A New Method for Fourier Analysis of Shapes of X-Ray Peaks and Its Application to Line Broadening and Integrated Intensity Measurements

1969 ◽  
pp. 208-235 ◽  
Author(s):  
R. L. Rothman ◽  
J. B. Cohen
Keyword(s):  
Fourier Analysis ◽  
New Method ◽  
Line Broadening ◽  
X Ray ◽  
Intensity Measurements ◽  
Integrated Intensity

A New Method for Fourier Analysis of Shapes of X-Ray Peaks and its Application to Line Broadening and Integrated Intensity Measurements

1968 ◽  
Vol 12 ◽  
pp. 208-235 ◽  
Author(s):  
R. L. Rothman ◽  
J. B. Cohen
Keyword(s):  
Particle Size ◽  
Fourier Analysis ◽  
Volume Fraction ◽  
Line Broadening ◽  
X Ray ◽  
Bcc Metals ◽  
Intensity Measurements ◽  
Integrated Intensity ◽  
Multiple Orders ◽  
Effect Of Particle Size

AbstractA method of Fourier analysis of x-ray line broadening is presented whereby microstrain, incoherent particle size, and fault probability can be calculated using only first-order peaks. This method can thus be used in studies of catalysts, vapor- and electrodeposits or heavily textured specimens for which second-order peaks are too broad or weak, in cases where the effect of particle size is not the same for all orders of a peak, or for multiphase specimens where overlap of peaks sometimes occurs. Examples of deformed FCG and BCC metals and alloys are presented, with comparisons to the method of multiple orders.One part of the procedure, first demonstrated by Pines and Sirenko, provides for reducing the effects of truncation on the Fourier coefficients. As a result, larger particle sizes can be analyzed and the integrated intensity can be determined more precisely. Application to determinations of volume fraction are given.

scholarly journals The structure of benzoquinone. A quantitative X-ray investigation

1935 ◽  
Vol 150 (869) ◽  
pp. 106-128 ◽  
Keyword(s):  
Carbon Atom ◽  
Fourier Analysis ◽  
Aromatic Compounds ◽  
X Ray ◽  
Intensity Measurements ◽  
Present Technique ◽  
Aliphatic Carbon ◽  
Ray Methods ◽  
Single Bonds ◽  
Chemical Evidence

One of the principal results of recent X-ray studies of aromatic compounds has been the proof that the benzene ring has the form of a regular plane hexagon, the distance from centre to centre of the carbon atoms being 1·41 A. It is not easy to state concisely to what limits of accuracy this has been established, because the precision of the intensity measurements varies somewhat from compound to compound according to the experimental difficulties. The accuracy of the results can probably best be judged by inspection of the contoured maps of electron density which have been obtained by Fourier analysis from the various structures. In favourable cases quite a small departure from regularity in the structure, say of the order of 0·03 A, would be detected with some certainty. This work has shown that the carbon atom in aromatic compounds differs in size as well as in the disposition of its valency bonds from the aliphatic carbon atom. As yet there has been no evidence of the alternating double and single bonds of the Kekulé formula, but, of course the X-ray work would not be expected to reveal any permanent difference in the links in the true aromatic compounds, because all the chemical evidence goes to show that the six corners of the ring are equivalent, and if the links are of two kinds their positions must interchange with great rapidity. But if the configuration is stabilized by the introduction of divalent groups or by other means, then it might be possible to detect a distortion in the shape of the ring by X-ray methods. We should expect a contraction at the double bonds and corresponding alteration of the valency angles. The effects would certainly be small but the present technique of X-ray analysis should be capable of revealing them.

scholarly journals Correction factors in the photographic measurements of x-ray intensities in crystal analysis

1930 ◽  
Vol 127 (804) ◽  
pp. 71-88 ◽  
Keyword(s):  
Background Radiation ◽  
Complete Solution ◽  
Special Technique ◽  
X Rays ◽  
X Ray ◽  
Intensity Measurements ◽  
Integrated Intensity ◽  
Lattice Planes ◽  
Complex Crystals ◽  
Lengthy Operation

For the complete solution of the structures of complex crystals, and in particular of organic substances, it is essential to be able to measure at least the relative intensities of reflexion of homogeneous X-rays from the more important lattice planes with some degree of accuracy. In most crystal problems a number of parameters governing the positions of the atoms in the lattice remain to be found after the geometrical requirements of the symmetry have been satisfied. These can only be determined from intensity measurements, so that in general, the greater the number of reflexions measured, the more closely will the deduced structure approach to the truth. Until comparatively recently the only instrument of precision available for X-ray intensity work has been the Bragg ionisation spectrometer. It has, however, three disadvantages when used for this purpose, which may be briefly summarised:— (1) Only the strongest planes are measurable with any degree of accuracy, owing to the “swamping” effect of the unremovable background radiation in the case of the weaker reflexions. (2) It is clearly impossible to use it, without very special technique, in the case of crystals which are volatile or even liquid at normal temperatures. (3) The measurement of the true integrated intensity is a somewhat lengthy operation in practice, with the result that experimenters are tempted to determine the peak values of the intensities instead; these, in general, are not in the same ratio as the integrated reflexions, so that a false idea of the reflexions may be obtained.

The Detection and Quantification of Low Concentrations of Quartz in Dolostone by X-Ray Powder Diffraction

1989 ◽  
Vol 4 (4) ◽  
pp. 209-213 ◽  
Author(s):  
Jeffrey A. Emig ◽  
Deane K. Smith
Keyword(s):  
Powder Diffraction ◽  
Weight Percent ◽  
Soil Samples ◽  
Quartz Sample ◽  
X Ray ◽  
Standard Preparation ◽  
Intensity Measurements ◽  
Low Concentrations ◽  
Integrated Intensity ◽  
Detection And Quantification

AbstractQuartz in dolostone can be determined quantitatively down to 0.03 weight percent using a standard preparation procedure for the sample and absolute integrated intensity measurements. Measurement reproducibilities of 3.2% were obtained. Calibration curves determined by spiking low-quartz dolostone allowed concentrations of 2.0 weight percent or lower to be established. Higher concentrations of quartz in some related soil samples were determined by comparing the absolute integrated intensity with that obtained from a pure quartz sample prepared in the same manner.

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