Microporous and Mesoporous Materials 132 (2010) 335–351

Contents lists available at ScienceDirect

Microporous and Mesoporous Materials

journal homepage: www.elsevier .com/locate /micromeso

A predictive model for the enthalpies of formation of zeolites

Romain Mathieu a,1, Philippe Vieillard b,*

a Centre de Recherches Pétrographiques et Géochimiques, CNRS-UPR 2300, Nancy Université, BP 20, 54501 Vandoeuvre les Nancy, Franceb CNRS/INSU UMR-6269 Hydrasa, 40 Ave du Recteur Pineau. 86022 POITIERS-Cedex, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 March 2009Received in revised form 19 January 2010Accepted 14 March 2010Available online 18 March 2010

Keywords:Anhydrous zeolitesEnthalpy of formationFramework densityZeolitesHydration

1387-1811/$ - see front matter � 2010 Elsevier Inc. Adoi:10.1016/j.micromeso.2010.03.011

* Corresponding author. Tel.: +33 5 49 45 38 61; faE-mail address: philippe.vieillard@univ-poitiers.fr

1 Present address: Geosciences Rennes CNRS-UMR 635042 Rennes Cedex, France.

To date, there is no available method for estimating the enthalpies of formation of different zeolites withidentical compositions and various degrees of hydration.

Fifty calorimetric data (from dissolution calorimetry in lead borate) for the enthalpies of formation ofvarious anhydrous zeolites from the stable oxides have been obtained.

A new formalism defining the enthalpies of formation from the oxides of anhydrous zeolites having azeolite-like structure is proposed. The formalism is based (1) on a relationship between the measuredenthalpies of formation of zeosils and a parameter characterizing the nature of the zeolitic frameworkrepresented by FD (defined by the number of tetrahedral atoms per 1000 Å3), and (2) on the electroneg-ativity difference. For a constant framework (or a same structural zeolite family), the enthalpy of forma-tion from the oxides is the sum of the products of the molar fraction of an oxygen atom bound to any twocations multiplied by the electronegativity difference defined by the DHO=Mz+ (zeol) between any twoconsecutive cations located in the extra-framework and tetrahedral sites. The enthalpy of formation ofan anhydrous zeolite from the constituent oxides is governed by three major factors, which are theframework density, the Al/Si ratio and the nature of the cation.

Therefore, the combination of the model tested on anhydrous zeolites with the model for estimatinghydration enthalpies published elsewhere allows estimation of the enthalpies of formation of hydratedzeolites and their comparison with the numerous calorimetric measurements of 148 natural zeolites,yielding a statistical error of ±0.5%.

� 2010 Elsevier Inc. All rights reserved.

= z+

1. Introduction

Zeolites are an important group of silicate minerals withwide-ranging practical applications (agricultural, commercial,and environmental). These minerals have been found in differentenvironments such as saline alkaline lakes, soils, diagenetic depos-its, deep marine sediments, altered mafic rocks and hydrothermalaltered silicic rocks [1]. Zeolites form naturally-occurring metasta-ble assemblages through hydrolysis of glasses and alteration ofbentonite by alkaline cement solutions [2,3].

The geochemical stability of natural zeolites has been outlinedby Chipera and Apps [1] using a thermodynamic approach. Variousempirical routines have been formulated for estimating the enthal-py of formation of zeolites. Three predictive methods are currentlyavailable. Chermak and Rimstidt [4] proposed a method of predict-ing the enthalpies of formation of hydrated zeolites based on thepolyhedral model. Later, a method of predicting the enthalpies offormation of zeolites from their crystal refinements was developed

ll rights reserved.

x: +33 5 49 45 42 41.(P. Vieillard).118, 263 Ave Général Leclerc,

by Vieillard [5], based on the concept of parameter DHO M(comp), calculated from optical and crystallographic data. Withthe enthalpies of formation of anhydrous aluminosilicates madeavailable, Navrotsky and Tian [6] developed sets of equation forpredicting the enthalpies of formation of anhydrous zeolites as afunction of the nature of the structure, the composition and thethermochemical data of the corresponding aluminosilicate glasses.The primary reason for using estimated thermodynamic data forzeolites despite the great number of measured data now availableis the highly variable chemistry typical of many zeolites.

In addition to the observed compositional variability of theexchangeable and tetrahedral cations, zeolites exhibit wide varia-tions in water content, readily responding to changes in tempera-ture and humidity. For the present calculations, all zeolites wereassumed to be fully hydrated, as would be expected for a zeolitebelow the water vapor saturation curve or at 100% relative humid-ity. The exact amount of water in an individual zeolite is stronglydependent on the exchangeable cations in the zeolite structureand on the total number of cations in zeolites.

It has been concluded [7,1] that temperature is an importantvariable in the stability of zeolites, partly because of their highwater content. Moreover, the significant cation exchange capabili-ties of zeolites give rise to an additional problem when modelling

336 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

their stability. The composition of the extra-framework cation ofmany zeolites will change with evolving water composition andmay not be representative of the original composition during for-mation (evaporation, binary cation exchange).

These estimation methods fail to distinguish between two dif-ferent zeolites having the same composition. For instance, themethod by Chermak and Rimstidt [4] does not allow discrimina-tion between a chabazite, a clinoptilolite and an erionite havingthe same composition, because only the coordination number ofthe cation is taken into account. The method by Vieillard [5], usingknown crystal structures of anhydrous zeolites, only considers theenthalpy of formation from the oxides as an exothermic value, atvariance with the recent calorimetric measurements. The methodby Navrotsky and Tian [6] does not allow discrimination betweenthe enthalpies of formation of the three zeolite minerals becauseit is based on the Al/Si ratio and on two types of constitutive ringsof the zeolitic framework (the small ring: 8- and 10-membered andthe large ring: 12-membered).

Zeolites commonly display multiple coupled solid solutions, ionexchange and order-disorder behaviours, variable degrees ofhydration, second-order displacive phase transitions and hydra-tion/dehydration reactions. These properties must be consideredin all attempts to determine accurate thermodynamic data (enthal-pies of formation, third-law entropy, heat capacity). Order-disorderbehaviours and second-order displacive phase transitions can beinvestigated by calorimetric measurements (entropy and heatcapacity).

The purpose of this paper is to provide a set of equations forpredicting consistent enthalpies of formation for those zeolitescontaining a great diversity of cations in the extra-framework siteand displaying varying water contents. We consider the depen-dence of the energetics on the framework density, aluminium con-tent, charge-balancing cations and degree of hydration.

Considering the decomposition reaction of hydrated zeolites inwater molecules and anhydrous zeolites:

Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON � nH2OðH2OÞ

!Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON þ nH2OðH2OÞ ð1Þ

The enthalpy of formation of hydrated zeolites can be expressedas follows:

DH�f ;298

Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON � nH2O � ðH2OÞ

" #

¼ DH�f;298

Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON

" #þ nH2ODH�f ;298ðH2OÞl þDHHdy�Z

ð2Þ

and the enthalpy of this reaction is the integral hydration enthalpy,DHHdy�Z.

Liquid water was used as a reference in all calculations and itsenthalpy of formation is DH�f H2OðliqÞ ¼ �285:83 kJ mol�1 [8]. Theaverage hydration enthalpy per mole of water, DHHdy�W, can bederived from the integral hydration enthalpy DHHdy�Z using thefollowing relationship (W refers to the water molecule):

DHHdy�W ¼ ðDHHyd�ZÞ=nH2O ð3Þ

DHHdy�W can be calculated using Vieillard and Mathieu’s [9]method. The computation of the hydration enthalpy per mole ofwater requires the knowledge of the chemical formula, interlayercharge, and molar volumes (or unit-cell volumes) of hydrated and

anhydrous zeolites. Vieillard and Mathieu’s [9] method of predictingthe enthalpy of hydration has been tested on 137 data derived fromvarious sources and provides a statistical error of ±3.5 kJ mol�1 H2O.

So, the enthalpies of formation of anhydrous zeolites are re-quired in order to calculate the enthalpies of formation of partially-or fully-hydrated zeolites. The enthalpies of formation from theoxides of some anhydrous zeolites have been compiled by Navrot-sky and Tian [6] and may be complemented by the addition ofsome recent experimental values. From a careful inventory of someenthalpies of formation of anhydrous zeolites, a method is pro-posed here, based on parameter DHO=Mz+ (c) characterizing theelectronegativity of the cation in a compound, as defined initiallyby Vieillard [10,11] and applied to numerous families such as hy-drated smectites [12], micas and chlorites [13] and to mineralsbelonging to the alunite group [14].

From this model tested on anhydrous zeolites, the enthalpies offormation of hydrated zeolites can be calculated and compared tothe numerous experimental values (112 calorimetric data derivedfrom lead borate dissolution calorimetry and 24 data derived fromHF calorimetry).

2. Methodology

2.1. Compilation and selection of experimental enthalpies of formationof anhydrous zeolites

The few HF calorimetric measurements carried out on anhy-drous zeolites at 298.15 K were performed on analcime [15]), clin-optilolite [16]) and mordenite [17]). Other measurements wereperformed by lead borate dissolution calorimetry (700 �C). Thesehigh-temperature measurements call for a more careful use ofthermodynamic data. Bish and Carey [18] observed three catego-ries of zeolite behaviour with temperature: (1) reversible dehydra-tion with little or no modification of the framework (continuousprocesses), (2) complete and reversible dehydration accompaniedby a large distortion of the framework (continuous and discontin-uous processes), and (3) reversible dehydration at low temperatureaccompanied by large modifications in the framework followed bya collapse of the framework structure (discontinuous processes).

Thermodynamically, continuous processes are neither phasetransitions (accompanied by a symmetry change and a discontinu-ity in the second-order reaction) nor phase transformations (accom-panied by a discontinuity in the first-order reaction). Discontinuousprocesses are phase transformations involving first-order disconti-nuities in enthalpy. Among the lead borate measurements for eachzeolite, three criteria were systematically used:

– Internal consistency of the data used in the thermochemicalcycles by checking the origin of enthalpy increments.

– Zeolite hydration/dehydration discontinuous processes leadingto a discontinuity in the first-order reaction (phase transitionenthalpy).

– Perfect balance of the chemical formula of zeolites.

The experimental data on zeolites that did not comply with allthree criteria were discarded upon the selection of data for anhy-drous zeolites.

The first criterion was applied to some anhydrous zeolites, suchas phillipsite and harmotome [19], brewsterite [20], chabazites[21–23], erionite [24], gmelinite [25], obtained from estimated en-thalpy increments or from estimated dehydration enthalpies.

As regards the second criterion, most zeolites selected by Bishand Carey [18] were zeolites with a collapse temperature above700 �C. However, some compounds with a collapse temperaturebelow 700 �C were added by these authors, i.e. stilbite and

Table 1Chemical composition, measured enthalpies of formation from the oxides, DH�oxðAnhyd:zeol:Þ, at 298.15 K and unit-cell volumes of some anhydrous zeolites.

Anhydrous zeolite minerals Chemical formula Vu.c. anhyd. (Å3) DH�ox:298:15 K (Anhy. zeol) (kJ mol�1)

Analcime (K0.01375Na0.9825)(Al0.9375Si2.0478)O6 157.65a �96.6 ± 4.51

Chabazite-Ca2 (Ca1.63K0.13Na0.03)(Al3.23Si8.77)O24.095 809.0b 99.558 ± 21.42

Clinoptilolite-Na (Na3.276)(Al3.276Si14.724)O36 1000.0b �253.98 ± 8.13

Clinoptilolite (Ca0.18Mg0.36K0.0666Na1.53)(Al3.276Si14.724)O35.7 1000.0b �178.2 ± 11.523

Clinoptilolite-Ca (Ca1.512Mg0.144)(Al3.276Si14.724)O36.018 1009.99b 61.38 ± 6.843

Clinoptilolite-K (K3.276)(Al3.276Si14.724)O36 1000.0b �477 ± 8.643

Clinoptilolite-K–Na (K1.53Na1.746)(Al3.276Si14.724)O36 1000.0b �375.48 ± 13.323

Edingtonite (Ba0.97K0.03Na0.04)(Al1.98Si3.01)O9.995 288.39c �198.8 ± 28.44

Gonnardite (Ca1.95Na0.16)(Al3.99Si5.99) O19.995 458.38d �80.6 ± 55.14

Heulandite (Ca0.86K0.06Na0.37)(Al2.14Si6.86)O18.005 465.98e �29.3 ± 10.85

Heulandite-K (K0.182)(Al0.182Si0.818)O2 51.78e �26.5 ± 0.486

Heulandite-Na (Na0.182)(Al0.182Si0.818)O2 51.78e �14.11 ± 0.456

Heulandite-Na (K0.095Na0.098)(Al0.182Si0.818)O2.0055 51.78e �20.86 ± 0.746

Heulandite-Na (Ca0.012K0.048Na0.11)(Al0.182Si0.818)O2 51.78e �13.43 ± 0.646

Laumonite (Ca)(Al2Si4)O12 331.50f �10.7 ± 2.87

Leonhardite (Ca1.005Mg0.005Mn0.005K0.012 Na0.008)(Al1.99Si3.99)O12 331.50f �10.7 ± 10.27

Leonhardite (Ca2)(Al4Si8)O24 663.0f �26.3 ± 2.08

Leonhardite (Ca1.3K0.8Na0.6)(Al4Si8)O24 663.0f �319.9 ± 23.68

Mesolite (Ca2.06Na1.81)(Al6Si9)O29.965 827.17 �398.4 ± 43.67

Mordenite-Ca (Ca0.09)(Al0.18Si0.82)O2 57.15h 2.49 ± 0.46

Mordenite-Ca (Ca0.056Na0.068)(Al0.18Si0.82)O2 57.15h �5.94 ± 0.666

Mordenite-K (K0.18)(Al0.18Si0.82)O2 57.15h �25.25 ± 0.576

Mordenite-Na (Na0.18)(Al0.18Si0.82)O2 57.15h �6.46 ± 0.46

Natrolite (Ca0.03Mg0.05Na1.8)(Al2.08Si2.95)O10 223.13i �257.3 ± 15.34

Tetranatrolite (Mg0.02K0.08Na1.83)(Al1.82Si3.15)O10.005 223.13i �234.8 ± 22.74

Scolecite (Ca)(Al2Si2.99)O9.98 279.48g �78.7 ± 18.74

Stellerite (Ca1.02)(Al2.01Si6.98)O17.995 507.40j 12.4 ± 7.59

Stilbite (Ca1.01Na0.12)(Al2.12Si6.88)O18.01 512.13k �2.8 ± 15.75

Thomsonite (Ca2.04Na0.88)(Al5.01Si5.03)O20.055 548.43l �196 ± 45.44

Yugawaralite (Ca0.98)(Al1.96Si6.04)O16 381.45m 17 ± 3.05

Zeolite silica Y (Na0.0027)(Al0.0027Si0.9973)O2 79.27n 13.06 ± 0.2610

Zeolite DAY (Na0.0636)(Al0.0636Si0.9364)O2 79.27n 7.78 ± 0.5310

Zeolite Y-Na (Na0.256)(Al0.256Si0.744)O2 79.27n �22.66 ± 0.5410

Zeolite Y-Na (H0.008Na0.276)(Al0.284Si0.716)O2 79.31o �22.66 ± 0.5911

Zeolite Y-Ca (H0.002Ca0.136Na0.014)(Al0.284Si0.715)O2 79.60p 3.41 ± 0.5311

Zeolite Y-Na (Na0.285)(Al0.285Si0.715)O2 79.27n �26.64 ± 0.4810

Zeolite Y-Rb (H0.018Rb0.20Ca0.002K0.004Na0.07)(Al0.286Si0.713)O2 79.69p �34.34 ± 0.5411

