Available online at www.sciencedirect.com

www.elsevier.com/locate/gca

Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

Kinetics of Cd sorption, desorption and fixation by calcite:A long-term radiotracer study

Imad A.M. Ahmed *, Neil M.J. Crout, Scott D. Young

School of Biosciences, Division of Agriculture & Environmental Sciences, University of Nottingham, Nottingham NG7 2RD, UK

Received 14 September 2007; accepted in revised form 9 January 2008; available online 31 January 2008

Abstract

Time-dependent sorption and desorption of Cd on calcite was studied over 210 days utilizing 109Cd as a tracer to distin-guish between ‘labile’ and ‘non-labile’ forms of sorbed Cd. Stabilizing the calcite suspensions for 12 months under atmo-spheric PCO2 and controlled temperature was necessary to reliably follow Cd dynamics following initial sorption. Resultsrevealed time-dependant Cd sorption and marked desorption hysteresis by calcite under environmentally relevant conditions.Data obtained were fitted to a first-order kinetic model and a concentric shell diffusion model. Both models described the pro-gressive transfer of Cd2+ to a less reactive form within calcite and subsequent desorption of Cd subject to different initial con-tact times. The kinetic model provided a better fit to the combined sorption and desorption data (R2 = 0.992). It differentiatesbetween two ‘pools’ of sorbed Cd2+ on calcite, ‘labile’ and ‘non-labile’, in which labile sorbed Cd is in immediate equilibriumwith the free Cd2+ ion activity in solution whereas non-labile Cd is kinetically restricted. For the diffusion model (R2 = 0.959),the rate constants describing Cd dynamics in calcite produced a half-life for Cd desorption of �175 d, for release to a ‘zero-sink’ solution. Results from this study allow comment on the likely mechanisms occurring at the calcite surface followinglong-term Cd sorption.� 2008 Published by Elsevier Ltd.

1. INTRODUCTION

Trace element incorporation into calcareous minerals ispotentially important for management of contaminatedsoils. Thus, environmental scientists and engineers haveshown interest in calcite as an important sorbent of tracemetals in soil remediation and groundwater protectiontechnologies. For example, Wang and Reardon (2001)showed the possibility of using a mixture of siderite andlimestone to remove Cd and As from wastewaters. In addi-tion, calcite can be deployed, as a component of PermeableReactive Barriers (PRBs) (Striegel et al., 2001). However,this application of calcite has been limited so far, and isuntenable where pH can drop to <7 because of excessive

0016-7037/$ - see front matter � 2008 Published by Elsevier Ltd.

doi:10.1016/j.gca.2008.01.014

* Corresponding author. Present address: School of Earth &Environment, University of Leeds, Leeds LS2 9JT, UK. Fax: +44 0113 34 36716.

E-mail address: I.Ahmed@See.Leeds.ac.uk (I.A.M. Ahmed).

dissolution. More commonly, calcite is applied to soils asa cheap remediation option with the dual role of sorbingmetals directly and increasing the sorption strength of exist-ing soil minerals and humus by increasing soil pH. Factorscontrolling sorption of trace metals by CaCO3 have beenstudied extensively (Lorens, 1981; Dromgoole and Walter,1990; Mucci and Morse, 1990; Gerth et al., 1993; Nakhoneand Young, 1993; Paquette and Reeder, 1993, 1995; Teso-riero and Pankow, 1996; Rimstidt et al., 1998).

There have also been many studies which have examinedthe time-dependent nature of trace element sorption by soilsand soil minerals (Tiller et al., 1984; Nakhone, 1989, 1997;Amacher et al., 1990; Hogg et al., 1993; Gray et al., 1998;Hamon et al., 1998; Coppin et al., 2003; Lock and Janssen,2003; Ma et al., 2006a). For example, utilizing radioactiveisotopes, the slow transfer of added Cd2+ or Zn2+ to ‘fixed’sites in soil particles with increasing contact times (of up to1 year) was reported by a number of workers (Ainsworthet al., 1994; Backes et al., 1995; McLaren et al., 1998; Eicket al., 1999). More recent investigations have employed

Kinetics of Cd sorption, desorption & fixation by calcite 1499

isotopic dilution to differentiate between ‘isotopicallyexchangeable’ (labile) and ‘fixed’ (non-labile) forms ofsorbed trace elements (e.g., Cd, Cu and P) on soil and soilminerals (Hamon and McLaughlin, 2002; Lombi et al.,2003; Ahmed et al., 2006; Ma et al., 2006b).

