Journal of Contaminant Hydrology 128 (2012) 19–32

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Journal of Contaminant Hydrology

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Research article

Porosity investigation of compacted bentonite using XRD profile modeling

Michael Holmboe⁎, Susanna Wold, Mats JonssonKTH School of Chemical Science and Engineering, Nuclear Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

a r t i c l e i n f o

⁎ Corresponding author. Fax: +46 8 7908772.E-mail address: holmboe@kth.se (M. Holmboe).

0169-7722/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.jconhyd.2011.10.005

a b s t r a c t

Article history:Received 29 March 2011Received in revised form 7 October 2011Accepted 12 October 2011Available online 20 October 2011

Many countries intend to use compacted bentonite as a barrier in their deep geological reposito-ries for nuclear waste. In order to describe and predict hydraulic conductivity or radionuclidetransport through the bentonite barrier, fundamental understanding of the microstructure ofcompacted bentonite is needed. This study examined the interlayer swelling and overall micro-structure of Wyoming Bentonite MX-80 and the corresponding homo-ionic Na+ and Ca2+

forms, using XRD with samples saturated under confined swelling conditions and free swellingconditions. For the samples saturated under confined conditions, the interparticle, or so-calledfree or external porosity was estimated by comparing the experimental interlayer distancesobtained from one-dimensional XRD profile fitting against the maximum interlayer distancespossible for the corresponding water content. The results showed that interlayer porosity domi-nated total porosity, irrespective of water content, and that the interparticle porosity was lowerthan previously reported in the literature. At compactions relevant for the saturated bentonitebarrier (1.4–1.8 g/cm3), the interparticle porosity was estimated to ≤3%.

© 2011 Elsevier B.V. All rights reserved.

Keywords:BentoniteClay swellingMicrostructurePorosityNuclear waste disposalXRD

1. Introduction

In future high level nuclear waste repositories, compactedbentonite has been proposed as an engineered barrier inmany countries. Due to the high compaction and high sorptioncapacity of the saturated bentonite barrier, the diffusive trans-port of radionuclides will be substantially retarded. It is widelyacknowledged that bentonite consists of turbostraticallystacked montmorillonite layers forming individual particles,and a smaller fraction of accessory minerals (Bergaya et al.,2006; Pusch, 2001). However, manymicrostructural propertiesof saturated compacted bentonite are still not well established.In the literature, several different approaches have beenused inorder to predict properties such as hydraulic conductivity anddiffusive transport of cationic and anionic radionuclides, usingmodels based on various assumptions regarding microstruc-ture. Themicrostructural properties are also of fundamental in-terest in the aspect of colloid transport in the bentonite barrier,since in the event of canister failure, radiocolloids can beformed in close proximity to the fuel. Transport of these

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radiocolloids would presumably be hindered by filtration, dueto the low interparticle porosity of saturated compacted ben-tonite (Holmboe et al., 2010; Kurosawa and Ueta, 2001). How-ever, bentonite also contains small amounts of organicmaterial, which if mobilized can enhance the transport of ra-dionuclides in the bentonite barrier (Ijimia et al., 2009; Woldand Eriksen, 2007). One main problem hitherto has been to es-timate the relative proportions of interlayer and interparticlevoids, and thus also the relative proportions of the internaland external waters, respectively. Since interlayer voids mayhave different sizes, geometry and surface properties thaninterparticle voids, the distinction between both types ofvoids is important. Many authors have suggested that interpar-ticle voids or local low density regions, i.e. a so-called free orexternal porosity, can comprise a significant fraction of thetotal porosity, depending on the dry density of the highly com-pacted bentonite (Bourg et al., 2003; 2006; Fernández andRivas, 2005; Kozaki et al., 2001; Muurinen, 2009; Muurinenet al., 2004; Suzuki et al., 2004; Van Loon et al., 2007; Wersin,2004), or even form a coherent interparticle network (Puschet al., 1990).

For instance in Pusch et al. (1990), a general microstruc-tural model was developed in order to estimate the hydraulic

20 M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

conductivity of bentonite, on the assumption of a coherent net-work of gel-filled pores or channels ranging from 10 to 80 nmdepending on the dry density of the bentonite. In Muurinenet al. (2004), the size of possible interparticle voids was esti-mated to several nm, increasing with decreasing compaction,from experimental basal spacings with the assumption thatthe particle size could be estimated from the BET surface areaof freeze-dried, Na-washed bentonite. In Van Loon et al.(2007), the accessible Cl− and the interparticle porosity wasestimated from diffusion experiments, assuming no interlayertransport due to anionic exclusion effects. In this study theinterparticle porosity for the dry density range 1.3–1.9 g/cm3

increased from 6 to 22% with decreasing dry density. Fromthe density and surface area of montmorillonite and the inter-layer distances reported by Kozaki et al. (1998; 2001). Bourget al. (2003; 2006) estimated that for bentonite having dry den-sities b1.8 g/cm3, the interparticle voids would constitute anon-depreciable fraction of the total porosity and that the vol-ume fraction of the interlayer voidswould increasewith increas-ing compaction. In Suzuki et al. (2004) a geometric layer-particlemodel was developed based also on the basal spacings reportedin Kozaki et al. (1998), in order to estimate the size of the inter-particle voids assuming planar and uniform void geometry be-tween individual particles. For high dry density values, theirmodel suggests small (or even negative) interparticle voids, butfor lower dry density values the size of the interparticle voids be-comes very large. For instance, for dry density 0.9 and 1.35 g/cm3, Suzuki et al. (2004) estimated the volume fraction ofthese interparticle voids to be 61% and 22%, respectively.

If the mineral composition is well characterized, micro-structural models of compacted bentonite on the nano-scalecan be based on accurate information of the basal spacings orthe corresponding interlayer distances within the montmoril-lonite particles. From the average interlayer distance, both theinterparticle and the interlayer porosity can be estimated at agiven dry density. The basal spacings, i.e. the d001 values ofmontmorillonite, can be measured by neutron and X-raysmall-angle scattering or diffraction. Traditionally, the appar-ent basal spacings are calculated with Bragg's law from thepeakmaxima of the 001 reflection. However, because of swell-ing heterogeneity and interstratification of different interlayertypes, i.e. different hydration states (0–4water layers, hereafterdenoted 0W–4W), resulting in broad and often asymmetricdiffraction peaks, accurate basal spacings for montmorillonitecannot be obtained by simply applying Bragg's law. Instead,one-dimensional XRD profile fitting is needed.

