Application of principle component analysis–artificial neural network for simultaneous determination of zirconium and hafnium in real samples

Spectrochimica Acta Part A 64 (2006) 477–482

Application of principle component analysis–artificial neural network for simultaneous determination of zirconium and hafnium in real samples A. Abbaspour ∗ , L. Baramakeh Department of Chemistry, College of Science, Shiraz University, Shiraz 71454, Iran Received 14 March 2005; accepted 21 July 2005

Abstract Determination of zirconium and hafnium were done by applying singular value decomposition and a feed forward Neural Network Algorithm with back propagation of error. The determination of trace amounts of mixtures of Zr(IV) and Hf(IV) in various matrices (river, tap and industrial wastewater) were investigated by PC–ANN using the complexes formed between Alizarin Red S, Zr and Hf. The results showed that measurement is possible in the ranges of 0.03–3.4 and 0.2–7.0 ␮g ml−1 for Zr(IV) and Hf(IV), respectively. The detection limits were 0.02 and 0.08 ␮g ml−1 for Zr(IV) and Hf(IV), respectively. The results also show very good agreement between true and predicted concentration values and have the ability to use in routine analysis. © 2005 Elsevier B.V. All rights reserved. Keywords: Principal component analysis; Neural network; Back propagation of error; Alizarin Red S; Zirconium; Hafnium

1. Introduction Zirconium is produced from two ore minerals. The principal economic source of zirconium is the zirconium silicate mineral, zircon (ZrSiO4 ). The mineral baddeleyite, a natural form of zirconium oxide or zirconia (ZrO2 ), is a distant second to zircon in its economic significance. Zircon is the primary source of all hafnium. Hafnium is found in nature in all zirconium minerals. The major end uses of the mineral zircon are refractories, foundry sands (including investment casting), and ceramic opacification. Zircon is also marketed as a natural gemstone, and its oxide is processed to produce cubic zirconia, a diamond and colored gemstone simulant. Zirconium metal is used in nuclear fuel cladding, chemical piping in corrosive environments, heat exchangers, and various specialty alloys. The principal uses of hafnium are in nuclear control rods, nickel-based superalloys, nozzles for plasma arc metal cutting, and high-temperature ceramics [1]. So they are strategical elements and their determination is ∗

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important. On the other hand, the determination of zirconium and hafnium is difficult due to a great similarity of their behavior. Simultaneous determination of trace amounts of metals in environmental samples is still a challenging analytical problem because of the sensitivity and specificity required in environmental monitoring and regulations. Chemometrics is the chemical discipline that uses mathematical and method to design or select optimal measurement procedures and experiments and to provide maximum chemical information by analyzing chemical data [2]. The simultaneous determination of several analytes in a given sample is now an interesting area in chemometrics [3–7]. ANN is a computing system made up of a number of simple and highly interconnected processing elements, which processes information by its dynamic state response to external inputs [8]. It is composed of many simple processing elements that usually do little more than take a weighted sum of all their inputs. The range of scope of applications of ANN comes from their capability to estimate complex functions that make them compatible for modelling non-linear relationships. The range of chemical applications of ANN is very large and it includes fields as diverse as modelling structure of protein, molecular dynamics, process

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control, interpretation of spectra, calibration, pattern recognition, optimization of the linear signal range and signal processing Meanwhile in OFCS technology, ANN is used in signal processing, data reduction and optimization, interpretation and prediction of spectra and calibration [9–11] In this present work we try to introduce a selective and sensitive method using PCA–ANN to determine zirconium in the presence of its most common interference, Hf. 2. Experimental 2.1. Chemicals and reagents All chemicals were of analytical-reagent grade and were used directly without further purification. Triply distilled water was used to prepare buffer and reagent solutions. Stock solutions of Zr and Hf (1000 ␮g ml−1 ) were prepared from fixed BDH spectrophotometer solutions. Alizarin Red S (Merck) solution (0.05 M) was prepared by dissolving appropriate amount of the powder in distilled water and diluting with water to 100 ml. An acetate buffer (pH 5) was according to the literature prepared [12]. 2.2. Apparatus and software UV–vis absorption spectra were recorded on a spectrophotometer model Citra 5, which equipped with a 1.00 cm path length quartz cells. The spectra of mixtures were recorded between 370 and 700 nm, digitized absorbance was sampled at 1 nm intervals. Measurements of pH were made with a Metrohm 654 pH meter (Metrohm Ltd., CH-9100-Hesau, Switzerland) using a combined glass electrode. The backpropagation neural network algorithm having three layers was used in Matlab (version 5.3, Math Work Inc.) using NNet toolbox. All programs were run on a Pentium (III), personal computer, with windows XP operating system. 2.3. Procedure To a series of 5 ml volumetric flasks, 1.2 ml of Alizarin Red S (0.05 M) was added, 2 ml buffer solution (pH 5). Finally an appropriate amount of each metal ion was added and the solutions were made up to the mark with distilled water. Excess concentration of reagent has been applied to ensure quantitative formation of the complexes in the whole range of determination. Data were processed by ANN which was trained with the back propagation of errors learning algorithm for simultaneous determination of Zr(IV) and Hf(IV) ions.

