Quantitative Analysis in addition to Matrix Corrections Raimond Castaing (1921-1999) Raimond Castaing (1921-1999)

Quantitative Analysis in addition to Matrix Corrections Raimond Castaing (1921-1999) Raimond Castaing (1921-1999) www.phwiki.com

Quantitative Analysis in addition to Matrix Corrections Raimond Castaing (1921-1999) Raimond Castaing (1921-1999)

Breznican, Anthony, Film Writer has reference to this Academic Journal, PHwiki organized this Journal Electron Probe Microanalysis EPMA UW-Madison Geoscience 777 Quantitative Analysis in addition to Matrix Corrections Revised 1/10/2016 Raimond Castaing (1921-1999) Advisor Andre Guinier studied defects (Cu-Al inclusions) in Al metals ( as long as airplanes) Defects too small to define by optical microscope Guinier famous X-ray crystallographer He suggested Castaing try to find inclusion compositions-measure X-rays generated by electron beam, using war-surplus TEM Castaing succeeded, PhD 1951 “Application of Electron Probes to Local Chemical in addition to Crystallographic Analysis” Raimond Castaing (1921-1999) His thesis laid out the basics of EPMA which have remained constant as long as the past 64 years Key concept: where K is the “K ratio” as long as element i, I is the X-ray intensity of the phase in addition to subscript i is one element.

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Using K-factor simplifies analysis counts acquired on BOTH unknowns in addition to st in addition to ards on the same instrument, under the same operating conditions, All physical parameters of the machine that would be needed in a rigorous physical model cancel each other out Castaing’s First Approximation Castaing’s “first approximation” follows this approach. The composition C of element i of the unknown is the K-ratio times the composition of the st in addition to ard. In the ‘simplest’ case where pure element st in addition to ards can be used, Cistd = 1 in addition to drops out. So how close are these K-ratios to the true composition Examples: some minerals Notice the “differences” (between K-ratio in addition to true compositions .So we need a MATRIX CORRECTION Fo90 Olivine Zircon ZrSiO4 Hafnon HfSiO4

Raw data needs correction This plot of Fe Ka X-ray intensity data demonstrates why we must correct as long as matrix effects. Here 3 Fe alloys show distinct variations. Consider the 3 alloys at 40% Fe. X-ray intensity of the Fe-Ni alloy is ~5% higher than as long as the Fe-Mn, in addition to the Fe-Cr is ~5% lower than the Fe-Mn. Thus, we cannot use the raw X-ray intensity to determine the compositions of the Fe-Ni in addition to Fe-Cr alloys. (Note the hyperbolic functionality of the upper in addition to lower curves) Absorption in addition to Fluorescence Note that the Fe-Mn alloys plot along a 1:1 line, in addition to so is a good reference. The Fe-Ni alloys plot above the 1:1 line (have apparently higher Fe than they really do), because the Ni atoms present produce X-rays of 7.278 keV, which is greater than the Fe K edge of 7.111 keV.Thus, additional Fe Ka are produced by this secondary fluorescence. The Fe-Cr alloys plot below the 1:1 line (have apparently lower Fe than they really do), because the Fe atoms present produce X-rays of 6.404 keV, which is greater than the Cr K edge of 5.989 keV. Thus, Cr Ka is increased, with Fe Ka are “used up” in this secondary fluorescence process. Theoretical approach to corrections Merlet in addition to Llovet . One can write an equation showing the relationship between x-ray intensity IA in addition to elemental concentration CA, using fundamental physical parameters: Rearranging the equation in addition to solving as long as CA is not that easy! So the material scientists, chemists in addition to geologists who took up the electron probe as a crucial tool came up with some alternatives

