A computational study of the surface structure and reactivity of

calcium fluoride

Nora H. de Leeuw*a,b and Timothy G. Cooperb,c

aSchool of Crystallography, Birkbeck College, University of London, Malet Street, London,UK WC1E 7HX. E-mail: n.deleeuw@mail.cryst.bbk.ac.uk

bDepartment of Chemistry, University College, 20 Gordon Street, London, UK WC1H 0AJcDepartment of Chemistry, University of Reading, Whiteknights, Reading, UK RG6 6AD

Received 15th August 2002, Accepted 2nd October 2002

First published as an Advance Article on the web 12th November 2002

Electronic structure calculations based on the density functional theory (DFT) are employed to investigate the

electronic structure of fluorite (CaF2) and the mode and energies of adsorption of water at the main {111}

cleavage plane. Electron density plots show the crystal to be strongly ionic with negligible ionic relaxation of

the unhydrated surface. We find associative adsorption of water at the surface with hydration energies between

41 and 53 kJ mol21, depending on coverage. We next employ atomistic simulation techniques to investigate the

competitive adsorption of water and methanoic acid at the planar and stepped {111}, {011} and {310}

surfaces. The hydration energies and geometries of adsorbed water molecules on the planar {111} surface agree

well with those found by the DFT calculations, validating the interatomic potential parameters. Methanoic acid

adsorbs in completely different configurations on the three surfaces, but always by one or both oxygen atoms

to one or more surface calcium atoms. Molecular Dynamics simulations at 300 K show that the effect of

temperature is to increase the difference in adsorption energy between methanoic acid and water at the planar

{111} surface. The methanoic acid remains bound to the surface whereas the water molecules prefer to form a

droplet of water between the two surface planes. We show in a series of calculations of the co-adsorption of

water and methanoic acid that the presence of solvent makes a significant contribution to the final adsorption

energies and that the explicit inclusion of solvent in the calculations is necessary to correctly predict relative

reactivities of different surface sites, a finding which is important in the modelling of mineral separation

processes such as flotation.

1 Introduction

Fluorite (CaF2) is a widely distributed mineral and it oftenoccurs in combination with a range of other ores, notably leadand tin ores, and together with calcite and apatites.1 It is themost important source material for hydrofluoric acid2 and assuch needs to be efficiently separated from any co-existingminerals, usually by the technique of froth flotation, e.g. refs. 3and 4. In addition to numerous investigations of the fluoritestructure itself, both experimental and computational, e.g.,refs. 5–7 its crystal growth and dissolution have been widelystudied, e.g., refs. 8–10, as well as its possible application as asubstrate for the epitaxial growth of thin films.11 The effect ofhydration on the CaF2 surface structure is of considerableinterest in all of these applications, while the adsorption oforganic surfactant molecules at the surfaces is important inmineral processing techniques, such as flotation, where theselectivity of the surfactants plays a major role in the design ofa successful separation process.3,4

In this paper, we describe our computational investigationsof the electronic structure of the fluorite crystal and the sur-face reactivity towards water and methanoic acid. We usemethanoic acid as a model of carboxylic acid surfactants suchas oleic acid, and study its adsorption at the major {111}, {011}and {310} surfaces of calcium fluoride, including a series ofstepped surface sites. The approach we have chosen to adopt isto use electronic structure calculations based on the densityfunctional theory (DFT) to study the main {111} cleavageplane of fluorite in order to obtain, firstly, details of thegeometry and electronic structure of the dry and hydratedsurfaces, and secondly, reliable estimates of the hydrationenergies to compare with when using classical interatomic

potential techniques to model larger scale systems. Comparisonof the geometries and energies of adsorbed water molecules atthe calcium fluoride surface, obtained using both quantummechanical and classical techniques, will give an indication asto whether the potential model used in the atomistic simu-lations is capable of reliably modelling fluorite–water interac-tions. If there is good agreement between the results of thedifferent methods, we can then be confident of applying ato-mistic simulations to larger systems, including both adsorbingspecies, which are currently beyond the capability of electronicstructure calculations.

