Interplay between Thermally Induced Aragonite–Calcite Transformation and Multistep Dehydration in a Seawater Spiral Shell (Euplica scripta)

Abstract

While heating a seawater spiral shell (Euplica scripta), thermally induced aragonite–calcite (A–C) transformation occurred within the temperature region of multistep thermal dehydration. Here, the kinetic interplay between the A–C transformation and thermal dehydration was studied as a possible cause of the reduction in the A–C transformation temperatures. The kinetics of the A–C transformation was systematically investigated under isothermal conditions by powder X-ray diffractometry and under linear nonisothermal conditions by Fourier transform infrared spectroscopy. The thermal dehydration was characterized as a partially overlapping, three-step process by thermogravimetry–differential thermal analysis coupled with mass spectroscopy for the evolved gases. The A–C transformation occurred in the temperature range of the final part of the second dehydration step and the initial part of the third dehydration step. The kinetics of A–C transformation and thermal dehydration were characterized by contracting geometry-type models, in which the respective transformations were regulated by a constant linear advancement rate and diffusional removal of water vapor, respectively. Based on the kinetic results, the mutual interaction of those thermally induced processes is discussed as a possible cause of the reduction in the A–C transformation temperature.

1. Introduction

Aragonite is one of the most typical phases observed for biomineralized CaCO₃ [1]. After heating, aragonite transforms into calcite prior to the thermal decomposition of CaCO₃ [2,3,4,5,6,7,8]. In crystallographic terms, the aragonite–calcite (A–C) transformation has been explained by a reorientation of the CO₃ group, accompanied by a variation in the distribution of the Ca atom from approximately hexagonal to cubic, close packings [9,10]. In addition, a detectable increase in the unit-cell volume has been observed during heating of aragonite samples [10,11,12,13]. Notably, in biomineralized aragonite, the thermally induced A–C transformation occurs in a lower temperature range, compared with mineral aragonite [5,13,14]. A large deformation of the crystal lattice during A–C transformation has been observed in biomineralized aragonite [15,16,17], in which water vapor is released during A–C transformation [2,3,4,5,6,7,8]. Therefore, the mechanistic and kinetic relationships between thermally induced A–C transformation and dehydration can provide further insight into the thermally induced A–C transformation in biomineralized aragonite to elucidate the reduction in the A–C transformation temperature.

During laboratory synthesis of aragonite using a hydrothermal urea decomposition method, needle-like crystals formed a columnar crystal with a lamellar structure [8]. After heating the columnar aragonite crystals, splitting of the lamellar structure to form a cauliflower-like construction occurred during the A–C transformation. Simultaneously, water vapor was released during the morphological change. Thus, during aragonite construction, water molecules are expected to be trapped in the lamellar structure. A higher order of lamella structures forming a stacking structure of aragonite plates and polymeric materials has been observed in biomineralized aragonite [18,19,20,21]. Thus, thermal dehydration in biomineralized aragonite is expected to occur as a multistep process, accompanied by the decomposition of polymeric materials and release of water molecules included in the lamellar structure, as well as absorbed water. After linearly heating biomineralized aragonite, thermal dehydration occurs as a partially overlapping, multistep process [22,23]. In our previous studies [22,23], the multistep thermal dehydration of coral aragonite and freshwater pearl were kinetically characterized using an advanced kinetic computation of kinetic deconvolution analysis (KDA) [24,25,26,27,28], and the relationships between each thermal dehydration step and the A–C transformation were discussed by comparing the temperature regions of these transformations. However, further detailed kinetic information about A–C transformation is needed for discussing the relationship between the thermal dehydration processes and A–C transformation in a kinetic scheme. Herein, we focus on the kinetics of thermally induced A–C transformation by systematically collecting the kinetic data under isothermal conditions using powder X-ray diffractometry (XRD) and under linear nonisothermal conditions using Fourier transform infrared spectroscopy (FT-IR) using a seawater spiral shell (Euplica scripta). In addition, the multistep thermal dehydration process of the shell was traced using thermogravimetry (TG) and analyzed based on KDA. The interplay of these thermally induced processes is discussed based on the kinetic results.

The biomimetic mineralization process of CaCO₃ has been extensively studied for realizing highly functional materials in biominerals [29,30,31,32,33,34,35]. The fundamental studies of biomineralization processes in living organisms and of the specific functionality and reactivity of various biominerals have provided information for promoting biomimetic mineralization studies [36,37,38]. Considering that the mutual relationship between A–C transformation and thermal dehydration examined in this study can be a specific phenomenon attributed to the constructional characteristics and reactivity specific to the biomineral, a detailed understanding of the mechanistic and kinetic features provides fundamental information about the biominerals to be used in studies of biomimetic mineralization, in addition to a physicochemical understanding of A–C transformation.

