Estimated free energies of formation of the A-carbonate apatites.
The principal material in the phosphate ores is composed of calcium fluorapatite Ca10(PO4)6F2, in which the various components have been partially substituted by magnesium, sodium, carbonate, and hydroxyl ions. These substitutions affect the stability of the material and its reactivity toward the acid attack. The present chapter reports the influence of carbonates and magnesium on these properties. Using different calorimeters, dissolution experiments of carbonated and noncarbonated Ca and Ca/Mg apatites were carried out in acid solutions leading to thermochemical quantities. The results show that substitution of carbonate for F ions in the channel (to get A-type carbonate F-apatites) results in increasing the stability of the edifice, while substitution of CO3 for PO4 in fluor- or hydroxyapatites (to get B-type apatites) leads to a decrease in stability. The latter phenomenon was also observed when substituting magnesium for calcium in F-apatites. The presence of the former in the apatite structure results in an increase of the speed of dissolution in acid solution that is enhanced when carbonate is also replacing phosphate groups. Dissolution mechanism of synthesized Ca/Mg F-apatites seems to be a one-step process, while dissolution of a Gafsa (TN) natural phosphate to get superphosphate fertilizer is more complex.
- carbonate apatites
- enthalpy of formation
- Gibbs free energy
- acid attack
- phosphate ore
- kinetic models
The “wet” manufacturing process of phosphoric acid is based on the attack of natural phosphates by nitric, hydrochloric, or sulfuric acid or the mixture of the latter with diluted phosphoric acid solution. Super phosphate fertilizers are produced industrially through the reaction of phosphoric acid with natural phosphates.
According to Pierre Becker , “the most important (mineral) for the phosphoric acid industry is the apatite group: (Ca,Na2,Mg)10(PO4)6-
It would be interesting to apprehend the contribution of each component in the stability and reactivity of the natural products. However, as it is impossible to reproduce the formation conditions of the latter, one can proceed by a progressive approach which consists in determining these properties for synthetic limit products then for their “derivative” which can be obtained by introduction of various elements or entities in the former. Thermodynamics allows to quantify the stability of the compounds through the determination of their Gibbs free energy of formation and gives a comparison between compounds having molar weights in the same order of magnitude. Kinetic studies of the acid attack allow to characterize the reactivity of the compounds in terms of rapidity, to propose an attack mechanism and highlight the influence of some parameters on the reaction rate.
Because of the predominance in the ore of the components cited above, Ca-fluorapatite (Ca-FAP), Ca10(PO4)6F2, has been considered as the more representative compound of natural phosphates and has been widely studied under various aspects. This is also because of the similarity of their crystal structures. Ca-hydroxyapatite (Ca-HAP), Ca10(PO4)6(OH)2, comes in the second position and constitutes the model compound in studying the properties of the mineral component of calcified tissues (enamel, dentine, and bones).
Ca-FAP seems to be crystallographically characterized for the first time by Leonhardt in 1923 (cited in ref. ). The structure has been confirmed in 1930 [2, 3]. Since then a wide varieties of works have been performed , but the first chapter related to thermochemistry of this compound has been published by Gottschall in 1958  who dissolved Ca-FAP in nitric acid and determined its formation enthalpy. At the end of the 1990s, a lot of thermochemistry works started on Ca-FAP and analogous compounds containing Ba, Sr, Mg, Cd, and Pb, in order to determine their dissolution energies and to deduce their formation enthalpies. In absence of formation entropies, these results allowed to compare the stability of the compounds based on the formation enthalpies and not on the Gibbs free energies, as required. Then the entropy factor has been estimated by a calculation procedure combining literature data . This allowed to propose a more realistic scale of stability of these compounds. The same calculation procedure has been applied for hydroxy and chlor-apatites containing the metal reported above. All these results are gathered in reference . Substitutions of calcium by alkali earth metals, Cd or Pb have also been considered thermochemically and have been widely published in literature. In the phosphate ore, these substitutions are minor in comparison to carbonate substitutions. This chapter deals with the stability and reactivity of some carbonate apatites and reports thermodynamic and kinetic studies of the attack of a sample ore from Gafsa (Tunisia) by phosphoric solution having different composition.
