Thermally Induced Aragonite-Calcite Transformation in Freshwater Pearl: A Mutual Relation with the Thermal Dehydration of Included Water.

This study focuses on the relationship between the aragonite-calcite (A-C) transformation and the thermal dehydration of included water in the biomineralized aragonite construction using freshwater pearl. These thermally induced processes occur in the same temperature region. The thermal dehydration of included water was characterized through thermoanalytical investigations as an overlapping of three dehydration steps. Each dehydration step was separated through kinetic deconvolution analysis, and the kinetic parameters were determined. A single-step behavior of the A-C transformation was evidenced using high-temperature X-ray diffractometry and Fourier transform infrared spectrometry for the heat-treated samples. The kinetics of the A-C transformation was analyzed using the conversion curves under isothermal and linear nonisothermal conditions. The A-C transformation occurred in the corresponding temperature region of the thermal dehydration, ranging from the second half of the second dehydration step to the first half of the third dehydration step. Because the thermal dehydration process is constrained by the contracting geometry kinetics, the movement of the thermal dehydration reaction interface can be a trigger for the A-C transformation. In this scheme, the overall kinetics of the A-C transformation in the biomineralized aragonite construction is regulated by a contracting geometry.

Introduction

Calcium carbonate (CaCO3) is a well-known inorganic raw material and historically used for a variety of applications including architectural materials and pigments.[1,2] There are many sources of CaCO3 available in nature as minerals and those produced through the biomineralization of living organisms. Effective reuse of CaCO3, recovered from waste architectural materials and food processing wastes, is also a focus of materials recycling.[3−11] Therefore, novel potential applications of CaCO3 have been continuously investigated to find additional value and establish cost-effective reuse of the material resource. Recently, the reversible reactions of the thermal decomposition of CaCO3 to form calcium oxide (CaO) and carbon dioxide (CO2) and the carbonation of CaO to form CaCO3, i.e., CaCO3 ⇄ CaO + CO2, have attracted considerable attention once again[12−26] The absorption of CO2 by the carbonation of CaO and recovery of the CaO absorbent by the thermal decomposition of CaCO3 function as a CO2 looping system to mitigate the greenhouse effect.[12−18] Because of the endothermic thermal decomposition of CaCO3 and exothermic carbonation of CaO, the reversible reactions can be used for the thermal storage of solar energy.[19−26] For these potential applications of the reversible reactions, the physicochemical properties and morphological characteristics of CaCO3 and CaO are recognized as important factors to determine the functionalities.

Two polymorphous crystals of CaCO3 are present in nature, i.e., calcite and aragonite, in addition to the synthetic crystalline phase of vaterite.[27] Naturally available aragonite is the metastable phase, which is transformed into calcite before the thermal decomposition of CaCO3 when it is heated under linear nonisothermal conditions.[28−34] The calcite generated by the thermally induced phase transition of aragonite has some specific morphological characteristics, which are different from the naturally available calcite, and its physicochemical properties and morphological characteristics may depend on the original structural construction of the aragonite and its transformation mechanism to calcite. Thus, a detailed understanding of the aragonite–calcite (A–C) transformation facilitates the control of the physicochemical and morphological characteristics of the as-produced calcite toward the effective use of its functionalities. Thermally induced A–C transformation has been studied from different perspectives. Microscopically, the transformation occurs via nucleation and subsequent growth of the calcite phase.[35−37] From a crystallographic viewpoint, the phase transition from aragonite to calcite is explained by reorientation of the CO3 group to Ca and changes in the Ca atom packing from approximately hexagonal to cubic close-packing, which is followed by the increase in the unit-cell volume.[38,39] The overall kinetic behavior of the A–C transformation has been investigated by focusing on its endothermic behavior using thermoanalytical techniques, including differential thermal analysis (DTA) and differential scanning calorimetry.[28−34,40−45] The nucleation–growth model has also been supported by the kinetic analysis of the thermoanalytical curves,[43−45] even though the reported kinetic parameters are largely distributed. The evolution of water vapor during the A–C transformation has also been revealed through thermoanalytical approaches using thermogravimetry (TG),[28−34] which has been generally observed for the biogenetic aragonite[28−32] and also confirmed for the synthetic aragonite.[29,34] When the A–C transformation and the thermal dehydration of included water occur in the same temperature region, the resulting endothermic behavior should be interpreted by considering the contributions of these two phenomena.[31−33] The evolution of water vapor originated from the thermally induced dehydration of included water in the aragonite construction.[28−34] The thermal dehydration contributes to the increase in the internal pressure of the aragonite construction, and the evolution of water vapor generates diffusion paths such as a micropore in the resulting calcite construction as observed microscopically.[46] Furthermore, the A–C transformation followed by the thermal dehydration of included water occurs at a lower temperature region compared to that of mineral aragonite.[31,46,47] Therefore, elucidation of the interaction between the A–C transformation and the thermal dehydration of included water is necessary to describe the physicogeometrical mechanistic features of the overlapping phenomena.