Most XRD studies regarding the swelling of smectiteshave traditionally been performed as a function of relativehumidity (%RH), using purified homo-ionic montmorillonitesunder free swelling conditions. However for the engineeredbarrier, bentonite clay containing different counter-ions, usu-ally Na+, Ca2+, Mg2+, K+, and accessory minerals will beused. Furthermore, saturation of the bentonite will proceedfrom the aqueous phase, inducing a high swelling pressure.Thus, most XRD data found in the literature may not be un-conditionally representative of the engineered barrier. Unfor-tunately, few studies to date have reported diffraction dataon crystalline swelling of montmorillonite at water contentsrelevant for the engineered barrier (>0.2 gH2O/gclay), saturateddirectly from the aqueous phase under confined conditions.Devineau et al. (2006), performed in situ neutron diffraction

and traditional XRD experiments in reflection mode witha Wyoming Bentonite MX-80 and a Na-montmorillonite satu-rated at four different water vapor pressures, i.e. %RH values,through water vapor adsorption conditions. Although no pro-file fitting was performed, it was concluded that the swellingof samples saturated under confined conditions and measuredin situ and that of samples saturated under free conditions wassimilar for low%RH.However, for the highestwater vapor pres-sure used, corresponding to 98 %RH, the apparent basal spacingof the confined samples was slightly larger than for samplessaturated through water vapor adsorption conditions underfree swelling conditions. Kozaki et al. (1998; 2001) reportedlow-angle XRD data from reflection mode measurements ofthe 001 reflection for a size-fractionated, washed Kunipia-FNa+-montmorillonite. Their samples were saturated underconfined conditions at low ionic strength in diffusion cellsand measured directly upon disassembly. Very distinct step-wise hydration of Na-montmorillonite as a function of dry den-sity (1.0–1.8 g/cm3) was found. There was no sign of osmoticinterlayer swelling, i.e. basal spacings >19 Å, at the lowestdry density values, in contrast to the results reported in Norrish(1954) for well-orientated Na-montmorillonite samples underunconfined conditions at similar water contents. Using bothlow-angle XRD and SAXS, Muurinen (2009; 2004) measuredthe basal spacings of a Na+ washed MX-80 bentonite saturatedunder confined conditions. Unfortunately, only four dry densityvalues were probed (approximately 0.7, 1.0, 1.3 and 1.6 g/cm3).The XRD results showed less pronounced stepwise hydrationcompared with that reported in Kozaki et al. (1998), while theSAXS results provided evidence of osmotic interlayer swelling.

In this study, we used XRD in reflection mode, togetherwith one-dimensional XRD profile fitting using the softwareMODXRSD (Plançon, 2002), in order to compare the distribu-tion of hydration states and the average basal spacings ofWyoming Bentonite MX-80 and the corresponding homo-ionic Na- and Ca-montmorillonites, as a function of watercontent. For compacted samples representative of the ben-tonite barrier in a deep geological repository, the interlayerdistances obtained were compared against the correspondingtheoretical maximum interlayer distances, in order to calcu-late the interparticle porosity.

1.1. The swelling of bentonite

In order to understand the microstructure of saturatedcompacted bentonite, it must be borne in mind that the micro-structure is primarily controlled by the magnitude of swelling,which in turn is controlled by the water content, accessiblecounter-ions and ionic strength. Upon water uptake thecounter-ions become hydrated, together with the montmoril-lonite surfaces. When the swelling is constricted by constantvolume, a high swelling pressure builds up, itself a function ofcompaction and type of counter-ions (Karnland et al., 2006).Because of the great swelling capacity of compacted bentonite,the voids between the individual particles could be expected todecrease in number and total volume upon water saturation.Due to the heterogeneity in shape and polydispersity regardingparticle size of both themontmorillonite and accessorymineralparticles, the distances between particles of the larger size frac-tion would be filled by particles belonging to the smaller sizefraction, reducing the interparticle or the external porosity.

21M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

Another factor anticipated to contribute to low interparti-cle porosity, which is not yet well described in the litera-ture, is the structural flexibility of themontmorillonite particles(Sato et al., 2001) in both the lateral (in-plane shearing andtwisting/turning) and perpendicular direction (bending).

Starting with a dried montmorillonite sample, one, two,three and sometimes four more or less discrete layers(0W–4W) with increasing water content are formed (hencethe term crystalline swelling). The 4W hydration state is un-common and has only been reported for MX-80 bentonite, notfor homo-ionic Na- or Ca-montmorillonites (Fernández andRivas, 2005; Norrish, 1954; Saiyouri et al., 2004). The discretebasal spacings of the different hydration states are not absolute-ly discrete, even for the same type of clay. Instead the basalspacings, which depend on the type of counter-ions present,also depend on the actual water content or activity (Ferrageet al., 2005b). This partly explains the variation in basal spacingsusually found in the literature in different diffraction investiga-tions, namely 12.2–12.7 (1 W), 15.2–15.7 (2W), 18.4–19 (3W)and 21.4–22 Å (4W). Although the increase in the basal spacingbetween two montmorillonite layers with increasing hydrationis a more or less stepwise process, the average increase in basalspacing upon water uptake has recently been reported to bemore of a continuous process due to swelling heterogeneity.This phenomenon is often attributed to layer charge heteroge-neities leading to different coexisting and interstratified inter-layer types, i.e. different hydration states, 0 W–4W (Devineauet al., 2006; Fernández and Rivas, 2005; Ferrage et al., 2005a;Ferrage et al., 2005b; Ferrage et al., 2007; Laird, 2006; Saiyouriet al., 2004; Warr and Berger, 2007; Wilson et al., 2004). Thus,depending on the actual water content, usually two or some-times three different types of water layers can be interstratified.

Increasing the water content further induces a transitionfrom crystalline swelling to osmotic interlayer swelling. ForNa-montmorillonite, this transition leads to a jump in thebasal spacing from ~19 (18.4–19) Å to approximately 35–40 Å,which is explained by the formation of repulsive diffuse doublelayers (Norrish, 1954). Thus, for osmotic interlayer swelling theinterlayer environment can best be described by two negativelycharged surfaces with repulsive diffuse double layers (DDL).The actual limits and behavior in the region of crystallineand osmotic swelling depend on the type of counter-ionsavailable and montmorillonite layer charge. For pure Ca-montmorillonite, osmotic interlayer swelling is probably notpossible at all (Amorim et al., 2007; Norrish, 1954) due to thehigher valence resulting in ion–ion correlation forces, whichreduce the electro-osmotic repulsion (Segad et al., 2010).The swelling also depends on the bulk ionic strength. ForNaCl, with increasing concentration the basal spacings of Na-montmorillonite has been shown to be proportional to[NaCl]−1/2, until [NaCl]b0.3 M,where osmotic interlayer swell-ing is not possible (Amorim et al., 2007; Norrish, 1954; Suzukiet al., 2005). Interestingly, above ~1.5 M NaCl (depending onlayer charge), the crystalline swelling of Na-montmorillonitedoes not extend beyond the 2W state (Slade et al., 1991).

