Microporous and Mesoporous Materials

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1 Microporous and Mesoporous Materials 132 (2010) Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: A predictive model for the enthalpies of formation of ites Romain Mathieu a,1, Philippe Vieillard b, * a Centre de Recherches Pétrographiques et Géochimiques, CRS-UPR 2300, ancy Université, BP 20, Vandoeuvre les ancy, France b CRS/ISU UMR-6269 Hydrasa, 40 Ave du Recteur Pineau POITIERS-Cedex, France article info abstract Article history: Received 11 March 2009 Received in revised form 19 January 2010 Accepted 14 March 2010 Available online 18 March 2010 Keywords: Anhydrous ites Enthalpy of formation Framework density Zeolites Hydration To date, there is no available method for estimating the enthalpies of formation of different ites with identical compositions and various degrees of hydration. Fifty calorimetric data (from dissolution calorimetry in lead borate) for the enthalpies of formation of various anhydrous ites from the stable oxides have been obtained. A new formalism defining the enthalpies of formation from the oxides of anhydrous ites having a ite-like structure is proposed. The formalism is based (1) on a relationship between the measured enthalpies of formation of zeosils and a parameter characterizing the nature of the itic framework represented by FD (defined by the number of tetrahedral atoms per 1000 Å 3 ), and (2) on the electronegativity difference. For a constant framework (or a same structural ite family), the enthalpy of formation from the oxides is the sum of the products of the molar fraction of an oxygen atom bound to any two cations multiplied by the electronegativity difference defined by the D H O = M z+ () between any two consecutive cations located in the extra-framework and tetrahedral sites. The enthalpy of formation of an anhydrous ite from the constituent oxides is governed by three major factors, which are the framework density, the Al/Si ratio and the nature of the cation. Therefore, the combination of the model tested on anhydrous ites with the model for estimating hydration enthalpies published elsewhere allows estimation of the enthalpies of formation of hydrated ites and their comparison with the numerous calorimetric measurements of 148 natural ites, yielding a statistical error of ±0.5%. Ó 2010 Elsevier Inc. All rights reserved. 1. Introduction Zeolites are an important group of silicate minerals with wide-ranging practical applications (agricultural, commercial, and environmental). These minerals have been found in different environments such as saline alkaline lakes, soils, diagenetic deposits, deep marine sediments, altered mafic rocks and hydrothermal altered silicic rocks [1]. Zeolites form naturally-occurring metastable assemblages through hydrolysis of glasses and alteration of bentonite by alkaline cement solutions [2,3]. The geochemical stability of natural ites has been outlined by Chipera and Apps [1] using a thermodynamic approach. Various empirical routines have been formulated for estimating the enthalpy of formation of ites. Three predictive methods are currently available. Chermak and Rimstidt [4] proposed a method of predicting the enthalpies of formation of hydrated ites based on the polyhedral model. Later, a method of predicting the enthalpies of formation of ites from their crystal refinements was developed * Corresponding author. Tel.: ; fax: address: philippe.vieillard@univ-poitiers.fr (P. Vieillard). 1 Present address: Geosciences Rennes CRS-UMR 6118, 263 Ave Général Leclerc, Rennes Cedex, France. by Vieillard [5], based on the concept of parameter D H O = M z+ (comp), calculated from optical and crystallographic data. With the enthalpies of formation of anhydrous aluminosilicates made available, avrotsky and Tian [6] developed sets of equation for predicting the enthalpies of formation of anhydrous ites as a function of the nature of the structure, the composition and the thermochemical data of the corresponding aluminosilicate glasses. The primary reason for using estimated thermodynamic data for ites despite the great number of measured data now available is the highly variable chemistry typical of many ites. In addition to the observed compositional variability of the exchangeable and tetrahedral cations, ites exhibit wide variations in water content, readily responding to changes in temperature and humidity. For the present calculations, all ites were assumed to be fully hydrated, as would be expected for a ite below the water vapor saturation curve or at 100% relative humidity. The exact amount of water in an individual ite is strongly dependent on the exchangeable cations in the ite structure and on the total number of cations in ites. It has been concluded [7,1] that temperature is an important variable in the stability of ites, partly because of their high water content. Moreover, the significant cation exchange capabilities of ites give rise to an additional problem when modelling /$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi: /j.micromeso