Heinrich summarizes the 4 actual types of models used as long as matrix corrections in EPMA: Empirical: simplest, based on known binary experimental data; ZAF: 1st generalized algebraic procedure; assumes a linear relation between concentration in addition to x-ray intensity; Phi-rho-Z: based upon depth profile (tracer) experiments; Monte Carlo: based upon statistical probabilities of electron-sample interactions, particularly as long as unusual specimen geometries. Actual approaches to corrections Heinrich, 1991, Strategies of electron probe data reduction, in Electron Probe Quantitation, Ed. Heinrich in addition to Newbury, Plenum, New York, 9-18. In his 1951 Ph.D. thesis, Castaing laid out two of the approaches that could be used to apply matrix corrections to the data, using his brilliant construct of the K-ratio: an empirical ‘alpha factor’ correction as long as binary compounds, where each pair of elements has a pair of constant a-factors representing the effect that each element has upon the other as long as measured X-ray intensity, in addition to a more rigorous physical model taking into account absorption in addition to fluorescence in the specimen. This later approach also now includes atomic number effects in addition to became known as the ZAF correction. This ZAF has been surplanted in many/most EPMA labs by the “phi-rho-Z” matrix correction (it can be a little confusing, discussed later, as the phrase is used in another context) Two approaches to corrections Atomic number effect only recognized in 1961-3 (Scott in addition to Ranzetta; Kirianenko; Archard in addition to Mulvey), in samples with widely different atomic numbers Z A F In addition to absorption (A) in addition to fluorescence (F), there are two other matrix corrections based upon the atomic number (Z) of the material: one dealing with electron backscattering, the other with electron penetration (or stopping). These deal with corrections to the generation of X-rays. C is composition as wt% element (or elemental wt fraction). We will now go through all these corrections in some detail, starting with the Z correction, which has two parts: the stopping power correction, in addition to the backscatter correction. Note that all these corrections require close attention to exactly what feature’s value is being input: the target (matrix), or the X-ray in question. Heinrich (1990) notes that this multiplicative scheme is not actually correct, as that assumes an ideal linear calibration curve, not justifiable on the physics involved However, it still is used much (“gives close enough answers many times”.)

Stopping Power Correction Incident electrons lose energy in inelastic interactions with the inner shell electrons of the target. The “stopping power” (energy lost by HV electrons per unit mass penetrated) is not constant but drops with increasing Z. A higher number of X-rays will be produced in higher Z targets. Thus, if the mean Z of the unknown is higher than that of the st in addition to ard, a downward correction in the composition must be applied. The stopping power correction factor is “S”, in addition to can be approximated by: Stopping power of pure elements as long as 20 keV electrons where J=11.5+ Z in addition to Emean= (E0+Ec)/2 (J is the mean ionization energy; J, Z in addition to A are of the target, Emean is of the X-ray) Reed, 1996, Fig. 8.6, p. 135 Backscatter Correction As we discussed earlier, the fraction of high energy incident elections that are backscattered (h) increases with atomic number. There then will be relatively less incident electrons penetrating into higher Z specimens, resulting in a smaller number of X-rays. Thus, if the mean Z of the unknown is higher than that of the st in addition to ard, a upward correction in the composition must be applied. The backscatter correction factor is “R”. R can be approximated by where W = Ec/E0 (the inverse of overvoltage), in addition to Z is of the target, in addition to W is of the X-ray Reed, 1996, Fig. 2.11, p. 17 Z correction The total atomic number correction is as long as med by multiplication of the R in addition to S of the unknown in addition to st in addition to ard thusly: Z = Rstd/Runk Sunk/Sstd Overall the backscatter in addition to the stopping power corrections tend to cancel each other out. But if there is a (small) correction, it is usually in the direction of the backscatter correction.

