A computational study of calcium cation locations and diffusion in chabazite

Microporous and Mesoporous Materials 31 (1999) 45–59

A computational study of calcium cation locations anddiffusion in chabazite

Thomas Grey a, Julian Gale a,*, David Nicholson a, Brian Peterson ba Department of Chemistry, Imperial College, London SW7 2AY, UK

b Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195-1501, USA

Received 9 November 1998; accepted for publication 9 February 1999

Abstract

The characteristics of calcium ions in high-silica chabazite are explored by treating the aluminium and calciumions as a defect in an otherwise purely siliceous bulk with the defect modelled using the Mott–Littleton method.Three generic sites are found for calcium, which correspond to the centre of the double six-ring unit, on the triad axisof the double six-ring unit but displaced into the cavity and in the eight-ring window. Distortion of the framework isalso examined. The main energetic barriers to cation migration are found. As expected these are large in relation tokT, even at elevated temperatures, and significant diffusion of the cations can be ruled out for anhydrous chabazite.© 1999 Elsevier Science B.V. All rights reserved.

Keywords: Chabazite; Extra-framework cations; Framework distortion; Mott–Littleton; Simulation

1. Introduction tial adsorption of nitrogen over oxygen to give anitrogen-enriched sorbed phase, and a correspond-

Zeolites are microporous aluminosilicates with ing oxygen-enriched gas phase. The preferentialthe nominal formula (Mq+)

x/qAlxSi(y−x)O(2y) where adsorption of nitrogen over oxygen is accepted as

Mq+ is an extra-framework cation. The presence being due to the larger nitrogen quadrupoleof aluminium in the framework gives rise to a moment, which means nitrogen experiences aformal anionic charge on the framework, which is stronger interaction with the cations in the zeolitebalanced by the cation. These cations are located than does oxygen [3]. Since the cations play suchin the pores and are relatively loosely bound to a major part in separation, any attempt to modelthe aluminosilicate framework [1]. The distribu- this phenomenon must model the locations of thetion of aluminium in the framework is thought to cations correctly. This paper forms part of anbe generally random [2], except that Lowenstein’s on-going project to simulate nitrogen adsorptionrule forbids Al–O–Al bonds. in cation containing chabazite and to look at the

The three main uses for zeolites are in catalysis, effect of partial occupancy and lattice defects onion-exchange, and small molecule separation such adsorption.as air-separation. Air-separation uses the preferen- Chabazite is one of several zeolites routinely

employed in air-separation and is a reasonablestarting point for theoretical studies as it has a* Corresponding author. Fax: +44-171-594-5850.

E-mail address: [email protected] (J. Gale) small unit cell (36 framework species) with high

1387-1811/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved.PII: S1387-1811 ( 99 ) 00056-6

46 T. Grey et al. / Microporous and Mesoporous Materials 31 (1999) 45–59

symmetry, R3:m [4], which reduces the number of connect the ellipsoidal cavities together. Naturallyoccurring chabazite, unlike the purely siliceouspossible unique aluminium distributions.

Chabazite is a naturally occurring zeolite with chabazite in Fig. 1, always contains some alumin-ium in the framework. However, the first sampletypical oxide formula CaO2Al2O324SiO226.5H2O.

Fig. 1 shows eight unit cells of purely siliceous of pure silica chabazite has just been synthesised[6 ].chabazite. The origin of each unit cell is shown

shifted by half a side-length along each axis with The need to include aluminium in the frame-work of chabazite arises from the method ofrespect to the unit cell used in crystallographic

studies. Each unit cell contains one double six-ring synthesis. During synthesis, chabazite is formedfrom gels under hydrothermal conditions. Theseunit (D6R unit). Eight D6R units together enclose

an ellipsoidal cavity of about 6.7 A by 10 A [5]. gels contain organic base templates that help todirect chabazite formation. These organic basesThe six-rings form the top and bottom of the D6R

units, which are approximately hexagonal prisms. are positively charged and so aluminium is incor-porated into the framework to counter the chargeThe two fully shaded four-rings connect the top

six-ring to the bottom six-ring, while the two half- on the template [7]. When the zeolite is calcinedthe template is destroyed and the protons thatshaded ones are those which link the D6R units

together to create the overall lattice. The eight- remain can be ion-exchanged for small cations,typically the cations of sodium, calcium or trans-ring can be seen outlined in the centre of the

figure. The eight-rings form the windows that ition metals. Samples of synthetic chabazite made

Fig. 1. Eight unit cells of chabazite. The dark atoms are oxygen and the light atoms are silicon. The three types of ring (four-ring,six-ring and eight-ring) have been highlighted.

47T. Grey et al. / Microporous and Mesoporous Materials 31 (1999) 45–59

in this way can show a range of silicon to alumin- energies as the silicon to aluminium ratio tendsto infinity.ium ratios, typically from about 2.6 to 7.6 [2].

In the Mott–Littleton method [16–19] threeconcentric spherical regions are specified toapproximate the response of the solid to the defectwith varying degrees of accuracy. These regions2. Methodare termed 1, 2a and 2b. Region 1 includes thedefect ions and as many immediate neighbours asAs the power of computers increases, the use

of computer simulation to predict the structure of is necessary for convergence or is feasible with thecomputational resources available. For a localisedsolids and rationalise processes through an atomic

level model is becoming increasingly common. The defect the radius should be close to the short-rangepotential cut-off. This region is treated explicitly,uses of computer simulation in connection with

zeolite structure include the prediction of frame- and all the ions are allowed to move and distortunder the influence of the interatomic potentials.work structures and stability [8], the location of

sorbed molecules [9] and the location of the extra- The approach to modelling region 1 consumesrelatively large amounts of computer resources forframework cations [10]. There have been a number

of recent simulation studies that use computational each unit of radius and, except for very short-ranged perturbations, it is not generally possiblemethods to investigate extra-framework cations

in zeolites. A few use ab initio methods [11] or to obtain good energetic convergence before region1 becomes prohibitively large [16 ]. To obtainstatistical thermodynamics [12], but most use

potential energy functions in conjunction with reasonable convergence, region 1 is embedded intwo further regions, 2a and 2b, which are treatedeither molecular dynamics [13], Monte-Carlo [14]

or simulated annealing (a hybrid of Monte-Carlo more approximately.In region 2a, ions are treated explicitly butwith structural optimisation) [15]. In this study we

use lattice minimisation to locate the energy using a simplified model of the potential energysurface. The ions are allowed to respond to theminima for calcium cations in high-silica chabazite.