Some attempt has been made to explain sorption kinet-ics in mechanistic terms. For calcite, Davis et al. (1987) pro-posed rapid exchange of Cd2+ for Ca2+ on surface sites withslow diffusion of the metal ions into the hydrated CaCO3

layer over 24 h, followed by superficial (Cd, Ca)CO3 copre-cipitation over 8 days. It was reported that only 12% of thesorbed Cd was isotopically exchangeable after 24 h, sug-gesting that the majority of the Cd had diffused into the cal-cite lattice. Other short-term studies on Cd sorption bycalcite, extending from minutes to hours, exist in the litera-ture (McBride, 1979; McBride, 1980; Lorens, 1981; Frank-lin and Morse, 1982; Pingitore, 1986; Fuller and Davis,1987). These investigations typically suggest that sorptionof metal ions on calcite occurs as two discrete reactionsteps: generally designated ‘rapid’ and ‘slow’. However,the time periods used are often not appropriate to charac-terize prolonged metal sorption by calcite in environmentalsystems where longer reaction times (weeks to months)should be considered. In the current study, contact timesof up to 210 days for Cd sorption and fixation were exam-ined, in calcite suspensions, using isotopic dilution with109Cd under conditions of ambient temperature, atmo-spheric PCO2 and pH � 7.45. The concentrations of ‘labile’and ‘non-labile’ Cd were quantified over time and the pro-cess of extended Cd2+ sorption was modeled using both ‘ki-netic’ and ‘diffusion’ models. Labile (sorbed) Cd canrespond rapidly to any change in Cd2+ activity in the solu-tion phase whereas non-labile Cd is unresponsive, possiblydue to occlusion within solid matrices or perhaps due to theformation of kinetically restricted surface complexes. Themain focus of this work was to examine the dynamics ofCd sorption, desorption and fixation on calcite rather thandetermine the underlying mechanisms.

2. MATERIALS AND METHODS

2.1. Materials

Cadmium stock solutions were prepared fromCd(NO3)2�4H2O (99.99%, Sigma–Aldrich) in 0.01 M CaCl2using ‘Milli-Q’ water (18.2 MX cm). Carrier-free 109Cd (c-emitter; Ec = 0.088 MeV; t1/2 = 464 d) was obtained fromPerkin-Elmer Life Sciences, USA. Synthetic powdered cal-cite (Baker Analyzed Reagent, J.T. Baker Inc., Phillips-burg, NJ, USA) with high phase purity (>99%) was used.The surface area of the as-received material (N2-BET)was 0.40 m2 g�1 and the mean particle diameter was givenas 20.5 lm.

2.2. Methods

2.2.1. Pre-equilibration of calcite suspensions

Calcite suspensions in 0.01 M CaCl2 were maintained at22 �C (±2 �C), in the dark, with air bubbled through at�10 mL min�1 to maintain atmospheric PCO2. The air

stream was passed through <0.2 lm cellulose nitrate mem-brane filters (Sartorius�, Germany) then 0.2 M HCl solu-tion, to remove atmospheric NH3, and finally Milli-Qwater to ensure vapour saturation. The concentration ofCO2 was monitored and recorded using an IR gas analyzer(Analytical Development Company Ltd., UK) connected toa data-logger (21X Micrologger�, Campbell Scientific) pro-grammed to record PCO2 every 3 min. For initial sorptionand desorption experiments, calcite stock suspensions werepre-equilibrated in this manner for 5 weeks. Following fur-ther trials, for all other sorption and desorption experi-ments calcite stock suspensions were pre-equilibrated for12 months prior to addition of Cd.

2.2.2. Measurement of pH

The pH of equilibrated suspensions were measured witha combined electrode (Radiometer pHC2701, Ag/AgCl ref)calibrated at pH 4.01 and 7.00. Prior to calibration, theglass electrode was alternately soaked in 0.1 M HCl and0.1 M NaOH. Suspensions were centrifuged at 2200g for10 min and the pH electrode was placed in the clear super-natant solution above the solid layer in order to avoid ‘sus-pension effects’ (Coleman et al., 1950).

2.2.3. Morphological analysis of calcite particles

The morphology of calcite particles were examined usingboth ‘Conventional’ and ‘Environmental’ Scanning Elec-tron Microscopy (SEM and ESEM, respectively). ForSEM, a small amount of oven dry (�80 �C) calcite was dis-persed in acetone, deposited on a Cu-holder and the samplesurface coated with a thin (<100 A) gold film using an Au–Pd sputter coater. An alternative technique was also ap-plied, using a conductive double-sided adhesive carbon discon a Cu-holder with a small sample of acetone-suspendedcalcite deposited on top. Samples were examined using aPhilips XL30 SEM, with an EDX facility, set at 20 kVand using an Si(Li) detector. The EDX facility was cali-brated with well-known phosphate standards. For ESEM-EDX analysis, a Philips XL30 Field-Emission Gun (FEG-ESEM) with a Peltier cooling stage was used.

