CN110646453A - Phase content calculation method and system based on energy spectrometer component detection data - Google Patents

Phase content calculation method and system based on energy spectrometer component detection data Download PDF

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CN110646453A
CN110646453A CN201910891102.XA CN201910891102A CN110646453A CN 110646453 A CN110646453 A CN 110646453A CN 201910891102 A CN201910891102 A CN 201910891102A CN 110646453 A CN110646453 A CN 110646453A
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phase
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梁栋
刘元意
王学斌
肖晨
石红燕
闻一帆
张毅
赵秀娟
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Shandong Iron and Steel Group Co Ltd SISG
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Abstract

The invention discloses a phase content calculation method and system based on energy spectrometer component detection data, wherein the method comprises the following steps: obtaining the detection content of m elements in a sample to be detected; wherein the detected content of the a-th element is TaA is more than or equal to 1 and less than or equal to m; obtaining n phases contained in a sample to be detected; establishing an optimization problem by taking the n phase contents as calculation variables, wherein the target is that the error between the detection content and the calculation content of the detection elements is minimum; the optimal solution to the optimization problem is the n phase content containing all the elements tested. The method can accurately calculate the content of the phase by analyzing the element data through an energy spectrometer; the phase of the content of the damaged refractory material can be quantitatively analyzed.

Description

Phase content calculation method and system based on energy spectrometer component detection data
Technical Field
The invention relates to the field of metallurgical technology detection, in particular to a phase content calculation method and system based on energy spectrometer component detection data.
Background
An Energy Spectrometer (Energy Dispersive Spectrometer) is used for analyzing the types and contents of the elements in the micro-area of the material, and is used together with a scanning electron microscope and a transmission electron microscope. The basic detection principle is as follows: the elements have own characteristic X-ray wavelength, the size of the characteristic wavelength depends on the characteristic energy Delta E released in the energy level transition process, and the energy spectrometer performs component analysis by utilizing the characteristic that the photon characteristic energy of different elements are different. In the specific operation process, after the probe receives the X-ray characteristic signals, the signals are photoelectrically converted into electric pulse signals with different heights, after the signals are amplified by the amplifier, the multichannel pulse analyzer programs the X-ray pulse signals representing different energies (wavelengths) into different channels according to the heights, the spectral lines are displayed on a fluorescent screen, and the element concentration is calculated through the intensity.
The energy spectrometer analysis has the advantage that the rapid quantitative analysis can be carried out on the components of the sample in a point scanning or line scanning mode, but in practical application, the phase components of the element composition are more concerned. Although XRD (X-ray diffraction analysis) can distinguish unknown phases of a sample, only qualitative analysis can be achieved, and the process depends strongly on phase information in a PDF database through a half peak height or a half quantitative method such as an external standard method, an adiabatic method, a K-value method, a RIR method and the like, and complex mineral data used in daily life are not complete in information. This limits the quantification of the composition of the phase.
Disclosure of Invention
The invention aims to solve the problems that the existing energy spectrometer analysis process can only obtain the percentage content of each element, the existing XRD phase quantitative detection technology is still inaccurate, the existing XRD phase quantitative detection technology strongly depends on phase information in a PDF database, and the daily complex mineral data information does not completely limit the quantitative determination of the phase components.
In order to achieve the above object, the present invention provides a method for calculating a phase content based on energy spectrometer component detection data, the method comprising:
obtaining the detection content of m elements in a sample to be detected; wherein the detected content of the a-th element is Ta，1≤a≤m；
Obtaining n phases contained in a sample to be detected;
establishing an optimization problem by taking the n phase contents as calculation variables, wherein the target is that the error between the detection content and the calculation content of the detection elements is minimum; the optimal solution to the optimization problem is the n phase content containing all the elements tested.
Preferably, the detection content of m elements in the sample to be detected is obtained by an energy spectrometer.
Preferably, the n phases contained in the sample to be detected are acquired by phase diagram or X-ray diffraction pattern.