2 336 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) their stability. The composition of the extra-framework cation of many ites will change with evolving water composition and may not be representative of the original composition during formation (evaporation, binary cation exchange). These estimation methods fail to distinguish between two different ites having the same composition. For instance, the method by Chermak and Rimstidt [4] does not allow discrimination between a chabazite, a clinoptilolite and an erionite having the same composition, because only the coordination number of the cation is taken into account. The method by Vieillard [5], using known crystal structures of anhydrous ites, only considers the enthalpy of formation from the oxides as an exothermic value, at variance with the recent calorimetric measurements. The method by avrotsky and Tian [6] does not allow discrimination between the enthalpies of formation of the three ite minerals because it is based on the Al/Si ratio and on two types of constitutive rings of the itic framework (the small ring: 8- and 10-membered and the large ring: 12-membered). Zeolites commonly display multiple coupled solid solutions, ion exchange and order-disorder behaviours, variable degrees of hydration, second-order displacive phase transitions and hydration/dehydration reactions. These properties must be considered in all attempts to determine accurate thermodynamic data (enthalpies of formation, third-law entropy, heat capacity). Order-disorder behaviours and second-order displacive phase transitions can be investigated by calorimetric measurements (entropy and heat capacity). The purpose of this paper is to provide a set of equations for predicting consistent enthalpies of formation for those ites containing a great diversity of cations in the extra-framework site and displaying varying water contents. We consider the dependence of the energetics on the framework density, aluminium content, charge-balancing cations and degree of hydration. Considering the decomposition reaction of hydrated ites in water molecules and anhydrous ites:! X i¼nc M i Al nal Si nsi O n H2 OðH 2 OÞ i¼1!! Xi¼nc M i Al nal Si nsi O þ n H2 OðH 2 OÞ ð1þ i¼1 The enthalpy of formation of hydrated ites can be expressed as follows: "! # X i¼nc DH f;298 M i Al nal Si nsi O n H2 O ðh 2 OÞ i¼1 "! # X i¼nc ¼ DH f;298 M i Al nal Si nsi O þ n H2 ODH f;298 ðh 2OÞ l þ DH HdyZ i¼1 and the enthalpy of this reaction is the integral hydration enthalpy, DH HdyZ. Liquid water was used as a reference in all calculations and its enthalpy of formation is DH f H 2O ðliqþ ¼285:83 kj mol 1 [8]. The average hydration enthalpy per mole of water, DH HdyW, can be derived from the integral hydration enthalpy DH HdyZ using the following relationship (W refers to the water molecule): DH HdyW ¼ðDH HydZ Þ=n H2 O DH HdyW can be calculated using Vieillard and Mathieu s [9] method. The computation of the hydration enthalpy per mole of water requires the knowledge of the chemical formula, interlayer charge, and molar volumes (or unit-cell volumes) of hydrated and ð2þ ð3þ anhydrous ites. Vieillard and Mathieu s [9] method of predicting the enthalpy of hydration has been tested on 137 data derived from various sources and provides a statistical error of ±3.5 kj mol 1 H 2 O. So, the enthalpies of formation of anhydrous ites are required in order to calculate the enthalpies of formation of partiallyor fully-hydrated ites. The enthalpies of formation from the oxides of some anhydrous ites have been compiled by avrotsky and Tian [6] and may be complemented by the addition of some recent experimental values. From a careful inventory of some enthalpies of formation of anhydrous ites, a method is proposed here, based on parameter D H O = M z+ (c) characterizing the electronegativity of the cation in a compound, as defined initially by Vieillard [10,11] and applied to numerous families such as hydrated smectites [12], micas and chlorites [13] and to minerals belonging to the alunite group [14]. From this model tested on anhydrous ites, the enthalpies of formation of hydrated ites can be calculated and compared to the numerous experimental values (112 calorimetric data derived from lead borate dissolution calorimetry and 24 data derived from HF calorimetry). 2. Methodology 2.1. Compilation and selection of experimental enthalpies of formation of anhydrous ites The few HF calorimetric measurements carried out on anhydrous ites at K were performed on analcime [15]), clinoptilolite [16]) and mordenite [17]). Other measurements were performed by lead borate dissolution calorimetry (700 C). These high-temperature measurements call for a more careful use of thermodynamic data. Bish and Carey [18] observed three categories of ite behaviour with temperature: (1) reversible dehydration with little or no modification of the framework (continuous processes), (2) complete and reversible dehydration accompanied by a large distortion of the framework (continuous and discontinuous processes), and (3) reversible dehydration at low temperature accompanied by large modifications in the framework followed by a collapse of the framework structure (discontinuous processes). Thermodynamically, continuous processes are neither phase transitions (accompanied by a symmetry change and a discontinuity in the second-order reaction) nor phase transformations (accompanied by a discontinuity in the first-order reaction). Discontinuous processes are phase transformations involving first-order discontinuities in enthalpy. Among the lead borate measurements for each ite, three criteria were systematically used: Internal consistency of the data used in the thermochemical cycles by checking the origin of enthalpy increments. Zeolite hydration/dehydration discontinuous processes leading to a discontinuity in the first-order reaction (phase transition enthalpy). Perfect balance of the chemical formula of ites. The experimental data on ites that did not comply with all three criteria were discarded upon the selection of data for anhydrous ites. The first criterion was applied to some anhydrous ites, such as phillipsite and harmotome [19], brewsterite [20], chabazites [21 23], erionite [24], gmelinite [25], obtained from estimated enthalpy increments or from estimated dehydration enthalpies. As regards the second criterion, most ites selected by Bish and Carey [18] were ites with a collapse temperature above 700 C. However, some compounds with a collapse temperature below 700 C were added by these authors, i.e. stilbite and

