THTUBE - XRF System characterization program

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When an X-ray tube is used as the excitation source in XRF analysis it is critical to know the number and the energy distribution of the photons striking the sample. This can become especially complicated when primary filters are used to modify the excitation source. In addition, knowledge about the detector crystal thickness and correction functions are also essential for elemental analyses. In order to facilitate the analysis process we have developed the THTUBE.exe program that in effect inverts the formula for determining the elemental concentrations to find the best estimate of the excitation function, detector crystal thickness and correction functions using known concentration values, sample and setup information.

The THTUBE program is used to generate an excitation file (TH.EXC) based on a theoretical Bremstrahlung spectrum filtered by intervening absorbers with the addition of a primary filter (PF) characteristic line component. In addition, an estimate of the detector thickness and the H(Z) correction factors are also generated and written to the files TH.HEK (for K x-rays) and TH.HEL (for L x-rays). This information is generated by fitting the theoretical yields of the excitation spectrum corrected for detector efficiency and x-ray absorber effects to the experimental yields, that is peak areas of elements obtained by fitting spectra from XRF "standards" materials. The certified concentration values can then be translated to theoretical yields or peak areas via:

Theoretical Peak Area(Z) = Conc(Z) * { ThYld(Z) * SA * Abs(Z) * DE(Z) }

Conc(Z) - fractioanl concentration of emement Z
ThYld(Z) - the calc yield of element Z in the given sample for the specified excitation spectrum per steradian per second in the given measuring system;
SA - solid angle detector makes wrt to sample;
Abs(Z) - the attenuation effect on pricipal line of element Z of x-ray absorbers between the sample and the detector;
DE(Z) - the detection efficiency of principal line of element Z in the specified detector.

The theoretical (or model) peak area is fitted to the experimental peak areas obtained from spectra of certified standard materials. What we treat as unknowns or parameters in the above system are the excitation function parameters and the detector crystal thickness. It is these parameters that will be fitted in order to best fit the theoretical areas to the experimental areas. The departure of the fit of experimental to thoeretical value at each point will represent the H(Z) value for that particular element.

The Excitation Function

The shape of the primary Brem spectrum exiting the tube is assumed to be of the form below:

Eq.(1) B(E) = (Eo/E-1)**p * (1 - E/Eo)

This primary brem. spectrum is filtered through any intervening absorbers. The PF characteristic line component is generated using the primary Brem radiation to fluoresce the PF K lines (at this time PF L flourescence is ignored) with the relative line intensities determined from the Brem radiation striking the front surface of the PF foil and self absorption of the lines within the foil. If we define Ci as the relative amount of characteristic x-rays of line i, then the relative amount of each line i of characteristic PF K x-ray radiation striking the sample will be given by

Eq.(2) Ci = N(PF) * fi * Sum(E){Nf(E) *(uE/(ui-uE))*[exp(-uE*t)-exp(-ui*t)]}* Abs(Ei)

N(PF) represents the total PF K x-ray production, fi is the production or branching ratio of the PF K lines, Sum(E) simply signifies the sum over E,
Nf(E) is the number of photons of energy E striking the PF foil,
uE represents the attenuation coef of photon of energy E in PF,
ui represents the attenuation coef of photon of ith line of PF K x-rays,
t is the thickness of the PF foil,
Abs(Ei) is the effect of post PF foil absorbers on the ith line.

We actually make no attempt to compute the absolute amount of PF K x-rays produced N(PF) that head in the direction of the sample as that would depend on the solid angle the illuminated spot on the PF foil makes with respect to the sample but instead will allow a fit to determine the ratio of PF characteristic radiation to Brem radiation striking the sample. Eq(2) above is simply used to apportion the PF K radiation between the various K lines.

Thus the radiation striking the sample will be given by the sum of the filtered Brem radiation component and the PF K lines. If Br(E) & PF(Ki) are normalized so that Sum(E){Br(E)} = 1 and the Sum(i){PF(Ki)} = 1 then for N x-rays per second on the sample and f representing the fraction of those x-rays that are due to the PF characteristic K lines we have

Eq.(3) N(E) = N * { (1-f) * Br(E) + f * PF(Ki) }

and Br(E), the normalized Brem radiation striking the sample, will be given by

Eq.(4) Br(E) = B(E) * Abs1(E) * Abs2(E) * Abs3(E) / Btot

Btot = Sum(E) {B(E) * Abs1(E) * AbsMo(E) * Abs2(E)},
Abs1(E) = Abs effect of filters between tube & PF foil as a fcn of E,
Abs2(E) = Abs effect of PF foil of x-rays of energy E,
Abs3(E) = Abs effect of filters between PF foil & sample as a fcn of E,

and PF(Ki), the normalized PF K radiation striking the sample, will be given by

Eq.(5) PF(Ki) = Ci / Citot

with Citot = Sum(i) { Ci }.

Thus the excitation function fit parameters are the total number of photons striking the sample per second (N(ph)), the fraction that are PF K line x-rays (f), and the two Bremstrahlung radiation parameters Eo & p. These parameters will be combined with the detector thicknesss parameter t(det) and information about the intervening absorbers, the sample and the measuring system to calculate the theoretical peak area for each certified element in the standard(s).