Since we will typically have many more T-sites electrostatic force due to the defects in region 1,but only as though they were situated in harmonicthan aluminium ions to place, the use of supercells

would quickly lead to an intractably large number wells. This approximation assumes that the defectimposes only a small change in the potential energyof possible aluminium configurations. It was there-

fore decided to use the Mott–Littleton method to surface relative to the bulk. In this case the ionswill be very close to the new energetic minimummodel the high-silica chabazite as a purely siliceous

framework containing a defect consisting of two and so the potential energy surface can be approxi-mated as harmonic. As a result of these assump-aluminiums substituting for T-site ions, and an

interstitial calcium ion. To further reduce the tions, this approximation requires that theperturbation of the region 2 ions by the defect willnumber of configurations the two aluminium sub-

stitutions were confined to occur in the same be small and also that the bulk lattice has beenoptimised prior to the defect calculation. Thedouble-six ring unit. If the concentration of alu-

minium is sufficiently low, a calcium ion near two outermost region, region 2b, uses a lattice summa-tion technique in which ions are implicitly regardedaluminiums will see the effect of the two alumini-

ums superimposed on the effects of a non-direc- as responding to the net charge of the defect bypolarisation. The Mott–Littleton method astional background of distant aluminiums.

Excluding the effects on the cell parameters, the described above was realised in the General UtilityLattice Program (GULP) [16 ].effect of this background, to the first approxima-

tion, is to lower the energy of all the local sites by The parameters for interatomic potentials forthe chabazite framework were taken from thea similar amount. In this way our study is able to

probe the relative energies of the sites in high- literature [20]. For the two-body terms aBuckingham exp-6 potential was coupled with ansilica chabazite as well as giving the absolute


electrostatic term: been initially created, it was optimised to thenearest local energy minimum. Optimisation was

V(rij

)=qiqj/rij+A

ijexp(−r

ij/r)−C

ijr−6ij carried out using a Newton–Raphson optimiser

with the update scheme of Broyden, Fletcher,where i and j are the interacting species, qi

and qj Goldfarb and Shanno (BFGS) [23].are their charges and r

ijis their separation. The

To test the convergence of the Mott–Littletonthree-body terms for the T–O–T angles were mod-method with respect to the region sizes, calcula-elled as harmonic:tions were first run for eight different radii ofregion 1 from 4 A to 18 A. When defect energyVangle-bending=

1

2k2(h−h

0)2

was plotted against region 1 radius, it was clearthat most defects require a region 1 radius of at

where h is the actual bond angle and h0 is theleast 10 A to give reliable results. Calculations

equilibrium bond angle. The parameters for thewere also run for three different choices for the

calcium–oxygen potential were derived from a fitposition of the centre of region 1. Convergence

to the experimental structure and elastic constantswas equally good for region 1 centred either at the

of calcium oxide [21]. The shell model [22] wasmidpoint of the aluminium ions or at the centre

applied to the oxygen ions to model their ionicof the double six-ring unit, but was not as good if

polarisability. The interaction between the corethe defect centre was placed at the middle of the

and shell was modelled with a spring potential:cavity. Most of the calculations were run with thedefect centre in the middle of the D6R as, although

V(rcs)=1

2k2r2cs+

1

24k4r4cs this may have reduced the convergence slightly,

shifting the defect centre between calculations (aswhere rcs is the core-shell separation. The parame- required for a defect centre at the midpoint of theter k2 (74.92 eV A−1 in this work) is related to the aluminiums) reduced the transferability.polarisabilty, a, of the ion by the equation: Initially calcium ions were placed at feasible

points in the solid (including the faces of rings asa=q2shell/(k2+d )

well as randomly chosen points) to attempt to findas many distinct low energy minima as possible.where qshell is the charge on the shell and d is an

environmental damping term. The interaction of Calculations were run three times with the Mott–Littleton regions centred between the aluminiumsthe silicon ions with calcium ions was treated as

purely electrostatic. A full list of the remaining and with the region 1 radius set to 14, 15 and16 A, respectively. Once likely minima were iden-parameters can be found in Table 1.

In each defect configuration, two aluminium tified, calculations were run for calcium ions inthese locations and all equivalent positions. Dueions were placed into the chabazite framework as

impurities, replacing two framework silicon atoms to the number of calculations needed, the size ofregion 1 had to be reduced to 10 A (about 300from within the same double six-ring unit. Five

symmetry non-equivalent configurations of alu- region 1 ions) to reduce the amount of computertime and memory required. Once optimisation wasminium ions were found that obeyed Lowenstein’s

rule (Fig. 2). The configurations are named by the complete the position of the Ca ion was examined.Since the defect was not replicated periodically,positions of the two aluminiums. If an arbitrary