1.2. Microstructural model

By treating montmorillonite as uniform discrete sheets,separated by discrete water layers, microstructural modelsof compacted bentonite or pure montmorillonite can be

formulated by performing a geometric bulk or mass balance.Both the interlayer (internal) and the interparticle (external)porosity can be estimated by comparing the average interlayerdistance for a certain dry density with the corresponding max-imum theoretical interlayer distance possible, thus represent-ing the case when the interlayer porosity equals the totalporosity. If the concept of dry density is used to express thewater content, accurate data are only needed for the montmo-rillonite density and themontmorillonite layer thickness. How-ever, if the water content is expressed by weight, knowledgeabout the water density is also necessary. The different valuesof the montmorillonite density found in the literature vary byalmost 10% (2.65–2.88 g/cm3), which is also true for themont-morillonite layer thickness (9.2–10.1 Å). Due to this, micro-structural models based on these parameters may lead torelatively large errors. For a pure montmorillonite, bytreating the layers as uniform discrete sheets, it follows thatboth properties must be related to each other, as wellas to the specific surface area of the montmorillonite faces,SA,faces, through the relationship:

ρMonttMont ¼2

SA;f acesð1Þ

Where ρMont and tMont are the montmorillonite densityand layer thickness, respectively. SA,faces can be calculatedfrom the surface area of the unit cell AUC (a×b=46.7±0.1 Å2)and the molecular weight MW (both known with an estimateduncertainty below 1%, Karnland et al., 2006) together with theAvogadro number NA, according to Eq. 2.

SA;f aces ¼ 2AUCNA

MW: ð2Þ

For the Na-montmorillonite used in this study, SA,faces wascalculated to be 756 m2/g, which is in close agreement with aNa-montmorillonite density of 2.80 g/cm3 (Karnland et al.,2006) and a single layer thickness of 9.5 Å. In practice, the latteris often assumed to be equal to or slightly smaller than the d001value for a dehydrated sample,which in this studywas found tobe≤9.55 Å. From the accessorymineral inventory ofWyomingBentonite MX-80 reported by Karnland et al. (2006), the acces-sory mineral average density was estimated to be 2.77 g/cm3,i.e. within the range of error of the estimated montmorillonitedensity. Because of this, no distinctionwasmade between ben-tonite andNa-montmorillonite density in this study. In order torelate dry density (g/cm3) to water content by weight, the ap-parent water density in the clay was assumed to be 1 g/cm3,which is well in line with gravimetric data in Van Loon et al.(2007), where compacted Wyoming Bentonite MX-80 wassaturated at dry density 1.3–1.9 g/cm3, corresponding towater contents of 0.17–0.41 gH2O/gclay assuming a benton-ite density of 2.80 g/cm3. These water contents correspondto approximately 2 W–4 W layers. However at lowerwater contents, equivalent to an overall hydration statecorresponding to 0 W–2 W layers, this assumption maynot be valid.

For a pure montmorillonite assuming a uniform sheet-likestructure and neglecting the layer edges, the theoretical

Fig. 1. Theoretical maximum basal spacing (dmax) in bentonite shown as afunction of montmorillonite fraction β, ranging from 0.5 to 1.0 (incrementsof 0.1) increasing in the direction of the arrows. The solid lines displaydmax versus clay dry density, g/cm3 (left axis) whereas the dashed lines dis-play dmax versus water content, mH2O/mclay (right axis).

Table 1Summary of the clay samples investigated.

Clay Subscript

Ca Sb Ads/Desc

Dry density, g/cm3 %RH

MX80x 0.5–1.8 0.5–1.0 0–100WyNax 0.5–1.8 – 0–100WyCax – – 0–100

a Saturated from aqueous phase with 1·10−3 M NaCl solution underconfined conditions.

b Saturated from aqueous phase under non-confined conditions.c Saturated from vapor phase under adsorption or desorption conditions.

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maximum basal spacing dmax and the corresponding inter-layer distance tmax can be approximated from the specificsurface area SA,faces and the respective dry density ρd, seeEq. 3.

tmax ¼ dmax−tMont ¼ 1= ρdrySA;f aces

2

� �−tMont ð3Þ

where the thickness of a single layer tMont is taken as 9.5 Å.For a bentonite containing accessory minerals and a lowersmectite content, as well as taking the montmorillonitelayer edge area into account, the total surface area of a ben-tonite, SA,Tot, can be expressed as:

SA;Tot ¼ 2AUCNA

MWβ

SA;f aces þ SA;edgesSA;f aces

!þ SA;acc 1−βð Þ ð4Þ

where β is the montmorillonite fraction in the sample. SA,edgeshas been estimated by AFM observations to be approximately1% of SA,faces (Cadene et al., 2005; Tournassat et al., 2003).In this study the specific surface area of the accessoryminerals SA,acc was assumed to be small, 10 m2/g. Thus,the last two terms have a minor effect on the total surfacearea of bentonite, SA,Tot.

From Eq. 3 and 4 and by taking the presence of the acces-sory minerals into account, the corresponding maximuminterlayer distance then becomes:

tmax ¼ 1−ρdryβρclay

−ρdry 1−βð Þ

ρacc

!= ρdry

SA;Tot2

� �: ð5Þ

From Eq. 5, it follows that the interlayer porosity, εIL, canbe defined as:

εil ¼ εTottavgtmax

: ð6Þ

Since the interparticle porosity εip can be defined as thedifference between the total porosity εTot and the interlayerporosity εil, it follows from Eq. 6 that the interparticle poros-ity can be described by:

εip ¼ εTot 1−tavgtmax

� �: ð7Þ

Fig. 1 shows the resulting maximum basal spacing forbentonites containing different montmorillonite contents asa function of water content.

2. Experimental

2.1. Materials and methods

In this study Wyoming Bentonite MX-80, characterizedin detail by Karnland et al. (2006) and hereafter denotedMX80, was investigated. The exchangeable counter-ionsin this bentonite by charge fraction was reported to be:75% Na+; 17% Ca2+; 7% Mg2+; 2% K+, and the montmo-rillonite content approximately 83%, by weight. The

representative structural formula of this montmorilloniteis:

Si7:92Al0:08ð ÞO20 OHð Þ4 Al3:11Fe0:37Ti0:01Mg0:48ð ÞNa0:65=Ca0:33:

Washed and dialyzed homo-ionic Na- and Ca-montmorillonite originating from MX80, denoted WyNa and WyCa,were supplied by Claytech AB, Sweden. For complete washingprocedure see Karnland et al. (2006). The CEC as measured bya trien-Cu(II) method (Karnland et al., 2006) for the MX80and the Na+ homo-ionic form were ~0.75 and ~0.85 mEq/g,respectively.

In order to compare saturation under different conditions(Table 1), the samples were saturated i) directly from theaqueous phase inside plastic cells or ii) under constant rela-tive humidity, see Table 2. In the former case, confinedplugs of compacted MX80 and WyNa with varying dry densi-ties were saturated with 1·10−3 M NaCl through metallicfilters in plastic PEEK cells with dimensions 10 mm diameterby 5 mm length. These samples were denoted MX80C andWyNaC. A similar set of MX80 samples was also saturated inplastic syringes through direct mixing with water in order toinvestigate differences in interlayer osmotic swelling at highwater contents in the absence of an induced swelling pressure.These samples were denoted MX80S (Table 1). All samples

Table 2Saturated salt solutions and the corresponding relative humidity (%RH) used in the adsorption and desorption experiments.