Zeolite Y-K (H0.02K0.252Na0.012)(Al0.288Si0.713)O2 79.79p �34.32 ± 0.4411

Zeolite Y-Cs (H0.006Cs0.208Ca0.002Na0.07)(Al0.288Si0.712)O2 79.69p �36.09 ± 0.4611

ZeoliteY-Li (H0.012Li0.212Ca0.001Na0.062)(Al0.292Si0.709)O2 79.31p �5.24 ± 0.4611

Zeolite-13X (Na0.444)(Al0.444Si0.556)O2 80.99n �41.79 ± 1.1610

Faujasite-Na (Na0.28)(Al0.28Si0.72)O2 79.31o �22.06 ± 0.566

Zeolite ß-Li (H0.01106Li0.04845Na0.00467)(Al0.06418Si0.9358)O2 65.36q 18.58 ± 2.812

Zeolite ß-Na (H0.02174Na0.04244)(Al0.06418Si0.9358)O2 65.36q 14.51 ± 2.812

Zeolite ß-K (H0.0198K0.0497Na0.000378)(Al0.0693Si0.9307)O2 65.36q 8.56 ± 2.812

Zeolite ß-Rb (H0.00642Rb0.05869Na0.00041)(Al0.06552Si0.93448)O2 65.36q 4.01 ± 2.812

Zeolite ß-Cs (H0.0138Cs0.05358Na0.0005)(Al0.06788Si0.93212)O2 65.36q 7.46 ± 2.812

Zeolite ß-K (H0.0147K0.0497Na0.005)(Al0.0693Si0.9307)O2 65.36q 8.56 ± 2.812

Zeolite ß-Rb (H0.0018Rb0.05869Na0.005)(Al0 .06552Si0.93448)O2 65.36q 4.01 ± 2.812

Zeolite ß-Cs (H0.0093Cs0.05358Na0.005)(Al0 .06788Si0.93212)O2 65.36q 7.46 ± 2.812

Zeolite Na-BEA (H0.032505Na0.181583)(Al0.214088Si0.785912)O2 65.36q �2.4 ± 2.8Zeolite Mg-BEA (H0.0131Mg0.0283Na0.001)(Al0. 0706Si0.9294)O2.00005 65.36q 26.82 ± 2.813

Zeolite Ca-BEA (H0.0092Ca0.0318Na0.001)(Al0. 0738Si0.9262)O2 65.36q 25.99 ± 2.814

Zeolite Sr-BEA (H0.0068Sr0.0296Na0.0007)(Al0 .0735Si0.9265)O1.9966 65.36q 18.28 ± 2.814

Zeolite Ba-BEA (H0.012Ba0.0305Na0.0007)(Al0. 0737Si0.9263)O2 65.36q 13.84 ± 2.814

Zeolite Mg-BEA (H0.0221Mg0.0852Na0.0044)(Al0 .1969Si0.8031)O2 65.36q 32.46 ± 2.814

Zeolite Ca-BEA (H0.0101Ca0.0936Na0.0009)(Al0 .1983Si0.8017)O1.99995 65.36q 26.14 ± 2.814

a[29]; b[18]; c[30]; dEstimated from unit-cell volume of the hydrated phase (Vu.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];pEstimated from Vu.c.hyd.using [42]; qAssumed equal to Vu.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].

R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351 337

heulandite, the measurements of which were performed by Kisel-eva et al. [26]. The latter indicated that the values of the integralhydration enthalpies include the phase transition enthalpies ob-served during dehydration of these minerals. By contrast, upondehydration, phillipsite turns into a collapsed structure withsqueezed channels and thomsonite actually undergoes a structuralbreakdown. For the latter compound, the calorimetric cycle pro-vides the enthalpy of formation of the anhydrous framework plusthe enthalpy of the structural modification.

The third criterion was applied to all minerals and provides onlythree anhydrous minerals with an incomplete structural formula.In the zeolite-Y group, the chemical formula of the eight com-

pounds was modified by assuming a proton in the extra-frame-work site such that the total charge of cations in the extra-framework site is strictly equal to the number of aluminium atomsof the zeolite Y. Only the H- and La-bearing zeolites Y [27] werediscarded. Among BEA zeolites, only the Li-bearing zeolites fromSun and Navrotsky [28] were discarded due to the presence ofnon-tetrahedral aluminium in the exchangeable sites.

A compilation of available calorimetric data on dehydrated zeo-lites obtained from numerous works has been performed and pro-vides 57 data from lead borate calorimetry and three data fromHF calorimetry. The thermochemical cycles used to derive heatsof formation from lead borate calorimetry lead first to the enthal-

Table 2Enthalpies of formation of oxides and ions at 298.15 K and calculated parameterDHO=Mz+ (aq) of selected cations.

Oxides DH�f :298:15 K Ions DH�f:298:15 K DHO=Mz+ (aq)(kJ mol�1) (kJ mol�1) (kJ mol�1)

Li2O �597.901 Li+(aq) �278.54 �40.90Na2O �414.801 Na+(aq) �240.34 65.80K2O �363.201 K+(aq) �252.14 141.00Rb2O �339.001 Rb+(aq) �251.124 163.24Cs2O �346.001 Cs+(aq) �258.01 170.0BaO �548.101 Ba+2(aq) �532.51 �15.6(NH4)2O �234.302 NHþ4 (aq) �133.31 32.3SrO �591.301 Sr+2(aq) �550.91 �40.4CaO �635.101 Ca+2(aq) �543.04 �92.1MgO �601.601 Mg+2(aq) �467.04 �134.6FeO �272.001 Fe+2(aq) �90.4165,6 �181.58MnO �385.201 Mn+2(aq) �220.81 �164.4ZnO �350.461 Zn+2(aq) �153.394 �197.07La2O3 �1793.683 La+3(aq) �7096 �124.8Fe2O3 �826.201 Fe+3(aq) �49.465,6 �242.43Al2O3 �1675.701 Al+3(aq) �538.44 �199.63SiO2 (quartz) �910.701 Si4+(aq) – –H2O liq �285.831 H+(aq) 0.01 �285.83

1[55]; 2[56]; 3[57]; 4[58]; 5[59]; 6[60].

338 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

pies of formation from the stable oxides of anhydrous zeolites, DH�ox

(Anhy.zeol). As the enthalpies of formation from the elements, DH�f(Anhy.zeol.), are derived from the measured enthalpies offormation from the stable oxides of dehydrated zeolites, DH�ox

(Anhy.zeol.), and from the sum of the enthalpies of formation fromthe elements of the stable constituent oxides, DH�f MiOxi

� �ðcÞ, the two

latter parameters are derived from the heat contents and enthalpiesof solutions and are subject to errors and inconsistencies. In order tolimit error propagation, the selected anhydrous zeolites are dis-played in Table 1 with their respective unit-cell volumes andenthalpies of formation from the stable oxides, DH�oxðAnhy:zeol:Þ.

2.2. Enthalpies of formation from the constituent oxides, DH�ox

Let us consider an anhydrous zeolite with the following chem-

ical formula: Ma1 ;Ma2 ; . . . ;Mai

� �A AltAl

Fe3þtFe; SitSi

� �TON where sub-

scripts A and T denote the extra-framework and tetrahedral sites,respectively, and letters a, tAl, tFe and tSi represent stoichiometricamounts of cation i having a charge zi. The extra-framework sitesmay be occupied by cations such as Li+, Na+, K+, Mg2+, and Ca2+.The enthalpy of formation of an anhydrous zeolite, DH�f(anhy.zeol.), is the sum of the enthalpies of formation from the ele-ments of the different stable constituent oxides, DH�f MiOxi

� �ðcÞ, plus

a second term, DH�ox, designating the enthalpy of formation fromthe stable constituent oxides (subscript ox.):

DH�f ðAnhy:zeol:Þ ¼Xi¼ns

i¼1

ðniÞ � DH�f MiOxi

� �ðcÞ þ DH�ox:ðAnhy:zeol:Þ

ð4ÞAs was shown in Ref. [6], the enthalpy of formation from the

stable constituent oxides is endothermic for some calcium and acidforms of synthetic zeolites (chabazite, clinoptilolite, mordenite,Y-zeolite) as well as for the Na-faujasite and all BEA zeolites(Table 1). The positive enthalpies of formation from the stable oxi-des do not allow application of the electronegativity differencemethod [10,11] based on Pauling’s concept [52], because of thepresence of stable oxides, DH�f MiOxi

� �ðcÞ, particularly quartz and

corundum that do not display a zeolite-like structure. Using thecorresponding-states theory [53] and considering zeolite-like oxi-des, let us define the enthalpies of formation of dehydrated zeolitesfrom the oxides having a zeolite-like structure (subscript ox. zeol),DHox.zeol(Anhy.zeol.) as follows:

DHox:zeolðAnhy:zeol:Þ ¼ DH�ox:ðAnhy:zeol:Þ � ðniÞ

� DH�f MiOxi

� �ðzeolÞ � DH�f MiOxi

� �ðcÞ

h ið5Þ

where DH�f MiOxi

� �ðzeolÞ and DH�f MiOxi

� �ðcÞ refer to the enthalpies of

formation of oxides having a zeolite-like structure and a stableform, respectively.

The enthalpy of formation of a dehydrated zeolite from the con-stituent oxides, in the zeolite structure, DH�ox;zeolðAnhy:zeol:Þ, anal-ogous to that given by Vieillard [10], contains two types ofinteractions between any two cations: those where cations are indifferent sites (inter-site interaction energy terms) and thosewhere cations are in the same site (2 intra-site interaction energyterms):

DH�ox;zeolðAnhy:zeol:Þ

¼ �N �

xAN

� �� xT

N

� �� DHO¼ðsite AÞ �DHO¼ðsite TÞf g

þPi¼nA

i¼1

Pj¼nA

j¼iþ1

xi;AN

� �� xj;A

N

� �� DHO¼M

zþi

i;A;zeol �DHO¼Mzþ

j

j;A;zeol

� �

þPi¼nT

i¼1

Pj¼nT

j¼iþ1

xi;TN

� �� xj;T

N

� �� DHO¼M

zþi

i;T;zeol �DHO¼Mzþ

j

j;T;zeol

� �

26666664

37777775ð6Þ

where xA and xT are the numbers of oxygen atoms balancing the ex-tra-framework and tetrahedral sites A and T, respectively. The totalnumber of oxygen atoms bound to different cations located in thetwo sites of the anhydrous zeolite must be equal to N, the totalnumber of oxygen atoms of the anhydrous zeolite.

xA þ xT ¼ N ð7Þ

Each of both sites (k = A and T) contains one or several cationsnc. The electronegativity of site k, DHO= (site k), represents theweighed average of electronegativities of different cations in site k:

DHO¼ðsite kÞ ¼Pi¼nc;k

i¼1 ni;k � xi DHO¼Mziþi;k;zeol

� �xk

ð8Þ

where parameter DHO¼Mziþi;k;zeol is the electronegativity of cation Mziþ

located in site k of a zeolite. The number of oxygen atoms balancingsite k (in extra-framework and tetrahedral sites) is then:

xk ¼Xi¼nc; k

i¼1

ni;k � xi ð9Þ

Parameter DHO¼Mziþi;k;zeol characterizing the electronegativity of the

cation in site k of the zeolite mineral environment can be expressedas follows:

DHO¼Mziþi;k;zeol ¼ 1=xi � DH�f MiOxi

� �ðzeolÞ � DH�f Mziþ

i

� �ðcÞ

h ið10Þ

where DH�f Mziþi

� �ðcÞ is the unknown enthalpy of formation of Mz+ in

the crystal state. Similarly, the electronegativity of cation Mziþ inthe stable oxide will be written as follows [54,10,5]:

DHO¼Mziþi;ox ¼ 1=xi � DH�f MiOxi

� �ðcÞ � DH�f Mziþ

i

� �ðcÞ

h ið11Þ

This expression is similar to that with parameter DHO¼Mziþi;aq:

DHO¼Mziþi;aq ¼ 1=xi � DH�f MiOxi

� �ðcÞ � DH�f Mziþ

i

� �ðaqÞ

h ið12Þ

where values are available and are given in Table 2. The differencebetween Eqs. (11) and (12) was further developed in Ref. [54].

Discarding DH�f Mziþi

� �ðcÞ between Eqs. (10) and (11) yields:

DHO¼Mziþi;k;zeol ¼ DHO¼Mziþ

i;ox þ 1=xi � DH�f MiOxi

� �ðzeolÞ � DH�f MiOxi

� �ðcÞ

h ið13Þ

Table 3Crystallographic data (lattice parameters, Z, unit-cell volume, framework density FD) and enthalpies of formation from quartz of some zeosils at 298.15 K.

Name Lattice parameters Z Unit-cell Vol (Å3) FD DH�f:298:15K: qz (kJ mol�1)

a (Å) b (Å) c (Å) a (�) b (�) c (�)

Quartz-a 4.912 4.912 5.402 90 90 120 3 112.881 26.58 0Silicalite orth. 20.07 19.92 13.42 90 90 90 96 5365.512 17.89 5.50 ± 0.8428

Silicalite orth. 20.04 19.92 13.4 90 90 90 96 5347.773 17.95 6.78 ± 0.829

Silicalite orth. 20.08 19.93 13.4 90 90 90 96 5360.864 17.91 8.01 ± 0.8229

Silicalite orth. 20.1 19.96 13.41 90 90 90 96 5379.375 17.85 2.20 ± 1.730

Silicalite orth. 20.02 19.9 13.38 90 90 90 96 5332.036 18.00Silicalite orth. 20.08 19.89 13.37 90 90 90 96 5341.207 17.97Mutinaite 20.2 19.99 13.47 90 90 90 96 5439.308 17.65Silicalite mono. 20.11 19.88 13.37 90 90.67 90 96 5343.329 17.97Ferriérite 18.56 13.89 7.249 90 90 90 36 1868.3410 19.27 6.6031

Linde Y 24.19 24.19 24.19 90 90 90 192 14151.4211 13.57Faujasite 24.26 24.26 24.26 90 90 90 192 14273.9312 13.45 13.60 ± 1.232

ZSM-12 (MTW) 24.88 5.02 12.15 90 107.7 90 28 1445.6713 19.37 8.70 ± 1.332

ZSM-12 (MTW) 24.86 5.012 24.33 90 107.7 90 56 2888.0814 19.39ZSM-11 (MEL) 20.12 20.12 13.44 90 90 90 96 5440.7115 17.64 8.20 ± 1.432

ZSM-11 (MEL) 20.07 20.07 13.41 90 90 90 96 5400.4016 17.78ZSM-11 (MEL) 20.02 20.02 13.38 90 90 90 96 5362.1717 17.90ZSM-11 (MEL) 20.06 20.06 13.4 90 90 90 96 5393.3918 17.80ZSM-18 13.18 13.18 15.85 90 90 120 34 2382.3519 14.27 13.90 ± 0.433

Chabaz. (CHA) 13.53 13.53 14.75 90 90 120 36 2337.8620 15.40 11.43 ± 1.4729

ITQ-7 (ISV) 12.85 12.85 25.21 90 90 90 64 4165.1521 15.37 14.37 ± 1.0729

ITQ-1 (MWW) 14.21 14.21 24.95 90 90 120 72 4361.0022 16.51 10.40 ± 1.4529

CIT-5 (CFI) 13.68 5.024 25.52 90 90 90 32 1754.9423 18.23 8.82 ± 0.8129

SSZ-23 (STT) 12.96 21.79 13.6 90 101.9 90 64 3758.3024 17.03 9.19 ± 1.2229

SSZ-23 (STT) 13.09 21.71 13.71 90 102.5 90 64 3802.9425 16.83ITQ-3 (ITE) 20.62 9.724 19.62 90 90 90 64 3935.0526 16.26 10.10 ± 1.2429

ITQ-4 (IFR) 18.65 13.5 7.631 90 102 90 32 1879.1727 17.03 10.00 ± 1.1729

1[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].