T-site is chosen as position 1 and the double six- translational symmetry is destroyed and the con-cept of a unit cell cannot be strictly applied. Ifring is viewed such that the ring containing posi-

tion 1 is nearest, then the positions on the same there is no unit cell then there are no fractionalcoordinates. Nevertheless, it was necessary to con-ring are numbered clockwise. The positions in the

other ring are also numbered clockwise from this vert the position of the calcium ion into a formsuitable for comparison with X-ray data. Thepoint of view, with position seven being directly

below position 1. Calcium ions were placed into position of the calcium ion in the optimised defectwas given in Cartesian coordinates relative to thethe solid as interstitial ions. Once the defect had


Table 1Parameters for the various interatomic species and potentials

Charges

Species Charge

Ca 2Si 4Al 3O core 0.869020O shell −2.869020

BuckinghamSpecies A (eV ) r (A) C (eV A6)

Ca–O shell 1234.966652 0.336931 0.0Al–O shell 1460.3 0.29912 0.0Si–O shell 1283.907 0.32052 10.66158O shell–O shell 22764 0.149 27.87

Three-body harmonicSpecies k2 (eV rad−2) h0 (°)

O shell–Si–O shell 2.09724 109.47O shell–Al–O shell 2.09724 109.47

Spring (core–shell)Species k2 (eV A−2) k4 (eV A−4)O core–O shell 74.92 0.0

and three calculations were run with the calciumion but with no aluminium. The values for thealuminiums without the calcium ions not onlyshowed the stability of the different aluminiumconfigurations but were also subtracted from thedefect energies obtained with calcium present to

Fig. 2. Schematic representation of the five symmetry non- give the calcium binding energies. The values forequivalent aluminium configurations examined in this study the calcium without the aluminium indicated the(filled circles are Al on the upper ring; open circles are Al on inherent stability of the various sites due to thethe lower ring). framework structure alone.

When the low energy minima had been iden-defect centre. To find approximate fractional coor- tified, work began to examine some of the barriersdinates, it was assumed that the centre of mass of to migration between these sites. The calculationsregion 1 remained approximately static, so that were started with the calcium ion optimised intothe defect centre could be used as a reference one of the sites; it was then shifted by up to 0.35 Apoint. This assumption lowers the accuracy of the in the general direction of a plausible transitionvalues obtained and, coupled with the effects of state. This ensures that there is a component ofincomplete convergence, leads to an estimated force in the direction of the transition state — auncertainty in the fractional coordinates of about necessary condition for successful optimisation.±0.01. For these calculations the RFO optimiser [24] was

Calculations were also run for the various alu- used, as this is able to locate minima and maximaof any order. No information about the pathwayminium configurations with no calcium ion present


between the maxima and minima was assumed. cations are present in site A∞, the overall defectenergy of sites 1_2 and 1_6 are comparable toWhen a maximum was found, the energy and

position of the calcium was recorded and the those configurations which obey Lowenstein’s rule.Since the calcium cations are not present when theposition of the calcium ion was again displaced

slightly away from the maximum. The structure chabazite is formed (their place being occupied byless electrostatically stabilising organic templates),was then optimised to the nearest local minima.

This process was repeated until the calcium ion the assumption of Lowenstein’s rule is likely to bestill valid.was in another of the identified low energy minima.

If the effect of the defect on the symmetry isignored, and all T-sites are regarded as equivalent,then three non-equivalent sites were found for3. Resultscalcium ions.$ Site N: in the centre of the D6R unit.The energies of the various configurations of

framework aluminium in the absence of calcium $ Site A: a two-fold site on the triad axis of theD6R but displaced into the cavity slightly.are shown in Fig. 3. The energy is almost exactly

inversely proportional to the number of bonds $ Site B: a six-fold site in the eight-ring windowsconnecting the cavities.separating the aluminiums. For a given number of

separating bonds, it is found to be slightly more The sites can be seen pictured in Fig. 4.The nomenclature for the sites is not formal.favourable to have the aluminiums in the same

ring and hence slightly further apart. Note that in Generally a prime indicates that a site is relatedto the site of the same name without a prime byorder to examine all four possible aluminium con-

figurations that break Lowenstein’s rule, we have the centre of inversion.It was found that with no aluminium presentincluded a configuration where the aluminiums

occur in different double six-ring units, denoted site N is not an energetic minimum. Of theremaining sites, site A gave a binding energy for1_X. All the configurations which break

Lowenstein’s rule are significantly higher in energy Ca2+ of 1097 kJ mol−1, while site B was only16 kJ mol−1 less favourable with a binding energythan those that do not. However, when calciumof 1081 kJ mol−1.

If the effect of the defect on symmetry is consid-ered then the three sites above become the 15 siteslisted in Table 2. The idealised site position for theB-sites given in columns 2–4 of Table 2 is intendedas an aid to understanding the relationship betweenthe different B-sites. The observed site positionsare quoted as mean values with standard deviationsas they would be for crystallographic data. It isimportant to understand that the calculations giverise to just a single value of energy and positionfor each calcium site per aluminium configuration.The mean values above have been obtained bysimply taking an average and standard deviationfor the positions of each site for all the possiblealuminium positions. Effectively this assumes that

Fig. 3. Defect energies of aluminium configurations in the pres- all aluminium configurations occur with equalence and absence of calcium. In the graph, the filled points are probability and so contribute equally to the meandefect energies in the absence of calcium and open points are

position observed by X-ray diffraction. The smalldefect energies in the presence of calcium in site A∞. For thesize of the sample should be borne in mind whenschematics, filled circles are aluminium positions on the upper

ring; open circles are aluminium positions on the lower ring. considering the values of the standard deviation.


Fig. 4. Sites A, B and N visualised. Site A is above the face of the six-ring. Site B is in the plane of the eight-ring. Site N is at thecentre of the double six-ring unit.

