Polygonal Graphic Representations Applied to Semi-Quantitative Analysis for 3 and 4 Elements in XRF. Marcia Garcia and Rodolfo Figueroa

Transcription

1 788 Polygonal Graphic Representations Applied to Semi-Quantitative Analysis for 3 and 4 Elements in XRF Marcia Garcia and Rodolfo Figueroa X-ray Fluorescence Laboratory, Department of Physics Sciences, La Frontera University, Francisco Salazar Ave , Temuco, Chile. Abstract In this paper polygonal graphic representations are applied with the purpose of making semiquantitative measurements in samples analyzed by X-ray Fluorescence (XRF). The position of the representative points of the sample peak areas is correlated with the position of the quantitative points in a choice polygonal graphic for a set of elements in known samples. This methodology is proposed for samples with different concentrations of neighboring elements in the Periodic Table. An empirical correlation factor is determined for each combination of elements. The elemental concentration of similar samples is calculated and compared with their respective values obtained by traditional quantitative methods. Vegetable and soil samples from the Chilean lx Region are considered in this application. Introduction The large number of peaks that can appear in a multielemental XRF spectrum makes it difficult to compare different samples. There are some methodologies which uses graphic representations and multivariate methods(.2). The authors of this paper have developed a new methodology based in polygonal graphic representations (3); it allows the simple representation of one sample of elemental multicomponents by n dimensional (no orthogonal) vectors, all contained in one plane. The application field of this methodology is very wide and not only is valid for the study of archaeological fragments or pieces (46), it also could be applied in quality control production process. One control criterion could be defined by means of one zone of representation of samples, discarding all samples where their respective points were out. The representative point of one set of elements in any material presents one defined position in the specific polygon of the corresponding representation, when the peak areas or the concentration of respective elements are considered. In this paper we are proposing one methodology that allows to make one linear correlation between the respective area or concentration points to obtain one semi-quantitative result by means of knowledge of the areas of the respective peaks.

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 789 Method The analytical variables associated with one sample can be represented as non orthogonal components of one pseudo-vector, defined by: r = ~,+~2+...+& (1) where Ci represents the concentration of one element or the intensity or the net area of the Ka or La corresponding line. To simplify the calculus and as the representation of this pseudo-vector is in one plane, is possible to express it in an ( X, y ) Cartesian coordinate system with common origin to the initial system of non orthogonal coordinates; in this way it is possible to find the representation point defined by the pseudo-vector( ). The triangular representation (n = 3, N = 1) presents one defined point by only one combination of the 3 normalized components of the corresponding pseudo-vector, defined by: CI =p rx+r,+o (2) c2=;(2ry+l) (3) 1 cj= $-&,+r,+li (4) where r, y r,, represent the Cartesian components of r vector. In N > 1 representation order it is impossible to find a unique relation between the Ci and r,, ry components, because the different combinations between the components can lead to the same point of representation. With the proposition to find only one combination for the N > 1 representation order it is necessary, at first, to consider three elements of the sample in the triangular representation; in this polygon the representative point is unique and then, the uniqueness of the components in the ( N + 1 ) representation ( n = 4 ) is affirmed. So, it is possible to obtain the successive polygonal representation. In order to find the components of one N > 1 representations order, it is necessary to consider the representative point of the problem sample in the N representation order and then, to obtain the corresponding r, vector. Next, it is necessary to represent one vector r, considering the previous ( N - 1) representation in the same graph with c, = 0. Then, it is necessary to trace one parallel to the direction of the r,, vector from the end of r vector, for cutting the incorporated element axis; the cut point determines the quantity (among 0 and 1) of the search component ( c, ). For example

4 790 in Figure 1, it is represented for N = 2 (square) with respect to the square representation axis, where c 1, c 2, c 3.are the r vector components obtained from the triangular representation ( N = 1 ), considering c 4 = 0, and c 4 is the unknown component of the added element (D). f B + x \ \ C Figure 1. Square representation axis ( N = 2 ), where r vector is obtained from the triangular representation ( N = 1 ), considering c 4 = 0, and c 4 is the unknown component of the added element (D). By geometrical considerations, applying sin law, we find: sin 4 cfq = r (5) sin[z-(4+a)] As we said before, the fifth component of the pentagonal representation is obtained by process which was described above; meaning that it is necessary to use the square base. In another way, in the representations there is one correlation between the area points and the concentration points, because the displacing vector between this point pair is approximately constant in similar samples; for example, it can be noted in Figure 2 for one soil sample. Resulting in; r,=d+fi (6)