2. Materials and Methods

2.1. Sample and Characterization

A seawater spiral shell (Euplica scripta), which is commercially available for handicrafts, was used as a sample of biomineralized aragonite (Figure S1 in Supplementary Information). The shells were classified into four categories in reference to the colors—brown, light brown, beige, and white—owing to differences in the degrees of natural blanching. The shells in each color classification were carefully ground using a stainless-steel mortar and pestle and sieved to different particle size fractions. The shell powders in the four different color classifications were characterized by energy dispersive X-ray (EDX) spectroscopy, XRD, FT-IR, and thermogravimetry (TG)/differential thermal analysis (DTA)–mass spectroscopy (MS). For the EDX spectroscopy, a pellet of the sample powders was prepared by mechanical pressing under a pressure of 8 MPa. The pellet was coated with a thin Pt layer by sputtering (JFC-1600, JEOL, Tokyo, Japan; 30 mA, 30 s). The sample surface was observed by scanning electron microscopy (SEM, JSM-6510, JEOL, Tokyo, Japan), and the EDX spectra were recorded using an instrument (x-act, Oxford Instruments, Tokyo, Japan) equipped with an SEM instrument. The XRD patterns were recorded using a diffractometer (RINT 2200V, Rigaku, Tokyo, Japan) by radiating Cu-K_α (40 kV, 20 mA) and scanning 2θ values from 5° to 60° at a scan speed of 4° min⁻¹ within a 0.02° interval. For FT-IR spectroscopy, the shell powders were quantitatively diluted to 10 wt% with KBr powder by mixing precisely weighed shell and KBr powders in an agate mortar with a pestle. The FT-IR spectra for each diluted sample were recorded using a spectrometer (FTIR 8400S, Shimadzu, Kyoto, Japan) with the diffuse reflectance method. Approximately 10 mg of each shell powder sample, weighted into a Pt pan (diameter, 5 mm; depth, 2.5 mm), were subjected to TG/DTA–MS measurements. Using a TG–DTA instrument (TG-8120, Thermoplus2 system, Rigaku, Tokyo, Japan), the sample was heated from room temperature to 1223 K at a heating rate (β) of 5 K min⁻¹ in a stream of dry helium gas at a flow rate (q_v) of 200 cm³ min⁻¹. During the TG–DTA measurements, a part of the outlet gas from the reaction chamber was continuously introduced into a quadrupole mass spectrometer (M-200QA, Anelva, Kanagawa, Japan) via a capillary tube (internal diameter, 75 μm; length, 0.7 m) heated at 500 K. The MS spectra of the outlet gas from the TG–DTA instrument were repeatedly recorded without breaks in the m/z range of 10–50 amu (EMSN, 1.0 mA; SEM, 1.0 kV). For the brown shell, cross-sectional surfaces of roughly crushed pieces of the shell and powdered sample particles were observed by SEM after the pieces were coated with a thin Pt layer by sputtering (30 mA, 30 s).

2.2. Investigation of Thermal Behavior

To obtain detailed information about the thermally induced changes, the brown shell powder in a sieved fraction within the range of 90–150 μm was used. The changes in the XRD patterns of the shell powder sample during thermal treatment were tracked using the RINT 2200V diffractometer equipped with a programable heating chamber (PTC-20A, Rigaku, Tokyo, Japan). The sample, fitted to a Pt plate sample holder by gentle pressing, was heated from room temperature to 1123 K at a β of 2 K min⁻¹ in a stream of dry N₂ gas at a q_v of 100 cm³ min⁻¹, during which isothermal holding sections for 15 min were inserted within a 50 K interval in the temperature range of 323–1123 K. The XRD patterns of the sample were recorded during each isothermal holding section under the same measurement conditions as those applied for the sample characterization at room temperature.

The TG–DTA measurements for the shell powder sample (brown shell; 90–150 μm) weighed in the Pt pan (initial mass (m₀), approximately 20.0 mg) were performed using a TG–DTA instrument (STA7300, TA7000 system, Hitachi High Tech, Tokyo, Japan) under different atmospheric conditions in a stream of dry N₂ gas or N₂–CO₂ mixed gas (20%-CO₂) at a q_v of 300 cm³ min⁻¹. Under both atmospheric conditions, the sample was heated from 303 to 1223 K at a β of 5 K min⁻¹.

2.3. Kinetic Data Measurement for the A–C Transformation

The A–C transformation of the shell powder sample (brown shell, 90–150 μm) at different temperatures was tracked by XRD. In a stream of dry N₂ gas (q_v = 100 cm³ min⁻¹), the sample press-fitted to the Pt plate was heated to a programed temperature (T = 643, 653, 663, or 673 K) at a β of 10 K min⁻¹, and the temperature was maintained until the transformation was completed, during which XRD measurements were repeated within a 15-min interval of the measurement starting time.