R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351 339

The second term of Eq. (13) represents the difference betweenDHO¼Mziþ

i;k;zeol and DHO¼Mziþox , analogous to dDHO=Mz+ for cation

Mz+ already defined by Vieillard [10], and is a function of the mod-ification in the crystal environment during the transfer from oxideM2/zO to a zeolite.

In Eq. (6), the interaction energy is defined by the differenceDHO¼Mziþ

i;k;zeol � DHO¼Mziþj;k;zeol, and this term characterizes short-

range interactions between cations in different sites or within asame site. The interaction energy must be strictly positive and isassumed to be equal to:

DHO¼Mziþi;k;zeol � DHO¼Mziþ

j;k;zeol

h i¼ 96:483 � vMi

� vMj

� �2ð14Þ

where a vMiand vMj

are the electronegativities (as defined by Pauling[52]) of ions and Mzjþ

j , respectively. Vieillard et al. [10,54,61,12,13]applied the principles of Pauling [52] regarding the predominanceof the nearest-neighbour interactions (short-range interactions)observed in the crystal structure of a mineral to the calculation of en-thalpy of formation. In anhydrous zeolites, all cations located in theextra-framework and tetrahedral sites are assumed to have one ormore common oxygen atoms between any two adjacent polyhedra.The interaction energy expressed by the last two terms in the generalequation of DH�ox;zeolðAnhy:zeolÞ, given in Eq. (6), is different from 0 ifthe site involved is occupied by two or more different cations and con-tributes to the calculation of the heat of formation of the anhydrouszeolites from the constituent oxides.

2.3. Enthalpies of formation of oxides in the zeolite structure

The method provided herein may be simplified if the differencebetween the enthalpy of formation of the stable oxide and that ofthe oxide having a zeolite-like structure is known for Si and Al.Among all the cations composing the zeolites, only silica has beensubjected to numerous calorimetric measurements from a greatnumber of polymorphs, particularly compounds with a zeolite-like

structure called zeosils. The enthalpies of formation of zeosils fromstable quartz, DH�ox;QtzðSiO2ÞZeosil, given in Table 3 with theirrespective crystallographic parameters, range between 2.2 and14.37 kJ mol�1 above the enthalpy of formation of quartz at298 K. The significance of these small enthalpies and their weakdependence on the framework type has been discussed by Petrovicet al. [62] and Piccione et al. [63]. Thus, the electronegativity of cat-ion Si4+ in the zeolite, defined as follows:

DHO¼Si4þzeol ¼ DHO¼Si4þ

ox þ 1=2 � DH�f ðSiO2ÞZeosil � DH�f ðSiO2ÞQuartz

h ið15Þ

can be a direct function of parameter DHO= of ion Si4+ of the stablequartz and of the enthalpy of formation of the zeosil from stablequartz, having the same structure as that of the zeolite.

In order to find out the enthalpy of formation of a zeolite,DH�f ðSiO2ÞðzeolÞ, parameter FD, called tetrahedral framework den-sity, is defined as a measurement of the number of Si atoms occu-pying the tetrahedral sites per volume unit [95,96]. FD is obtainedas [(Si)/Unit-cell Vol] * 1000 (i.e. number of silicon atoms per1000 Å3). The smaller this number, the more pore space is avail-able, regardless of the accessibility of this space. The frameworkdensities of zeosils are calculated from cell parameters (Table 3)and show values ranging from 19.39 for MTW to 13.45 for fauja-site, values that are much lower than that of quartz (FD = 26.58).Fig. 1 displays the relationships between the enthalpies of forma-tion of zeosils from quartz and framework density FD. Piccioneet al. [63] observed a relationship between DH�f ðSiO2ÞZeosil and themolar volume. A second-degree polynomial function is obtainedby constraining the curve to pass through the stable quartz(FD = 26.548):

DH�f ðSiO2Þzeol � DH�f ðSiO2Þquartz

¼ �0:61087 � ðFD� 26:548Þ þ 0:0442 � ðFD� 26:548Þ2 ð16Þ

Fig. 1. Relationship between DH�f ðSiO2Þzeol � DH�f ðSiO2Þquartz and framework densityFD for all zeosils.

340 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

with R2 = 0.9788 and a standard error of e = ±1.35 kJ mol�1 forN = 17 data.

For cation Al+3, in which the stable form is corundum (a-Al2O3),no data relative to the enthalpy of formation of oxide Al2O3with astructure similar to that of the zeolitic framework is known. Al2O3

with an Al atom in tetrahedral coordination is not a naturally-occurring compound. There is a small number of polymorphs ofcorundum with measured enthalpies of formation [97]) and knowncrystal structures [98,99]). Corundum contains only octahedrally-coordinated Al atoms, with the other polymorphs j-Al2O3 et c-Al2O3 having their Al atoms in two tetrahedral and octahedral posi-tions but in variable and hardly quantifiable proportions. Using theunit-cell volume, the FD value is maximum for corundum(FD = 47.08) and decreases in polymorphs (FD = 44.6 for j-Al2O3

and 42.5 for c-Al2O3). Therefore, parameter DHO= of aluminiumin zeolites, DHO¼Al3þ

zeol, will differ from that of aluminium incorundum, DHO¼Al3þ

ox , and will be assumed to be a function of theframework density. In the absence of data about the tetrahe-drally-coordinated Al2O3, the enthalpy of formation of oxideAl2O3, DH�f ðAl2O3Þzeol:, and parameter DHO¼Al3þ

zeol with a zeolite-likestructure can be determined assuming the following relationshipbetween DH�f ðAl2O3Þzeol: and parameter FD:

DH�f ðAl2O3Þzeol � DH�f ðAl2O3Þcorind ¼ A � ðFD� 47:08Þ ð17Þ

where A is a parameter relating the enthalpy of formation of Al2O3

to the framework density and 47.08 is the framework density ofcorundum. Therefore, the electronegativity of cation Al3+ in the zeo-lite, defined as follows:

DHO¼Al3þzeol ¼ DHO¼Al3þ

ox þ 1=3 � DH�f ðAl2O3Þzeol: � DH�f ðAl2O3Þcorind:

� ð18Þ

can be a direct function of the electronegativity of Al3+ of the stablecorundum and of the enthalpy of formation of tetrahedral Al2O3

from stable corundum, having the same structure as that of thezeolite.

In a given anhydrous zeolite, the framework density is obtainedas [(Al + Fe + Si)/Unit-cell Vol] * 1000 (i.e. number of tetrahedralatoms per 1000 Å3). The determinations of unit-cell volumes per-formed on a zeolite that has been heated and then returned to roomtemperature (without being sealed) are strongly affected by the fastrehydration of the zeolite. Therefore, only the determinations ofunit-cell volumes performed ‘ex situ’ (i.e. under anhydrous condi-

tions) are considered reliable and are much less numerous thanthose performed under hydrated conditions. According to recentworks [100], the unit-cell volumes are generally larger for hydratedzeolites than for anhydrous zeolites (at the same temperature). As aresult, the unit-cell volumes of dehydrated zeolites (at 298.15 K)have systematically been compiled from the recent bibliographicdata provided by Cruciani [100] and are given in Table 1. For mostzeolites, since the tabulated unit-cell volume values do not corre-spond exactly to those with a given chemical composition, theunit-cell volume values of the anhydrous zeolites are assumed tobe evaluated with a 2% accuracy [9].

2.4. Example of calculation of the enthalpy of formation from theoxides for an anhydrous zeolite

Using a mesolite with formula (Ca2.06Na1.81)(Al6Si9) O29.965 as anexample, the cations located in the extra-framework site and in thetetrahedral framework site can be written as the following sums ofoxides 2.06 * CaO + 0.905 * Na2O and 3 * Al2O3 + 9 * SiO2, respec-tively. The number of oxygen atoms balancing the cation in the ex-tra-framework site and in the tetrahedral framework site will be2.965 and 27, respectively, giving the total number of oxygenatoms N = 29.965. Then, parameters DHO=(site A) and DHO=(siteT) can be written as follows:

DHO¼ðsite AÞ ¼2:06 � DHO¼Ca2þ

zeol

� �þ 0:905 � DHO¼Naþzeol

� �2:965

ð19Þ

DHO¼ðsite TÞ ¼9 � DHO¼Al3þ

zeol

� �þ 18 � DHO¼Si4þ

zeol

� �27

ð20Þ

Parameters DHO¼Si4þzeol and DHO¼Al3þ

zeol can be calculated fromEqs. (15) and (18), respectively. Then, the enthalpy of formationfrom the constituent oxides of anhydrous chabazite in the zeolitestructure is expressed as follows:

DH�ox;zeolðMesoliteÞ

¼ �N �

27N

� �� 2:965

N

� �� DHO¼site A� DHO¼site Tð Þ

þ 2:06N

� �� 0:905

N

� �� DHO¼Naþzeol � DHO¼Ca2þ

zeol

� �þ 9

N

� �� 18

N

� �� DHO¼Al3þ

zeol � DHO¼Si4þzeol

� �

266664

377775 ð21Þ

The first term characterizing the interaction energy betweensites A and T can be developed and actually contains four interac-tion energies between cations Na+ and Ca2+ of the extra-frameworksite A and cations Al3+ and Si4+ of the tetrahedral site T such that:

27N

� �� 2:965

N

� �� DHO¼site A� DHO¼site Tð Þ

¼

0:905N

� �� 9

N

� �� DHO¼Naþzeol � DHO¼Al3þ

zeol

� �þ 0:905

N

� �� 18

N

� �� DHO¼Naþzeol � DHO¼Si4þ

zeol

� �þ 2:06

N

� �� 9

N

� �� DHO¼Ca2þ

zeol � DHO¼Al3þzeol

� �þ 2:06

N

� �� 18

N

� �� DHO¼Ca2þ

zeol � DHO¼Si4þzeol

� �

26666666664

37777777775: ð22Þ

The enthalpy of formation from the stable oxides of Ca-bearingchabazite is then obtained:

DH�ox:ðmesoliteÞ ¼ DH�ox:zeolðmesoliteÞ

þ 9 � DH�f ðSiO2Þmesolite � DH�f ðSiO2Þquartz

h iþ 3 � DH�f ðAl2O3Þmesolite: � DH�f ðAl2O3Þcorund:

� ð23Þ

R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351 341

It appears that the calculation of the enthalpy of formationfrom the stable oxides of the anhydrous mesolite requiredthe knowledge of six parameters such as DHO¼Ca2þ

zeol;DHO¼Kþzeol;

DHO¼Naþzeol;DHO¼Al3þox ;DHO¼Si4þ

ox and the framework densityFD calculated from the unit-cell volume of the anhydrousmesolite.

3. Results and discussion

3.1. Minimization

Parameter DHO¼Mzþzeol of nine cations including H+, Na+, K+,

Rb+, Cs+, Mg2+, Ca2+, Sr2+ and Ba2+ in the extra-framework siteon the one hand, and parameters DHO¼Si4þ

ox ;DHO¼Al3þox and A

(Eq. (17)) on the other hand, were determined by minimizationof the difference between the experimental enthalpies of forma-tion from the oxides in the zeolite state (Eq. (5)) and those com-puted using the general equation (Eq. (6)). Constraints ofminimization involve short-range interactions and positive valueterms of interaction energies between two different cations inaccordance with Eq. (14). For the nine cations located in theextra-framework site, the values of DHO¼Mziþ

i;k;zeol given in Table 4are assumed to be constant and independent of the nature of thezeolite structure.

The values of DHO¼Si4þox ¼ �209:26 kJ mol�1 and DHO¼Al3þ

ox ¼�210:6 kJ mol�1 represent the values of DHO= of Si4+ and Al3+ inquartz and corundum, respectively. The following equations allowevaluation of DHO¼Si4þ

zeol and DHO¼Al3þzeol in different zeolites from

the knowledge of the framework density, FD:

DHO¼Si4þzeol ¼ �209:26þ 1=2 � ½�0:61087 � ðFD� 26:548Þ

þ 0:0442 � ðFD� 26:548Þ2� ð24ÞDHO¼Al3þ

zeol ¼ �210:60þ 1=3 � ½�0:71 � ðFD� 47:08Þ� ð25Þ

The presence of proton H+ in the extra-framework sites of anhy-drous zeolites is essentially observed in zeolite Y [27] and zeolite-ß[50,28,51].

Assuming DH�f HþðcÞ ¼ DH�f HþðaqÞ ¼ 0, the electronegativity ofthe proton in the oxide state can be written from the enthalpy offormation of water:

DHO¼Hþox ¼ 1=2 � DH�f ðH2OÞðlÞ � DH�f ðHþÞðcÞ

h i¼ �285:83 kJ mol�1 ð26Þ

The minimization is optimized by setting DH�f ðH2OÞðzeolÞand DHO¼Hþzeol at �239.55 kJ mol�1. This deviation correspondsto the difference between the proton in the extra-frameworksite and the proton of liquid water. The new value of DHO¼Hþzeol

represents the reference value of DHO=Mz+ (zeol) for differentcations located in the extra-framework site A of a zeolite mineral.Therefore, for anhydrous zeolites with a proton in the extra-framework sites, Eq. (5) should be modified by the followingequation:

Table 4Values of parameter DHO¼Mziþ

zeol obtained by minimization.

Ions DHO=Mz+

(aq)(kJ mol�1)

DHO=Mz+

(zeol)(kJ mol�1)

Ions DHO=Mz+

(aq)(kJ mol�1)

DHO=Mz+

(zeol)(kJ mol�1)

Cs+ 170.00 231.85 Ba2+ �15.6 50.00Rb+ 163.24 237.75 Sr2+ �40.4 2.00K+ 141 195.85 Ca2+ �92.1 �135.45Na+ 65.8 84.61 Mg2+ �134.6 �190.00Li+ �40.9 �76.52 H+ �285.83 �239.55

DH�ox:ðAnhy:zeol:Þ � DHox:zeolðAnhy:zeolÞ

¼ðnSiÞ � DH�f ðSiO2Þzeosil � DH�f ðSiO2Þquartz

h iþðnAl=2Þ � DH�f ðAl2O3Þzeol � DH�f ðAl2O3Þcorund:

� þðnH=2Þ � DH�f ðH2OÞzeol � DH�f ðH2OÞwater

� 8>><>>:

9>>=>>; ð27Þ

which contributes to the determination of the enthalpy of forma-tion from the constituent oxides of anhydrous zeolites, DH�ox;zeol

ðAnhy:zeolÞ 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 anhy-drous zeolite minerals, DH�ox;zeolðAnhy:zeol:Þ. Some calculation de-tails are provided in this table, such as:

– the framework density FD of the anhydrous zeolite,– the number of oxygen atoms and parameter DHO= site A for

extra-framework cations,– the number of oxygen atoms and parameters DHO¼Si4þ

zeol;

DHO¼Al3þzeol and DHO= site T for tetrahedral cations of the zeolite

framework,– the predicted enthalpy of formation from the constituent oxides

DH�ox;zeolðAnhy:zeol:Þ and DH�oxðAnhy:zeol:Þ calculated from Eqs.(6) and (27), respectively, and

– the experimental enthalpy of formation from the oxidesDH�oxðAnhy:zeol:Þ given in Table 1.