RH% ~0 11 23 33 43 54 67 75 85 94.5 97.6 ~100

Salt Drieda LiCl KAc MgCl2 K2CO3 Mg(NO3)2 NH4NO3 NaCl KCl KNO3 K2SO4 No salt

a Oven-dried at 393 K for minimum 24 h.

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saturated from the aqueous phase with 1·10−3 M NaCl weresaturated for ≥4 weeks prior to XRD and water contentmeasurements.

The samples saturated under relative humidity wereequilibrated for 8 weeks using the saturated salt solutionsdisplayed in Table 2. The dehydrated samples (~0 %RH)were prepared by drying at 393 K for minimum 24 h, whilethe fully saturated samples, i.e. ~100 %RH, were equilibratedusing Milli-Q water. For each type of clay (MX80, WyNa andWyCa), both water vapor adsorption and desorption experi-ments as a function of %RH were performed. For the samplesin the water vapor adsorption experiment, approximately0.3 g of the dried clay was placed in a closed vessel contain-ing a smaller open vessel with the relevant oversaturatedsalt solution. In the water vapor desorption experiments, anequal mass of clay was first soaked with a small aliquot ofwater before being placed in a separate closed vessel contain-ing the relevant oversaturated salt solution. These samplesare denoted MX80Ads or MX80Des etc. in the following text.

The XRD measurements were conducted in reflectionmode using a PANalytical X'Pert PRO instrument and Cu-Kα

radiation. The size of the two Soller slits was 2.3° and thescan speed 2°/min. Due to the small sample diameter, allsamples were measured with a programmable divergenceslit (PDS) and rotated at 16 rpm. Prior to the XRD experi-ments, the samples were quickly covered with a thin Kap-ton® film. This was in order to avoid any change in watercontent during XRD sample preparation and measurement,which was verified by performing repetitive XRD test scans,with and without this Kapton® film. Since the height of theXRD sample holder was smaller than the height of theMX80C and WyNaC samples, each plug was divided in twousing a sharp knife, enabling exposure of a fresh surfaceand elimination of filter effects. The water content of all sam-ples was determined gravimetrically directly after the mea-surements and after drying at 393 K for at least 24 h.

2.2. XRD profile fitting

In this study the software MODXRSD by Plançon (2002)was used to fit the XRD profiles of MX80 bentonite andWyNa/WyCa samples at low water contents, approximatelyb0.35–0.4 gH2O/gclay, i.e. crystalline swelling only. For practicalreasons a single layer type formalism described in Reynolds(1989) was used to model the XRD profiles at high water con-tents displaying well-defined 001 reflections due to osmoticinterlayer swelling. The underlying theories to these modelsare described in detail elsewhere (Drits and Tchoubar, 1990;Ferrage, 2005; Moore and Reynolds, 1989; Reynolds, 1989).In its general form, the diffracted X-ray intensity for a layeredclay mineral form can be expressed as:

I θð Þ ¼ LPG2Φ⋅EX ð8Þ

where LP is the combined Lorentz and Polarization factorand G the one-dimensional layer structure factor. Φ is the in-terference factor, which basically describes the Bragg reflec-tions of a periodic structure with unit integrated peakintensity, with the peak breadth of the reflections being in-versely proportional to the number of periods. The reflec-tions' peak shapes are dependent on the size distribution ofthe coherent scattering domain, CSD, i.e. the crystallite thick-ness observed with XRD, which for smectites is thought to besmaller than the physical size of the montmorillonite parti-cles (Plançon, 2002). In order to achieve satisfying peakshapes in this study, the concept of mean defect-free (MDF)domain size was used (Ergun, 1970). The EX term comprisesinstrumental and measurement-specific parameters. Some ofthese parameters depend on measurement geometry andothers are needed in order to scale the modeled XRD profilesto absolute intensities (Moore and Reynolds, 1989; Reynolds,1983). In order to deal with interstratification, every possiblesequence of the different scattering interlayers with differentd001 values and layer structure factors G(θ) must beaccounted for. For this purpose, the MODXRSD software byPlançon (2002) utilizing the Reichweite nomenclature to-gether with the matrix formalism described in Drits andTchoubar (1990) was used in this study.

In order to determine the average basal spacings for sam-ples subjected to crystalline swelling only, the experimentalXRD profiles were fitted manually with a linear combinationof MODXRSD pre-generated XRD profiles. This was accom-plished for the hydration states corresponding to 0 W–4 W,by i) varying the interstratification in each of the 0 W–4 Wstates and ii) varying and averaging the mean defect-free do-main size, MDF, and iii) the second type of size strain accord-ing to Guinier (see Drits and Tchoubar, 1990 for details) afterintensity normalization. Furthermore, in the fitting procedurethe modeled XRD profiles were further adjusted in order toaccount for iv)mean particle orientation,σ*, v) fixed footprintintensities (i.e. PDS mode) and vi) the ideal discrete basalspacings (independently). Since σ*=1° was used for thepre-generatedmodeled XRD profiles, themean particle orien-tation, i.e. rocking angle, was accounted for by multiplicationwith an angle-dependent ratio of ψ(θ)σ*= fitted/ψ(θ)σ*=1°,where ψ(θ) is the powder ring distribution factor. The resulting250 (25×5×2 for i, ii and iii above, respectively) modeled pro-files (and averages thereof) were then used to fit the experimen-tal XRD profiles. The overall fit between the normalizedexperimental and modeled XRD profile over all angular incre-ments between 3° and 10° 2θ was made by minimization ofthe unweighted RP parameter (Howard, 1989). Due to limita-tions of the MODXRSD software and since the occurrence andprobability of more than two interlayer types within the sameCSD was expected to be very low, only interstratified profiles ofneighboring hydration states were used, i.e. 0 W and 1W, 1Wand 2W and so on. In order to adequately fit the experimentalXRD profiles, it was found to be sufficient to use four different

24 M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

amounts of random interstratification, namely 1, 0.9, 0.75 and0.5. Table 3 summarizes the parameters and their respectivevalues used for the modeled MODXRSD profiles.