2. Carbonate substitutions in the apatites
The model compound, Ca-FAP, crystallizes in the hexagonal system with space group
Carbonate can substitute for F (or OH) along the channel or for PO4 groups, leading to “A” or “B” type carbonate apatites, respectively. A-type carbonate apatites are synthesized by solid gas/reaction at high temperature while the B-type ones are precipitated in aqueous solution. AB-type carbonate apatites have either been prepared by solid/gas reaction performed on rich carbonate B-type ones , or by precipitation in conditions similar to that used for the synthesis of Ca-deficient hydroxyapatites . Each type of compounds are characterized crystallographically by specific displacements of some rays on the X-ray profiles and spectroscopically by the appearance of special bands on the IR recordings. They also differ in some properties among them, the thermodynamic ones, as seen below.
Fluoride (or hydroxyl) replacement mechanism leading to A-type carbonate apatites is commonly supposed to be accompanied by the appearance of an anion vacancy along the channel. This seems to be accepted without any ambiguity while in the B-type ones, substitution of PO4 by CO3 has been subjected to a large number of suggestions resulting from various methods of treatment of the analytical results.
In 1993, De Mayer and Verbeeck  gathered the various substitution mechanisms that can be considered in B-type carbonate hydroxyapatites containing sodium. These mechanisms are as follows:
where VCa and VOH stand for vacancies of Ca2+ and OH−
Replacement mechanisms I– IV are accompanied by creation of a vacancy in the Ca or OH site, while in mechanism V, PO4 is replaced by the tandem (CO3OH). The latter mechanism has been suggested considering the analogy with the fluoride analogous apatites in which the chemical analysis reveals the presence of more fluoride than in free carbonate fluorapatite.
In Na free B-type hydroxyapatites, only mechanisms I, II, and V have to be considered. So “
For the fluoride homologous compounds the formula becomes as:
This formula is equivalent to that proposed in 1963 by Kühl and Nebergall who “appear to have been the first to propose the formula: Ca10-
3. Thermochemistry of some A-type carbonate apatites
Thermochemistry dissolution of A- and B-type carbonate apatites has been undertaken in the beginning considering experiments performed with low values of the solid/liquid ratio. This led to a simple dissolution without the appearance of any precipitate. As reported, the latter appears with higher values of this ratio.
3.1. Enthalpies of dissolution in nitric acid solution
Calcium, strontium, and barium A-type carbonate hydroxyapatites have been prepared by solid/gas carbonatation of the corresponding hydroxyapatites, according to the general reaction scheme:
where M stands for calcium, strontium, or barium.
The starting solids were heated in pure CO2 flowing gas at temperature between 700 and 1000°C during half an hour to 6 days. By varying the temperature and time they were progressively carbonated until full substitution of hydroxyl ions leading to pure A-carbonate apatites. The synthesized products were characterized by X-ray and IR analyses. All of them showed the IR bands characterizing such kinds of apatites and exhibit a nonmonotonous slight variation of “
The solids were then dissolved in a 3 or 9 wt% nitric acid solution using a home-made isoperibol calorimeter. The device was previously described in detail . Carbon dioxide gas was continuously bubbled in the liquid phase to avoid its retention after dissolution of carbonated products. The heat effect produced in the calorimetric cell was manifested by the variation of the temperature of the reaction medium which was detected by a thermistance probe acting as one of the four arms of a Wheatstone bridge. The balance voltage was amplified by a Keithley multimeter and then recorded over time. The solid to be dissolved or the liquid to be diluted was carefully introduced in a thin-walled glass bulb that was manufactured at one of the extremities of a Pyrex tube (5 mm diameter). Experiment started by searching a quasi-steady state in which the electrical current was practically null and the baseline deviated slightly from the vertical line. The reaction was started by breaking the bulb using a thin glass baton and the heat effect dissipated in the medium results in a deviation of the signal, which then became parallel to the previous baseline. The shift between the baselines is proportional to the corresponding heat effect. More details on the calibration and heat effect determination are exposed in Ref. . Experimental results processing and errors calculation are developed in Ref. .
Depending on the cation, the enthalpy of solution decreases (Sr in 9 wt% HNO3), increases (Ba in 3% HNO3), or shows a bell-shaped curve (Ca in 9 wt% HNO3).
3.2. Formation enthalpies of A-type carbonate apatites
The solution enthalpy of a particular compound can be involved in a hypothetical reaction containing other compounds for which the enthalpies of formation are previously tabulated. The difference between the enthalpies of solution of the compounds in both sides of that reaction leads to the formation enthalpy of the product in concern. Example, M10(PO4)6(CO3)
The dissolution reactions or their reverse are schematized as follows. Their “sum” leads to the final reaction.
