Soil samples were collected from three different crop production sites in west Texas. Sampling was restricted to the depths of 0–15 cm (surface) and 15–30 cm (subsurface) on representative soils from three important agricultural soil series in the SHP, namely the Amarillo (A), Pullman (P), and Mansker (M), for a total of six composite soil samples (Table 1). Soils and sites of interest were identified using the Web Soil Survey (WSS) of the Natural Resources Conservation Service (NRCS). Soil samples were collected using a digging spade marked at 0–15 and 15–30 cm depths. At each field, representative soil samples were collected from approximately 12–15 spots within the field and combined to get a composite sample of about 10 kg of each soil depth. The selected depths are the typical ones commonly examined in most soil fertility and nutrient management studies (Havlin et al., 2013).

A subsample of each original (untreated) soil was ground, passed through a 2 mm sieve, and stored in plastic bags at a room temperature of approximately 23 ∘C. Soil samples were analyzed for a suite of chemical and physical properties. Soil pH1:2 and EC1:2 were determined on a 1:2 soil / water ratio using the applicable methods described by Sparks et al. (1996). Soil OM was estimated using the loss on ignition method (at 400 ∘C and 8 h) following the procedure by Nelson and Sommers (1982). Percentages of CaCO3 were determined using the tensimeter method 4E and 4E1 of the United States Department of Agriculture NRCS-Soil Survey Investigation Report (Soil Survey Staff, 2014). Soil particle size was determined using the modified hydrometer method as described by Gee and Bauder (1986). Plant-available micronutrients (Cu, Fe, Mn, and Zn) were determined using diethylene triamine pentaacetic acid (DTPA) extraction following the procedure by Lindsay and Norvell (1978). Soil test P was determined using the Mehlich 3 procedure (Mehlich, 1984). Total elemental analysis was conducted with the DigiPREP digestion system using USEPA Method 3050B. Concentrations of elements in all extracts were measured using inductively coupled plasma optical emission spectroscopy (ICP-OES; iCAP 7400, Thermo Scientific, Waltham, MA).

Each composite soil sample was thoroughly mixed and a representative portion taken to fill a 4 L plastic pot. Sorghum (Sorghum bicolor) was then planted and grown over a period of 35 days in the greenhouse with no nutrients added. This practice was optional and primarily aimed at depleting the original micronutrient level of the soils prior to treatment application. Following this practice, samples were crushed, air dried, thoroughly mixed, ground, and passed through a 2 mm sieve. Two sets of 250 g samples were weighed from each soil. One set was treated with a mixture of chelated (EDTA) micronutrients and the other with a mixture of non-chelated micronutrients, using 80 mL solution of each fertilizer compound's mixture, prepared in order to add 5 mg of each micronutrient (Cu, Mn, Zn, and Fe) to 1 kg of soil. The non-chelated micronutrient compounds used were CuSO4.5H2O, MnSO4.H2O, ZnSO4.H2O, and FeSO4.7H2O, and the chelated compounds were Cu-EDTA, Mn-EDTA, Zn-EDTA, and Fe-EDTA. There were a total of six soil samples and two sets of micronutrient amendments for a total of 12 soil-fertilizer treatments, each replicated twice. Subsamples were taken from each treated sample at 2, 5, 7, 14, 21, 28, 35, 49, 63, 77, and 90 days after treatment and analyzed for plant-available micronutrients using a DTPA extraction technique (Lindsay and Norvell, 1978). After each subsampling event, the remaining soil samples were wetted with water to approximately field capacity. Within the first 7 days, the soils were wetted after each subsampling; however, after the first 7 days, sampling was conducted at 7–14 days intervals, so the soil samples were watered every 7 days. The periodic wetting of the soil was to simulate the wetting and drying cycle obtainable under field conditions and also provide a medium to facilitate chemical reactions in the soil.

