Determination of Ammonium Nitrate in Dynamite without Separation by Multivariate Analysis Using Xray Diffractometer
Toshiyuki MITSUI and Motoyasu SATOH
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Introduction
Ammonium nitrate in dynamite has ordinarily been determined by ion chromatography, distillation or titration[1]. However, these methods have been troublesome and are liable to cause experimental error. Further, chromatography was generally used as a method to separate each component from the sample and determine it. However, there are cases in which the identification of each component is difficult to confirm if only chromatography is used for the identification because different compounds have the same retention time. Also, an error in the dilution of samples can arise from the determination by ion chromatography. Therefore, we have additionally applied Infrared spectroscopy and mass spectrometry, etc., for identification of compounds in forensic science at the same time.
In this paper, we investigated the application of an Xray diffraction method (XRD) to determine ammonium nitrate in dynamite more simply and accurately without a separation procedure. XRD was very useful for qualitative analysis of inorganic compounds. It was free from disturbance by a splinter of wood and synthetic polymers even if they were mixed in the sample. Thus, separation of ammonium nitrate from the sample with water is unnecessary. Therefore, experimental error is decreased compared with gravimetric measurement by separation of ammonium nitrate. In this method, organonitro compounds were removed from the sample using diethyl ether for safety, and the residue was dried. Next, the sample was directly measured by XRD. As a general rule, the reproducibility of the determination using the integrated intensity (2 ) of a specific peak obtained by XRD diffraction method is about 10 %. However, when the integrated intensity of various peaks (2 ) for one sample was used for the determination, the reproducibility was less than 1.0 %. The determination of ammonium nitrate content was calculated by multivariate analysis[2  4] such as cluster analysis and principal component analysis (PCA).
Reagents and apparatus
The utilized reagents were all obtained from Wako Pure Chemicals Co. A Rigaku RINT 1100 Xray diffractometer equipped with a copper source (= 1.54056 A ) was used for the measurements of the samples. The samples were measured continuously or by an integration method. This was done at 40 kV and 40 mA. The scan speed was 5.00 per min. An NEC PC9801 RX personal computer was used for the calculation of the data. The language used in the program was Basic. The software of Principal component regression analysis (PCR) and Partial least squares regression analysis (PLS) were used Pirouette (GL Sciences Co., Ltd.).
Xray diffraction method
To form the data base, 9 ammonium nitrate and sodium chloride samples were prepared. The blend composition ratio was changed from 0.02 g to 2 g for about 0.25 g of sodium chloride. An artificial unknown sample was prepared in the same way.
Fig.1 Xray diffraction pattern
(Ammonium nitrate : Sodium chloride = 1 : 4)
Pretreatment of a real sample (dynamite) was as follows. Twenty mL of diethyl ether was added to about 1 g of the sample and organonitro compounds were removed. This operation was repeated twice. The residue was dried and about 0.25 g sodium chloride was added for safety and as an internal standard. These compounds were analyzed by an Xray diffraction method. The pattern of ammonium nitrate : sodium chloride = 1 : 4 is shown in Fig. 1.
Preparation of data base
To perform cluster analysis and principal component analysis, the integrated intensities (CPS) of the spectra obtained by Xray diffraction were used. The data to perform the analysis were prepared as follows. First, several peaks with more than 1000 cps of intensities were selected out of the pattern of ammonium nitrate : sodium chloride = 1 : 1, and the same peaks were also selected from 9 known samples. For each of 9 known samples, the intensities of the peaks derived from ammonium nitrate were then divided by the intensities of the peaks derived from sodium chloride. At this time, 18 categories (9 x 2) obtained from 9 peaks (2 = 17.98, 22.48, 28.94, 32.96, 36.14, 37.78, 39.86, 40.16, 51.09 for ammonium nitrate) each divided by 2 normalization factors (2 = 31.72, 56.50 for sodium chloride) were obtained. The obtained matrix (9 x 18) was used in Quantification IV[5]. Quantification IV is a method for selecting a useful category in multivariate analysis. The eigen vectors were obtained as a result of Quantification IV, and the categories whose eigen vectors were in the range of 0.500 to +0.500 were selected in 18 categories. The categories indicating more than +0.500 or less than 0.500 of the eigen vectors were hardly differentiated or changed at random compared with the variation in ammonium nitrate content. They were not used for the multivariate analysis. At this time, 17 categories were selected. One category was not very good for use in the multivariate analysis. In the quantitative analysis of ammonium nitrate, the 17 categories were also selected for 9 known samples and one unknown sample.
Determination of ammonium nitrate in dynamite
At first, the cluster analysis was carried out using the matrix (10 x 17) data (one unknown and 9 known samples) for the qualitative analysis. To equalize the weight, the values of the matrix (10 x 17) were reformed to average deviation values of 50. To use the reformed matrix (10 x 17) data , the cluster analysis was performed for the approximate content of ammonium nitrate in an unknown sample. Next, finer determination [6  8] of its content was investigated using principal component scores ( PCSs ) obtained by the reformed matrix (10 x 17) data and PCA. The PCSs of one unknown and 9 known samples were calculated using the reformed matrix (10 x 17), eigen value, and principal component. The calculation is carried out as follows. The first PCSs (PCSs(1)) value of each sample is obtained from equation (1).
PCSs(1) =((Uij  50.000) x F1j ) / D1 . . . . . (1)
where PCSs(1), Uij, F1j and D1 are the first principal component score for the each sample, the reformed deviation value for sample number i, the first principal component and the first eigen value of the first principal component, respectively. If the second eigen value of the second principal component is larger than 1.000, the second PCSs (PCSs(2)) are obtained from equation (2).
PCSs(2) =((Uij  50.000) x F2j ) / D2 . . . . . (2)
where PCSs(2), F2j and D2 are the second principal component score for each sample, the second principal component and the second eigen value of the second principal component, respectively.
In the case of the conventional method (calibration curve method), only one peak for both the standard and unknown samples has been used for the determination of ammonium nitrate content, the other peaks have not been used because they were not very good for use in the determination of ammonium nitrate content. Single linear regression is used to derive a relationship between the concentration and the measurement. Also, the calibration curve is prepared only for the measured values for known samples. The determination is carried out by substituting the measured value for the unknown sample for the calibration curve. In PCA, the measured values for unknown and known samples were calculated for the determination of ammonium nitrate content at the same time. The obtained PCSs corresponding to the measurement values of the calibration curve were used for the determination of the ammoniun nitrate content. Therefore, the PCSs of the 9 known samples were changed according to the unknown sample. The determination of ammonium nitrate content by PCA is carried out from the PCSs for each row for the eigen value of > 1.00. If the PCSs for all rows are used for the determination, the calculation becomes more precise than the above but as a result, the calculating time for the PCA becomes very long and the result of the determined value between the PCS for each row eigen value of > 1.00 and the PCS for all rows is almost the same. So we made the determination using the PCS for each row based on an eigen value of >1.00.
The method of determination is shown below.
Chart 1 Example of ammonium nitrate content in dynamite from principal component analysis
Select 17 categories from Xray diffraction result using Quantification IV
Input data