Due to the great difference in the number of oxygen atoms amonganhydrous zeolites, the enthalpies of formation from the oxidessuch as DH�ox;zeolðAnhy:zeolÞ and DH�oxðAnhy:zeol:Þ are given forone mole of tetrahedra TO2. The last column provides the differencebetween the value predicted using the model and the measured va-lue, and yields an average deviation of ±4.5 kJ mol�1 TO2, i.e. lowerthan that obtained with the Navrotsky and Tian [6] method(±5.6 kJ mol�1 TO2).

3.2. Fundamental properties of the enthalpy of formation of anhydrouszeolites

To illustrate the fundamental properties of the enthalpy of for-mation of anhydrous zeolites from the stable oxides as a functionof the crystallochemical properties, we selected anhydrous com-pounds with CaAl2Si4O12 as a chemical formula, characterizing ananhydrous chabazite, an anhydrous faujasite or an anhydrouswairakite.

Let’s consider chabazite (Al/Si = 0.5) in which Na or K has beensubstituted for Ca. As the unit-cell volume is supposed to be thesame for all three compounds, the framework density (FD)and parameters DHO= of cations Al3+ and Si4+ remain constant(Table 6). For a given structure characterized by a constant frame-work density, and for a constant charge (constant Al/Si ratio), thelowest enthalpies of formation from the oxides, DHox.(Anhy.zeol.)and DHox.zeol(Anhy.zeol.), are obtained for the electropositive cat-ions located in site A, which show a DHO= value very different fromthe DHO= of the tetrahedral site.

A relationship between DHO= Mz+(aq) and DHO= Mz+(zeol) in theextra-framework site can be observed (Fig. 2) and exhibits thesame behaviour of cation electronegativity in the exchangeablesites [12,13]. In a same crystallographic family characterized by aconstant molar volume or unit-cell volume, the difference betweenDHox.(Anhy.zeol.) and DHox.zeol(Anhy.zeol.) is constant and inde-pendent of the nature of the cations in the exchangeable sites.

Now let’s vary the Al/Si ratio of an anhydrous calcium chabazitefrom 0 to 1 (Table 6). As the unit-cell volume remains relatively con-stant, the framework density FD and parameters DHO= of cationsCa2+, Al3+ and Si4+ remain constant. The enthalpy of formation fromthe oxides having a zeolite-like structure becomes exothermic as

Table 5Anhydrous zeolites: comparison of the predicted enthalpies of formation from the stable oxides (Eq. (27)) calculated from parameter DHO= of sites A and T and framework densityFD with experimental values.

Anhyd. zeolites FD xA DHO= site A(kJ mol�1)

xT DHO=Si4þðzeolÞ

(kJ mol�1)

DHO=Al3þðzeolÞ

(kJ mol�1)

DHO= site T(kJ mol�1)

DH�ox:zeol

(kJ mol�1)Pred. DH�ox

(kJ mol�1)Exper. DH�ox

(kJ mol�1)Difference(kJ mol�1)

(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k)

Analcime 18.94 0.50 86.14 5.50 �205.66 �203.94 �205.22 �44.93 �36.89 �32.201 4.69Chabazite-Ca 14.83 1.71 �120.93 22.39 �202.65 �202.97 �202.72 �11.02 1.68 8.262 6.59Clinoptilolite-Na 18.00 1.64 84.61 34.36 �205.04 �203.72 �204.85 �25.44 �16.64 �14.113 2.53Clinoptilolite 18.00 1.34 �16.09 34.36 �205.04 �203.72 �204.85 �14.11 �5.24 �9.983 �4.74Clinoptilolite-Ca 17.82 1.66 �140.19 34.36 �204.92 �203.67 �204.74 �5.96 3.04 3.413 0.36Clinoptilolite-K 18.00 1.64 195.85 34.36 �205.04 �203.72 �204.85 �35.10 �26.31 �26.503 �0.19Clinoptil.-K-Na 18.00 1.64 136.56 34.36 �205.04 �203.72 �204.85 �30.06 �21.27 �20.863 0.41Edingtonite 17.34 1.00 50.00 9.00 �204.57 �203.56 �204.24 �45.99 �36.15 �39.784 �3.55Gonnardite 21.82 2.03 �126.78 18.00 �207.32 �204.62 �206.42 �15.65 �9.74 �8.064 1.69Heulandite 19.31 1.08 �88.33 16.93 �205.90 �204.03 �205.54 �13.94 �6.47 �3.255 3.21Heulandite-K 19.31 0.09 195.85 1.91 �205.90 �204.03 �205.63 �35.29 �27.99 �26.506 1.49Heulandite-Na 19.31 0.09 84.61 1.91 �205.90 �204.03 �205.63 �25.63 �18.33 �14.1162 4.22Heulandite-Na 19.31 0.10 139.37 1.91 �205.90 �204.03 �205.63 �32.15 �24.87 �20.806 4.06Heulandite-Na 19.31 0.09 84.93 1.91 �205.90 �204.03 �205.63 �25.85 �18.55 �13.436 5.12Laumonite 18.10 1.00 �135.45 11.00 �205.11 �203.74 �204.73 �11.04 �2.07 �1.787 0.28Leonhardite 18.05 1.03 �133.04 10.97 �205.07 �203.73 �204.71 �11.69 �2.69 �1.787 0.91Leonhardite 18.10 2.00 �135.45 22.00 �205.11 �203.74 �204.73 �11.04 �2.07 �2.198 �0.13Leonhardite-K 18.10 2.00 �36.18 22.00 �205.11 �203.74 �204.73 �27.15 �18.17 �26.668 �8.48Mesolite 18.13 3.00 �62.10 27.00 �205.13 �203.75 �204.67 �27.14 �18.07 �26.594 �8.49Mordenite-Ca 17.50 0.09 �135.45 1.91 �204.69 �203.60 �204.53 �6.18 3.22 2.496 �0.73Mordenite-Ca 17.50 0.09 �52.32 1.91 �204.69 �203.60 �204.53 �13.53 �4.14 �5.946 �1.80Mordenite-K 17.50 0.09 195.85 1.91 �204.69 �203.60 �204.53 �34.65 �25.26 �25.256 0.01Mordenite-Na 17.50 0.09 84.61 1.91 �204.69 �203.60 �204.53 �25.09 �15.70 �6.466 9.24Natrolite 22.41 1.00 84.61 9.00 �207.62 �204.76 �206.67 �53.46 �47.98 �51.464 �3.48Tetranatrolite 22.41 1.00 84.61 9.00 �207.62 �204.76 �206.67 �53.46 �47.98 �46.944 1.02Scolecite 17.89 1.00 �135.45 9.00 �204.96 �203.69 �204.54 �12.89 �3.59 �15.774 �12.15Stellerite 17.72 1.02 �135.45 16.98 �204.84 �203.65 �204.63 �7.71 1.48 1.389 �0.10Stilbite 17.57 1.07 �123.11 16.94 �204.74 �203.62 �204.53 �9.49 �0.11 �0.315 �0.20Thomsonite 18.23 2.50 �91.44 17.50 �205.20 �203.77 �204.59 �26.39 �17.20 �19.554 �2.40Yugawaralite 20.97 1.00 �135.45 15.00 �206.87 �204.42 �206.38 �9.00 �3.10 2.135 5.23Zeolite Silice Y 12.61 0.00 84.61 2.00 �200.72 �202.44 �200.72 �0.39 16.69 13.0610 �3.63Zeolite DAY 12.61 0.03 84.61 1.97 �200.72 �202.44 �200.80 �9.09 7.70 7.7810 0.08Zeolite Y-Na 12.61 0.13 84.61 1.87 �200.72 �202.44 �201.07 �34.72 �18.87 �22.6610 �3.79Zeolite Y-Na 12.61 0.14 75.48 1.86 �200.71 �202.44 �201.11 �37.10 �21.19 �21.3211 �0.13Zeolite Y-Ca 12.55 0.14 �125.47 1.86 �200.66 �202.43 �201.06 �10.75 5.08 3.4111 �1.67Zeolite Y-Na 12.61 0.14 84.61 1.86 �200.72 �202.44 �201.11 �38.34 �22.63 �26.6410 �4.01Zeolite Y-Rb 12.54 0.15 166.49 1.86 �200.64 �202.42 �201.05 �50.55 �34.33 �34.3411 �0.01Zeolite Y-K 12.55 0.14 160.49 1.86 �200.65 �202.43 �201.06 �48.57 �32.29 �34.3211 �2.03Zeolite Y-Cs 12.55 0.14 181.14 1.86 �200.65 �202.43 �201.07 �52.03 �36.09 �36.0911 0.00ZeoliteY-Li 12.62 0.14 �49.04 1.86 �200.72 �202.44 �201.13 �21.21 �5.25 �5.2411 0.01Zeolite-13X 12.35 0.22 84.61 1.78 �200.47 �202.38 �201.18 �57.11 �41.85 �41.7910 0.06Faujasite-Na 12.61 0.14 84.61 1.86 �200.71 �202.44 �201.10 �37.72 �21.98 �22.066 �0.08Zeolite ß-Li 15.30 0.03 �92.89 1.97 �203.03 �203.08 �203.03 �3.50 9.15 18.5812 9.43Zeolite ß-Na 15.30 0.03 �25.20 1.97 �203.03 �203.08 �203.03 �5.66 7.24 14.5112 7.27Zeolite ß-K 15.30 0.03 71.88 1.97 �203.03 �203.08 �203.03 �9.49 3.35 8.5612 5.21Zeolite ß-Rb 15.30 0.03 190.02 1.97 �203.03 �203.08 �203.03 �12.69 �0.16 4.0112 4.17Zeolite ß-Cs 15.30 0.03 134.93 1.97 �203.03 �203.08 �203.03 �11.32 1.38 7.4612 6.08Zeolite ß-K(2) 15.30 0.03 95.61 1.97 �203.03 �203.08 �203.03 �10.23 2.49 8.5612 6.07Zeolite ß-Rb(2) 15.30 0.03 212.94 1.97 �203.03 �203.08 �203.03 �13.41 �0.98 4.0112 4.99Zeolite ß-Cs(2) 15.30 0.03 156.42 1.97 �203.03 �203.08 �203.03 �12.03 0.57 7.4612 6.89Zeolite Na-BEA 15.30 0.11 35.39 1.89 �203.03 �203.08 �203.04 �24.41 �11.44 �2.4013 9.04Zeolite Mg-BEA 15.30 0.04 �195.30 1.96 �203.03 �203.08 �203.03 �0.28 12.41 26.8214 14.41Zeolite Ca-BEA 15.30 0.04 �145.44 1.96 �203.03 �203.08 �203.03 �2.10 10.49 25.9914 15.50Zeolite Sr-BEA 15.30 0.03 �21.76 1.96 �203.03 �203.08 �203.03 �5.97 6.59 18.3114 11.73Zeolite Ba-BEA 15.30 0.04 3.18 1.96 �203.03 �203.08 �203.03 �7.46 5.19 13.8414 8.65Zeolite Mg-BEA 15.30 0.10 �189.43 1.90 �203.03 �203.08 �203.04 �1.34 11.41 32.4614 21.05Zeolite Ca-BEA 15.30 0.10 �139.75 1.90 �203.03 �203.08 �203.04 �6.00 6.46 26.1414 19.68

(a) Framework density FD of the anhydrous zeolite calculated from the unit-cell volume Vu.c. anhyd. given in Table 1.(b) number of oxygen atoms balancing the extra-framework sites A (Eq. (9)).(c) DHO= (site A) (in kJ mol�1) (Eq. (9)).(d) number of oxygen atoms balancing the tetrahedral sites T (Eq. (6)).(e) DHO¼Si4þ

zeol (in kJ mol�1) (Eq. (24));(f) DHO¼Al3þ

zeol (in kJ mol�1) (Eq. (25)).(g) DHO=(site T) (in kJ mol�1) (Eq. (8)).(h) DH�ox;zeolðAnhy:zeol:Þ (in kJ mol�1TO2 basis) (Eq. (6)).(i) DH�oxðAnhy:zeol:Þ (in kJ mol�1 TO2 basis) (Eq. (27)).(j) Measured values of DH�oxðAnhy:zeol:Þ (in kJ mol�1 TO2 basis).(k) Difference = (column j) � (column i) (in kJ mol�1 TO2 basis).The number of references is the same as given at the end of Table 1.

342 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

Table 6Unit-cell volume, framework density, parameter DHO= of cations in exchangeable and tetrahedral sites, enthalpy of formation from the oxides in the zeolitic structure (Eq. (6)) andenthalpy of formation from the stable oxides (Eq. (27)) of CaAl2Si4O12 (chabazite, faujasite and laumontite in the anhydrous state).

Al/Si Vu.c. anhy. (Å3) FD DHO= site A(kJ mol�1)

DHO¼Si4þðzeolÞ

(kJ mol�1)

DHO¼Al3þðzeolÞ

(kJ mol�1)

DH�ox: zeol

(kJ mol�1)DH�ox

(kJ mol�1)

Chabazite-Ca Ca(Al2Si4)O12 0.50 404.5 14.83 �135.45 �202.65 �202.97 �62.31 13.48Chabazite-Na Na2(Al2Si4)O12 0.50 404.5 14.83 84.61 �202.65 �202.97 �264.03 �188.23Chabazite-K K2(Al2Si4)O12 0.50 404.5 14.83 195.85 �202.65 �202.97 �366.01 �290.21

Zeosil CHA SiO2 0.00 389.6a 15.40 – – – 0.00 12.31Chabazite Ca0.5(AlSi5)O12 0.20 404.5 14.83 �135.45 �202.65 �202.97 �32.62 44.96Chabazite Ca(Al2Si4)O12 0.50 404.5 14.83 �135.45 �202.65 �202.97 �62.31 13.48Chabazite Ca1.5(Al3Si3)O12 1.00 404.5 14.83 �135.45 �202.65 �202.97 �89.09 �15.07

Chabazite-Na Na2(Al2Si4)O12 0.50 404.5 14.83 84.61 �202.65 �202.97 �264.03 �188.23Analcime Na2(Al2Si4)O12 0.50 315.3 19.03 84.61 �205.72 �203.96 �269.21 �220.92

Laumontite Ca(Al2Si4)O12 0.50 331.5 18.10 �135.45 �205.11 �203.74 �66.24 �12.39Chabazite Ca(Al2Si4)O12 0.50 404.5 14.83 �135.45 �202.65 �202.97 �62.31 13.48Faujasite Ca(Al2Si4)O12 0.50 477.6 12.56 �135.45 �200.67 �202.43 �63.75 29.53

a [83].

Fig. 2. Relationship between DHO=Mz+ (zeol) and DHO=Mz+ (aq) for cations in theextra-framework sites.

R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351 343

the Al/Si ratio increases. When Al/Si = 0, silica exhibits a chabazite-like structure [83], which explains why parameter DHOx.Zeol

(Anhy.zeol.) becomes null. On the other hand, parameter DHox.

(Anhy.zeol.) represents the enthalpy of the zeosil CHA from quartzand is 12.31 kJ mol�1, which is close to the experimental value, i.e.DH�f ;qtz ¼ 11:43 kJ mol�1 [63]. Consequently, it is readily understoodthat the enthalpies of formation from the stable oxides may be po-sitive in some anhydrous zeolites.

Still starting from calcium chabazite, let’s consider an anhy-drous calcium faujasite and an anhydrous laumontite exhibitingthe same Al/Si ratio. The unit-cell volume is the only explicativeparameter of all three calcium compounds having the same Al/Siratio. This parameter is very high in faujasite (big pores and lowFD value) and decreases toward chabazite to laumontite (smallpores and high FD value). When the silicate framework density in-creases (the pore volume decreases), DHox.zeol(Anhy.zeol.) remainsconstant but DHox.(Anhy.zeol.) becomes more exothermic. Thesame trend is observed between sodium chabazite and analcimewith Al/Si = 0.5. As a result, for an anhydrous zeolite with twooxygen atoms (TO2), with a constant Al/Si ratio and a sameexchangeable cation, the enthalpy of formation from the stableoxides decreases to about 3 kJ mol�1 when the molar volumeincreases by 1 cm3 mol�1.