To obtain the heat-treated samples characterized by different conversion fractions (α_tr) of A–C transformation, approximately 20 mg of the shell powder in the Pt pan was heated from 303 K to temperatures within the range of 657–707 K at β values of 1, 3, 5, and 10 K min⁻¹ in a stream of N₂–CO₂ mixed gas (20%-CO₂) using a TG–DTA instrument (TG/DTA 220, SII). The thermally treated sample was recovered after naturally cooling to room temperature in the instrument. The heat-treated sample was quantitatively diluted to 10 wt% with KBr. The FT-IR spectra of the heat-treated samples were recorded using an FT-IR 8400S spectrometer under the measurement conditions identical to those applied during the characterization of the original sample.

2.4. Kinetic Data Measurement for the Multistep Thermal Dehydration

The kinetic behavior of multistep thermal dehydration was tracked using TG–DTA measurements (STA7300, TA7000 system, Hitachi High Tech) in a stream of N₂–CO₂ mixed gas (20%-CO₂). The sample (m₀ = 20.00 ± 0.04 mg; in a Pt pan) was heated from 303 to 1223 K at β values of 1, 2, 3, 5, 7, and 10 K min⁻¹.

3. Results and Discussion

3.1. Sample Characterization

Irrespective of the shell samples in different color groups, the major component elements were Ca, C, and O, although a detectable trace of Na was observed for all samples (Figure S2). The XRD patterns exhibited diffraction peaks attributed to aragonite (orthorhombic, space group (SG) = Pmcn(62), a = 4.9652, b = 7.9636, c = 5.7484, α = β = γ = 90.000, ICDD PDF 01-075-9982) [39,40] and calcite (trigonal, SG = R-3c(167), a = b = 4.9896, c = 17.0610, α = β = 90.000, γ = 120.000, ICDD PDF 00-047-1743) [41] (Figure S3). The mixed ratio of aragonite and calcite, determined using the Rietveld and reference intensity ratio methods, indicated that the more dilute color sample exhibited a greater content of calcite, as listed in Table S1. The brown shell sample exhibited the greatest content of the aragonite phase (95.3%). The shell samples with different colors exhibited IR absorption peaks attributable to vibration modes of CO₃²⁻ and O–H [42,43,44] (Figure S4). The presence of water molecules was confirmed by the O–H stretching vibration in the range of 2600–3600 cm⁻¹ and the H–O–H bending vibration at ~1650 cm⁻¹ (Figure S4a). The v₄ mode of CO₃²⁻ appeared as two split absorption peaks at 700 and 713 cm⁻¹, characteristic of the aragonite phase. The other CO₃²⁻ vibration modes of v₂, v₁, and v₃ were observed at 863, 1082, and 1504 cm⁻¹, respectively. Regarding the two split absorption peaks at 700 and 713 cm⁻¹, the ratio of absorbance of these peaks varied with the shell samples in different color groups, in which the ratio of the peak at 713 cm⁻¹ increased as the shell color was diluted (Figure S4b). This finding can be interpreted in relation to the increase in the content ratio of calcite because the calcite phase does not exbibit the absorption peak at 700 cm⁻¹. The content ratio of aragonite and calcite was determined from the ratio of the area of IR absorption peaks [43,44,45,46,47,48,49] (Figure S5). After the FT-IR spectra were converted to the absorption spectra using the Kubelka–Munk conversion, the specific double peaks with maxima at 700 and 713 cm⁻¹ were deconvoluted using the Lorentzian function (Equation (S1)) (Figure S5a). Thereafter, the content ratio of aragonite and calcite was determined using a calibration curve method with reference to the peak areas attributed to aragonite and calcite (Figure S5b). This procedure was detailed in our previous study [23] and is outlined in the Supplementary Information. The content of aragonite determined from the IR spectra is also listed in Table S1. The content ratios of aragonite determined by XRD and FT-IR spectroscopy were practically identical, and the brown sample exhibited the greatest content of aragonite.

Figures S6 and S7 show the SEM images of the cross-sectional surfaces of the roughly crushed brown shell and the powdered sample particles, respectively. The Euplica scripta shell comprised outer, middle, and inner layers, as generally observed for spiral shells [18,19,20,21]. The middle layer with a thickness of approximately 20 μm had a construction built with plate-like first-order lamella (Figure S6a). The first-order lamella was constructed by the second-order lamella and further by the third-order lamella, which is the basic building block (Figure S6b). A similar construction was observed for the inner layer (Figure S6c,d). In the powdered sample, submicrometer-sized particles generated by crushing adhered to the surface of each particle (Figure S7a). The constructional lamellar structures of the shell were exposed on the surfaces of the main body of the particles (Figure S7b).