reagents used for the spectrophotometric determination of zirconium [13,14]. Without any exception all of the spetrophotometric determination of zirconium have two common difficulty, poor selectivity, and poor sensitivity [15]. Recently some good results was reported using solid phase extraction and liquid chromatography, these methods not only are very expensive but also they needs time consuming pretreatments and using hazardous solvents too [16]. In our previous work we developed a sensitive and selective method for determination of zirconium [17]. In this present work we try to introduce a simple, selective and more sensitive method for determination of zirconium in the presence of its most common interference, Hf. Fig. 1 shows the absorption spectra of Zr(IV)–ARS and Hf(IV)–ARS solutions. The reaction between Zr(IV) and Hf(IV) with ARS was sensitive at pH 5, over this condition, and useful for analytical measurements but there is a clear overlapping of spectrums and so it is impossible to determine each of them at other presence. 3.2. Optimization of experimental conditions For finding the optimum condition, the influence of pH values on the spectrum of each complex at a constant concentration of metals from pH 1 to 6 (2.54 and 1.7 ␮g ml−1 of Zr and Hf, respectively) was studied separately. The formed complexes of Hf and Zr was affected similarly with pH (Fig. 2). Since at pH values larger than 6, Alizarin Red S has a high molar absorptivity, the pH value selected as an optimum pH for simultaneous determination of Hf(IV) and Zr(IV) was pH 5 at which the absorbances for both of the complexes were maximum, while the absorbance of ARS was low. Effect of the concentration of the Alizarin Red S was also investigated (Fig. 3). The absorbance values of the solutions containing a constant concentration of Zr (2.0 ␮g ml−1 ) or Hf (3.8 ␮g ml−1 ) at pH 5 were obtained at varied concentration of Alizarin Red S. The results showed that the absorbance reaches to a maximum value almost at 0.012 M Alizarin Red S. This value was chosen as the optimum concentration for Alizarin Red S.

3. Results and discussion 3.1. Absorption spectra Alizarin and Alizarin Red S (ARS; 1,2-dihydroxyanthraquinone-3-sulfonic acid, sodium salt) were among the first

Fig. 1. Absorption spectra of (a) 1.85 ␮g ml−1 of Zr and (b) 4.58 ␮g ml−1 of Hf with 0.012 M Alizarin Red S at pH 5.

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tion of Alizarin Red S has been chosen to ensure quantitative formation of the complexes). Because of this non-linearity, the linear chemometrics methods are unsuitable for simultaneous analysis of mixtures. Thus, in order to reduce effect of analyte–analyte interaction and non-linearity, ANN [18,19] is proposed as a powerful non-linear technique for solving these problems. The data obtained from application of singular value decomposition on conventional spectra were processed by ANN in order to increase determination range of determination and to obtain wider dynamic ranges in simultaneous determination of Zr(IV) and Hf(IV). Fig. 2. Effect of pH on the absorbance’s of the Zr (2.57 ␮g ml−1 ) and Hf (1.7 ␮g ml−1 ) complexes (in 0.012 M of Alizarin Red S, pH 5 at 540 and 527 nm for Zr and Hf, respectively).

