Logarithmic solubility products of the various polymorphs of calcium carbonate CaCO3 as a function of temperature.
Due to the insufficiency of freshwater resources and to supply the drinking water populations, many desalination processes such as reverse osmosis, electrodialysis and distillation are widely used. However, these processes are of large-scale consumers of energy and confronted with various problems such as corrosion and scale formation. In most cases, scales are made of calcium carbonate CaCO3. In the present chapter, an overview on the effect of operating parameters such as temperature, pH and supersaturation on the precipitation kinetics, microstructure, and polymorphism of CaCO3 is given. Additionally, I put special emphasis on the effect of foreign ions such as magnesium, sulphate, and iron ions on CaCO3 precipitation since they are present at significant concentrations in natural waters. Also, the mechanisms by which these ions affect the crystal growth of CaCO3 were pointed out. Knowledge about these operating parameters as well as the effects of foreign ions allow elucidating the polymorphs growth during water treatment. The control of these operating parameters allows reducing scale formation during drinking water and wastewater treatment. The economic impact is of greatest importance since this favorably affects the treatment costs, increases the equipment life, and allows enhanced product water recovery.
- water treatment
- calcium carbonate
Calcium carbonate CaCO3 is a commercial material and a major constituent in many natural systems. CaCO3 is widespread in the natural environment such as eggshells, corals, and sedimentary rocks [1, 2, 3]. CaCO3 is applied as filler and pigment in the production of paper, rubber, plastic, paint, textiles, and pharmaceuticals [4, 5]. More interesting, CaCO3 is used in ionic cements which are widely used in bone and dental replacement biomaterials. Original compositions of bioresorbable and biocompatible cements including a significant proportion of synthetic CaCO3 have been developed to meet a need for biomedical cements with increased resorption properties. Bone substitutes based on chemically treated natural CaCO3 are biocompatible and bioactive. They are used in the form of powder and porous ceramics [6, 7, 8, 9, 10, 11]. Because of the higher solubility of calcium carbonates compared to calcium phosphates, the introduction of a significant amount of a metastable variety of CaCO3 (vaterite or aragonite) should give mineral cements a higher rate of resorption and thus promote faster bone reconstruction [11, 12].
On the other hand, CaCO3 has a significant impact on energy production and water treatment. The insufficiency of the freshwater resources and the requirements of drinking water will be increasingly manifest in the years to come. It is very probable that the problem of water, just like that of the energy resources, will be regarded as one of the determining factors of the stability of a country. The surest and economic means to supply the drinking water populations require the desalination of brackish, saline or sea waters by using different processes of desalination (reverse osmosis, electrodialysis, distillation, etc). However, these processes are generally of large-scale consumers of energy and confronted with various problems, such as corrosion and scale formation (Figure 1) which cause enormous energy losses. In most cases, scales are made of the sparingly soluble salt CaCO3 [13, 14, 15, 16, 17, 18, 19]. Because of its poor thermal conductivity and its good adherence to the walls, CaCO3 decreases the heat transfer rate, reduces the water flow rate, and even shortens equipment life by corrosion [20, 21]. The crystallization of CaCO3 depends on several operating parameters such as the mineralogical water composition, the supersaturation of the treated water, the pH, and the temperature.
In the present overview chapter, I was interested in the scale problem through CaCO3 precipitation encountered during drinking water and wastewater treatment plants. The effect of the operating parameters such as temperature, pH, supersaturation, and foreign ions on the CaCO3 crystal growth, microstructure and polymorphism was exposed. Knowledge about these operating parameters for CaCO3 crystallization as well as the effects of foreign ions, especially magnesium, sulphate, and iron ions, is very important in the elucidation of the CaCO3 polymorphs growth during water treatment. The presence of mineral ions can have a major influence on the crystal growth and microstructure of CaCO3 since they are present with significant concentrations in natural waters. The economic impact is of the utmost importance. Indeed, the control of the operating parameters makes it possible to inhibit or reduce the scale formation during the treatment of drinking water and wastewater in different industrial processes such as desalination units, water pumps and heat exchangers. This positively affects processing costs, increases the life of the equipment, and enhances the product water recovery.
2. Polymorphism of calcium carbonate
Calcium carbonate has six different polymorphs: one amorphous CaCO3, two hydrated crystalline ones (hexahydrate CaCO3·6H2O and monohydrate CaCO3·H2O), and three anhydrous crystalline polymorphs that are the hexagonal vaterite, the orthorhombic aragonite and the rhombohedra calcite [22, 23, 24, 25]. The X-ray diffraction (XRD) diagrams of these polymorphs are shown in Figure 2. For CaCO3 polymorphs, the solubility increases in the order of calcite, aragonite, and vaterite [26, 27]. Calcite is the most stable polymorph under ambient atmospheric conditions . In the presence of water, vaterite, which is the least thermodynamically stable polymorph, easily transforms into the more stable calcite or aragonite . Environmental conditions play effective roles in crystal growth and morphological changes, namely, the solution supersaturation, calcium concentration, pH, and temperature. These experimental parameters should operate together and control the polymorphism of CaCO3.