The particle size distribution (PSD) of calcite was deter-mined by laser diffraction using a wet module on a Beck-man Coulter LS230 laser particle analyzer which uses thePolarization Intensity Differential Scattering (PIDS) meth-od and has a dynamic range between 0.04 and 2000 lm.Calcite samples were prepared by dispersing �1.0 g of solidin �200 mL deionised water, with a few drops of the surfac-tant Triton� X-100 (purity 99.5%, Merck, Germany) to re-duce particle agglomeration.

2.2.4. Batch experiments

2.2.4.1. The effect of Cd speciation on Cd sorption by calcite.

Prior to use, a calcite stock suspension was pre-equilibratedwith air for 12 months. Cd sorption on calcite suspensions(0.0167 kg L�1 in 40 mL polycarbonate centrifuge tubes)was measured, in triplicate, for three background electro-lytes (CaCl2, Ca(NO3)2 and a 1:1 mixture of CaCl2 andCa(NO3)2) at an ionic strength of 0.03 M (0.01 M Ca),and temperature of 22 ± 2 �C. Minor adjustments of pHwere carried out to maintain pH 7.4 using 0.01 M HCl or

1500 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

0.01 M NaOH. Cadmium was added to calcite suspensionsin centrifuge tubes as a 109Cd-spiked solution(�6.5 kBq lmol�1 in 0.01 M CaCl2) to give Cd loadingsof 0.38 to �2.5 mmol Cd kg�1. Initially samples were gentlymixed on a vertical rotary shaker (�10 rpm) and left toequilibrate for 50 days in a dark room at constant temper-ature (22 ± 2 �C). To measure the concentration of totaldissolved Cd (CdSoln), supernatant solutions were first sep-arated by centrifugation at 2200g for 30 min and then fil-tered (<0.2 lm polyethersulfone (PES) membrane filter,Minisart�, Sartorius) and weighed in a counting vial priorto radio-assay for 109Cd using a gamma-spectrometer with3 � 3 inch. NaI detector system (Packard, COBRA-II). Aradiochemical test showed that retention of 109Cd by thePES filters and syringes used was negligible in the presenceof the background electrolyte and at typical Cd concentra-tions used. Blanks and standards were counted togetherwith samples; all samples were of equal volume (4.0 mL)to ensure constant sample geometry.

2.2.4.2. Effect of contact time on the concentration of Cd

‘fixed’ by calcite. The determination of total sorbed Cd(CdTS), labile sorbed Cd (CdLS) and fixed Cd (CdNL) hasbeen described in detail in our previous paper (Ahmedet al., 2006), a brief review of the used technique is providedhereafter. Sorption and desorption of Cd in calcite suspen-sions in 0.01 M CaCl2 was undertaken, as described in theprevious section, at Cd loadings of 0.38 to�2.72 mmol Cd kg�1. Initially, samples were gently shakenby rotary action for contact times of 5–210 days prior to as-say of dissolved Cd (CdSoln; lmol Cd L�1) in supernatantsolutions. Concentrations of CdSoln and CdTS were calcu-lated according to Eqs. (1) and (2), respectively.

CdSoln ¼ASolnð1Þ

A�ð1Þ

CdTS ¼CdTot �

ASolnð1Þ�V Soln

A�

� �W

ð2Þ

where CdTot is the total amount of Cd added to the system(lmol), ASoln(1) is the radioactivity measured in the sepa-rated supernatant (Bq L�1; the subscript ‘Soln(1)’ indicatesthe addition of a single spike of 109Cd), VSoln is the volumeof solution (L), A* is the specific activity of the Cd stocksolution (Bq lmol�1 Cd), and W is the mass of calcite(kg) in the suspension.

Where there is no pre-existing Cd it is possible to employa single isotope spike, added with Cd, to follow progressivesorption. It is also then possible to use second spikes, addedfollowing selected equilibration times, to determine howmuch of the sorbed Cd is still isotopically exchangeable.The advantage of this ‘double-labeling’ approach is thatsystematic errors arising from any mismatch between chem-ical and radio-chemical assay are eliminated. This approachwas applied and described in detailed previously (Ahmedet al., 2006). Thus, to determine the concentration of isoto-pically exchangeable Cd, a second spike (0.2 mL) of carrier-free 109Cd (�14 kBq mL�1 in 0.01 M CaCl2) to equilibratedsuspensions was introduced directly after the determinationof CdSoln by radio-assay of the first spike, Eq. (1). Follow-

ing a further isotope-equilibration time of 48 h (Younget al., 2000; Degryse et al., 2004; Ahmed et al., 2006), thesolution phase was separated for a second radio-assay.

The concentration of Cd in solution following the addi-tional equilibration period of the second spike (48 h) wasestimated from a polynomial fit to the trend in CdSoln withtime. In practice this gave values (CdSoln(2)) which were al-most identical to those measured after the first period ofequilibration. Consequently, the concentration of labilesorbed Cd (CdLS; lmol Cd kg�1) can be determined as inEq. (3):

CdLS ¼ASolidð2Þ � CdSolnð2Þ

ASolnð2Þð3Þ

where ASoln(2) (Bq kg�1) is the amount of radioactivity fromthe second spike of 109Cd transferred to the solid phase, andnon-labile Cd(CdNL; lmol Cd kg�1) can be determined bydifference from Eq. (2).