In addition to the dissolution reaction of the apatite (Step 1), this scheme includes the dissolution of
3.3. Enthalpy of mixing in the solid state
The molar enthalpy of mixing can be determined from the solution enthalpies of the reactants and product as follows:
This quantity can also be deduced from Figure 5 by considering the difference between the enthalpy of formation of the solid solution for a given composition and that deduced from the straight line joining the points corresponding to the limit products. The later quantity equals the enthalpy of formation of the heterogeneous mixture of the limit products. Figure 6 shows the results for calcium and barium compounds. For strontium, Figure 5 shows a linear variation over “
3.4. Estimation of the Gibbs free energy of the A-carbonate apatites
The stability of compounds having similar chemical formulae can be estimated considering in a first approximation numerical values of their formation enthalpies. The lower the value, the more stable is the corresponding compound. This way of doing supposes the formation entropy as zero. This quantity is negative and this assumption supposes zero as the upper limit of ∆r
Carbonate apatite having the general formula M10(PO4)6(OH)(2-2
The standard entropy of this reaction at T° (298K), ∆r
Because of the increase in disorder accompanying this reaction, its entropy should be negative and so
The absolute entropy of the CO3-apatite can be derived from the entropy of its formation, ∆r
Taking into account the inequality above, one can derive the following relationship:
The second term of this inequality is negative and constitutes the upper limit value of the formation entropy, instead of zero. If one supposes ∆r
And so the standard formation entropy of the apatite is linear over the carbonate content (
|X in Ca ap.||∆f||∆f||∆f|
This figure confirms the less stability of Sr compouds and the particular behavior of the Ca ones.
4. Thermodynamics of some B-type carbonate Ca-fluorapatites
4.1. Formation enthalpy
Beside the procedure developed previously for determining the formation enthalpy of an apatite, this quantity can also be obtained from dissolving the apatite then other compounds whose dissolutions lead to the same entities in solution as that obtained with the apatite. However, dissolution of the later introduces new entities in the thermochemical cycle. These entities are compensated by considering supplementary reactions involving dissolution or formation of well-known products. A typical case is illustrated by the cycle leading to the formation enthalpy of the apatite of formula: Ca10-
With 0 ≤
This cycle gathers a succession of 13 steps whose “summation” leads to step 14 which represents the formation reaction of the apatite. Steps 1, 2, 4, 6, 8, 10, and 12 are dissolution reactions (or their reverse) of the carbonate apatite and well-known products. Their enthalpies were determined by performing experiments at 298 K in the same solvent (aqueous solution having 26.22 wt% H3PO4) using a SETARAM microcalorimeter. Steps 3, 5, 7, 9, 11, and 13 are formation reactions or their reverse. The corresponding enthalpies were picked from the literature.
4.2. Formation of Gibbs free energy
Calculation of the formation entropy has been undertaken according to the procedure developed above considering the negative entropy value of the following reaction between CaO, Ca3(PO4)2, and CaF2 as:
with 0 ≤
This led to derive the formation entropy of the carbonate apatite as a function of
|Chemical formula||Δf||Δf||Δf||S°/J mol−1 K−1|
5. Thermochemistry of B-type carbonate Ca/Mg fluorapatites
In natural phosphates, calcium is weekly substituted by other cations, among them magnesium is the most important. Even existing in a few amounts, this element influences the thermochemical properties of the apatite and its reactivity toward the acid attack.
In contrast with other elements such as strontium, barium, lead, or cadmium, substitution of calcium by magnesium in fluor and hydroxyl-apatites does not exceed one atom per unit cell , while substitution by the other elements can lead to continuous solid solutions.
A series of B-type carbonate Ca/Mg fluorapatites containing various amounts of carbonate and 0.90 ± 0.01 Mg atom per unit cell have been prepared, characterized, and chemically analyzed. They were then dissolved in a 3 wt% HCl solution [or HCL, 53.53 H2O] using the isoperibol calorimeter. During dissolution, the solution was saturated by a continuous bubbling of CO2 gas. Many other complementary experiments were performed in the same device and solvent in order to get the formation enthalpies of the synthesized products. These processes concern dissolution of solids CaCl2, 2H2O, and MgCl2 and dilution of [H3PO4, 0.756 H2O], [HF, 1.708 H2O]. The results were combined with the required formation enthalpies picked from the literature to give the formation enthalpies represented in Figure 8 together with that corresponding to free magnesium carbonates. The curve corresponding to the latter was drawn from values reported in reference .