Preferably, the n phase contents are used as calculation variables to establish an optimization problem, and the target is that the error between the detected content and the calculated content of the detection elements is minimum; the optimal solution of the optimization problem is the n phase contents containing all the detection elements, and specifically comprises the following steps:
establishing an optimization problem:
the target is as follows:
Figure BDA0002208774640000021
the constraint conditions are as follows:
Figure BDA0002208774640000023
Figure BDA0002208774640000029
Figure BDA0002208774640000024
wherein the content of the first and second substances,
Figure BDA0002208774640000025
is the ith phase content, is an unknown variable; a isiFor the a-th element in the i-th phase omegaiThe mass percentage of the components is as follows:
Figure BDA0002208774640000026
wherein M isaIs the molar mass of the a-th element, MiIs the molar mass of the i phase;
Figure BDA0002208774640000027
calculated content for the a-th element; the optimal solution to the optimization problem described above
Figure BDA0002208774640000028
Namely the content of the ith phase.
Preferably, the optimization problem is solved by a simplex-based linear programming algorithm or a genetic algorithm.
The invention provides a phase content calculation system based on energy spectrometer component detection data, which comprises:
the energy spectrometer is used for obtaining the detection content of m elements in a sample to be detected; wherein the detected content of the a-th element is Ta，1≤a≤m；
The phase analysis module is used for acquiring n phases contained in a sample to be detected;
the phase content calculation module is used for establishing an optimization problem by taking the n phase contents as calculation variables, and the target is that the error between the detection content and the calculation content of the detection elements is minimum; the optimal solution to the optimization problem is the n phase content containing all the elements tested.
Preferably, the specific implementation process of the phase content calculation module is as follows:
establishing an optimization problem:
the target is as follows:
Figure BDA0002208774640000031
Figure BDA0002208774640000032
the constraint conditions are as follows:
Figure BDA0002208774640000033
Figure BDA0002208774640000034
Figure BDA0002208774640000035
wherein the content of the first and second substances,
Figure BDA0002208774640000037
is the ith phase content, is an unknown variable; a isiFor the a-th element in the i-th phase omegaiIn (1)
Figure BDA0002208774640000036
Namely the content of the ith phase.
Compared with the prior art, the invention has the advantages that:
1. the method can accurately calculate the content of the phase by analyzing the element data through an energy spectrometer;
2. the method can quantitatively analyze the phase contained in the damaged refractory material;
3. the method can combine the phase diagram and XRD detection data and improve the calculation speed and accuracy through algorithms such as genetic optimization and the like;
4. the method of the invention infers the phase species contained by EDS element percentage content detection data in combination with a phase diagram or XRD, and realizes the phase quantification by an optimization model through a mass conservation principle.
Drawings
FIG. 1 is a diagram of an input interface for detecting components of an energy spectrometer according to the present invention;
FIG. 2 is an interface diagram of a facies content inference model based on planning solution and genetic algorithm optimization in accordance with the present invention;
FIG. 3 is a sample view of ultra-microporous carbon bricks after the lower part of the tuyere region of the blast furnace is in service;
FIG. 4(a) is a spectrum 1-14 of the SEM and EDS analysis of FIG. 3 according to the present invention;
FIG. 4(b) is a spectrum 15-36 of the SEM and EDS analysis of FIG. 3 according to the present invention;
FIG. 4(c) is a spectrum 37-54 of the SEM and EDS analysis of FIG. 3 according to the present invention;
FIG. 5 is a model calculation phase content distribution of the present invention;
figure 6 is a sample XRD measurement of the invention based on figure 3.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
The invention provides a phase content calculation method based on energy spectrometer component detection data.
The method specifically comprises the following steps:
1) model definition
According to the principle of conservation of substances, the phases of all the substances in the substances are compounded by elements, and then the relationship exists:
Figure BDA0002208774640000041
wherein, TaThe total mass percentage of the first element a in the sample; omegaiThe mass percentage of the ith phase in the sample is shown; a isiThe mass percentage of the a-th element in the i-th phase can be determined by the molar mass ratio of the a-element to the phase omega, i.e. the content of the a-th element in the i-th phase is
Figure BDA0002208774640000042
n is the total of n phases in the sample.
Equation (1) can be written in matrix form, i.e. (2):
Figure BDA0002208774640000043
Figure BDA0002208774640000044
in the formula (2), the reaction mixture is,
Figure BDA0002208774640000045
is a vector Ai(1×n)The invertible basic condition is a full rank square matrix, for aiThe dimension of the row vector is 1 x n, there is a set of n x 1 order column vectors, such that
Figure BDA0002208774640000046
Then vector will be
Figure BDA0002208774640000051
Referred to as vector Ai(1×n)In a generalized inverse matrix of, wherein En×nIs a full rank square matrix. The concept of "division" can thus be realized.
