Optimization method for quantitative calculation of clay minerals in soil Libo Hao, Qiaoqiao Wei, Yuyan Zhao∗, Jilong Lu and Xinyun Zhao Department of Geochemistry, Jilin University, Changchun 130026, China. ∗Corresponding author. e-mail: [email protected] Determination of types and amounts for clay minerals in soil are important in environmental, agricultural, and geological investigations. Many reliable methods have been established to identify clay mineral types. However, no reliable method for quantitative analysis of clay minerals has been established so far. In this study, an attempt was made to propose an optimization method for the quantitative determination of clay minerals in soil based on bulk chemical composition data. The fundamental principles and processes of the calculation are elucidated. Some samples were used for reliability verification of the method and the results prove the simplicity and efficacy of the approach. 1. Introduction clay minerals. This method is based on the relation between diffracted intensity and concentration of Clay minerals are major components of soil, their clay mineral. The contents of clay minerals are types and amounts are influenced by several fac- calculated by comparison with intensities yielded tors, such as climate, topography, vegetation, and by standard samples with known components. The bedrock type. Clay minerals are excellent tracers analytical uncertainties can be influenced by many of weathering processes of bedrock, especially some factors, such as the choice of standard sample, the typical clay minerals, such as kaolinite, montmo- sample preparation technique, and the interference rillonite, and illite (Griffi 1968; Fateer 1969;Tang due to other minerals present in the sample. Conse- et al. 2002). Moreover, the types and amounts quently, this method is semi-quantitative (Mitchell of clay minerals are considered as important con- 1993;DingandZhang2002; Zhang and Fan 2003). straints on the physical and chemical properties Furthermore, this method can only determine the of soil. Quantitative knowledge of the clay min- relative amounts of clay minerals in soil samples. erals is an important index in geological survey, As it is more difficult to quantify non-clay minerals agricultural production, and environmental assess- in soil (Singh and Agrawal 2012), it is far less likely ment (Baldock and Skjemstad 2000; Lichner et al. to obtain a high precision result. Some researchers 2006; Brennan et al. 2014). Many reliable meth- have tried to calculate the amount of clay miner- ods have been established to identify clay mineral als based on their molecular formulae (Chen and types (Chung 1974a, b;Liao1995;Wu1994, 1996), Han 1998), or by the method of solving mass bal- such as X-ray powder diffractometry, differential ance equations (Li and Li 1995). However, both the thermal analysis (DTA), and infrared analysis methods are obviously defective. While the former (IR). However, no reliable method for quantita- suffers from random variation of analytical results, tive analysis of clay minerals has been established the latter does not provide a unique solution. In our so far. Since the 1960s, X-ray diffraction analysis research, a linear programming model was adopted has been a useful tool for quantitative analysis of to determine the amount of clay minerals in soils Keywords. Calculation method; clay minerals; soil; mineral composition; chemical composition; optimization method. J. Earth Syst. Sci. 124, No. 3, April 2015, pp. 675–680 c Indian Academy of Sciences 675 676 LiboHaoetal. on the basis of data on soil chemical analysis. This Am1X1+Am2X2+···+AmnXn+Xn+2m−1−Xn+2 m=bm method is simple, has relatively less interferences X ,X ,...,X ,X ,...,X ≥ 0. in the procedure, and higher precision. 1 2 n n+1 n+2m (3) According to the method for solving linear equa- 2. Basic principles tions, the amounts of each mineral in a soil and their residual errors can be obtained. The mineralogical constitution of soil is rather complex. Soil generally consists of primary minerals 3. Calculation procedures (e.g., quartz, feldspar), secondary minerals (e.g., kaolinite, montmorillonite, and illite), carbonate 3.1 Choice of oxides minerals, Fe–Mn-colloids, and minor amount of organic matter. The types and amounts of minerals The contents of MnO, TiO2,andP2O5 in soil sam- in soils from different regions vary greatly. How- ples are quite low, and exert little constraint on the ever, each mineral commonly comprises a group of calculation. Moreover, the analytical precision on oxides, though some of them may show heteromor- these oxides is low, which may affect the accuracy phism. If the soil sample consists of n different min- of the calculation. The LOI (loss on ignition) is con- erals, the chemical composition of the sample can tributed by several phases in samples, such as the be expressed as the following