3. System CaCO3-H2O-CO2
Scaling is a complex phenomenon that takes a long time to manifest itself in industrial or domestic facilities. Several techniques, such as mechanical stirring , aeration , electrochemical precipitation , magnetic water treatment  have been used in laboratories to assess the effectiveness of chemical or physical treatment, and the influence of certain parameters on scale formation over time. However, the most interesting method used for CaCO3 precipitation is the CO2 repelling method [16, 17, 33] where the CO2 containing solution is air bubbled which increases the solution pH and provokes the CaCO3 precipitation (Figure 3). Indeed, this method is an accelerated simulation of the natural scaling phenomenon in which the precipitation of CaCO3 takes place, in a short experiment time that do not exceed 90 min, following the removal of the dissolved CO2 by the atmospheric air, according to the following reaction [16, 17]:
The saturation index (SI) is a measure of the deviation of the system from equilibrium. When SI < 0, the solution is undersaturated and no crystallization occurs. When SI = 0, the solution is in equilibrium, and when SI > 0, the solution is supersaturated, and crystallization could occur spontaneously. For CaCO3, SI is given by the following equation:
where is the supersaturation ratio of the solution with respect to CaCO3 and IAP and Ksp represent respectively, the ionic activity product and the thermodynamic solubility product of CaCO3. The solubility products of the different polymorphs of CaCO3, given in Table 1, were determined by the temperature dependent equations given by Plummer and Busenberg  and Brecevic and Kralj .and are the activities of the ions Ca2+ and CO32−, respectively. The activity coefficients and are calculated using the extended Debye-Huckel equation:
|Polymorphs||−log Ks||T in the range||Ref.|
|Calcite||171.9065 + 0.077993 T − 2839.319/T − 71.595 log(T), T in K||0–90°C|||
|Vaterite||172.1295 + 0.077996 T − 3074.688/T − 71.595 log(T), T in K||0–90°C|||
|Aragonite||171.9773 + 0.077993 T − 2903.293/T − 71.595 log(T), T in K||0–90°C|||
|Amorphous||6.1987 + 0.0053369 T + 0.000109 T2, T in °C||10–55°C|||
|CaCO3·H2O||7.050 + 0.000159 T2, T in °C||10–50°C|||
|CaCO3·6H2O||7.1199 + 0.011756 T + 0.000075556 T2, T in °C||10–25°C|||
where ci is the concentration of the i-species.
In the carbonation process, the CO2 gas firstly dissolves into water to form the carbonic acid H2CO3 which transforms into , and according to the following equations:
where KH, K1 and K2 are the Henry’s law coefficient, first and second dissociation constants of carbonic acid (given in Table 2 ), respectively and (), () and (CO2) are the activities of the ions , and CO2, respectively.
|Carbonation process||CO2 (g) ↔ CO2 (lq)||CO2 (lq) + H2O ↔ H2CO3|
H2CO3 ↔ HCO3− + H+
|HCO3− ↔ CO32− + H+|
|Equilibrium constants||KH × 10−5|
The electric neutrality of the calco-carbonic solution gives:
From Eq. (8), the activity of is determined by:
where and are the activities coefficients of the ions and , respectively. It is worth to note that the concentration of ions can be assumed to be equal to the total alkali concentration (TAC) for pH in the range 6–8.8. Indeed, and are small in this pH range  and in a first approximation:
4. Effect of operating parameters on CaCO3 precipitation
The solubility of CaCO3 polymorphs increases in the order of calcite, aragonite, and vaterite [26, 27]. Environmental conditions play effective roles in the crystal growth and morphological changes of CaCO3. Indeed, the nucleation and growth kinetics of CaCO3 as well as the morphology and polymorphism of the obtained precipitates are affected by various key operating parameters such as supersaturation [23, 28, 38], temperature [37, 39, 40], and pH [41, 42, 43]. These experimental parameters operate together and control the polymorphism of CaCO3. For example, it was shown that vaterite can be obtained at high superasaturations and low calcium concentrations typically below 10−2 M , solution pH in the range 8.5–10  and/or low temperatures in the range 20–40°C [45, 46].
Söhnel and Mullin  showed that the crystal growth rate of CaCO3 increased with increasing the solution supersaturation. Vaterite was favored in moderate (S < 6.5) to enhanced supersaturation solutions [28, 44] and smaller vaterite crystals were obtained when supersaturation increased . High supersaturations in the range 4−14 prevented the transformation of vaterite into calcite and increased the crystal growth rate [16, 23].
It is worth noticing that the initial calcium concentration in the solution has an important impact on the polymorphism of CaCO3. Indeed, it was found that calcite did not crystallize at decreased Ca2+ concentrations (typically below 10−2 M), and only vaterite was obtained when CaCO3 was prepared, at 25°C, by a CO2/N2 mixed gas bubbled into a solution of CaCO3 . This agrees with the results of Korchef  who showed that vaterite was the predominant polymorph at 28°C, for a supersaturation in the range 4–14, and calcite was not detected, because of the low initial calcium concentration (4 × 10−3 M). Thus, for a solution supersaturated with respect to calcite (∼15–62), aragonite (4–17) and vaterite (10–38), vaterite was favored for an initial calcium concentration 4 × 10−3 M (<10−2 M), a precipitation pH in the range 8.4–8.8 and a temperature of 28°C .
