Multi-variate Analysis of Trace Elements from XRF Studies for Classification According to Origin
C. T. YAP* Department of Physics, University of California, Riverside, California 92521
The concentrations of twelve trace elements (Mn, Fe, Co, Ni, Cu, Zn, As, Rb, Sr, Y, Zr, and Nb) in 143 pieces of Chinese porcelain made in Jingdezhen, China and elsewhere were obtained with the use of the energy-dispersive x-ray fluorescence technique. An elegant method of multi-variate analysis, known as principal component analysis, was suc- cessfully employed in fingerprinting the geographical origin of the por- celain samples.
Index Heading: X-ray fluorescence.
INTRODUCTION
In the study of Chinese porcelains, we have used two- variable I-3 and three-variable 4 plots of certain trace el- ements found in Chinese porcelains as a method of de- tecting modern reproductions of antique pieces. Such plots can also be used to identify porcelains with respect to their geographical origin. The certainty of such iden- tification increases as the number of relevant variables increases; hence, the importance of multi-variate anal- ysis.
Our previous studies 1-15 on the attribution of Chinese porcelains show that major and minor elements are not useful. However, a number of trace elements are relevant, including those in the rubidium-niobium 7 region. Of course, there are normally many trace elements in por- celain samples that are not relevant or useful in such studies.
Human beings are probably the best recognizers of patterns, and therefore trace element data are normally presented graphically. However, the human eye cannot visualize data plotted in more than three dimensions; it follows that only the variation of three variables can be studied at a time. This limitation is rather unsatisfactory since multi-element analysis normally yields a large number of trace elements--hence, the necessity of using multi-variate analysis.
In this paper, we shall use one of the elegant methods of multi-variate analysis--principal component analysis. It is applied to the measured concentrations of trace elements from manganese (Z = 25) to niobium (Z = 41) of 143 samples of Chinese porcelains, with the use of the energy-dispersive x-ray fluorescence technique. The re- sults are discussed.
EXPERIMENTAL
The x-ray fluorescence spectrometer consisted of a Si(Li) detector with associated electronics and a micro-
Received 31 December 1991. * On sabbatical leave from the National University of Singapore, where
par t of the work was done.
processor-based multi-channel analyzer with a 12.5-#m beryllium window. It was connected to a microcomputer for storage and spectral analysis. Figure 1 shows the con- figuration of the x-ray fluorescence spectrometer. For good statistics, each sample was exposed for about 10,000 s with overnight exposures of around 50,000 s. For most samples, the statistical errors at 2a were roughly 2 % for Rb, 3% for Sr, 4% for Zr, and 8% for Y and Nb for an exposure time of 10,000 s. All the spectra obtained were analyzed by the commercial program AXIL (--Analysis of X-ray spectra by Iterative Least-squares fitting).
In this experiment an annular i°gCd radioisotope source was used. The samples were placed at a particular source- sample distance so that the intensity of the fluorescent x-ray as seen by the detector was uniform. Is When one is working with samples that might not be homogeneous, placing the sample at this particular distance is impor- tant. All the samples were Chinese: 131 pieces were made during the Qing dynasty (1644-1911) in Jingdezhen, the famous porcelain city of China, while the others were made elsewhere. They were either blue-and-white or polychrome pieces, some of which were imperial ware.
Calibration is necessary to determine the concentra-
SAMPLE ~ SOURCE \ HOLOER /
I SOURCE / HOLDER
TO LIQUID NITROGEN (??K)
" " TO DEWAR
Fro. 1. Si(Li) detector assembly and radioisotope excitation system with annular source configuration for direct irradiation.
Plot of ln[intensity(cps)/concentration(% )] vs. ln[energy(keV)] for elements from Mn to Nb in porcelain matrix.
tions of the measured elements. In accordance with Yap e t a l . , 4 Fig. 2 was obtained, showing the calibration graph for elements from Mn to Nb in a plot of ln[intensity(cps)/ concentration(% )] against ln[energy(keV)] with the use of the same annular 1°9Cd source and the same geometry. This calibration curve can now be used to obtain the concentrations of twelve elements (Mn, Fe, Co, Ni, Cu, Zn, As, Rb, St, Y, Zr, and Nb) for the porcelain samples.