One can notice that the introduction of 0.90 ± 0.01 Mg atom in the unit cell results in the increase of the formation enthalpy and so a decrease in stability. This is in agreement with the results reported by Drouet  in the compilation of thermodynamic quantities of a large number of apatites. Besides, the difference in stability depends on the carbonate content in the lattice, the higher the latter the less stable is the Mg-bearing apatite compared to its homologous Mg-free one.
6. Thermochemistry of some B-type carbonate hydroxyapatites
B-carbonate Ca-hydroxyapatites have been synthesized, characterized, and chemically analyzed. They were then dissolved in a 9 wt% nitric acid solution (or H3PO4, 35.35 H2O) using the isoperibol calorimeter. The dissolution reaction of the compound having the general formula Ca10-(
The mole numbers
|∆solH (kJ mol−1)||∆fH (kJ mol−1)|
As with the fluorine homologous compounds, the formation enthalpy increases with the amount of carbonate and thus the stability decreases.
It is assumed that only two kinds of carbonates are present in such compounds, consequently, among “
Ca2+ + PO43− ↔ VCa + CO32− + VOH and Ca2+ + 2PO43− ↔ VCa + 2CO32− (and not mechanism V as reported erroneously in the conclusion and abstract of reference ).
7. Reactivity of B-carbonate fluorapatites toward the acid attack
7.1. Simple dissolution of Ca-CO3apatites
One of the criterions characterizing a phosphate ore is the speed of its reaction with acid solutions. This influences the reaction yield at a certain time and the self-heating rate of the reactional medium. The acid attack of synthetic and natural phosphates has been largely reported in the literature, but the quasitotality of works was performed by analysis of samples taken from the reactional medium. This way of doing does not give a true image of what is happening during the reaction. Microcalorimetry can overcome this drawback. However, this requires some preliminary experiments and signal treatment.
A C-80 SETARAM microcalorimeter has been adjusted in order to get calibration experiments in the same conditions as the chemical processes. This has been done by supplying the reversal cells of the device with electrical resistances that have been connected to a DC power supplier. When electrical energy is injected during a certain time in the reaction cell, this corresponds to an energy supplied in a “rectangular” shape but leads to a delayed and deformed recorded signal. This is because of the inertia of the various components of the device. A mathematical treatment allows to determine the time constants of the device and to get back the “rectangular” shape of the signal . This “deconvolution” operation is particularly needed in studying fast phenomena. The time constants determined in the electrical calibration operation are then used for the chemical process in order to get a “deconvoluted” calculated curve which represent more accurately what happened inside the reaction cell when the reactants were mixed.
A series of B-type carbonate apatites having 1.53–5.94 wt% carbonate have been synthesized and characterized and then dissolved in 19w/w P2O5 solution between 25 and 55°C using the C80- microcalorimeter. Dissolution of 10–60 mg of solid in 4.5 ml acid solution is a simple phenomenon without any resulting precipitate. The drawing of the energy released as a function of the solid amount led to the molar dissolution enthalpies as −201 ± 4, −208 ± 5, and −205 ± 5 kJ mol−1 for the 1.05, 3.05, and 5.94 wt% carbonate, respectively . These values are lower than that corresponding to dissolution of carbonate-free fluorapatite in the same conditions (−171 kJ mol−1). Introduction of B-carbonate in the lattice decreases the dissolution enthalpy and so confirms the decrease in stability.
As the dissolution is very fast, the deconvoluted curves were calculated taking into account the time constant values determined in calibration experiments. They were then analyzed according to Avrami model. This model links the reactant transformed fraction “
Applying this model to B-carbonate apatites reveals the existence of two processes, Figure 9, with a very short duration of the first one (33 seconds). It has been attributed to a surface phenomenon. The second one that lasts till 1200 seconds has been exploited to get a kinetic model of the acid attack. The results seem to be in agreement with a homogeneous model having an order of 2 with respect to the apatite. Activation energy values were deduced as 15.8 ± 1.4, 15.5 ± 0.9, and 8.5 ± 0.5 kJ mol−1 for the 1.58, 3.05, and 5.94 wt% carbonate, respectively . These values are of the same order of magnitude as that determined for pure FAP below 45°C (16 kJ mol−1) but drastically lower than that determined at higher temperature for the latter compound (101 kJ mol−1) . The lower value of the activation energy indicated that the reaction is rather controlled by a diffusion phenomenon.