Our previous study on the A–C transformation of coral aragonite revealed that the accompanying thermal dehydration of included water appears as a partially overlapping multistep process.[48] Thus, the mechanistic correlations of each thermal dehydration step to the A–C transformation may provide additional information to characterize the physicogeometrical mechanisms of the A–C transformation. In this study, biomineralized freshwater pearl (FW-pearl) was used as an aragonite system because fewer contaminants of metal cation other than the calcium ion were expected compared to those mineralized in a seawater environment.[49] The kinetic behaviors of the A–C transformation and the multistep thermal dehydration of included water were separately investigated by following the respective processes using different physicochemical techniques: high-temperature powder X-ray diffractometry (HTXRD) and Fourier transform infrared spectroscopy (FT-IR) for the former and TG for the latter. By comparing the kinetic results, the relationship between the A–C transformation and multistep thermal dehydration in the temperature coordinate was discussed to evaluate the correlations between each thermal dehydration step and the A–C transformation. Further, the physicogeometrical mechanisms of the overall A–C transformation process in the biomineralized construction are discussed in detail by considering the contributions of the thermal dehydration of included water.

Experimental Section

Sample and Its Characterization

In this study, FW-pearls produced in China with a diameter size of 7–9 mm were used for experiments (Figure S1). The pearls were crushed and ground using a stainless-steel mortar and pestle. The as-produced pearl powder was sieved using stainless steel sieves with different meshes and an electric shaking apparatus (MVS-1, AS ONE). The powder in the sieved fraction with an aperture size of 90–150 μm was used as the sample (Figure S2). The sample was characterized by powder XRD, FT-IR, and simultaneous TG–DTA measurements. The XRD pattern was recorded using a diffractometer (RINT2200V, Rigaku) by irradiating monochrome Cu Kα (40 kV, 20 mA) and scanning in a 2θ range of 5–60° at a rate of 4° min–1 in steps of 0.02°. For the FT-IR spectrum measurement, the sample was diluted with KBr. The FT-IR spectrum was recorded in a spectrometer (FT-IR 8400S, Shimadzu) using the diffuse reflectance method. Figure S3 shows the XRD pattern and FT-IR spectrum of the FW-pearl. The XRD pattern (Figure S3a) is in agreement with that reported for aragonite (CaCO3, orthorhombic, S.G. = Pmcn(62), a = 4.9623, b = 7.9680, c = 5.7439, α = β = γ = 90.000, ICDD-PDF 00-041-1475).[50,51] The FT-IR spectrum (Figure S3b) shows all of the major IR absorption peaks attributed to aragonite.[52−54] The absorptions attributed to the ν4 mode of CO32– in the aragonite structure are observed at 700 cm–1 and 713 cm–1. The IR absorption peaks at 864, 1082, and 1483 cm–1 are attributed to the ν2, ν1, and ν3 modes of the CO32– vibrations, respectively. The absorption peaks at 1650 and 2600–3600 cm–1 correspond to the H–O–H bending and O–H stretching modes of H2O, respectively, suggesting the presence of H2O in the aragonite structure as included water, similar to that previously reported for the natural and biomineralized aragonites.[28−34] The atomic constitution of FW-pearl was determined by energy-dispersive X-ray (EDX) spectrometry using an instrument (X-act, Oxford) equipped with a scanning electron microscope (JSM-6510, JEOL). Only Ca, C, and O atoms were detected as the components (Figure S4).