Beers Law The intensity I of X-rays that pass through a substance are subject to attenuation of their initial intensity I0 by the material over the distance they travel within the material. The attenuation follows an exponential decay with a characteristic linear attenuation length 1/m, where m is the (linear) absorption coefficient. Beers Law can also be expressed in terms of mass, using density terms: I = I0 exp -(m/r)(r Z) where (m/r) is the mass absorption coefficient (cm2/g), r is the material density (g/cm3), in addition to Z is the distance (cm) Als-Nielsen in addition to McMorrow, 2001, Fig 1.10, p. 19 Mass Absorption Coefficients Mass absorption coefficients (MACs) have been tabulated as long as many X-rays through many substances (though some are extrapolations). They exist as a matrix of numbers: absorption of a particular X-ray line (emitter, e.g. Ga ka) by a absorber or target (e.g. As) will have one value (51.5). Note that the absorption of As Ka by Ga is a totally different phenomenon with a distinct MAC (221.4) . Emitter = X-ray (here, Ka) Absorber = matrix material Goldstein et al, 1992, p. 750. See following discussion Mass Absorption Coefficients Emitter = X-ray (here, Ka) Absorber = matrix material Goldstein et al, 1992, p. 750. Terminology: “the mass absorption of Ga Ka by As” Question as long as you: Is the mass absorption of As Ka by Ga the same as the mass absorption of Ga Ka by As Why or why not

Absorption X-rays produced within the material will be propagated in all directions, in addition to will suffer attenuation in the process. Note that the path length of travel of the X-ray to the spectrometer is z cosecy, where y (psi) is the takeoff angle (cosec = 1/sin). Castaing’s approach was to integrate the Beer’s Law equation over the depth at the given y, producing the absorption correction factor f(c) where c is defined as m cosec y where m is the MAC. The absorption (A) correction is then defined as A= f(c)std / f(c)sample Reed, 1993,, p. 219 c = “Chi” “Photoelectric absorption” is an “all or nothing” process. When it occurs the photon energy kicks out an electron with lower binding energy, in addition to said electron is ejected with the kinetic energy of the photon minus its binding energy. Absorption To be able to correct as long as this absorption of the measured X-rays, we need to know how the production of X-rays varies with depth (Z) in the material. The distribution of X-rays generated as a function of depth is known as the f(rz) [phi-rho-z] function, where a “mass depth” parameter is used instead of simple z (bottom right). The f(rz) function is defined as the intensity generated in a thin layer at some depth z, relative to that generated in an isolated layer of the same thickness. This can then be integrated over the total depth where the incident electrons exceed the binding energy as long as that particular characteristic x-ray. Reed, 1993, p. 219 Absorption One commonly used simplified as long as m (Philibert 1963) was where c = m cosec y , s is a measure of electron absorption in addition to depends on effective electron energy, where The Philibert approximation breaks down, however, at the near surface, creating errors when dealing with low energy light elements, in addition to we need to go to more complicated in addition to accurate as long as ms of the f(rz) function.

f(rz) [phi-rho-z] Curves To be able to correct properly as long as absorption – particularly as long as light elements, the exact shape of the f(rz) [phi-rho-z] curve must be known. Each X-ray has its own curve. There are 3 main parameters that affect the shape of the curve: Reed, 1993, p. 220 E0 (accelerating voltage) Ec (critical excitation energy of a particular element line mean Z of the material Tracer Method The f(rz) [phi-rho-z] curves are usually determined by the “tracer method”, where successive layers are deposited by vacuum evaporation. The tracer layer B is deposited atop substrate A, with successive layers of A deposited on top. Characteristic X-rays from the tracer element are measured (“emitted”) in addition to then a generation curve is calculated by correcting each step as long as absorption in addition to fluorescence effects Artistic license Fluorescence Correction The X-rays produced within a specimen have the potential as long as producing a second generation of X-rays: this is secondary fluorescence, generally shortened to fluorescence. This occurs when the characteristic X-ray has an energy greater than the absorption edge energy of another element present in the specimen. As we saw earlier, Ni Ka (7.48 keV) is able to fluoresce Fe Ka (Ec 7.11 keV). This effect is maximized when there is a small amount of the fluoresced element present, e.g. Fe in a Ni-Fe alloy. Reed, 1996, Fig. 8.10, p. 139 Reed gives an example where the Fe intensity is 142% of what it “should be”. Also, the continuum above an absorption edge also causes fluorescence, although this is generally weak.