7.2. Simple dissolution of Ca/Mg-CO3apatites
Different masses of Ca/Mg bearing B-type carbonate apatites having various amounts of carbonate have been dissolved in 3 wt% HCl solution at 25–55°C using the C-80 microcalorimeter. For low values of the solid/liquid ratio, no solid resulted and the recorded signals show the appearance of a process lasting until 2000 seconds. The drawing of the energy released at 25°C as a function of the solid mass allows to deduce the molar dissolution enthalpies from the slopes of the lines, Table 4.
|Ca10(PO4)6F2||−151.7 ± 0.7||Ca8.60Mg0.09(PO4)5 .16(CO3)0.84F1.83||−209.7 ± 1.1|
|Ca9.09Mg0.91(PO4)6F2||−180.6 ± 0.1||Ca8.36Mg0.09(PO4)4.77(CO3)1.23F1.75||−222.7 ± 0.3|
|a9.09Mg0.09(PO4)5 .52(CO3)0.48F1.90||−192.3 ± 05|
These values are higher than that obtained by dissolving the same products in the isoperibol calorimeter  and their difference increases with the carbonate amount. This is because the latter experiments were performed in a CO2 saturated solution, and so the solution is supposed to retain any further CO2, while in the microcalorimeter the dissolution occurs in a hermetic cell and the CO2 released is partially dissolved in the resulting solution. This results in an exothermal increment in the dissolution energy that increases with the carbonate amount in the solid apatite. Appearance of such effect is in agreement with the diminution of solubility of gases in liquids when increasing temperature.
One can notice a decrease in the dissolution enthalpy when Mg is incorporated and a further decrease when introducing carbonates. Introduction of magnesium and carbonate deceases considerably the molar dissolution enthalpy.
The recorded signals were processed in order to get the corresponding deconvoluted (or thermogenesis) curves . As previously, the Avrami curves drawn from the latter show at first very short phenomenon followed by a longer one. Treatment of the data reveals as previously, that the experimental results are in agreement with a homogeneous kinetic scheme with an order of 2 with respect to the apatite and an activation energy,
However, the homogeneous kinetic model is far from the experimental reality since the reaction occurs between a solid and a liquid. Isoconversional model is more suitable for heterogeneous processes. According to this model, the converted fraction
Considering the Arrhenius law,
At a certain conversion rate,
Examples of plots of ln(
One can notice that the activation energy of any apatite is practically constant along all the process, suggesting a single-step reaction. Statistical calculations allowed to determine this quantity together with its error. The values are in the range 21.1 ± 0.3–6.2 ± 0.2 kJ mol−1 for the series of compounds. It should be noticed that these values of
7.3. Dissolution of more amounts of Ca-CO3apatites
As with pure fluorapatite reported in Ref. , progressive dissolution of carbonated Ca-apatites in the same amount of a 19% w/w P2O5 solution (4.5 ml) results in the occurrence of successive phenomena. This appears through the graph representing the energy released as a function of the solid amount. Figure 12 shows an example corresponding to dissolution of the 1.58 carbonate sample versus the solid mass. One can notice the presence of three domains, each one corresponding to a particular process.
Domain 1 corresponds to a simple dissolution, no precipitate appeared at the end of the process, while in domain 2 dissolution is followed by precipitation of CaF2 and in domain 3 precipitation of a mixture of the latter with MCPM (mono-calcium phosphate monohydrate, Ca(H2PO4)2,H2O). These precipitates were characterized by X-ray diffraction performed on the solids after reaction . All the raw thermograms recorded in these domains indicated a unique phenomenon, while the thermogenesis curves in domains 2 and 3 show the successive appearance of two or three phenomena .
8. What about the phosphate ore?
It would be interesting to compare the behavior of the phosphate ore to that of these products. However, as the latter contains many compounds, dissolving a few dozens of milligrams is not representative of what is really happening. The differential reaction calorimeter (DRC) allows to overcome this difficulty. This device is composed of two symmetrical glass reactors of about half a liter maintained at the same temperature by a fluid circulating in a double envelop. Two axial agitators running at the same speed allow to disperse the solid in the liquid bulk. The former is initially introduced in a tubular sample holder and tightly separated from the liquid by a thin film blocking up the lower extremity of the tube. The recorded signal is a DC voltage resulting from the temperature difference between the two reactors that is detected by two thermocouples whose junctions are immersed in the liquids. The device has been calibrated and tested by experiments performed on key reactions .