3 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) Table 1 Chemical composition, measured enthalpies of formation from the oxides, DH oxðanhyd::þ, at K and unit-cell volumes of some anhydrous ites. Anhydrous ite minerals Chemical formula V u.c. anhyd. (Å 3 ) DH ox:298:15 K (Anhy. ) (kj mol1 ) Analcime (K a )(Al Si )O a 96.6 ± Chabazite-Ca2 (Ca 1.63 K 0.13 a 0.03 )(Al 3.23 Si 8.77 )O b ± Clinoptilolite-a (a )(Al Si )O b ± Clinoptilolite (Ca 0.18 Mg 0.36 K a 1.53 )(Al Si )O b ± Clinoptilolite-Ca (Ca Mg )(Al Si )O b ± Clinoptilolite-K (K )(Al Si )O b 477 ± Clinoptilolite-K a (K 1.53 a )(Al Si )O b ± Edingtonite (Ba 0.97 K 0.03 a 0.04 )(Al 1.98 Si 3.01 )O c ± Gonnardite (Ca 1.95 a 0.16 )(Al 3.99 Si 5.99 )O d 80.6 ± Heulandite (Ca 0.86 K 0.06 a 0.37 )(Al 2.14 Si 6.86 )O e 29.3 ± Heulandite-K (K )(Al Si )O e 26.5 ± Heulandite-a (a )(Al Si )O e ± Heulandite-a (K a )(Al Si )O e ± Heulandite-a (Ca K a 0.11 )(Al Si )O e ± Laumonite (Ca)(Al 2 Si 4 )O f 10.7 ± Leonhardite (Ca Mg Mn K a )(Al 1.99 Si 3.99 )O f 10.7 ± Leonhardite (Ca 2 )(Al 4 Si 8 )O f 26.3 ± Leonhardite (Ca 1.3 K 0.8 a 0.6 )(Al 4 Si 8 )O f ± Mesolite (Ca 2.06 a 1.81 )(Al 6 Si 9 )O ± Mordenite-Ca (Ca 0.09 )(Al 0.18 Si 0.82 )O h 2.49 ± Mordenite-Ca (Ca a )(Al 0.18 Si 0.82 )O h 5.94 ± Mordenite-K (K 0.18 )(Al 0.18 Si 0.82 )O h ± Mordenite-a (a 0.18 )(Al 0.18 Si 0.82 )O h 6.46 ± atrolite (Ca 0.03 Mg 0.05 a 1.8 )(Al 2.08 Si 2.95 )O i ± Tetranatrolite (Mg 0.02 K 0.08 a 1.83 )(Al 1.82 Si 3.15 )O i ± Scolecite (Ca)(Al 2 Si 2.99 )O g 78.7 ± Stellerite (Ca 1.02 )(Al 2.01 Si 6.98 )O j 12.4 ± Stilbite (Ca 1.01 a 0.12 )(Al 2.12 Si 6.88 )O k 2.8 ± Thomsonite (Ca 2.04 a 0.88 )(Al 5.01 Si 5.03 )O l 196 ± Yugawaralite (Ca 0.98 )(Al 1.96 Si 6.04 )O m 17 ± Zeolite silica Y (a )(Al Si )O n ± Zeolite DAY (a )(Al Si )O n 7.78 ± Zeolite Y-a (a )(Al Si )O n ± Zeolite Y-a (H a )(Al Si )O o ± Zeolite Y-Ca (H Ca a )(Al Si )O p 3.41 ± Zeolite Y-a (a )(Al Si )O n ± Zeolite Y-Rb (H Rb 0.20 Ca K a 0.07 )(Al Si )O p ± Zeolite Y-K (H 0.02 K a )(Al Si )O p ± Zeolite Y-Cs (H Cs Ca a 0.07 )(Al Si )O p ± ZeoliteY-Li (H Li Ca a )(Al Si )O p 5.24 ± Zeolite-13X (a )(Al Si )O n ± Faujasite-a (a 0.28 )(Al 0.28 Si 0.72 )O o ± Zeolite ß-Li (H Li a )(Al Si )O q ± Zeolite ß-a (H a )(Al Si )O q ± Zeolite ß-K (H K a )(Al Si )O q 8.56 ± Zeolite ß-Rb (H Rb a )(Al Si )O q 4.01 ± Zeolite ß-Cs (H Cs a )(Al Si )O q 7.46 ± Zeolite ß-K (H K a )(Al Si )O q 8.56 ± Zeolite ß-Rb (H Rb a )(Al Si )O q 4.01 ± Zeolite ß-Cs (H Cs a )(Al Si )O q 7.46 ± Zeolite a-bea (H a )(Al Si )O q 2.4 ± 2.8 Zeolite Mg-BEA (H Mg a )(Al Si )O q ± Zeolite Ca-BEA (H Ca a )(Al Si )O q ± Zeolite Sr-BEA (H Sr a )(Al Si )O q ± Zeolite Ba-BEA (H Ba a )(Al Si )O q ± Zeolite Mg-BEA (H Mg a )(Al Si )O q ± Zeolite Ca-BEA (H Ca a )(Al Si )O q ± a [29]; b [18]; c [30]; d Estimated from unit-cell volume of the hydrated phase (V u.c. hyd. ) using [31]; e [32]; f [33]; g [34]; h [35]; i [36]; j [37]; k [38]; l [39]; m [40]; n [41]; o [42]; p Estimated from V u.c.hyd. using [42]; q Assumed equal to V u.c.hyd. of [43]. 1 [44]; 2 [23]; 3 [45]; 4 [46]; 5 [26]; 6 [6]; 7 [47]; 8 [48]; 9 [49]; 10 [41]; 11 [27]; 12 [50]; 13 [51]; 14 [28]. heulandite, the measurements of which were performed by Kiseleva et al. [26]. The latter indicated that the values of the integral hydration enthalpies include the phase transition enthalpies observed during dehydration of these minerals. By contrast, upon dehydration, phillipsite turns into a collapsed structure with squeezed channels and thomsonite actually undergoes a structural breakdown. For the latter compound, the calorimetric cycle provides the enthalpy of formation of the anhydrous framework plus the enthalpy of the structural modification. The third criterion was applied to all minerals and provides only three anhydrous minerals with an incomplete structural formula. In the ite-y group, the chemical formula of the eight compounds was modified by assuming a proton in the extra-framework site such that the total charge of cations in the extraframework site is strictly equal to the number of aluminium atoms of the ite Y. Only the H- and La-bearing ites Y [27] were discarded. Among BEA ites, only the Li-bearing ites from Sun and avrotsky [28] were discarded due to the presence of non-tetrahedral aluminium in the exchangeable sites. A compilation of available calorimetric data on dehydrated ites obtained from numerous works has been performed and provides 57 data from lead borate calorimetry and three data from HF calorimetry. The thermochemical cycles used to derive heats of formation from lead borate calorimetry lead first to the enthal-

