Thermal behaviour and kinetics of dehydration in air

Eur. J. Mineral. 2009, 21, 985–993 Published online September 2009

Thermal behaviour and kinetics of dehydration in air of bassanite, calcium sulphate hemihydrate (CaSO40.5H2O), from X-ray powder diffraction PAOLO BALLIRANO* and ELISA MELIS

Dipartimento di Scienze della Terra, Sapienza Universita` di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy *Corresponding author, e-mail: [email protected] Abstract: Thermal behaviour and kinetics of dehydration in air of bassanite (calcium sulphate hemihydrate, CaSO40.5H2O) have been investigated in situ real-time using laboratory parallel-beam X-ray powder diffraction data. Thermal expansion has been analyzed between 303 and 383 K at increments of 5 K. The bassanite ! g-anhydrite conversion starts at 388 K and is completed at 408 K. Thermal expansion of hemihydrate is isotropic and not related to the expansion of CaO8–9 polyhedra. Lattice parameters and volume dependence from T is linear within the studied temperature range. Kinetics of dehydration has been investigated from isothermal diffraction data collected at 10 temperatures between 378 and 423 K with steps of 5 K using a fresh sample at each temperature. Transformed fraction a vs. t curves were fitted with seven different kinetic models. The best fit was found for the Avrami-Erofe’ev equation that provided an empirical activation energy Ea of the process of 73(5) kJ/mol. Ea was found to be substantially independent from the kinetic model selected. Key-words: bassanite, CaSO40.5H2O, thermal behaviour, kinetics of dehydration, X-ray powder diffraction, Rietveld method. eschweizerbartxxx author

1. Introduction Bassanite (CaSO40.5H2O) is a metastable phase (Freyer & Voigt, 2003; Mirwald, 2008) whose rare natural occurrence has been recently reported (Tiemann et al., 2002; Mees & Stoops, 2003). Under atmospheric pressure conditions, dehydration of gypsum at temperatures smaller than ca. 373 K produces sub-hydrate phases CaSO4nH2O with 0.5 n , 1 and a further heating produces g-anhydrite (see for example Ballirano & Melis, 2009a). Despite the publication of several studies devoted to the crystal chemical characterization of different subhydrate phases, considerable debate persists on their stability and on their existence itself. Moreover, the maximum water content and the position of water molecules within the structures have been discussed controversially. As a further complication, nomenclature has been often used in unclear way. For a review of early structural reference data on subhydrates see Ballirano et al. (2001). Among the other sub-hydrates, a- and b-hemihydrate have been thoroughly investigated mainly because of their relevance for the chemistry of cements. a-hemihydrate is formed by dehydration of gypsum in acidic aqueous suspension or at hydrothermal conditions in presence of electrolytes. b-hemihydrate is formed by dehydration of gypsum in a low water vapour atmosphere at T . 373 K or by re-hydration of g-anhydrite at low relative humidity

condition (Freyer & Voigt, 2003; Ballirano & Melis, 2009a). It corresponds to the natural phase bassanite. The structure of all the phases pertaining to the CaSO4H2O system is based on chains of alternating edge-sharing, SO4 tetrahedra and CaO8 dodecahedra extending along the c direction. In g-anhydrite and sub-hydrates the chains are arranged to form channels eventually housing guest water molecules. Winkler (1996), by neutron spectroscopic investigations, has reported that at room temperature the water molecules of bassanite are dynamically disordered, because of the weak coupling of the water molecules and the framework, and indicating for the disordering process an activation energy of 28 kJ/mol. Voigtla¨nder et al. (2003) performed experiments using high-resolution synchrotron radiation powder diffraction and neutron powder diffraction techniques pointing out that the thermal expansion of bassanite in the 10–298 K temperature range has an isotropic behaviour consistent with that of g-anhydrite (Ballirano & Melis, 2009b). Moreover, Voigtla¨nder et al. (2003) reported that the atomic coordinates of both the framework atoms and the oxygen atoms of the water molecules are substantially unchanged with increasing temperature. Very recently, Christensen et al. (2008) have published a synchrotron radiation powder diffraction investigation focused on the phase conversions in the CaSO4-H2O system. They confirmed the structure of bassanite (corresponding to the b-hemihydrate, CaSO40.5H2O of 0935-1221/09/0021-1973 $ 4.05