Tracking of the Thermally Induced Transformations

Approximately 10.0 mg of the sample, weighed into a platinum pan (5 mm in diameter and 2.5 mm in depth), was heated in a TG–DTA instrument (TG8120, Thermoplus 2, Rigaku) from room temperature to 1223 K at a heating rate (β) of 5 K min–1 in flowing He gas at a rate of 200 cm3 min–1. A portion of the outlet gas from the reaction chamber of the TG–DTA instrument was continuously introduced to the quadruple mass spectrometer (M-200QA, Anelva) through a silica capillary tube (0.075 mm inner diameter and 0.7 m in length) heated at 500 K. The mass spectra (MS) of the outlet gas were repeatedly measured in an m/z range from 10 to 50 amu (EMSN: 1.0 mA; SEM: 1.0 kV).

HTXRD measurements were used to track the crystallographic phase changes during heating the sample in the aforementioned XRD instrument by equipping a heating chamber with a programmable temperature controller (PTC-20A, Rigaku). The sample press-fitted to a platinum plate sample holder, ensuring a fine powder bed, was heated in flowing dry N2 gas at a rate of 100 cm3 min–1 according to two different heating programs. For tracking the crystallographic phase changes in a wide temperature range from 323 to 1123 K, a stepwise isothermal program, composed of 15 min of temperature holding at different temperatures in steps of 50 K during linear heating at a rate of 2 K min–1, was used to heat the sample, and XRD measurements were performed at each temperature holding section. For tracking the structural phase transition from aragonite to calcite, the sample was initially heated linearly to 703 K at a β of 10 K min–1; subsequently, the sample temperature was maintained at 703 K for 5 h. XRD measurements were repeated 20 times during the isothermal holding section.

The sample of approximately 20 mg, weighed in a platinum pan (5 mm in diameter and 2.5 mm in depth), was subjected to the TG–DTA measurement. TG–DTA curves were recorded using a horizontal thermobalance (TG8121, Thermoplus Evo2, Rigaku) by heating the sample from room temperature to 1223 K at a β of 5 K min–1 in flowing dry N2 gas at a rate of 300 cm3 min–1. TG–DTA measurements were also carried out in flowing N2–CO2 mixed gas (20%-CO2) at a rate of 300 cm3 min–1 for tracking the water release process observed right before the thermal decomposition of CaCO3 in the TG–DTA measurements under flowing dry N2 gas. The TG–DTA curves in the flowing N2–CO2 mixed gas were recorded at different β values of 1, 2, 3, 5, 7, and 10 K min–1, in which the concentration of CO2 in the outlet gas from the instrument was continuously monitored using a CO2 concentration meter (LX-710, IIJIMA).

TG–DTA measurements (β = 5 K min–1) in the flowing N2–CO2 mixed gas were stopped at different temperatures in a range of 503–763 K, and the thermally treated samples were recovered after natural cooling to room temperature in the instrument. FT-IR spectra of the thermally treated samples were recorded using the diffuse reflectance method after diluting the samples with KBr (1:10) for determining the mixed ratio of aragonite/calcite. To obtain the calibration curve for determining the aragonite/calcite ratio, FT-IR spectra of standard samples with known aragonite/calcite mixed ratios were also recorded using the same measurement conditions.

Results and Discussion

Thermal Behavior of FW-Pearl

Figure shows the TG–DTA curves for the powder sample of FW-pearl, along with the MS ion thermograms for m/z = 18 (H2O+) and m/z = 44 (CO2+) in the gas evolved during heating the sample. The major mass-loss process is observed at a temperature higher than 800 K, followed by the significant endothermic effect. Because the major gaseous product is CO2, the major mass-loss process is attributed to the thermal decomposition of CaCO3. A detectable mass loss, followed by a slight endothermic effect is observed in a temperature range of 500–800 K, previously to the major mass-loss process. The preliminary mass-loss process is characterized by the evolution of water vapor, i.e., the thermal dehydration of included water.

Figure 1

TG–DTA curves for the powdered FW-pearl (m0 = 9.918 mg) recorded by heating at a β of 5 K min–1 in flowing He gas at a rate of 200 cm3 min–1 along with the MS ion thermograms for m/z = 18 (H2O+) and m/z = 44 (CO2+) in the evolved gas.