4 338 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) pies of formation from the stable oxides of anhydrous ites, DH ox (Anhy.). As the enthalpies of formation from the elements, DH f (Anhy..), are derived from the measured enthalpies of formation from the stable oxides of dehydrated ites, DH ox (Anhy..), and from the sum of the enthalpies of formation from the elements of the stable constituent oxides, DH f M i O xi, the two ðcþ latter parameters are derived from the heat contents and enthalpies of solutions and are subject to errors and inconsistencies. In order to limit error propagation, the selected anhydrous ites are displayed in Table 1 with their respective unit-cell volumes and enthalpies of formation from the stable oxides, DH ox ðanhy::þ Enthalpies of formation from the constituent oxides, DH ox Let us consider an anhydrous ite with the following chemical formula: M a1 ; M a2 ;...; M ai A Al t Al Fe 3þ t Fe ; Si tsi O where subscripts A and T denote the extra-framework and tetrahedral sites, T respectively, and letters a, t Al, t Fe and t Si represent stoichiometric amounts of cation i having a charge z i. The extra-framework sites may be occupied by cations such as Li +,a +,K +,Mg 2+, and Ca 2+. The enthalpy of formation of an anhydrous ite, DH f (anhy..), is the sum of the enthalpies of formation from the elements of the different stable constituent oxides, DH f M i O, plus xi ðcþ a second term, DH ox, designating the enthalpy of formation from the stable constituent oxides (subscript ox.): DH f ðanhy::þ ¼Xi¼ns ðn i ÞDH f M i O þ xi ðcþ DH ox: ðanhy::þ i¼1 ð4þ As was shown in Ref. [6], the enthalpy of formation from the stable constituent oxides is endothermic for some calcium and acid forms of synthetic ites (chabazite, clinoptilolite, mordenite, Y-ite) as well as for the a-faujasite and all BEA ites (Table 1). The positive enthalpies of formation from the stable oxides do not allow application of the electronegativity difference method [10,11] based on Pauling s concept [52], because of the presence of stable oxides, DH f M i O xi, particularly quartz and ðcþ corundum that do not display a ite-like structure. Using the corresponding-states theory [53] and considering ite-like oxides, let us define the enthalpies of formation of dehydrated ites from the oxides having a ite-like structure (subscript ox. ), DH ox. (Anhy..) as follows: DH ox: ðanhy::þ ¼DH ox: ðanhy::þðn iþ h DH f M i O i xi ðþ DH f M i O xi ð5þ ðcþ where DH f M i O and xi ðþ DH f M i O xi refer to the enthalpies of ðcþ formation of oxides having a ite-like structure and a stable form, respectively. The enthalpy of formation of a dehydrated ite from the constituent oxides, in the ite structure, DH ox;ðanhy::þ, analogous to that given by Vieillard [10], contains two types of interactions between any two cations: those where cations are in different sites (inter-site interaction energy terms) and those where cations are in the same site (2 intra-site interaction energy terms): DH ox; ðanhy::þ 2 x A x T f DH O ¼ ðsite AÞD H O ¼ ðsite TÞg i¼n þ P A j¼n P A x i;a x j;a DH O ¼ M zþ i i;a; ¼ D HO ¼ M z þ j i¼1 j¼iþ1 6 i¼n þ P 4 T j¼n P T x j;t DH O ¼ M zþ i D i;t; HO ¼ M zþ j i¼1 j¼iþ1 x i;t j;a; j;t; ð6þ where x A and x T are the numbers of oxygen atoms balancing the extra-framework and tetrahedral sites A and T, respectively. The total number of oxygen atoms bound to different cations located in the two sites of the anhydrous ite must be equal to, the total number of oxygen atoms of the anhydrous ite. x A þ x T ¼ Each of both sites (k = A and T) contains one or several cations n c. The electronegativity of site k, D H O = (site k), represents the weighed average of electronegativities of different cations in site k: P i¼nc;k D H O ¼ i¼1 n i;k x i D H O ¼ M z iþ i;k; ðsite kþ ¼ ð8þ x k where parameter D H O ¼ M z iþ i;k; is the electronegativity of cation Mz iþ located in site k of a ite. The number of oxygen atoms balancing site k (in extra-framework and tetrahedral sites) is then: i¼n x k ¼ X c; k n i;k x i i¼1 Parameter D H O ¼ M z i þ i;k; characterizing the electronegativity of the cation in site k of the ite mineral environment can be expressed as follows: h D H O ¼ M z iþ ¼ 1=x i;k; i DH f M i O xi ðþ i DH f M z iþ i ð10þ ðcþ where DH f M z iþ is the unknown enthalpy of formation of i ðcþ Mz+ in the crystal state. Similarly, the electronegativity of cation M z i þ in the stable oxide will be written as follows [54,10,5]: h D H O ¼ M z iþ ¼ 1=x i;ox i DH f M i O xi ðcþ i DH f M z iþ i ð11þ This expression is similar to that with parameter D H O ¼ M z i þ h D H O ¼ M z iþ ¼ 1=x i;aq i DH f M i O xi ðcþ i DH f M z iþ i ðcþ ðaqþ i;aq : ð7þ ð9þ ð12þ where values are available and are given in Table 2. The difference between Eqs. (11) and (12) was further developed in Ref. [54]. Discarding DH f M z i þ i between Eqs. (10) and (11) yields: ðcþ h D H O ¼ M z iþ ¼ D i;k; HO ¼ M z iþ þ 1=x i;ox i DH f M i O i xi ðþ DH f M i O xi ðcþ ð13þ Table 2 Enthalpies of formation of oxides and ions at K and calculated parameter D H O = M z+ (aq) of selected cations. Oxides DH f:298:15 K Ions DH f:298:15 K D H O = M z+ (aq) (kj mol 1 ) (kj mol 1 ) (kj mol 1 ) Li 2 O Li + (aq) a 2 O a + (aq) K 2 O K + (aq) Rb 2 O Rb + (aq) Cs 2 O Cs + (aq) BaO Ba +2 (aq) (H 4 ) 2 O H þ 4 (aq) SrO Sr +2 (aq) CaO Ca +2 (aq) MgO Mg +2 (aq) FeO Fe +2 (aq) , MnO Mn +2 (aq) ZnO Zn +2 (aq) La 2 O La +3 (aq) Fe 2 O Fe +3 (aq) , Al 2 O Al +3 (aq) SiO 2 (quartz) Si 4+ (aq) H 2 O liq H + (aq) [55]; 2 [56]; 3 [57]; 4 [58]; 5 [59]; 6 [60].