3.2. Thermal Behavior

Figure 1 shows the results of the TG/DTA–MS measurements for the different shell powder samples. As shown for the brown sample, the thermal decomposition of CaCO₃ accompanied by the evolution of CO₂ was observed as the major mass loss process while heating the samples (Figure 1a). Notably, preliminary to the thermal decomposition of CaCO₃, a detectable mass loss accompanied by the evolution of water vapor was observed in the temperature range of 400–800 K. The sample with the deep colors exhibited large mass loss values, owing to preliminary thermal dehydration (Figure 1b). This outcome was confirmed by the large peak area of the MS thermogram for m/z = 18 of the deep-colored samples (Figure 1c). In the deep-colored samples, the major peak of m/z = 18 was accompanied by a small but detectable peak of m/z = 44. Because the temperature region of the thermal dehydration is much lower than the thermal decomposition of CaCO₃, the simultaneous evolution of water vapor and CO₂ may be attributed to the thermal degradation of component polymeric materials. In our previous study of biomineralized calcite, i.e., avian eggshell [50], similar simultaneous evolution of water vapor and CO₂ was observed as a part of preliminary dehydration process occurring prior to the thermal decomposition of calcite, for which the thermal degradation of fibrous protein substances was microscopically confirmed in the corresponding temperature range. It is expected that the degradation of component polymeric materials contributes to a part of the multistep thermal dehydration of the shell samples. It is deduced from the comparisons of the A–C composition and thermal dehydration behavior between differently colored shell samples that the natural whitening resulted from weathering of the shell, leading to the degradation of polymeric material and partial A–C transformation. Therefore, the brown shell, characterized by the least content of calcite and the largest mass loss value during the preliminary dehydration process, was selected for investigating the relationship between the A–C transformation and thermal dehydration.

The changes in the XRD pattern while heating the brown sample powder using the stepwise isothermal heating mode indicated that A–C transformation occurred in the temperature range of 523–723 K (Figure S8), followed by thermal decomposition of calcite to form CaO in the temperature range of 923–1023 K. The temperature range of A–C transformation was covered by the temperature range of the thermal dehydration process, as reported for biomineralized aragonite samples [22,23]. When the sample was heated in a stream of N₂–CO₂ mixed gas characterized by a high partial pressure of CO₂, only the mass loss process, owing to the thermal decomposition of calcite, shifted to high temperatures without detectable changes in the mass loss process of preliminary thermal dehydration (Figure S9). As a result, the temperature ranges of the thermal dehydration and the subsequent thermal decomposition of calcite were experimentally separated, which was desirable for analyzing the kinetics of the thermal dehydration.

3.3. Kinetics of the A–C Transformation

A–C transformation at different temperatures was traced by XRD (Figure 2). The contents of aragonite and calcite at each duration of isothermal heat treatment were determined by analyzing each XRD pattern, from which the α_tr value at each duration was calculated. The α_tr versus time plots at different temperatures were used as the kinetic data for A–C transformation (Figure 3). The time-dependent change in the α_tr values and its temperature dependence indicated that it was a kinetically controlled process.

The experimentally determined kinetic data (symbols in Figure 3) were analyzed using conventional kinetic calculation procedures for solid-state reactions under isothermal conditions (Figure 4). The rate constant (k_tr) for A–C transformation at each temperature was determined by examining the linear correlations of the kinetic model function g(α_tr) versus time plots using different g(α_tr), as listed in Table S2 [51].

$$g\left({\alpha }_{\mathrm{t}\mathrm{r}}\right)=k_{\mathrm{t}\mathrm{r}}t$$

(1)

The most statistically significant linear correlation of the g(α_tr) versus t plot was confirmed when the first-order reaction model (F(1): g(α_tr) = −ln(1 − α_tr)) or the three-dimensional phase boundary controlled reaction (R(3): g(α_tr) = 1 − (1 − α_tr)^1/3) was used, as shown in Figure 4a and b, respectively. The k_tr values are listed in Table S3. The Arrhenius-type temperature dependence was applicable to the k_tr values (Figure 4c).

$$\ln k_{\mathrm{t}\mathrm{r}}=\mathrm{l}\mathrm{n}{A}_{\mathrm{t}\mathrm{r}}-\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT},$$

(2)

where A_tr and E_a,tr are the preexponential factor and apparent activation energy for the transformation, respectively, and R is the gas constant. The Arrhenius plots for the k_tr values, determined by assuming F(1) and R(3) to be suitable kinetic model functions, exhibited a parallel shift with practically the same slope. The shift was due to the A_tr values, which were related to the geometrical constraints assumed in the respective g(α_tr).

Table 1. The Arrhenius parameters for the A–C transformation under isothermal conditions.

g(αtr)	Ea,tr/kJ mol−1	ln(Atr/s−1)	−γ a
F(1)	281.1 ± 6.6	42.7 ± 1.3	0.9994
R(3)	271.7 ± 6.9	39.6 ± 1.3	0.9993

^a Correlation coefficient of the linear regression analysis of the Arrhenius plot.

summarizes the as-determined Arrhenius parameters. The overall kinetic curves for A–C transformation at each temperature were simulated using these kinetic parameters (Figure 3). The overall kinetic curves based on the R(3) model exhibited a better fit to the experimental data points in comparison with those based on the F(1) model.