3.3. Individual determination (linear range and sensitivity) To find the linear dynamic range of each component calibration graph were obtained. Two standard solution series of Zr(IV) and Hf(IV) ions of various concentrations were prepared; the operation was made according to the experimental procedure. The absorption spectra were recorded over 370–700 against a reagent blank. Linear range for each metal ion was determined by plotting the absorbances at its λmax versus sample concentration. Conventional calibration curves were linear between 0.1–3.6 ␮g ml−1 of Zr(IV) and 0.2–6.4 ␮g ml−1 of Hf(IV) with regression coefficients higher than 0.998 in both Zr(IV) and Hf(IV). 3.4. Simultaneous determination Fig. 1 shows that the spectral overlapping of Zr(IV)–ARS and Hf(IV)–ARS complexes. It can be seen that significance overlapping prevents resolution of the mixtures by conventional method to obtain an accurate measurement of each in the mixed complexes. Moreover, in the binary mixture of these metal ions, linearity for each metal in mixture is very limited in the presence of each other and deviation from Beer–Lambert law is more extensive (an excess concentra-

Fig. 3. Effect of addition of Alizarin Red S solution (0.05 M) on absorbance’s of Zr (2.0 ␮g ml−1 ) and Hf (3.8 ␮g ml−1 ) at pH 5, at 540 and 527 nm for Zr and Hf, respectively.

3.5. Multivariate calibration 3.5.1. Mixture design The first step in simultaneous determination of different species by multivariate methods involves constructing the calibration set for binary mixtures of them. The multivariate calibration requires a careful experimental design of the standard composition of calibration set to provide the best predictions. In order to select the mixtures that provide more information using a few experimental trials, from calibration set, their compositions were randomly designed. Thirty binary mixtures were selected as the calibration set. Training set of Zr(IV) and Hf(IV) ions in calibration set were between 0.03–3.4 ␮g ml−1 of Zr(IV) and 0.2–7.0 ␮g ml−1 of Hf(IV). In order to constructed ANN model a prediction set was prepared involve 23 synthetic test samples. The prediction set was also randomly designed. In order to evaluate the quality of the model, we prepared an independent validation set consisted of 20 binary mixtures of Zr(IV) and Hf(IV) which analyzed with the optimized model. The compositions of the prediction and validation sets are given in Tables 1 and 2. 3.5.2. Data processing and model building The data matrix used as input for the neural network was the spectrum of complexes made by Alizarin Red S and different concentration of Zr and Hf, at 1 nm intervals. Since the large number of nodes in the input layer of the network (i.e. the number of wavelength readings for each solution) increases the CPU time for ANN modelling, the data matrix was factor analyzed before introducing into the network and PC–ANN model was run [21,22]. Consider that the data matrix D has a dimension of n × p where n and p are the number of standard solutions and the number of measured wavelengths for each solution, respectively. The score and loading of this matrix were calculated by the singular value decomposition (SVD) [23]. ANN method, which was trained with the back propagation of errors learning algorithm was run on the calibration data constructed with principle component analysis. A three layer back-propagation networks, an input, a hidden and an output layer, were used. The input nodes transferred the weighted input signals to the nodes in the hidden layer, and the same as the hidden nodes for the output layers. A connection between the nodes of different layers was represented by a weight, wij , and during the training pro-

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Table 1 Composition of prediction set, their results obtained by suggested method for simultaneous determination of analytes Zr (␮g ml−1 )

Hf (␮g ml−1 )

Actual

Found

Actual

Found

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0.230 0.150 0.500 0.350 0.400 0.300 0.700 0.906 0.885 0.872 0.036 1.358 1.538 1.520 1.498 2.500 1.647 2.952 2.919 2.909 3.120 0.300 0.700

0.226 0.165 0.552 0.368 0.403 0.314 0.787 0.937 0.881 0.843 0.032 1.346 1.607 1.386 1.436 2.590 1.579 3.092 2.928 2.915 3.141 0.314 0.709

1.953 4.198 0.000 0.200 3.531 6.985 2.000 3.400 5.000 7.000 1.900 2.060 0.400 1.140 2.630 1.200 0.150 0.000 0.150 1.420 0.080 2.650 6.500

1.925 4.198 −0.010 0.220 3.531 6.970 2.015 3.396 5.000 7.000 1.893 2.064 0.400 1.140 2.621 1.200 0.149 0.008 0.146 1.418 0.079 2.650 6.500

R.S.E. (%)

0.002

0.009

cess, the connection of weight was performed according to delta rule. Assuming that C = f (A) + E

(1)

Table 2 Composition of validation set, their results obtained by suggested method for simultaneous determination of analytes Zr (␮g ml−1 )

Hf (␮g ml−1 )

Actual

Found

Actual

Found

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.115 0.050 0.800 0.400 1.010 0.898 0.879 0.866 1.900 1.000 1.515 1.503 1.969 1.548 3.406 2.263 2.941 0.706 0.355 0.338

