial crystal with negative elongation. The crystals of sol rubber which we obtained, melted between 9.5° and 11.0° C. Crystals of gel rubber melted between −2° and 14° C., but the melting ranges within this interval were not the same for all samples. Numerous observations have repeatedly confirmed the data. About 90 per cent of the rubber in solution may be obtained as birefringent material at −65° C. Temperatures between −40° and −50° C. have been preferred, however, because better crystals are obtained in that range.

SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE

2020 ◽  
Vol 386 (4) ◽  
pp. 6-12
Author(s):  
R. T. Abdraimov ◽  
B. E. Vintaykin ◽  
P. A. Saidakhmetov ◽  
N. K. Madiyarov ◽  
M. A. Abdualiyeva
Keyword(s):  
Spectral Analysis ◽  
Fourier Analysis ◽  
Least Squares ◽  
Phase Analysis ◽  
Least Squares Method ◽  
Spectral Lines ◽  
X Rays ◽  
Cauchy Function ◽  
X Ray ◽  
Smoothing Functions

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

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