Figure a shows the changes in the XRD pattern of the sample during the stepwise isothermal heating from 323 to 1123 K in steps of 50 K in flowing dry N2 gas. The structural phase transition from aragonite to calcite (trigonal, S.G. = R–3c, a = b = 4.9780, c = 17.3540, JCPDS PDF 01-086-2341)[55] (Figure b) occurred in the temperature range of 573–773 K by gradual attenuations of aragonite diffraction peaks and compensative growth of those attributed to calcite. The wide temperature range of the A–C transformation observed by the changes in the XRD pattern practically corresponds to that of the first mass-loss process characterized by the evolution of water vapor in the TG–MS (Figure ). The as-produced calcite phase decomposes to calcium oxide (Figure c) with further heating at temperatures ranging from 873 to 1073 K. The temperature range is approximately 100 K higher than that of the thermal decomposition of calcite observed in the TG–MS. The shift in the temperature range of the thermal decomposition of calcite is explained by the effect of self-generated CO2 on the reaction under the conditions of the sample press-fitted on the platinum plate for the HTXRD measurement.

Figure 2

Changes in the XRD pattern of FW-pearl during the stepwise isothermal heating in flowing dry N2 gas: (a) XRD patterns at different temperatures, (b) XRD pattern at 873 K, and (c) XRD pattern at 1123 K.

Figure shows the change in the XRD pattern of FW-pearl during the isothermal heating at 703 K in flowing dry N2 gas. The diffraction peaks of aragonite gradually attenuated as the duration time increased (Figure a). In contrast, the intensity of the calcite diffraction peaks increased. The changes in the fractional transition (αtr) from aragonite to calcite as a function of time (Figure b), calculated from the XRD patterns using the reference intensity ratio (RIR) method, indicate that the transformation completion at 703 K lasted approximately 150 min. The kinetically controlled feature of the transformation is deduced from the time-dependent transformation behavior at constant temperatures and also from the wide temperature range of the transformation under the stepwise isothermal condition.

Figure 3

Changes in the XRD pattern of FW-pearl during the isothermal heating at 703 K in flowing dry N2 gas: (a) XRD patterns at different times and (b) changes in the fractional transition (αtr) from aragonite to calcite, evaluated by the RIR method.

Figure shows the comparison of the TG/derivative TG(DTG)–DTA curves for FW-pearl recorded at a β of 5 K min–1 in flowing dry N2 and N2–CO2 (20%-CO2) mixed gases. The first mass-loss process characterized by the evolution of included water in the temperature range corresponding to A–C transformation is not influenced by the atmospheric CO2. Conversely, the second mass-loss process of the thermal decomposition of calcite significantly shifts to higher temperatures due to the effect of atmospheric CO2. These observations demonstrate that the measurement of the thermally induced transformation processes in FW-pearl under atmospheric CO2 allows monitoring the evolution of water vapor along with the A–C transformation by separating from the subsequent thermal decomposition of calcite.

Figure 4

Comparison of TG/DTG–DTA curves for FW-pearl (m0 = approximately 20.0 mg) recorded at a β of 5 K min–1 in flowing dry N2 and N2–CO2 (20%-CO2) mixed gases.

Kinetics of Thermal Dehydration of Included Water

Figure shows the TG–DTG curves recorded at different β values in flowing N2–CO2 (20%-CO2) mixed gases by focusing on the temperature range of the thermal dehydration process of included water. The relative mass-loss value for thermal dehydration was 3.98 ± 0.05%. The TG–DTG curves systematically shifted to higher temperatures providing evidence of a kinetically controlled process. The DTG curves during thermal dehydration apparently show three mass-loss peaks partially overlapping. The TG–DTG curves were converted to kinetic curves by calculating the fractional reaction (α) values for the total mass-loss value during the thermal dehydration process (Figure S5).

Figure 5

TG–DTG curves for the first mass-loss process of FW-pearl (m0 = 19.996 ± 0.026 mg) characterized by the evolution of included water recorded at various β values (1 ≤ β (K min–1) ≤ 10) in flowing N2–CO2 (20%-CO2) mixed gases.