5 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) Table 3 Crystallographic data (lattice parameters, Z, unit-cell volume, framework density FD) and enthalpies of formation from quartz of some zeosils at K. ame Lattice parameters Z Unit-cell Vol (Å 3 ) FD DH f:298:15k: qz (kj mol1 ) a (Å) b (Å) c (Å) a ( ) b ( ) c ( ) Quartz-a Silicalite orth ± Silicalite orth ± Silicalite orth ± Silicalite orth ± Silicalite orth Silicalite orth Mutinaite Silicalite mono Ferriérite Linde Y Faujasite ± ZSM-12 (MTW) ± ZSM-12 (MTW) ZSM-11 (MEL) ± ZSM-11 (MEL) ZSM-11 (MEL) ZSM-11 (MEL) ZSM ± Chabaz. (CHA) ± ITQ-7 (ISV) ± ITQ-1 (MWW) ± CIT-5 (CFI) ± SSZ-23 (STT) ± SSZ-23 (STT) ITQ-3 (ITE) ± ITQ-4 (IFR) ± [64]; 2 [65]; 3 [66]; 4 [67]; 5 [68]; 6 [69]; 7 [70]; 8 [71]; 9 [72]; 10 [73]; 11 [74]; 12 [75]; 13 [76]; 14 [77]; 15 [78]; 16 [79]; 17 [80]; 18 [81]; 19 [82]; 20 [83]; 21 [84]; 22 [85]; 23 [86]; 24 [87]; 25 [88]; 26 [89]; 27 [90]; 28 [91]; 29 [63]; 30 [92]; 31 [93]; 32 [62]; 33 [94]. The second term of Eq. (13) represents the difference between D H O ¼ M z iþ i;k; and D H O ¼ M z iþ ox, analogous to dd HO = M z+ for cation M z+ already defined by Vieillard [10], and is a function of the modification in the crystal environment during the transfer from oxide M 2/z O to a ite. In Eq. (6), the interaction energy is defined by the difference D H O ¼ M z i þ D i;k; HO ¼ M z i þ j;k;, and this term characterizes shortrange interactions between cations in different sites or within a same site. The interaction energy must be strictly positive and is assumed to be equal to: h i D H O ¼ M z iþ D 2 i;k; HO ¼ M z iþ j;k; ¼ 96:483 v Mi v Mj ð14þ where a v Mi and v Mj are the electronegativities (as defined by Pauling [52]) of ions and M z jþ j, respectively. Vieillard et al. [10,54,61,12,13] applied the principles of Pauling [52] regarding the predominance of the nearest-neighbour interactions (short-range interactions) observed in the crystal structure of a mineral to the calculation of enthalpy of formation. In anhydrous ites, all cations located in the extra-framework and tetrahedral sites are assumed to have one or more common oxygen atoms between any two adjacent polyhedra. The interaction energy expressed by the last two terms in the general equation of DH ox;ðanhy:þ, given in Eq. (6), is different from 0 if the site involved is occupied by two or more different cations and contributes to the calculation of the heat of formation of the anhydrous ites from the constituent oxides Enthalpies of formation of oxides in the ite structure The method provided herein may be simplified if the difference between the enthalpy of formation of the stable oxide and that of the oxide having a ite-like structure is known for Si and Al. Among all the cations composing the ites, only silica has been subjected to numerous calorimetric measurements from a great number of polymorphs, particularly compounds with a ite-like structure called zeosils. The enthalpies of formation of zeosils from stable quartz, DH ox;qtz ðsio 2Þ Zeosil, given in Table 3 with their respective crystallographic parameters, range between 2.2 and kj mol 1 above the enthalpy of formation of quartz at 298 K. The significance of these small enthalpies and their weak dependence on the framework type has been discussed by Petrovic et al. [62] and Piccione et al. [63]. Thus, the electronegativity of cation Si 4+ in the ite, defined as follows: h i D H O ¼ Si 4þ ¼ D HO ¼ Si 4þ ox þ 1=2 DH f ðsio 2Þ Zeosil DH f ðsio 2Þ Quartz ð15þ can be a direct function of parameter D H O = of ion Si 4+ of the stable quartz and of the enthalpy of formation of the zeosil from stable quartz, having the same structure as that of the ite. In order to find out the enthalpy of formation of a ite, DH f ðsio 2Þ ðþ, parameter FD, called tetrahedral framework density, is defined as a measurement of the number of Si atoms occupying the tetrahedral sites per volume unit [95,96]. FD is obtained as [(Si)/Unit-cell Vol] * 1000 (i.e. number of silicon atoms per 1000 Å 3 ). The smaller this number, the more pore space is available, regardless of the accessibility of this space. The framework densities of zeosils are calculated from cell parameters (Table 3) and show values ranging from for MTW to for faujasite, values that are much lower than that of quartz (FD = 26.58). Fig. 1 displays the relationships between the enthalpies of formation of zeosils from quartz and framework density FD. Piccione et al. [63] observed a relationship between DH f ðsio 2Þ Zeosil and the molar volume. A second-degree polynomial function is obtained by constraining the curve to pass through the stable quartz (FD = ): DH f ðsio 2Þ DH f ðsio 2Þ quartz ¼0:61087 ðfd 26:548Þþ0:0442 ðfd 26:548Þ 2 ð16þ

6 340 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) can be a direct function of the electronegativity of Al 3+ of the stable corundum and of the enthalpy of formation of tetrahedral Al 2 O 3 from stable corundum, having the same structure as that of the ite. In a given anhydrous ite, the framework density is obtained as [(Al + Fe + Si)/Unit-cell Vol] * 1000 (i.e. number of tetrahedral atoms per 1000 Å 3 ). The determinations of unit-cell volumes performed on a ite that has been heated and then returned to room temperature (without being sealed) are strongly affected by the fast rehydration of the ite. Therefore, only the determinations of unit-cell volumes performed ex situ (i.e. under anhydrous conditions) are considered reliable and are much less numerous than those performed under hydrated conditions. According to recent works [100], the unit-cell volumes are generally larger for hydrated ites than for anhydrous ites (at the same temperature). As a result, the unit-cell volumes of dehydrated ites (at K) have systematically been compiled from the recent bibliographic data provided by Cruciani [100] and are given in Table 1. For most ites, since the tabulated unit-cell volume values do