DOI: 10.1127/0935-1221/2009/0021-1973

# 2009 E. Schweizerbart’sche Verlagsbuchhandlung, D-70176 Stuttgart

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P. Ballirano, E. Melis

Table 1. List of different activation energy determinations for the dehydration process of bassanite. Author McAdie (1964) McConnell (1965) Ball & Urie (1970) Sarma et al. (1998) Borrachero et al. (2008)

Ea (kJ/mol)

Analytical method Thermogravimetry Thermogravimetry Thermogravimetry Raman spectroscopy Thermogravimetry

87–130 42 27–205 33.1 59.7

Bushuev et al., 1983 and to the SH1 of Bezou et al., 1995) proposed by Ballirano et al. (2001) renaming such phase as a-subhydrate Moreover, they reinvestigated the structure of the SH2 phase of Bezou et al. (1995) (corresponding to the a-hemihydrate, CaSO40.67H2O of Bushuev et al., 1983) renamed as b-subhydrate. Reinvestigation of the b-subhydrate structure led to a different symmetry, trigonal, space group P31 and, more important, a water content n ¼ 0.5 indicating that a- and b-subhydrates are true polymorphs. Differences between the two polymorphs are very small being limited to small distortions of the framework and a different distribution pattern of the water molecules within the channels. The dehydration mechanisms of bassanite, and the corresponding activation energies Ea, have been studied in the past using different analytical techniques and different experimental conditions (Table 1). The results obtained consistently indicate that the dehydration process of bassanite follows a single step mechanism and g-anhydrite represents the product of such transformation (Putnis et al., 1990). The aim of this work is to investigate the thermal behaviour of bassanite from room temperature until the dehydration temperature. Moreover, because of the very broad range of the reported activation energies for the dehydration process, we will analyse the corresponding kinetics in air by in situ real-time parallel-beam laboratory X-ray powder diffraction.

eschweizerbartxxx author

Notes Wet N2 fluxes with different PH2 O High-vacuum Values depending on PH2 O Relative humidity 60 % N2 atmosphere

were maintained constant throughout experiments. The temperature dependent behaviour of bassanite was investigated in the 303–443 K temperature range at steps of 5 K. The behaviour of bassanite was evaluated up to 383 K because of the strong correlations due to the almost perfect overlap of the reflections of hemihydrate and g-anhydrite. The bassanite ! g-anhydrite conversion is very fast, starts at a temperature of 388 K and is completed at 393 K. A magnified view of the complete data set is reported in Fig. 1 as a pseudo-Guinier plot. The dehydration of bassanite can be monitored from the shift of the (010) and (110) reflections (indexing referred to the trigonal pseudo-cell of the bassanite) as reported in the inset. Kinetics of bassanite dehydration were studied at isothermal conditions using SiO2-glass capillaries opened at both ends to allow the escape of the out coming water molecules. The dehydration was analysed in the 378–423 K temperature range with a step of 5 K using a fresh sample at each temperature. The counting time was chosen according to the rate of the conversion and ranged from 0.1 to 1 s/step (counting time for pattern varying from 11 to 107 min). Data were evaluated by the Rietveld method to obtain structural information and converted fraction. Diffraction data used to define the temperature dependent behaviour of bassanite were analysed following a two-step

2. Experimental methods Powder of synthetic analytical-grade, CaSO42H2O (Analar, product 10071) was heated in an oven at 383 K for 2 weeks to form g-anhydrite. Subsequently g-anhydrite was slowly re-hydrated at RT (humidity 5 %) to form bassanite following the same procedure used by Ballirano et al. (2001). The powder was loosely loaded in a 0.5 mm diameter borosilicate-glass capillary for the thermal expansion experiment and in 0.7 mm diameter SiO2glass capillaries for the isothermal experiments. X-ray powder diffraction data were collected on a parallelbeam Bruker AXS D8 Advance, operating in transmission in y–y geometry. The instrument is fitted with an incidentbeam Go¨bel mirror, a PSD, and a prototype of a capillary heating chamber (Ballirano & Melis, 2007). Within the cabinet a T of 296 K and a relative humidity of ca. 50 %, corresponding to a vapour partial pressure of ca. 0.014 bar,

Fig. 1. Magnified view (10–60 2y) of the full data set used to investigate the thermal expansion of bassanite shown as a pseudoGuiner plot. Inset: the shift of the (010) and (110) reflections is related to the conversion of bassanite to g-anhydrite.