These fundamental properties show that the enthalpy offormation of an anhydrous zeolite from the constituent oxides is

governed by three major factors, which are the framework density(obtained from the unit-cell volume), the Al/Si ratio and the natureof the cation.

3.3. Accuracy of the predictive method for anhydrous zeolites

With the values of the enthalpies of formation of oxides listed inTable 2, the enthalpies of formation of anhydrous zeolites were cal-culated from the experimental and predicted enthalpies of forma-tion from the oxides. Fig. 3 shows a plot of standard errors ofestimation when using the model presented here and the averageerror obtained when using the Navrotsky and Tian [6] method. Thehorizontal and vertical dashed lines show the ±0.5% error for eachmodel. For some points that are outside of the ±0.5% interval, an er-ror bar has been added and corresponds to the error in the exper-imental measurements. The average error for 57 data is ±0.48%with the present model, which is better than the Navrotsky andTian [6] model (0.69% for 55 data)

Using the model by Navrotsky and Tian [6], the zeolites Y satu-rated with cations Ca, Li, K, Rb and Cs show overestimated enthal-pies of formation. This is explained by the insufficientconsideration of the pore size contribution. The introduction ofthe zeolitic framework density (parameter FD) on the one handand the contribution of the protons located in the extra-frameworksites on the other hand allowed reduction of the discrepancy be-tween the measured and estimated enthalpies of formation fromthe oxides in the present model.

As regards zeolites ß, the discrepancies between the measuredand estimated enthalpies of formation from the oxides remaingreater than 0.5%, but are smaller than those evaluated using Nav-rotsky and Tian’s [6] algorithm. The inaccuracy probably resultsfrom uncertain measurements of the unit-cell volume of zeoliteß because Higghins et al. [43] have shown that this compound ap-pears as a hybrid of two intergrowing polymorphs.

3.4. Enthalpies of formation of hydrated zeolites

For hydrated zeolites with available chemical compositions andmolar volumes, the enthalpy of formation can be considered as thecontribution of the enthalpies of formation of anhydrous zeolitesand hydration enthalpy (Eq. (2)). Using this method applied toanhydrous zeolites and the fundamental relationship of hydrationenthalpy developed by Vieillard and Mathieu [9], the enthalpy offormation of hydrated zeolites can be known and tested against agreat number of experimental data.

Fig. 3. Plots of the errors (%) for determinations from the model of [6] against the errors for values from the model presented here and applied to anhydrous zeolites. Thehorizontal and vertical dashed lines represent a ±0.5% error used in this model.

344 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

Among the calorimetric data of the anhydrous zeolites (Table 1),some compounds yielded the number of moles of hydration waterand their hydration enthalpies as measured by TTD calorimetry,thus contributing to the calculation of the enthalpies of formationof hydrated zeolites (Table 7). This table also shows the enthalpiesof formation from the oxides of anhydrous zeolites as estimated inthe present work, the enthalpies of hydration per mole of water asestimated by Vieillard and Mathieu [9] and the enthalpy of forma-tion from the oxides of hydrated zeolites using the followingformula:

DH�ox;298

Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON:nH2O:ðH2OÞ

" #

¼ DH�ox;298

Xi¼nc

i¼1

Mi

!AlnAl

SinSi

� �ON

" #þ nH2O � DHHdy�W ð28Þ

The differences between the measured and estimated enthal-pies of formation of hydrated zeolites can be expressed as follows:

– either as one compound (Al, Si)O2 if the enthalpy of formationfrom the oxides is used (column g in Table 7).

– or as a percentage of the enthalpy of formation from the ele-ments (column i in Table 7). These differences are used to com-pare the accuracy of this model with that of Chermak andRimstidt [4] (Fig. 4).

The model developed in the present work yields a ±0.69% errorfor 67 data whereas the oxide summation method gives an uncer-tainty of ±1.16% for 49 data. The number of data tested in the pres-ent model is greater than the number of data tested in thepolyhedral model [4], which was not applied to Li-, Rb-, Cs-, Sr-and Ba-bearing hydrated zeolites.

Fig. 4 shows that BEA zeolites are the only points exhibiting adiscrepancy greater than 0.5% in the present model andgreater than 1% in the polyhedral model [4]. Consideringthe alkaline BEA zeolites [50] (empty triangles), for which datameasured in two different hydration states are given, thepresent model yields a mean error of �0.61%, which is muchsmaller than the one obtained with the polyhedral model [4](�1.66%).

Sun et al. [51] provided a set of data of enthalpies of formationof a BEA–Na–zeolite in different hydration states characterized bya variable number of water moles ranging from 0.06 to 0.94 permole of TO2 (black squares in Fig. 4). The enthalpies of formationestimated in this work give a constant error around �0.99%. Usingthe oxide summation method, the discrepancy between the exper-imental and estimated values increases from the hydrated state(�1.03%) to the very lowly hydrated state (�2.21%). This showsthat the oxide summation model developed by Chermak and Rims-tidt [4] can not be applied to zeolites with incomplete hydrationstates.

Table 7Hydrated zeolites: comparison of experimental enthalpies of formation from the stable oxides (from lead borate calorimetry), DH�oxðHydr: zeol:Þ, with predicted enthalpies of formation from the stable oxides.

Nb. H2O DH�ox: hydr. meas.(kJ mol�1)

DH�f hydr. calc.(kJ mol�1)

DH�ox: anhy. pred.(kJ mol�1)

DH�hyd-W pred.(kJ mol�1)

DH�ox hydr. pred.(kJ mol�1)

Differ./TO2 DH�f hydr. pred.(kJ mol�1)

Differ. (%)

(a) (b) (c) (d) (e) (f) (g) (h) (i)

Analcime 1 �138.301 �3280.82 �110.66 �38.22 �148.88 3.53 �3291.41 �0.32Chabazite-Ca 12.54 �310.52 �15652.9 20.22 �24.60 �288.27 �1.85 �15630.71 0.14Clinoptiloite-Na 10.296 �565.23 �20341.5 �299.58 �21.70 �522.99 �2.34 �20299.28 0.21Clinoptilolite 9.504 �479.883 �20010.7 �93.55 �26.54 �345.80 �7.51 �19876.59 0.67Clinoptilolite-Ca 11.628 �255.243 �20779.7 54.81 �28.90 �281.26 1.45 �20805.74 �0.13Clinoptilolite-K 7.794 �717.843 �19694.5 �473.51 �20.11 �630.23 �4.87 �19606.85 0.44Clinopti.-K-Na 8.91 �627.843 �19968.5 �382.88 �21.15 �571.33 �3.14 �19911.98 0.28Edingtonite 4 �287.44 �6392.07 �186.66 �34.04 �322.81 7.07 �6427.48 �0.55Gonnardite 6 �396.44 �12198.6 �97.57 �56.59 �437.14 4.07 �12239.34 �0.33Heulandite 6.1 �238.75 �10656.5 �58.22 �33.58 �263.06 2.71 �10680.85 �0.23Laumontite 4 �154.16 �7251.02 �12.39 �40.35 �173.81 3.29 �7270.73 �0.27Leonhardite 3.518 �153.36 �7110.95 �16.15 �42.48 �165.59 2.05 �7123.24 �0.17Leonhardite 7 �306.77 �14214.7 �24.79 �42.82 �324.54 1.49 �14232.55 �0.13Leonhardite 7 �521.27 �14254.4 �218.09 �37.66 �481.70 �3.29 �14214.86 0.28Mesolite 8 �748.94 �17943.9 �270.98 �44.87 �629.94 �7.93 �17824.98 0.66Natrolite 2 �372.64 �5766.86 �239.92 �52.07 �344.07 �5.71 �5738.33 0.49Tetranatrolite 2 �349.44 �5743.66 �239.92 �52.07 �344.07 �1.07 �5738.33 0.09Scolecite 3 �200.34 �6100.69 �17.94 �45.62 �154.78 �9.10 �6055.17 0.75Stellerite 7.04 �200.18 �10900.9 13.32 �30.01 �197.96 �0.24 �10898.77 0.02Stilbite 7.27 �2325 �11017.9 �0.99 �29.68 �216.75 �1.69 �11002.93 0.14Thomsonite 6 �529.44 �12464.7 �171.97 �48.23 �461.36 �6.80 �12396.69 0.55Yugawaralite 4 �1336 �9051.32 �24.80 �46.31 �210.05 9.63 �9128.37 �0.85Zeolite Y-Ca 1.24 �18.169 �1351.25 5.09 �21.80 �21.95 3.79 �1355.04 �0.28Zeolite Y-Cs 1.023 �52.239 �1286.98 �36.00 �16.88 �53.27 1.04 �1288.02 �0.08Zeolite Y-K 1.096 �48.039 �1303.04 �32.01 �17.00 �50.64 2.61 �1305.65 �0.20Zeolite Y-Li 1.252 �28.319 �1355.09 �5.17 �19.93 �30.12 1.81 �1356.90 �0.13Zeolite Y-Na 1.241 �42.399 �1345.5 �21.10 �17.10 �42.33 �0.06 �1345.44 0.00Zeolite Y-Rb 1.027 �52.299 �1286.69 �34.06 �17.48 �52.02 �0.27 �1286.41 0.02Zeolite ß-Li 0.8 9.4210 �1142.28 9.16 �9.93 1.22 8.20 �1150.48 �0.72Zeolite ß-Li 0.06 17.2910 �922.899 9.16 �16.74 8.16 9.13 �932.03 �0.99Zeolite ß-Na 0.78 5.3510 �1135.51 7.27 �9.53 �0.16 5.51 �1141.02 �0.49Zeolite ß-Na 0.08 12.810 �927.982 7.27 �15.59 6.03 6.77 �934.75 �0.73Zeolite ß-K 0.74 3.5810 �1125.52 3.40 �8.76 �3.08 6.66 �1132.18 �0.59Zeolite ß-K 0.04 8.0510 �920.968 3.40 �14.22 2.83 5.22 �926.19 �0.57Zeolite ß-Rb 0.72 0.210 �1122.47 �0.13 �6.61 �4.89 5.09 �1127.57 �0.45Zeolite ß-Rb 0.04 3.6110 �924.701 �0.13 �10.48 �0.55 4.16 �928.86 �0.45Zeolite ß-Cs 0.7 1.8410 �1115.34 1.42 �7.68 �3.95 5.79 �1121.13 �0.52Zeolite ß-Cs 0.06 6.5710 �927.68 1.42 �11.89 0.71 5.86 �933.54 �0.63Zeolite ß-K(2) 0.74 3.5810 �1125.75 2.53 �8.22 �3.55 7.13 �1132.88 �0.63Zeolite ß-K(2) 0.04 8.0510 �921.198 2.53 �13.31 2.00 6.05 �927.25 �0.66Zeolite ß-Rb(2) 0.72 0.210 �1122.77 �0.98 �6.21 �5.45 5.65 �1128.42 �0.50Zeolite ß-Rb(2) 0.04 3.6110 �924.992 �0.98 �9.83 �1.37 4.98 �929.97 �0.54Zeolite ß-Cs(2) 0.7 1.8410 �1115.63 0.60 �7.25 �4.47 6.31 �1121.94 �0.57Zeolite ß-Cs(2) 0.06 6.5710 �927.97 0.60 �11.19 �0.07 6.64 �934.61 �0.72Zeolite Na-BEA 0.06 �3.4611 �958.019 �10.64 �34.07 �12.68 9.22 �967.24 �0.96Zeolite Na-BEA 0.1 �5.4511 �971.442 �11.20 �33.97 �14.60 9.15 �980.59 �0.94Zeolite Na-BEA 0.238 �9.4511 �1014.89 �11.20 �30.89 �18.56 9.11 �1023.99 �0.90Zeolite Na-BEA 0.274 �9.5111 �1025.24 �11.20 �30.14 �19.46 9.95 �1035.19 �0.97Zeolite Na-BEA 0.354 �11.0211 �1049.61 �11.20 �28.52 �21.30 10.28 �1059.89 �0.98Zeolite Na-BEA 0.449 �13.411 �1079.15 �11.20 �26.72 �23.20 9.80 �1088.95 �0.91Zeolite Na-BEA 0.529 �14.1411 �1102.75 �11.20 �25.29 �24.58 10.44 �1113.19 �0.95Zeolite Na-BEA 0.644 �13.3211 �1134.8 �11.20 �23.37 �26.25 12.93 �1147.73 �1.14Zeolite Na-BEA 0.726 �14.5611 �1159.48 �11.20 �22.08 �27.24 12.68 �1172.16 �1.09

(continued on next page)

R.M

athieu,P.Vieillard

/Microporous

andM

esoporousM

aterials132

(2010)335–

351345

Tabl

e7

(con

tinu

ed)

Nb.

H2O

DH� ox:

hyd

r.m

eas.

(kJm

ol�

1)

DH� f

hyd

r.ca

lc.

(kJm

ol�

1)

DH� ox:

anh

y.pr

ed.

(kJm

ol�

1)

DH� h

yd-W

pred

.(k

Jmol�

1)

DH� ox

hyd

r.pr

ed.

(kJm

ol�

1)

Dif

fer.

/TO

2D

H� f

hyd

r.pr

ed.

(kJm

ol�

1)

Dif

fer.

(%)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Zeol

ite

Na-

BEA

0.85

5�

15.1

511

�11

96.9

4�

11.2

0�

20.2

1�

28.4

813

.33

�12

10.2

8�

1.11

Zeol

ite

Na-

BEA

0.94

�17

.821

1�

1223

.91

�11

.20

�19

.06

�29

.12

11.3

0�

1235

.21

�0.

92Ze

olit

eM

g-B

EA0.

0824

.861

2�

922.

668

12.4

1�

22.3

210

.63

14.2

3�

936.

90�

1.54

Zeol

ite

Mg-

BEA

0.89

14.9

12

�11

64.1

512

.41

�12

.44

1.34

13.5

6�

1177

.71

�1.

17Ze

olit

eC

a-B

EA0.

0923

.711

2�

929.

057

10.5

0�

20.4

88.

6615

.05

�94

4.11

�1.

62Ze

olit

eC

a-B

EA0.

8613

.941

2�

1158

.92

10.5

0�

11.8

10.

3413

.60

�11

72.5

1�

1.17

Zeol

ite

Sr-B

EA0.

0616

.961

2�

924.

155

6.59

�18

.33

5.49

11.4

9�

935.

63�

1.24

Zeol

ite

Sr-B

EA0.

88.

841

2�

1143

.79

6.59

�10

.87

�2.

1110

.97

�11

54.7

4�

0.96

Zeol

ite

Ba-

BEA

0.04

12.9

712

�92

2.37

15.

19�

18.3

84.

468.

51�

930.

88�

0.92

Zeol

ite

Ba-

BEA

0.79

4.77

12

�11

44.9

45.

19�

10.8

3�

3.36

8.13

�11

53.0

8�

0.71

Zeol

ite

Mg-

BEA

0.08

29.7

812

�94

4.77

11.4

3�

48.8

27.

5322

.25

�96

7.02

�2.

36Ze

olit

eM

g-B

EA1.

0912

.881

2�

1250

.36

11.4

3�

22.3

7�

12.9

525

.83

�12

76.1

8�

2.07

Zeol

ite

Ca-

BEA

0.08

23.0

812

�95

7.11

66.

49�

43.6

53.