5 791 where r, y r i are the position vectors of concentration points and area points of one set of elements from the problem sample, respectively, and d is their respective displacing vector, for one considered polygonal representation. Ti 0 6concentration points 0 area points CO Ca Figure 2. Correlation between the area points and the concentration points for a square representation. r e y r i are the position vectors of concentration points and area points, respectively, of four elements from one soil sample; d is the displacing vector. This correlation allows to infer the position of one concentration point from one area point. This means that we can find the concentration point corresponding to one polygonal representation for three or more than three elements from the problem sample, knowing only the peak areas or their respective line intensities. According to that, and since it is possible to find the qualitative components of representative points in different polygons, it is also possible to find the respective quantitative components. It is then a semi-quantitative analysis. Results From the results obtained with three vegetable samples and three soil samples, used as standards, the elemental concentrations of six vegetable samples and six soil samples are calculated; these results are compared with those obtained by a traditional quantitative method, using XRF. In Table 1 the values of the concentrations calculated by the proposed method and their respective values obtained by conventional XRF for three soil samples and one standard soil sample (Soil-7 IAEA Standard) are presented. In Table 2, the same comparison for two vegetable samples and one standard vegetable sample (Tomato leaves NBS Standard) is presented.

6 792 Table 1. Soil Samples Concentrations calculated by proposed method ( ppm ) Samples Ca Ti Mn co Standard Concentrations obtained by conventional XRF ( ppm ) Samples Ca Ti Mn co Standard Standard Reference Material (IAEA) ( ppm ) Standard Ca Soil Ti Mn co Table 2. Vegetable Samples Concentrations calculated by proposed method ( ppm ) Samples Fe cu Zn Br Standard Concentrations using conventional XRF ( ppm ) Samples Fe cu Zn Br Standard Standard Reference Material 1573 (NBS) ( ppm ) Standard Fe Tomato leaves 690 cu 11 Zn 62 Br 26

7 793 Discussion It is possible to obtain a good agreement between the concentrations calculated by this method and those obtained from a conventional quantitative XRF method using standards. Our method is more efficient for representations with three elements than representations with four or more, because the error increases with the number of elements incorporated in the polygon. In samples where elements are contained in similar concentrations, this method is more accurate, in spite of any important difference between the calculated concentration of one element and the standard certificate value. The comparison must be with respect to the conventional method. The results of vegetable samples are better than those of soil samples because of the matrix effect which is more important in the latter samples. Conclusions The proposed method allows one to obtain elements concentration values with a good accuracy from an intensities analysis of one elements set of a problem sample. The accuracy of concentration values calculated by this method increases when the compared elements are in similar concentration, belonging to samples from the same origin. The relative error increases when the element analyzed is found in very low concentration with respect to others considered in the same representation polygon. This method is a good proposition for semi-quantitative analysis applied to several kinds of samples, whenever that correlation is made between similar samples to assert a linear correlation factor, neglecting the different matrix effects. References l.- Murata, K. J. - A new method of plotting chemical analysis of basaltic rock. Am. J. Sci., Vol , pp ,196O. 2.- Lebreque, J. J.; Rosales, P. A. and Carias, 0. - Non Destructive Analysis of Venezuelan Artifacts of Different Sizes and Shapes for Provenience Studies. Advances in X-Ray Analysis, Vol. 34, pp. 307, P. Press, Figueroa, R. and Caro, D. - A New Method of Graphic Representation of Samples Analyzed by XRF. Advances in X-ray Analysis, Vol. 37, pp , P. Press, Figueroa, R. - Un Nuevo MCtodo Grafico Para Representar y Comparar Muestras Geologicas, Actas, I Simp. Sobre Geologia de1 Sur de Chile, P. Varas, de Oct. de Figueroa, R.; Caro, D. and Vargas, A. - Non Destructive Analysis of Archaeological Samples by EDXRF. Investigation Tecnologica, Vo1.6, pp , No. 4, Figueroa, R.; Caro, D. and Vargas, A. - Proceedence Study of Samples Analyzed by XRF and Compared by Polygonal Graphic Representations. Journal of Radioanalytical and Nuclear Chemistry, Vol. 198, No. 2, 1995.