System and method for determining mass fractions in a test sample with wave-length dispersive x-ray fluorescence spectrometers
System, method and computer program product for determining mass fractions of one or more elements in a test sample based on a measurement with a wave-length dispersive x-ray fluorescence (WDX) spectrometer measuring gross intensities associated with respective elements with to-be-determined mass fractions (MFi) in the test sample. A mass fraction module determines mass fractions (MFi) by using a calibration equation (CE1) with the respective measured gross intensity and a respective calculated scattering efficiency as inputs. The calibration equation (CE1) associates net intensities of characteristic fluorescence lines of the sample elements with respective mass fractions. The net intensity for a particular peak is obtained by subtracting a respective calculated scattering efficiency times a scaling factor from the calibration equation (CE1) from the measured gross intensity of the particular peak. The elemental composition of the test sample is determined either via an iteration module or via an EDX quantification module.
1. A computer-implemented method for determining mass fractions of one or more elements in a test sample based on a measurement with a wave-length dispersive x-ray fluorescence spectrometer, referred to as WDX spectrometer, comprising:
receiving, from a detector of the WDX spectrometer, one or more gross intensities associated with respective one or more elements with corresponding one or more to-be-determined mass fractions (MFi) in the test sample; and
determining each of the one or more to-be-determined mass fractions (MFi) by using a calibration equation (CE1) with the respective measured gross intensity and a respective calculated scattering efficiency as inputs, wherein the calculated scattering efficiency is defined as a ratio between incoming intensity and scattered intensity for a particular elemental composition and energy, the calibration equation (CE1) associating net intensities of characteristic fluorescence emission lines of the sample elements with respective mass fractions, wherein the net intensity for a particular peak is obtained by subtracting the respective calculated scattering efficiency times a scaling factor from the calibration equation (CE1) from the measured gross intensity of the particular peak, with the particular elemental composition of the test sample being estimated by either:
iteratively determining mass fraction estimates for the particular elemental composition based on the measured gross intensities associated with elements in the test sample; or
obtaining mass fraction estimates for the particular elemental composition from a quantification using an Energy Dispersive X-Ray detector, referred to as EDX detector.
2. The method of claim 1 , wherein the calibration equation (CE1) has a set of calibration parameters obtained from a previous calibration step using one or more calibration samples with known elemental compositions.
3. The method of claim 2 , wherein in the previous calibration step, the parameters of the calibration equation are adjusted based on known properties of the one or more calibration samples.
4. The method of claim 1 , wherein iteratively determining mass fraction estimates for the particular elemental composition comprises:
initializing current mass fraction estimates of the elements with arbitrary values;
computing, for each gross intensity associated with a to-be-determined mass fraction, the respective calculated scattering efficiency using the current mass fraction estimates with the energy of the fluorescence line of the respective element;
computing, with the calibration equation, the one or more to-be-determined mass fractions as the current mass fraction estimates;
repeating the computing of the respective calculated scattering efficiency and of the current mass fraction estimates as long as a mass fraction difference (MFD) between the one or more to-be-determined mass fractions of a latest iteration and the respective one or more to-be-determined mass fractions of a preceding iteration exceed a predefined threshold (T 1 ).
5. The method of claim 1 , wherein, for iteratively determining the one or more to-be-determined mass fractions, gross-intensities are measured by the detector of the WDX spectrometer or by the EDX detector.
6. The method of claim 1 , wherein obtaining the one or more to-be-determined mass fractions from a quantification using an EDX detector comprises any one of the following:
measuring the test sample with the EDX detector before measuring the sample with the detector of the WDX spectrometer,
measuring the test sample with the EDX detector in parallel with the measuring of the sample with the detector of the WDX spectrometer, and
measuring the test sample with the EDX detector after measuring the sample with the detector of the WDX spectrometer.
7. The method of claim 1 , wherein the elemental composition of the test sample being used for determining calculated scattering efficiencies is limited to elements in the test sample with a mass fraction exceeding a predefined threshold.
8. A computer system for determining mass fractions of one or more elements in a test sample based on a measurement with a wave-length dispersive x-ray fluorescence spectrometer, referred to as WDX spectrometer, comprising:
an interface adapted to receive one or more gross intensities associated with respective one or more elements with corresponding one or more to-be-determined mass fractions (MFi) in the test sample obtained by a detector ( 204 ) of the WDX spectrometer from said test sample;
a mass fraction module adapted to determine each of the one or more to-be-determined mass fractions (MFi) by using a calibration equation (CE1) with the respective measured gross intensity and a respective calculated scattering efficiency as inputs, wherein the calculated scattering efficiency is defined as a ratio between incoming intensity and scattered intensity for a particular elemental composition and energy, the calibration equation (CE1) associating net intensities of characteristic fluorescence emission lines of the sample elements with respective mass fractions, wherein the net intensity for a particular peak is obtained by subtracting a respective calculated scattering efficiency times a scaling factor from the calibration equation (CE1) from the measured gross intensity of the particular peak;
an elemental composition module adapted to estimate the particular elemental composition of the test sample either:
via an iteration module adapted to iteratively determine mass fraction estimates for the particular elemental composition based on the measured gross intensities associated with elements in the test sample; or
via an EDX quantification module adapted to obtain mass fraction estimates for the particular elemental composition from a quantification using an Energy Dispersive X-Ray detector, referred to as EDX detector.