The preparation of DTPA extractant and the extraction procedure followed the method described by Lindsay and Norvell (1978), the most commonly used technique for extracting available micronutrient cations such as Fe, Mn, Cu, and Zn (Liang and Karamanos, 1993). Briefly, 10 g of air-dried soil were placed in a 50 mL plastic tube and 20 mL of DTPA extracting solution was added. The tubes were placed on a reciprocal shaker for 2 h at approximately 25 ∘C and 180 oscillations per minute. After shaking, samples were centrifuged for 10 min at 4000 rpm, and the resulting solutions were filtered into 16 mm borosilicate glass tubes using Whatman^® 2 filter paper. Soil extraction was conducted in duplicate. All filtrates were analyzed for Fe, Cu, Zn, and Mn using ICP-OES (iCAP 7400, Thermo Scientific, Waltham, MA) following USEPA Method 200.7 (USEPA-ICP Users Group, 1982). Instrument calibration was performed using standard reference materials and checked using second source standards from a different vendor. Check samples were inserted after every 20–25 samples. The relative percentage difference between duplicates was also examined and 10 % was set as the acceptance standard.

Statistical analyses were performed using statistical analysis software (SAS 9.4; SAS Institute, Cary, NC, USA). Where applicable, differences among means were examined using PROC GLM, and a mean comparison was conducted using Fisher's Least Significance Difference test at α level of 0.05. The data obtained from the kinetic studies were fitted to selected kinetic models (Table 6) to derive the needed parameters using the PROC NLIN procedure. Single linear regression analyses used in examining changes in available Cu with respect to other micronutrients were conducted using the PROC REG procedure.

Selected chemical and physical properties of the studied soils are summarized in Table 1. Average soil pH was 8.05. Soil pH was generally higher in the 15–30 cm depth by 0.08, 0.28, and 0.50 pH units for the Mansker, Amarillo, and Pullman soil series, respectively. The average soil OM content was 1.33  %, falling within a range of 0.93 to 1.57 % among soil depths. These values are typical of the semiarid alkaline soils of the SHP. Average soil EC value was 0.24 dS m-1, falling within a narrow range of 0.22–0.27 dS m-1. The observed soil EC values indicate that these agricultural soils are not salt impacted. Calcium carbonate content varied from 0.13 to 5.59 % among depths and were almost twofold higher in the 15–30 cm depth in the Amarillo and Pullman soils. Average clay contents within the 0–15 and 15–30 cm depths were 26.2 and 32.9 %, respectively, with a difference of 0.24, 6.2, and 14.1 % for Pullman, Amarillo, and Mansker, respectively. Accordingly, the textural classes vary from sandy loam (Amarillo) to clay (Mansker) as presented in Table 1. The soil properties discussed here are typical of those of soils of the semiarid climates (Chesworth, 2008).

The results of the total elemental analysis are presented in Table 2. The concentrations of elements such as Ca, Mg, Na, K, and P in these semiarid soils are typical of those of most agricultural soils (Adriano, 2001; Udeigwe et al., 2009), particularly those not receiving any form of organic amendments. Likewise, the concentrations of heavy metals such as Fe, Cu, Mn, and Zn were within the typical background levels found in most non-polluted agricultural soils (Adriano, 2001; Kabata-Pendias, 2010). No one soil was consistently higher in all the elements measured and there was no consistent trend in the concentration of the elements with depth in each soil series.

The initial background levels of available nutrients are shown in Table 3. Means of the DTPA-extractable Fe, Mn, Cu, and Zn are 5.30, 5.01, 0.81, and 0.38 mg kg-1, respectively. These concentrations indicate an insufficient level of these nutrients and are typical of most semiarid soils (Havlin et al., 2013). Soil test P varied more widely, ranging from 8.93 to 123 mg kg-1, and was generally higher in the top soil, suggesting a possible P input to some of these soils through fertilization.