2 Methodology

In the electronic structure calculations, the total energy andstructure of the simulation system, comprising slabs of solidmaterial separated by a vacuum gap, which together arerepeated periodically in three dimensions, was determinedusing the Vienna Ab Initio Simulation Program (VASP).12–15

The basic concepts of density functional theory (DFT) and theprinciples of applying DFT to pseudopotential plane-wavecalculations has been extensively reviewed elsewhere.16–18

Furthermore, this methodology is well established and hasbeen successfully applied to the study of adsorbed atoms andmolecules on the surface of ionic materials.19–22 The VASPprogram employs ultra-soft pseudo-potentials,23,24 whichallows a smaller basis set for a given accuracy. Within thepseudo-potential approach only the valence electrons aretreated explicitly and the pseudo-potential represents theeffective interaction of the valence electrons with the atomiccores. In our calculations the core consisted of orbitals up to

DOI: 10.1039/b208004d J. Mater. Chem., 2003, 13, 93–101 93

This journal is # The Royal Society of Chemistry 2003

and including the 1s orbital for fluorine and oxygen and the 3porbital for Ca (H has no core). The valence orbitals arerepresented by a plane-wave basis set, in which the energy ofthe plane-waves is less than a given cutoff (Ecut).For surface calculations, where two energies are compared, it

is important that the total energies are well converged. Thedegree of convergence depends on a number of factors, two ofwhich are the plane-wave cutoff and the density of k-pointsampling within the Brillouin zone. We have by means of aseries of test calculations on bulk CaF2, where these parameterswere varied systematically, determined values for Ecut (500 eV)and the size of the Monkhorst–Pack25 k-point mesh (36 36 3)so that the total energy is converged to within 0.05 eV.The electronic structure calculations were performed within

the generalized-gradient approximation (GGA), using theexchange-correlation potential developed by Perdew andWang,26 which approach has been shown to give reliableresults for the energetics of adsorbates, e.g., water on CaO,27

TiO2 and SnO2.28

The larger scale systems were modelled using the lesscomputationally expensive atomistic simulation techniques,based on the Born model of solids,29 where simple para-meterised analytical forms are used to describe the forcesbetween atoms. In this work we employ the METADISEcode30 to investigate the surface systems by energy minimisa-tion, which is achieved by adjusting the atoms in the systemuntil the net forces on each atom are zero. Energy minimisationsimulations will yield adsorption energies, which have pre-viously been shown to give good agreement with experimentalsurface sampling techniques such as temperature programmeddesorption, e.g., ref. 31, as well as lowest energy configurationsof the adsorbate/solid interface.In addition, we employed Molecular Dynamics (MD)

simulations to derive the potential parameters for the water–methanoic acid interactions and also to investigate whether theinclusion of temperature in the calculations would affect theadsorption behaviour and/or energies. The MD code used wasDL_POLY32 where the integration algorithms are basedaround the Verlet leap-frog scheme.33 We used the Nose–Hoover algorithm for the thermostat,34,35 as this algorithmgenerates trajectories in both NVT and NPT ensembles, thuskeeping our simulations consistent. The Nose–Hoover para-meters were set at 0.5 ps for both the thermostat and barostatrelaxation times. The surface simulations were run for at least500 ps each (approximately 2.5 6 106 timesteps) as an NVTensemble, i.e., a constant number of particles, constant volumeand a constant temperature of 300 K.We used a combination of three potential models for a

description of the interactions of the various atoms in thesystems, namely by Catlow et al., for the calcium fluoridecrystal;36 the cvff forcefield for methanoic acid;37 and the waterpotential model by de Leeuw and Parker.38 The parameters forthe interactions between water and methanoic acid with thefluoride surfaces were derived following the approach bySchroder et al.,39 while the water–methanoic acid parameterswere fitted to the experimental solvation energy of methanoicacid.40 The full potential model is given in Table 1.

3. Results and discussion

Calcium fluoride has the cubic fluorite crystal structure withspace group Fm3m and a ~ b ~ c ~ 5.4323 A, where eachcalcium ion is surrounded by eight fluoride ions, which are inturn coordinated to four calcium ions in a tetrahedralarrangement, shown in Fig. 1. The calcium ions are arrangedon a cubic face-centred lattice, and if we divide the unit cell into8 smaller cubes, we find the fluoride ions in the centres of thesecubes.41 The cleavage plane is the {111} surface, which consistsof planes of calcium ions in a hexagonal array with a layer of

fluoride ions both above and below.9 The {111} surface is thusterminated with fluorine atoms and just below the surface areseven-coordinate calcium ions. We first employed DFTmethods to investigate the dehydrated {111} surface, calculat-ing lattice parameters of a ~ b ~ c ~ 5.4051 A, in excellentagreement with experiment. Fig. 2 shows the relaxed {111}surface, including the electron density distribution around thecalcium and fluoride ions and interatomic distances, fromwhich it is clear that the ionic relaxation of the surface is small,a dilation of the topmost F–Ca spacing of 0.01 A, followed by acontraction of the second interlayer distance by 0.02 A. Thecontour plots of the electron density show that the crystal isstrongly ionic with electron density firmly centred on theanions. The distortion of the electron density round the surfaceions is minimal, which leads to the negligible ionic relaxation ofthe surface layer.

