Quantitative ALCHEMI With Error Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 468-469
Author(s):  
C.J. Rossouw ◽  
P.S. Turner ◽  
T.J. White ◽  
A.J. O’Connor
Keyword(s):  
Multivariate Analysis ◽  
Error Analysis ◽  
Crystal Orientation ◽  
Degrees Of Freedom ◽  
Ratio Method ◽  
X Ray ◽  
Site Distribution ◽  
Host Atom ◽  
Error Amplification ◽  
Image Position

The ALCHEMI technique for determining the site distribution fi of an impurity element x on host element lattice sites i is well known: Changes in x-ray emission from host atoms i and impurity x with crystal orientation ARE monitored under strong planar or axial diffraction conditions, and fi derived via a ratio method. However analysis involving count ratios (and ratios of ratios) leads to severe error amplification. Neglect of delocalization leads to further error. To overcome these inherent errors in the standard ALCHEMI method, we make the single assumption that the impurity count Nx may be written as a linear combination of the host atom counts Ni, i.e.where the coefficients αi and their errors are determined by multivariate analysis. For m separate EDX spectra and fitted parameters αi (i = 1 to v), the criterion v ≤ m must be satisfied for m - v degrees of freedom.

scholarly journals Improved crystal orientation and physical properties from single-shot XFEL stills

2014 ◽  
Vol 70 (12) ◽  
pp. 3299-3309 ◽  
Author(s):  
Nicholas K. Sauter ◽  
Johan Hattne ◽  
Aaron S. Brewster ◽  
Nathaniel Echols ◽  
Petrus H. Zwart ◽  
...  
Keyword(s):  
Crystal Orientation ◽  
Degrees Of Freedom ◽  
Reciprocal Lattice ◽  
Single Shot ◽  
X Ray Diffraction ◽  
Reciprocal Lattice Point ◽  
X Ray ◽  
Structure Factors ◽  
Rotational Degrees Of Freedom ◽  
Diffraction Patterns

X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographicRfactors and sharpening anomalous differences that are near the level of the noise.

X-Ray Analysis of Frozen Hydrated Sections:The Unconventional Approach

1982 ◽  
Vol 40 ◽  
pp. 754-757
Author(s):  
R. Beeuwkes ◽  
A. Saubermann ◽  
P. Echlin ◽  
S. Churchill
Keyword(s):  
Ratio Method ◽  
Frozen Sections ◽  
Technical Problems ◽  
Sample Handling ◽  
X Ray ◽  
Common Group ◽  
Ideal Method ◽  
Classic Paper ◽  
Physical Principles ◽  
The Ideal

Fifteen years ago, Hall described clearly the advantages of the thin section approach to biological x-ray microanalysis, and described clearly the ratio method for quantitive analysis in such preparations. In this now classic paper, he also made it clear that the ideal method of sample preparation would involve only freezing and sectioning at low temperature. Subsequently, Hall and his coworkers, as well as others, have applied themselves to the task of direct x-ray microanalysis of frozen sections. To achieve this goal, different methodological approachs have been developed as different groups sought solutions to a common group of technical problems. This report describes some of these problems and indicates the specific approaches and procedures developed by our group in order to overcome them. We acknowledge that the techniques evolved by our group are quite different from earlier approaches to cryomicrotomy and sample handling, hence the title of our paper. However, such departures from tradition have been based upon our attempt to apply basic physical principles to the processes involved. We feel we have demonstrated that such a break with tradition has valuable consequences.

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.

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.

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

Direct Observation of Monolayer Zones in Al-wt 4% Cu

1990 ◽  
Vol 48 (1) ◽  
pp. 14-15
Author(s):  
B. Jouffrey ◽  
D. Dorignac ◽  
A. Bourret
Keyword(s):  
Solid Solution ◽  
Synchrotron Radiation ◽  
Direct Observation ◽  
Supersaturated Solid Solution ◽  
Original Model ◽  
X Ray ◽  
Image Position

Since the early works on GP zones and the model independently proposed by Preston and Guinier on the first steps of precipitation in supersaturated solid solution of aluminium containing a few percent of copper, many works have been performed to understand the structure of different stages in the sequence of precipitation.The scheme which is generally admitted can be drawn from a work by Phillips.In their original model Guinier and Preston analysed a GP zone as composed of a single (100) copperrich plane surrounded by aluminum atomic planes with a slightly shorter distance from the original plane than in the solid solution.From X-ray measurements it has also been shown that GP1 zones were not only copper monolayer zones. They could be up to a few atomic planes thick. Different models were proposed by Guinier, Gerold, Toman. Using synchrotron radiation, proposals have been recently made.

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