PRINCIPAL C O M P O N E N T ANALYSIS
The objective of principal component analysis is to take multiple variables (in this case, the concentrations of the twelve trace elements Mn, Fe, Co, Ni, Cu, Zn, As, Rb, Sr, Y, Zr, and Nb) and find linear combinations to produce new variables known as principal components that are uncorrelated, with principal component 1 having the largest variance, principal component 2 the second largest variance and so on. Therefore, if the data are highly correlated positively or negatively, we can reduce the number of dimensions drastically from twelve to two or three, depending on the data, since in general there is a good deal of redundancy in the original variables, as most of them are measuring similar things.
The concentrations of the twelve elements measured on 143 samples form a data matrix XCN×M) where x,m is the value of the concentration of element m measured
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Modern (possibly Thailand)
@ t
Yuan
-:~ f -I i r i i i -2 0 I ~ 3 4 5 ~
Principal Component I
Plot of Chinese porcelain samples, made in Jingdezhen (China) Fro. 3. and elsewhere, for principal components 1 and 2 using the concentra- tions of twelve elements (Mn, Fe, Co, Ni, Cu, Zn, As, Rb, Sr, Y, Rb, and Nb).
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Oing { Jingdezhen)
,,,,.,,,~ ~ Moder'n
(possibly Thailand)
,f. /
Yuan
i I I I I / I I I I -4 - -2 -1 0 1 2 3 4 5 6 7
Principal Component 1
FIG. 4. Plot of Chinese porcelain samples, made in Jingdezhen (China) and elsewhere, for principal components 1 and 2 using the concentra- tions of eight elements (Fe, Co, Ni, Rb, St, Y, Zr, and Nb).
8 4 4 V o l u m e 4 6 , N u m b e r 5 , 1 9 9 2
,~ 3
~ 2 o oe 1
~0 t~ c -1
-2
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FIG. 5.
Modern (Indonesia)
Modern
Mod e r n _ ~ ~ ~ ( T a i w a n }
(possib ly Ta iwan]
Qing (Jingdezhen)
j u Modern
(possibly Thailand)
/ Yuan
I I I I I I r I I I I -3 -2 "1 0 1 2 3 4 5 6 7
Principal Component 1
P l o t o f C h i n e s e porcelain samples made in Jingdezhen (China) and elsewhere for principal components 1 and 2 using the concentra- tions of seven elements (Fe, Co, Rb, Sr, Y, Zr, and Nb).
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o
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Principal Component 1
FIG. 6. Plot of Chinese porcelain samples made in Jingdezhen (China) and elsewhere for principal components 1 and 2 using the concentra- tions of five elements (Rb, Sr, Y, Zr, and Nb).
on sample n. The mean xm and standard deviation sm of the concentration of each element are given by:
~ = ~ x°m (1)
1 N 8 2 - - - - ~ ( X n m - - Xm) 2. (2)
N 1 . = 1
In order that the concentration of any element would not have too much influence on the principal compo- nents, the data were auto-scaled to have zero mean and unit variance by using the new variable Z,,m defined be- low:
Z.m (3) Sm
The principal components P are calculated 17 as linear combinations of the original variables (concentrations of elements) so that the first principal component has the largest variance, the second principal component has the second largest variance and is orthogonal to the first, and so on. This is expressed as
M
Pnk = ~_# ZnmVmk mffil
where P,,k is the value of the kth principal component for sample n, and V,,,k the ruth term of the kth eigenvector of the (M x M) correlation matrix. All calculations were done with the SAS (Statistical Analysis System) pro- gram.
RESULTS AND DISCUSSION
Principal component analysis was applied to the con- centrations of all the twelve measured trace elements of the 143 porcelain samples. Figure 3 shows a plot of the principal components I and 2, which together have a cumulative variance of only 44 % of the total variance. Generally, there is reasonable segregation into groups, although there is overlapping. From the table of corre- lations and from the negligible contribution to the ei- genvectors of principal components I and 2, it is obvious that elements Mn, Cu, Ni, and As are not useful for purposes of classification of porcelain origin.