3.1 Hydrated {111} surface

We next investigated the adsorption of water at the {111}surface to evaluate the energies of adsorption and the relaxedhydrated surface structure. We studied both the adsorption of afull monolayer (i.e. one water molecule per surface calcium ion)and a 50% partial coverage. We used a range of differentstarting configurations of associatively adsorbed water mole-cules on the surface to ensure that the final convergedconfiguration would be a global, rather than a local, minimumenergy configuration. The hydration energy per water mole-cule for the partial coverage of 50% was calculated to be253.4 kJ mol21 compared to the sum of the energies for thedry surface and an isolated gaseous water molecule, whichdecreased to 241.4 kJ mol21 for full monolayer coverage.These calculated hydration energies of approximately 41–53 kJ mol21 suggest that the water molecules are physisorbedrather than chemisorbed onto the surface. At 50% partialcoverage (Fig. 3), the water molecules adsorb almost flatlyonto the surface and are much more closely coordinated tothe surface than at full monolayer coverage; the calcium–oxygen distance increases from 2.37 A to 2.62 A and thefluorine–hydrogen distance from 1.52 A to 1.67 A when thecoverage is increased. This result suggests that the latticespacing of fluorine is not large enough to accommodate a fulllayer of water molecules in an optimum position.The DFT calculations did not show any dissociation of the

water molecules to form a hydroxylated surface at eithercoverage, so in order to be certain that there was no lowerenergy configuration with dissociatively adsorbed watermolecules, we also simulated a fully hydroxylated surface asa starting configuration. A hydroxyl group was placed aboveeach surface calcium ion and a proton above each surfacefluoride ion. However, the dissociatively adsorbed watermolecules reassembled to form molecular water. Fig. 4 showsthe sequence of reformation of the water molecules on the{111} surface, from initial configuration to a midway snapshot,where tilting of the hydroxyl group towards the proton andlengthening of the H–F bond (from 1.2 A to 1.7 A) is observed,to the final configuration with associatively adsorbed watermolecules. The distance between the hydroxyl oxygen atomand the proton decreases from an initial hydrogen-bonddistance of 2.22 A to a normal O–H bond of 1.01 A. Thecalculated hydration energy of 241.3 kJ mol21 is identical tothe associative starting configuration (monolayer coverage),giving us confidence that the lowest energy configuration hadbeen found. The easy reformation of undissociated watermolecules indicates that there is no significant energy barrier tothis process.The preference for associatively rather than dissociatively

adsorbed water on the main CaF2 {111} surface agreesqualitatively with previous atomistic and electronic structurecalculations of water adsorption at the vacuum interface of

94 J. Mater. Chem., 2003, 13, 93–101

MgO, another ionic crystal of cubic space group Fm3m, whichshowed that dissociative adsorption is energetically unfavour-able on the perfect {100} cleavage plane, e.g., refs. 19,31,42,43,

and only occurs at defects and low-coordinated surface sites44–46 or at the liquid water interface where H3O

1 species are takeninto account.43 Electronic structure calculations of the main

Table 1 Potential parameters used in this work (short range cutoff 20 A)

Ion

Charges (e)

Core-shell interaction/eV A22Core Shell

F 11.380 22.380 101.200000Oxygen of carbonate group (O) 10.587 21.632 507.400000Oxygen of water (Ow) 11.250 22.050 209.449602Ca 12.000Carbon of carbonate group (C) 11.135Hydrogen of water (Hw) 10.400Doubly-bonded oxygen of methanoic acid (OD) 20.380Hydroxy oxygen of methanoic acid (OH) 20.380Carbon of methanoic acid (CD) 10.310Hydroxy hydrogen of methanoic acid (HO) 10.350Hydrogen attached to carbon of methanoic acid (HC) 10.100

Buckingham potentialIon pair A/eV r/A C/eV A6

Ca–O 1550.0 0.29700 0.0Ca–F 1272.8 0.2997 0.0Ca–Ow 1186.6 0.29700 0.0Hw–O 396.3 0.23000 0.0Hw–Ow 396.3 0.25000 10.0O–O 16372.0 0.21300 3.47F–F 99731833.99084 0.12013 17.02423O–Ow 12533.6 0.21300 12.09Ca–OH 563.64 0.29700 0.0F–Ow 79785220.99 0.12013 26.78752F–Hw 715.339 0.2500 10.00Ca–OD 563.64 0.29700 0.0OH–O 37898119 0.12013 11.309OD–O 37898119 0.12013 11.309OH–F 37898119 0.12013 25.1OD–F 37898119 0.12013 25.1Ow–OH 4797.6 0.213 30.2Ow–OD 4797.6 0.213 30.2Ow–HO 396.3 0.25 0.0Ow–HC 396.3 0.25 0.0Ow–CD 895 0.26 0.0