The amount of the phase for the entire content of each known element in the sample can be calculated by the formula (2), but when a certain phase does not exist in the form of a simple substance, for example, the composition of the ω phase is in the form of AxByCz, which contains a combination of a plurality of elements. The values of the content of the ω -phase calculated by each element are contradictory and cannot be unified.
Thus, the problem is transformed into a planning solution problem.
Figure BDA0002208774640000052
Figure BDA0002208774640000053
Wherein the content of the first and second substances,
Figure BDA0002208774640000054
is the percentage of the phase content to be calculated; e.g. of the typejThe absolute error between the detected content and the calculated content of the a-th element; e estimates the sum of absolute errors for all m elements.
2) Model structure
goal：
Figure BDA0002208774640000055
cons：
Figure BDA0002208774640000056
Figure BDA0002208774640000057
Figure BDA0002208774640000058
A linear optimization structure of the form of equation (5) is used to perform the calculation of the phase content. Taking the contents of all phases as calculation variables, aiming at the principle that the detection and calculation errors are minimum, and E can be written as a linear function of the contents of all estimated phases:
Figure BDA0002208774640000059
wherein, TaDetecting the content of the a-th element scanned by an energy spectrometer;
the phase content inference model takes the content of each phase as a calculation variable, cons is a constraint condition for detection and calculation, and target goal is the minimum error of the content of each estimated phase for detection and calculation
Figure BDA00022087746400000510
The constraints are divided into three categories: 1) relaxation constraint of single element calculated quantity, defining the fluctuation of the upper limit and the lower limit of the relaxation constraint to be +/-2%; 2) non-negative restriction, and the content of each phase fluctuates between 0 and 100. 3) The sum of the contents of the phases is 100, and the relaxation constraint is adopted, and the fluctuation of the upper limit and the lower limit is +/-0.001%.
The model optimization method adopts two modes, 1) linear programming solution based on simplex type; 2) and (4) genetic algorithm optimization. The simplex method has a high solving speed, but sometimes an optimal solution is difficult to obtain, and in this case, optimization is performed by combining a genetic algorithm.
The model method is instantiated in excel form through VBA technology, and the interface is as shown in the figure. The whole model is divided into two interfaces, 1) the input of the detection components of the spectrometer, as shown in figure 1; 2) and (3) a phase content inference model based on planning solution and genetic algorithm optimization, which is shown in figure 2.
In the process of overhauling a certain blast furnace, the tuyere composite brick is found to have pulverization, the surface of the tuyere composite brick is whitened and has serious efflorescence phenomenon, the carbon brick is flaky and is peeled off like a figure 3, and the pulverization and the fracture phenomena are caused by slight force. The reason why the carbonaceous refractory deteriorates in this region is a high-value guide for the long-life operation of the blast furnace in the future, and therefore, quantitative analysis of the phase of the content of the damaged refractory is important.
Sampling and detecting a scanning electron microscope and an energy spectrometer. The uneven surface of the carbon brick can be seen through a scanning electron microscope. The spectrometer multi-point (54 point) scan is as in fig. 4(a), 4(b), 4 (c).
The energy spectrometer of table 1 detects the data of each element, and it can be seen that C, O, K, Zn four elements are the most important four elements in the sample. The element C is the main part of the original refractory material, and high content of elements K and Zn are found in the part of the sample. The highest K content is 52.57 percent, and the average K content is 15.48 percent; the Zn content is 82.87 percent at most, and the average Zn content is 11.03 percent.
TABLE 1 summary of point scan data for an energy spectrometer
Figure BDA0002208774640000061
From this, it can be preliminarily concluded that high contents of K and Zn elements may cause a decline in the strength of the carbon brick.
And (5) substituting the mean value of the detection data of the energy spectrometer into the model. The calculated phase contents are shown in FIG. 5. The calculated results of the comparison of the total element content and the detected content are shown in Table 2.
