Quantification of Carbon in a Binary System by the ...

QUANTIFICATION OF CARBON IN A BINARY SYSTEM BY THE FUNDAMENTAL PARAMETER METHOD

Franz A. Weber, Luiz B. Da Silva, Troy W. Barbee, Jr., and Dino Ciarlo University of California, Lawrence Livermore P.O. Box 808, Livermore, CA 94551, USA

National Laboratory,

Michael Mantler Institute of Applied and Technical Physics Technical University Vienna, A- 1040 Vienna, Austria

SUMMARY This paper discusses the results obtained from experiments using specially prepared carbon grids on top of metallic substrates and subsequent treatment of the data by means of a theoretical approach which is based on the conventional fundamental parameter theory but also includes secondary excitation effects by photoelectrons. Carbon gridlines with known parameters have been deposited on top of medium 2 disks in order to achieve well defined both absorption and excitation geometries. The grids having various thicknesses exhibit satisfactory performance in terms of mechanical stability, homogeneity and uniformity of the coating. However, due to the manufacturing process only a modulation in thickness could be obtained for thicknesses greater than 0.5 pm rather than a line/spacing pattern of any kind. Detailed evaluation of the measurement results reveals that with increasing energy of the primary radiation there is a more rapid increase of the associated C-Ka countrate from the coated samples compared to the pure elements. We tend to attribute this effect to the contribution of secondary enhancement effects, including those resulting from photoelectrons generated after the primary ionization event. A theoretical model has been developed which predicts increasing photon counts to be expected from coated specimens at higher acceleration voltages but shows deviation on the order of about 20 % from experimental results at lower primary beam energies.

Copyright (C) JCPDS-International Centre for Diffraction Data 1997 Copyright 0 JCPDS-International

Centre for Diffraction Data 1997

In order to be able to take advantage of high excitation efficiency, which requires reasonable intensities of the primary beam in the low energy region of the spectrum, appropriate target and window materials for an otherwise conventional x-ray tube have to be employed. In addition, reflectivity and spatial resolution requirements for the dispersing elements in the long wavelength spectrometer dictate the use of only a certain combination of multilayer component materials.

INTRODUCTION In the past couple of years it has become increasingly important to turn low energy XRF measurements into quantitative results. Most recent demands from semiconductor’ and steel industries show that this is particularly true for specimens containing (low concentrations of) low atomic number elements such as boron and carbon. Quantitative X-ray fluorescence analyses based on empirical and semiempirical coefficient methods’ have associated inherent inaccuracies which are, at least in part, due to the existence of secondary and higher order enhancement effects. The same argument applies to processing measurement results by means of fundamental algorithms3-5. The repetitive ionizing ability of photo- and Auger electrons after the primary ionization has a significant impact on the fluorescence radiation formation process particularly at higher overvoltage ratios since the most excitation-effective long wavelength contribution of the primary spectrum is absorbed in the tube window. The related enhancement mechanisms have been acknowledged in the literature to some extent6 but are not yet properly implemented in commercially available software packages. A modification of the standard fundamental parameter model7 has been introduced’ and will be briefly outlined below. It accounts for the effects mentioned above and has been adapted for computations relevant to the current sample geometry. Both the experimental results based on measurements and the calculations based on the theoretical model presented in this paper are part of a combined effort intended to determine the magnitude of such effects in both pure element and compound specimens containing low Z materials.

THEORY The basic work of Shiraiwa and Fujino’ describes the standard fundamental parameter approach to quantification problems by means of X-ray fluorescence analysis. The number of primary and secondary excited fluorescence photons emitted by the element of interest within a given sample can be expressed as a function of the element’s fundamental parameters, the incident spectrum and the geometrical situation with regard to the radiation source and the detection system, respectively. If, however, enhancement effects due to photoelectrons generated after the primary ionization are to be taken into account the following formularO has to be applied:

i-2 “i, prim+e=const.-eKi 47c

.oi

Me(h”)-q(h)-I(h).dh --CL(V

shy,

+

W>

(1)

siny,

Equation 1 represents accurate means for quantitative assessment for concentration of chemical elements which emit the associated (K-) fluorescence line(s) in the long wavelength region of the spectrum (definitely above 40 A). The constant includes the geometrical factors, R denotes the solid angle covered by the

Copyright (C) JCPDS-International Centre for Diffraction Data 1997

detection system, K is the detector efficiency, w the fluorescent yield, S the absorption edge jump, p the transition probability for the line of interest, c the weight fraction of the element of interest, z is the massphotoaprption coefficient, l_tthe total mass-absorption coefficient, I(h)*dh the number of source photons per cm per second at the specimen surface, and ~1 and ~2 are the angles of the incident and fluorescence photons, respectively, and i as an index relates a parameter to the emission process and properties of primary fluorescence radiation. In addition,

MeCL*> = 1+

CW

ne--,ph

1 1 _; =--h %dge

1

(2b)

h

where

%-,ph

=-

O3

.

(3)

Equation 3 which in its basic form has been derived by Green and Cosslett” gives the number of electronproduced x-ray photons &.#, . N is Avogardos’ number, A the atomic weight, o the fluorescent yield, p the density, and Q the ionization cross-section for the observed shell. The electron looses its initial energy E, along its path s (among other possibilities of interaction) by ionizing atoms in the shell of interest, as long as the electron energy exceeds their K-absorption edge energy denoted as Ec. The backscattering factor, R, is assumed to be 1, as the photoelectrons are generated already within the specimen. However, a certain loss of photoelectrons has to be expected in case of highly absorbing materials where photoelectrons are generated within the top surface layer. Appropriate expressions for the associated ionization cross-section Q and the stopping power relation dE/dps have to be employed in order to be able to accurately summarize the secondary enhancement effects due to photoelectrons by the factor M(h*) given in equation 2a. The effect has an inherently multiplicative nature and can therefore be represented by the term M(h*) in the numerator in the excitation integral of equation 1. Additional possibilities of secondary excitation effects include Auger electrons as well as L alpha photons after K-shell ionization. Each primary K-shell ionization in a heavy matrix element (and K-photon emission with probability wK) triggers a cascade of subsequent transitions with a high probability for an LZ or Ljshell vacancy. In turn, L-photons with the corresponding yield Q (note that oL