The temperature and the solution pH are considered as critical parameters in controlling the kinetics crystallization, polymorphism, and morphology of CaCO3 particles. At room temperature, calcite is the most predominant phase. At temperatures higher than 50°C, CaCO3 precipitates as needles-like aragonite crystals [47, 48, 49, 50]. At conditions of spontaneous CaCO3 formation preceded by the lapse of induction time, the increase of temperature, at fixed ionic strength, results to the decrease of the induction time and to the increase of the crystalline growth rate and also the amount precipitated . Chen and Xiang  investigated the effect of temperature on the structures and morphology of CaCO3 crystals obtained by double injection of CaCl2 and NH4HCO3 solutions with a 1:1 molar ratio. At 30−40°C, they obtained crystals of lamellar vaterite. At higher temperatures of 50–70°C, a mixture of calcite and aragonite formed, and only aragonite whiskers crystallized at a temperature of 80°C. However, aragonite was not detected when CaCO3 precipitated by mixing calcium acetate Ca(C2H3O2)2 and ammonium carbonate (NH4)2CO3 .
In their recent publication, Korchef and Touabi  studied the effect of temperature and initial solution pH on the crystallization of CaCO3 by CO2 repelling. They showed that vaterite and aragonite were the polymorphs of CaCO3 collected at 28°C and 50°C and the increase in temperature from 28–50°C leads to the acceleration of CaCO3 nucleation and crystal growth. This is was explained by higher supersaturations with respect to aragonite (in the range ∼ 40–69) and vaterite (between ∼12 and 21) obtained at 50°C than those obtained at 28°C. The increase of the initial solution pH accelerates the CaCO3 precipitation. Indeed, the solution supersaturation increases with increasing the initial pH of the solution. This accelerates the nucleation and growth of CaCO3. For example, at the initial solution pH 7, the supersaturation ratios with respect to calcite and vaterite are in the ranges ∼17–30 and ∼5–8, respectively. For the initial solution pH 9, CaCO3 precipitation is instantaneous and the supersaturation ratios with respect to calcite and vaterite significantly increase, i.e., in the range ∼51–84 for calcite and in the range ∼14 –23 for vaterite. However, at constant supersaturation, it was shown that the growth rate of calcite decreases with increasing pH from 7.5 to 12 . This is because the surface concentration of active growth sites decreases with increasing pH of the solution. Ramakrishna et al.  prepared CaCO3 crystals by mixing Na2, CO3, and CaCl2 solutions injected simultaneously into distilled water at different pH values. They showed that pure aragonite needles were formed at pH 10 and a mixture of calcite and aragonite was obtained when increasing the pH from 11 to 12. At high pH values, typically greater than 12, calcite was favored , and at pH lower than 8, vaterite was obtained . Using a constant composition method, Tai and Chen  showed that vaterite was the predominant phase obtained, at 24°C, in the pH range 8.5−10, which is comparable to the precipitation pH range obtained when CaCO3 was precipitated by the CO2 repelling method (8.4−8.8) [16, 17]. For solution pH lower than 7–7.5, no precipitation of CaCO3 was detected . This result is of utmost importance in inhibiting CaCO3 precipitation during scale formation in water and wastewater treatment processes, as will be discussed in the last paragraph of the present chapter.
5. Effect of foreign ions on CaCO3 precipitation
The presence of mineral ions can significantly influence the crystal growth and microstructure of CaCO3 [50, 51, 52, 53, 54, 55, 56, 57, 58, 59]. Among mineral ions, sulphate and magnesium ions are widely studied [50, 53, 54, 55, 56, 57, 58, 59] since they are present at significant concentrations in natural waters. Compared to sulphate and magnesium ions, the impact of iron on the precipitation of calcium carbonate seems to be less studied and it appears to be a lack of reliable data on its impact on CaCO3 precipitation, especially at elevated temperature and different pH. Figure 4 shows a tank highly containing iron-rich water. Iron ions can be present in the aqueous phase either from the corrosion of metallic parts in water desalination processes, such as tanks and pipes  or they may be present in groundwater at concentration levels depending on the mineral composition of the aquifer . The water treatment processes are selected according to the water salt concentration. Indeed, membrane technological processes are used to desalinate brackish water containing salt concentrations below 10 g/L, however, reverse osmosis and thermal distillation are generally used to desalinate sea water with salt concentration above 30 g/L. Note that the typical iron concentration in the water used for the above mentioned processes is approximately 2.8 mg/L . Groundwaters containing more than 0.2 mg/L of iron should be treated if used for drinking water . Therefore, it is of great importance to understand how iron and calcium ions interact with each other during CaCO3 precipitation. Throughout the followings, I put a special emphasis on the effects of magnesium, sulphate and iron ions on the precipitation kinetics, microstructure, and polymorphism of CaCO3. Also, the mechanisms by which these ions affect the crystal growth of calcium carbonate were pointed out. Knowledge about the effects of these ions is very important in the elucidation of the growth polymorphs during water treatment.
5.1 Effect of magnesium and sulphate ions
It was shown that both sulphate and magnesium ions inhibit CaCO3 crystallization [50, 55, 56], even though some discrepancies on the effect of sulphate ions were revealed. For example, at fixed temperature and ionic strength, Karoui et al.  showed that, the addition of sulphate ions to the CaCO3 solution increased the induction time and decreased both the crystal growth rate and the amount of the precipitated CaCO3. Comparable results were found by Vavouraki et al. . However, Tlili et al.  showed that sulphate ions increase the growth rate of CaCO3 precipitated electrochemically. Many works [51, 65, 66] have shown that sulphate ions inhibit vaterite transformation and enhance the calcite formation for low concentrations. At high concentrations, it was shown that sulphate ions (i) increased the nucleation time , (ii) decreased the precipitation rate of calcite formation  and (iii) promoted the formation of aragonite via a dissolution−precipitation process after long reaction times [55, 59].