Because the experimental XRD profiles were measured inPDS mode and thus needed background subtraction, the com-bined modeled XRD profiles were also background subtractedin order to fit the experimental XRD profiles. Traditionally,modeled one-dimensional XRD profiles have frequently beenreported to overestimate the scattered intensity at angleslower than the 001 reflection (Ferrage et al., 2005b; Lanson,2011; Plançon, 2002; Wilson et al., 2004; Yuan and Bish,2010). This inconsistency may be explained by the fact thatthese models lack consideration of the interference betweenneighboring CSDs. In the MODXRSD code this inconsistency isaccounted for, however in a way that unfortunately leads tonon-negligible differences in 001 position and intensity, thusthis feature was not accounted for in the current study. Itshould be noted however that a more recent code of Sakharov(2005) has successfully been applied to smectites in both thelow and high angle regions (McCarty et al., 2009). Because ofthis inconsistency at low angles and the background subtrac-tion made, the obtained relative intensities of the different00l reflectionsmay be erroneous, leading to biased particle ori-entations and CSD estimates. For themontmorillonite layer, therecommended atomic positions from Moore and Reynolds(1989) were used after modification to a base-centered unitcell. As for the interlayer species, the cations were positionedin the center of the interlayer. For H2O Gaussian-like distribu-tions in the interlayers were used in order to successfully fit ex-perimental XRD profiles over a wide angular range (Ferrageet al., 2005a). This was accomplished for the 1 W–3W statesby fitting amodeled XRDprofile to an experimental XRDprofileof a montmorillonite sample displaying a nearly homogeneous1 W–3W state, by varying the Gaussian-like H2O distributionsusing a trial and error approach. However, this procedure wasnot possible for the 4 W state, which appears less frequently.Fig. 2 shows the XRD profiles demonstrating virtually homoge-neous 0 W–3W states in montmorillonite, while Fig. 3 showsthe corresponding fitted XRD profiles from MODXRSD andthe interlayer H2O distributions. It should be pointed out, how-ever, that the actual H2O distributions in the interlayers are nottruly Gaussian and much more realistic H2O distributions canbe found in the literature regarding molecular simulation ofclays (Chang et al., 1995; Chávez-Páez et al., 2001a; Chávez-

Table 3Parameters varied in the two layer type modeled XRD profiles.

nW:d001a/Å PAb Size strain MDF/layers σ*/deg°

0:9.5 1 0 0.9 11:12.4 0.9 20 1.5 22:15.6 0.75 3.0 33:18.9 0.5 4.5 44:21.8 0.25 7.0 6

0.1 80 10

122245

a Ideal basal spacings later adjusted independently ±0.50 Å.b Interstratification fraction of component A, where PA+PB=1.

Páez et al., 2001b; Ferrage et al., 2005a; 2011; Tambach et al.,2004; Tao et al., 2010).

3. Results and Discussion

3.1. XRD results

The fitting procedure using pre-generated XRD profiles wasgenerally quite satisfying for the samples with low water con-tents, approximately b0.35–0.4 gH2O/gclay, i.e. subjected onlyto crystalline swelling. Usually 3–5 pre-generated XRD profileswere required to achieve a good fit. Fig. 4 shows an example ofan XRD profile from aMX80C sample displaying significant hy-dration heterogeneity dominated by non-randomly interstrati-fied 2W and 3W states, and a possibly small amount of 4 W, atthe dry density planned for the bentonite barrier in the KBS-3concept, 1.58 g/cm3 (0.273±0.012 gH2O/gbentonite). Five pre-generated profiles of different interstratified states were re-quired to fit the experimental XRD profile, namely [2W;3W]:15% [0.9;0.1]; 20% [0.75;0.25]; 20% [0.25;0.75]; 35% [0.1;0.9]and [3W;4W]: 10% [0.9/0.1]. The corresponding optimalbasal spacings for the 2 W, 3 W and 4W states were 15.65,18:95 and 21.8 Å, resp. For comparison, Fig. 4 shows fittedXRD profiles with average basal spacings ranging from 17.6 to18.0 Å, produced by varying the relative fractions of the afore-mentioned pre-generated profiles. As can be seen in Fig. 4, adifference in average basal spacing of 0.1 Å gives a significantdeviation in the composite 001 reflection. For the higherorder reflections in the range of 10–20° 2θ, the overall fit wasgenerally not perfect using the pre-generated XRD profiles.However for the overlapping 003(0W), 004(1W), 005(2 W),006(3 W) and 007(4 W) reflections at approximately 28° 2θ,the overall fit was usually very good and was used to optimizethe specific d001 values for the different 0W–4W hydrationstates.

3.1.1. Saturation from the aqueous phaseFig. 5 shows a selection of experimental and fitted XRD pro-

files from the MX80C, MX80S and the WyNaC series as a func-tion of dry density. For these samples, quite broad and oftenasymmetric peaks were observed with no apparent sign of av-erage and homogeneous stepwise hydration with decreasingdry density, in contrast to results reported by Kozaki et al.(1998). Hence, the evolution of the crystalline swelling andthe overall microstructure seemed to havemore of a heteroge-neous character, in agreement with Ferrage et al. (2007). Forthe MX80C samples, the minimum FWHM values observedfor the interstratified 001 reflections displaying 2 W and 3Wstates were approximately 0.85° 2θ. At higher water contents(b1.3/cm3), where the introduction of osmotic interlayerswelling would be anticipated, significant differences werefound between theMX80C and theMX80S samples. For the for-mer set of samples, no clear transition to osmotic interlayerswelling could be observed, despite the apparent decrease inreflection intensity due to the crystalline swelling state. The ab-sence of reflections due to osmotic interlayer swelling at lowdry density values is also in line with the results by Kozakiet al. (1998) and Muurinen et al. (2004), who also saturatedtheir samples under confined conditions. For the MX80S sam-ples, however, relatively well-defined reflections could be ob-served at angles corresponding to both crystalline (3W and

Fig. 2. Background subtracted, normalized experimental (black +) and modeled (gray curves) XRD profiles of the hydration states corresponding to 0 W, 1 W,2 W and 3 W.

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4W) and osmotic interlayer swelling. Thus, although not al-ways observable with XRD, this shows that osmotic interlayerswelling forMX80 at thesewater contents is possible, as previ-ously also shown in small-angle X-ray scattering (SAXS) inves-tigations (Muurinen, 2009; Segad et al., 2010). Because of this,only considering the diffraction peakdue to crystalline swellingin a XRD profile of bentonite may be erroneous for sampleswith dry density b1.4 g/cm3 when calculating the averagebasal spacing.

For the WyNaC samples in Fig. 5, seemingly similar compos-ite 001 reflections compared with the MX80C samples at highdry density values (>1.3 g/cm3) were observed. As with theMX80C samples, the minimum FWHM value observed for the2W and 3W 001 reflections for the WyNaC samples was ap-proximately 0.85° 2θ. At higher water contents, however, verywell-defined 001 reflections due to osmotic interlayer swellingwere found except at very high water contents, i.e. very lowdry density (b0.6 g/cm3) and intermediate water contents,where both crystalline and osmotic interlayer swelling wouldbe anticipated (Norrish, 1954).

The 001 and 002 (and occasionally 003) reflections due toosmotic interlayer swelling were modeled with the singleinterlayer type formalism, using very small particle size andconsiderable size strain (α). It must be pointed out that precisebasal spacing determination at these low angles is problematic

Fig. 3. Gaussian-like distribution used to approximate the H2O distributionin the interlayers of the 0 W–4 W hydration states.

with the XRD setup used in this study. This ismainly because ofthe large dependence on accurate sample alignment, uncer-tainties in background intensity, surface roughness effects, aswell as the Lorentz–Polarization factor (LP) and layer structurefactor (G) used to fit the XRD profiles. Thus the reported basalspacings for the WyNaC samples resulting from osmotic inter-layer swelling in this study are only approximate.