Lennard–Jones potentialA/eV A12 B/eV A6

Ow–Ow 39344.98 42.15HC–O 2915.25 4.222HO–O 2915.25 4.222CD–O 3315.91 19.846OD–Hw 1908.1 5.55OH–Hw 1908.1 5.55HC–F 2915.25 9.3784HO–F 2915.25 9.3784CD–F 3315.91 44.012

Morse potentialD/eV a/A21 r0/A

C–O 4.710000 3.80000 1.18000Hw–Ow 6.203713 2.22003 0.92376CD–HC 4.66 1.77 1.10OH–HO 4.08 2.28 0.96CD–OH 4.29 2.00 1.37CD–OD 6.22 2.06 1.23

Three-body potentialk/eV rad22 H0

Ocore–C–Ocore 1.69000 120.000000H–Owshell–H 4.19978 108.693195OH–HO–CD 4.29 112.000000CD–HC–OH 4.72 110.000000CD–OD–HC 4.72 120.000000CD–OD–OH 12.45 123.000000

Four-body potentialk/eV rad22 H0

C–Ocore–Ocore–Ocore 0.11290 180.0

Intermolecular Coulombic interaction (%)Hw–Ow 50Hw–Hw 50

J. Mater. Chem., 2003, 13, 93–101 95

TiO2 cleavage plane, the {110} surface, show hydroxylation ofthe surface at half coverage.20,28 However, Lindan et al. foundthat at full coverage a mixture of associatively and dissocia-tively adsorbed water molecules is observed, where the watermolecule is adsorbed almost flat onto the surface to maximisehydrogen-bonding to oxygen atoms of both the hydroxyl groupand the mineral surface.20 This configuration of the associa-tively adsorbed water molecules on the TiO2 {110} surface isthus like that on the CaF2 {111} surface, where almost flat

Fig. 1 Bulk structure of CaF2 showing cubic face-centred calciumlattice with the fluoride ions in the centres of each of eight smaller cubesmaking up the cubic unit cell (Ca ~ black, F ~ pale grey).

Fig. 2 Side view of the relaxed CaF2 {111} surface showing electrondensity contour plots and interatomic distances (Ca ~ dark grey, F ~pale grey, contour levels are from 0.05 to 0.35 e A23 at 0.05 e A23

intervals, bond lengths in A).

Fig. 3 Plan view of the minimum energy structure of the CaF2 {111}surface with 50% coverage of associatively adsorbed water molecules,showing almost flat adsorption of the water molecules (fluorite shownas framework, water space-filled; Ca ~ black, F ~ pale grey, O ~black, H ~ white).

Fig. 4 Reassembly of dissociatively adsorbed water molecules on theCaF2 {111} surface: (a) side view showing initial configuration ofhydroxylated surface; (b) snapshot during minimisation processshowing tilting of hydroxyl group and lengthening of F–H bond; (c)side view of the final configuration showing associatively adsorbedwater molecules (crystal shown as framework, water space-filled; Ca~black, F ~ pale grey, O ~ black, H ~ white).

96 J. Mater. Chem., 2003, 13, 93–101

adsorption of the water molecules and a network of hydrogen-bonding is preferred over dissociative adsorption.Our calculations indicate that the binding of the water

molecule’s oxygen atom to a surface calcium atom is the maininteraction. This finding suggests that increasing the coordina-tion of the surface cation to the bulk value, from seven- toeight-coordinate for the {111} surface, is the driving forcebehind the adsorption. From these calculations we wouldtherefore suggest that, as with MgO, dissociative adsorption ofwater takes place at defects and low-coordinated surface sitesrather than the higher-coordinated cations of the perfect {111}cleavage plane.