0020

.08

�97

7.20

�2.

10Ze

olit

eC

a-B

EA0.

956.

431

2�

1222

.44

6.49

�22

.75

�15

.12

21.5

5�

1243

.99

�1.

76

(a)

Nu

mbe

rof

mol

esof

wat

erof

the

hyd

rate

dze

olit

e.(b

)M

easu

red

DH� oxðH

ydra

ted

zeol:Þ.

(c)

Mea

sure

dD

H� fðH

ydra

ted

zeol:Þ

(Eq.

(4))

from

colu

mn

b.(d

)Pr

edic

ted

DH� oxðA

nh

y:ze

ol:Þ

(Eq.

(27)

).(e

)Pr

edic

ted

DH� h

yd:-

Wfr

om[9

].(f

)Pr

edic

ted

DH� oxðH

ydra

ted

zeol:Þ

(Eq.

(28)

)fr

omco

lum

ns

a,d

and

e;(g

)D

iffe

ren

ce=

colu

mn

b�

colu

mn

f(i

nkJ

mol�

1TO

2ba

sis)

.(h

)Pr

edic

ted

DH� fðH

ydra

ted

zeol:Þ

(Eq.

(4))

from

colu

mn

f.(i

)D

iffe

ren

ce=

(col

um

nc�

colu

mn

h)

*10

0/(c

olu

mn

c).

1[4

4];

2[2

3];

3[4

5];

4[4

6];

5[2

6];

6[4

7];

7[4

8];

8[4

9];

9[2

7];

10[5

0];

11[5

1];

12[2

8].

Fig. 4. Plots of the errors (%) for determinations from the model of [4] against theerrors for values from the model presented here and applied to hydrated zeolites(the enthalpy of formation of which is derived from anhydrous zeolites).

346 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

As regards the other data on the BEA zeolites saturated withalkaline earth ions [28] and to a lesser extent on the other BEA zeo-lites, the error is greater and one may wonder whether this signif-icant discrepancy is related to the presence of interstratificationswithin these compounds [101]. If the unit-cell volumes of theanhydrous and hydrated phases on the one hand, and the struc-tural chemistry of ions (particularly Al) on the other hand areknown, these discrepancies could probably be reduced.

Other values of enthalpies of formation of hydrated zeoliteswere directly measured by lead borate calorimetry and are shownin Table 8 along with the structural formulas. Among the 45 newdata, most hydrated zeolites are derived from Shim et al. [23] withthe introduction of Ca, Li, Na and K-bearing chabazites having dif-ferent Al/Si ratios and different numbers of water molecules.

The unit-cell volumes of anhydrous and hydrated zeolites arerequired in the computation of the enthalpy of formation fromthe oxides of anhydrous zeolites (this model, column e in Table8) and the enthalpy of hydration [9] (column f in Table 8). Theyalso contribute to the calculation of the enthalpies of formationfrom the oxides (Eq. (28)) and from the elements of hydrated zeo-lites (column g and i, respectively, in Table 8). Differences betweenthe predicted and experimental enthalpies of formation of hy-drated zeolites are given in kJ per mole of (Al, Si)O2 (column h inTable 8) or in% (column j in Table 8). The model developed forthe 45 data yields a ±0.32% error whether the oxide summationmodel gives an uncertainty of ±0.39% for 33 data. The best accuracyof the present model with respect to the polyhedral model [4] isrepresented in Fig. 5 where a great homogeneity of values is shownfor the 17 different zeolites.

Twenty new data of enthalpy of formation from the elements ofhydrated zeolites experimentally determined by the hydrofluricacid (HF) calorimetry are given in Table 9. These zeolites exhibita great diversity of minerals such as analcime with various Al/Si ra-tios [122], merlinoite [123] and (Si–Al)–MFI [92]. By applying thesame approach as in Table 8 and using the unit-cell volumes ofanhydrous and hydrated zeolites, the enthalpy of formation of hy-drated zeolites derived from the contribution of the enthalpy offormation from the oxides of anhydrous zeolites as evaluated inthe present work and from the enthalpy of hydration [9] is given

Table 8Hydrated zeolites: comparison of experimental enthalpies of formation (from lead borate calorimetry) with the enthalpies of formation predicted in this work.

Vu.c anhy

(Å3)Vu.c hydr

(Å3)DH�ox: hydr.meas.(kJ mol�1)

DH�f hydr.calc.(kJ mol�1)

DH�ox: anhy.pred.(kJ mol�1)

DH�hyd�W

pred.(kJ mol�1)

DH�ox hydr.pred.(kJ mol�1)

Differ./TO2

(kJ mol�1)

DH�f hydr.pred.(kJ mol�1)

Differ.(%)

(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

Amichite (Ca0.22K3.84Na3.88)(Al8.06Si 7.9)O32.03–9.86 H2O 938.77a 1054.96a �1499.81 �19924.0 �1036.3 �40.03 �1431.0 �4.3 �19855.2 0.35Bikitaite (Li2)(Al2Si4)O12–2 H2O 297.65b 295.62b �231.12 �6719.2 �80.9 �52.10 �185.1 �7.7 �6673.2 0.68Brewsterite (Ba0.66Sr1.3K0.02Na0.06)(Al4Si12)O32–10.1 H2O 830.79c 917.40u �692.03 �19005.2 �311.6 �33.51 �650.0 �2.6 �18963.2 0.22Chabazite-Ca (Ca1.65K0.1Na0.24)(Al3.79Si8.25)O24.005–12.47 H2O 809.00d 822.40d �347.24 �15716.1 �5.3 �26.50 �335.7 �1.0 �15704.6 0.07Chabazite-Ca1 (Ca1.58K0.36)(Al3.34Si8.66)O24.09–12.83 H2O 809.00d 822.40d �271.45 �15692.5 �17.3 �24.02 �325.5 4.5 �15746.6 �0.34Chabazite-Ca3 (Ca2.24K0.52)(Al4.91Si7.09)O24.045–14.68 H2O 809.00d 822.40d �391.85 �16675.5 �87.4 �25.44 �460.8 5.7 �16744.5 �0.41Chabazite-Ca4 (Ca2.29K0.04Na0.04)(Al4.07Si7.93)O24.295–13.4 H2O 809.00d 822.40d �349.95 �16281.9 �2.5 �26.31 �355.2 0.4 �16287.1 �0.03Chabazite-Ca5 (Sr0.08Ca2.8K0.06)(Al4.8Si7.2) O24.51–12.95 H2O 809.00d 822.40d �413.35 �16530.0 �44.6 �28.78 �417.4 0.3 �16534.1 �0.02Chabazite-Ca6 (Ca2.84)(Al4.71Si7.29)O24.485–15.16 H2O 809.00d 822.40d �428.95 �17151.0 �20.0 �24.86 �396.8 �2.6 �17119.0 0.19Chabazite-K See footnote I 820.72e 834.32w �657.74 �15924.4 �332.2 �22.75 �621.8 �3.0 �15888.6 0.23Chabazite-K1 (K3.23)(Al3.31Si8.69)O23.96–8.9 H2O 825.96e 839.63q �712.45 �14530.1 �444.2 �19.68 �619.4 �7.8 �14437.1 0.64Chabazite-K2 (K3.39)(Al3.18Si8.82)O24.105–9.88 H2O 825.96e 839.63q �734.75 �14871.1 �471.6 �18.28 �652.2 �6.8 �14788.6 0.55Chabazite-K3 (K4.79)(Al4.89Si7.11)O23.95–10.63 H2O 825.96e 839.63q �959.75 �15440.1 �706.8 �24.59 �968.2 0.7 �15448.6 �0.06Chabazite-K4 (K5.39)(Al5.87Si6.13)O23.76–10.71 H2O 825.96e 839.63q �1101.15 �15641.9 �802.3 �29.11 �1114.0 1.1 �15654.9 �0.08Chabazite-Li1 Li3.05K0.01Na0.13)(Al3.25Si8.75)O23.97–11.79 H2O 809.00e 822.40d �378.25 �15380.3 �47.9 �23.73 �327.7 �4.2 �15329.9 0.33Chabazite-Li2 Li3.17K0.01Na0.15)(Al3.32Si8.68)O24.005–10.88 H2O 809.00e 822.40d �368.95 �15145.9 �57.3 �25.30 �332.6 �3.0 �15109.5 0.24Chabazite-Li3 (Sr0.17Li3.75K0.02Na0.15)(Al 4.89Si7.11)O23.685–

12.52 H2O809.00e 822.40d �522.75 �15929.8 �124.0 �28.11 �475.9 �4.0 �15883.0 0.29

Chabazite-Li4 (Li3.27K0.02Na0.62)(Al3.96Si 8.04)O23.975–2.59 H2O 809.00e 822.40d �520.55 �15868.8 �128.2 �24.76 �439.9 �6.7 �15788.2 0.51Chabazite-Li5 (Li3.76K0.01Na0.2)(Al4.04Si7.96)O23.965–12.7 H2O 809.00e 822.40d �464.35 �15895.8 �96.9 �25.31 �418.4 �3.8 �15849.9 0.29Chabazite-Li6 (Li4.7K0.01Na0.24)(Al4.96Si7.04)O23.995–14.52 H2O 809.00e 822.40d �435.15 �16609.1 �152.3 �25.09 �516.6 6.8 �16690.6 �0.49Chabazite-Li7 (Li5.6Na0.02)(Al5.75Si6.25)O23.935–15.17 H2O 809.00e 822.40d �574.35 �17098.1 �167.7 �25.75 �558.3 �1.3 �17082.1 0.09Chabazite-Na1 (K0.01Na3.33)(Al3.31Si8.69)O 24.015–11.69 H2O 827.62e 841.33q �515.15 �15236.2 �290.5 �19.91 �523.3 0.7 �15244.4 �0.05Chabazite-Na2 (K0.01Na3.95)(Al4Si8)O23.98–12.57 H2O 827.62e 841.33q �666.85 �15717.7 �367.7 �21.67 �640.1 �2.2 �15691.0 0.17Chabazite-Na3 (K0.02Na4.28)(Al3.98Si8.02)O 24.16–11.89 H2O 827.62e 841.33q �735.65 �15663.9 �409.0 �22.32 �674.3 �5.1 �15602.6 0.39Chabazite-Na4 (Zn0.02K0.01Na4.4)(Al4.86Si7.14)O23.775–13.36 H2O 827.62e 841.33q �693.15 �16007.5 �423.3 �23.94 �743.1 4.2 �16057.5 �0.31Chabazite-Na5 (Ca0.02K0.01Na5.51)(Al5.85Si6.15)O23.855–16.5 H2O 827.62e 841.33q �755.25 �17130.9 �552.5 �24.07 �949.6 16.3 �17325.3 �1.13Clinoptilolite (Ca0.53Mg0.08K0.25Na0.08)(Al 1.61Si7.39)O18–

5.56 H2O505.00f 522.35f �191.76 �10314.9 �20.8 �26.66 �169.0 �2.5 �10292.2 0.22

Dachiardite (Ca0.66Mg0.1K0.35Na2.21)(Al4.41Si19.67)O47.99–11.8 H2O

1383.84g 1383.8h �612.07 �26594.4 �199.9 �25.08 �495.8 �4.8 �26478.3 0.44

Edingtonite (Ba1.93K0.08Na0.06)(Al3.96Si6.03)O20–7.38 H2O 576.78i 598.06i �580.78 �12584.3 �369.5 �35.42 �630.9 5.0 �12634.6 �0.40Erionite (Ca2.06Mg1.18K2.37Na0.47)(Al8.5Si27.3)O72.01–

26.47 H2O2279.50d 2282.0d �779.09 �42874.8 �259.0 �26.18 �951.9 4.8 �43047.7 �0.40

Ferri.-mord. (Ca1.2Mg0.48K0.3Na2.52)(Al6.12Si29.82)O72–17.34 H2O 1974.89j 2022.8j �801.010 �39694.8 �212.7 �26.85 �678.3 �3.4 �39572.1 0.31Garronite (Sr0.02Ca2.66K0.1Na0.54)(Al6.43Si9.67)O31.985–

12.98 H2O871.89k 1012.2k �656.71 �20392.0 �134.5 �40.44 �659.4 0.2 �20394.7 �0.01

Gismondite (Ca0.85K0.01Na0.07)(Al1.98Si2.11)O8.08–4.32 H2O 215.59l 261.71l �170.51 �5542.0 �32.2 �36.65 �190.5 4.9 �5562.0 �0.36Gmelinite (Ca0.14Mg0.07K0.49Na7.67)(Al8.26Si15.66)O48–

24.4 H2O1646.62m 1666.9x �1311.011 �31278.2 �801.1 �22.65 �1353.7 1.8 �31320.9 �0.14

Heulandite (Sr0.1Ca0.75K0.04Na0.41)(Al2.28Si6.75)O18.001–6.11 H2O

465.98n 524.16n �339.26 �10772.5 �73.3 �34.56 �284.4 �6.1 �10717.7 0.51

Leonhardite-Ca

(Ca2)(Al4Si8)O24–7.3 H2O 663.00o 676.00y �315.312 �14309.1 �24.8 �41.95 �331.0 1.3 �14324.8 �0.11

Leonhardite-K (Ca1.1K2.1Na0.1)(Al4Si8)O24.2–2.6 H2O 663.00o 676.00y �545.112 �13026.0 �379.1 �46.11 �499.0 �3.8 �12979.8 0.35Leonhardite-

Na(Ca0.4K0.1Na3)(Al4Si8)O23.95–5.6 H2O 663.00o 676.00y �465.912 �13597.9 �346.4 �37.01 �553.7 7.3 �13685.7 �0.65

Morden.-epistil.

(Ca0.6K0.04Na0.26)(Al1.48Si4.52)O12.01–3.85 H2O 339.40p 339.50p �128.613 �7027.68 �29.73 �31.78 �152.08 3.91 �7051.15 �0.33

Pollucite I (Rb0.04Cs0.77Na0.14)(Al0.91S i2.08)O6–0.34 H2O 159.99q 159.99q �180.814 �3103.7 �159.1 �35.26 �171.1 �3.2 �3094.0 0.31Stilbite-1 (Ca1.01Na0.12)(Al2.12Si6.88)O18.01–7.27 H2O 512.13r 554.82z �232.015 �11018.2 �1.0 �29.68 �216.8 �1.7 �11002.9 0.14Thomsonite (Ca8.16Na3.52)(Al20Si20.12)O80.22–25.36 H2O 2193.72s 2250.51s �2066.48 �50324.3 �639.4 �46.92 �1829.3 �5.9 �50087.2 0.47

(continued on next page)

R.M

athieu,P.Vieillard

/Microporous

andM

esoporousM

aterials132

(2010)335–

351347

Tabl

e8

(con

tinu

ed)

Vu

.can

hy

(Å3)

Vu

.ch

yd

r

(Å3)

DH� ox:

hyd

r.m

eas.

(kJm

ol�

1)

DH� f

hyd

r.ca

lc.

(kJm

ol�

1)

DH� ox:

anh

y.pr

ed.

(kJm

ol�

1)

DH� hy

d�W

pred

.(k

Jmol�

1)

DH� ox

hyd

r.pr

ed.

(kJm

ol�

1)

Dif

fer.

/TO

2

(kJm

ol�

1)

DH� f

hyd

r.pr

ed.

(kJm

ol�

1)

Dif

fer.

(%)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Wai

raki

teSe

efo

otn

ote

II31

1.83

t32

1.42

q�

123.

516

�66

48.8

�20

.7�

56.7

2�

134.

11.

