# A Matrix Effect Correction Method for Portable X-ray Fluorescence Data
## 3 Results and Discussion
### Evaluation of the Correction Results  
#### 3.3.1 Different Correction Effects  
The regression results show that the matrix effect correction (MEC) and SLR methods had different correction effects on V, Cr, Co, Mo, Cd, Sn, Ta and W. It can be seen that their regression values calculated by the SLR method were quite different from their reference values, while the results of the MEC method were much closer (Figure 2), indicating that the MEC method was better than the SLR method. The statistical parameters of \(R^{2}\), \(P_{\text{RE}}\), \(MAE\), \(MAPE\), \(RMSE\) and \(RMSPE\) were calculated for the detected elements to evaluate the correction effect of these two methods. Not surprisingly, the MEC method had large \(R^{2}\) values, \(P_{\text{RE}}\) values close to one and small \(MAE\), \(MAPE\), \(RMSE\) and \(RMSPE\) values (Figures 3-5), while the results for the SLR method were the opposite. \begin{table}
\begin{tabular}{c c c} \hline
**Element** & **Multiple Linear Regression Equations** & **Simple Linear Regression Equations** \\ \hline Mg & \(y=1.312x-0.019106\text{Fe}-0.035\) & \(y=1.299x-0.610\) \\ Al & - & \(y=0.846x-0.037\) \\ Si & - & \(y=1.052x-0.058\) \\ P & \(y=0.882x+0.011691\text{Ti}-0.002\) & \(y=0.911x+0.019\) \\ S & \(y=1.136x+0.088753\text{Si}-1.965\) & \(y=1.075x-0.893\) \\ K & - & \(y=0.888x+0.005\) \\ Ca & - & \(y=0.879x+0.150\) \\ Ti & - & \(y=0.828x-0.003\) \\ V & \(y=0.066x+17.255\text{Fe}+43.219\) & \(y=1.107x-47.244\) \\ Cr & \(y=0.827x+27.540\text{Ti}-11.885\) & \(y=0.878x+4.045\) \\ Mn & - & \(y=0.853x-0.004\) \\ Fe & - & \(y=0.935x+1.353\) \\ Co & \(y=-0.172x+5.366\text{Fe}+5.390\) & \(y=0.028x+17.870\) \\ Ni & \(y=0.914x+3.297\text{Fe}-0.558\) & \(y=0.956x-1.632\) \\ Cu & \(y=0.928x-10.245\text{Al}+147.296\) & \(y=0.928x+54.855\) \\ Zn & \(y=1.171x-0.000\text{Mn}-888.827\) & \(y=1.168x-810.710\) \\ As & \(y=1.018x-25.559\text{Al}+422.940\) & \(y=1.021x+46.514\) \\ Se & \(y=1.692x-0.406\text{Al}-13.035\) & \(y=2.483x-37.067\) \\ Rb & \(y=0.841x+1.068\text{Al}-2.205\) & \(y=0.866x+2.394\) \\ Sr & \(y=0.787x+0.690\text{Ca}_{\pm}0.001\) & \(y=0.790x+3.256\) \\ Y & \(y=0.719x-0.357\text{Ti}+1.495\) & \(y=0.710x+4.660\) \\ Zr & \(y=0.814x+0.0007\text{Ti}+14.385\) & \(y=0.844x+15.891\) \\ Nb & \(y=0.604x+10.429\text{Ti}-0.092\) & \(y=0.776x-8.625\) \\ Mo & \(y=0.340x-0.172\text{Al}-1.664\) & \(y=0.333x-10.07\) \\ Cd & \(y=1.879x+331.155\text{Mn}-13.213\) & \(y=1.737x-113.910\) \\ Sn & \(y=0.635x+4.047\text{Al}-6.683\) & \(y=0.494x-1.312\) \\ Sb & \(y=1.110x-5.948\text{Al}-106.578\) & \(y=1.088x-59.504\) \\ Ba & \(y=0.069x+596.818\text{K}-566.860\) & \(y=0.076x+270.120\) \\ Ta & \(y=0.033x+1.880\text{Ti}+4.516\) & \(y=0.038x-0.070\) \\ W & \(y=0.286x+4.80\text{Al}-9.415\) & \(y=0.360x+3.3911\) \\ Tl & \(y=1.199x+23.460\text{Al}-59.340\) & \(y=0.011x+0.554\) \\ Pb & \(y=1.314x-9284.000\text{Si}+3365.584\) & \(y=1.381x-540.560\) \\ Bi & \(y=4.199x+0.428\text{Al}-5.591\) & \(y=2.358x-13.724\) \\ U & \(y=0.7463x-0.006\text{Al}-0.641\) & \(y=0.739x-7.474\) \\ \hline \end{tabular} Note: \(x\) and \(y\) represent the testing and regression values of the element to be tested, respectively. The unit is the same as in Figure 1.  
\end{table} 
Table 3: Correction equations for elements detected by pXRF analysis. Figure 3: The \(R^{2}\) and \(P_{RE}\) values for the correction results of the new and SLR methods. Figure 2: Scatter plots of the new method and the simple linear regression method. The unit is the same as in Figure 1.  
Compared with the other detected elements, these elements were more closely related to the major elements, including Fe, Mn, Ti and Al, mainly due to their adjacent positions in the periodic table and similar chemical properties. As a result, the determination of these elements may inevitably have been affected by major components during pXRF analysis. In fact, the influence of the matrix effect mainly comes from the absorption or enhancement of the characteristic X-ray fluorescence intensity of the element to be tested by adjacent elements, especially major elements.