0.111 0.072 0.755 0.386 1.069 0.876 0.816 0.887 1.897 1.001 1.409 1.467 2.105 1.598 3.327 2.237 3.032 0.693 0.351 0.296

3.401 6.643 0.005 4.666 5.597 4.119 5.227 7.581 0.766 0.996 1.515 2.255 1.278 0.654 1.356 3.200 2.300 1.400 0.173 2.0389

3.360 6.702 0.004 4.593 5.603 4.106 5.287 7.885 0.734 0.926 1.648 2.275 1.217 0.621 1.325 3.213 2.268 1.433 0.185 2.082

R.S.E. (%)

0.057

0.086

where An×p represents the measurement spectral matrix, in which each row denotes one of the n mixture spectra obtained at p different wavelengths, Cn×m denotes the corresponding concentration matrix with each row expressing the concentration vector for one known mixture sample containing m distinct components in the training set. The task for the BP–ANN technique is to find a non-linear mapping, denoted by f in Eq. (1), which specifies the mathematical relationship between matrices C and A. This procedure is known as supervised training in BP–ANN in which the network is trained to generate correct outputs from inputs. After this mathematical relationship f has been determined, one can easily find the concentration matrix of an unknown sample, Cunknown ,k×m , from the corresponding measurement spectral matrix, Aunknown,k×p , according to the following equation: Cunknown,k×m = f (Aunknown,k×p )

(2)

This procedure, defined by Eq. (2), is known as the prediction step in BP–ANN. The training procedure, defined by Eq. (1), is achieved by supervised learning, which corrects weights after one sample spectrum (a multivariate signal) passes through the network. The correction of weights is based on the error (difference) between the desired target and the actual output. The iteration would be finished when the error of prediction reached a minimum. The digitized absorbance of calibration mixtures were gathered in a 30 × 6 data matrix and absorbances of prediction matrixes were collected in a 23 × 6 data matrix. To further investigate the prediction ability of method neural net worked models for individual component were also made with respect to output layer considered as a single node corresponding to the analyte. In order to evaluate the performance of the models, the neural network model was also tested on an additional validation set which, its samples belonging to neither the calibration nor the prediction. In our system sigmoidal transfer function was applied between the input and output of a node in hidden layer and purelin output layer function was found to be optimum for calculations. The variables of network consist of the number of nodes in the hidden layer and the number of epochs, learning rate were optimized for each element separately. As learning rates were being investigated, momentum values were also varied in the hopes of finding a ratio for the relative combination of the two parameters that would give the most rapid optimization of network. The optimum of learning rate and momentum were evaluated by obtaining those, which yielded a minimum in the relative error of prediction. The proper number of nodes in the hidden layer was determined by training ANN with different number of nodes in hidden layer and computing relative standard error of prediction, a minimum in RSEP occurred when five and nine nodes were used in the hidden layers of Zr(IV) and Hf(IV), respectively. The optimum number of epochs for each metal ion was also obtained; continued training beyond 2500 iterations for both Zr(IV) and Hf(IV) frequently resulted in a slight increase in root mean square of prediction as the num-

A. Abbaspour, L. Baramakeh / Spectrochimica Acta Part A 64 (2006) 477–482 Table 3 Optimized parameters used for construction of ANN models Parameters

the complex relationship between the concentration of ions and corrected absorbance in the wider ranges. The reasonable relative standard errors for each analyte in both sets indicate the accuracy of the proposed method.

Compound

Input nodes Hidden nodes Output nodes Learning rate Momentum Number of iteration

481

Zr

Hf

6 5 1 0.04 0.7 2500

6 9 1 0.01 0.7 2500

3.6. Interference study The influence of various species on the absorbance of a solution mixture containing 3 ␮g ml−1 of Zr(IV) and 2 ␮g ml−1 of Hf(IV) was investigated. An ion was considered as interference when its presence produced a variation in the absorbance of the sample greater than 5%. This increment of absorbance was evaluated at two wavelengths, 540 and 527 (corresponding to the maximum absorption of Zr(IV) and Hf(IV) complexes, respectively), in order to establish the different effects of the interfering ions on each analyte. Among the interfering ions tested: Mn2+ , V4+ , Ca2+ , Ag+ , Hg2 2+ , Zn2+ , Tl3+ , Ba2+ , Mg2+ , Cs+ , SO4 2− , Na+ , Co2+ , K+ , CH3 COO− , NO3 − , IO3− , and Br− did not interfere at concentrations 1000 times higher than those of the analytes and Cu2+ , C2 O4 2− , Tl+ , Ni2+ did not interfere at concentrations 100 times higher than those of the analytes. Fe(III), Al(III) showed interference in determination of Zr(IV) and Hf(IV) at concentrations five times higher than that of analyte. These ions could easily be masked by sodium dithionite and sulfosalicylic acid, respectively.