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Fluorescence Correction The as long as m of the correction F is where If/Ip is the ratio of emitted X-rays from fluorescence, compared to the X-ray intensity from inner shell ionization. In a compound, this term is summed overall all the elements that could fluorescence the element of interest. Next Generation (>1980): Phi-Rho-Z models We saw above how Castaing, as early as the 1950s, developed models of x-ray generation in addition to absorption within the target material, in addition to called these curves “phi-rho-Z” curves. Finding proper mathematical models, however, was hard in addition to so simplistic approximations were used. Over time, in addition to particularly with improvements in technology, people desired to use EPMA to measure the “light elements” (B, C, N, O, F) where absorption by the matrix is severe. Increased research as well as development of computing power, led to a new variant, where the “Z” correction is subsumed within the Phi-Rho-Z paradigm. Additionally, more experiments occurred to determine more correct mass absorption coefficients as long as the light elements. Next Generation (>mid 1980s): Phi-Rho-Z models Names you will see in regards to these models: “PAP” – Jean-Louis Pouchou in addition to Francoise Pichoir ( in addition to ‘simplified’ version = XPP) “PROZA” – Guillaume Bastin “X-PHI” – Claude Merlet

How do EPMA theoriticians ‘prove’ their matrix correction is “correct” Example: Here, use 826 “high quality” x-ray K-ratio data (element pairs) to show that a given matrix correction provides the correct answer (= the actual binary composition) How do EPMA theoriticans ‘prove’ their matrix correction is “correct” Here, in a 1991 book, Pouchou in addition to Pichoir show compare their “PAP” matrix correction to a ZAF version. Note that both contain not an insignificant number of data >5% error, in addition to a heck of a lot >2% error. And these are binary compounds.

“State of EPMA parameters” As David Joy points out in his 2001 article “Constants as long as Microanalysis”, there are problems in our knowledge of many parameters: there are experimental stopping power profiles as long as 12 elements in addition to 12 compounds, which raise questions about the traditional Bethe equation only half of the elements whose K lines are used as long as EPMA have measured K shell ionization cross-sections ; only 6 elements have measured L shell cross-sections; there are zero M shell cross-sections K shell fluorescent yields are the best documented parameters; there are gaps in the data as long as L shell yields; there are only 5 measured M shell yields despite the fact that backscatter coefficients have been measured as long as 100 years, the data has many gaps in addition to is of poor precision (i.e. 30%) At the Eugene EPMA workshop in September 2003, John Armstrong reviewed the state of EPMA matrix corrections Big problem with software/manufacturers, not documenting which corrections used. Some have picked “improved” parameters which do not fit with the other parameters, e.g. in some, where no as long as mal fluorescence correction, the absorption correction was tweaked to take fluor into account, in addition to then when later fluorescence corrections developed, to use this in addition to absorption correction, has an overcorrection as long as fluorescence. Problem with researchers not stating in their publications which correction they used; NIST is trying to develop some protocols which people can reference (brief notation with pointer to NIST as long as full description). There are a few errors/typos in the long accepted X-ray tables (i.e., Bearden) – 3 are major errors. Actually measured mass absorption factors are rare! Measurements exist as long as Na Ka by Al; Si Ka by Al in addition to Ni; Mg Ka by O, Al, Ti in addition to Ni; in addition to Al Ka by O, Na There is over 30% variation in published values of some macs as long as geologically relevant elements; they can’t all be correct! “So what do we do” We have discussed various ways to correct the raw data, the goal being to come up with the most accurate in addition to precise analytical procedures to give us the most trustworthy data. We have just mentioned that everything is not as rosy as one would hope. So, can we trust the numbers we get out of the probe In many/most cases, given care, yes. But we cannot blindly look at the electron probe in addition to computer as a black box! Stay tuned as long as an upcoming installment, where we discuss st in addition to ards, accuracy in addition to precision in EPMA.

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