scholarly journals The absorption of monochromatic X-ray beams, of wave-length in the region 50 to 20 X -units, in lead, tin, copper, and iron

1935 ◽  
Vol 152 (876) ◽  
pp. 402-417 ◽  
Author(s):  
John Read ◽  
John Cunningham McLennan
Keyword(s):  
Absorption Coefficient ◽  
Atomic Number ◽  
Wave Length ◽  
Detailed Account ◽  
Photoelectric Absorption ◽  
Absorption Coefficients ◽  
X Ray ◽  
Method Of Measurement ◽  
Absorption Measurements

In a previous paper an account has been given of the measurement of the absorption of monochromatic X-ray beams of wave-length in the region 50 to 20 x -units, in carbon and aluminium. The relation of the measured coefficient of absorption to the wave-Iength did not differ from that predicted by the Klein-Nishina formula by more than 1%. The method used in that experiment has been improved, and used to measure the absorption coefficients of lead, tin, copper, and iron for similar monochromatic beams. Because lead has been used very extensively for absorption measurements the primary aim has been to measure as accurately as possible the dependence of its absorption coefficient on the wave-length of the radiation. It has not been possible to make such accurate measurements on tin, copper, and iron, but enough data has been obtained to determine the variation of the photoelectric absorption coefficient per electron with the atomic number of the absorbing element, with fair accuracy, for radiation in this region of wave-lengths. Since these absorption coefficients may find considerable application, it is considered well to give a more detailed account of the method of measurement, so that an independent judgment of their reliability may be made.

scholarly journals The absorption of X-rays

1918 ◽  
Vol 94 (664) ◽  
pp. 510-524 ◽  
Keyword(s):  
Absorption Coefficient ◽  
Atomic Absorption ◽  
Atomic Number ◽  
Wave Length ◽  
Fourth Power ◽  
X Rays ◽  
Absorption Coefficients ◽  
Characteristic Radiation ◽  
Crystal Face ◽  
X Ray

Introduction . —Previous to the discovery of the behaviour of X-rays with regard to crystals, the most homogeneous radiation obtainable was that of the characteristic radiation of an element which is excited when that element is exposed to X-radiation of suitable hardness. These characteristic radiations are now found, however, by the new method of analysis, to be constituted of a number of radiations of different wave-lengths. Moseley, shortly after the discovery of the reflection of X-rays, showed that the characteristic radiations of most of the metals he examined consisted of two prominent wave-lengths; Bragg later found that, in the case of rhodium, palladium and silver, each of these lines could be further resolved into two components. Hence the spectra of the characteristic radiation of the K series of these elements consist of at least four different wave-lengths. The analysis of a beam of X-rays into its constituent radiations by reflection at a crystal face provides a means, therefore, of obtaining radiation of a definite wave length and of such intensity as to enable its absorption coefficient in different materials to be accurately measured. Bragg and Pierce have already measured the absorption coefficients of the two most prominent lines in the spectra of the elements Rh, Pd and Ag, in a number of metals. To make the absorption coefficient more directly comparable with other atomic characteristics, they gave their results in the form of atomic absorption coefficients: the atomic absorption coefficient expresses the proportion of the energy of an X-ray pencil which is absorbed in crossing a surface on which lies one atom to every square centimetre. The ordinary mass absorption coefficient can be calculated from this quantity by dividing it by the mass of the absorbing atom. The experimental results showed that the ratio of two absorption coefficients is independent of the wave-length of the radiation over considerable ranges, a result previously deduced by Barkla from his experiments; also, that the atomic absorption coefficient is proportional to the fourth power of the atomic number of the absorber.

scholarly journals A critical-absorption photometer for the study of the Compton effect

1928 ◽  
Vol 119 (783) ◽  
pp. 526-530
Keyword(s):  
Absorption Coefficient ◽  
Wave Length ◽  
Light Element ◽  
Compton Effect ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Length Changes ◽  
Absorption Measurements ◽  
Ray Scattering

That a change of wave-length occurs in X-ray scattering was first indicated by absorption measurements with the ionisation chamber, which showed that the absorption coefficient of a light element like aluminium was slightly greater for the scattered than for the primary X-rays. Later more conclusive and direct evidence was obtained when spectrometric analysis of the scattered X-rays was made first by the ionisation and afterwards by the photographic method. This analysis disclosed the existence of an unshifted as well as the shifted line, and showed also that the latter becomes relatively more prominent with diminishing wave-length and lower atomic number of the scattering element. After the main features of the Compton effect were established by means of spectrometric measurements, however, absorption measurements with the ionisation method have again been employed for a detailed study of the phenomenon, for such measurements are much quicker than the spectrum experiments, where the final energy available is much smaller on account of the double scattering involved. As mentioned above, the absorption measurements were based on the slight increase in the absorption coefficient of a light element when the wave-length changes from the unmodified to the modified value. The much larger and sudden diminution in absorption of X-rays when the frequency is altered from the short to the long wave-length side of the critical K-absorption limit of the element used as a filter, furnishes us with an easy and convenient method of exhibiting the wave-length change in X-ray scattering. In the present paper will be described a photographic wedge photometer based on this principle, which enables the characteristics of the Compton effect to be readily observed. It may be pointed out that the same idea could no doubt be utilised also in connection with the ionisation measurements of the Compton effect.