The temperature and the ratio of magnesium to calcium control the precipitation kinetics, the type of polymorph and the morphology of the CaCO3 precipitates [37, 64, 67]. For example, it was shown that when the Mg2+/Ca2+ ratio passes from 0 to 4, with a Ca2+concentration of 4 × 10−3 mol L−1, the scaling time increases from 50 to 400 min, respectively . Mejri et al.  studied the effect of magnesium ions on the CaCO3 precipitation, by the CO2 repelling method, at different temperatures between 30°C and 60°C and with different magnesium to calcium molar ratios (R) in the range 2–5. They showed that, at a fixed temperature, the increase of Mg2+ concentration significantly increased the induction time (tn) and decreased both the initial crystal growth rate (Vi) and the amount precipitated (Rp). For example, at 40°C, tn passed from 7 to 30 min, Vi passed from 0.57 to 0.49 M min−1 and Rp decreased from 81 to 56% when R passed from 0 to 5, respectively. The increase in temperature from 30–60°C weakens the impact of magnesium ions on the retardation of CaCO3 precipitation. These results agree with previous works [38, 67, 68, 69], showing that the induction time significantly increased due to the presence of Mg2+. At high concentrations of magnesium, amorphous CaCO3 exhibited a prolonged stability, while it transformed instantly to calcite and vaterite in pure water . In the presence of high amounts of Mg2+, CaCO3 exclusively precipitated as aragonite while calcite and vaterite formed when no Mg2+ ions are present . At low temperature of 30°C, the addition of Mg2+ ions favored the crystallization in the bulk solution of secondary aragonite, resulted from the transformation of vaterite nuclei, while primary aragonite was favored, at high temperature of 60°C, with larger particles sizes than those obtained at 30°C .
5.2 Effect of iron ions
The results reported in literature on the effect of iron ions on CaCO3 precipitation are often contradictory. For example, Kelland  found that iron ions concentrations below 25 ppm did not affect the CaCO3 precipitation in high pressure dynamic tube blocking tests. Comparable results were found by Lorenzo et al.  who studied the effect of ferrous iron ions on the CaCO3 growth by the constant composition method. However, Herzog et al.  found that, in magnetic water treatment devices, an excess of ferrous ions (5.6 ppm) strongly inhibits both calcite growth and the transformation of aragonite to calcite. The inhibiting effectiveness depends strongly on the solution supersaturation [16, 17, 74, 75, 76]. Indeed, at high supersaturations, the inhibition effectiveness of iron on CaCO3 crystallization is small. In that case, the inhibition effectiveness can be improved by lowering the solution pH, increasing the iron concentration and/or by lowering the solution supersaturation [16, 17]. At relatively low supersaturations, the addition of iron ions retards the CaCO3 precipitation. Past the onset of nucleation, iron ions enhance the growth rate of CaCO3 and most of CaCO3 amounts precipitate in the bulk solution instead of on the cell walls minimizing, therefore, the risks of scaling. Scaling is defined as the precipitation on the cell walls . These results agree with those of Katz et al.  and Takasaki et al.  showing that lower supersaturations require less iron for the same extent of CaCO3 growth inhibition.
It was shown  that for both temperatures 28°C and 50°C, the addition of iron retarded the nucleation of CaCO3 and, most important, it decreased the CaCO3 precipitation in the cell walls which can be easily collected, reducing therefore scale phenomena in water treatment devices. At a fixed temperature of 50°C, the increase in the iron concentration in the solution to 0.5 mg/FeL did not significantly affect the CaCO3 precipitation . Comparable result was obtained by Macadam and Parsons  who showed that addition of 0.5 mg L−1 of iron did not affect the induction time of CaCO3 precipitation by magnetic stirring at 40°C. For higher iron concentrations, the solution supersaturation decreased, and the inhibition effectiveness of iron ions became more pronounced . At 50°C, the addition of iron ions in the solution promoted aragonite formation rather than vaterite. Indeed, with the increase in the iron ions concentration, the solution supersaturation decreased and the dissolution of vaterite became, most likely, faster which promotes aragonite formation. However, at 28°C, the addition of iron ions did not affect the nature of the precipitated phases vaterite and aragonite, and vaterite with rough surfaces was the predominant polymorph. This was explained that iron ions substituted partially Ca2+, which inhibits vaterite dissolution and prevents the transformation of vaterite into aragonite [16, 17].
For a given iron concentration, increasing the initial pH causes the decrease in the induction time and the increase in the initial crystal growth rate. However, increasing iron ions concentration at a fixed pH in the range 7–9, results in the decrease in both the induction time and the crystal growth rate of CaCO3 . Additionally, the increase in iron ions concentration at a fixed pH reduced the amount of the precipitates obtained and, however, enhanced the precipitation of CaCO3 in the bulk solution, reducing therefore the risks of scaling. Therefore, the CaCO3 precipitation on cell walls, which causes the major phenomenon of scaling, could be lowered by enhancing the initial solution pH or by controlling the concentration of iron ions in the solution. However, the increase of the initial solution pH leads to high amounts of CaCO3 precipitates and even when formed in the bulk solution, they can agglomerate and block up different parts of the water treatment devices such as pipes and conducts, resulting in the blockage of fluid cooling. This increases processing costs, decreases equipment life, and decreases the product water recovery.