Thermal behaviour and kinetics of dehydration in air of bassanite

procedure. In fact, they were preliminarily evaluated using the GSAS crystallographic suite of programs (Larson & Von Dreele, 2000) with the EXPGUI graphical interface (Toby, 2001) in order to exploit its versatile bond distance restraints option for complete structural analyses. Peak shapes were modelled by a pseudo-Voigt function (Thompson et al., 1987) modified to incorporate asymmetry (Finger et al., 1994). The absorption coefficient (including the aluminium contribution of the chamber windows) was determined at room temperature and subsequently kept fixed for the non-ambient data. The structure refinements were restrained following bond-valence requirements using Brese & O’Keeffe (1991) parameters and using a final weight of two following the same procedure described in Ballirano et al. (2001). Isotropic displacement parameters for groups of equal atoms (all Ca atoms, all S atoms, all O atoms, and all O atoms of the water molecules) were refined. Starting structural data were those of Ballirano et al. (2001). A preliminary check of the presence of texture was carried out by means of a generalised spherical-harmonic approach (Von Dreele, 1997). However, refined values of the texture index J very close to one indicated, as expected, the absence of preferred orientation that was, therefore, unrefined. As a second step, final structural data were used as input for further refinements using TOPAS v. 4.1 (Bruker, 2008). This program implements the Fundamental Parameters Approach FPA (Cheary & Coelho, 1992) and is claimed to be able to provide a more accurate description of the peak-shape allowing a more reliable extraction of microstructural parameters. In fact, despite of keeping fixed all structural data we experienced a reduction of the various agreement indices. Experimental details and miscellaneous data of the two series of refinements are reported in Table 2. Isothermal diffraction data were directly evaluated using the TOPAS software. The quantitative analyses


987

were carried out using the structural data of hemihydrate and g-anhydrite determined during the thermal expansion analysisatthecorrespondingtemperaturevalue(g-anhydrite data: Ballirano & Melis, 2009b). Cell parameters of the two phases and instrumental parameters were also kept fixed to the corresponding average values calculated from all refinements before (hemihydrate) and after the conversion (g-anhydrite) following the same strategy used for the investigation of gypsum dehydration (Ballirano & Melis, 2009a).

3. Discussion 3.1. Thermal expansion and structure modification Rietveld refinements were performed in space group I2 and refined cell parameters at 303 K are consistent with those from earlier data (Bezou et al., 1995; Ballirano et al., 2001; Voigtla¨nder et al., 2003). The relative expansion of the bassanite cell parameters and volume with temperature are shown in Fig. 2. From an evaluation of the integral widths bi of the individual reflections, microstructural parameters such as e0 microstrain (lattice strain), defined as bi ¼ 4e0 tan y, and volume-weighted mean column height Lvol, defined as bi ¼ l/Lvol cos y (Delhez et al., 1993), were extracted. It is worth noting (Fig. 3) that Lvol remains remarkably constant and equal to 63.0(14) nm for both reactant (bassanite) and product (g-anhydrite) of the conversion. On the contrary, e0 is constant until the beginning of the conversion process in correspondence of which we observe a significant increase of strain. Thermal expansion of bassanite is nearly isotropic in agreement with low temperature data reported by Voigtla¨nder et al. (2003). In fact within the 303–383 K temperature range a and b parameters expand by ca. 0.10 % while the c parameter expands by ca. 0.12 %. On

Table 2. Experimental details and miscellaneous data of the two series of refinements. Instrument X-ray tube Incident beam optic Sample mount Soller slits Divergence slit Detector Detector opening angle ( ) 2y range ( ) Step size ( ) Counting time (s) w2 GoF Rwp % Rp % RF2 % RBragg DWd Refined parameters