3.2 Hydration of planar and stepped surfaces

In order to study larger-scale systems, we employed atomisticsimulation techniques to model two more fluorite surfaces inaddition to the {111} surface, namely the {011} and {310}surfaces, as well as two stepped {111} surfaces, as a morerealistic model for experimental surfaces. We investigatedadsorption of both water and methanoic acid on the surfaces toevaluate their relative structures and adsorption energies.We first modelled the unhydrated surfaces to calculate their

stabilities, after which we hydrated the surfaces to evaluate anychanges in stability. The surface stabilities are measured by thesurface energy, which is calculated as follows:

c~Us{Ub

A

where Us is the energy of the ions in the surface simulation cellandUb is the energy of an equal number of bulk ions, while A isthe area of the surface. A low, positive value for the surfaceenergy indicates a stable surface, which will be important in themorphology of the mineral. The surface energies of the dry andhydrated surfaces are collected in Table 2, where the surfaceenergy of the hydrated surface is calculated with respect to bulkwater. The {111} surface is clearly the most stable of the threesurfaces considered, both in dry and aqueous conditions, inagreement with the fact that this is experimentally the perfectcleavage plane of calcium fluoride.41 The dry {310} surface isvery unstable, but its stability is increased substantially whenthe surface is hydrated, making it now more stable than the{011} surface.We first considered adsorption of water on the planar {111}

surface, where comparison to the equivalent DFT calculationsgives an indication of the accuracy of the potential model. Thewater molecules adsorb flat onto the surface at a Ca–O distanceof 2.47 A and H–F distances of 2.13–2.18 A. As suggested bythe DFT calculations, the Ca–Ca interatomic spacing of 3.85 Ais too small for a water molecule to adsorb on each calcium ion,and hence only 50% of the available adsorption sites arecovered by water molecules. We again calculated the adsorp-tion energies with respect to isolated gaseous water moleculesto enable direct comparison with experimental techniques suchas temperature programmed desorption (TPD). We calculateda hydration energy of 261.8 kJ mol21 at a partial coverage of50%, which is in acceptable agreement with the DFT result of253.4 kJ mol21. The discrepancy in the hydration energies isdue to the fact that the atomistic simulations predict acompletely flat mode of adsorption for the water molecules,

with close coordination of both hydrogens to surface fluorideions, while the water molecules in the DFT calculations adsorbslightly tilted, with one hydrogen atom pointing away from thesurface, giving very different H–F distances for the two hydro-gens (1.52 A and 2.85 A). When a full monolayer is adsorbed,the average adsorption energy drops to 38.5 kJ mol21,compared to 41.4 kJ mol21 for the DFT calculations. Due tolack of space on the surface for a full monolayer, the watermolecules do not adsorb flat onto the surface and the lesserbinding between surface fluoride ions and hydrogen atomsleads to an even better agreement for the adsorption energiesbetween the two computational techniques. On the {011} and{310} surfaces, the Ca–Ca spacings are large enough easily toaccommodate a full monolayer of water. On the {011} surface,the water molecules adsorb in an upright fashion, withoutsignificant H–F interactions. However, the increased stabilityof the hydrated {310} surface is due to flat adsorption of thewater molecules, similar to the {111} surface, and an extensivenetwork of hydrogen-bonding between both hydrogens andsurface fluoride ions.As ‘real’ surfaces are never completely free from defects, we

have also included stepped surface sites in our calculations. Weconsidered two steps on the {111} surface that differ in theorientation of the F2 groups, which either lean backwards at anobtuse angle of 135u with respect to the underlying plane orforwards at an acute angle of 45u (Fig. 5). From the adsorptionenergies in Table 3, we see that hydration of the acute step edgeis less favourable than the planar surface, due to the restrictedspace available for the adsorbing water molecule under thestep. However, the more open adsorption site at the obtuse stepedge, combined with the step ions’ lower coordination number,makes hydration of this step more exothermic than the planarsurface.

3.3 Adsorption of methanoic acid

When we considered adsorption of methanoic acid at the samesurface sites, we found that the methanoic acid moleculesadsorb onto the planar surfaces in three distinctly different

Table 2 Surface energies of the calcium fluoride surfaces

Surface energies/J m22

Surface Unhydrated Hydrated

{111} 0.52 0.40{011} 0.82 0.90{310} 1.56 0.67

Fig. 5 (a) Acute and (b) obtuse steps on the CaF2 {111} surface (Ca~black, F ~ pale grey).