As a preliminary trial, the overall thermal dehydration process was analyzed kinetically by assuming a single-step reaction using the fundamental kinetic equation that considers the variation of the normalized reaction rate (dα/dt) depending on temperature (T) and α values[56−58]where A, Ea, and R are the Arrhenius pre-exponential factor, apparent activation energy, and gas constant, respectively. f(α) is the kinetic model function that describes the change in the (dα/dt) values as a function of α at a constant temperature. By taking logarithms of eq , the fundamental kinetic equation is converted to express the isoconversional kinetic relationship, i.e., at a selected α value.[56−58]At the selected α value, the data points of (dα/dt, T) extracted from the series of kinetic curves should fulfill the linear correlation between ln(dα/dt) and T–1 under the restriction of a constant ln [Af(α)] value (Friedman plot[59]). The results of the Friedman plots, examined at various α values, are shown in Figure . An acceptable linear correlation of the Friedman plots was observed at different α values over the course with the correlation coefficient better than −0.98 in the α range of 0.12–0.95 (Figure a). However, the Ea value calculated from the slope of the Friedman plots varied during the reaction (Figure b). Three distinguishable α ranges exhibiting different Ea variation trends can be identified: (1) the initial Ea increasing range (approximately from 80 to 190 kJ mol–1 in 0.01 ≤ α ≤ 0.20), (2) the constant Ea range with an average value of 188.8 ± 3.8 kJ mol–1 (0.20 ≤ α ≤ 0.80), and (3) the final Ea increasing range (approximately from 190 to 250 kJ mol–1 in 0.80 ≤ α ≤ 0.99). The observed Ea variation trends also support the overlapping three-step behavior of the thermal dehydration as expected from the shape of the DTG curves at sight (Figure ). A similar three-step behavior observed for the thermal dehydration of included water was reported for a coral aragonite.[48]

Figure 6

Results of Friedman plots for the thermal dehydration of included water in FW-pearl: (a) Friedman plots at various α and (b) Ea values at various α.

When the component reaction steps during the thermal dehydration of included water are kinetically independent, the overall process is described by a simple cumulative kinetic equation[57,60−62]where N is the total number of component reaction steps and c is the contribution of each reaction step to the overall process. The subscript i identifies the component reaction step. The kinetic calculation based on eq is the simultaneous determination of all kinetic parameters for all component reaction steps via the nonlinear least-squares analysis to minimize the sum of the squares of the residue between the experimental and calculated data points in the overall kinetic curves (kinetic deconvolution analysis (KDA))[57,60−62]where M is the total number of data points in a kinetic curve and j identifies the data point. The mathematical procedure always accompanies the possibility to fall in the local minimum, providing the superficial kinetic parameters for all component reaction steps. Setting up the kinetically meaningful initial values at least for several kinetic parameters before the KDA is an approach to increase the reliability of the highly mathematical procedure. In this study, preliminary kinetic analysis for the partially overlapping three-step process (N = 3) was performed based on the mathematical deconvolution analysis (MDA) of the overall process using a statistical function.[57,61−64] The MDA provides the initial c values from the ratio of the separated peak area of the differential kinetic curves. Furthermore, the initial Ea values for each reaction step are obtained by the conventional isoconversional kinetic analysis. The details of the kinetic analysis based on the MDA are described in the Supporting Information (Section S3: Figures S6–S8 and Table S1).

To achieve the superior curve fitting through the KDA, an empirical kinetic model function f(α), known as Šesták–Berggren model SB(m, n, p),[65−67] was applied to all component reaction steps.The c and Ea, values evaluated through the MDA (Table S1) and SB(0, 1, 0), corresponding to the first-order kinetic model, were introduced into eq as the initial values. Subsequently, the initial A values were determined by comparing graphically the positions of the experimental and calculated kinetic curves in the temperature coordinate. Thereafter, all kinetic parameters in eq with eq , a total of 18 parameters, were simultaneously optimized through the nonlinear least-squares analysis (eq ).