With the objective of investigating the difference betweenthe MX80C and WyNaC samples at high water contents, theimpact of the accessory minerals and Ca2+ fraction in ben-tonite on the XRD profiles at high water contents was tested.This was done by preparing both a WyCaC sample and a syn-thetic MX-80 Bentonite sample (denoted MX80synt) consist-ing of 80% WyNa and 20% WyCa.

Fig. 6 shows representative XRD profiles for MX80Synt,MX80C and MX80S, as well as for WyNaC and WyCaC samplesat high water contents and low ionic strength. As can be seen,without the accessory minerals a diffraction peak at ~2.2° 2θ(~40 Å) was present in the MX80synt sample, similar to thatfound in theMX80S and theWyNaC samples, displaying explicitosmotic interlayer swelling. However, in contrast to theMX80Ssamples, the observed osmotic interlayer swelling for theMX80Synt samples was not found to be easily destroyed by in-appropriate sample handling, such as smearing of the samplesurface. In all, this indicates that the accessoryminerals in ben-tonite, especially when subjected to an elevated swelling pres-sure, hinder the ability to give rise to diffraction due to osmoticinterlayer swelling. From comparisons between the WyCaCsample, which displays a distinct 3 W state and no osmoticinterlayer swelling, and theMX80synt sample, the overall effectof the Ca2+ fraction in MX80 appears to be small.

3.1.2. Saturation at constant relative humidityThe XRD profiles of the MX80Ads/Des, WyNaAds/Des and

WyCaAds/Des samples, saturated under staticwater vapor adsorp-tion or desorption conditions at different relative humidityvalues, are shown in Fig. 7a and b, respectively. In the watervapor adsorption experiment, therewas a large difference in hy-dration behavior as a function of relative humidity between the

Fig. 4. Comparison between experimental (black +) and modeled XRD profiles (solid gray lines), using pre-generated XRD profiles from MODXRSD. Note thedivided x-axis and the magnification factor for angles >10° 2θ.

26 M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

WyCaAds and WyNaAds samples, which can be explained by thehigher ionic potential of Ca2+ compared with Na+ (Ferrage etal., 2005b). As expected, the hydration of the MX80Ads sampleswas seen to proceed in a very similar manner to that of theWyNaAds samples, which can be explained by its counter-ion in-ventory being dominated by Na+. Interestingly, for half the

Fig. 5. XRD profiles of a) MX80C (black +), fitted (solid line) and MX80S (gray +) bAverage basal spacings in Å obtained through XRD profile modeling (see later in th

relative humidity values investigated, the basal spacings of theMX80Ads samples were slightly larger than that of the corre-sponding WyNaAds samples, indicating that the small amountof divalent counter-ions influences crystalline swelling(Fig. 7a). However, it is striking that neither WyNaAds norMX80Ads proceeded to a 3W-dominated hydration state, even

) WyNaC (black +) and fitted (solid line), as a function of dry density, g/cm3

e text).

.

Fig. 6. Experimental XRD profiles at high water contents of MX80C (black),MX80S (gray), MX80synt (light gray). WyNaC (+) and WyCaC (circles) arealso shown for comparison.

27M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

after 2 months at ~100 %RH. As in the water vapor adsorptionexperiment, a large difference between the WyCaAds and theWyNaAds hydration behaviorwas observed in the desorption ex-periment (Fig. 7b). The MX80Ads samples generally followed thesame pattern as the WyNaAds samples. However, unlike in thewater vapor adsorption experiment, the hydration of the MX-80Ads samples was often seen to be slightly less than that of theWyNaAds samples, which the authors cannot presently explain.

3.2. XRD profile fitting results

Fig. 8a shows the relative abundance of the different inter-layer types (0W–4W) obtained from the MX80C samples. Thevertical error bars correspond to±0.1 Å. Starting at the highest

Fig. 7. Experimental and fitted XRD profiles of MX80Ads, WyNaAds andWyCaAds as a fb) equilibration through water vapor desorption.

dry density investigated, 1.8 g/cm3, the 2 W state is the domi-nant interlayer type, with only small amounts of 1 W and3W states. With decreasing dry density, a gradual increase inthe 3 W state proceeds to almost 100% at approximately1.4–1.5 g/cm3 at the expense of the 1 W and 2W states.Below 1.4 g/cm3 the amount of the 4 W state increases rapidly,but not to the same extent as the 2W and 3W states at higherdry density. This suggests that the 4 W state alone is not ener-getically stable but merely acts as a bridge between crystallineand osmotic interlayer swelling. Below 1.3 g/cm3 the fittingprocedure using pre-generated XRD profiles was not success-ful, indicating transition to osmotic interlayer swelling. Fig. 8bshows the relative interlayer type abundance for WyNaC to-gether with the corresponding data for MX80C, recalculatedto the equivalent montmorillonite dry density. Starting at thehighest dry density investigated for the WyNaC samples,1.8 g/cm3, the overall hydration state of the montmorilloniteparticles consisted of 67% of the 2W state and 33% of the 1 Wstate. With decreasing dry density the amount of the 2 Wstate was seen to increase in a seemingly gradual manner toover 90%, at the expense of the 1 W and 3W states. Comparedwith the MX80C samples, the WyNaC samples evidently dis-played a more homogeneous overall hydration state between1.5 and 1.8 g/cm3 compared with MX80C, although theFWHM values for both the MX80C and WyNaC samples weregenerally very similar. Between 1.3 and 1.5 g/cm3 in dry densi-ty, no significant difference in the relative interlayer type abun-dance was observed between the WyNaC and the MX80Csamples (Fig. 8). For instance, at the calculated dry density ofmontmorillonite 1.47 g/cm3 to be used in the KBS-3 concept

unction of relative humidity: a) equilibration through water vapor adsorption

Fig. 8. Relative abundance of the 0 W–4 W interlayer types for a) MX80C as afunction of bentonite dry density. b) WyNaC and MX80C as a function ofmontmorillonite dry density.

Fig. 9. The relative abundance of the 0 W–4 W interlayer types versus therelative humidity, %RH, for the tests: a) WyNaAds/Des, b) WyCaAds/Des and c)MX80Ads/Des.

28 M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

(assuming a bentonite with dry density of 1.58 g/cm3 and asimilar montmorillonite content as MX80), the overall hydra-tion state of WyNaC was estimated to be 60–65% 3W and35–40% 2W, i.e. very similar to the MX80C samples. This indi-cates that the presence of the accessory minerals does not af-fect crystalline swelling at these dry density values. Below1.3 g/cm3 the XRD profile fitting indicated an apparent 4 Wstate for WyNaC (at dry density 1.28 g/cm3). However, sinceto the best of our knowledge a 4 W state has never been provento exist for a homo-ionic Na-montmorillonite, this may be theresult of 3 W states interstratified with montmorillonite layerssubjected to osmotic interlayer swelling.