Figure 5 shows the FT-IR spectra of the sample preheated to different temperatures at different β values. Irrespective of β, the split peaks at 700 and 713 cm⁻¹ attributable to the v₄ mode of CO₃²⁻ gradually converged to a single peak at 713 cm⁻¹ with an increase in the temperature, exhibiting the transformation from aragonite to calcite. The α_tr value of the preheated sample was determined from each spectrum by the quantitative analysis of the peak areas of the split peaks using the calibration curve method, as used for the sample characterization. The changes in the α_tr values with preheated temperature were drawn at each β value, as shown in Figure 6.

The series of data points of α_tr versus T at each β value in Figure 6 were used as kinetic data in the integral form under linearly increasing temperature conditions. The kinetic data at each β value were analyzed using the Coats and Redfern method [52].

$$\mathrm{l}\mathrm{n}\frac{g\left({\alpha }_{\mathrm{t}\mathrm{r}}\right)}{T^2}=\mathrm{l}\mathrm{n}\left[\frac{A_{\mathrm{t}\mathrm{r}}R}{\beta E_{\mathrm{a},\mathrm{t}\mathrm{r}}}\left(1-\frac{2RT}{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}\right)\right]-\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT}$$

(3)

The statistically significant linear correlation of ln[g(α_tr)/T²] versus T⁻¹ was obtained when the F(1) or R(3) model was used as g(α_tr), irrespective of the β value (Figure S10). The Arrhenius parameters determined for A–C transformation at each β value are listed in Table S4. As observed for solid-state reactions, the E_a,tr and ln A_tr values determined using the Coats and Redfern method decreased with an increase in the β value [53,54,55,56]. In addition, the E_a,tr and ln A_tr values at a β value calculated using different kinetic models were different [57,58]. Furthermore, these E_a,tr and ln A_tr values at different β values and kinetic models exhibited a linear correlation of ln A_tr versus E_a,tr (Figure S11), known as the kinetic compensation effect (KCE) [59,60,61,62,63,64,65,66]. Even so, the kinetic triplets (E_a,tr, ln A_tr, g(α_tr)) obtained by assuming F(1) and R(3) reproduced the practically identical kinetic curves at each β value, as shown in Figure 6.

The kinetic curves for A–C transformation under isothermal and linear nonisothermal conditions, simulated using the kinetic parameters determined from the changes in the XRD patterns and FT-IR spectra, respectively, were subjected to isoconversional kinetic analysis, as shown in Figure 7. Kinetic analysis was performed based on the differential kinetic equation [51]:

$$\frac{\mathrm{d}{\alpha }_{\mathrm{t}\mathrm{r}}}{\mathrm{d}t}=A_{\mathrm{t}\mathrm{r}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT}\right)f\left({\alpha }_{\mathrm{t}\mathrm{r}}\right),$$

(4)

where f(α_tr) is the kinetic model function in differential form. The Friedman plots of ln(dα_tr/dt) versus T⁻¹ at selected α_tr values were separately examined for the transformations under isothermal and linear nonisothermal conditions, according to the logarithmic form of Equation (4) [67]:

$$\mathrm{l}\mathrm{n}\left(\frac{\mathrm{d}{\alpha }_{\mathrm{t}\mathrm{r}}}{\mathrm{d}t}\right)=\mathrm{l}\mathrm{n}\left[A_{\mathrm{t}\mathrm{r}}f\left({\alpha }_{\mathrm{t}\mathrm{r}}\right)\right]-\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT}.$$

(5)

In each heating mode, the Friedman plots [67] exhibited statistically significant linear correlations with the correlation coefficients better than −0.99 at different α_tr values over 0.01 ≤ α_tr ≤ 0.99 (Figure 7a). Graphically, the Friedman plots for A–C transformation under isothermal and linear nonisothermal conditions show a parallel translation, resulting from different sampling conditions. However, the Friedman plots for the transformations under isothermal and linear nonisothermal conditions at a selected α_tr value exhibited different slopes and intercepts. This behavior can be interpreted as a typical KCE caused by the different experimental conditions of kinetic data measurements [59,60,61,62,63,64,65,66]. The E_a,tr variation trends were largely different between the transformations under isothermal and linear nonisothermal conditions (Figure 7b). Under isothermal conditions, the constant E_a,tr value of 271.7 ± 0.1 kJ mol⁻¹ was obtained during the reaction, which was the same as the value used for the simulation of the isothermal kinetic curves. Conversely, the E_a,tr values systematically decreased under linear nonisothermal conditions as the transformation proceeded; it rapidly decreased from approximately 440 to 330 kJ mol⁻¹ in the initial stage of the transformation and subsequently decreased gradually to 300 kJ mol⁻¹ at the end of the transformation, with the average E_a,tr value of 312.5 ± 9.1 kJ mol⁻¹ (0.3 ≤ α_tr ≤ 0.9). This variation in the E_a,tr values determined by the isoconversional method was attributed to the variation of E_a,tr value depending on β values obtained using the Coats and Redfern method (Figure S10 and Table S4).

