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 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 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 On the absorption and scattering of γ-rays

1924 ◽  
Vol 106 (735) ◽  
pp. 8-19 ◽  
Keyword(s):  
Absorption Coefficient ◽  
Experimental Determination ◽  
Atomic Absorption ◽  
Atomic Number ◽  
Apparent Absorption ◽  
Wide Range ◽  
Γ Rays

An account of an experimental determination of the comparative absorption of penetrating γ-rays by a wide range of elements has recently been given by one of us. It is the object of the present paper to consider the results somewhat more fully, especially those concerned with scattering, which was not previously discussed. The rays used were those from RaB + C after filtration through 1 cm. lead. The absorption was primarily measured in terms of aluminium, whose apparent absorption coefficient was measured directly. It was shown that the apparent atomic absorption, for the absorber in one particular position, could be represented with considerable accuracy by μ a' = a Z + b Z 4 (1) where Z is the atomic number.

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.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

X-ray microanalysis of thin specimens in the transmission electron microscope at voltages up to 1000 Kv.

1978 ◽  
Vol 36 (1) ◽  
pp. 540-541
Author(s):  
G. Cliff ◽  
M.J. Nasir ◽  
G.W. Lorimer ◽  
N. Ridley
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Weight Fraction ◽  
Present Series ◽  
Constant Independent ◽  
X Ray ◽  
Transmission Electron ◽  
Series Of Experiments ◽  
Image Position ◽  
X Ray Absorption

In a specimen which is transmission thin to 100 kV electrons - a sample in which X-ray absorption is so insignificant that it can be neglected and where fluorescence effects can generally be ignored (1,2) - a ratio of characteristic X-ray intensities, I1/I2 can be converted into a weight fraction ratio, C1/C2, using the equationwhere k12 is, at a given voltage, a constant independent of composition or thickness, k12 values can be determined experimentally from thin standards (3) or calculated (4,6). Both experimental and calculated k12 values have been obtained for K(11<Z>19),kα(Z>19) and some Lα radiation (3,6) at 100 kV. The object of the present series of experiments was to experimentally determine k12 values at voltages between 200 and 1000 kV and to compare these with calculated values.The experiments were carried out on an AEI-EM7 HVEM fitted with an energy dispersive X-ray detector.

Thickness and composition determinations from T.E.M. specimens using both x-ray and backscattered electron data

1984 ◽  
Vol 42 ◽  
pp. 576-577
Author(s):  
M.D. Ball ◽  
H. Lagace ◽  
M.C. Thornton
Keyword(s):  
Electron Microscope ◽  
Atomic Number ◽  
Transmission Electron Microscope ◽  
Convenient Method ◽  
Flow Chart ◽  
X Ray ◽  
Intensity Measurements ◽  
Transmission Electron ◽  
Electron Intensity ◽  
Backscattered Electron

The backscattered electron coefficient η for transmission electron microscope specimens depends on both the atomic number Z and the thickness t. Hence for specimens of known atomic number, the thickness can be determined from backscattered electron coefficient measurements. This work describes a simple and convenient method of estimating the thickness and the corrected composition of areas of uncertain atomic number by combining x-ray microanalysis and backscattered electron intensity measurements.The method is best described in terms of the flow chart shown In Figure 1. Having selected a feature of interest, x-ray microanalysis data is recorded and used to estimate the composition. At this stage thickness corrections for absorption and fluorescence are not performed.

Contribution of x-ray total reflection to the background intensity in EPMA

1990 ◽  
Vol 48 (2) ◽  
pp. 202-203
Author(s):  
Werner P. Rehbach ◽  
Peter Karduck
Keyword(s):  
Atomic Number ◽  
Target Material ◽  
Total Reflection ◽  
Background Intensity ◽  
X Rays ◽  
Characteristic Radiation ◽  
X Ray

In the EPMA of soft x rays anomalies in the background are found for several elements. In the literature extremely high backgrounds in the region of the OKα line are reported for C, Al, Si, Mo, and Zr. We found the same effect also for Boron (Fig. 1). For small glancing angles θ, the background measured using a LdSte crystal is significantly higher for B compared with BN and C, although the latter are of higher atomic number. It would be expected, that , characteristic radiation missing, the background IB (bremsstrahlung) is proportional Zn by variation of the atomic number of the target material. According to Kramers n has the value of unity, whereas Rao-Sahib and Wittry proposed values between 1.12 and 1.38 , depending on Z, E and Eo. In all cases IB should increase with increasing atomic number Z. The measured values are in discrepancy with the expected ones.

Gaussian ϕ(ρz) curves: Comparison with other models

1990 ◽  
Vol 48 (2) ◽  
pp. 192-193
Author(s):  
Alberto Riveros ◽  
Gustavo Castellano
Keyword(s):  
Good Description ◽  
Bulk Sample ◽  
Incident Electron Energy ◽  
Power Mean ◽  
General Shape ◽  
Ionization Cross ◽  
X Ray ◽  
Mass Absorption ◽  
Absorption Correction ◽  
Image Position

X ray characteristic intensity Ii , emerging from element i in a bulk sample irradiated with an electron beam may be obtained throughwhere the function ϕi(ρz) is the distribution of ionizations for element i with the mass depth ρz, ψ is the take-off angle and μi the mass absorption coefficient to the radiation of element i.A number of models has been proposed for ϕ(ρz), involving several features concerning the interaction of electrons with matter, e.g. ionization cross section, stopping power, mean ionization potential, electron backscattering, mass absorption coefficients (MAC’s). Several expressions have been developed for these parameters, on which the accuracy of the correction procedures depends.A great number of experimental data and Monte Carlo simulations show that the general shape of ϕ(ρz) curves remains substantially the same when changing the incident electron energy or the sample material. These variables appear in the parameters involved in the expressions for ϕ(ρz). A good description of this function will produce an adequate combined atomic number and absorption correction.

The Possibilities for Analytical Methods in Photoemission and Low-Energy Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 348-349
Author(s):  
Ernst Bauer
Keyword(s):  
Chemical Characterization ◽  
Emission Angle ◽  
Relative Energy ◽  
Objective Lens ◽  
Chemical Information ◽  
Magnetic Lens ◽  
Incident Intensity ◽  
X Ray ◽  
Leed Pattern ◽  
Image Position

One of the major shortcomings of conventional PEEM and of LEEM is the lack of chemical information about the surface. Although the imaging of the LEED pattern in the back focal plane of the objective lens of a LEEM instrument allows chemical characterization via the crystalline structure derived from the LEED pattern, this method fails in the absence of a characteristic LEED pattern. Direct information about the atomic composition of the surface is then needed which can be best obtained from inner shell electrons either directly by x-ray-induced photoemission (XPEEM) or by x-ray- or electron-induced Auger electron emission (AEEM). These modes of excitation and imaging can be combined with conventional PEEM and LEEM in one instrument which is presently being developed. Thus a complete structural and chemical characterization becomes possible in one instrument, with parallel detection and high resolution.In contrast to LEEM, in which up to more than 50% of the incident intensity is available for image formation, the intensity of the emitted electrons is much lower in XPEEM and AEEM and the signal is much lower than the background in AEEM. Therefore, intensity I and resolution d have to be optimized simultaneously which is best done by maximizing Q = I/d2 with respect to maximum emission angle α and relative energy distribution ε = ΔVo/V accepted by the instrument. For a well-designed magnetic lens section of the cathode lens its aberrations are determined by the accelerating field F in front of the specimen. For a homogeneous accelerating field F and a cosine emission distribution one obtains for the optimum α and ε values αo,εo a radius of the minimum disc of confusion of

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