Fig. 9a–c shows the relative interlayer abundance of thesamples saturated at constant relative humidity under freeswelling conditions. For the WyNa samples significant differ-ences in the hydration states were found at most relative hu-midity values investigated, indicating possible swellinghysteresis effects. In general, a more homogeneous overall hy-dration state was found in the desorption experiment com-pared with the water vapor adsorption experiment. This wasalso observed for the WyCaAds/Des samples at low relative hu-midity, b50 %RH. However for higher relative humidity values,no significant differences were found between the water vaporadsorption and desorption experiments. Compared with the

WyNaAds/Des samples, the WyCaAds/Des samples generally dis-played much more distinct hydration steps and an overall ho-mogeneous hydration state. One noteworthy observationcharacteristic for the WyCaAds/Des samples was the dominance

Fig. 10. Increase in average basal spacings with water content, mH2O/mclay forthe a) WyNa samples b) WyCa samples c) MX80 samples. The dashed linesrepresent the maximum basal spacing possible assuming an apparentwater density of 1 g/cm3. The horizontal lines show the approximate basalspacings for the 1 W, 2 W and 3 W states.

29M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

of the 2 W state over a broad range of relative humidity. Also,theWyCaAds/Des samples saturated at 0 %RH, contained approx-imately 5% 1W, i.e. revealed insufficient dehydration upon dry-ing at 393 K for 24 h. Due to this thewater contents of allWyCasamples had to be corrected for this excess interlayer water,which was estimated to be approximately 0.006 gH2O/gclay. Ingeneral, the MX80Ads/Des samples displayed more resemblanceto theWyNaAds/Des than theWyCaAds/Des samples. However, forthe MX80Ads/Des samples less discrepancy between the watervapor adsorption and desorption experiments was generallyfound, except at the two highest relative humidity values in-vestigated (98 %RH and 100 %RH).

Instead of reporting the average basal spacings in thewater vapor adsorption and desorption experiments as afunction of %RH, it is useful to present them as a function ofwater content (mH2O/mclay) in order to compare them withthe samples saturated under confined conditions from theaqueous phase (see Fig. 10a–c). The dashed lines in the fig-ures represent the maximum basal spacing possible assum-ing an apparent water density of 1 g/cm3. For clarification,the horizontal lines show the approximate basal spacingsfor the 1 W, 2 W and 3 W states. For the WyNa samples, rel-atively large differences were found in average basal spacingsbetween the WyNaC, WyNaAds and WyNaDes samples, sug-gesting that the different sample preparation methods signif-icantly influenced the hydration behavior. For the WyNaAdssamples, pronounced stepwise hydration was actuallyfound. This behavior was quite contrary to that of the WyNa-Des samples, which also showed a much higher total wateruptake and yet a marked resistance to evolve from the 2 Wstate to the 3 W state, leaving a large fraction of the totalwater outside the interlayers, in interparticle voids. This lat-ter hydration behavior is very much similar to the hydrationversus %RH reported for synthetic smectites with differentlayer charge (Ferrage et al., 2010; Ferrage et al., 2011). Forthe WyNaC samples neither stepwise hydration nor a largedeviation from the theoretical line was found. Instead, the av-erage basal spacings of the WyNaC samples displayed a grad-ual increase with increasing water content. Compared withthe WyNaAds samples, the WyCaAds samples did not displayany noticeable stepwise hydration with increasing watercontent. However, similarly to the WyNaDes samples, theWyCaDes samples displayed a plateau at the 2 W state, mean-ing that a large fraction of the total water content was locatedin the interparticle voids. The MX80Ads and MX80Des samplesshowed similar hydration behavior, except at the highest rel-ative humidity values investigated. Except at water contentscorresponding to 0 W–1 W, the MX80Des samples concurredquite well with the theoretical line, as did the MX80C samplesat water contents corresponding to b3 W.

From Fig. 10 it is evident that samples saturated underfree swelling conditions at constant %RHmay not be as repre-sentative of the bentonite barrier as those saturated underconfined conditions. This is because the latter samples dis-played almost exclusively larger swelling compared withthe free swelling samples, supporting findings by Devineauet al. (2006) for high water contents. Furthermore, significanthysteresis was observed between the samples saturatedunder water vapor adsorption and desorption conditions, es-pecially at the water contents relevant for the bentonite bar-rier (>0.2 gH2O/gclay).

3.3. Interparticle porosity estimation

Fig. 11 compares the average basal spacings obtained fromtheXRDprofile fitting for the samples saturatedunder confinedconditions, i.e. MX80C andWyNaC, and basal spacings reportedin the literature for other Na-montmorillonites saturated undersimilar conditions. The theoretical maximumbasal spacings forMX80 (upper curve) and Na-montmorillonite (lower curve)are also shown for comparison. For the MX80C and theWyNaC samples, the basal spacings are close to the maximumspacing possible. For samples at dry density values below ap-proximately 1.3 g/cm3, the average basal spacings could notbe determined using the pre-generated XRD profiles corre-sponding to only crystalline swelling, 0 W–4W, indicating a

Fig. 11. Reported basal spacings for clay samples saturated from the aqueousphase. The theoretical maximum basal spacings for MX80 (upper curve) andWyNa (lower curve) calculated from Eq. 3 and Eq. 5 are also shown for com-parison. MX80C (white circles), WyNaC (gray circles), Na-montmorillonitefrom washed Kunipia-F (light gray triangles), obtained from Kozaki et al.(1998, 2001), Na-montmorillonite from washed MX-80 (black diamonds),obtained from Muurinen et al. (2004).

Fig. 12. Left axis: comparison of the basal spacings fromMX80C and MX80Desobtained from XRD profile fitting (white circles) and from Bragg's law (blackcircles). Right axis: difference between apparent basal spacings using Bragg'slaw and the fitted basal spacings. The horizontal lines show the approximatebasal spacings for the 1 W, 2 W and 3 W states.

Fig. 13. Interparticle porosity as a function of dry density calculated fromaverage interlayer distance and the corresponding theoretical maximuminterlayer distance for: MX80C (white circles); WyNaC/S (gray circles); Norrish(1954) Na-montmorillonite (white squares); Kozaki et al. (1998, 2001). Na-montmorillonite (light gray triangcles); and Muurinen et al. (2004) washedMX-80 bentonite (black diamonds). Comparison with theoretical estimatesfor the interparticle porosity of Na-montmorillonite by Bourg et al. (2003)(dashed line); Suzuki et al. (2004) (white triangles); and Van Loon et al.(2007) (black crosses).

30 M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

transition to osmotic interlayer swelling. Note that for benton-ite, the transition from crystalline swelling to osmotic inter-layer swelling is anticipated to occur at approximately thesame dry density as for Na-montmorillonite, approximately1.4 g/cm3, despite the lower smectite content. This is due to aweak fourth water layer at 21.8 Å.

Albeit linked to large uncertainties, it is interesting to seethat the average basal spacings from the WyNaS samples atvery high water contents obtained using the single interlayertype formalism, corresponded well with the theoretical line,see insert in Fig. 11. These spacings are well in line withthose due to osmotic interlayer swelling reported by Norrish(1954), at similar water contents.