The experimental master plots for transformation under isothermal and linear nonisothermal conditions were drawn by calculating the hypothetical reaction rate (dα_tr/dθ_tr) at an infinite temperature using the average E_a,tr values of 271.7 ± 0.1 kJ mol⁻¹ (0.01 ≤ α_tr ≤ 0.99) and 312.5 ± 9.1 kJ mol⁻¹ (0.3 ≤ α_tr ≤ 0.9), respectively [68,69,70,71,72,73,74,75].

$$\frac{\mathrm{d}{\alpha }_{\mathrm{t}\mathrm{r}}}{\mathrm{d}{\theta }_{\mathrm{t}\mathrm{r}}}=\left(\frac{\mathrm{d}{\alpha }_{\mathrm{t}\mathrm{r}}}{\mathrm{d}t}\right)\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT}\right)=A_{\mathrm{t}\mathrm{r}}f\left({\alpha }_{\mathrm{t}\mathrm{r}}\right)\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{with}\hspace{1em}\hspace{1em}\hspace{1em}{\theta }_{\mathrm{t}\mathrm{r}}={\int }_0^t\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{E_{\mathrm{a},\mathrm{t}\mathrm{r}}}{RT}\right)\mathrm{d}t,$$

(6)

where θ_tr is Ozawa’s generalized time [74,75] for A–C transformation. Under isothermal conditions, the experimental master plot exhibited a deceleration process that fit perfectly using the R(3) model with an A_tr value of (1.63 ± 0.01) × 10¹⁷ s⁻¹, which was identical to that determined by conventional isothermal kinetic analysis for the XRD data. The experimental master plot for transformation under linear nonisothermal conditions exhibited a completely different shape from that of isothermal transformation, exhibiting the maximum rate midway through the transformation at α_tr = 0.42. The experimental master plot was fitted using an empirical kinetic model known as the Šesták–Berggren model (SB(m, n, p)) because of the high flexibility to fit different rate behaviors [76,77,78].

$$\mathrm{S}\mathrm{B}\left(m,n,p\right):f\left({\alpha }_{\mathrm{t}\mathrm{r}}\right)={\alpha }^m{\left(1-\alpha \right)}^n{\left[-\mathrm{l}\mathrm{n}\left(1-\alpha \right)\right]}^p$$

(7)

The experimental master plot was perfectly fitted using SB(0.06, 0.70, 0.33) with the A_tr value of (4.24 ± 0.01) × 10²¹ s⁻¹.

Table 2. Kinetic parameters for the A–C transformation under isothermal and linear nonisothermal conditions.

Heating Condition	Ea,tr /kJ mol−1	Atr/s−1	f(αtr)	R2, a
Isothermal	271.7 ± 0.1	(1.63 ± 0.01) × 1017	R(2.99 ± 0.01)	>0.9999
Nonisothermal	312.5 ± 9.1	(4.24 ± 0.01) × 1021	SB(0.06 ± 0.01, 0.70 ± 0.01, 0.33 ± 0.01)	>0.9999

^a Determination coefficient of the nonlinear least-squares analysis for fitting the experimental master plot using f(α_tr).

summarizes the kinetic results obtained by isoconversional kinetic analysis and the subsequent master plot method for simulated kinetic curves under isothermal and linear nonisothermal conditions. The different rate behaviors between the A–C transformations under isothermal and linear nonisothermal conditions, revealed by the experimental master plots, should be interpreted by considering the different sampling conditions for the measurements of kinetic data. Furthermore, E_a,tr and A_tr values exhibit mutually dependent variations between the transformations under isothermal and linear nonisothermal conditions along KCE [59,60,61,62,63,64,65,66].

3.4. Kinetics of the Multistep Thermal Dehydration

Figure 8 shows TG–derivative TG (DTG) curves for thermal dehydration of the brown shell powder sample (m₀ = 20.00 ± 0.04 mg) recorded at different β values in a stream of N₂–CO₂ mixed gas (20%-CO₂, q_v = 300 cm³ min⁻¹). Three distinguishable DTG peaks appeared by partial overlapping. The first mass loss step initiated near room temperature and may be attributed to the dehydration of absorbed water. The major mass loss process in multistep dehydration, observed in the temperature range of 450–700 K (second mass loss step), is the process accompanied by detectable evolution of CO₂ and likely originated from thermal degradation of the component polymeric materials. The third mass loss step was observed at temperatures higher than the A–C transformation and probably were due to the evaporation of water molecules trapped in the lamellar structure of aragonite crystals [8]. As a preliminary kinetic estimation, the overall process of thermal dehydration was subjected to formal kinetic analysis based on the isoconversional kinetic relationship (Figure S12). The TG–DTG curves were converted to kinetic curves by normalizing the mass loss value to the fractional reaction (α) with reference to the total mass loss value during the overall thermal dehydration process (Figure S12a). The Friedman plots applied to overall thermal dehydration exhibited variations in their slopes in three ranges of α, corresponding to each DTG peak (Figure S12b). The apparent activation energy (E_a) for thermal dehydration varied among three α ranges of α ≤ 0.15, 0.15 ≤ α ≤ 0.8, and 0.8 ≤ α (Figure S12c). Therefore, the feature of the DTG curves and apparent results of the Friedman plots supported the partially overlapping three-step reaction for thermal dehydration.