Values of CdSoln, CdTS, CdLS and CdNL were deter-mined in calcite samples following contact times of 5, 10,20, 30, 40, 60, 80, 105, 130 and 210 days. As a countercheck,CdSoln was determined in separate samples using GraphiteFurnace-AAS (GF-AAS). Concentration of total dissolvedCa was measured by flame emission spectroscopy. The pHof the solution was measured routinely at the beginning andat the end of each contact time. Cadmium in solution wasspeciated using the PHREEQC speciation model (Parkhustand Appelo, 1999; Toran and Grandstaff, 2002) with WA-TEQ4F thermodynamic database to determine the freeCd2+ ion activity. Moreover, all analysis was undertakenin three replicates, except for pH measurements were under-taken in duplicates, and experimental error was calculatedand described in terms of coefficient of variation (desig-nated e).

2.2.4.3. Desorption experiments. Following Cd adsorptionfor a prescribed time, desorption was initiated by replacing50% of the supernatant solution with a Cd-free desorbingsolution. The desorbing solution used was a filtered(<0.2 lm) aerated suspension of calcite in 0.01 M CaCl2to ensure that the only change in composition was Cd con-centration. Samples were allowed to re-equilibrate (withgentle shaking) over a period of 48 h in order to attain anew equilibrium. Supernatant samples were then separatedfor radio-assay as described earlier. This desorption proce-dure was repeated 5–15 times for each sample and CdSoln

was determined both chemically (i.e., using GF-AAS) andradiochemically. The adsorption and desorption protocolsadopted were developed in response to several pilot studiesin which, for example, sorption experiments were under-taken for contact times of 10, 20 and 40 d using suspensionspre-equilibrated in air for just 5 weeks and employing0.01 M CaCl2 as the desorbing solution. These are brieflydiscussed in Section 3.

2.2.5. Model development and implementation

The time-dependence of Cd sorption by calcite may beascribed to either reaction kinetics or a diffusion-basedmechanism. The former implies a single sorption reactionstep (e.g., labile to non-labile) occurring at a rate

Kinetics of Cd sorption, desorption & fixation by calcite 1501

determined by an energy barrier. The reaction might in-volve, for example, formation of inner-sphere complexesin which part of an ion’s hydration shell is removed beforesorption to the solid surface. For reacted metal ions, theremay be an even greater energy barrier in the opposite direc-tion (non-labile to labile) and so reversibility is not evident.A ‘diffusion controlled’ sorption process suggests that thesorption mechanism may not be kinetically restricted, andall sorbed ions are ‘locally labile’, but access to sorptionsites within the mineral matrix may produce a time-depen-dent sorption pattern and apparent sorption hysteresis. Ofcourse, both mechanisms may operate.

2.2.5.1. Formulation of the KM model. The mathematicalformulation and assumptions of the kinetic (KM) and theintracrystalline diffusion (DM) models, applied previouslyto sorption on zeolite, have been described in detail byAhmed et al. (2006) and Ahmed (2006). In this study, theKM model describes the sorption and subsequent immobi-lization of Cd2+ within calcite. Sorbed Cd is assumed to ex-ist in two states: labile and non-labile. Labile sorbed Cd(CdLS) is in instantaneous equilibrium with the free ionactivity of Cd2+ in solution, {Cd2+}, whereas non-labileCd (CdNL) is assumed to be connected by a kinetically con-trolled process. A schematic representation of this model isshown in Fig. 1.

Instantaneous partitioning between CdLS and Cd2+ isassumed to be governed by a single Langmuir–Freundlich(LF) relationship, Eq. (4),

CdLS ¼kLF � QLF � fCd2þgm

1þ ðkLF � fCd2þgmÞð4Þ

where kLF is the Langmuir–Freundlich constant, QLF is themaximum sorption density and the exponent term m is adimensionless constant where 0 6 m 6 1. The LF relation-ship reduces to a Freundlich model at low Cd concentra-tions and to a Langmuir model at higher Cdconcentrations. With the relatively wide range of Cd con-centrations used in this study, the LF model was used be-cause it allows for a progressive weakening of sorptionaffinity but with an ultimate sorption maximum.

From the speciation model used, the ratio of CdSoln to{Cd2+}, (h), can be obtained. Hence, {Cd2+}, lmol L�1,

CdCl+, CdCl20, etc.