J. Mater. Chem., 2003, 13, 93–101 97

fashions. On the {011} surface, the lattice spacing is largeenough to allow full monolayer coverage with one methanoicacid molecule per surface calcium. The methanoic acidmolecule adsorbs with both oxygen ions to two surface calciumions, bridging between them (Fig. 6). The doubly bondedoxygen ion closely coordinates to the calcium ion at a distanceof 2.2 A while the oxygen atom of the hydroxyl group is at2.65 A from the second calcium ion. The hydrogen of thehydroxyl group relaxes into the surface and coordinates to afluorine atom at 2.4 A. The lattice spacing on the {310} surfaceis also large enough to accommodate full monolayer coverage(Fig. 7). The doubly bonded oxygen ion is again bonded to asurface calcium ion at 2.15 A, while more loosely coordinated

to calcium ions further away in the next layer (3.93 A).Furthermore, the doubly bonded oxygen ions coordinate tohydroxyl hydrogens of other adsorbed methanoic acidmolecules (2.4 A), while the hydrogen bonded to the carbonatoms coordinates to surface fluoride ions (2.35 A).Due to the much smaller interatomic distance on the {111}

surface, only a 50% coverage of methanoic acid can beaccommodated, which is a reasonable coverage if we compareit with experimental work by Mielczarski et al., who observed a30% coverage of oleic acid, which is a carboxylic acid with along carbon chain instead of the hydrogen of methanoic acid.47

The molecules adsorb in a fairly flat configuration onto thesurface, bridging between two calcium ions, with both oxygenions coordinated to a calcium at 2.2 A for the doubly bondedoxygen ion and at 2.9 A for the oxygen ion of the hydroxylgroup (Fig. 8). The hydrogen atom of the hydroxyl groupcoordinates to two surface fluoride ions at 2.5 and 2.7 A. Whenadsorbed at the step edges, we see that the trend in adsorptionenergies is reversed from the hydration pattern. More energy isnow released upon adsorption at the acute step edge than at theobtuse edge, while both steps are calculated to be morefavourable adsorption sites than the terraces of the planarsurface. The reason for the higher exothermicity at the acutestep edge is the fact that in addition to the same interactionsbetween methanoic acid and the terrace atoms, as shown foradsorption on the planar surface, the doubly bonded oxygenatom also bonds to a low-coordinated calcium ion on the stepedge, hence bridging the gap between step and terrace, whichwas not possible in the adsorption of water. The hydrogens alsointeract with fluoride ions both on the edge and the terrace,leading to a network of hydrogen-bonding between the surfaceand adsorbate. It is these multiple interactions that cause themethanoic acid adsorption at the steps to be more exothermicthan on the planar surfaces.

3.4 The effect of temperature: Molecular Dynamics simulationsof the (111) surface

As energy minimisation techniques do not take into accounttemperature, in this section we employ Molecular Dynamicssimulations (MD) to explicitly investigate the effect of tempera-ture on the interaction of water and methanoic acid at the{111} plane at 300 K. We started the simulations with amonolayer of water adsorbed at the surface. However, duringthe simulation water molecules desorbed from the surface anddiffused through the gap between the two surfaces, forminga droplet (Fig. 9). From the mean square deviation, thediffusion coefficient of the water molecules is calculated to be

Table 3 Adsorption energies of water and methanoic acid at thesurfaces

Adsorption energies/kJ mol21

Surface Water Methanoic acidMethanoic acidin water

Planar {111} 238.5 256.3 296.7Acute {111} 229.1 290.8 234.1Obtuse {111} 250.8 279.5 221.2{011} 233.4 2102.4 —{310} 2250.7 2110.9 —

Fig. 6 Side view of the {011} surface, showing the crystal as a latticeframework (Ca ~ black, F ~ pale grey) and the methanoic acidmolecule (space-filled, O ~ black, C ~ pale grey, H ~ white)coordinated by its oxygens to two surface calcium ions.

Fig. 7 Side view of the {310} surface, showing the crystal as a latticeframework (Ca ~ black, F ~ pale grey) and the methanoic acidmolecule (space-filled, O ~ black, C ~ pale grey, H ~ white) closelycoordinated by its doubly bonded oxygen atom to a surface calcium ionand hydrogen-bonding to a surface fluorine.

Fig. 8 Plan view of the {111} surface with adsorbed methanoic acidmolecule, showing the crystal as a lattice framework (Ca~ black, F~pale grey) and the methanoic acid molecule (space-filled O ~ black,C ~ pale grey, H ~ white).