Bruker AXS D8 advance Cu at 40 kV and 40 mA Multilayer (Go¨bel) X-ray mirrors Rotating capillary (60 rpm) 1 (2.3 divergence) þ 1 radial 0.4 mm ˚ NTEC-1 PSD VA 6 10–140.827 (6082 data points) 0.0215 1 GSAS TOPAS 1.276–1.421 1.09–1.15 5.65–5.95 5.56–5.88 4.42–4.59 4.39–4.50 2.57–3.19 1.08–1.23 1.542–1.730 1.55–1.72 100 58

Statistic indicators as defined in Young (1993).

Fig. 2. Relative expansion of the unit cell parameters and volume for bassanite between 307 and 395 K.

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The limited temperature range, the very small thermal expansion, and the presence of pseudo-symmetry render difficult to analyse in detail the variations of bond distances with increasing temperature. An evaluation of the structural data shows that bond distances are constant within some minor random scattering that is generally ˚ for Ca–O and 0.003 A ˚ for S–O bond less than 0.015 A distances (Table 5). 3.2. Kinetics of dehydration CaSO40.5H2O ! g -CaSO4 + 0.5H2O Under the present experimental conditions, the dehydration process of bassanite follows a single step Fig. 3. Dependence of volume-weighted mean column height Lvol and e0 strain as a function of temperature. Lvol maintains the same value before and after conversion whereas e0 increases abruptly. Solid lines refer to the average value, dotted lines indicate associated standard deviations.

the contrary, b is insensitive to temperature. Therefore, the expansion is very small and explains the fairly scattered evolution of lattice parameters, in particular of a and b. It is worth noting that the volume per formula unit of g-anhydrite is greater than that of bassanite at eachtempffiffiffi perature as a result of bassanite ahex (calculated as a 3) and b cell parameters smaller and c cell parameter greater than those corresponding for g-anhydrite (Fig. 4). This could be the reason for the discontinuity of the e0 values of the two phases observed at the transition temperature. The dependence of lattice parameters from temperature within the restricted 303–383 K temperature range is linear and as such has been empirically modelled with the function p ¼ a0 þ a1T where a0 is the value of the corresponding parameter at 0 K, a1 is the first-order coefficient of expansion, and T the temperature in K. Results of the fitting are reported in Table 3. Dependence of cell parameters and volume is reported in Table 4.


Fig. 4. Comparison of the dependence of cell parameters from temperature of bassanite and g-anhydrite (Ballirano & Melis, 2009b). A significant gap is observed at the transition temperature.

CaSO4 0:5H2 O ! -CaSO4 þ 0:5H2 O without intermediate sub-hydrate phases of the type CaSO4nH2O (0 , n , 0.5). Dehydration may be monitored from the increase of the intensity ratio for the 100 and 110 reflections (indexing referred to the trigonal pseudo-cell of hemihydrate) from ca. 1:1 (hemihydrate) to 2:1 (g-anhydrite) (Ballirano et al., 2001). Before starting the complete data collection, a series of measurements were carried out in order to quantify the effects of a few experimental parameters on the measurement of the overall reaction rates. In particular, we tried to quantify the role played by bassanite hygroscopicity. In fact, we expected that a water surface layer was adhering to each grain and that this presence would possibly modify the overall path of conversion locally producing a high steam water vapour. Therefore, two subsequent cycles of dehydration/rehydration were performed at 383 K on the same capillary and the corresponding a vs. t curves were constructed (Fig. 5). As can be seen subsequent cycles result in the reduction of the induction time t0 without altering the overall kinetics. Moreover, because b-anhydrite has been reported to suffer from strong strain release after thermal pre-treatments (Ballirano & Melis, 2007), and strain release is expected to profoundly influence the kinetics of solidstate decompositions, we investigate such possible occurrence. However, differently from b-anhydrite no significant change in cell parameters was observed for the sample at the start of each thermal cycle indicating no strain release. The full data set consists of isothermal diffraction patterns collected within the 378–423 K thermal range with a step of 5 K using a fresh sample for each temperature. Due to the presence of limited longitudinal thermal gradients, the bassanite ! g-anhydrite conversion at temperatures lower than 378 K was found to be incomplete while at temperatures exceeding 423 K it was very fast rendering impossible a full data collection. The transformed fraction vs. time curves are sigmoidal (Fig. 6). This is a remarkable difference with respect to dehydration carried out under dynamically reduced pressure for which a deceleratory behaviour was reported (Carbone et al., 2008). Following the same procedure used by Gualtieri & Ferrari (2006) for investigating the kinetics of illite


989

Table 3. Results from data-fitting procedures using the a first-order polynomial p ¼ a0 þ a1T.