Cd2+

CdLS

Aqueous

k1

k2

Fig. 1. Compartmental representation of the kinetic model of Cd sorptiocomponents in the system whereas the arrows � denote kinetically contransfer between labile and non-labile states.

can be calculated from the mass balance of the total labileCd (CdTL, lmol Cd kg�1) and combined with Eq. (4) togive the following implicit function:

fCd2þg ¼ CdTL �kLF � QLF � fCd2þgm

1þ ðkLF � fCd2þgmÞ

!" #

� WV Soln � h

� �: ð5Þ

Transfer between CdLS and CdNL is assumed to followfirst-order kinetics, thus:

dðCdTLÞdt

¼ � dðCdNLÞdt

¼ �k1CdLS þ k2CdNL ð6Þ

The solution of Eq. (6) requires the following initialconditions:

½CdTL�t¼0 ¼Cdi � V Soln

Wand ½CdNL�t¼0 ¼ 0 ð7Þ

where the rate coefficients, k1 and k2(d�1), are estimatedfrom experimental data and Cdi is the concentration ofadded Cd (lmol L�1).

2.2.5.2. Formulation of the DM model. Diffusion of Cd incalcite particles was modeled following the procedure de-scribed previously for zeolites (Ahmed, 2006; Ahmedet al., 2006). This involves a transient diffusion equation(Eq. (8)) solved numerically by assuming transfer between‘concentric shells’ within a hypothetical spherical calciteparticle. Initially all labile Cd2+ ions are present withinthe outer-most shell. The non-labile Cd lies within the par-ticle and is thus distributed within all ‘internal’ shells. Theconcentration of non-labile Cd is the summation of Cd inall the internal shells. The apparent diffusion coefficient(Dapp; cm2 s�1) of Cd in calcite was determined by fittingthe DM model to CdNL data over the contact time of theexperiment.

dCdNL

dt¼ Dapp

o2CdNL

ox2ð8Þ

2.2.5.3. Model implementation, parameter estimation and

model comparison. For both models (KM and DM), differen-tial equations were solved by a fourth-order Runge–

CdNL

phase

Calcite solid phase

Ca2+, H+, CO2

n on calcite. The arrows represent dynamic equilibrium betweentrolled mass transfer; k1 and k2 are the rate coefficients describing

Fig. 2. The morphology of calcite particles shown by ESEM in thewet mode.

1502 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

Kutta procedure; the bisection method was used to find theroot of the implicit function in Eq. (5). Estimation of theadjustable parameters (kLF, QLF, m, k1, k2, Dapp) was carriedout using a Levenberg–Marquardt procedure, which mini-mizes the residual standard deviation (RSD):

RSD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi¼ji¼1ðOi � P iÞ2

df

sð9Þ

where Oi and Pi are the log-transformed observed and pre-dicted data, respectively, and df is the degrees of freedom.All these methods are described in detail by Press et al.(2002).

To compare the KM and DM models, the MinimumDescription Length (MDL) method was used (Eq. (10)).MDL is a measure of ‘generalizability’ that takes accountof the possibility of over-fitting (Pitt and Myung, 2002;Myung and Pitt, 2004); it is sensitive to the functional formof the model as well as to the number of parameters. Thus,the model with the lowest MDL value is regarded as mostsuitable for purposes of prediction. In Eq. (10), the firstterm provides a measure for lack of fit whereas the secondand third terms together provide a measure of the model’scomplexity (Grunwald, 2000; Pitt and Myung, 2002;Myung and Pitt, 2004; de Brauwere et al., 2005; Myunget al., 2006),

MDL ¼ � lnðLðx�Þ þ n2

lnn

2p

� �þ ln

Z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidetðIðxÞÞ

pdx

ð10Þ

where L(x*) is the model’s maximized likelihood, n is thenumber of parameters in the model, n is the sample size,R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

detðIðxÞÞp

dx denotes the Fisher information integralterm, and I(x) is the Fisher information matrix.

3. RESULTS AND DISCUSSION

3.1. Morphological and PSD analysis

Several methods (see Section 2.2.3) were used to charac-terize the geometry and dimensions of calcite particles, butparticle aggregation could not be prevented and so imageanalysis was not possible. Generally, ESEM providedclearer micrographs than conventional SEM. Calcite parti-cles exhibited well developed rhombohedral or cubic crys-tals with sharp straight edges although some crystals wereimperfect possibly because crystal growth processes wereincomplete during synthesis (Fig. 2). None of the micro-graphs obtained contained needle-like (i.e., aragonite) orspherulitic (i.e., amorphous calcium carbonate, ACC)CaCO3 particles. This is important because amorphousCaCO3 (i.e., ACC) has a higher solubility than the crystal-line phase (Brecevic and Nielsen, 1989). Phase purity of thecalcite was confirmed by X-ray powder Diffraction (XRD)analysis. The mean spherical particle diameter was 27 lm,determined by laser diffraction, which is in reasonableagreement with the particle size determined by the manu-facturer (i.e., 20.5 lm). GF-AAS analysis for Cd on severalsamples of starting calcite material dissolved in HCl showed

no detectable concentration of Cd, which indicates that Cd-content is less than 0.445 nmol kg�1.