98 J. Mater. Chem., 2003, 13, 93–101

1.2 6 1029 m2 s21, which is identical to that calculated forwater molecules in a box of pure liquid water at 300 K underNPT conditions.38 The hydration energy of 232.7 kJ mol21 at300 K is less than the intermolecular interactions betweenwater molecules themselves, calculated to be 243.0 kJ mol21

at the same temperature in agreement with experiment(243.4 kJ mol21).48 Hence, at this low water density, wemay conclude that on energetic grounds the water molecules onthe fluorite {111} plane prefer not to adsorb to the surface butto cluster together. We next repeated the calculation withmethanoic acid as the adsorbate rather than water. This time,however, the methanoic acid remained bound to the {111}surface rather than diffuse through the gap. Clustering of themethanoic acid molecules also took place, but unlike thewater molecules, surface diffusion of the methanoic acid wasfollowed by the formation of clusters at the surface, in a similaradsorption pattern as was observed in the energy minimi-sation calculations above, by both oxygen atoms to surfacecalcium ions (Fig. 10). Similar clustering of methanoic acid wasobserved experimentally by Iwasawa et al. to occur at terraceson the TiO2 (110) surface.49 The energy of interaction ofmethanoic acid with the surface is calculated at 291 kJ mol21,higher than in the energy minimisation simulations. Hence, the

effect of temperature, included in calculations through theemployment of Molecular Dynamics simulations, is to exacer-bate the difference in adsorption energies between water andmethanoic acid at the fluorite (111) surface. The MD simu-lations also showed that although the methanoic acid diffusesalong the surface, it remains adsorbed, while competitiveinteractions between the water molecules themselves outweighinteractions between the solid surface and water molecules,which as a result leave the surface.Of course, in ‘‘real’’ mineral separation processes, water

and the organic flotation reagents co-exist and we have henceextended our calculations to include both water and methanoicacid in the simulations.

3.5 Co-adsorption of water and methanoic acid

The adsorption energies from the energy minimisations forboth water and methanoic acid onto the three surfaces arecollected in Table 3. The hydration energies for the differentcalcium fluoride surfaces vary considerably due to the presence(or absence) of hydrogen-bonding to the surface fluoride ions,in addition to the calcium–oxygen interactions. The adsorptionenergies for methanoic acid onto the mineral surfaces areconsiderably larger than the hydration energies on the domi-nant {011} and planar and stepped {111} surfaces due to thecapability of the acid molecules to bridge, by their oxygenatoms, between two or more surface calcium atoms and theclose hydrogen-bonding to surface fluoride ions. These calcu-lations would therefore suggest that it would be energeticallypreferential for the methanoic acid molecules to adsorb to thesesurfaces, displacing the water molecules from the adsorptionsites, which was borne out by the MD simulations of water andmethanoic acid at the {111} surface at 300 K, where the waterdesorbed from the surface while the methanoic acid remainedadsorbed. However, in order to verify whether this assumptionbased on separate calculations of the adsorbates is valid, werepeated the calculations of methanoic acid adsorption at theplanar and stepped {111} surfaces, but this time including alayer of water in the simulations, hence studying the compe-titive adsorption of water and methanoic acid directly. Theadsorption energies were now calculated with respect to thehydrated surface and a solvated methanoic acid molecule. Inorder to model the co-adsorption of methanoic acid and waterat the fluorite surfaces, we needed to derive interatomicpotential parameters for the water–methanoic acid interac-tions. We fitted these potential parameters to the experimentalsolvation energy of methanoic acid, in a series of MolecularDynamics simulations of a methanoic acid molecule in a box of255 water molecules (Fig. 11). The final parameters thusderived (Table 1) gave a solvation energy for methanoic acidof 241.7 kJ mol21, compared to the experimental value of247.4 kJ mol21.40

The data listed in Table 3 show that on the planar {111}surface, the presence of water increases the adsorption energyof methanoic acid, the reason for which becomes clear ifwe compare the adsorption pattern of the methanoic acidwith that of water at the same surface sites. The methanoic acidonly replaces one adsorbed water molecule at the planarsurface and as the intermolecular interactions between thewater molecules themselves (43 kJ mol21) or with themethanoic acid (40 kJ mol21) are very similar, the watermolecules have no preference for interacting with either themethanoic acid or each other. The regular adsorption patternof the water on the surface is not disturbed by the presence ofthe surfactant, but the adsorbate is stabilised by the forma-tion of a network of hydrogen-bonded interactions to neigh-bouring water molecules. However, at the stepped surface sitesthe co-adsorption of water lowers the adsorption energies formethanoic acid (Table 3), both processes becoming much lessexothermic. Again, the reason is two-fold, based on both the

Fig. 9 Water droplet formation between two {111} surfaces in aMolecular Dynamics simulation at NVT and 300 K.

Fig. 10 Adsorption and clustering of methanoic acid molecules at the{111} surface in a Molecular Dynamics simulation at NVT and 300 K.