At 28°C and initial pH 8, calcite and vaterite were obtained. The increase in iron concentration in the solution resulted in an increased formation of calcite. At initial pH 9 and iron concentration of 4 mg/FeL, calcite was the only phase detected. At 28°C, the increase of the initial solution pH resulted in the disappearance of aragonite and the precipitation of vaterite and calcite. Iron ions addition up to 4 mg/FeL accelerated the transformation of vaterite into calcite and only calcite with stepped surfaces (Figure 5) was obtained at initial pH 9 . The stepped surfaces were explained by iron ions adsorption or to difficulties in incorporating building units into the surfaces of calcite crystals .
5.3 Effect of chloride ions
For high concentrations, chloride might affect the stability of calcium in the solution, and thus the precipitation of CaCO3. However, at relatively low temperatures between 15°C and 85°C, the equilibrium association constants of calcium ions with chloride ions in aqueous solution reported in literature are small. In fact, logK varies between −0.28 and −0.04 [79, 80, 81, 82, 83] which indicates, therefore, the instability of the ion pairs. Korchef and Touabi  showed that, at 28 and 50°C and for low concentrations of chloride below 0.18 mM, calcium chloride ion pairs either do not form or have stability fields too small to remarkably decrease the free calcium ion concentration in the solution and to reduce, therefore, the CaCO3 growth rate. Calcium chloride ion pairs form at higher temperatures, i.e., for temperatures in the range 100-360°C, the stability field for CaCl+ decreases with enhancing temperature, whereas that for increases significantly . It should be noted that higher order calcium chloride ion pairs do not form or have small stability fields.
In addition, chloride ions can be added as sodium chloride NaCl. Tai and Chen  studied the effect of ionic strength and additives concentration on the polymorphism of CaCO3 formed in a constant composition environment. They adjusted the ionic force by NaCl addition which is, they found, inactive in the polymorphic form. Moreover, Takita et al.  showed that low concentrations of NaCl in the range 0.1–0.5 M did not remarkably affect the solubility of CaCO3. However, when an excess of NaCl (2.5 M) was added, the solubility of CaCO3 increased which promoted the vaterite to calcite transformation. The resulting high concentration of CaCO3 favored crystal growth rather than nucleation.
5.4 Effect of additives and dissolved organic matter
Ukrainczyk et al.  investigated the effect of salicylic acid derivatives on calcite precipitation kinetics and morphology. Their results showed that the adsorption of additive molecules lowered the CaCO3 growth rate by blocking the propagation of growth sites. This causes the formation of steps and jagged and discontinuous surfaces. Comparable results were obtained for magnesium- containing solutions, where calcite crystal edges were rough and growth steps were apparent . Comparable effects were also found when iron was added [16, 17]. The presence of additives, such as monoethylene glycol (MEG), prevents the vaterite to calcite transformation and stabilizes the formation of the relatively unstable vaterite polymorph. For example, Natsi et al.  showed that, in the presence of low concentrations of MEG of (10−20% v/v), vaterite was stabilized. At stable supersaturated solutions, seeded with quartz and calcite crystals, the growth of CaCO3 was significantly reduced with the increase of MEG concentrations. At 60% of MEG, the vaterite/aragonite- to-calcite transformation was prevented, whatever the synthesis temperature .
On the other hand, it was shown that dissolved organic matter (DOM) inhibits CaCO3 crystal growth . The inhibition effect was related to the formation of calcium complexes and the occupation of the CaCO3 growth sites which resulted in CaCO3 rough surfaces. Dzacula et al.  studied in vitro precipitation of aragonite in artificial seawater at a high supersaturation of 11, and at a low supersaturation of 5.8. In either chemical systems, different concentrations of soluble organic matter (SOM), extracted from the symbiotic coral B. europea (SOM-Beu) and the a-symbiotic one L. pruvoti (SOMLpr) were added in order to investigate their effect on crystal growth or nucleation processes. They showed that, at high supersaturation, the SOMs increased the induction time but did not change the growth rate, and they were incorporated within nanoparticles aggregates. At low supersaturation, the SOMs affected the overgrowing crystalline unit aggregation and did not substantially affect the growth rate.
6. Possible mechanisms
According to the Ostwald  law, the least stable phase, that has the highest solubility, precipitates first and subsequently transforms to the more stable one. This transformation can be either a solid-state transition that invokes internal rearrangements of atoms, ions or molecules [92, 93] or a solution mediated transformation that invokes the dissolution of the metastable phase in the solution and simultaneous precipitation of the stable phase [94, 95]. It was shown that the amorphous calcium carbonate is a precursor in spontaneous precipitation of CaCO3 at relatively high supersaturations. The amorphous phase, which consists of spherical particles with the diameter in the range 50–400 nm, dissolves rapidly in an undersaturated solution and it undergoes a rapid transformation to one of the more stable anhydrous forms (calcite, vaterite and aragonite) . Therefore, the unstable amorphous calcium carbonate is firstly formed . Then, it transforms into crystalline phases which are vaterite, calcite and aragonite. The vaterite can be transformed gradually into calcite or aragonite following two steps that are (i) the vaterite dissolution and (ii) the calcite or aragonite growth . The second step controlled the overall rate of vaterite transformation to the most stable phase calcite or aragonite . The two hydrated crystalline forms of calcium carbonate, calcium carbonate hexahydrate CaCO3·6H2O and calcium carbonate monohydrate CaCO3·H2O, are more stable than the amorphous CaCO3. Calcium carbonate monohydrate crystallized in well-defined spherical crystals with diameters in the range 15–30 mm and calcium carbonate hexahydrate crystallizes in well-defined rhombohedral crystals in the size range between 10 and 40 mm. Generally, hydrated forms precipitate from supersaturated solutions before the more stable anhydrous forms calcite, vaterite and aragonite .