Table 2Site nomenclature and fractional coordinates relative to the centre of the cavity (see Tables 6 and 7 later for data shifted tocrystallographic origin)

Site name Idealised fractional coordinates Observed fractional coordinates Defect centre position

x/a y/b z/c x/a y/b z/c x/a y/b z/c

N 0.5 0.5 0.5 0.497(3) 0.500(0) 0.493(5) 0.5 0.5 0.5A – – – 0.34(1) 0.34(1) 0.345(6) 0.5 0.5 0.5A∞ – – – 0.672(7) 0.67(1) 0.66(1) 0.5 0.5 0.5B1 0.5 0 0 0.596(6) 0.08(2) 0.07(2) 0.5 0.5 0.5B2 0 0.5 0 0.07(1) 0.608(4) 0.09(1) 0.5 0.5 0.5B3 0 0 0.5 0.07(3) 0.09(3) 0.594(6) 0.5 0.5 0.5B1∞ 0.5 1 1 0.390(9) 0.93(1) 0.91(2) 0.5 0.5 0.5B2∞ 1 0.5 1 0.91(2) 0.403(4) 0.93(1) 0.5 0.5 0.5B3∞ 1 1 0.5 0.882(5) 0.948(3) 0.402(6) 0.5 0.5 0.5B1@2 0.5 1 0 0.503(3) 0.984(4) 0.042(2) 0.5 0.6 0.4B1@3 0.5 0 1 0.496(6) 0.03(1) 0.97(1) 0.5 0.4 0.6B2@1 1 0.5 0 0.971(3) 0.505(1) 0.021(3) 0.6 0.5 0.4B2@3 0 0.5 1 0.02(1) 0.503(8) 0.97(1) 0.4 0.5 0.6B3@1 1 0 0.5 0.975(5) 0.023(2) 0.497(1) 0.6 0.4 0.5B3@2 0 1 0.5 0.029(3) 0.98(1) 0.495(5) 0.4 0.6 0.5

The energies of the site A, site A∞ and site N are calcium ion with two aluminium ions, we lookedbriefly at a single aluminium configuration withshown in Fig. 5. The energies of the B-sites are

shown in Figs. 6 and 7. two calcium and four aluminium ions. The config-uration we chose for aluminium was 1,3,10,12In all cases, the energies of symmetry equivalent

configurations were found to differ by less than because it is quite symmetrical and should be quitelow in energy. We placed calcium ions in sites A1 kJ mol−1, this suggests that the energies are

accurate to within about 1 kJ mol−1. and A∞, sites A and N, sites A and B1, sites A∞and B1, and sites N and B1. As expected we foundFollowing detailing of the results for a single


that site N is not an energetic minimum wheneither site A or site A∞ is occupied. The lowestenergy arrangement we found was for a combina-tion of sites A and A∞ with a total binding energyof 3676 kJ mol−1. Simultaneous occupation of siteA∞ and site B1 (opposite sides of the D6R unit)at 3494 kJ mol−1 is only slightly more favourablethan occupation of the adjacent site A and site B1at 3419 kJ mol−1. Surprisingly it was found thatsite N is not an energetic minimum even with theother calcium ion in site B1.

3.1. Configurations with the two aluminiums on thesame ring (1_4, 1_5)

Fig. 5. Defect energies of sites A, A∞ and N for a range ofaluminium configurations.

The most strongly bound site is always site A∞which is above the face of the ring containing thetwo aluminiums. The binding energy differedslightly for the two different aluminium configura-tions and was 1629 kJ mol−1 for 1_4 and1639 kJ mol−1 for 1_5. The other A-sites (abovethe face of the six-ring, on the opposite side of thedouble six-ring unit and containing no aluminium)lie in both cases about 125 kJ mol−1 higher inenergy.

The relative energies of the sites are almostentirely determined by the distances from thealuminiums. A plot of binding energy againstS(1/r), where ‘r’ is the aluminium–calcium separa-tion, can be fitted to a straight line with correlation

Fig. 6. Defect energies of a range of B-sites for different alumin- coefficients 0.89 and 0.91 for 1_4 and 1_5,ium configurations. respectively.

For configuration 1_4, the aluminium ions lieon opposite sides of the same ring. This reducesthe symmetry of the D6R unit to a mirror plane,but maintains the equivalence of calcium ion sitesB2 and B3, while site B1 lies on the mirror planeand is unique. Similarly, B2∞ and B3∞ are equiva-lent, B1∞ is unique. The following pairs of sites arealso equivalent: B1@2 with B1@3, B2@1 withB3@1, and B2@3 with B3@2. The equivalent sitesall gave energies that differed by less that1 kJ mol−1.

The spread of binding energies associated withthe B-sites was about 86 kJ mol−1 from1435 kJ mol−1 to about 1522 kJ mol−1. Note thatthe most strongly bound B-site is stillFig. 7. Defect energies of various B-sites for a range of alumin-

ium configurations. 109 kJ mol−1 above site A∞ (two aluminiums in


six-ring) but their energies bracket the energy of energies is almost identical to that of the 1_4 case.The most strongly bound sites are B1@2 andthe other A-site (no aluminium in six-ring).

For configuration 1_5, the aluminiums, clus- B2@3, closely followed by B3 and B3∞. The formertwo sites are slightly more strongly bound thantered on one side of the ring, destroy all symmetry.

