**3.4.2. Classification of the dissolution models**

The models, which are usually applied for the description of dissolution of apatites, include the following [187]:


The nucleation rate is assumed as a function of mean ion activity. The lateral growth rate of nuclei is assumed proportional to the difference between total concentration of calcium ions in the saturated solution and in a solution, while the rate constant is related to the frequency for calcium ions to make a diffusion jump into a kink and, simultaneously, partly dehydrate. Recent investigation reveals that the rate-determining step was not the diffusion but two-dimensional surface nucleation [187].

**3. Self-inhibition model**: assumes the formation of self-inhibition calcium-rich layer on the surface of apatite during the dissolution. According to this model, apatite is dissolved by

<sup>37</sup> The ranges of Si near zero are generally considered to be within the equilibrium zone for the mineral. The ranges of SI = 0 ± 0.5 and 0 ± (5%) (lg *K*mineral) were used in various studies [200].

ionic detachment of calcium and phosphate ions from the surface to a solution. When an initial portion of apatite has been dissolved, some amount of calcium cations (probably, in connection with anionic counter ions) is returned from the solution and adsorbed back onto the surface of apatite. The latter process results in the formation of a semipermea‐ ble ionic membrane, which is formed from positively charged layer containing strongly adsorbed calcium ions, i.e. calcium-rich layer [187], [201],[209],[210],[211].

**4. Congruent and incongruent dissolution model**: was already described above.

**i.** SI < 0 undersaturation

**iii.** SI > 0 supersaturation

the following [187]:

PO4

3−, and OH<sup>−</sup>

surface with a definite lateral rate.

diffusion but two-dimensional surface nucleation [187].

= 0 ± 0.5 and 0 ± (5%) (lg *K*mineral) were used in various studies [200].

**ii.** SI = 0 saturation, i.e. mineral37

**3.4.2. Classification of the dissolution models**

156 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

or salt is in equilibrium with solution

The models, which are usually applied for the description of dissolution of apatites, include

**1. Diffusion and kinetically controlled models**: the dissolution of apatite was found to be the diffusion (transport) controlled in some cases [201],[202], kinetically (surface) controlled in other ones [203],[204], and even intermediate [205], i.e. both diffusion and kinetically controlled. Both models usually operate with the so-called driving force which means either the concentration gradient within the Nernst diffusion layer (the diffusion controlled model) or the gradient of ionic chemical potentials between the apatite crystal surface and bulk solution (the kinetically controlled model). Moreover, the results obtained on these models are valid only within the experimental conditions studied; no extrapolation can be made beyond the tested ranges. For example, after, let´s say, a slight agitation decrease or temperature increase, an initially kinetically controlled dissolution might be controlled by the diffusion. Thus, high sensitivity to applied experimental

**2. Polynuclear model**: is based on the study of dissolution and kinetics of growth of apatite under constant composition conditions [191],[193],[206],[207],[208]. Polydispersed samples of apatite were put into a stirred undersaturated (for dissolution experiments) or supersaturated (for those on crystal growth) solutions, and the pH of solution and the amount of added chemicals (an acid for the dissolution experiments and a base for those on crystal growth) were permanently recorded as the functions of time. The results obtained were plotted versus either undersaturation or supersaturation values: straight lines were obtained in the specific logarithmic coordinates typical for this model. According to the model, the dissolution nuclei, i.e., the collections of vacant sites for Ca2+,

ions, are formed on the crystal surface of apatite and spread over the

The nucleation rate is assumed as a function of mean ion activity. The lateral growth rate of nuclei is assumed proportional to the difference between total concentration of calcium ions in the saturated solution and in a solution, while the rate constant is related to the frequency for calcium ions to make a diffusion jump into a kink and, simultaneously, partly dehydrate. Recent investigation reveals that the rate-determining step was not the

**3. Self-inhibition model**: assumes the formation of self-inhibition calcium-rich layer on the surface of apatite during the dissolution. According to this model, apatite is dissolved by

<sup>37</sup> The ranges of Si near zero are generally considered to be within the equilibrium zone for the mineral. The ranges of SI

conditions appears to be the main drawback of these models [187].

**5. Chemical model**: This model was developed from the self-evident supposition that it would be highly unlikely if apatite were dissolved by the detachment of "single mole‐ cules" equal to the unit cells and consisting of 18 ions. Moreover, in the crystal lattice, practically all ions are shared with neighboring unit cells and often cannot be attributed to given "single molecule." Based on the experimental results obtained on one hand, and on analysis of the data found in references on the other hand, a sequence of four succes‐ sive chemical reactions was proposed to describe the process of apatite dissolution [112], [187],[212],[213]:

$$\text{Ca}\_3\text{(PO}\_4\text{)}\_3\text{(F,OH)} + \text{H}\_2\text{O} + \text{H}^+ \rightarrow \text{Ca}\_3\text{(PO}\_4\text{)}\_3\text{(H}\_2\text{O}^+) + \text{HF, H}\_2\text{O} \tag{44}$$

$$2\text{ Ca}\_3\text{(PO}\_4\text{)}\_3\text{(H}\_2\text{O}^+) \rightarrow 3\text{ Ca}\_3\text{(PO}\_4\text{)}\_2 + \text{Ca}^{2+} + 2\text{ H}\_2\text{O}\tag{45}$$

$$\text{Ca}\_3\text{(PO}\_4\text{)}\_2 + 2\text{H}^+ \rightarrow \text{Ca}^{2+} + 2\text{ CaHPO}\_4 \tag{46}$$

$$\text{CaHPO}\_4 + \text{H}^+ \rightarrow \text{Ca}^{2+} + \text{H}\_2\text{PO}\_4 \tag{47}$$