THE ABSORPTION OF GAMMA-RAYS FROM Co60

1947 ◽  
Vol 25a (6) ◽  
pp. 303-314 ◽  
Author(s):  
W. V. Mayneord ◽  
A. J. Cipriani
Keyword(s):  
Absorption Coefficient ◽  
Atomic Number ◽  
Gamma Rays ◽  
Heavy Elements ◽  
Photoelectric Absorption ◽  
Lead Absorber ◽  
Absorption Coefficients ◽  
Cobalt Radiation ◽  
Good Agreement ◽  
Made In

Measurements of the absorption of gamma-rays from Co60 and radium have been made in a number of materials. Variation of absorption coefficient of the gamma-rays from radium with thickness of lead absorber is in agreement with recent experimental determinations. The gamma-rays from Co60 are approximately monochromatic and are therefore suitable for testing theoretical absorption formulae. The absorption coefficient per electron for materials of atomic number equal to or less than that of aluminium was in agreement with the Klein–Nishina formula, assuming the cobalt radiation to consist of two lines at 1.10 and 1.30 Mev. respectively. The photoelectric absorption coefficients per electron for heavy elements are in good agreement with the theory developed by Hulme, McDougall, Buckingham, and Fowler. This coefficient varies approximately as Z3.5.

The Photoelectric Absorption of Gamma Rays

1931 ◽  
Vol 27 (1) ◽  
pp. 103-112 ◽  
Author(s):  
L. H. Gray
Keyword(s):  
Absorption Coefficient ◽  
Atomic Number ◽  
Gamma Rays ◽  
Wave Length ◽  
X Rays ◽  
Photoelectric Absorption ◽  
Empirical Law ◽  
Γ Rays ◽  
Image Position

No satisfactory formula has so far been derived theoretically for the photoelectric absorption of X-rays and γ-rays. The empirical lawhas hitherto been generally accepted as giving approximately the variation of the photoelectric absorption coefficient per electron, with atomic numberZand wave length λ for X-rays of wave length greater than 100 X.U., and the validity of this law has often been assumed for γ-rays also.

Is there a “universal” MAC equation?

1990 ◽  
Vol 48 (2) ◽  
pp. 228-229
Author(s):  
Robert E. Ogilvie
Keyword(s):  
Absorption Coefficient ◽  
Atomic Absorption ◽  
Atomic Number ◽  
X Ray ◽  
Time Period ◽  
Image Position

The search for an empirical absorption equation begins with the work of Siegbahn (1) in 1914. At that time Siegbahn showed that the value of (μ/ρ) for a given element could be expressed as a function of the wavelength (λ) of the x-ray photon by the following equationwhere C is a constant for a given material, which will have sudden jumps in value at critial absorption limits. Siegbahn found that n varied from 2.66 to 2.71 for various solids, and from 2.66 to 2.94 for various gases.Bragg and Pierce (2) , at this same time period, showed that their results on materials ranging from Al(13) to Au(79) could be represented by the followingwhere μa is the atomic absorption coefficient, Z the atomic number. Today equation (2) is known as the “Bragg-Pierce” Law. The exponent of 5/2(n) was questioned by many investigators, and that n should be closer to 3. The work of Wingardh (3) showed that the exponent of Z should be much lower, p = 2.95, however, this is much lower than that found by most investigators.

scholarly journals The absorption of hard monochromatic γ-radiation

1930 ◽  
Vol 128 (807) ◽  
pp. 345-359 ◽  
Keyword(s):  
Absorption Coefficient ◽  
High Frequency ◽  
Wave Length ◽  
Low Frequency ◽  
Photoelectric Effect ◽  
Fourth Power ◽  
X Rays ◽  
Photoelectric Absorption ◽  
Initial Direction ◽  
Γ Radiation

Energy may be removed from a beam of γ -rays traversing matter by two distinct mechanisms. A quantum of radiation may be scattered by an electron out of its initial direction with change of wave-length, or it may be absorbed completely by an atom and produce a photoelectron. The total absorption coefficient, μ, is defined by the equation d I/ dx = -μI, and is the sum of the coefficients σ and τ referring respectively to the scattering and to the photoelectric effect. For radiation of low frequency, such as X-rays, the photoelectric absorption is very much more important than the absorption due to scattering, and many experiments have shown that the photoelectric absorption per atom varies as the fourth power of the atomic number and approximately as the cube of the wave-length. For radiation of high frequency, such as the more penetrating γ -rays, the photoelectric effect is, even for the heavy elements, smaller than the scattering absorption; and, since the scattering from each electron is always assumed to be independent of the atom from which it is derived, it is most convenient to divide μ. defined above by the number of electrons per unit volume in the material and to obtain μ e the absorption coefficient per electron.