not correspond exactly to those with a given chemical composition, the unit-cell volume values of the anhydrous ites are assumed to be evaluated with a 2% accuracy [9] Example of calculation of the enthalpy of formation from the oxides for an anhydrous ite Fig. 1. Relationship between DH f ðsio2þ DH f ðsio2þ quartz and framework density FD for all zeosils. with R 2 = and a standard error of e = ±1.35 kj mol 1 for = 17 data. For cation Al +3, in which the stable form is corundum (a-al 2 O 3 ), no data relative to the enthalpy of formation of oxide Al 2 O 3 with a structure similar to that of the itic framework is known. Al 2 O 3 with an Al atom in tetrahedral coordination is not a naturallyoccurring compound. There is a small number of polymorphs of corundum with measured enthalpies of formation [97]) and known crystal structures [98,99]). Corundum contains only octahedrallycoordinated Al atoms, with the other polymorphs j-al 2 O 3 et c- Al 2 O 3 having their Al atoms in two tetrahedral and octahedral positions but in variable and hardly quantifiable proportions. Using the unit-cell volume, the FD value is maximum for corundum (FD = 47.08) and decreases in polymorphs (FD = 44.6 for j-al 2 O 3 and 42.5 for c-al 2 O 3 ). Therefore, parameter D H O = of aluminium in ites, D H O ¼ Al 3þ, will differ from that of aluminium in corundum, D H O ¼ Al 3þ ox, and will be assumed to be a function of the framework density. In the absence of data about the tetrahedrally-coordinated Al 2 O 3, the enthalpy of formation of oxide Al 2 O 3, DH f ðal 2O 3 Þ :, and parameter D H O ¼ Al 3þ with a ite-like structure can be determined assuming the following relationship between DH f ðal 2O 3 Þ : and parameter FD: DH f ðal 2O 3 Þ DH f ðal 2O 3 Þ corind ¼ A ðfd 47:08Þ ð17þ where A is a parameter relating the enthalpy of formation of Al 2 O 3 to the framework density and is the framework density of corundum. Therefore, the electronegativity of cation Al 3+ in the ite, defined as follows: D H O ¼ Al 3þ ¼ D HO ¼ Al 3þ ox þ 1=3 DH f ðal 2O 3 Þ : DH f ðal 2O 3 Þ corind: ð18þ Using a mesolite with formula (Ca 2.06 a 1.81 )(Al 6 Si 9 )O as an example, the cations located in the extra-framework site and in the tetrahedral framework site can be written as the following sums of oxides 2.06 * CaO * a 2 O and 3 * Al 2 O * SiO 2, respectively. The number of oxygen atoms balancing the cation in the extra-framework site and in the tetrahedral framework site will be and 27, respectively, giving the total number of oxygen atoms = Then, parameters D H O = (site A) and D H O = (site T) can be written as follows: 2:06 D H O ¼ Ca 2þ þ 0:905 D H O ¼ a þ D H O ¼ ðsite AÞ ¼ D H O ¼ ðsite TÞ ¼ 9 D H O ¼ Al 3þ Parameters D H O ¼ Si 4þ 2:965 þ D H O ¼ Si 4þ ð19þ ð20þ and D H O ¼ Al 3þ can be calculated from Eqs. (15) and (18), respectively. Then, the enthalpy of formation from the constituent oxides of anhydrous chabazite in the ite structure is expressed as follows: DH ox; ðmesoliteþ :965 DH O ¼ site A D H O ¼ 3 ð site TÞ ¼ þ 2:06 0:905 DH O ¼ a þ D HO ¼ Ca 2þ ð21þ 18 DH O ¼ Al 3þ D HO ¼ Si 4þ þ 9 The first term characterizing the interaction energy between sites A and T can be developed and actually contains four interaction energies between cations a + and Ca 2+ of the extra-framework site A and cations Al 3+ and Si 4+ of the tetrahedral site T such that: 27 2 ¼ 6 4 2:965 ðd H O ¼ site A D H O ¼ site TÞ 0:905 9 DH O ¼ a þ D 3 HO ¼ Al 3þ þ 0: DH O ¼ a þ D HO ¼ Si 4þ : ð22þ þ 2:06 9 DH O ¼ Ca 2þ D HO ¼ Al 3þ DH O ¼ Ca 2þ D HO ¼ Si 4þ þ 2:06 The enthalpy of formation from the stable oxides of Ca-bearing chabazite is then obtained: DH ox: ðmesoliteþ ¼DH ox: h ðmesoliteþ i þ 9 DH f ðsio 2Þ mesolite DH f ðsio 2Þ quartz þ 3 DH f ðal 2O 3 Þ mesolite: DH f ðal 2O 3 Þ corund: ð23þ

7 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) It appears that the calculation of the enthalpy of formation from the stable oxides of the anhydrous mesolite required the knowledge of six parameters such as D H O ¼ Ca 2þ ; D HO ¼ K þ ; D H O ¼ a þ ; D HO ¼ Al 3þ ox ; D HO ¼ Si 4þ ox and the framework density FD calculated from the unit-cell volume of the anhydrous mesolite. 3. Results and discussion 3.1. Minimization Parameter D H O ¼ M zþ of nine cations including H +, a +, K +, Rb +, Cs +, Mg 2+, Ca 2+, Sr 2+ and Ba 2+ in the extra-framework site and A (Eq. (17)) on the other hand, were determined by minimization of the difference between the experimental enthalpies of formation from the oxides in the ite state (Eq. (5)) and those computed using the general equation (Eq. (6)). Constraints of minimization involve short-range interactions and positive value terms of interaction energies between two different cations in accordance with Eq. (14). For the nine cations located in the on the one hand, and parameters D H O ¼ Si 4þ ox ; D HO ¼ Al 3þ ox extra-framework site, the values of D H O ¼ M z iþ i;k; given in Table 4 are assumed to be constant and independent of the nature of the ite structure. ¼ 210:6 kj mol 1 represent the values of D H O = of Si 4+ and Al 3+ in quartz and corundum, respectively. The following equations allow The values of D H O ¼ Si 4þ ox ¼209:26 kj mol1 and D H O ¼ Al 3þ ox evaluation of D H O ¼ Si 4þ and D H O ¼ Al 3þ in different ites from the knowledge of the framework density, FD: D H O ¼ Si 4þ ¼209:26 þ 1=2 ½0:61087 ðfd 26:548Þ þ 0:0442 ðfd 26:548Þ 2 Š D H O ¼ Al 3þ ¼210:60 þ 1=3 ½0:71 ðfd 47:08ÞŠ ð25þ ð24þ The presence of proton H + in the extra-framework sites of anhydrous ites is essentially observed in ite Y [27] and ite-ß [50,28,51]. Assuming DH f Hþ ðcþ ¼DH f Hþ ðaqþ ¼0, the electronegativity of the proton in the oxide state can be written from the enthalpy of formation of water: h i D H O ¼ H þ ox ¼ 1=2 DH f ðh 2OÞ ðlþ DH f ðhþ Þ ðcþ ¼285:83 kj mol 1 ð26þ The minimization is optimized by setting DH f ðh 2OÞ ðþ and D H O ¼ H þ at kj mol 1. This deviation corresponds to the difference between the