Present work R2 A0 a1

a

b

c

V

0.969 11.9967(21) 1.34(6) 104

0.981 6.9021(11) 8.9(3) 105

0.996 12.6185(10) 1.86(3) 104

0.996 1044.76(23) 4.07(7) 102

Table 4. Evolution of cell parameters and volume with temperature. T(K)

˚) a(A

˚) b(A

˚) c(A

b( )

˚ 3) V(A

303 308 313 318 323 328 333 338 343 348 353 358 363 368 373 378 383

12.0366(5) 12.0376(5) 12.0378(5) 12.0393(5) 12.0392(5) 12.0397(5) 12.0407(5) 12.0411(5) 12.0408(5) 12.0421(5) 12.0441(5) 12.0436(5) 12.0451(5) 12.0452(5) 12.0466(5) 12.0455(5) 12.0482(5)

6.9287(3) 6.9297(3) 6.9299(3) 6.9302(3) 6.9306(3) 6.9307(3) 6.9314(3) 6.9322(3) 6.9332(3) 6.9328(3) 6.9329(3) 6.9341(3) 6.9341(3) 6.9351(3) 6.9348(3) 6.9355(3) 6.9360(3)

12.6742(3) 12.6759(3) 12.6765(3) 12.6782(3) 12.6787(3) 12.6796(3) 12.6804(3) 12.6814(3) 12.6822(3) 12.6835(3) 12.6844(3) 12.6852(3) 12.6863(3) 12.6869(3) 12.6881(3) 12.6883(3) 12.6895(3)

90.267(3) 90.270(3) 90.265(3) 90.268(3) 90.271(3) 90.267(3) 90.273(3) 90.276(3) 90.269(3) 90.270(3) 90.268(3) 90.274(3) 90.263(3) 90.272(3) 90.266(3) 90.262(3) 90.264(3)

1057.00(7) 1057.37(7) 1057.48(7) 1057.80(7) 1057.89(7) 1058.02(7) 1058.29(7) 1058.52(7) 1058.71(7) 1058.88(7) 1059.15(7) 1059.33(7) 1059.57(7) 1059.78(7) 1059.95(7) 1059.99(7) 1060.40(7)


˚ ) and corresponding dispersion of relevant bond distances in the 303–383 K thermal range. Table 5. Average values (A

Ca1

Average Ca3

Average S1

Average S3

Average

O1 2 O4 2 O7 2 O12 2 OW1 O1 O3 O5 O5 O7 O9 O9 O11 OW2 O3 O4 O7 O8 O2 O5 O9 O12

Present work

Ballirano et al. (2001)

2.541(12) 2.619(12) 2.521(13) 2.417(9) 2.391(17) 2.510 2.664(14) 2.364(12) 2.437(14) 2.465(13) 2.445(14) 2.688(24) 2.406(14) 2.526(15) 2.457(11) 2.499 1.485(2) 1.472(3) 1.472(3) 1.478(2) 1.477 1.478(3) 1.477(2) 1.471(2) 1.466(3) 1.473

2.53(2) 2.64(2) 2.53(2) 2.42(1) 2.37(3) 2.51 2.68(2) 2.35(1) 2.40(2) 2.51(2) 2.48(1) 2.72(2) 2.39(2) 2.46(2) 2.39(2) 2.50 1.471(7) 1.464(7) 1.469(7) 1.473(7) 1.469 1.458(7) 1.483(7) 1.480(7) 1.473(7) 1.474

Present work

Ballirano et al. (2001)

Ca2

O2 2 O3 2 O8 2 O11 2

2.513(15) 2.602(10) 2.528(10) 2.405(8)