The apparent discrepancy between the basal spacingsreported by Kozaki et al. (1998, 2001) using Kunipia-F washedNa-montmorillonite, and byMuurinen et al. (2004), using aNa-montmorillonite originating from Wyoming Bentonite MX-80,and the corresponding average basal spacings of the WyNaCsamples reported in this studymay partly be due to water con-tents and partly to the fact that only apparent d001 values usingBragg's law, without any profile fitting, were reported in theirstudies. Due to the orientation-dependent Lorentz–Polarizationfactor, LP, different layer structure factors, G0W–4W, and inter-layer hydration state heterogeneity as well as dependence ofthe peak intensity maxima on the magnitude of interstratifica-tion, an apparent basal spacing obtained from Bragg's lawmaydiffer significantly from the true average basal spacing. Fig. 12shows a comparison between the apparent d001 values usingBragg's law and the corresponding modeled average basalspacing of the MX80C and MX80Des samples as a function ofwater content. As can be seen, the apparent d001 values displaymuch more pronounced stepwise hydration behavior than themodeled average basal spacing. Thus the apparent d001 valuesmay both overestimate and underestimate the average basalspacing by as much as approximately 1 Å, depending on thewater content.

In addition, the pronounced stepwise and seemingly ho-mogeneous hydration observed by Kozaki and co-workerscould perhaps be explained by a particle size effect. The

FWHM for the measured 001 reflections in Kozaki et al.(1998) was significantly lower than the FWHM values fornatural smectites found in this study, approximately 0.45°2θ for both the 2 W and the 3 W states, respectively, whichare indicative of very large montmorillonite particles. Tamuraet al. (2000) compared the swelling of a natural montmoril-lonite and a synthetic high-quality montmorillonite with aparticle size (>10 μm) and found very small FWHM values,approximately 30% of the 001 reflection, for the syntheticcompared with the natural montmorillonite. Whereas thesynthetic montmorillonite showed a very pronounced step-wise hydration sequence with increasing %RH, while the nat-ural sample did not.

Fig. 13 shows the resulting interparticle porosities usingEq. 7 for the samples saturated under confined conditions inthis study, as well as interparticle porosities reported in the lit-erature, except in thework of Fernández and Rivas (2005) for aCa–Mg–Na bentonite. At dry density >1.4 g/cm3, the averageinterparticle porosity for the MX80C and the WyNaC samplesused in this study was found to be 1.5±1.5%, i.e. ≤3% and

31M. Holmboe et al. / Journal of Contaminant Hydrology 128 (2012) 19–32

significantly lower than previously reported in the literature.Due to the low interparticle porosity values and the experi-mental uncertainty, the expected decrease in the interparticleporosity with increasing dry density could not be verifiedstatistically.

At dry density ≤0.8 g/cm3, both Norrish (1954) samplesand the WyNaS samples demonstrated that the interparticleporosity at these low compactions would also constitutequite low volume fractions as at dry density >1.4 g/cm3.This indicates that the interparticle porosity may also besmall in the transition region between crystalline and osmot-ic interlayer swelling, meaning that the apparent increase ininterparticle porosity at dry density b1.4 g/cm3 may beexplained by the transition from crystalline to osmotic inter-layer swelling with decreasing dry density.

In all, the results from this study suggest that the interpar-ticle porosity in saturated compacted bentonite may be lowerthan frequently reported in the literature. Relating these re-sults to the microstructural models mentioned earlier, twohypothetical cases can be considered: i) the interparticle po-rosity is distributed approximately equally between the par-ticles, as in the models in Bourg et al. (2003); Bourg et al.(2006); Muurinen (2009); Muurinen et al. (2004); Suzukiet al. (2004); and ii) the interparticle porosity is more locallyconcentrated in between fewer particles, as in the micro-structural model in Pusch et al. (1990). Assuming an inter-particle porosity of ≤3%, with an average of 10–20montmorillonite layers/particle, in case i) the interparticlevoids would be of the same magnitude as the interlayer dis-tance itself for wedge-shaped voids, and hence the interpar-ticle porosity would offer similar transport pathways to theinterlayer porosity. Case ii) would give larger but fewer inter-particle voids, so they could expect to be isolated from eachother and consequently unable to affect transport processessignificantly in compacted saturated bentonite. Any interme-diate state between these two cases would not comprise asignificant transport pathway, since it would contain eithermany dead ends (especially in the region of crystalline swell-ing) or comprise a network of interparticle voids with similarconstraints as the interlayer voids (in the region of crystal-line/osmotic interlayer and osmotic interlayer swelling).Thus the dominant impact of the interparticle porosity overthe interlayer porosity on solute transport should perhapsbe questioned. Our interpretation of the interparticle porosityresults for the WyNaC and MX80C samples in this study is asfollows. Even for dry density b1.4 g/cm3, the interparticle po-rosity may be quite small. In fact, the main microstructuralvoids for dry density b1.4 g/cm3 seem to be the interlayervoids formed by osmotic interlayer swelling. With decreasingdry density, these voids will increase in number, but not insize, until the corresponding dry density becomes b~0.7 g/cm3 for bentonite and b~0.8 g/cm3 for Na-montmorillonite(see Fig. 11). For higher dry density values in the region ofonly crystalline swelling (>1.4 g/cm3), the interparticle po-rosity is below 3% and may decrease with increasing drydensity.

4. Conclusions

This study examined interlayer swelling of Wyoming MX-80 Bentonite and the corresponding homo-ionic Na- and Ca-

montmorillonites as a function of saturation method andwater content. The method of saturation was shown to sub-stantially influence the interlayer swelling. Saturation underfree swelling conditions as a function of relative humidityresulted in noticeable interlayer swelling hysteresis betweenthe water vapor adsorption and desorption samples, espe-cially at high relative humidity (>80 %RH), which corre-sponds to the water content range relevant for thecompacted bentonite barrier, 0.2–0.3 gH2O/gclay (approxi-mately 1.4–1.8 g/cm3). Furthermore, saturation under freeswelling conditions as a function of relative humidity gener-ally resulted in lesser interlayer swelling compared with sat-uration from the aqueous phase under confined conditions.Thus, when studying the microstructure of bentonite in thecontext of the bentonite barrier, saturation under free swell-ing conditions as a function of relative humidity is not recom-mended. The interparticle porosities obtained for compactedand saturated Wyoming Bentonite MX-80 (MX80C) and thecorresponding homo-ionic Na-montmorillonite (WyNaC)were shown to be similar, ≤3% in the region of only crystal-line swelling (dry density 1.4–1.8 g/cm3) and thus signifi-cantly lower than frequently reported in the literature.Because of the small interparticle porosity found in thisstudy, it is possible that the interparticle voids may not com-prise the only significant pathway for solute transport in sat-urated compacted bentonite. In order to confirm these resultsin future work, high quality in situ diffraction data from ben-tonite samples saturated from the aqueous phase under con-fined conditions would be needed.

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