Calcite suspensions were continuously mixed to avoiddepletion of Cd close to the mineral surface. Mixing wascarried out at a low speed (10 rpm) to minimize attritionof calcite particles. However, any movement of the mineralsuspension raises the possibility of attrition and therefore achange in surface area. To examine this possibility, fewchecks were undertaken throughout the experiment bySEM. Only minor changes in the particle size distributionwere observed.

3.2. Pilot sorption and desorption experiments

Pilot experiments examining Cd sorption on calcite, pre-equilibrated for 5 weeks in aerated 0.01 M CaCl2, wereundertaken with contact times of 10, 20 and 40 d. Results(Fig. 3) showed continuing Cd sorption with contact time.However, desorption into added 0.01 M CaCl2 (freshly pre-pared and equilibrated with air) following sorption for 10 d,demonstrated an unexpected desorption trend in whichCd2+ activity increased before decreasing with furtherdesorption cycles (Fig. 3). This trend was observed consis-tently but its cause was not pursued. In all further desorp-tion experiments we used filtered 0.01 M CaCl2 solutionwhich had been pre-equilibrated with calcite at atmosphericPCO2 (see Section 2.2.4.3) rather than freshly prepared0.01 M CaCl2.

A further problem revealed by the pilot studies was thelarge experimental error associated with the determinationof CdSoln (e = 6–15%). These experiments were repeatedseveral times at various Cd loadings and by using more rig-orous methods for solid separation including centrifugationat 40,000g at �4 �C followed by filtration using <0.2 lm or<0.1 lm PES membrane filters; losses of 109Cd activity tothe filter or centrifuge tubes were negligible. In repeatedsorption experiments, CdSoln was determined both chemi-cally (GF-AAS) and radiochemically; results showed goodagreement but with experimental error in the chemical anal-ysis slightly greater than that of the radio-assay. Unfortu-nately, more rigorous solid separation methods onlyproduced a small reduction in variability between replicate

Desorption inthis direction

Freundlich Isotherm n = 0.728 kF (10d) = 4052 kF (20d) = 4381 kF (30d) = 4795

{Cd2+} mol Cd L-1

Sorb

ed C

d (

mol

Cd

kg-1

)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500

250

500

750

1000

1250

1500

1750

2000

2250

2500

CdTS: 10 dCdTS: 20 dCdTS: 40 dCdTD: 10 d

Fig. 3. Pilot study of Cd sorption/desorption on calcite previously equilibrated in aerated suspensions of 0.01 M CaCl2 for 5 weeks. Closedsymbols represent Cd sorption at 10, 20 and 40 d whereas open symbols represent 15 successive desorption cycles. Solid lines represent aFreundlich isotherm fit to experimental data. The solid arrows represent the direction of desorption cycles following Cd sorption for 10 d.Error bars are standard errors.

Kinetics of Cd sorption, desorption & fixation by calcite 1503

suspensions. Similar problems were reported by Parkmanet al. (1998) who undertook a batch study of Sr (85Sr) sorp-tion by powdered calcite but without any pre-equilibrationof calcite suspensions in air. They reported relatively largeexperimental errors with poor reproducibility of SrSoln. Inthe current study, when sorption experiments were repeatedusing calcite suspensions equilibrated in air for 8–10 weeks,a small improvement in the reproducibility in CdSoln wasfound which suggested that air-equilibration of calcite sus-pensions for a longer time may be necessary. Thus, in all la-ter experiments aerated calcite suspensions wereequilibrated for 12 months at constant temperature(22 ± 2 �C) before the addition of Cd.

3.3. pH of calcite suspension and effect of calcite pre-

equilibration

It has been suggested by many authors (e.g., Elzinga andReeder, 2002; Elzinga et al., 2006) that calcite must be agedfor several weeks or months prior to sorption studies,otherwise dissolution–precipitation reactions may result inco-precipitation of added metal ions. Furthermore, the sur-faces of solid particles contain imperfections, such as cleav-age steps, dislocations and point defects. The surface energyof such features differs from that of the flat plane and theiraffinity for adsorbing ions may be very high. Details of the‘terrace-step-kink’ model which describes the morphologyof mineral surfaces are given elsewhere (Luth, 1993; Jeongand Williams, 1999). A pre-equilibration step allows localdissolution–precipitation reactions to ‘heal’ surface defectsand thereby minimize surface free energy; ‘Ostwald ripen-ing’ (Marqusee and Ross, 1983) may be one of the processes

involved. These processes may be accompanied with smallchanges in the pH of calcite suspensions. As shown inFig. 4, the pH of the calcite suspension fell frompH � 7.80 to pH 7.45 after two weeks. This is consistentwith a gradual reduction in solid phase activity of CaCO3

(towards 1.0) if the solubility product (KSP) of calcite iswritten as:

KSP ¼fCa2þgPCO2

fCaCO3gðSÞfHþg2

ð11Þ

The concentration of CO2 in the controlled temperatureroom (22 �C) was reasonably consistent at 334 ± 35 ppm(PCO2 = 3.38 � 10�4 bar) and the Ca2+ ion activity,{Ca2+} can also be regarded as constant in the 0.01 M elec-trolyte. Fig. 4 also shows a temporary drop in pH followingthe addition of Cd-solution, possibly due to an initial reac-tion with bicarbonate ions in solution.