2.51(2) 2.61(2) 2.48(2) 2.41(2)

Ca4

O2 O4 O6 O6 O8 O10 O10 O12

2.512 2.695(17) 2.502(16) 2.793(12) 2.399(13) 2.435(11) 2.444(11) 2.449(11) 2.468(13)

2.50 2.72(2) 2.48(1) 2.76(2) 2.40(2) 2.45(1) 2.44(2) 2.46(2) 2.47(2)

S2

O1 O6 O10 O11

2.516 1.482(2) 1.473(3) 1.475(3) 1.472(3) 1.476

2.51 1.478(7) 1.470(7) 1.485(7) 1.462(7) 1.474

Reference data of Ballirano et al. (2001) at room temperature are reported for comparison.

990


Fig. 5. Transformed fraction a vs. time curves of dehydration of bassanite as measured at 383 K during two subsequent dehydration/ re-hydration cycles.

where k is the rate constant, a the transformed fraction, t the total time, and t0 the induction time. As preliminary step of the analysis, the logarithmic transform of the Avrami-Erofe’ev rate equation, under n the general form a ¼ 1 exp½ðkðtt0 Þ was used to build ln [ ln(1 a)] vs. ln(t t0) plots in order to derive the reaction order n from the slope of the corresponding regression lines. The fitting process of the ln ln plots (Fig. 7) produced very satisfactory correlation values R2 for n values ranging from 2.31(8) to 2.98(14) corresponding to an average n of 2.7(2). This dispersion can be, at least partly, due to the difficulty to reliably measure both the start and the final yield leading to a distortion of the a–t curve (Brown et al., 1980). This is particularly true for the present data analysis as the whole data set was used, without removing experimental points with a , 0.1 and a . 0.9, in order to avoid bias. Reaction order n values and the corresponding correlation values are reported in Table 6.


Fig. 6. Transformed fraction a vs. time curves of dehydration of bassanite in the 378–428 K temperature range. Isothermal data collected with a T of 5 K.

dehydroxylation, analysis of the data was carried out testing different kinetic models. In particular the following g(a) ¼ k(t t0) equation were selected (Brown et al., 1980): 0

An : Avrami - Erofe ev

g ðaÞ ¼

R2 : Contracting area

g ðaÞ ¼

1 ½ lnð1 aÞn 1 1 ð1 aÞ2 1 1 ð1 aÞ3 2

R3 : Contracting volume g ðaÞ ¼ D1 : 1 - dimensional g ðaÞ ¼ a diffusion D2 : 2 - dimensional g ðaÞ ¼ ð1 aÞ lnð1 aÞ þ a diffusion D3 : 3 - dimensional diffusion D4 : Ginstling - Brounshtein

1 2

g ðaÞ ¼ 1 ð1 aÞ3 gðaÞ ¼ 1

2a 3

2

ð1 aÞ3

Fig. 7. Linear fitting of the Avrami-Erofe’ev function under the form ln [ ln(1 a)] vs. ln(t t0) in order to derive the reaction order n.

Table 6. Reaction order n values and corresponding correlation values R2 as obtained from ln [ ln(1 a)] vs. ln(t t0) plots.

378 K 383 K 388 K 393 K 398 K 403 K 408 K 413 K 418 K 423 K

R2

n

0.992 0.998 0.984 0.995 0.986 0.981 0.995 0.993 0.987 0.999

2.34(7) 2.68(4) 2.47(18) 2.51(6) 2.31(8) 2.87(13) 2.78(9) 2.98(14) 2.86(19) 2.82(6)

0.980 0.962 0.980 0.993 0.981 0.976 0.993 0.967 0.992 0.998 3.8(1) 105 5.3(3) 105 6.6(4) 105 7.4(2) 105 8.8(3) 105 1.55(7) 104 1.95(7) 104 1.91(2) 105 3.3(2) 104 5.2(1) 105 378 383 388 393 398 403 408 413 418 423

991

Legend: An: Avrami-Erofe’ev; R2: contracting area; R3: contracting volume; D1: 1-dimensional diffusion; D2: 2-dimensional diffusion; D3: 3-dimensional diffusion; D4: GinstlingBrounshtein.