The final optimization result accumulated error Δ E is 3.2%, which means that the difference between the total of all elements contained in the inferred contents of the phases of the model and the actual detection value is 3.2%, and the result also shows that the model accuracy is good, and the substance content can be inferred to a certain extent.
XRD detection is carried out on part of the samples after pulverization, and the analysis result is shown in figure 6.
Table 2 comparison of the quantitative estimation with the actual measurement
Figure BDA0002208774640000062
Figure BDA0002208774640000071
As can be seen from the comparison between FIG. 5 and FIG. 6, the phases calculated by the model can completely cover the phases indicated by XRD, and trace element phases such as In, Rb and the like cannot be detected In the XRD sample detection, which may be caused by the non-uniformity of the distribution of the elements In the sample, so that the elements are not present In part of the sample area. As can be seen from the calculation and XRD detection comparison, the model method can better realize the phase quantification.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A method of phase content calculation based on energy spectrometer composition detection data, the method comprising:
obtaining the detection content of m elements in a sample to be detected; wherein the detected content of the a-th element is Ta，1≤a≤m；
Obtaining n phases contained in a sample to be detected;
establishing an optimization problem by taking the n phase contents as calculation variables, wherein the target is that the error between the detection content and the calculation content of the detection elements is minimum; the optimal solution to the optimization problem is the n phase content containing all the elements tested.
2. The method for calculating the phase content based on the energy spectrometer component detection data according to claim 1, characterized in that the detection content of m elements in the sample to be detected is obtained by an energy spectrometer.
3. The method for calculating the content of a phase based on the energy spectrometer component detection data according to claim 1, characterized in that n phases contained in the sample to be detected are obtained by a phase diagram or an X-ray diffraction pattern.
4. The method for calculating the phase content based on the energy spectrometer element detection data according to one of claims 1 to 3, characterized in that the n phase contents are used as calculation variables to establish an optimization problem with the goal of minimizing the error between the detected content of the detection element and the calculated content; the optimal solution of the optimization problem is the n phase contents containing all the detection elements, and specifically comprises the following steps:
establishing an optimization problem:
the target is as follows:
Figure FDA0002208774630000011
the constraint conditions are as follows:
Figure FDA0002208774630000013
Figure FDA0002208774630000014
Figure FDA0002208774630000015
wherein the content of the first and second substances,
Figure FDA0002208774630000016
is the ith phase content, is an unknown variable; a isiFor the a-th element in the i-th phase omegaiThe mass percentage of the components is as follows:wherein M isaIs the molar mass of the a-th element, MiIs the ith object
The molar mass of the phases;
Figure FDA0002208774630000021
calculated content for the a-th element; the optimal solution to the optimization problem described aboveNamely the content of the ith phase.
5. The method of calculating the phase content based on the energy spectrometer component detection data according to claim 4, wherein the optimization problem is solved by a simplex-based linear programming algorithm or a genetic algorithm.
6. A system for calculating a phase content based on energy spectrometer composition detection data, the system comprising:
the energy spectrometer is used for obtaining the detection content of m elements in a sample to be detected; wherein the detected content of the a-th element is Ta，1≤a≤m；
The phase analysis module is used for acquiring n phases contained in a sample to be detected;
the phase content calculation module is used for establishing an optimization problem by taking the n phase contents as calculation variables, and the target is that the error between the detection content and the calculation content of the detection elements is minimum; the optimal solution to the optimization problem is the n phase content containing all the elements tested.
7. The system for calculating the phase content based on the energy spectrometer component detection data according to claim 6, wherein the phase content calculation module is implemented by the following steps:
establishing an optimization problem:
the target is as follows:
Figure FDA0002208774630000023
Figure FDA0002208774630000024
the constraint conditions are as follows:
Figure FDA0002208774630000025
Figure FDA0002208774630000026
Figure FDA0002208774630000027
wherein the content of the first and second substances,
Figure FDA0002208774630000028
is the ith phase content, is an unknown variable; a isiFor the a-th element in the i-th phase omegaiThe mass percentage of the components is as follows:
Figure FDA0002208774630000029
wherein M isaIs the molar mass of the a-th element, MiIs the molar mass of the i phase;calculated content for the a-th element; the optimal solution to the optimization problem described above
Figure FDA0002208774630000032
Namely the content of the ith phase.
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