The overall spread of B-site binding energies is might be predicted from the distances to the alu-miniums. This is despite the lower Ca–O distancesgreater than for 1_4 by about 126 kJ mol−1. This

is almost entirely due to the much stronger binding for B3 and B3∞ which suggests better coordination.It seems likely then that the increased bindingof site B1∞ arising from its position above the two

aluminiums. The most weakly bound site is still energy of sites B1@2 and B2@3 is an artefactarising from the use of a shifted defect centre.B1 and it is only 5.8 kJ mol−1 less stable here than

for 1_4. For both 1_4 and 1_5, site B1 lies on the Configuration 1_10 has a centre of inversionthat maps sites B1–B3 onto sites B1∞–B3∞ respec-opposite side of the unit cell from the aluminiums.tively and each of the B@-sites with the sameinitial number to each other (e.g. B1@2 to B1@3).3.2. Configurations where the aluminiums are in

different rings (1_11, 1_10, 1_12) The energy differences between these equivalentsites are all less than 1 kJ mol−1. The spread ofB-site binding energies for 1_10 is lower than forFor these aluminium positions, a new site is

observed, in addition to the sites mentioned above. any other configuration. This is almost entirelydue to the increased binding energies of the mostSite N lies at the centre of the D6R unit. The two

rings are now equivalent, as are the two A-sites. weakly bound sites. This increase is due to theincreased symmetry of the configuration, whichThe binding energy is about 1570 kJ mol−1 and

lies about halfway between the two old values, as distributes the aluminium more evenly amongstthe sites. In contrast to 1_10, configuration 1_12would be expected. Site N has a binding energy

of about 1490 kJ mol−1 and lies about has no symmetry associated with it and features aclustering of the aluminiums on one side of the180 kJ mol−1 higher in energy than the A-sites.

The binding energy of site N is thus very close to ring. This gives it the greatest B-site energy spreadof all the configurations with both the most andthat of the high energy A-sites mentioned in the

last section. least stable sites seen for any configuration.Plots of binding energy against S(1/r) (where

‘r’ is the aluminium–calcium separation) show, for 3.3. Energetic barriers to migrationall sites, reduced correlation coefficients for linearfits. However, if site N is removed from the linear The energetic barriers for migration between

site A, site A∞ and (in cases where the aluminiumsfit then the correlation coefficients are comparableto those seen for aluminiums on different rings. are on different rings) site N were examined for

all configurations. The results are given in Table 3.Site N lies well above the fit line, indicating thatit is much less stable than its proximity to the For configurations 1_4 and 1_5 where the alumini-

ums are on the same ring the barriers to migrationaluminiums would suggest.The A-sites are still the most strongly bound from site A to site A∞ were 112 kJ mol−1 and

108 kJ mol−1, respectively. Since site A∞ is muchsites, but for configuration 1_12, the clustering ofthe aluminiums on one side of the D6R unit lower in energy, the barrier to migrate back from

site A∞ to site A was over twice as high:increases the binding energies of nearby B-sites toabout the same magnitude as the A-sites. 233 kJ mol−1 and 232 kJ mol−1, respectively. The

transition state for both these cases was situatedFor configuration 1_11 the presence of thealuminiums reduces the symmetry to a single C2 about halfway between the A-site and the centre

of the double six-ring unit. For the remainingaxis. This axis makes sites B1and B2∞, sites B2 andB1∞, and sites B3 and B3∞ equivalent. The energies configurations it might be expected that site N

would lower the energetic barrier to migration,of these equivalent sites were all found to differby less than 0.5 kJ mol−1. The spread of B-site however this was not found to be the case. In


Table 3Energetic barriers to migration for calcium between two sites

Configuration EA (kJ mol−1)A to N N to A∞ A∞ to N N to A

1_11 113 12.1 115 12.11_10 112 24.4 112 24.41_12 117 19.1 112 25.0

general the barriers to move from site A into site to (I ) the centre of the D6R unit, (II ) on the triadN were of a similar magnitude to those to move axis of the six-ring unit but displaced slightly intodirectly from site A to site A∞. The lower binding the cavity, and (III ) on the face of one of theenergy of site A∞ for these configurations did mean four-rings that connect the D6R units to eachit was easier for the cation to move (via site N) other.from site A∞ back to site A. The transition state The earlier study [4] by Smith was for naturalfor these cases was generally situated about three chabazite, ion-exchanged to give a composition ofquarters of the way towards site N. Ca1.95Al3.9Si8.1O24. Due to cracking of the crystal

In addition to the barriers shown in Table 3, during dehydration and the limitations of thefor configurations 1_4 and 1_10 the barriers for methods used, the accuracy of the intensities wasmigration site B1∞ to site A∞ were also examined. not as good as can normally be obtained. SmithThe energy of the transition state was similar for initially found two cation sites but when the total1_4 and 1_10. However, the lower binding energy number of calcium ions proved to be significantlyof site B1 for configuration 1_4 meant that the less than that found by chemical analysis hebarrier for migration from site B1∞ to site A∞, re-examined the data and found some evidence for91.8 kJ mol−1, was significantly lower than for the third site.1_10, 174 kJ mol−1. A similar but much less The second study, by Mortier et al. [25], ismarked effect was observed for migration from more recent and was for a Ca chabazite with thesite A∞ to site B1∞, for 1_4 the barrier was composition Ca1.91Al3.81Si8.19O24 (given by micro-212 kJ mol−1 and for 1_12 it was 253 kJ mol−1. probe analysis). This paper is the work usually

cited for calcium cation positions.A study of Co(II )-exchanged chabazite by4. Discussion

Calligaris et al. [26 ] also gives values for dehy-drated Ca-exchanged chabazite. They quote theTwo X-ray diffraction studies of dehydrated Casame two sites but give the fractional coordinateschabazite have been reported in the literature andof site II as (0.1600, 0.1600, 0.1600).are summarised in Table 4. The sites correspond

Comparison of our study with experiment isdifficult because all the experimental data are for

Table 4chabazite samples with Si/Al ratios of about two.Calcium ion sites observed in X-ray diffraction studies fromIt is not appropriate to place exact values on thethe literatureSi/Al ratio in our study except to say that it is

Site Multiplicity x/a y/b z/c sufficiently high that the calcium and aluminiumlocalised in one unit cell do not feel the effects ofI [4] 1 0.000 0.000 0.000any other calcium and aluminium. FurthermoreII [4] 2 0.169 0.169 0.169

III [4] 12 0.09(3) 0.18(8) 0.47(0) the experimental data is from X-ray diffraction,I [25] 1 0 0 0 which strictly only probes the bulk average struc-II [25] 2 0.15996 0.15996 0.15996

ture, whilst our study is limited to local behaviour.