Percent estimates of fixed Cu determined after the first 14 days (designated as the short term), and 90 days (the long term) are presented in Table 4. The result is presented as the averages for all soils within each depth examined because the examination of individual soils showed no justifiable difference or pattern among the soils that is worth discussing. Comparison was made between the chelated and non-chelated micronutrient treatments. Average values from the three soil series examined revealed that within the non- chelated system, approximately 32 and 39 % of the added Cu was fixed in the 0–15 and 15–30 cm depths, respectively, after the first 14 days. When compared to the chelated system, approximately 13.7 and 14.1 % of the added Cu were fixed in the 0–15 and 15–30 cm depths, respectively. The averages for both depths after the first 14 days were 35.5 and 13.9 % for non-chelated and chelated systems, respectively. These numbers strongly suggest that chelating with EDTA reduced the fixation of Cu by soil constituents (Chiu et al., 2005), rendering Cu more available in these semiarid alkaline soils.

Copper fixation after 90 days (long-term fixation) was also examined. Approximately 48 and 56 % of available Cu was fixed after 90 days in the non-chelated system within the 0–15 and 15–30 cm depths, respectively. These numbers compared to the chelated system were 43.2 and 47.2 % for the 0–15 and 15–30 cm depths, respectively. Average fixations for both depths (all soils) after 90 days were 52.1 % for the non-chelated system and 45.2 % for the chelated system. The findings indicated a narrower difference of approximately 7 % between the non-chelated and chelated systems in the long term (90 days) compared to the 22 % observed in the short term (14 days). This could possibly be attributed to the fact that the strength of the chelate decreases with time; thus, more Cu is fixed by other soil constituents over time. The findings here are partly supported by the study of Meers et al. (2005), who estimated a half life of 39 to 59 days for EDTA in doses of 0.8 to 1.6 mmol experimented in a heavy metal phytoextraction study, suggesting that the effectiveness of EDTA on micronutrient mobilization in soil systems will decrease over time. The slightly higher fixation of Cu in the subsurface soil could be partly attributed to its higher clay content. Strong soil-clay–heavy-metal interactions have previously been documented in soils of this region (Udeigwe et al., 2015) and such interactions could reduce the amount of plant-extractable Cu.

The changes in the concentration of available Cu over the experimental period of 90 days were compared to those of other micronutrients in the mixture. Relationships within individual soils were examined, but this did not show findings worth focusing the discussion on; thus the findings summarized are averages for the soils at each depth and for both depths combined (Table 5). Regression analyses were used to evaluate the strengths of the relationships and to further examine the gradient of the change between Cu and each of the other micronutrient elements. In each depth, the amount of available Cu positively and significantly changes with each of the other micronutrients, although to varying degrees.

Overall, the strengths of the relationships were higher in the non-chelated systems (R2: 0.68–0.94) compared to the chelated (R2: 0.42–0.81). For each of the relationships examined, the slope was generally higher in the non-chelated systems, suggesting that more Cu will be fixed for each unit of the other micronutrients fixed in the non-chelated system. The findings indicate that in each depth, the change in available Cu with respect to change in Zn (Cu–Zn) was higher than those of Cu–Fe, and Cu–Mn in both the non-chelated and chelated systems, as evidenced from the slope of the equations. When both depths were combined for each element, within the non-chelated system, the slopes were 0.40 (Cu–Fe), 0.31 (Cu–Mn), and 1.04 (Cu–Zn), and 0.26 (Cu–Fe), 0.22 (Cu–Mn), and 0.90 (Cu–Zn) for the chelated system. Within the non-chelated system, the findings suggest that a 1 mg kg-1 change in the concentration of available Fe, Mn, and Zn, is associated with a 0.40, 0.31, and 1.04 mg kg-1 change in available Cu, respectively, in these semiarid alkaline soils of the SHP. The information obtained here has not previously been reported for these soils and provides a good approximation of how Cu changes in respect to other micronutrients in both chelated and non-chelated systems in these semiarid alkaline soils.

Copper fixation in the chelated and non-chelated systems were further examined by fitting the data obtained from kinetic experiments to various kinetic models. A number of kinetic models (Table 6) were examined based on the experimental conditions of this study and evidence gathered from previous studies (Dang et al., 1994; Reyhanitabar and Gilkes, 2010; Rajashekhar Rao, 2015). Coefficient of determination (R2) and standard error (SE) were employed as criteria for evaluating the best fit among the models examined (Dang et al., 1994; Reyharitabar and Gilkes, 2010). Fixation kinetics were studied within soils and depths. However, the individual examination of soils did not show justifiable reasons to focus the discussion on the comparison among them as earlier intended. Thus, for further examination, average data points for all three soils were used, an approach that also enhanced the statistical evaluations.