proton in the extra-framework site and the proton of liquid water. The new value of D H O ¼ H þ represents the reference value of D H O = M z+ () for different cations located in the extra-framework site A of a ite mineral. Therefore, for anhydrous ites with a proton in the extraframework sites, Eq. (5) should be modified by the following equation: Table 4 Values of parameter D HO ¼ M z iþ obtained by minimization. Ions D H O = M z+ (aq) (kj mol 1 ) D H O = M z+ () (kj mol 1 ) Ions D H O = M z+ (aq) (kj mol 1 ) D H O = M z+ () (kj mol 1 ) Cs Ba Rb Sr K Ca a Mg Li H DH ox: ðanhy::þdh ox:ðanhy:þ 8 h i 9 >< ðn Si Þ DH f ðsio 2Þ zeosil DH f ðsio 2Þ quartz >= ¼ þðn Al =2Þ DH f ðal 2O 3 Þ DH f ðal 2O 3 Þ corund: >: þðn H =2Þ DH f ðh 2OÞ DH f ðh >; 2OÞ water ð27þ which contributes to the determination of the enthalpy of formation from the constituent oxides of anhydrous ites, DH ox; ðanhy:þ having a proton in the extra-framework sites. Table 5 displays the comparison between the predicted and experimental enthalpies of formation from the oxides of anhydrous ite minerals, DH ox;ðanhy::þ. Some calculation details are provided in this table, such as: the framework density FD of the anhydrous ite, the number of oxygen atoms and parameter D H O = site A for extra-framework cations, the number of oxygen atoms and parameters D H O ¼ Si 4þ ; D H O ¼ Al 3þ and D HO = site T for tetrahedral cations of the ite framework, the predicted enthalpy of formation from the constituent oxides DH ox; ðanhy::þ and DH oxðanhy::þ calculated from Eqs. (6) and (27), respectively, and the experimental enthalpy of formation from the oxides DH oxðanhy::þ given in Table 1. Due to the great difference in the number of oxygen atoms among anhydrous ites, the enthalpies of formation from the oxides such as DH ox; ðanhy:þ and DH oxðanhy::þ are given for one mole of tetrahedra TO 2. The last column provides the difference between the value predicted using the model and the measured value, and yields an average deviation of ±4.5 kj mol 1 TO 2, i.e. lower than that obtained with the avrotsky and Tian [6] method (±5.6 kj mol 1 TO 2 ) Fundamental properties of the enthalpy of formation of anhydrous ites To illustrate the fundamental properties of the enthalpy of formation of anhydrous ites from the stable oxides as a function of the crystallochemical properties, we selected anhydrous compounds with CaAl 2 Si 4 O 12 as a chemical formula, characterizing an anhydrous chabazite, an anhydrous faujasite or an anhydrous wairakite. Let s consider chabazite (Al/Si = 0.5) in which a or K has been substituted for Ca. As the unit-cell volume is supposed to be the same for all three compounds, the framework density (FD) and parameters D H O = of cations Al 3+ and Si 4+ remain constant (Table 6). For a given structure characterized by a constant framework density, and for a constant charge (constant Al/Si ratio), the lowest enthalpies of formation from the oxides, DH ox. (Anhy..) and DH ox. (Anhy..), are obtained for the electropositive cations located in site A, which show a D H O = value very different from the D H O = of the tetrahedral site. A relationship between D H O = M z+ (aq) and D H O = M z+ () in the extra-framework site can be observed (Fig. 2) and exhibits the same behaviour of cation electronegativity in the exchangeable sites [12,13]. In a same crystallographic family characterized by a constant molar volume or unit-cell volume, the difference between DH ox. (Anhy..) and DH ox. (Anhy..) is constant and independent of the nature of the cations in the exchangeable sites. ow let s vary the Al/Si ratio of an anhydrous calcium chabazite from 0 to 1 (Table 6). As the unit-cell volume remains relatively constant, the framework density FD and parameters D H O = of cations Ca 2+,Al 3+ and Si 4+ remain constant. The enthalpy of formation from the oxides having a ite-like structure becomes exothermic as

8 342 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) Table 5 Anhydrous ites: comparison of the predicted enthalpies of formation from the stable oxides (Eq. (27)) calculated from parameter D H O = of sites A and T and framework density FD with experimental values. Anhyd. ites FD x A D H O = site A (kj mol 1 ) x T D H O = Si 4þ ðþ (kj mol 1 ) D H O = Al 3þ ðþ (kj mol 1 ) D H O = site T (kj mol 1 ) DH ox: (kj mol 1 ) Pred. DH ox (kj mol 1 ) Exper. DH ox (kj mol 1 ) (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) Difference (kj mol 1 ) Analcime Chabazite-Ca Clinoptilolite-a Clinoptilolite Clinoptilolite-Ca Clinoptilolite-K Clinoptil.-K-a Edingtonite Gonnardite Heulandite Heulandite-K Heulandite-a Heulandite-a Heulandite-a Laumonite Leonhardite Leonhardite Leonhardite-K Mesolite Mordenite-Ca Mordenite-Ca Mordenite-K Mordenite-a atrolite Tetranatrolite Scolecite Stellerite Stilbite Thomsonite Yugawaralite Zeolite Silice Y Zeolite DAY Zeolite Y-a Zeolite Y-a Zeolite Y-Ca Zeolite Y-a Zeolite Y-Rb Zeolite Y-K Zeolite Y-Cs ZeoliteY-Li Zeolite-13X Faujasite-a Zeolite ß-Li Zeolite ß-a Zeolite ß-K Zeolite ß-Rb Zeolite ß-Cs Zeolite ß-K(2) Zeolite ß-Rb(2) Zeolite ß-Cs(2) Zeolite a-bea Zeolite Mg-BEA Zeolite Ca-BEA Zeolite Sr-BEA Zeolite Ba-BEA Zeolite Mg-BEA Zeolite Ca-BEA (a) Framework density FD of the anhydrous ite calculated from the unit-cell volume V u.c. anhyd. given in Table 1. (b) number of oxygen atoms balancing the extra-framework sites A (Eq. (9)). (c) D H O = (site A) (in kj mol 1 ) (Eq. (9)). (d) number of oxygen atoms balancing the tetrahedral sites T (Eq. (6)). (e) D H O ¼ Si 4þ (in kj mol1 ) (Eq. (24)); (f) D H O ¼ Al 3þ (in kj mol1 ) (Eq. (25)). (g) D H O = (site T) (in kj mol 1 ) (Eq. (8)). (h) DH ox; ðanhy::þ (in kj mol1 TO 2 basis) (Eq. (6)). (i) DH ox ðanhy::þ (in kj mol1 TO 2 basis) (Eq. (27)). (j) Measured values of DH ox ðanhy::þ (in kj mol1 TO 2 basis). (k) Difference = (column j) (column i) (in kj mol 1 TO 2 basis). The number of references is the same as given at the end of Table 1.