While we expect to see broadly the same sites, we aluminiums present. The addition of the two alu-miniums lowers the energy and creates a smallwould not expect to find exactly the same distribu-

tions over them. Indeed, the small variations in minimum. Our study would suggest that the occu-pancy of site N should be negligible since it onlyposition may lie within the thermal ellipsoids of

the sites, making them difficult to resolve in X-ray occurs when aluminiums lie on different rings andeven then is not a particularly favourable site. Thediffraction.

The coordinates of site N observed in this study occupation of site N in the experimental studies islikely to arise from the increased amounts of(shifted back to the crystallographic origin) are

given in Table 5 and are seen to be in good aluminium present. Since the maximum numberof aluminium atoms in a unit cell (assumingagreement with the experimental site I special

position. The deviations found here from the ide- Lowenstein’s rule to be obeyed) is six, then theamount of aluminium in most unit cells is unlikelyalised site probably arise from the limited number

of configurations sampled. Similarly, the values to be less than four given the average composition.Since there can be a maximum of three aluminiumsobtained by the X-ray diffraction studies are effec-

tively an average of millions of possible local in a given ring, most unit cells will contain doublesix-ring units with aluminium on both rings andaluminium environments. For this study the values

obtained are an average over only the five local hence a site N. Furthermore, site N for the experi-mental chabazite is likely to be more stable as thealuminium configurations examined. As can be

seen from the table, the precise location of site N number of adjacent aluminium atoms is increasedand the number of silicon near neighbours will bevaries with the positions of the aluminiums. It

seems likely that if the number of aluminium decreased. Unfortunately, for the single exampleof four aluminium T-sites we examined, this wasenvironments were increased then the values

obtained would converge to those seen not the observed behaviour. Since site N is not aminimum in the presence of site A, site A∞ or siteexperimentally.

One of the slightly surprising results of our B1, it seems likely that site N can only arise whenthere is a local imbalance with four aluminiumsstudy is the comparative instability of site N. Most

X-ray diffraction studies have accepted site N (site and one calcium ion. Alas, calculations run on thissystem still show site A to be about 40 kJ mol−1I ) on the basis of the favourable octahedral coordi-

nation. Site N is in fact much less stable than its more stable. However, site B1 was about260 kJ mol−1 less stable. It is questionable howproximity to the aluminium atoms might suggest.

It seems likely then that site N is destabilised by accurate the defect approach is for high aluminiumsystems, where the effect of aluminium ions inrepulsive interactions with the 12 T-site atoms of

the D6R. This is backed up by the absence of site adjacent unit cells can be expected to affect thestability of the sites. It would be of interest toN for configurations where the aluminiums are on

the same ring or for the case where there are no make a more detailed study of systems closer incomposition to the experimental results.

If all the T-sites are assumed to be equivalentthen coordinates of site A∞ can be treated as

Table 5equivalent to site A. The coordinates of site A andComparison of site N coordinates with literature site Isite A∞ are given in Table 6 shifted to the crystallo-

x/a y/b z/c graphic origin. Good agreement is found with theexperimental site II. Agreement appears to be

This studybetter for site A than for site A∞. However, whenAl configuration 1_11 −0.0097 0.0089 −0.0034we examine the variation of the site positions withAl configuration 1_10 −0.0016 0.0010 −0.0033

Al configuration. 1_12 −0.0152 0.0192 −0.0217 aluminium configuration (Table 7) it can be seenAverage −0.003(3) 0.000(0) −0.007(5) that the apparent improved agreement for site ALiterature is more likely to be due to a favourable cancellationSite I [4,25] 0.000 0.000 0.000

of errors. Nevertheless, the values suggest that the


Table 6 zite. Mortier et al. [27] studied chabazite withComparison of sites A and A∞ with experimental site II composition Na3.8Al3.8Si8.2O24. With three cations

per unit cell it is no longer possible to accommo-x/a y/a z/adate all the cations in the A-sites (we find that site

This study A∞ 0.172(7) 0.17(1) 0.16(1) N is not a minimum in the presence of site A asThis study A 0.16(1) 0.16(1) 0.155(6) they are mutually exclusive and a similar situationSmith [4] 0.169 0.169 0.169

is found experimentally for analogous sites inMortier et al. [25] 0.15996(9) 0.15996(9) 0.15996(9)faujasite [25]). The presence of the sodium cationscauses a change of unit cell making direct compari-son difficult. Nevertheless, three distinct types ofTable 7

Variation of site A and site A∞ position with aluminium site were found. The first two correspond to A-configuration and N-type sites. The third type of site corresponds

to the eight-ring window and lends weight to theAl configuration x/a y/b z/cproposition that this site is an unoccupied site in

Both aluminiums on ring nearest site A∞ calcium chabazite. Another situation where cations1_4 A∞ 0.1654 0.1564 0.1521 are seen in the eight-ring windows is in hydrated

A 0.1682 0.1625 0.1668 chabazite [28], where the solvated ions occupy a1_5 A∞ 0.1478 0.1723 0.1529

site at (0.579(1), 0.579, 0.231(1)). Shifted to theA 0.1695 0.1621 0.1669origin used in this study this corresponds toAluminiums on both rings

1_11 A∞ 0.1601 0.1714 0.1508 (0.079(1), 0.079, 0.731(1)).A 0.1720 0.1604 0.1578 In Na chabazite, the placement of cations in

1_10 A∞ 0.1644 0.1679 0.1501 the eight-ring windows causes considerable distor-A 0.1679 0.1662 0.1570

tion of the framework. In calcium chabazite, the1_12 A∞ 0.1608 0.1730 0.1509distortions seen experimentally (in terms of theA 0.1736 0.1492 0.1721range of T–O–T bond angles) are somewhat less(~17°) than in Na chabazite (41°) [27]. We exam-ined bond angles for configurations 1_4, 1_10 andposition of the site may vary slightly in all direc-

tions to give an average value as seen by X-ray for the configuration with two calcium cations andfour aluminiums, 1_3_10_12. We found gooddiffraction.