Experimental data from kinetic studies were fitted to zero-, first-, and second-order models, as well as to power function models, and findings are summarized in Table 7. In all the models, qt represents the amount of DTPA-extractable (plant-available) Cu remaining at time t, in days. Close examination reveals a comparable trend between the depths of 0–15 and 15–30 cm and hence there were no findings among depths worth discussing. As a result, discussions will be concentrated on models derived using the average values of all soils and depths. It was evident that fixation of available Cu was poorly described by the zero-, first-, and second-order models (R2: 0.61–0.79, SE: 0.030–0.751) but slightly better by the power function model (R2= 0.91, SE = 0.081). A better fit to the power function model suggests that the fixation of plant-available Cu in this mixed system of non-chelated micronutrients is somewhat nonlinear over the 90 days' experimental period (Fig. 1), an indication of a more complex reaction type. This finding was similar to that obtained when Cu was examined in a single system (data not shown). Within the chelated system, the finding was somewhat different (Fig. 2) as Cu fixation was better described by the second-order model (R2= 0.95, SE = 0.010) compared to the other models (R2: 0.86–0.92). This better fit to the second-order model could imply that the reaction rate depends on the concentration of two reactants (Evangelou, 1998; Sparks, 2003), i.e., Cu and another soil constituents, for e.g., other micronutrients such as Fe, Mn, or Zn. In retrospect, a better fit to the zero-order model implies that the rate of reaction does not depend on the concentration of the reactant (Cu), while a better fit to the first-order model will imply that the rate of reaction is dependent on the concentration of only one reactant (e.g., Cu) (Evangelou, 1998; Sparks, 2003).

Further examination of the data points suggests a possible discontinuity in the slope or pattern of the data distribution before and after day 35, suggesting a likely difference in the mechanisms of Cu fixation before and after the first 35 days. These sets of data points were further separated and examined (Fig. 3 and Table 7). Within the non-chelated system, Cu fixation in the first 35 days was better described by the power function model (R2= 0.96, SE = 0.081) (Fig. 3). When compared to the chelated system, Cu fixation followed the second-order and power function models more closely at about the same degree (R2= 0.87) (Fig. 4). The findings revealed that the reduction in the amount of available Cu occurred at a slower pace in the chelated system compared to the non-chelated system as evidenced from the reaction rate constants of 0.104 and 0.192 mg kg-1 day-1, respectively.

The adherence of the fixation of non-chelated Cu in the examined semiarid soils to the power function model is an indication of a more complex reaction type when compared to the chelated Cu which followed the second-order model. Findings substantiate the need to apply Cu micronutrient in the chelated form on these semiarid soils as significantly less chelated Cu was fixed, particularly within the first 14 days. Findings further suggest the significance of timing, given that about 68 % of the total Cu fixed was in the first 14 days and that the effectiveness of the chelated compound tended to decrease over time, leading to a narrower difference between chelated and non-chelated compounds. The relationships developed from the examination of the change in available Cu with respect to other micronutrients could be used as predictive tools. The reaction rate constants obtained from this study could be used to approximate how much of added Cu micronutrient will be available at a specific point in time in both chelated and non-chelated systems in these semiarid soils. A very important application of the findings from this study will be for the comparison of the fixation pattern of Cu to those of other micronutrients within these semiarid soils. Reaction rate constants could be compared to those obtained for Cu in other soils. The applications developed from this study provide a basis for a more mechanistic approach to evaluating the effectiveness of commercial micronutrient products and comparisons among products by examining their fixation patterns and kinetic parameters. A database of the reaction rate constants derived for different chelated and non-chelated Cu compounds can be compared among themselves and used as a tool for making a more informed decision on Cu management on these semiarid soils.