A sample ore from Gafsa, Tunisia, has been previously chemically and structurally analyzed. It contains about 5.7 w% CaCO3 and 82.4 wt% of an apatite phase of formula: Ca9.25Na0.52 Mg0.23(PO4)5.14(CO3)0.86F2.34. Various amounts (up to 40 g) of solid have been dissolved at 25–65°C in 100 g of an acidic solution having 20, 25, or 30 wt% P2O5. These compositions are of the same order of magnitude as that used in industrial manufacturing process of superphosphate fertilizer. As with B-type CO3 apatites at 25°C, attack of progressive amounts of solid by the same quantity of liquid show three domains each one corresponding to a particular phenomenon, Figure 13. Similar curves were obtained with 25 and 30 wt% P2O5.
The first domain corresponds to a simple dissolution with ∆diss
The kinetic model of the attack in domain 3 has established considering the thermogenesis curves. The Shrinking Core Model (SCM) seems to be in agreement with experimental results. According to this model, the reaction occurring between a solid and a liquid is controlled by one of the main following processes:
(1) diffusion of the liquid reactant through a liquid film surrounding the particle of the solid to the surface of the latter, (2) chemical reaction at the surface of the nonreacting solid, leading to the reaction product (or ash), and (3) diffusion of the resulting liquid through the ash back to the external surface of the solid. The following equations have been proposed for these processes :
Calculation performed on the thermogenesis curves lead to conclude that the experiment results are in agreement with the third process. An activation energy value has been deduced as 25.4 ± 1.8 kJ mol−1, and so the acid attack seems to be controlled by the ash diffusion phenomenon.
However, this model describes globally the process and does not take into account the evolution of the reaction scheme resulting from the modification of the grain surface during the reaction. The isoconversional model allows to take into account this phenomenon. Applying this model to the process occurring in domain 3 led to straight lines representing ln(
In conclusion, thermodynamic determinations allow to point out the influence of the various components on the stability and reactivity of the apatites. The results show that introduction of carbonate along the channel contributes to increase the stability of F-apatites, while in B-type fluor- and hydroxyl-apatites, the carbonate ions contribute to decrease the stability. It is also for the substitution of calcium by magnesium. B-CO3 and Mg-substitutions increase the reactivity of synthetic F-apatites toward the acid attack that seems to be a one step process, while the acid attack of natural phosphate is more complicated.
The author would like to thank his collaborators F. Bel Hadi Yahia, K. Brahim, H. Chihi, S. Jebri, I. Khattech, A. Soussi-Baatout, and H. Zendah who contributed in the papers reported under their names in the reference list.
Becker P. Phosphates and Phosphoric Acid, Raw Materials, Technology and Economics of the Wet Process. 2nd ed. New York, Basel: Marcel Dekker Inc; 1989. p. 740
Naray-Szabo S. The structure of apatite (CaF)Ca4(PO4)3. Zeitschrift für Kristallographie. 1930; 75:387
Mehmel M. Zeitschrift für Kristallographie. 1930; 75:323
Elliott J. Structure and Chemistry of the Apatites and Other Calcium Orthophosphates. Amsterdam, London: Elsevier; 1994. p. 389
Gottschall AJ. Journal of South Africa. 1958; II:45
Jemal M. Thermochemistry and relative stability of Apatite Phosphates. Phosphorus Research Bulletin. 2004; 15:119-124
Jemal M. Thermochemistry and kinetics of the reactions of Apatite Phosphates with acid solutions. In: Mizutani T, editor. Application of Thermodynamics to Biological and Materials Science. Croatia: Intech Open Access Publisher; 2011. pp. 547-572
Lafon JP, Champion C, Bernache-Assollant D, Gibert R, Danna AM. Thermal decomposition of carbonated calcium phosphate apatites. The Journal of Thermal Analysis and Calorimetry. 2004; 72(3):1127-1134