9 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) Table 6 Unit-cell volume, framework density, parameter D H O = of cations in exchangeable and tetrahedral sites, enthalpy of formation from the oxides in the itic structure (Eq. (6)) and enthalpy of formation from the stable oxides (Eq. (27)) of CaAl 2 Si 4 O 12 (chabazite, faujasite and laumontite in the anhydrous state). Al/Si V u.c. anhy. (Å 3 ) FD D H O = site A (kj mol 1 ) D H O ¼ Si 4þ ðþ (kj mol 1 ) D H O ¼ Al 3þ ðþ (kj mol 1 ) DH ox: (kj mol 1 ) DH ox (kj mol 1 ) Chabazite-Ca Ca(Al 2 Si 4 )O Chabazite-a a 2 (Al 2 Si 4 )O Chabazite-K K 2 (Al 2 Si 4 )O Zeosil CHA SiO a Chabazite Ca 0.5 (AlSi 5 )O Chabazite Ca(Al 2 Si 4 )O Chabazite Ca 1.5 (Al 3 Si 3 )O Chabazite-a a 2 (Al 2 Si 4 )O Analcime a 2 (Al 2 Si 4 )O Laumontite Ca(Al 2 Si 4 )O Chabazite Ca(Al 2 Si 4 )O Faujasite Ca(Al 2 Si 4 )O a [83]. governed by three major factors, which are the framework density (obtained from the unit-cell volume), the Al/Si ratio and the nature of the cation Accuracy of the predictive method for anhydrous ites Fig. 2. Relationship between D H O = M z+ () and D H O = M z+ (aq) for cations in the extra-framework sites. the Al/Si ratio increases. When Al/Si = 0, silica exhibits a chabazitelike structure [83], which explains why parameter DH Ox.Zeol (Anhy..) becomes null. On the other hand, parameter DH ox. (Anhy..) represents the enthalpy of the zeosil CHA from quartz and is kj mol 1, which is close to the experimental value, i.e. DH f;qtz ¼ 11:43 kj mol1 [63]. Consequently, it is readily understood that the enthalpies of formation from the stable oxides may be positive in some anhydrous ites. Still starting from calcium chabazite, let s consider an anhydrous calcium faujasite and an anhydrous laumontite exhibiting the same Al/Si ratio. The unit-cell volume is the only explicative parameter of all three calcium compounds having the same Al/Si ratio. This parameter is very high in faujasite (big pores and low FD value) and decreases toward chabazite to laumontite (small pores and high FD value). When the silicate framework density increases (the pore volume decreases), DH ox. (Anhy..) remains constant but DH ox. (Anhy..) becomes more exothermic. The same trend is observed between sodium chabazite and analcime with Al/Si = 0.5. As a result, for an anhydrous ite with two oxygen atoms (TO 2 ), with a constant Al/Si ratio and a same exchangeable cation, the enthalpy of formation from the stable oxides decreases to about 3 kj mol 1 when the molar volume increases by 1 cm 3 mol 1. These fundamental properties show that the enthalpy of formation of an anhydrous ite from the constituent oxides is With the values of the enthalpies of formation of oxides listed in Table 2, the enthalpies of formation of anhydrous ites were calculated from the experimental and predicted enthalpies of formation from the oxides. Fig. 3 shows a plot of standard errors of estimation when using the model presented here and the average error obtained when using the avrotsky and Tian [6] method. The horizontal and vertical dashed lines show the ±0.5% error for each model. For some points that are outside of the ±0.5% interval, an error bar has been added and corresponds to the error in the experimental measurements. The average error for 57 data is ±0.48% with the present model, which is better than the avrotsky and Tian [6] model (0.69% for 55 data) Using the model by avrotsky and Tian [6], the ites Y saturated with cations Ca, Li, K, Rb and Cs show overestimated enthalpies of formation. This is explained by the insufficient consideration of the pore size contribution. The introduction of the itic framework density (parameter FD) on the one hand and the contribution of the protons located in the extra-framework sites on the other hand allowed reduction of the discrepancy between the measured and estimated enthalpies of formation from the oxides in the present model. As regards ites ß, the discrepancies between the measured and estimated enthalpies of formation from the oxides remain greater than 0.5%, but are smaller than those evaluated using avrotsky and Tian s [6] algorithm. The inaccuracy probably results from uncertain measurements of the unit-cell volume of ite ß because Higghins et al. [43] have shown that this compound appears as a hybrid of two intergrowing polymorphs Enthalpies of formation of hydrated ites For hydrated ites with available chemical compositions and molar volumes, the enthalpy of formation can be considered as the contribution of the enthalpies of formation of anhydrous ites and hydration enthalpy (Eq. (2)). Using this method applied to anhydrous ites and the fundamental relationship of hydration enthalpy developed by Vieillard and Mathieu [9], the enthalpy of formation of hydrated ites can be known and tested against a great number of experimental data.