As shown above, both sulphate and magnesium ions inhibit CaCO3 crystallization [50, 55, 56]. The inhibition effect of magnesium ions was explained by (i) the increase in calcite solubility induced by magnesium ions insertion into the calcite crystals by substituting calcium ions . This substitution depends on the Mg2+, Ca2+ and ions concentrations , (ii) accumulated strain provoked by smaller magnesium ions incorporation [50, 56] and (iii) adsorption of magnesium ions on calcite surfaces . Indeed, based on the calculation of defect-forming energies in the crystalline lattice of aragonite, Mandakis et al.  showed that Mg2+ ions can substitute Ca2+ ions. This substitution may take place in the volume of the orthorhombic lattice of aragonite or on the crystal surfaces. Assessing the mechanism by which Mg2+ ions act to inhibit the crystalline growth of CaCO3 requires an understanding of the changes that must occur when an ion is transferred from the solution to its location in the crystalline lattice. In the solution, Mg2+ ions are surrounded by six molecules of H2O . The incorporation of Mg2+ ions implies therefore the replacement of the H2O molecules by six carbonate groups of the CaCO3 lattice. This is done by partial dehydration (replacement of three H2O molecules by oxygen from the calcite lattice) and then diffusion to a growth site and total dehydration (replacement of the three remaining H2O molecules) . According to Folk , the adsorption and incorporation of Mg2+ ions into the calcite lattice leads to the distortion of the crystalline lattice because of the lower ion radius of Mg2+ than that of Ca2+ (Figure 6). Thus distorted, the crystalline structure of the calcite can no longer accept the following Ca2+, which comes to seek its position in the CaCO3 lattice. Therefore, the crystalline growth of calcite is inhibited. This results in a solubility of calcite containing Mg2+ ions greater than that of pure calcite (without Mg2+) .
Sulphate ions can be incorporated into the CaCO3 lattice structure. Kitano et al.  demonstrated that this incorporation is easier in calcite than in aragonite and that with the increase in NaCl concentration in the solution, the sulphate ions content in calcite decreases significantly while in aragonite it remains constant. A simple model that describes the incorporation of sulphate into the calcite lattice was proposed by Kontrec et al. . In this model, a carbonate group can be replaced by sulphate. Three oxygen atoms of the tetrahedral sulphate structure, which occupies an area of 256.4 Å2, are accommodated in place of the planar carbonate group occupying a smaller surface area of 212.1 Å2. Sulfur and the fourth oxygen of the sulphate group are outside the carbonate plane. As a result, this substitution causes the crystalline lattice of calcite to be distorted. The distortion on the c-axis is more important than on the other two axes (a and b). A comparable model was proposed for the incorporation of sulphate ions into the orthorhombic structure of aragonite [50, 51]. In addition, sulphate ions can be adsorbed on the CaCO3 surfaces . This adsorption was explained by a mechanism involving a change in the surface charge of CaCO3 and a contribution of the Ca2 ions to the release of carbonate ions from the surface of CaCO3. Indeed, Strand et al.  showed that the negatively charged carbonate ions are released from the surface of CaCO3 (desorption) which leads to a positively charged surface. It should be noted that the causes of this desorption have not been mentioned but it was shown that, using a measure of zeta potential, sulphate and calcium ions generate the properties of the CaCO3/water interface. The sulphate ions are adsorbed on this surface and the released carbonate ions react with the Ca2+ ions to form CaCO3 on this same surface (Figure 7). This adsorption increases with temperature and/or Ca2+ ion concentration .
The inhibitory effectiveness of iron ions on CaCO3 nucleation, and growth was generally attributed to that (i) iron ions are blocking the growth sites of CaCO3 by incorporating the growing layers, which leads to a strained lattice where calcium ions no longer fit  (ii) the formation of colloidal iron oxides, i.e., Fe2O3  (iii) iron precipitates mainly in the form of siderite, which acts as heterogeneous sites for CaCO3 precipitation and improves the scale inhibition effectiveness.
The formation of iron oxides and their interactions with CaCO3 remain controversial. For example, experiments were conducted by Herzog et al.  on various forms of ferric hydroxide to test if a form is effective for the heterogeneous nucleation of CaCO3. They found that the tested forms of iron hydroxides or hydrated iron oxides did not have any effect on CaCO3 nucleation and growth. This disagrees with the results of Mejri et al. . In fact, they studied the CaCO3 precipitation in 2 mM Ca(HCO3)2 solution in the presence of iron ions concentrations between 5 and 20 mg L−1. They showed that iron ions addition promotes CaCO3 precipitation. This was attributed to the formation of iron hydroxide before the onset of CaCO3 precipitation which plays a role of seed and initiates the CaCO3 nucleation. Coetzee et al.  showed that the addition of iron had a small effect on the crystal morphology but reduced the induction times. The enhanced nucleation rates were explained by the formation of hematite Fe2O3 colloids that act as seed crystals and increase the heterogeneous nucleation process. What is more, it was shown that the presence of Fe2+ ions in contact with calcite surfaces accelerates calcite dissolution sites during its oxidation and co-precipitation onto calcite surfaces as ferric iron hydroxide, which was rapidly transformed into FeOOH nanoparticles . Thus, the water being treated can be softened by iron precipitation and the final product can be reused as mineral filler powders or as a pigment for industrial applications.
