Semi-empirical method for analysis of cultivated soils

The main objective of the present work to develop Semi-empirical Method (SEM) which can provide analysis of cultivated soil-samples non-destructively. Gamma-ray transmission measurement of soil-sample provides information about its parameters such as mass attenuation coefficient, mass-density, water content and porosity. These parameters further quantify soils suitability for particular crop and irrigation system to be used for the cultivation of particular crop. Soil-samples have been collected from the cultivated soils of Punjab (India). Chemical-compositions of these samples have been measured with XRDR (x-ray Diffraction followed by Rietveld analysis). Three standard γ-ray point-isotropic sources have been used for experimental measurements of these parameters for the samples in the energy-range (59.54–1332.5 keV). A standardized self-designed computer program has been used for theoretical computations of these parameters. Good agreement between spectrometric-method (experimental) and theoretical-method (TM) have been observed with ±5% fluctuations. It is concluded that by measuring chemical composition of soil, its other parameters can be computed theoretically, thus the present methods is named as SEM. Thus, SEM is a non-destructive soil analysis (NDSA) without any loss of valuable information.


Introduction
The cultivated soils consist of minerals, organic matter, moisture, air and some nutrients. The quality of cultivated-soil varies with its geographical location. Generally soil-samples consist of various oxides in different concentration-range {SiO2 (40%-90%), Al2O3 (5%-20%), Fe 2 O 3 (2%-20%) and TiO 2 +CaO+MgO+K 2 O+Na 2 O(0.1%-5%)} [1,2]. For any soil-sample its mass-density, water-content and porosity are the parameters which decide its quality for the agricultural purpose. Knowledge of above parameters is required for the selection of particular crop and irrigationsystem for the soil. Both X and γ-rays have been used for non destructive analysis and investigation in various fields such as materials science, engineering and research [3]. The γ-rays have been extensively used in the analysis of soils and materials using their chemical composition, effective atomic number, electron density, buildup factor etc [4][5][6][7][8][9]. Gamma-ray transmission method has been used for studying the soils compaction, moisture, degradation of soils and its effect on ecosystem [10][11][12][13][14][15][16]. The said method is based on measurement of γ-ray intensities before and after traversing the sample-medium.
In this work, a semi-empirical method (SEM) is suggested for the estimation of many useful parameters of cultivated soils. SEM computes mass-attenuation coefficient, mass-density, water-content, and porosity of soil-sample from its chemical composition. It will replace the time-consuming traditional methods (TM) used for the measurements of these parameters. SEM has been validated by comparing the experimentally measured values with the computed values by it for the chosen soil-samples. The suggested method (SEM) can analyze properties of soils for agricultural purpose using non destructive soil analysis (NDSA). This work may be useful in designing of portable soil testing devices.

Materials and methods
The samples of cultivated soils have been collected from five districts of Punjab (India). The sample names and their chemical composition have been listed in the figure 1. The objective of this work is to standardize SEM Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
for quick-analysis of cultivated soil-samples. SEM has been validated using experimentally measured values of the parameters for all the chosen samples of cultivated-soils. The lecture delivered by Vaz on automatic gamma-ray equipment for multiple soil physical properties measurements [17] serves as the motivation for present work.

Experimental measurements
The following section explains both methods (TM and SEM) used for the measurement of each parameter.

TM for mass density
Soil's mass density is mass of oven-dried soil per unit volume. The volume of soil includes the volume of the solids and of pore-spaces present in soil-sample [18]. A double-cylinder, hammer-driven core sampler was used to obtain many solid core samples per site, which enabled the direct calculation of its mass density [19]. Each sample core had a radius of 5 cm with a depth of 8 cm. This equates to the known soil volume of 628.3 cm 3 per sample. The soil-samples were oven dried at 105°C for 48 h before determination of its mass. The dry mass density for each core sample was then calculated by dividing the mass of the dried-soil to its volume [19]. Thereby, average density of soil for each site was obtained. An electronic weighing balance with accuracy of ±0.01 g (Contech Instruments Ltd, India) has been used for measuring the mass of a sample. The volume of the plastic cubical container has been measured with digital vernier caliper with accuracy ±0.02 mm (Mitutoyo Corp., Kawasaki, Japan). The uncertainty in mass density measurement has been found to be ±6×10 −5 g cm −3 . The amount of organic matter present in the sample does not affect the results considerably as it consists of only low-Z (C-H-O) compounds.

SEM for mass density
The spectroscopic-method i.e. γ-ray transmission measurement offers non-destructive method to estimate the mass-density of soil-sample. If the samples are oven-dried, mass-density of the sample can be obtained by using the well known Lambert-Beer's law [20]: where I o and I(t) represent the incident and transmitted monoenergetic γ-ray intensities from soil-sample of linear-thickness, t (cm) and μ m represents the mass-attenuation coefficient of the soil.