Sample Categories No.
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 0 0 1 0 0 0 0 0 5 9 32 12 0 3 5 8 0
2 0 1 1 0 0 0 0 0 8 27 62 75 6 4 19 14 0
3 1 1 4 0 0 2 1 0 24 61 191 203 10 18 74 40 9
4 2 3 6 1 1 2 2 0 58 127 232 271 20 25 70 66 9
5 3 7 11 1 1 3 3 0 94 204 335 375 23 34 96 80 10
6 5 12 25 2 2 7 5 1 101 242 496 691 33 33 134 102 21
7 8 22 34 4 4 13 10 1 117 337 519 749 56 65 204 147 19
8 12 27 57 5 8 17 20 3 204 459 966 1263 82 133 296 348 44
9 28 60 110 7 13 27 30 4 288 611 1126 2326 73 130 280 303 39
10 8 18 33 2 3 11 11 1 133 318 563 529 37 54 197 189 21

The data are multiplied by 100. Sample number 10 : real unknown sample
Reformed to average deviation values of 50
Calculate the principal component
Categories Principal component
No. 1 2 3 4 5 6

1 0.957 0.285 0.016 0.032 0.022 0.010
2 0.967 0.246 0.062 0.004 0.029 0.010
3 0.977 0.208 0.015 0.032 0.022 0.010
4 0.987 0.058 0.093 0.112 0.049 0.008
5 0.982 0.153 0.047 0.101 0.012 0.025
6 0.989 0.068 0.081 0.044 0.059 0.055
7 0.991 0.072 0.076 0.053 0.073 0.004
8 0.992 0.075 0.085 0.013 0.029 0.055
9 0.987 0.008 0.019 0.135 0.001 0.073
10 0.985 0.048 0.127 0.100 0.008 0.050
11 0.989 0.102 0.025 0.093 0.005 0.007
12 0.970 0.200 0.039 0.044 0.113 0.006
13 0.949 0.275 0.096 0.077 0.085 0.011
14 0.974 0.171 0.068 0.096 0.008 0.071
15 0.950 0.276 0.112 0.010 0.058 0.066
16 0.955 0.255 0.111 0.014 0.084 0.036
17 0.948 0.270 0.108 0.070 0.056 0.075
Eigen values 16.116 0.600 0.104 0.089 0.048 0.031

 Calculate the principal component score

 PCSi =(Uij  50.000) x F1j ) / D1
 PCSi : first principal component score for sample number i (i = 1,2,....,10)
Uij : average deviation value of sample number i (i = 1,2,.....,10)
F1j : first principal component
D1 : first eigen value of principal component
 Example (sample No. 1)