Figure shows a typical result of the KDA applied to the thermal dehydration of included water in FW-pearl. Regardless of the kinetic curves at different β values, the statistically significant fit to the overall kinetic curves was achieved, followed by the practically invariant kinetic parameters as listed in Table . The largest contribution is observed for the second reaction step, while the contributions of the first and third reaction steps are limited to 10–15%. The increase in the Ea, value followed by the decrease in the A value as the reaction step progresses are in agreement with the order of the reaction steps for the reaction temperature. The Arrhenius plots obtained using the optimized kinetic parameters are compared in Figure S9. Using empirical SB(m, n, p) exponents, the master plots for each reaction step were calculated based on the Ozawa’s generalized time (θ).[68−75]As shown in Figure , the master plots exhibit a deceleration process with concaved shapes in all reaction steps, which indicates that the diffusional removal of water molecules through the solid phase is the rate-limiting step.

Figure 7

Typical result of the KDA applied to the thermal dehydration of included water in FW-pearl.

Table 1

Optimized Kinetic Parameters for the Component Reaction Steps of the Thermal Dehydration of Included Water in FW-Pearl, Averaged Over Different β Values (Determination Coefficient R2 = 0.9971 ± 0.001)

				fi (αi) = αimi (1 – αi)ni[−ln(1 – αi)]pi
i	ci	Ea,i/kJ mol–1	Ai/s–1	mi	ni	pi
1	0.14 ± 0.01	160.4 ± 0.8	(1.28 ± 0.03) × 1016	1.53 ± 0.02	8.29 ± 0.43	–1.84 ± 0.03
2	0.73 ± 0.04	193.6 ± 0.5	(5.85 ± 0.03) × 1014	5.67 ± 0.70	0.47 ± 0.02	–6.40 ± 0.64
3	0.13 ± 0.04	219.6 ± 1.2	(1.66 ± 0.01) × 1013	–2.54 ± 0.26	1.09 ± 0.13	0.88 ± 0.06

Figure 8

Master plot for each reaction step of the thermal dehydration of included water calculated using the optimized kinetic exponents in SB (m, n, p).

Thermally Induced Aragonite–Calcite Transformation

Figure displays the FT-IR spectra of the samples, which were previously heated to different temperatures within the range corresponding to the thermal dehydration of included water at a β of 5 K min–1 in flowing N2–CO2 mixed gas (20%-CO2). The characteristic double peaks at 700 and 713 cm–1 attributed to the ν4 mode of CO32– in the aragonite structure are maintained until approximately 700 K (Figure a). Subsequently, the peak at 700 cm–1 attenuates gradually by heating to higher temperatures, and the absorption peak converges with the single peak at 713 cm–1 characteristics of the calcite structure. Compared with the temperature range of the thermal dehydration of included water, the A–C transformation occurs in the temperature range between the maximum rates for the second and third thermal dehydration steps. By a quantitative analysis of the absorption peaks using the calibration curve method, the αtr value for the A–C transformation at distinct temperatures was determined (Figure b). From the temperature−αtr profile, the temperature range of the A–C transformation at a β of 5 K min–1 was approximately determined to be from 700 to 750 K, and the αtr value systematically increased as the sample temperature increases within the temperature range. The details for the quantitative analysis of the IR absorption peaks are described in the Supporting Information (Section S4: Figures S10–S13 and Tables S2–S4).[53,54,76−80]

Figure 9

Analysis of FT-IR spectra for the heat-treated sample by heating to different temperatures at a β of 5 K min–1 in flowing N2–CO2 mixed gases (20%-CO2) at a rate of 300 cm3 min–1: (a) changes in the FT-IR spectra for the ν4 mode of CO32– and (b) temperature–fractional transition (αtr) profile from aragonite to calcite determined by the quantitative analysis of the peak area.