0.766 0.708 0.765 0.779 0.777 0.805 0.841 0.772 0.851 0.891 6.7(9) 106 9(1) 106 1.2(3) 105 1.1(2) 105 1.5(2) 105 3.0(4) 105 3.8(7) 105 3.5(8) 105 6(1) 105 1.1(2) 104 0.677 0.586 0.690 0.723 0.696 0.727 0.765 0.693 0.795 0.814 1.0(2) 105 1.5(3) 105 1.9(6) 105 1.5(3) 105 2.4(4) 105 5.1(9) 105 7(1) 105 6(2) 105 1.0(3) 104 2.0(5) 105 0.806 0.762 0.801 0.805 0.814 0.837 0.874 0.805 0.875 0.921 2.4(3) 105 3.0(5) 105 4.2(9) 105 4.0(6) 105 5.6(6) 105 1.1(1) 104 1.3(2) 104 1.2(3) 104 2.2(5) 104 3.6(6) 104 0.873 0.846 0.864 0.858 0.880 0.890 0.923 0.857 0.913 0.958 2.9(3) 105 3.6(4) 105 5.0(9) 105 5.3(6) 105 7.0(6) 105 1.2(1) 104 1.5(2) 104 1.4(2) 104 2.5(5) 104 4.0(5) 104 0.894 0.850 0.888 0.915 0.904 0.905 0.935 0.873 0.935 0.962 1.9(2) 105 2.5(3) 105 3.3(5) 105 3.4(3) 105 4.4(3) 105 8.2(8) 105 1.0(1) 104 9.6(9) 105 1.7(3) 104 2.8(3) 104 0.927 0.900 0.920 0.935 0.933 0.933 0.960 0.905 0.953 0.983

R k R k R k R k R k R k

2.4(2) 105 3.1(3) 105 4.2(5) 105 4.43(3) 105 5.7(4) 105 1.02(8) 104 1.26(1) 104 1.16(2) 104 2.1(3) 104 3.33(2) 104

k

D4 2

D3 2

D2 2

D1 2

R3 2

R2 2

An


Table 7. Rate constants k and R2 correlation values obtained from application of the various kinetic models.

Rate constants k and corresponding R2 correlation values at each temperature for every tested model are reported in Table 7. Finally, rate constants k for each model were plotted against temperature as ln k vs. 1/T i.e.Ethe logarithmic a form of the Arrhenius equation k ¼ A expð =RT Þ , to calculate Ea (Fig. 8). From evaluation of Table 7 it is clear that the AvramiErofe’ev model produces a significantly better fit than the remaining rate equation, as indicated by R2 values greater than 0.96. Nevertheless, the Arrhenius plots built from the rate constants arising from each kinetic model show common features. In fact, the linear dependence of ln k on 1/T suggests that, within the analysed temperature range, the mechanism of dehydration of bassanite does not change with temperature. The calculated activation energy for the An model is of 73(5) kJ/mol. Such value is smaller than that required for gypum dehydration under the same experimental conditions (109(12) kJ/mol: Ballirano & Melis, 2009a). This is reasonable because of the significantly larger structural rearrangement required for the CaSO42H2O ! CaSO40.5H2O dehydration. Our results confirm that the activation energies calculated from isothermal data by model-fitting method (Fig. 8) appear to be model independent as indicated by Khawam & Flanagan (2006). The value of 73(5) kJ/mol is in good agreement with the early results of McAdie (1964) and Ball & Urie (1970) for comparable water vapour pressures. Moreover, the value exceeds that of ca. 60 kJ/mol reported by Borrachero et al. (2008) from data collected in a similar temperature range but under constant N2 flow. The present value is also significantly greater than that reported by Sarma et al. (1998) from data collected approximately under the same water vapour pressure. However, the value calculated by Sarma et al. (1998) seems unreasonable because it is of the same order of magnitude as the energy required for water disordering within the channel, as reported by Winkler (1996). As previously indicated, isothermal kinetics data indicated a sigmoidal behaviour of the transformed fraction vs. time curves. This could be an indication that dehydration of bassanite in steady air follows a different reaction mechanism with respect to dehydration under a dynamically reduced pressure that showed a deceleratory behaviour (Carbone et al., 2008). The latter shape of transformed fraction vs. time curves is indicative of a diffusion-controlled mechanism (Khawam & Flanagan, 2006). The same mechanism was previously proposed for bassanite dehydration by Ball & Urie (1970) independently of the water partial pressure. Numerical reevaluation of the data of Carbone et al. (2008) provides a clear linear fit for a one-dimensional diffusion mechanism (Fig. 9), indicating an Ea of 62(4) kJ/mol under vacuum, very close to that reported by Borrachero et al. (2008) under nitrogen flux. The onedimensional mechanism seems to be very reasonable because of the structural similarity between starting (bassanite) and final (g-anhydrite) products and the relatively simple reversibility of the conversion. Moreover, Voigtla¨ nder et al. (2003) indicate bassanite as an ideal host-guest system. Therefore, following the