Further application of principal component analysis on the remaining eight elements (Fe, Co, Ni, Rb, Sr, Y, Rb, and Nb) results in less overlapping. Figure 4 shows the plot for principal components 1 and 2, which have a cumulative variance of 61% of the total variance. The 131 pieces made during the Qing dynasty are much com- pressed now, and there is no overlapping with the Taiwan pieces. From the table of correlations, Ni should be elim- inated and possibly Fe and Co as well.
However, principal component analysis was performed on all possible combinations by removing one element at a time. Figure 5 gives the best seven-element plot for principal components 1 and 2. As expected, this is the plot in which Ni has been eliminated. In this case, the cumulative variance for these two principal components amounts to 69% of the total variance. The various groups are now well separated except the two Taiwan groups, which are close together though distinct. The table of correlation reveals little correlation between Fe and Co and also between these two elements and the other five
FIG. 7. Plot of Chinese porcelain samples made in Jingdezhen (China) and elsewhere for principal components 1, 2 and 3 using the concentrations of five elements (Rb, Sr, Y, Zr, and Nb).
elements, whereas the correlation of Rb, St, Y, Zr, and Nb among themselves is rather good. Therefore, we would expect to have better segregation into groups if Fe and Co were removed.
Figure 6 shows a plot of principal components 1 and 2 for the five elements Rb, Sr, Y, Zr, and Nb. The cu- mulative variance for these two components is 76% of the total variance. There is good segregation into groups with no overlapping, including the two Taiwan groups. This is especially the case if we look at Fig. 7, in which principal component 3 is added. The two Taiwan groups, which appear rather close in the two-dimensional plot, are now very well separated.
This study shows that principal component analysis can be employed to separate out trace elements that are useful in fingerprinting the geographical origin of por- celain samples from those that are not useful. It seems that for trace elements up to Z = 41, the elements Rb, Sr, Y, Zr, and Nb are essential in indicating the origin
of porcelain samples, and such elements are present in very low concentrations, from about 10 ppm to hundreds of ppm for the samples used in this study, as shown below:
These figures should be compared 13 with those for por- celain pieces made during the Qing dynasty in Jingde- zhen:
200 ppm _< Rb -< 450 ppm 6 0 p p m - < S r _< 140ppm 10ppm_<Y _< 23ppm 3 5 p p m - < Z r _< 55ppm l l p p m _ < N b _ < 20ppm.
846 Volume 46, Number 5, 1992
ACKNOWLEDGMENTS
I would like to thank Professor Sun-yiu Fung and his department for the warm hospitality at the University of California, Riverside. I would also like to thank several colleagues there, particularly Professor Benjamin Shen, for their assistance in one way or another.
1. C. T. Yap, Archaeometry 28, 197 (1986). 2. C. T. Yap, Appl. Spectrosc. 40, 839 (1986). 3. C. T. Yap, X-Ray Spectrosc. 16, 55 (1987). 4. C. T. Yap, P. P. Saligan, and V. Leenanupan, Appl. Spectrosc. 41,
906 (1987). 5. C. T. Yap and S. M. Tang, "On Mn/Co Ratio of Recent Chinese
Blue-and-White Porcelains," in Proceedings of the Second Inter- national Symposium on Radiation Physics (Universiti Sains Ma- laysia, Penang, Malaysia, 1983), pp. 797-801.
6. C. T. Yap and S. M. Tang, Archaeometry 25, 78 (1984). 7. C. T. Yap and S. M. Tang, Appl. Spectrosc. 38, 527 (1984). 8. C. T. Yap and S. M. Tang, Archaeometry 27, 61 {1985). 9. C. T. Yap and S. M. Tang, X-Ray Spectrom. 14, 157 (1985).
10. C. T. Yap and S. M. Tang, Appl. Spectrosc. 39, 1040 (1985). 11. C. T. Yap, X-Ray Spectrom. 16, 229 (1987). 12. C. T. Yap, Appl. Spectrosc. 41, 1446 (1987). 13. C. T. Yap, Zeitschrift fur Naturforschung 42A, 1253 (1987). 14. C. T. Yap, J. Archaeolog. Sci. 16, 173 (1988). 15. C. T. Yap, X-Ray Spectrom. 18, 31 (1989). 16.
17.
C. T. Yap and P. P. Saligan, Nuclear Instrum. Methods A251, 140 (1986). W. W. Cooley and P. R. Lohnes, Data Analysis (John Wiley, New York, 1971).