9. The system of claim 8 , wherein the calibration equation (CE1) has a set of calibration parameters obtained from a previous calibration step using one or more calibration samples with known elemental compositions.
10. The system of claim 9 , further comprising a calibration module configured to perform the previous calibration step to adjust the parameters of the calibration equation based on known properties of the one or more calibration samples.
11. The system of claim 8 , wherein the iteration module for iteratively determining mass fraction estimates for the particular elemental composition is adapted to:
initialize current mass fraction estimates of the elements with arbitrary values;
compute, for each gross intensity associated with a to-be-determined mass fraction, the respective calculated scattering efficiency using the current mass fraction estimates with the energy of the fluorescence line of the respective element;
compute, with the calibration equation, the one or more to-be-determined mass fractions as the current mass fraction estimates; and
repeat the computing of the respective calculated scattering efficiency and of the current mass fraction estimates as long as a mass fraction difference (MFD) between the one or more to-be-determined mass fractions of a latest iteration and a respective one or more to-be-determined mass fractions of a preceding iteration exceed a predefined threshold (T 1 ).
12. The system of claim 8 , wherein gross intensities used by the iteration module are measured by the WDX spectrometer or by the EDX detector.
13. The system of claim 8 , wherein the one or more to-be-determined mass fractions obtained via the EDX quantification module are based on any of the following:
a measurement of the test sample with the EDX detector before measuring the sample with the detector of the WDX spectrometer,
a measurement of the test sample with the EDX detector in parallel with the measuring of the sample with the detector of the WDX spectrometer, and
a measurement of the test sample with the EDX detector after measuring the sample with the detector of the WDX spectrometer.
14. The system of claim 8 , wherein the elemental composition of the test sample being used for determining calculated scattering efficiencies is limited to elements in the test sample with a mass fraction exceeding a predefined threshold.
15. A computer program product for determining mass fractions of one or more elements in a test sample based on a measurement with a wave-length dispersive x-ray fluorescence spectrometer, referred to as WDX spectrometer, the computer program product being tangibly embodied on a computer-readable storage medium and including computer readable instructions that, when loaded into a memory of a computing device and executed by at least one processor of the computing device, causes the computing device to:
receive, from a detector of the WDX spectrometer, one or more gross intensities associated with respective one or more elements with corresponding one or more to-be-determined mass fractions (MFi) in the test sample; and
determine each of the one or more to-be-determined mass fractions (MFi) by using a calibration equation (CE1) with the respective measured gross intensity and a respective calculated scattering efficiency as inputs, wherein the calculated scattering efficiency is defined as a ratio between incoming intensity and scattered intensity for a particular elemental composition and energy, the calibration equation (CE1) associating net intensities of characteristic fluorescence emission lines of the sample elements with respective mass fractions, wherein the net intensity for a particular peak is obtained by subtracting the respective calculated scattering efficiency times a scaling factor from the calibration equation (CE1) from the measured gross intensity of the particular peak, with the particular elemental composition of the test sample being estimated by either:
iteratively determining mass fraction estimates for the particular elemental composition based on the measured gross intensities associated with elements in the test sample; or
obtaining mass fraction estimates for the particular elemental composition from a quantification using an Energy Dispersive X-Ray detector, referred to as EDX detector.
16. The computer program product of claim 15 , wherein the calibration equation (CE1) has a set of calibration parameters obtained from a previous calibration step using one or more calibration samples with known elemental compositions.
17. The computer program product of claim 15 , wherein iteratively determining mass fraction estimates for the particular elemental composition comprises:
initializing current mass fraction estimates of the elements with arbitrary values;
computing, for each gross intensity associated with a to-be-determined mass fraction, the respective calculated scattering efficiency using the current mass fraction estimates with the energy of the fluorescence line of the respective element;
computing, with the calibration equation, the one or more to-be-determined mass fractions as the current mass fraction estimates;
repeating the computing of the respective calculated scattering efficiency and of the current mass fraction estimates as long as a mass fraction difference (MFD) between the one or more to-be-determined mass fractions of a latest iteration and the respective one or more to-be-determined mass fractions of a preceding iteration exceed a predefined threshold (T 1 ).
18. The computer program product of claim 15 , wherein, for iteratively determining the one or more to-be-determined mass fractions, gross-intensities are measured by the detector of the WDX spectrometer or by the EDX detector.
19. The computer program product of claim 15 , wherein obtaining the one or more to-be-determined mass fractions from a quantification using an EDX detector comprises any one of the following:
measuring the test sample with the EDX detector before measuring the sample with the detector of the WDX spectrometer,
measuring the test sample with the EDX detector in parallel with the measuring of the sample with the detector of the WDX spectrometer, and
measuring the test sample with the EDX detector after measuring the sample with the detector of the WDX spectrometer.
20. The computer program product of claim 15 , wherein the elemental composition of the test sample being used for determining calculated scattering efficiencies is limited to elements in the test sample with a mass fraction exceeding a predefined threshold.