8�

6659

.4�

0.16

Zeol

ite

Y(N

a 0.2

81

8)(

Al 0

.28

18Si

0.7

18

15)O

1.9

99

9–1

.276

5H

2O

79.3

6u78

.46u

�46

.71

7�

1360

.2�

22.2

�16

.45

�43

.2�

3.5

�13

56.6

0.26

Zeol

ite

A(N

a 0.5

06

7)(

Al 0

.50

1Si

0.4

97

4)O

1.9

99

65–1

.090

6H

2O

77.1

6u77

.43u

�74

.21

7�

1363

.8�

49.6

�27

.68

�79

.85.

6�

1369

.4�

0.41

(a)

Un

it-c

ell

volu

me

ofan

hyd

rou

sze

olit

e(i

nÅ

3).

(b)

Un

it-c

ell

volu

me

ofh

ydra

ted

zeol

ite

(in

Å3).

(c)

Mea

sure

dD

H� oxðH

ydra

ted

zeol:Þ.

(d)

Mea

sure

dD

H� fðH

ydra

ted

zeol:Þ

(Eq.

(4))

from

colu

mn

c.(e

)Pr

edic

ted

DH� oxðA

nh

y:ze

ol:Þ

(Eq.

(27)

).(f

)Pr

edic

ted

DH� h

yd:-

Wfr

om[9

].(g

)Pr

edic

ted

DH� oxðH

ydra

ted

zeol:Þ

(Eq.

(28)

)fr

omco

lum

ns

ean

df.

(h)

Dif

fere

nce

=co

lum

nc�

colu

mn

g(i

nkJ

mol�

1TO

2ba

sis)

.(i

)Pr

edic

ted

DH� fðH

ydra

ted

zeol:Þ

(Eq.

(4))

from

colu

mn

g.(j

)D

iffe

ren

ce=

(col

um

nd�

colu

mn

i)*

100/

(col

um

nd)

.I,

(Ba 0

.01Sr

0.0

3C

a 1.0

2K

1.9

6N

a 0.3

4)(

Al 3

.96Si

7.9

2)O

23

.99�

12.7

3H

2O

.II

,(C

a 0.9

73M

g 0.0

01

25K

0.0

01

25N

a 0.

00

75)(

Al 1

.98Si

4.0

21)O

11

.99

6�

2.05

1H

2O

.a [1

02];

b[1

03];

c [104

];d[1

8];

e Esti

mat

edfr

onV

u.c

.h

yd

..u

sin

g[1

8];

f [105

];g A

ssu

med

tobe

equ

alto

Vu

.c.

hy

dr.;

h[1

06];

i [30]

;j [1

07];

k[1

08];

l [109

];m

[110

];n[3

2];

n[3

3];

p[1

11]

;q[1

12];

r [38]

;s [3

9];

t [113

];u[1

14];

v [20]

;w

[115

];x[2

5];

y [47]

;z [4

9].

1[1

16];

2[1

17];

3[2

0];

4[2

2];

5[2

3];

6[1

18];

7[1

06];

8[1

19];

9[2

4];

10[1

20];

11[2

5];

12[4

8];

13[1

11];

14[1

21];

15[4

9];

16[4

7];

17[1

14].

Fig. 5. Plots of the errors (%) for determinations from the model of [4] against theerrors for values from the model presented here and applied to hydrated zeolites(the enthalpy of formation of which is derived from TTDC measurements).

348 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

in column g in Table 9. Fig. 6 shows that both predictive modelsyield homogeneous and comparable results. It is reminded thatthe calorimetric data of analcime [15], heulandite [124], mesolite,natrolite and scolecite [125] were used to build the polyhedralmodel [4].

Other values of enthalpies of formation of zeolites derived fromhigh-pressure and high-temperature phase equilibrium experi-ments were ignored due to greater errors related to a lack of dataconsistency.

The enthalpies of formation of the hydrated forms coming fromdifferent families of compounds like the faujasite [27], chabazite[23], analcime [122] and merlinoite [123], can be used to checkthe reliability of the predictive model for the enthalpy of formationof zeolites from two thermodynamic entities, i.e. the enthalpy offormation of anhydrous zeolites and the enthalpy of hydration. In-deed, the errors obtained represent ±0.12%, ±0.30%, ±0.19% and±0.13% for faujasites (6 data), chabazites (42 data), analcimes (8data) and merlinoites (6 data), respectively. Using the oxide sum-mation method [4], errors are ±0.74% (3 data), ±0.41% (16 data),±0.20% (8 data) and ±0.15% (6 data), respectively.

As a conclusion, the predictive model for the enthalpy of for-mation from the oxides of anhydrous zeolites based upon theframework density on the one hand and on the electronegativitydifference between the A and T sites on the other hand is valid.The predictive model for the enthalpy of formation of anhydrouszeolites presented in this paper coupled with the predictive mod-el for the enthalpy of hydration [9] yield enthalpies of formationof hydrated zeolites that are perfectly consistent with the numer-ous measured enthalpies of formation of zeolites having varyinghydration degrees and chemical compositions (Al/Si ratios, greatdiversity of cations in the exchangeable sites). This is true forall the great zeolite families characterized by the frameworkdensity.

This model will be considered as a powerful tool for performingthe following tasks:

– understanding the behaviour of several zeolites in saturatedsystems,

Table 9Hydrated zeolites: comparison of experimental enthalpies of formation (from HF calorimetry) with the enthalpies of formation predicted in this work.

Vu.c. anhy.

(Å3)Vu.c. hydr.

(Å3)DH�f hydr. calc.(kJ mol�1)

DH�ox: anhy. pred.(kJ mol�1)

DH�hyd-W pred.(kJ mol�1)

DH�ox hydr. pred.(kJ mol�1)

DH�f hydr. pred.(kJ mol�1)

Differ.(%)

(a) (b) (c) (d) (e) (f) (g) (h)

Analcime (Na0.96)(Al0.96Si2.04)O6–1 H2O 159.13a 161.45k �3305.801 �105.06 �38.57 �143.63 �3290.73 0.46Analcime (Na1)(Al1Si2)O6–1 H2O 157.46a 161.25l �3303.202 �110.54 �39.99 �150.53 �3303.01 0.01Analcime (Na0,96)(Al0,96Si2,04)O6–1.02 H2O 157.46a 161.25l �3301.802 �105.78 �38.80 �145.35 �3298.17 0.11Analcime (Na0,95)(Al0,95Si2,05)O6–1.025 H2O 157.46a 161.25l �3294.102 �104.58 �38.50 �144.04 �3296.94 �0.09Analcime-BZI (Na1.03)(Al1.03Si1.97)O6–0.985 H2O 157.49a 161.29l �3314.902 �114.07 �40.86 �154.32 �3306.55 0.25Analcime-MSHG (Na1.016)(Al1.016Si1.984)O6–0.992 H2O 157.91a 161.71l �3312.302 �112.24 �40.36 �152.28 �3304.63 0.23Analcime-MVI (Na0.946)(Al0.946Si2.054)O6–1.027 H2O 157.11a 160.90l �3298.702 �104.25 �38.44 �143.74 �3296.67 0.06Analcime-SBC (Na1.049)(Al1.049Si1.951)O6–0.976 H2O 158.15a 161.96l �3319.502 �116.02 �41.27 �156.31 �3308.52 0.33Clinoptilolite See footnote I 1009.99b 1044.51b �20645.003 �159.46 �25.68 �439.95 �20605.01 0.19Heulandite (Ba0.065Sr0.175Ca0.585K0.132 Na0.383)(Al2.165Si6.835)O18–6 H2O 465.98c 524.16c �10594.604 �106.35 �32.64 �302.21 �10669.81 �0.71Heulandite (Ba0.065Sr0.175Ca0.585K0.132Na0.383)(Al2.165Si6.835)O18–6 H2O 465.98c 524.16c �10622.55 �106.35 �32.64 �302.21 �10669.81 �0.45Merlinoite-1 (K0.19Na0.81)(Al1Si1.94)O5.88–2.13 H2O 161.73d 183.82m �3591.206 �117.98 �30.20 �182.31 �3598.23 �0.20Merlinoite-2 (K0.8Na0.2)(Al1Si1.94)O5.88–1.81 H2O 163.50d 185.85m �3519.006 �148.33 �29.48 �201.68 �3510.40 0.24Merlinoite-3 (K1)(Al1Si1.94)O5.88–1.69 H2O 162.37d 184.56m �3481.806 �158.21 �29.45 �207.99 �3477.25 0.13Merlinoite-4 (K0.19Na0.81)(Al1Si1.81)O5.62–2.18 H2O 165.04d 187.59m �3488.306 �114.28 �29.14 �177.81 �3489.63 �0.04Merlinoite-5 (K0.91Na0.09)(Al1Si1.81)O5.62–1.79 H2O 162.70d 184.93m �3387.306 �151.32 �28.86 �202.98 �3384.76 0.08Merlinoite-6 (K1)(Al1Si1.81)O5.62–1.69 H2O 160.92d 182.90m �3360.006 �156.17 �29.25 �205.61 �3356.48 0.10Mesolite (Ca0.657Na0.676)(Al1.99Si3.01)O10–2.647 H2O 275.72e 284.52n �5961.207 �91.03 �44.84 �209.72 �5932.30 0.48Mordenite (Ca0.289Na0.361)(Al0.94Si5.06)O11.9995–3.468 H2O 344.59f 346.57f �6756.205 �14.71 �23.12 �94.89 �6740.28 0.24Natrolite (Na2)(Al2Si3)O10–2 H2O 223.13g 281.25n �5732.707 �239.92 �52.07 �344.07 �5738.33 �0.10Pollucite (H0.137Rb0.028Cs0.65Na0.185)(Al1Si2)O6–0.256 H2O 159.03h 159.03h �3098.508 �132.95 �45.16 �144.52 �3052.08 1.50Scolecite (Ca1)(Al2Si3)O10–3 H2O 279.48e 286.18n �6063.107 �17.94 �45.62 �154.78 �6055.17 0.13Stilbite (Ca1.019K0.006Na0.136)(Al2.18Si6.82)O18–7.33 H2O 512.13 i 554.82o �11033.69 �4.91 �29.91 �224.13 �11033.22 0.00(Si, Al)-MFI (H3)(Al3Si93)O192–28.8 H2O 5360.00j 5360.00j �95976.2010 840.96 �13.99 438.12 �95431.18 0.57

I, (Ba0.062Sr0.036Ca0.761Mg0.124Mn0.002K0.543Na0.954)(Al3.45Si14.533)O36–10.922 H2O.(a) Unit-cell volume of anhydrous zeolite (in Å3).(b) Unit-cell volume of hydrated zeolite (in Å3).(c) Measured DH�f ðHydrated zeol:Þ.(d) Predicted DH�oxðAnhy:zeol:Þ (Eq. (27)).(e) Predicted DH�hyd:-W from [9].(f) Predicted DH�oxðHydrated zeol:Þ (Eq. (28)) from columns d and e.(g) Predicted DH�f ðHydrated zeol:Þ (Eq. (4)) from column f.(h) Difference = (column c � column g) * 100/(column c).aEstimated from Vu.c. hydr. using [18]; b[105]; c[32]; dEstimated from Vu.c.hydr. using [126]; e[127]; f[17]; g[36]; h[112]; i[38]; j[67]; k[15]; l[122]; m[123]; n[125]; o[128].1[15]; 2[122]; 3[16]; 4[124]; 5[17]; 6[123]; 7[125]; 8[129]; 9[128]; 10[92].

R.M

athieu,P.Vieillard

/Microporous

andM

esoporousM

aterials132

(2010)335–

351349

Fig. 6. Plots of the errors (%) for determinations from the model of [4] againstthe errors for values from the model presented here and applied to hydratedzeolites (the enthalpy of formation of which is derived from HF calorimetricmeasurements).

350 R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351

– finding out whether the presence of water is crucial to theformation of zeolites,

– modelling the thermal behaviours (unit-cell, frameworkdensity) of zeolites as a function of temperature,

– modelling the cationic exchanges as a function of relativehumidity.

Acknowledgments

Financial support for this report was partly provided by CentreNational de la Recherche Scientifique (CNRS, France) and AgenceNationale pour la gestion des Déchets Radio-Actifs (ANDRA,France). Mme Nathalie Fradin is thanked for providing the linguis-tic reviewing. This is CRPG Contribution No. 2050.

A computation software (excel) can be provided upon request.

References

[1] S.J. Chipera, J.A. Apps, in: D.L. Bish, D.W. Ming (Eds.), Natural Zeolites:Occurence, Properties Applications, Blacksburg (VA), 2001, pp. 117–161.

[2] S. Ramı´ rez, P. Vieillard, A. Bouchet, A. Cassagnabère, A. Meunier, E. Jacquot,Appl. Geochem. 20 (2005).

[3] P. Vieillard, S. Ramı´ rez, A. Bouchet, A. Cassagnabère, A. Meunier, E. Jacquot,Appl. Geochem. 19 (2004) 1699–1709.

[4] J.A. Chermak, J.D. Rimstidt, Am. Mineral. 74 (1989) 1023–1031.[5] P. Vieillard, Zeolites 15 (1995) 202–212.[6] A. Navrotsky, Z.R. Tian, Chem. Eur. J. 7 (2001) 769–774.[7] S.J. Chipera, D.L. Bish, in: H. Kodama, A.R. Mermut, J.K. Torrance (Eds.),

Proceedings of the 11th International Clay Conference, Clays for Our Future,1997, pp. 595–602.

[8] J.D. Cox, D.D. Wagman, V.A. Medvedev, CODATA Key Values for Thermo-dynamics, Hemisphere Publishing Corporation, New York, 1989.

[9] P. Vieillard, R. Mathieu, Am. Mineral. 94 (2009) 565–577.[10] P. Vieillard, Geochim. Cosmochim. Acta 58 (1994) 4049–4063.[11] P. Vieillard, Geochim. Cosmochim. Acta 58 (1994) 4065–4107.[12] P. Vieillard, Clays Clay Mineral. 48 (2000) 459–473.[13] P. Vieillard, Clays Clay Mineral. 50 (2002) 352–363.[14] S. Gaboreau, P. Vieillard, Geochim. Cosmochim. Acta 68 (2004) 3307–3316.[15] G.K. Johnson, H.E. Flotow, P.A.G. O’Hare, W.S. Wise, Am. Mineral. 67 (1982)

736–748.[16] G.K. Johnson, I.R. Tasker, R. Jurgens, P.A.G. O’Hare, J. Chem. Thermodyn. 23

(1991) 475–484.[17] G.K. Johnson, I.R. Tasker, H.E. Flotow, P.A.G. O’Hare, Am. Mineral. 77 (1992)

85–93.

[18] D.L. Bish, J.W. Carey, in: D.L. Bish, D.W. Ming (Eds.), Natural Zeolites:Occurrence, Properties Applications, Mineralogical Society of America,Blacksburg, 2001, pp. 403–452.

[19] L.V. Mel’chakova, L.P. Ogorodova, I.A. Kiseleva, I.A. Belitskii, Russ. J. Phys.Chem. 77 (2003) 1–4.

[20] L.P. Ogorodova, L.V. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, Geochem. Int. 43(2005) 721–723.

[21] L.P. Ogorodova, L.V. Mel’chakova, I.A. Kiseleva, I.V. Pekov, Geochem. Int. 42(2004) 191–194.

[22] L.P. Ogorodova, I.A. Kiseleva, L.V. Mel’chakova, I.A. Belitskii, Geochem. Int. 40(2002) 466–471.

[23] S.H. Shim, A. Navrotsky, T.R. Gaffney, J.E. Macdougall, Am. Mineral. 84 (1999)1870–1882.

[24] L.P. Ogorodova, L.V. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, Vest. Moskov.Univ. Ser. 4 Geol. 56 (2001) 56–59.