The formation of siderite FeCO3 on the CaCO3 surfaces blocks growth sites and/or forms a protection layer. This layer retards the CaCO3 precipitation and decreased the corrosion rate of mild steel in simulated saline aquifer environments . The formation of siderite, before the onset CaCO3 precipitation, was experimentally observed by scanning electron microscopy . FeCO3 was formed at relatively low supersaurations and serves as a seed for heteronucleation of vaterite. At high supersaturations, however, FeCO3 either does not form or has stability fields too small to remarkably affect the CaCO3 precipitation. In fact, it was shown that CaCO3 crystallizes in higher amounts than FeCO3 in a solution supersaturated with respect to both FeCO3 and CaCO3 , and FeCO3 precipitation is not probable, at high supersaturations, because calcium ions increase the solubility of FeCO3 decreasing, therefore, its precipitation rate [107, 108]. It was shown that, when the carbonate system presents relatively high concentrations, iron solubility is controlled by FeCO3 rather than by Fe(OH)2 in CO2 saturated solutions . This was confirmed by Korchef’s work . Indeed, according to Korchef’s mechanism , FeCO3 forms first from amorphous iron hydroxide, i.e., consistent with the so-called nonclassical nucleation theory  and then serves as a template for heteronucleation of CaCO3. When the concentration of the iron ions increases, the amount of FeCO3 formed increases, which increases the number of heterogeneous sites and enhances the inhibition effectiveness of scale. Then, FeCO3 could be incorporated in a solid solution FexCa1−xCO3 (0 ≤ x ≤ 1) by a solid–solid transition (Figure 8). Indeed, the solids CaCO3 and FeCO3 are isostructural, and their constituent cations (Ca2+ and Fe2+) can coexist, as a mixed metal carbonate, in the substitutional solid solution FexCa1−xCO3 . The FeCO3 dissolution was recently reported by Rizzo et al.  who studied the effect of CaCO3 precipitation on the corrosion of carbon steel, covered by a protective FeCO3 layer. The authors showed that CaCO3 precipitation lead to an undersaturated solution with respect to FeCO3 followed by dissolution of the protective FeCO3 layer. The partial substitution of Ca2+ by Fe2+ suppresses the transformation of vaterite into aragonite which results in the decrease of the aragonite amount with increasing iron ions concentration. Comparable results were found for Fe(II),  Fe(III), [74, 76] and Zn(II) . In fact, Zn(II) precipitated mainly as ZnCO3 which, like siderite, acts as heterogeneous sites in the bulk of solution and decreased the number of crystals on the surface. As a result, scale is reduced .
It is worth noticing that, since FeCO3 precipitates at lower pH values than CaCO3 , maintaining the solution pH at relatively low values (<7) allowed obtaining only FeCO3. FeCO3 can form protective film on different steel parts of industrial processes which, reduces or completely prevents their corrosion. This reduces remarkably the treatment costs and increases the equipment life.
7. Scale inhibition
Al-Hamza et al.  studied the inhibition effect of poly(acrylic acid) (PAA) with different end groups and molar masses on the formation of CaCO3 scale at low and high temperatures. They showed that the inhibition of CaCO3 precipitation was affected by the hydrophobicity of the end groups of PAA. The best inhibition was found for PAA with hydrophobic end groups of moderate size (6–10 carbons). Also, the scale inhibitors stabilize the less thermodynamically stable polymorph (vaterite) to a degree proportional to their ability to inhibit precipitation. At room temperature, the lowest molar mass of PAA with hydrophilic end group showed good efficiency in the inhibition of CaCO3 precipitation making it suitable to be used as a scale inhibitor in reverse osmosis desalination. However, the lowest molar mass PAA with end groups of moderate hydrophobicity are more suitable as scale inhibitors in MSF desalination. The effectiveness of the inhibitors declined with increasing temperature. Comparable results were found by Li et al.  who studied the scale inhibition effect of six varieties of commercial scale inhibitors in highly saline conditions at high temperature. Indeed, they showed that the inhibition efficiency was influenced by scale inhibitor dosage, temperature, heating time and pH. The best scale inhibitor (SQ-1211) could effectively retard scaling at high temperature and when the concentration of Ca2+ was 1600 mg L−1, the scale inhibition rate reached 90.7% at 80°C and pH 8. The crystal structure of CaCO3 changed from calcite to aragonite. Xu et al.  studied the inhibition of CaCO3 scaling on stainless steel surfaces using sodium carboxymethyl cellulose (SCMC). They showed that SCMC exhibited a promising performance of scaling inhibition, and the inhibition efficiency increased with increasing SCMC concentration starting from 50 to 200 mg L−1. For example, the inhibition efficiency reached 93.2% for SCMC concentration of 200 mg L−1. The inhibition effect was explained by the formation of a protective film on the stainless-steel surfaces by adsorption of the constituent of SCMC in the presence of SCMC, preventing the deposition of CaCO3. Zuho et al.  investigated the feasibility of electrochemical methods to study the scale inhibition performance of 1-hydroxyethylidene-1,1-diphosphonic acid (HEDP) and 2-phosphonobutane-1,2,4-tricarboxylic acid (PBTCA), polyacrylic acid (PAA) on titanium surfaces. They showed that, for electrochemically deposited CaCO3 scale, PBTCA, HEDP and PAA have great inhibitory effects and the order of the scale inhibition efficiency of the three inhibitors is PBTCA > HEDP > PAA. The deposition of CaCO3 on the surface of TA1 metal mainly results in dendritic aragonite crystals and when scale inhibitors were added, the aragonite crystal polymorph was gradually modified to vaterite. Yu et al.  designed and prepared phosphorus-free and biodegradable scale inhibitors. In fact, two series of starch-graft-poly(acrylic acid) (St-g-PAA) samples with different grafting ratios and grafted-chain distributions, that are, the number and length of grafted PAA chains on the starch backbone were elaborated. They showed that St-g-PAA with relatively low grafting ratio (typically ≤97%) inhibited scale formation more effectively than samples with similar grafted-chain distributions. However, under the similar grafting ratios, samples with higher number of branched chains with shorter grafted chains showed better scale efficiency.