equation: organic matter, carbonate, and H2Oinclaymin- erals (e.g., kaolinite, montmorillonite, and illite). n As the content of organic matter is unknown, it is Aij Xj +Δi =bi (1) hard to estimate the contribution of LOI from each j=1 phase. So these phases will not be considered in the where X is the content of mineral j in soil sample, calculation. During the sample preparation pro- j cess, Fe2+ may turn into Fe3+, which changes the Aij is the content of oxide i in mineral j,Δi is the residual error of oxide i (including analytical actual contents of Fe2O3 andFeO.Therefore,we take the sum of Fe2O3 and FeO as TFe (total iron). errors, etc.), and bi is the content of oxide i (e.g., Consequently, we use SiO2,Al2O3, CaO, Na2O, SiO2,Al2O3,andK2O) in soil sample. K2O, MgO, and TFe as variables for the calculation. The residual error Δi can be either positive or negative, so we make Δi = αi −βi,whereαi, βi ≥ 0 3.2 Estimation of mineral phases (αi is negative residual error, βi is positive resid- ual error). The values for mineral contents in soil The number of mineral phases in soil controls the cannot be negative, which is a constraint. If there number of variables in the equation. The mineral are n minerals in a soil whose composition can be phases can be obtained from data available in the expressed in terms of m oxides, equations can be literature or by qualitative analysis with XRD. written as: ··· − A11X1+A12X2+ +A1nXn + α1 β1 =SiO2 3.3 Chemical composition of minerals (Construction of the matrix A) A21X1 +A22X2+ ···+A2nXn+α2 −β2 =Al2O3 ....... A X +A X +···+A X +α −β =b Chemical compositions of minerals with complex m1 1 m2 2 mn n m m m components such as those of biotite, kaolinite, illite, ≥ X1,X2,...,Xn 0 and montmorillonite can be determined by tak- α1,α2,...,αm ≥ 0 ing the respective averages of several analyses. ≥ (2) Minerals such as calcite, Fe–Mn colloids, and β1,β2,...,βm 0 quartz with simpler components can be assumed Our objective now is to obtain the estimated values to have compositions suggested by their empiri- m of αi and βi for which z = i=1(αi + βi)isthe cal formulas. For feldspar, after decomposing into lowest. Then, we can use the optimization method three end members (An, Ab and Or), the oxide con- with linear programming to solve the problem. tent of each end member are calculated according Taking αi and βi as Xn+2i−1 and Xn+2i, to their molecular formulae. The above param- equation (2) can be written in the normal form of eters and the coefficients for the residual errors linear programming: constitute the matrix A. m Mole percentages of the Or, Ab and An com- min z = (Xn+2i−1 + Xn+2i) ponents of plagioclase were estimated. Using the i=1 phase diagram of Rittmann and Gottini (1973), A X +A X +···+A X +X −X =SiO 11 1 12 2 1n n n+1 n+2 2 these values were recast into a K-feldspar compo- A21X1+A22X2+···+A2nXn+Xn+3−Xn+4=Al2O3 nent and a plagioclase component, having compo- ....... sition corresponding to the values of the Ab and Calculation method for clay minerals in soil 677 An components. Finally, the results were converted For comparison, we determined mineral contents into mass percentages. of the samples with X-ray diffraction quantitative analysis. The results are presented in table 5.The comparison shows that the contents of quartz and feldspar calculated by the optimization method are 3.4 Example lower than those determined by X-ray diffraction The samples used for demonstrating the calcula- analysis, while the contents of clay minerals are tion methodology adopted here were collected from higher than those obtained by X-ray diffraction Daxinganling, located in the frigid alpine region analysis, especially kaolinite and illite. of northeast China. The rocks of this area have To investigate the differences between the two undergone more physical weathering compared to methods above, we calculated back the contents chemical weathering. Chemical compositions of the of the oxides in the soil samples from the mineral samples are listed in table 1. Some researchers have composition given by X-ray diffraction analysis. concluded that primary minerals in soils of this However, the calculated SiO2 contents are much region are mainly quartz, plagioclase, K-feldspar, higher than that obtained by chemical analysis. It and small amount of biotite; secondary minerals demonstrates that the felsic primary mineral con- are mainly montmorillonite, illite, and kaolinite tents determined by X-ray diffraction analysis are (Ma et al. 2003; Hao et al. 2004). It is supported higher than their actual contents, while the clay by XRD qualitative analysis. Based on the param- mineral contents are lower. The sample preparation eters listed in table 2 and equation (3), using the method may be an important factor that affects the function ‘linprog’ in the optimization toolbox of accuracy of X-ray diffraction analysis (Chen et al.