To separate the overlapping reaction steps, an empirical analysis of the DTG peak deconvolution using a statistical function (F_i(t)) was performed [25,26,27,28,79,80].

$$\frac{\mathrm{d}m}{\mathrm{d}t}=\sum _{i=1}^N{F}_i\left(t\right),$$

(8)

where N is the total number of peaks, and i is the reaction step. After testing the mathematical deconvolution analysis (MDA) using available functions, the logistic power peak function (Equation (S4)) was selected as a suitable F_i(t) for multistep thermal dehydration. From the MDA results, the contributions (c_i) of each reaction step were estimated from the area of the deconvoluted peaks, and the kinetic curves at different β values for each reaction step were obtained. The kinetic curves for each reaction step were formally analyzed using the Friedman plot and subsequent master plot method. The MDA results and subsequent formal kinetic analysis for each reaction step are detailed in the Supplementary Information (Figures S13–S17, Table S5).

When the multistep process comprised the kinetically independent reaction steps, the overall kinetics was expressed by a cumulative kinetic equation [24,25,26,27,28].

$$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=\sum _{i=1}^N{c}_i{A}_i\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{E_{\mathrm{a},i}}{RT}\right)f_i\left({\alpha }_i\right)\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{with}\hspace{1em}\hspace{1em}\hspace{1em}\sum _{i=1}^N{c}_i=1\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{and}\hspace{1em}\hspace{1em}\hspace{1em}\sum _{i=1}^N{c}_i{\alpha }_i=\alpha ,$$

(9)

where α_i is the fractional reaction of each reaction’s step i. Based on the cumulative kinetic equation with SB(m, n, p) for f_i(α_i), the preliminary determined kinetic parameters via MDA and the subsequent formal kinetic analysis (Table S5) were optimized through nonlinear least-squares analysis to minimize the square sum (F) of the residue when fitting the overall experimental kinetic curve using the curve calculated according to Equation (9) [24,25,26,27,28].

$$F=\sum _{j=1}^M{\left[{\left(\frac{\mathrm{d}\alpha }{\mathrm{d}t}\right)}_{\mathrm{e}\mathrm{x}\mathrm{p},j}-{\left(\frac{\mathrm{d}\alpha }{\mathrm{d}t}\right)}_{\mathrm{c}\mathrm{a}\mathrm{l},j}\right]}^2,$$

(10)

where M is the total number of data points in an experimental kinetic curve. The kinetic calculation based on Equation (9) is called as KDA. Figure 9 shows the results of KDA for multistep thermal dehydration. Statistically significant fits were achieved as the partial overlapping of three reaction steps via KDA irrespective of the experimental kinetic curves at different β values (Figure 9a), and the optimized kinetic parameters for each reaction step did not change among the results for the different β values.

Table 3. Optimized kinetic parameters for multistep thermal dehydration (determination coefficient R² = 0.9968 ± 0.0017).

i	ci	Ea,i/kJ mol−1	Ai/s−1	${\mathit{f}}_{\mathit{i}}\left({\mathit{\alpha }}_{\mathit{i}}\right)={{\mathit{\alpha }}_{\mathit{i}}}^{{\mathit{m}}_{\mathit{i}}}{\left(1-{\mathit{\alpha }}_{\mathit{i}}\right)}^{{\mathit{n}}_{\mathit{i}}}{\left[-\mathbf{l}\mathbf{n}\left(1-{\mathit{\alpha }}_{\mathit{i}}\right)\right]}^{{\mathit{p}}_{\mathit{i}}}$
				mi	ni	pi
1	0.10 ± 0.01	114.9 ± 1.6	(1.47 ± 0.07) × 1016	5.84 ± 0.72	1.85 ± 0.14	−5.80 ± 0.67
2	0.77 ± 0.02	129.1 ± 1.0	(8.19 ± 0.40) × 1010	9.25 ± 0.76	0.73 ± 0.23	−9.80 ± 0.66
3	0.13 ± 0.01	339.1 ± 4.0	(1.55 ± 0.01) × 1013	−28.85 ± 2.12	8.55 ± 0.90	20.71 ± 2.05

lists the optimized kinetic parameters for each reaction step, averaged over the values determined for different β values. Although the kinetic exponents in SB(m, n, p) exhibited unrealistic values that were not expected for the simple physico-geometrical reaction models, the kinetic features expressed by the optimized kinetic exponents were graphically interpreted as the diffusion-controlled-type processes with a contracting-geometry scheme irrespective of the reaction step because each process was characterized by the deceleration process with a concave shape in f_i(α_i)/f_i(0.5) versus α_i plots (Figure 9b).