More interesting, Korchef and Touabi  showed that high amounts of precipitates were obtained with increasing the initial solution pH, and even when formed in the bulk solution, these precipitates can agglomerate and block up pipes pumps and conducts of water in water treatment devices leading to the complete blockage of fluid cooling. For solution pH lower than 7–7.5, no precipitation of CaCO3 was detected . For that reason, the solution pH should be maintained at low values (pH below 7). This can be easily achieved by avoiding CO2 repelling from the solution. This allows reducing or completely preventing scale in different water treatment processes and favorably affects the water treatment costs and increases the equipment life. In practice, this is achievable by avoiding the contact between water and the atmospheric air. For example, in the desalination units using the solar multiple condensation evaporation cycle (SMCEC) principle, the supersaturation of the feed water increases remarkably with the number of the condensation–evaporation cycles  and accordingly, it is expected that iron ions do not inhibit the formation of CaCO3 as scale in the SMCEC desalination units. In that case, it is mandatory to regulate the pH of feed water below 7 to prevent scale formation.
Water desalination processes such as reverse osmosis, electrodialysis and distillation are confronted with scale formation which causes enormous energy losses and shortens the equipment life. In most cases, scales are made of CaCO3 which possesses six polymorphs. Environmental conditions play effective roles in the nucleation and growth kinetics of CaCO3 as well as the morphology and polymorphism of the obtained precipitates. In the present chapter, an overview on the effect of operating conditions such as supersaturation, temperature, and pH, on the crystal growth and microstructure of CaCO3 is given. Additionally, I put special emphasis on the effect of foreign ions, especially magnesium, sulphate, chloride, and iron ions. Also, the mechanisms by which these ions affect the crystal growth of CaCO3 were pointed out. The experimental parameters should operate together and control the growth rate and polymorphism of CaCO3. Throughout the present chapter, it was reported that:
the unstable amorphous CaCO3 is firstly formed. Then, it transformed into crystalline phases which are namely vaterite, aragonite and calcite. The vaterite can be transformed gradually into calcite or aragonite following two steps which are the dissolution of vaterite and the growth of calcite or aragonite. The dissolution of vaterite is affected by the presence of foreign ions, i.e., magnesium, sulphate, and irons ions. The two hydrated crystalline forms of calcium carbonate, calcium carbonate hexahydrate CaCO3·6H2O and calcium carbonate monohydrate CaCO3·H2O, are more stable than the amorphous CaCO3.
the crystal growth rate of CaCO3 increases with increasing the solution supersaturation.
the increase of temperature results to the decrease of the induction time and to the increase of the growth rate of CaCO3 and, also the amount precipitated. At room temperature, calcite is the most predominant phase. At temperatures higher than 50°C, CaCO3 scale precipitates as needles-like aragonite crystals.
the increase of the initial solution pH accelerates the CaCO3 precipitation. For solution pH lower than 7–7.5, no precipitation of CaCO3 was detected. At pH lower than 8, vaterite was obtained. Pure aragonite needles were formed at pH 10 and a mixture of calcite and aragonite was obtained when increasing the pH from 11 to 12. At high pH values, typically greater than 12, calcite was favored.
both sulphate and magnesium ions inhibit CaCO3 crystallization, even though some discrepancies on the effect of sulphate ions were revealed.
iron ions inhibit the CaCO3 growth. The inhibiting effectiveness depends strongly on the solution supersaturation. At relatively low supersaturations, the addition of iron ions retards the CaCO3 precipitation crystals. Past the onset of nucleation, iron ions increased the CaCO3 growth rate and most of CaCO3 amounts precipitated in the bulk solution rather than on the cell walls. This results in the decrease of scaling defined as the precipitation on the cell walls. At high supersaturations, the inhibition effectiveness of iron is small. In that case, the inhibition effectiveness can be enhanced by controlling the operating parameters, i.e., lowering the solution pH, increasing the iron concentration, and/or lowering the solution supersaturation.
the control of the operating parameters and the water composition allows completely inhibiting or, at least, reducing scale formation in various industrial devices such as desalination units and heat exchangers.
in practice, the solution pH should be maintained at low values (below 7) by avoiding CO2 removal from the solution which allows reducing or completely preventing scale. This is realizable by preventing the contact between water and the atmospheric air. The economic impact is of greatest importance since this reduces considerably the treatment costs, enhances the equipment life, and allows increased product water recovery.
The author would like to express his gratitude to King Khalid University (KKU), Saudi Arabia, for providing administrative and technical support. The author gratefully acknowledged the researchers, engineers, and technicians of the Laboratory of Natural Water Treatment (LabTEN) of the Centre of Researches and Technologies of Waters (CERTE), Technopark of Borj-Cedria (Tunisia), for many years of fruitful collaboration.
Conflict of interest
The author declares no conflict of interest.