J. Mater. Chem., 2003, 13, 93–101 99

geometry of the surface sites and the relative adsorptionenergies of the surfactant and the water molecules. Hydrationof the stepped sites (29–51 kJ mol21) is energetically similar tothe planar fluorite surface (average y38.5 kJ mol21). Bindingof the methanoic acid to the steps is stronger than water(averagey85 kJ mol21) and it therefore remains closely boundto the step site even in the presence of water, as shown inFig. 12 for the obtuse step. However, its presence at the stepdisturbs the regular pattern of water adsorption, at least in theimmediate vicinity of the step, leading to a smaller adsorptionenergy. Thus, before the addition of water to the system we findsimilar adsorption energies for the three different surface siteson the {111} surface (56–91 kJ mol21), but once water has beenintroduced in the calculations, the adsorption energies show amuch bigger variation with adsorption site (21–97 kJ mol21)and even a reversal of the relative stabilities, indicating that weneed to include solvent effects explicitly if we are to predictrealistic adsorption behaviour.

4 Conclusions

We have shown in this work that computational techniques arewell placed to provide insight at the atomic level into theinteractions between substrate and adsorbate molecules. We

have presented calculations of the adsorption of water andmethanoic acid at calcium fluoride surfaces, using a combina-tion of computational techniques. Accurate density functionaltheory calculations were used to obtain the electronic struc-ture of the {111} surface together with hydration modesand energies; and atomistic simulation techniques to elucidatethe geometry and relative adsorption energies of water andmethanoic acid at a range of different surface sites. From oursimulations we can draw the following conclusions.Electron density plots generated by DFT calculations of the

{111} surface show calcium fluoride to be a strongly ioniccrystal, with no discernible distortion in the surface layer withrespect to bulk layers, leading to minimal ionic relaxation ofthe surface.Associative adsorption of water is preferred at the {111}

surface, without significant energy barrier to reformation ofdissociated water molecules into molecular water. The hydra-tion energy is dependent upon coverage and both the decreasein hydration energy and lesser coordination to the surface uponincreasing coverage indicates repulsive interactions between theadsorbed water molecules.Modelling hydration of the {111} surface using atomistic

simulation techniques gives similar hydration energies andconfigurations of the adsorbed water molecules to the DFTcalculations, although there may be some overbonding of theH–F hydrogen-bonding in the interatomic potential approach.Adsorption of methanoic acid up to full monolayer coverage

is possible on both {011} and {310} surfaces, but on the {111}surface, due to the smaller calcium–calcium distance, onlyadsorption up to 50% is preferred. On this surface, themethanoic acid molecules adsorb by their oxygen atoms to twocalcium atoms, forming a bridge between them. This mode ofadsorption is particularly favourable, which is also seen at thestepped sites on the {111} surface. On both the {011} and thedominant {111} fluorite surfaces the energies of adsorption ofmethanoic acid compared to water show that adsorption ofmethanoic acid is energetically more favourable and hencemethanoic acid should compete effectively with water foradsorption at these surfaces. Molecular Dynamics simulationsof the two adsorbates at the {111} surface show that theeffect of temperature is to widen the gap in adsorption energiesbetween methanoic acid and water. The latter adsorbate leavesthe surface and forms a water droplet between the {111}planes.Simulations of methanoic acid adsorption in the presence of

water bear out the suggestion that methanoic acid competeseffectively with water as an adsorbate, as the methanoic acidremains adsorbed at the {111} terrace and steps forming closeinteractions with the surrounding water molecules. However,these latter calculations have also shown that interactionsbetween surfactant and water molecules can have a radicaleffect on adsorption behaviour, and it is therefore not suffi-cient to calculate the interactions of surfactant molecules withmineral surfaces in isolation, as the presence of solvent in thecalculations makes a significant contribution to the finaladsorption energies and relative stabilities of the surface sites.The implication of these findings for the search for flotationreagents is that we need to explicitly include solvent in thecalculations if we are to successfully predict the affinity of themineral for particular surfactants.

Acknowledgements

We acknowledge the Engineering and Physical SciencesResearch Council, grant no. GR/N65172/01, and the RoyalSociety, grant no. 22292, for funding and the Minerals andMaterials Consortia for the provision of computer time on theCray T3E.

Fig. 11 Average configuration of methanoic acid molecule in asimulation cell of 255 water molecules during a Molecular Dynamicssimulation at NPT and 300 K (the apparently dissociated watermolecules are, in fact, water molecules, but shown split up as an artefactof the periodic boundary conditions).

Fig. 12 Co-adsorption of water and methanoic acid at the obtuse stepon the {111} surface (fluorite as framework, methanoic acid space-filled, water as triangles; Ca ~ dark grey, F ~ pale grey, O ~ black,C ~ grey, H ~ white).

100 J. Mater. Chem., 2003, 13, 93–101

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