scholarly journals Absorption Corrections for X-Ray Fluorescence Analysis of Environmental Samples

1975 ◽  
Vol 19 ◽  
pp. 381-391 ◽  
Author(s):  
F. Bazan ◽  
N. A. Bonner
Keyword(s):  
Absorption Coefficient ◽  
Environmental Samples ◽  
Fluorescence Analysis ◽  
Coherent Scattering ◽  
Absorption Coefficients ◽  
X Ray

The discovery of a very simple and useful relationship between the absorption coefficient of a particular element and the ratio of incoherent to coherent scattering by the sample containing the element is discussed. By measuring the absorption coefficients for a few elements in a few samples, absorption coefficients for many elements in an entire set of similar samples can be obtained.

Absorption Coefficients of Inelastic Dynamic X-Ray Diffraction

2014 ◽  
pp. 483-502
Keyword(s):  
Absorption Coefficient ◽  
Inelastic Scattering ◽  
Waller Factor ◽  
Time Dependent ◽  
X Ray Diffraction ◽  
Absorption Coefficients ◽  
X Ray ◽  
Charge Current ◽  
Dispersion Equations ◽  
Debye Waller Factor

The X-ray inelastic scattering phenomena during the time-dependent perturbations are described with the aid of dynamical dispersion equations coupled with charge current in the Maxwell equations towards the appearance of the Debye-Waller factor driving the absorption coefficient, either for inelastic thermal diffusion and the Compton scattering, respectively.

Measurement of Mass Absorption Coefficients Using Compton-Scattered Cu Radiation in X-ray Diffraction Analysis

1990 ◽  
Vol 34 ◽  
pp. 325-335 ◽  
Author(s):  
Steve J. Chipera ◽  
David L. Bish
Keyword(s):  
Chemical Composition ◽  
Solid State ◽  
Absorption Coefficient ◽  
Mass Absorption Coefficient ◽  
X Rays ◽  
X Ray Diffraction ◽  
Absorption Coefficients ◽  
Solid State Detector ◽  
X Ray ◽  
Mass Absorption

AbstractThe mass absorption coefficient is a useful parameter for quantitative characterization of materials. If the chemical composition of a sample is known, the mass absorption coefficient can be calculated directly. However, the mass absorption coefficient must be determined empirically if the chemical composition is unknown. Traditional methods for determining the mass absorption coefficient involve measuring the transmission of monochromatic X-rays through a sample of known thickness and density. Reynolds (1963,1967), however, proposed a method for determining the mass absorption coefficient by measuring the Compton or inelastic X-ray scattering from a sample using Mo radiation on an X-ray fluorescence spectrometer (XRF). With the recent advances in solid-state detectors/electronics for use with conventional powder diffractometers, it is now possible to readily determine mass absorption coefficients during routine X-ray diffraction (XRD) analyses.Using Cu Kα radiation and Reynolds’ method on a Siemens D-500 diffractometer fitted with a Kevex Si(Li) solid-state detector, we have measured the mass absorption coefficients of a suite of minerals and pure chemical compounds ranging in μ/ρ from graphite to Fe-metal (μ/ρ = 4.6-308 using Cu Kα radiation) to ±4.0% (lσ). The relationship between the known mass absorption coefficient and the inverse count rate is linear with a correlation coefficient of 0.997. Using mass absorption coefficients, phase abundances can be determined during quantitative XRD analysis without requiring the use of an internal standard, even when an amorphous component is present.

X-Ray Mass Absorption Coefficients: Measurements and Uses in the Quantitative Diffraction Analysis of Pyrite in Coals

1989 ◽  
Vol 33 ◽  
pp. 475-483 ◽  
Author(s):  
David L. Wertz ◽  
Charles B. Smithhart ◽  
Stacey L. Wertz
Keyword(s):  
Absorption Coefficient ◽  
Diffraction Method ◽  
Solid Material ◽  
Diffraction Peak ◽  
Powdered Sample ◽  
Reflection Method ◽  
Absorption Coefficients ◽  
X Ray ◽  
Mass Absorption ◽  
Crystalline Substrate

The mass absorption coefficient (μ) of a weakly absorbing solid material may be measured by either the transmission or the reflection method. The latter typically employs a crystalline substrate and the diffraction method, measuring the transmission of the diffraction peak(s) of the substrate through the analyte. Compressing or compacting a powdered sample is not required when the reflection method is used.

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