[25] L.P. Ogorodova, L.V. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, Vest. Moskov.Univ. Ser. 4 Geol. (2002) 71–73.

[26] I. Kiseleva, A. Navrotsky, I.A. Belitskii, B. Fursenko, Am. Mineral. 86 (2001)448–455.

[27] S.Y. Yang, A. Navrotsky, Micropor. Mesopor. Mater. 37 (2000) 175–186.[28] P. Sun, A. Navrotsky, Micropor. Mesopor. Mater. 109 (2008) 147–155.[29] G. Cruciani, A. Gualtieri, Am. Mineral. 84 (1999) 112–119.[30] K. Stahl, J.C. Hanson, Eur. J. Mineral. 10 (1998) 221–228.[31] L.P. Van Reeuwijk, The Thermal Dehydratin of Natural Zeolites: Meded

Landbouwhogeschool Wageningen, 1974, pp. 1–88.[32] T. Armbruster, M.E. Gunter, Am. Mineral. 76 (1991) 1872–1883.[33] T. Fridriksson, D.L. Bish, D.K. Bird, Am. Mineral. 88 (2003) 277–283.[34] K. Stahl, R. Thomasson, Zeolites 14 (1994) 12–17.[35] A. Martucci, M. Sacerdoti, G. Cruciani, C. Dalconi, Eur. J. Mineral. 15 (2003)

485–493.[36] W.H. Baur, W. Joswig, Neues Jahrb. Mineral. Monat. (1996) 171–187.[37] R. Arletti, E. Mazzucato, G. Vezzalini, Am. Mineral. 91 (2006) 628–634.[38] G. Cruciani, G. Artioli, A. Gualtieri, K. Stahl, J.C. Hanson, Am. Mineral. 82

(1997) 729–739.[39] K. Stahl, R. Thomasson, J. Appl. Cryst. 25 (1992) 251–258.[40] G. Artioli, K. Stahl, G. Cruciani, A. Gualtieri, J.C. Hanson, Am. Mineral. 86

(2001) 185–192.[41] I. Petrovic, A. Navrotsky, Micropor. Mater. 9 (1997) 1–12.[42] W.J. Mortier, E. Bossche (van den), J.B. Uytterhoeven, Zeolites 4 (1984) 41–44.[43] J.B. Higgins, R.B. LaPierre, J.L. Schlenker, A.C. Rohrman, J.D. Wood, G.T. Kerr,

W.J. Rohrbaugh, Zeolites 8 (1988) 446–452.[44] L.P. Ogorodova, I.A. Kiseleva, L. Mel’chakova, I.A. Belitskii, B. Fursenko,

Geochem. Int. 34 (1998) 980–984.[45] S. Yang, A. Navrotsky, R. Wilkin, Am. Mineral. 86 (2001) 438–447.[46] I.A. Kiseleva, L.P. Ogorodova, L.V. Mel’chakova, I.A. Belitskii, B.A. Fursenko,

Eur. J. Mineral. 9 (1997) 327–332.[47] I. Kiseleva, A. Navrotsky, I.A. Belitskii, B.A. Fursenko, Am. Mineral. 81 (1996)

658–667.[48] I. Kiseleva, A. Navrotsky, I.A. Belitskii, B.A. Fursenko, Am. Mineral. 81 (1996)

668–675.[49] I.A. Kiseleva, A. Navrotsky, I.A. Belitskii, B. Fursenko, Geochem. Int. 39 (2001)

170–176.[50] P. Sun, S. Deore, A. Navrotsky, Micropor. Mesopor. Mater. 91 (2006) 15–22.[51] P. Sun, S. Deore, A. Navrotsky, Micropor. Mesopor. Mater. 98 (2007) 29–40.[52] L. Pauling, The Nature of the Chemical Bond, third ed., Cornell University

Press, New York, 1960.[53] M.K. Karapet’yants, Comparative Calculation Methods for Physicochemical

Properties (in Russian), in: Nauka Izd (Ed.), Izd. Nauka, Moscow, 1965.[54] P. Vieillard, Y. Tardy, CR Acad. Sci. Paris 306 (1988) 423–428.[55] R.A. Robie, B.S. Hemingway, US Geol. Surv. Bull. 2131 (1995) 416.[56] D.E. Wilcox, L.A. Bromley, Ind. Eng. Chem. 55 (1963) 32–39.[57] R.A. Robie, B.S. Hemingway, J.R. Fisher, US Geol. Surv. Bull. 1452 (1978) 456.[58] J.W. Johnson, E.H. Oelkers, H.C. Helgeson, Comput. Geosci. 18 (1992) 899–

947.[59] V.B. Parker, I.L. Khodakovskii, J. Phys. Chem. Ref. Data 24 (1995) 1699–1745.[60] E.L. Shock, H.C. Helgeson, Geochim. Cosmochim. Acta 52 (1988) 2009–

2036.[61] P. Vieillard, Y. Tardy, CR Acad. Sci. Paris 308 (1989) 1539–1545.[62] I. Petrovic, A. Navrotsky, M.E. Davis, S.I. Zones, Chem. Mater. 5 (1993) 1805–

1813.[63] P.M. Piccione, C. Laberty, S.Y. Yang, M.A. Camblor, A. Navrotsky, M.E. Davis, J.

Phys. Chem. B 104 (2000) 10001–10011.[64] K. Ogata, Y. Takeuchi, Y. Kudoh, Z. Krist. 179 (1987) 403–413.[65] D.H. Olson, G.T. Kokotailo, S.L. Lawton, W.M. Meier, J. Phys. Chem. 85 (1981)

2238–2243.[66] G.D. Price, J.J. Pluth, J.V. Smith, J.M. Bennett, R.L. Patton, J. Am. Chem. Soc. 104

(1982) 5971–5977.[67] H. Lermer, M. Drager, J. Steffen, K.K. Unger, Zeolites 5 (1985) 131–134.[68] K.J. Chao, J.C. Lin, Y. Wang, G.H. Lee, Zeolites 6 (1986) 35–38.[69] H. Van Koningsveld, H. Van Bekkum, J.C. Jansen, Acta Crystallogr. B 43 (1987)

127–132.[70] H. Van Koningsveld, Acta Crystallogr. B 46 (1990) 731–735.[71] G. Vezzalini, S. Quartieri, E. Galli, A. Alberti, G. Cruciani, A. Kvick, Zeolites 19

(1997) 323–325.[72] H. Van Koningsveld, J.C. Jansen, H. Van Bekkum, Zeolites 10 (1990) 235–242.[73] H. Gies, R.P. Gunawardane, Zeolites 7 (1987) 442–445.

R. Mathieu, P. Vieillard / Microporous and Mesoporous Materials 132 (2010) 335–351 351

[74] J.B. Parise, D.R. Corbin, L. Abrams, D.E. Cox, Acta Crystallogr. C 40 (1984)1493–1497.

[75] J.A. Hriljac, M.M. Eddy, A.K. Cheetham, J.A. Donohue, G.J. Ray, J. Sol. StateChem. 106 (1993) 66–72.

[76] R.B. LaPierre, A.C. Rohrman, J.L. Schlenker, J.D. Wood, M.K. Rubin, W.J.Rohrbaugh, Zeolites 5 (1985) 346–348.

[77] C.A. Fyfe, H. Gies, G.T. Kokotailo, B. Marler, D.E. Cox, J. Phys. Chem. 94 (1990)3718–3721.

[78] G.T. Kokotailo, P. Chu, S.L. Lawton, W.M. Meier, Nature 278 (1978) 119–120.[79] C.A. Fyfe, H. Gies, G.T. Kokotailo, C. Pasztor, H. Strobl, D.E. Cox, J. Am. Chem.

Soc. 111 (1989) 2470–2474.[80] M. Hochgrafe, B. Marler, H. Gies, C.A. Fyfe, Y. Feng, H. Grondey, G.T. Kokotailo,

Z. Krist. 211 (1996) 221–227.[81] O. Terasaki, T. Ohsuna, H. Sakuma, D. Watanabe, Y. Nakagawa, R.C. Medrud,

Chem. Mater. 8 (1996) 463–468.[82] S.L. Lawton, W.J. Rohrbaugh, Science 247 (1990) 1319–1322.[83] M.J. Diaz-Cabanas, P.A. Barrett, M.A. Camblor, J. Chem. Soc. Chem. Commun.

17 (1998) 1881–1882.[84] L.A. Villaescusa, P.A. Barrett, M.A. Camblor, Angew. Chem. Int. Ed. 38 (1999)

1997–2000.[85] M.A. Camblor, A. Corma, M.J. Diaz-Cabanas, C. Baerlocher, J. Phys. Chem. B 102

(1998) 44–51.[86] P.A. Barrett, M.J. Diaz-Cabanas, M.A. Camblor, R.H. Jones, J. Chem. Soc. Faraday

Trans. 94 (1998) 2475–2481.[87] M.A. Camblor, M.J. Diaz-Cabanas, J. Perez-Pariente, S.J. Teat, W. Clegg, I.J.

Shannon, P. Lightfoot, Angew. Chem. Int. Ed. 37 (1998) 2122–2126.[88] M.A. Camblor, M.J. Diaz-Cabanas, P.A. Cox, I.J. Shannon, P.A. Wright, R.E.

Morris, Chem. Mater. 11 (1999) 2878–2885.[89] M.A. Camblor, A. Corma, P. Lightfoot, L.A. Villaescusa, P.A. Wright, Angew.

Chem. Int. Ed. 36 (1997) 2659–2661.[90] P.A. Barrett, M.A. Camblor, A. Corma, R.H. Jones, L.A. Villaescusa, Chem. Mater.

9 (1997) 1713–1715.[91] G.K. Johnson, I.R. Tasker, D.A. Howell, J.V. Smith, J. Chem. Thermodyn. 19

(1987) 617–632.[92] J. Patarin, M. Soulard, H. Kessler, J.L. Guth, M. Diot, Thermochim. Acta 146

(1989) 21–38.[93] E.C. Moloy, L.P. Davila, J.F. Shackelford, A. Navrotsky, Micropor. Mesopor.

Mater. 54 (2002) 1–13.[94] A. Navrotsky, in: P.J. Heaney, C.T. Prewitt, G.V. Gibbs (Eds.), Silica: Physical

Behavior, Geochemistry and Materials Applications, Mineralogical Society ofAmerica, 1994, pp. 309–329.

[95] W.M. Meier, D.H. Olson, in: E.M. Flanigen, L.B. Sand, (Eds.), Molecular SieveZeolites, 1971, pp. 155–170.

[96] W.M. Meier, D.H. Olson, C. Baerlocher, Zeolites 17 (1996) 1–230.[97] S.C. Carniglia, J. Am. Ceram. Soc. 66 (1983) 495–500.[98] L. Smrcok, V. Langer, K. Jan, Acta Crystallogr. C 62 (2006) i83–i84.[99] H.L. Gross, W. Mader, J. Chem. Soc. Chem. Commun. (1997) 55–56.

[100] G. Cruciani, J. Phys. Chem. Sol. 67 (2006) 1973–1994.[101] A. Alberti, G. Cruciani, E. Galli, S. Merlino, R. Millini, S. Quartieri, G. Vezzalini,

S. Zanardi, J. Phys. Chem. B 106 (2002) 10277–10284.

[102] G. Vezzalini, A. Alberti, A. Sani, M. Triscari, Micropor. Mesopor. Mater. 31(1999) 253–262.

[103] O. Ferro, S. Quartieri, G. Vezzalini, C. Ceriani, E. Fois, A. Gamba, G. Cruciani,Am. Mineral. 86 (2004) 94–104.

[104] A. Alberti, G. Vezzalini, S. Quartieri, G. Cruciani, S. Bordiga, Micropor.Mesopor. Mater. 42 (2001) 277–287.

[105] T. Armbruster, Am. Mineral. 78 (1993) 260–264.[106] L.P. Ogorodova, L.V. Melchakova, I.A. Kiseleva, Russ. J. Phys. Chem. 81 (2007)

1748–1750.[107] C. Dalconi, A. Alberti, G. Cruciani, J. Phys. Chem. B 107 (2003) 12973–12980.[108] L. Schröpfer, W. Joswig, Eur. J. Mineral. 9 (1997) 53–56.[109] G. Vezzalini, S. Quartieri, A. Alberti, Zeolites 13 (1993) 34–42.[110] L. Benco, J. Hafner, F. Hutschka, H. Toulhoat, J. Phys. Chem. B 107 (2003)

9756–9762.[111] L.P. Ogorodova, L.V. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, B.A. Fursenko,

Vestnik Mosk. Univ. Ser. 4: Geol. 5 (2000) 61–64.[112] D.S. Coombs, A. Alberti, T. Armbruster, G. Artioli, C. Colella, E. Galli, J.D. Grice,

Liebau, Can. Mineral. 35 (1997) 1571–1606.[113] Y.V. Seryotkin, V.V. Bakakin, I.A. Belitskii, B.A. Fursenko, J. Struct. Chem. 43

(2002) 802–808.[114] S. Turner, J.R. Sieber, T.W. Vetter, R. Zeisler, A.F. Marlow, M.G. Moreno-

Ramirez, M.E. Davis, G.J. Kennedy, W.G. Borghard, S. Yang, A. Navrotsky, B.H.Toby, J.F. Kelly, R.A. Fletcher, E.S. Windsor, J.R. Verkouteren, S.D. Leigh,Micropor. Mesopor. Mater. 107 (2008) 252–267.

[115] A. Alberti, E. Galli, G. Vezzalini, E. Passaglia, P.F. Zanazzi, Zeolites 2 (1982)303–309.

[116] L.P. Ogorodova, L. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, Russ. J. Phys. Chem.77 (2003) 1543–1545.

[117] L.V. Mel’chakova, L.P. Ogorodova, I.A. Kiseleva, I.A. Belitskii, B.A. Fursenko,Geochem. Int. 37 (1999) 1224–1227.

[118] N. Petrova, CR Acad. Bulg. Sci. 50 (1997) 69–72.[119] I.A. Kiseleva, L.P. Ogorodova, L.V. Mel’chakova, I.A. Belitskii, B.A. Fursenko,

Vestnik Mosk. Univ. Ser. 4 Geol. 3 (1998) 27–32.[120] L.V. Mel’chakova, L.P. Ogorodova, I.A. Kiseleva, I.A. Belitskii, Zh. Fiz. Khim. 78

(2004) 2300–2301.[121] L.P. Ogorodova, L. Mel’chakova, I.A. Kiseleva, I.A. Belitskii, Thermochim. Acta

403 (2003) 251–256.[122] P.S. Neuhoff, G.L. Hovis, G. Balassone, J.F. Stebbins, Am. J. Sci. 304 (2004) 21–

26.[123] R.J. Donahoe, B.S. Hemingway, J.G. Liou, Am. Mineral. 75 (1990) 188–200.[124] G.K. Johnson, H.E. Flotow, P.A.G. O’Hare, W.S. Wise, Am. Mineral. 71 (1985)

1065–1071.[125] G.K. Johnson, H.E. Flotow, P.A.G. O’Hare, Am. Mineral. 68 (1983) 1137–1145.[126] B.M. Skofteland, O.H. Ellestad, K.P. Lillerud, Micropor. Mesopor. Mater. 43

(2001) 61–71.[127] K. Stahl, J.C. Hanson, J. Appl. Cryst. 27 (1994) 543–550.[128] D.A. Howell, G.K. Johnson, I.R. Tasker, P.A.G. O’Hare, W.S. Wise, Zeolites 10

(1990) 525–531.[129] K.O. Bennington, R.P. Beyer, G.K. Johnson, U.S. Bur. Mines Rep. Invest. 8779

(1983) 1–18.