3.5. Kinetic Relationship between A–C Transformation and Multistep Thermal Dehydration

Figure 10 compares the kinetic curves the A–C transformation and the component reaction steps of thermal dehydration, simulated for the processes at a fixed β of 5 K min⁻¹. The first dehydration step was positioned at a considerably lower temperature than the temperature region of A–C transformation, and the contribution was limited, i.e., c₁ = 0.10. Therefore, a direct correlation between A–C transformation and the first dehydration step was not expected. A–C transformation occurred at the final stage of the second dehydration step and the initial stage of the third dehydration step. The relationships of the processes along the temperature coordinate empirically showed that the second dehydration step triggered A–C transformation, which resembles the crystallization of hydrated amorphous compounds, such as hydrated ZnO₂ and TiO₂ [81,82]. Conversely, A–C transformation triggered the third dehydration step, in which liberated water molecules accompanied by A–C transformation were removed through diffusion in the third dehydration step.

A simple physico-geometrical model of the interrelationship between A–C transformation and thermal dehydration in biomineralized aragonite was proposed, as shown in Figure 11. Stacks of aragonite plates were the common architecture of many biomineralized aragonites, in which the plate comprised aragonite crystals with lamellar structures and stacked with polymeric materials [18,19,20,21]. Multistep thermal dehydration initiated by the evaporation of absorbed water with c₁ = 0.10. The second dehydration step was the major process in multistep thermal dehydration with c₂ = 0.77, which is attributed to thermal degradation of polymeric materials positioned between aragonite crystals. Thermal degradation of polymeric materials can produce the space for the volume increase in aragonite crystals [10,11,12]. A–C transformation of the biomineralized aragonite occurred at a low temperature, compared with that of mineral aragonite [5,13,14]. The spaces produced by thermal degradation of polymeric materials can allow for a volume increase in the aragonite unit cell and A–C transformation. In addition, there are still water molecules trapped in the aragonite crystals, which is later released during the third dehydration step with c₃ = 0.13. The possible increase in the internal pressure of aragonite crystal construction with increasing temperature due to the trapped water can be an alternative cause promoting A–C transformation. The water molecules trapped in the aragonite crystal construction were released by A–C transformation and removed via diffusion. All component thermal dehydration steps were constrained by the geometry of the aragonite constructions. Thus, it was expected that A–C transformation in biomineralized aragonite could not occur in a manner of random nucleation and growth across the bulk because the formation of the reactive sites for A–C transformation were geometrically constrained in a contacting-geometry scheme.

4. Conclusions

A–C transformation of biomineralized aragonite originated from a seawater spiral shell (Euplica scripta), occurring in a temperature range of 650–710 K when it was linearly heated. The temperature region of A–C transformation was covered by multistep thermal dehydration. The mutual relationship between A–C transformation and thermal dehydration was investigated by revealing the kinetic features of these two phenomena. The rate of A–C transformation exhibited significant temperature dependence; therefore, the process was analyzed as a kinetic process via formal kinetic calculation procedures based on the kinetic data obtained using high-temperature XRD under isothermal conditions at different temperatures and using FT-IR spectroscopy for a series of samples thermally treated under linear nonisothermal conditions at different β values. Under isothermal and linear nonisothermal conditions, the overall kinetic behavior of A–C transformation was described using a kinetic model of the contracting geometry type. The E_a,tr values were determined to be 271.7 ± 0.1 and 312.5 ± 9.1 kJ mol⁻¹ under isothermal and linear nonisothermal conditions, respectively. Thermal dehydration was characterized as a partially overlapping three-step process under linear nonisothermal conditions. The first to third mass loss steps were interpreted as attributable to dehydration of absorbed water, degradation of the component polymeric materials, and release of trapped water in the aragonite crystal construction, respectively. All component reaction steps of multistep thermal dehydration exhibited diffusion controlled kinetic behaviors constrained by the contracting geometry with E_a values of 114.9 ± 1.6, 129.1 ± 1.0, and 339.1 ± 4.0 kJ mol⁻¹ for the first to third mass loss steps, respectively. A–C transformation occurred in the reaction tail of the second thermal dehydration step and the initial stage of the third thermal dehydration step. The cause-and-effect relationship between A–C transformation and thermal dehydration was expected from similar geometrical constraints and described by a simple physico-geometrical model as follows. The second reaction step of thermal dehydration, characterized as a major dehydration process with the largest contribution to overall thermal dehydration and attributed to thermal degradation of the component polymeric materials, produced a space required for the expansion of the aragonite crystal lattice and subsequent A–C transformation. Conversely, the A–C transformation and subsequent crystal growth of calcite promoted the release of trapped water molecules, occurring during the third reaction step of thermal dehydration. Considered that a similar kinetic relationship between A–C transformation and thermal dehydration has been observed for different biomineralized aragonites, the mutually dependent phenomena should be considered a cause of the variation in the temperature region of A–C transformation among different aragonite materials.