R2


992


Fig. 8. Arrhenius ln k vs. 1/T plots for the bassanite ! g-anhydrite conversion.


Fig. 9. Test for one-dimensional diffusion mechanism for lowpressure data reported by Carbone et al. (2008).

classification scheme based on the water evolution type (WET) proposed by Galwey (2000), the dehydration process should be classified of type WET 1A (crystal structure maintained, diffusion control). WET 1A has been reported to be consistent with the water evolution pattern from ion-exchanged zeolites. However, it was concluded that in such cases kinetic parameters were of empirical value and that Arrhenius constants cannot be identified with specific processes (Galwey, 2000). As previously indicated, the logarithmic transform of the Avrami-Erofe’ev equation provided a n value of 2.7(2). This value is close to 2.5 that reference data (Hulbert, 1969) indicate as consistent with a diffusion controlled constant nucleation rate process. In fact, n is a composite term defined as n ¼ b þ l/2 (0 , b , 1; l ¼ 1, 2, or 3) and this is a case that it provides an univocal solution for b ¼ 1, indicating a constant nucleation rate,

and l ¼ 3, indicating a 3D growth (Hulbert, 1969; Brown et al., 1980). However, such model does not appear to properly fit the water evolution pattern inferred from structural information and from vacuum measurements. In fact, the remarkably constant volume-weighted mean column height Lvol observed throughout the conversion confirms the absence of any recrystallization process. Therefore, two possible explanations can be invoked to explain the reported differences between present and reference data. The first explanation is that experimentallyrelated parameters can contribute to apparently modify the conversion path. First of all, a capillary allows the evacuation of the evolved water only along its axis and the effectiveness of the process strongly depends on powder packing. Moreover, it is easy to obtain different degrees of packing of the powder within different capillaries, because of the difficulty to control this parameter during sample preparation. Clearly, the presence of a fluxing medium or a dynamic vacuum renders more efficient the process of removal of the evolved water. A further drawback is due to the presence of longitudinal thermal gradients. The second explanation is that the mechanism of dehydration effectively changes from the dynamic vacuum conditions to steady atmosphere and/or as a function of temperature. Dehydration is expected to proceed via concurrent movements between alternative interpore positions. In fact, at room temperature bassanite is characterized by an ordered pattern of the oxygen of the water molecules (but disordered H positions) within the structural channel showing alternating full and empty sites. This mechanism can be modified by readsorption of the product water vapour as found by Ballirano & Melis (2009b) in the 343–383 K thermal range during the analysis of the thermal behaviour of g-anhydrite in air. Therefore, evaluation of the overall reaction rates does not provide sufficient information to describe completely and unambiguously the dehydration mechanism. However, it is important to remember that the activation energies calculated from isothermal data by the modelfitting method appear to be model independent, as indicated by Khawam & Flanagan (2006) and confirmed by the present work, rendering therefore fully reliable the calculated value of 73(5) kJ/mol, regardless the model used. Acknowledgements: The manuscript greatly benefited from constructive reviews of two anonymous referees and Associate Editor B. Winkler. Financial support by Sapienza Universita` di Roma is acknowledged.

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Received 29 January 2009 Modified version received 3 July 2009 Accepted 15 July 2009