The progress of the A–C transformation with time at a constant temperature of 703 K, monitored by XRD measurements (Figure ), and with temperature at β = 5 K min–1, monitored by FT-IR measurements, were subjected to kinetic analysis as shown in Figure . Because the sensitivity and number of data points of the kinetic data determined using HTXRD and FT-IR are largely limited in comparison with those in TG for the thermal dehydration process, classical integral methods were employed for the kinetic calculation as the only possible method. The changes in αtr with time at a constant temperature can be correlated by the following integral kinetic equation[58]where g(αtr) and k are the kinetic model function in the integral form and the rate constant, respectively. By examining g(αtr) versus t plots using various g(α) values listed in Table S5, the random nucleation and subsequent growth (Johnson–Mehl–Avrami model; JMA(m))[81−84] and phase boundary-controlled reaction (R(n)) models exhibited the most statistically significant linear correlation between g(αtr) versus t with reference to the correlation coefficient (γ) of the linear regression analysis, as shown in Figure a. The JMA(4) model explains the constant rate nucleation of calcite in the aragonite matrix and subsequent three-dimensional growth of the nuclei. Conversely, the R(1) model describes the one-dimensional advancement of the transformation interface. Considering the sampling condition of the XRD measurement characterized by the press-fitting on the platinum plate, the physicogeometrical mechanism described by the R(1) model is interpreted by the initiation of the A–C transformation at the top surface of the press-fitted sample and advancement of the transformation interface into the depth. When the thermal dehydration of included water covering the temperature range of the A–C transformation is considered as a possible trigger for the phase transition, the R(1) model is valid as the overall physicogeometrical mechanism because the thermal dehydration characterized by the diffusion-controlled process (Figure ) occurs with the same geometrical constraint.

Figure 10

Kinetic plots for the aragonite–calcite transformation: (a) g(αtr) versus t plot for the isothermal transformation at T = 703 K tracked using HTXRD (Figure ) and (b) Coats and Redfern plots[85] for the nonisothermal transformation at β = 5 K min–1 tracked using FT-IR (Figure ).

The changes in the αtr value with T recorded using the FT-IR measurements for a series of samples with different thermal treatments can be used as the integral kinetic data at a constant β value, which can be kinetically analyzed using the Coats and Redfern (CR) method[85]where Atr and Ea,tr are the Arrhenius pre-exponential factor and apparent activation energy for the A–C transformation, respectively. By assuming that the logarithmic term on the right-hand side of eq is constant, the plot of ln [g(αtr)/T2] versus the reciprocal temperature represents a linear correlation when an appropriate g(α) is used. The Ea,tr and Atr values are then obtained from the slope and intercept of the plot, respectively. As in the kinetic analysis of the isothermal kinetic data, the statistically significant linear correlation of the CR plot is observed when the JAM(m) or R(n) models are adopted (Figure b). The kinetic parameters determined by the CR plots are listed in Table . The exponent m in JMA(m) representing the optimal linearity of the CR plot was 1.0 or 1.5, which is different from JMA(4) estimated from the HTXRD data under isothermal conditions. Although the physicochemical meaning of the m value is explained by several theoretical interpretations based on the kinetics and geometry of successive nucleation and growth,[81−84] the JMA(m) model is fundamentally derived for bulk processes. Therefore, a significant change in the m value depending on the sampling conditions is not expected. The calculated exponent n in the R(n) model determined using the CR plot was 3, which was different from the R(1) estimated from the HTXRD data under isothermal conditions. However, when considering the sample assemblage as the reactant body, the shrinkage dimension of the reaction interface is different depending on the sampling conditions. It is generally accepted that the Arrhenius parameters determined by the CR plot vary depending on g(α) even if statistically significant linear correlations are observed.[86,87] Therefore, the Arrhenius parameters determined by the CR plot can have a certain physical meaning only when the physicogeometrical characteristics are elucidated and a most appropriate kinetic model is selected. Nevertheless, the kinetic triplet, i.e., Ea,tr, Atr, and g(αtr), determined by the CR plot can be used for simulating the kinetic curves, although the applicability of the determined kinetic parameters to the kinetic prediction under different conditions should be further critically examined. Figure compares the experimental kinetic curve (Figure b) and the kinetic curves calculated using the kinetic triplet listed in Table . The three different sets of the kinetic parameters satisfactorily reproduced the experimental kinetic curve.

Table 2

Arrhenius Parameters for the Aragonite–Calcite Transformation Determined by the Coats and Redfern Plot by Adopting Several g(α) Values

function	g(αtr)	Ea,tr/kJ mol–1	Atr/s–1	–γa
JMA(1)	–ln(1 – αtr)	247.5 ± 6.8	(1.47 ± 0.01) × 1015	0.9985
JMA(1.5)	[−ln(1 – αtr)]2/3	161.0 ± 4.5	(7.23 ± 0.01) × 108	0.9984
R(3)	1 – (1 – αtr)1/3	221.6 ± 7.7	(5.43 ± 0.01) × 1012	0.9976

Correlation coefficient of the linear regression analysis.