**Eqs. 44–47** can be used instead well-known net reactions [187]:

$$\begin{aligned} \text{Ca}\_{\text{s}} \text{(PO}\_{4}\text{)}\_{\text{3}} \text{(F,OH)} + \text{H}\_{2}\text{O} + 7\text{H}^{+} &\rightarrow \text{5 Ca}^{2+} + \text{3 HPO}\_{4} \\ \text{1} + \text{HF, H}\_{2}\text{O} &\end{aligned} \tag{48}$$

$$\mathrm{Ca\_{s}(PO\_{4})\_{3}(F,OH)\to5\ Ca^{2+}+3\ PO\_{4}^{3-}+F, OH^{-}}\tag{49}$$

In principle, the dissolution process could also happen according to reaction 49 followed by chemical interaction in the solution among ions of apatite and acid near the crystal surface [214]:

$$\begin{aligned} \text{5 }\text{Ca}^{2+} + \text{3 }\text{PO}\_4^{3-} + \text{F}^-, \text{OH}^- + \text{7 }\text{H}^+ &\rightarrow \text{5 }\text{Ca}^{2+} + \text{3 }\text{H}\_2\text{PO}\_4^- \\ + \text{4HF, H}\_2\text{O} \end{aligned} \tag{50}$$


#### **3.4.3 Methods for the evaluation of reactivity of phosphate rocks**

Chemical methods are used for the evaluation of reactivity of different phosphate rocks from which the fertilizers are manufactured for their possible direct application as fertilizers via empirical solubility test. Citric acid, formic acid, neutral ammonium citrate,38 and alkaline ammonium citrate are used as solvents for the extraction of P2O5. The latter is used mainly for the evaluation of calcined aluminum phosphates. Most of these reagents were not originally intended to evaluate the reactivity of phosphate rocks. For instance, neutral and alkaline ammonium citrate solutions were originally intended to separate chemical reaction products in superphosphate and other fertilizers from unreacted rock on the assumption that unreact‐ ed rock was insoluble in these reagents. The citric acid extraction was developed to evaluate basic slag, a popular fertilizer material in European countries. The formic acid extraction was developed specifically for phosphate rocks [220].

Nearly all extraction methods use the ratio of sample weight to extraction volume 1 g:100 ml. 39 The extraction time usually ranges from 30 min to 1 hour. The temperature and the agita‐ tion during extraction test may be specified. For example, the AOAC method uses neutral ammonium citrate40 of specified concentration (1 g of sample and 100 ml of solution) with the extraction time of 30 min at 65°C. The Wagner method uses 2% solution of citric acid, the

<sup>38</sup> Neutral ammonium citrate is prepared by dissolving required amount of citric acid and neutralizing it with ammonium hydroxide. The pH of the reagent is adjusted to neutral [221].

<sup>39</sup> The amount of used solution is also expressed in the name of the method, e.g. 100 ml method or 150 ml method [222].

<sup>40</sup> The neutral ammonium citrate test was used as the official method in the United States, and the test by acidic acid was developed for the comparison [222].

extraction time of 30 min and the temperature of 17.5°C [220],[221],[222],[223]. Unavailable phosphoric acid is usually expressed as the portion of fertilizer, which is *insoluble* in neutral ammonium citrate [769]. Phosphate removed during the neutral ammonium test is termed as *citrate-soluble*. The sum of *water-soluble* and *citrate-soluble* phosphate is termed as *available* [224].

Fused magnesium phosphate (FMP) is highly soluble in 2% citric acid41 but is less soluble in neutral citrate, while calcined defluorinated phosphate (CDP) and Thomas slag (Thomas phosphate) are fairly soluble in both citric acid and citrate. Actually, FMP dissolves fairly rapidly in neutral citrate at the beginning, but the dissolution is hindered by gelatinous silica, which forms on the surface of the FMP particles. This layer can be broken by vigorous stirring [222].

One disadvantage of all these methods is that the percentage of leached P2O5 depends on the grade of the rock, especially when the rock contains inert gangue minerals such as silica. In order to eliminate the adventitious effect of grade, the concept of absolute citrate solubility index (ASC) was developed [225],[226]:

$$\text{ASC} = \frac{\text{AOAC criteria solubility } P\_2O\_5 \text{[\%]}}{\text{Theoretical } P\_2O\_5 \text{in capacitor } \begin{bmatrix} \% \end{bmatrix}} \tag{51}$$

The percentage of dissolved P2O5 is expressed as the gangue-free apatite [220]. If rocks contain free calcium of magnesium carbonate, these carbonates should be removed by the extraction with a suitable reagent before carrying out the test in order to obtain correct indication of reactivity [227].

It was also found that the length of the *a*-axis in the apatite unit cell (*a*0) is statistically related to the ASC according to the relationship [225]:

$$\text{ASC} = 421.4 \left( 9.369 - a\_o \right) \tag{52}$$