TM for water-content
Gravimetric soil water content determination method required the transportation of sealed soil-samples from the trial sites to a soil-testing laboratory. The water content of the sample can be computed as the mass of water per unit mass of the dried-soil and is expressed as ratio [21]:  where θ TM is the water content on a dry-weight basis (g g −1 ), M w is the mass of water (g) contained in the sample and M s is the mass of the soil sample used (g) [22].

SEM for water-content
The reduction of γ-ray intensity by soil-samples is caused by solid minerals, water-content and trapped air in soil. The attenuation by the trapped air is insignificant as compared to that of soil particles and moisture [23][24][25][26]. The attenuation equation [27] for the soil-water system has been used to compute the water-content of the sample as follows: where μ m and μ w (cm 2 g −1 ) represents the mass-attenuation coefficients of dry soil and water, respectively, θ (g cm −3 ) represents the water-content of the soil and t represents the thickness of soil-sample (cm).

Porosity
Porosity (f) is the measure of free space present inside soil-sample [28,29].

TM for porosity
Sample's f can be measured from the bulk and particle densities relationships [27][28][29]: and ρ s (g cm −3 ) represent the particle density and bulk density of the soil-sample, respectively.

SEM for porosity
The spectroscopic-method can be used to measure f of soils using the saturation-method [13,17]. If I s represents transmitted γ-ray intensity through dried soil-sample with thickness t s and I w represents transmitted γ-ray intensity through the moist soil-sample of thickness t, then their attenuation-equations can be written as:

Samples preparation 2.2.1. Elemental composition
The chosen soil-samples have been dried in oven (60°C for six hours) then ground to very fine powder (grain size <75×10 −6 m) using a double cup vibrating automatic grinder.

Experimental arrangements
The powdered samples of soils without any treatment have been placed in a plastic cubic container (each side 50 mm) one by one for γ-ray measurements as shown in figure 1. Three point-isotropic sources of γ-rays (Am-241, Cs-137 and Co-60) have been used for the measurement in the selected energy range. The radioactive source has been placed in lead-container as shown in figure 1. The NaI(Tl) detector (Canberra, model: 802) placed at a distance of 680 mm away from the source. Three lead collimators of 3 mm opening have been used for the narrow beam condition. The narrow beam condition has been verified by using scatter acceptance angle (θ SC ) such that θ SC <3° [29]. The measurement of θ SC has been explained in figure 2. The calibration of NaI detector has been obtained by plotting a calibration-curve for four monoenergic γ-rays with the help of a multi channel analyser (2k) and MAESTRO software (ORTEC, USA).

Chemical composition
The composition of soil-samples have been measured using x-ray diffraction (XRD)-diffractometer (PANalytical, model XPERT-PRO) followed by Rietveld analysis [32][33][34]. Figure 3 indicates the XRD-peaks and graphically provided the measured chemical compositions of the soil-samples.

Required parameters
For each soil-sample, the mass-attenuation coefficients have been measured using relative γ-ray intensities at four energies viz. 59.54, 661.66, 1173.24 and 1332.50 keV. On the other side these parameters have been computed using the measured chemical-compositions of samples with the help of a computer program, GRIC2toolkit [7]. For the dried soil-samples, measured values of the mass-attenuation coefficients have been plotted along with their theoretically computed values in figure 4. Figure 4 indicates the agreement between measured and computed values of mass attenuation coefficients for the soils. Whereas, the SD in for TM and SEM values of water-content has been found to vary between 0.001-0.053. Similarly, SD for porosity (%) has been found to vary from 0.259 to 8.306. This much deviation seems to be due to the presence of scattered photons in the transmission geometry and systematic propagation of errors in the computations of the parameters. For the chosen samples, the measured value (TM) of mass density has been found the minimum (1.221 g cm −1 ) for JS, whereas the maximum density (1.879 g cm −1 ) for FS. The measured value (TM) of water-content has been observed to vary from 0.255 g cm −1 for FS to 0.429 g cm −1 for JS. The TM value for porosity (%) has been found 28.730 for AS (minimum) and 66.815 for JS (maximum). The variation in the interaction probabilities of γ-ray photons such as photoelectric absorption, Compton scattering and pair production with energy, also cause uncertainties in the measured values of these parameters.

Conclusions
It has been concluded that the proposed SEM can be used for analysis of cultivated soils using the three parameters viz. mass-density, water-content and porosity. These parameters help to decide the crop-suitability for the selected land and selection proper irrigation system for better production. All these parameters are implicit-function of the mass-attenuation coefficient (μ m ) thus these parameters can be computed with GRIC2toolkit (theoretically). It is concluded that for NDSA of field samples the suggested SEM provides the results with good accuracy. Thus in future the SEM (GRIC2-toolkit) can serve as non destructive tool for multiple soil physical properties measurements.