Aging calcite suspensions for 12 months may thereforeensure the stability of the calcite surface and the solutionpH. The pH within Cd-spiked suspensions remained rela-tively constant throughout sorption experiments, with fluc-tuation 60.1 pH units.

3.4. Effect of supporting electrolyte on Cd sorption

The hypothesis that Cd2+ alone rather than its com-plexes (e.g., CdCl+) controls sorption onto calcite wastested by using different background electrolytes, as de-scribed in Section 2.2.4.1. As shown in Fig. 5, all sorptiondata collected after a contact time of 50 d, with calcite sus-pension pre-aged for 12 months, followed a single trend if

Equilibration Time (day)

pH

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 457.20

7.25

7.30

7.35

7.40

7.45

7.50

7.55

7.60

7.65

7.70

7.75

7.80

7.85

7.90

pH at equilibrium

Temporary drop in pH at the time of Cd spike

Fig. 4. The pH of a calcite suspension, in 0.01 M CaCl2, over the duration of a short pre-equilibration time and after the addition of Cd tosuspension.

{Cd2+} mol L-1

Tota

l Sor

bed

Cd

(m

ol C

d kg

-1)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.500

300

600

900

1200

1500

1800

2100

2400

2700

3000

CaCl2: 50dCa(NO3)2 : 50dCaCl2/Ca(NO3)2: 50d

LF Isotherm kLF = 0.00041 QLF = 257 × 104

m = 1.26 R2 = 0.971

Fig. 5. Cd sorption by calcite, as a function of {Cd2+}, in three background electrolytes all at I = 0.03 M, T = 22 �C, pH = 7.4 at a contacttime of 50 d. The solid line represents a Langmuir–Freundlich model fitted to all data. Experimental error, e, in CdSoln ranged between 4% and6%.

1504 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

sorption was expressed as a function of {Cd2+}, as opposedto CdSoln. Good reproducibility (i.e., e = 4–6%) in CdSoln

was achieved with the pre-aged suspensions used and vari-ation between the electrolytes used was not systematic withrespect to chloride concentration. In support of these find-ings, O’Connor et al. (1984) found reasonable coincidenceof sorption isotherms, expressed as {Cd2+} against CdTS,when 0.005 M of CaSO4, Ca(ClO4)2 and CaCl2 were usedas background electrolytes to suspend calcareous soils.

3.5. Testing the validity of the double-labeling assay

It was shown previously that the double-labeling tech-nique provided reliable measurements of time-dependentfixation of Cd in synthetic zeolites (e.g., zeolite-X and zeo-lite-Y) and was validated using both samples of naturalchabazite and Ca-exchanged Chelex-100, which demon-strated wholly reversible Cd2+ ion exchange (Ahmed,2006; Ahmed et al., 2006). However, the assumptions

Kinetics of Cd sorption, desorption & fixation by calcite 1505

behind this approach were re-tested for calcite because ofpossible differences in the dynamics of 109Cd exchange.Cd-spiked calcite samples were equilibrated for 20 and130 days and the concentration of isotopically exchange-able Cd was determined using three different isotope-equil-ibration times for the second spike: 48, 72 and 96 h. Fig. 6,shows that the relationship between {Cd2+} and CdLS wasconsistent across this range of isotope and Cd equilibrationtimes. Thus, the radio-labile assay appears able to distin-guish a chemically reactive Cd pool from non-reactive Cdforms in the presence of fixed Cd; the displacement of CdLS

data between 20 and 130 days equilibration gives some ideaof the extent of Cd fixation over this period.