 PCS1 = (41.665  50.000) x 0.957/16.116 + (41.369  50.000) x 0.967/16.116 + .....
 + (37.849  50.000) x 0.948/16.116 = 10.54
10.54 + 50.00 = 39.46
Principal component score of each sample

Sample No. Principal component score NH_{4}NO_{3}/NH_{4}NO_{3}+NaCl

1 39.46 0.0922
2 39.96 0.1808
3 42.12 0.3082
4 43.50 0.3985
5 45.47 0.4963
6 48.81 0.6128
7 53.45 0.6962
8 63.37 0.7925
9 71.58 0.9047
Real unknown sample 52.27 


Determination of ammonium nitrate content

log 48.81 = 61.28 x a + b
 log 53.45 = 69.62 x a + b
 a = 4.676 x 10 b = 1.403
 log 52.27 = 4.676 x 10 x x + 1.403
 x = 67.37 %
sample weight : 0.8985 g
residue weight (remove organic nitro compound) : 0.7146 g
add NaCl weight : 0.3050 g
y / (3.050 x 10 + y) = 6.737 x 10
y = 6.297 x 10 g (ammonium nitrate weight in sample weight)
(6.297 x 10 / 7.146 x 10 ) x 100 = 88.12 % (in residue)
6.297 x 10 / 8.985 x 10 = 7.008 x 10
70.08 % (in sample )
The PCS1 of the known sample was larger than that of the unknown sample (PCSx) and nearest to it, and another (PCS2) was smaller than that of the unknown sample and nearest to it. The linear relationship was computed from equations (3) and (4).

log PCS1 = M1 x a + b . . . . . (3)
log PCS2 = M2 x a + b . . . . . (4)
where M1 and M2 are the ammonium nitrate contents of the known samples for PCS1 and PCS2, and a and b are the slope and the intercept of the linear. The ammonium nitrate content of an unknown sample was obtained from equation (5).

log PCSx = X x a + b . . . . . (5)
where X is the ammonium nitrate content of the unknown sample. An example of the determination of ammonium nitrate content is shown in Chart 1. These determination (calculation) results are listed in Table 1. The reproducibility obtained with this method was about 0.94% (n = 10) using unknown
Table 1 Analytical results (prepared unknown sample)

Sample Content of NH_{4}NO_{3} ( % )
No. PCA PCR PLS CM TV

1 18.63 17.82 18.15 21.01 18.08
2 40.14 38.11 38.76 40.13 41.46
3 53.90 55.78 55.40 53.64 55.52
4 69.62 69.58 69.60 63.65 69.62
5 74.75 73.97 73.69 76.59 73.77
6 90.13 88.65 88.87 88.66 90.47

PCA:Principal component analysis
PCR:Principal component regression analysis
PLS:Partial least squares regression analysis
CM :Conventional method (calbration curve method)
TV :Theoretical value
sample No. 3. However, in the case of the conventional method using calibration curves prepared by the category indicating the best correlation coefficient in the seventeen categories mentioned above, reproducibility was about 4.9 % (n = 10). The PCA was the best method in PCA, PCR and PLS. The PCA method is thus suggested to be useful in quantitative analysis by the Xray diffraction method. Similarly, ammonium nitrate in four real dynamite samples was determined. The results are shown in Table 2.
Table 2 Analytical results for 4 real dynamite samples

Sample Content of NH_{4}NO_{3} ( % )
No. PCA PCR PLS CM

1 67.00 65.54 66.65 72.55
2 70.08 68.42 69.88 66.18
3 77.48 77.31 77.36 82.00
4 78.14 78.29 78.34 80.07

Conclusions
The procedure described herein (PCA) is a useful technique for the quantitative analysis of ammonium nitrate by an Xray diffraction method. The principal component score was used to determine the ammonium nitrate content. The calculated values are in fair agreement with the theoretical values.
References
(1) Japanese Industrial Standard, "Analytical Method of Explosives", K4809, 1968, pp. 15  16.
(2) C. Chatfied, A. J. Collins, "Introduction to Multivariate Analysis", Chapman & Hall Ltd., London, 1980.
(3) G. H. Dunteman, "Introduction to Multivariate Analysis", SAGE Publication, London, 1984.
(4) M. A. Sharaf, D. L. Illman, B. R. Kowalski, "Chemometrics", John Wiley & Sons, London, 1986.
(5) Y. Tanaka, N. Wakimoto, "Methods of Multivariate Statistical Analysis", Gendai Sugakusha, Ltd., Kyoto, 1985.
(6) T. Mitsui, S. Okuyama, Y. Fujimura, Nippon Kagaku Kaishi, 7, 979 (1991).
(7) T. Mitsui, S. Okuyama, Y. Fujimura, Anal.Sci., 7, 941 (1991).
(8) S. Okuyama, T. Mitsui, Y. Fujimura, Advances in Xray Chemical Analysis Japan, 24, 161 (1993).
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