De Maeyer EAP, Verbeeck RMH. Possible substitution mechanisms for sodium and carbonate in calcium hydroxyapatite. The Bulletin des Societes Chimiques Belges. 1993; 102:601-609
Kühl G von, Nebergall WH. Hydrogenphosphat- and carbonatapatite. Zeitschrift für anorganische und allgemeine Chemie. 1963; 324:313-320. Cited in reference 4 page 234
Jebri S, Khattech I, Jemal M. Standard enthalpy, entropy and Gibbs free energy of formation of ‘A’ type carbonate phosphocalcium Hydroxyapatites. The Journal of Chemical Thermodynamics. 2017; 106:84-94
Jebri S, Bouzhzala H, Bechrifa A, Jemal M. Structural Analysis and Thermochemistry of ‘A’ type phosphostrontium carbonate hydroxyapatites. The Journal of Thermal Analysis and Calorimetry. 2012; 107:963-972
Jebri S, Bechrifa A, Jemal M. Standard enthalpies of formation of ‘A’ type cabonate phosphobaryium hydroxyapatites. The Journal of Thermal Analysis and Calorimetry. 2012; 109:1059-1067
Ben Chérifa A, Jemal M. Sur la réaction de dissolution des phosphates dans les acides: Enthalpie de dissolution du phosphate tricacique β dans l’acide nitrique. Annales de Chimie - Science des Materiaux. 1985; 10:543-548
Stull DR, Prophet H. JANAF Thermochemical Tables. 2nd ed. Washington, DC: NSRDS-NBS 37; 1971
Lide DR. Handbook of Chemistry and Physics. 79th ed. London, NY: CRC Press; 1998-1999
Zendah H, Khattech I. Standard enthalpy, entropy and Gibbs free energy of formation of “B” type carbonate fluorapatites. The Journal of Chemical Thermodynamics. 2015; 87:29-33
Ben Abdelkader S, Khattech I, Rey C, Jemal M. Synthèse, caractérisation et thermochimie d’apatites calco-magnésiennes hydroxylées et fluorées. Thermochimica Acta. 2001; 276:25-36
Chihi H, Khattech I, Jemal M. Preparation, characterization and thermochemistry of magnesium co-substituted fluorapatites. The Journal of Thermal Analysis and Calorimetry. 2017; 127(3):2427-2438. DOI: 10.1007/s10973-016-5693-2
Drouet C. A comprehensive guide to experimental and predicted thermodynamic properties of phosphate apatite minerals in view of applicative purpose. The Journal of Chemical Thermodynamics. 2015; 81:143-159
Bel Hadj Yahia F, Jemal M. Synthesis, structural analysis and thermochemistry of B-type carbonate hydroxyapatites. Thermochimica Acta. 2010; 505:22-32
Brahim K, Khattech K, Dubès JP, Jemal M. Eude cinétique et thermodynamique de la dissolution de la fluorapatritedans l’acide phosphorique. Thermochimica Acta. 2005; 436:43-50
Zendah H, Khattech I, Jemal M. Thermochemical and kinetic studies of the acid attack of “B” type carbonate fluorapatites at different temperatures (25–55°C). Thermochimica Acta. 2013; 265:46-51
Brahim K, Antar K, Khattech I, Jemal M. Effect of temperature on the attack of fluorapatite by a phosphoric acid solution. Scientific Research and Essays. 2008; 3(1):035-039
Chihi H, Khattech I, Jemal M. Thermochemistry and kinetics of the attack of magnesium-carbonate co-substituted fluorapatites by hydrochloric acid at different temperatures (25–55) °C. Thermochimica Acta. 2016; 646:16-25
Zendah H, Khattech I, Jemal M. Synthesis, characterization and thermochemistry of acid attack of “B” type carbonate fluorapatites. The Journal of Thermal Analysis and Calorimetry. 2012; 100:855-861
Soussi-Baatout A, Hichri M, Ben Cherifa A, Khattech I. Test and calibration processes for the differential reaction calorimeter (DRC). Application. Dissolution of calcium fluorapatite in the hydrochloric acid. The Journal of Thermal Analysis and Calorimetry. 2014; 580:85-92
Soussi-Baatout A. Contribution à l’étude thermochimique et cinétique de l’attaque phosphorique d’un phosphate naturel tunisien [thesis]. Tunisia: Tunis El Manar University; 2016.
Levenspiel O. Chemical Reaction Engineering. 3rd ed. New York, Chichester, Toronto: John Wiley and Sons; 1999. p. 668
Vyazovkin SV, Lesnikovich AI. An approach in the solution of the inverse kinetic problem in the case of complex processes. Thermochimica Acta. 1990; 165:273-280