ber of epochs increased while root mean square of calibration decreased slightly. The optimized parameters for ANN models used are given in Table 3. The detection limits obtained for Zr(IV) and Hf(IV) were 0.02 and 0.08 ␮g ml−1 , respectively. 3.5.3. Statistical parameters The root-mean-square error (RMSE) of prediction is defined as follows [24]:
   r n 2 1/2 ((t − y )/t ) s si si s=1 i=1 RMSE = (3) rn both summations in the above equation run over all r input objects of the test set (the objects in prediction set) and over all n output variables (the number of analytes studied). The RMSE value measures how good output ys values are in comparison with the target values ts . The aim of any training is to reach as smallest RMSE values as possible in the shortest possible time. Also the prediction error of a single component in the mixture was calculated as the relative standard error (R.S.E.) of the prediction concentration [20]: ⎛ ⎞1/2 N ˆ j − Cj )2 (C j=1 ⎠ R.S.E. (%) = 100 × ⎝ N (4) 2 j=1 (Cj )

3.7. Applications of the method for determination of real samples Exactly 0.2 g of soil sample was completely dissolved in a Teflon beaker with 15 ml of a mixed acid (45 ml Hf, 15 ml H2 SO4 and 5 ml HNO3 ). After complete dissolution, the solution was evaporated till dryness. The residue was dissolved in a mixture of 5 ml HNO3 and 25 ml distilled water and heated to boil for few minutes then the solution transferred to a 100 ml flask and made up to the mark with distilled water. One milliliter of this solution transferred to a 5 ml flask and then the above mentioned procedure was followed.

where N is the number of samples, Cj the concentration of ˆ j is the estimated conthe component in the jth mixture and C centration. The low RMSE and R.S.E. were obtained indicate that the networks used, can process spectral data and model Table 4 Application of the method for determination of Zr and Hf in some ore samples Ore name

Pegmatite Granite

Zr (␮g ml−1 )

Hf (␮g ml−1 )

ICP

Present method

Recovery (%)

ICP

Present method

Recovery (%)

2.15 3.5

2.20 3.48

102.3 99.4

0.3 0.15

0.29 0.16

97.0 104

Table 5 Actual composition and calculated concentration of Zr(IV) and Hf(IV) in different matrices Source

River water Industrial waste water Tap water

Zr (␮g ml−1 )

Hf (␮g ml−1 )

Actual

Found

Recovery (%)

Actual

Found

Recovery (%)

2.15 0.500 3.17

2.07 0.53 3.08

96.0 106.0 97.0

6.32 2.40 0.20

6.27 2.40 0.19

99.0 100.0 95.0

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The proposed method was successfully applied to the determination of some mixtures of Zr(IV) and Hf(IV). For this purpose several spiked samples were prepared by adding aliquots (a few microliters) of Zr(IV) and Hf(IV) solution to river, tap and waste water and the effect of matrix were investigated. Results show (Tables 4 and 5) that this method has good results and it is applicable for routine measurements.

4. Conclusion A principle component ANN calibration model was proposed for the simultaneous determination of zirconium and hafnium. Modelling with ANNs is a more robust, simpler, practically applicable method, utilized for predicting the concentration of unknown samples than standard methods using calibration lines. Based on the results obtained in this work, application of ANN method, which was trained with the back propagation of errors learning algorithm can construct a powerful model for simultaneous determination of Zr(IV) and Hf(IV) in an effective and accurate way. A PCA–ANN was used to build an efficient model for predicting concentrations of Zr and Hf in mixed solutions. Non-linear effects resulting from analyte–analyte interaction in this system can be modelled by artificial neural network. There is no need to know the exact form of the analytical function on which the model should be built also it requires no complex pretreatment or chromatographic separations of the samples containing analytes. This technique is simple, fast and affordable.

Acknowledgement We are gratefully acknowledging the support of this work by the Shiraz University Research Council.

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