None of the studies above showed calcium ions agreement with experiment for 1_10 with thecalcium in site A or A∞ with a range of T–O–Tin site B. However, since there were only two

calcium ions per unit cell, this is not remarkable angles of approximately 16°. Similarly, for1_3_10_12, with site A and site A∞ we see a rangeif we assume that for chabazite with Si/Al of about

two, the two A-sites are the most stable sites. In of bond angles of about 18°. For configuration1_4 where the aluminiums lie on the same ring thecontrast, for low aluminium content our calcula-

tions suggest this may not be the case. For config- agreement was worse due to the much greaterdistortion caused by occupation of site A∞, theurations where the aluminiums lie on the same six-

ring of the D6R unit, several of the B-sites are range of T–O–T angles was 22°. This suggests thatfor the experimental studies, aluminium was pre-more stable than site A, and for configurations

where the aluminiums lie on different six-rings of sent in both rings in the majority of unit cells,which is what we would expect.the D6R unit, about half the B-sites are more

stable than site N. The calculations run with two The degree of framework distortion caused byoccupation of site N was surprisingly high with acalcium ions and four aluminiums (see above) do

suggest that simultaneous occupation of site A and T–O–T angle range of about 29°. Examination ofthe defect showed this to be due to calcium formingsite A∞ is about 180 kJ mol−1 more stable than

simultaneous occupation of site A∞ and site B1. a near octahedral coordination to six alternateoxygens of the D6R unit. The drop in T–O–TFor experimental evidence of site B we have to

turn to X-ray diffraction studies of sodium chaba- angle for those oxygens coordinated to the calcium


forces the T–O–T angles of the uncoordinated coordination (in terms of the Ca–O distances) wasseen for B@-sites even though one might expectoxygens to increase considerably. The calcium to

oxygen distances (for this configuration at least) the four-rings to be less flexible than the six-rings.Better coordination was also seen when the princi-were split into three opposing pairs with lengths

of 2.45 A, 2.63 A and 2.69 A. The shortest two pal coordinating oxygen was bonded to alumin-ium. This is presumably due to the reducedcoordination distances were associated with the

two oxygens bonded to aluminium. This confirms repulsion from the triple positive aluminium whencompared to the four positive effective charges onthe suspicion of Mortier et al. [25] that the appar-

ent framework oxygen position seen by X-ray the silicon atoms.The energetic barriers to migration controldiffraction (which gave a coordination distance of

2.81 A) was in fact mainly determined by the diffusion of calcium through the solid. The mostsevere dehydration conditions for Ca chabazitebonding to calcium in the more populated site A.

The much less symmetric configuration 1_12 gave seen in the literature involved heating to 350–370°C [4]. At this temperature kT has a value ofa similar range for the T–O–T angles and visualisa-

tion showed a similar arrangement of alternating about 5.3 kJ mol−1 which is still less than half theenergy of the lowest barrier to migration. Thiscoordination to calcium.

Occupation of the eight-ring window sites confirms that minimal cation diffusion would beexpected even at quite high temperatures.caused quite high distortion of the framework.

The range of T–O–T angles varied very little and The transition states for migration between sitesA, A∞ and N lie within the D6R unit, suggestingwas about 20° for all the eight-ring sites of both

configurations. This is considerably less than for that migration occurs along a path which approxi-mately follows the three-fold axis of the D6R unit.Na chabazite. The distortion for Ca chabazite

seems to be reduced because the larger calcium Fig. 8 shows the position of the transition state( labelled ‘TS’) for migration from site B to site A.ion can coordinate to three adjacent oxygens and

so lie off-centre in the eight-ring. This means that The transition state lies close to the cavity wall,the large, energetically unfavourable distortionsassociated with bridging the eight-ring window areunnecessary. In all cases the calcium was primarilybound to one oxygen at Ca–O distances from 2.28to 2.42 A (the standard Ca–O distance for octahe-dral coordination is 2.4 A [25]). The calcium wasthen bound to a lesser extent to the oxygens oneither side. In chabazite, four types of oxygenexist. The first is an oxygen which is part of afour-ring connecting the D6R units to each other,the second type is part of a four-ring connectingthe two six-rings of the D6R units to each other.The final two types are both part of one of thesix-rings themselves, but the third type points intothe six-ring, whereas the fourth type points out ofthe six-ring. In all cases the two oxygens on eitherside of the principal coordinated oxygen were ofthe first type (from different four-rings). However,due to the displacement of the calcium towardsthe D6R containing the aluminium for theB@-sites, the principal oxygen is of the secondtype and for the remaining B-sites the principal Fig. 8. Positions of sites B and A∞ and the transition state for

movement between them.oxygen was of the last type. Surprisingly better


suggesting that the migrating cation follows the magnitude for all aluminium configurations. In allcases, diffusion of the cations at reasonable temper-surface of the cavity wall as we would expect.atures is unlikely under anhydrous conditions.