Figure 11

Comparison of the experimental data points with the simulated kinetic curves calculated using the kinetic triplet determined by the Coats and Redfern plots.

Mutual Relation between the Thermal Dehydration and Aragonite–Calcite Transformation

The evolution of water vapor observed before the thermal decomposition of calcite during linearly heating the FW-pearl was characterized as an overlapping three-step process. Meanwhile, the A–C transformation occurs in the middle of the thermal dehydration of included water at temperatures ranging between the second and third dehydration steps. FW-pearl is defined as the construction of polygonal plates composed of an agglomerate of aragonite crystals, as previously reported for the synthetic aragonite[34] and biomineralized aragonite such as coral aragonite.[48] The included water may be present at the interstices between the aragonite plates and between aragonite crystals. Therefore, the following model for a mutual relationship between the thermal dehydration of included water and A–C transformation was proposed.[48] The first dehydration step is attributed to the included water between the aragonite plates, which enables the subsequent dehydration of the included water between the aragonite crystals in the aragonite plate. Prior to the A–C transformation, an increase in the lattice spacing of the aragonite crystal occurs.[39] Partial dehydration of the included water in the aragonite plate probably provides spaces required for the expansion of the crystal lattice. Consequently, the second dehydration step triggers the A–C transformation. In turn, the A–C transformation enhances the thermal dehydration of the residual included water in the aragonite plates, which appears to be the third dehydration step.

Regardless of the dehydration steps, the movement of the reaction interface controlled by the diffusional removal of water vapor in a contracting geometry scheme is the characteristic kinetic behavior for the thermal dehydration of included water. Therefore, the preparation for the A–C transformation advances with geometrical restrictions of the thermal dehydration. Generally, bulk nucleation and growth, as expressed by the conventional JMA(m) model, are expected for the structural phase transitions. However, the contracting geometry-type model controlled by the constant rate advance of the transformation interface, as expressed by the R(n) model, accurately describes the apparent kinetic behavior of the A–C transformation. The kinetic behaviors of the thermal dehydration process and A–C transformation revealed in this study also support the physicogeometrical model considering the mutual interaction between the thermal dehydration of included water and the A–C transformation in biomineralized aragonites.

Conclusions

As in several biomineralized aragonites, the thermally induced A–C transformation in FW-pearl occurred in the temperature region of approximately 650–750 K by overlapping with the thermal dehydration of included water in the construction. The thermal dehydration of included water was characterized by partially overlapping three dehydration steps. All dehydration steps were kinetically controlled by diffusional removal of water molecules through the construction of aragonite crystals, in which the apparent Ea, values increased as the dehydration step advances, whereas the A values exhibited the opposite variation trend. Notably, the second dehydration step accounted for approximately 73% of the mass-loss value for the overall mass-loss value observed during the thermal dehydration of included water. Conversely, the A–C transformation was characterized by a single-step process, exhibiting smooth change in the fractional transition as a function of time and temperature under the isothermal and linear nonisothermal conditions, respectively. By comparing the temperature regions of the multistep thermal dehydration of the included water and the A–C transformation on the temperature axis of linearly increasing temperatures, the temperature region of the A–C transformation was positioned across the second-half of the second dehydration step to the first-half of the third dehydration step. From the time sequence of the overall phenomena, the A–C transformation induced by the second dehydration step and the subsequent third dehydration step induced by the A–C transformation are deduced as the cause and effect relations. In a physicogeometrical viewpoint, the thermal dehydration of included water occurs in a scheme of contracting geometry because the diffusional removal of water vapor is needed. Therefore, the potential sites of the A–C transformation in the construction of the biomineralized aragonite are produced by the movement of the reaction interface of the thermal dehydration of included water (second dehydration step). Although the microscopic mechanism of the A–C transformation is explained by the nucleation and growth mechanism as previously discussed in several studies, the overall rate behavior of the A–C transformation in the construction of biomineralized aragonite can be controlled by the contracting geometry scheme. This physicogeometrical kinetic model considering the mutual kinetic relationship of the thermal dehydration of included water and the A–C transformation is supported by the kinetic analysis of the A–C transformation, resulting in a possible physicogeometrical constraint described by the phase boundary-controlled model (R(n)).