5. ConclusionsAcknowledgements

Highly siliceous chabazite has been modelledWe would like to thank Air Products andusing the Mott–Littleton method. Three types of

Chemicals, Inc. for supporting this project. Wesite for calcium cations were found, correspondingwould also like to thank EPSRC for computingto the centre of the D6R unit, on the triad axis offacilities.the D6R unit but displaced into the cavity and in

the eight-ring windows. The first two sites correlatewell with the sites seen by X-ray diffractionalthough the local nature of the structures probed Referencesby our study, together with the difference in Si/Alratio, makes fuller comparison difficult. The third [1] C.R.A. Catlow, in: C.R.A. Catlow (Ed.), Modelling of

Structure and Reactivity in Zeolites, Academic Press,site is not seen experimentally for Ca chabaziteLondon, 1992, p. 1.but is a known site for Na chabazite and hydrated

[2] D.E. Akporiaye, I.M. Dahl, H.B. Mostad, R. Wendelbo,Ca chabazites. There is strong evidence thereforeJ. Phys. Chem. 100 (1996) 4148.

to propose that the site found is an unoccupied [3] K. Watanabe, N. Austin, M.R. Stapleton, in: K.E. Gub-site in Ca chabazite. Even if some occupation of bins, N. Quirke (Eds.), Molecular Simulation and Indu-

strial Applications: Methods, Examples and Prospects,the third site does occur, the high multiplicityGordon and Breach, 1996, p. 433.would make it difficult to resolve. We are not

[4] J.V. Smith, Acta Crystallogr. 15 (1962) 835.aware of any X-ray diffraction studies on Al-chab,[5] D.W. Breck, E. Robert, Zeolite Molecular Sieves, Krie-

a chabazite with a Si/Al ratio of one [29] but with gar, 1974.three calcium ions per unit cell and only two non- [6 ] M.-J. Dıaz-Cabanas, P.A. Barrett, M.A. Camblor, Chem.

Commun. (1998) 1881.eight-ring window sites available; we await the[7] D.J. Willock, D.W. Lewis, C.R.A. Catlow, G.J. Hutchings,location of the third cation with interest.

J.M. Thomas, J. Mol. Catal. A: Chem. 119 (1997) 415.Distortion of the framework by the cations is[8] N.J. Henson, A.K. Cheetham, J.D. Gale, Chem. Mater. 6

found to be similar to the values found by X-ray (1994) 1647.diffraction for configurations where the aluminium [9] A.R. George, C.R.A. Catlow, J.M. Thomas, Micropor.

Mater. 11 (1997) 97.atoms are on different rings of the D6R unit.[10] A.M. Gorman, C.M. Freeman, J.M. Newsam, FaradayOccupation of the site in the centre of the D6R

Discuss. 106 (1997) 489.unit is found to cause considerable distortion of[11] L. Campana, A. Selloni, J. Weber, A. Goursot, J. Phys.

the framework. This is due to formation of near- Chem. B 101 (1997) 9932.octahedral coordination to six alternate oxygens [12] J.J. van Dun, W.J. Mortier, J. Phys. Chem. 92 (1988) 6740.

[13] H. Himei, M. Yamadaya, Y. Oumi, M. Kubo, A. Stirling,of the 12 oxygens in the D6R unit. This causesR. Vetrivel, E. Broclawik, A. Miyamoto, Micropor. Mater.reduction in the T–O–T angles for the coordinated7 (1996) 235.oxygen and forces an increase in the T–O–T angles

[14] J.M. Newsam, C.M. Freeman, A.M. Gorman, B. Vessal,for the uncoordinated oxygens. Occupation of the Chem. Commun. (1996) 1945.eight-ring window sites causes considerable distor- [15] B.H. Li, P.C. Sun, Q.H. Jin, J.Z. Wang, D.T. Ding, J. Mol.

Struct. (THEOCHEM) 391 (1997) 259.tions but much less than is seen for sodium. This[16 ] N.F. Mott, M.J. Littleton, Trans. Faraday Soc. 34would seem to be due to coordination of calcium

(1938) 485.off-centre in the eight-ring, which removes the[17] A.B. Lidiard, J. Chem. Soc., Faraday Trans. 2 (85)

need for the large distortions associated with bridg- (1989) 341.ing the eight-ring window. Finally the energetic [18] C.R.A. Catlow, J. Chem. Soc., Faraday Trans. 2 (85)

(1989) 335.barriers to migration are found to be of a similar


[19] J.D. Gale, J. Chem. Soc., Faraday Trans. 93 (1997) 629. [25] W.J. Mortier, J.J. Pluth, J.V. Smith, Mater. Res. Bull. 12(1977) 97.[20] R.A. Jackson, C.R.A. Catlow, Mol. Sim. 1 (1988) 207.

[21] T.S. Bush, J.D. Gale, C.R.A. Catlow, P.D. Battle, [26 ] M. Calligaris, G. Nardin, L. Randaccio, Zeolites 4(1984) 251.J. Mater. Chem. 4 (1994) 831.

[22] B.G. Dick, A.W. Overnauser, Phys. Rev. 112 (1958) 90. [27] W.J. Mortier, J.J. Pluth, J.V. Smith, Mater. Res. Bull. 12(1977) 241.[23] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flan-

nery, Numerical Recipes, 2nd edn.Cambridge University [28] A. Alberti, E. Galli, G. Vezzalini, E. Passaglia, P.F.Zanazzi, Zeolites 2 (1982) 303.Press, Cambridge, 1992.

[24] A. Banerjee, N. Adams, J. Simons, R. Shepard, J. Phys. [29] K.A. Thrush, S.M. Kuznicki, J. Chem. Soc., FaradayTrans. 87 (1991) 1031.Chem. 89 (1986) 52.

Documents

A computational study of calcium cation locations and diffusion in chabazite