3.6. Effect of contact time on Cd sorption and desorption

Fig. 7 shows a progressive increase in Cd sorption(pH = 7.4, I = 0.03 M) by calcite over contact times of 5–210 d. In contrast, the relationship between CdLS and{Cd2+} was described for all data, irrespective of contacttime, by a single LF relationship with values of fittedparameters of m = 1.18 (±0.007), kLF = 0.045 (±0.0008),QLF = 6943 (±106). Fig. 8 shows marked desorption hys-teresis, measured at 40 and 210 d. All lines in Figs. 7 and8 represent a single fit of the kinetic model (KM model)simultaneously to both the sorption and desorption data.Generally the fit of the KM model was very good(R2 = 0.999); there was substantial deviation from the mod-el trend only for desorption after 40 days, at high Cd load-ings, where desorption was greater than would be predicted.The time-dependant sorption of Cd by calcite is qualita-tively consistent with that found by Nakhone and Young

{Cd2+}

Lab

ile

Sorb

ed C

d (

mol

kg-1

)

0.1 0.2 0.3 0.4 0.5 0.6 020

30

4050

70

100

200

300

400500

700

1000

2000

Fig. 6. Effect of isotope (109Cd) equilibration time (48, 72 and 96 h) onT = 22 ± 2 �C) in 0.01 M CaCl2. Measurements were undertaken after ausing the double-labeling technique. The dotted and solid lines representand 130 d, respectively.

(1993) for Cd sorbed by calcareous clay. Fig. 7 shows thatthe error in model fitting is larger at 5 and 10 days than atlater times with the model predicting higher values forCdSoln than those determined experimentally. Moreover,as shown in Fig. 8, the KM model shows poorer fitting todesorption data at 40 d and at high Cd concentrations com-pared to that at lower Cd concentrations or extended reac-tion times. The reason for these two observations isprobably that the relative change in Cd dynamics is greatestfor small contact times but the weight of the more conser-vative data at greater contact times constrains the fittingof the model.

3.6.1. Analysis of the KM model

The KM model described in Section 2.2.5.1 was testedwith several alternative sorption models: Freundlich, one-site Langmuir, two-sites Langmuir (Sposito, 1982), Lang-muir–Freundlich (Sips, 1948), Toth (Toth, 1995) and Sibbe-sen (Sibbesen, 1981). The lowest value of MDL obtainedwas with the Langmuir–Freundlich equation into the KMmodel, otherwise the Freundlich and Sibbesen models per-formed as well as the Langmuir–Freundlich. As shown inFig. 7, the LF sorption isotherm is almost linear to�2000 lmol Cd kg�1 which is in some agreement with re-sults of Papadopoulos and Rowell (1988) who found thatthe sorption isotherm was linear up to 1000 lmol Cd kg�1

calcite. Papadopoulos and Rowell (1988) estimated a sitedensity of �1220 lmol of surface Ca atoms kg�1 (or8.13 lmol Ca m2) for a specific surface area of their calcitesample of 150 m2 kg�1. In this study, the specific surfacearea of an aged (for 12 months) calcite sample, determinedusing the conventional N2-BET technique, was 248

R2 = 0.979

R2 = 0.997

mol L-1

.7 0.8 1 2 3 4 5

LS (20 d): 48 hLS (20 d): 72 hLS (20 d): 96 hLS (20 d): LF modelLS (130 d): 48 hLS (130 d): 72 hLS (130 d): 96 hLS (130 d): LF model

the concentration of labile sorbed Cd by calcite (pH = 7.45 ± 0.05;Cd contact time of 20 d (closed symbols) and 130 d (open symbols)Langmuir–Freundlich isotherms fitted to all data collected after 20

{Cd2+} mol L-1

Sorb

ed C

d (

mol

kg-1

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.000

300

600

900

1200

1500

1800

2100

2400

2700

5d

10d

20d

30d40d60d80d105d130d

210d

CdLS

CdTS

Fig. 7. Cd sorption, as a function of {Cd2+}, on calcite following contact times of 5, 10, 20, 30, 40, 60, 80, 105, 130 and 210 d. Solid linesrepresent the kinetic model (KM) fitted to the total sorbed Cd data; the single dotted line represents the same model (same parameter values)fitted to the labile sorbed Cd data; values of fitted parameters were m = 1.18 (±0.007), kLF = 0.045 (±0.0008), QLF = 6943 (±106).Experimental errors in {Cd2+}, e, were in the range of 4–8%, error bars were removed for greater clarity.

{Cd2+} μmol L-1

Sorb

ed C

d (μ

mol

kg-1

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.500

300

600

900

1200

1500

1800

2100

2400

2700

TS: 40dTD: 42 - 50 dTS: 210dTD: 212 - 220 d

210 d 40 d

Sorption

Desorption

Desorptioncycles (1 - 5)

Fig. 8. Cd sorption and desorption, as a function of {Cd2+}, on calcite after contact times of 40 and 210 d. Closed symbols represent sorptiondata whereas open symbols represent data from 5 successive desorption cycles. Solid lines represent the kinetic model (KM) fitted to the totalsorbed Cd data; the dotted lines represents the same model (same parameter values) fitted to the desorbed Cd data; values of fitted parameterswere m = 1.18 (±0.007), kLF = 0.045 (±0.0008), QLF = 6943 (±106). Experimental error in {Cd2+}, e, was in the range of 5–10%.

1506 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

(±5) m2 kg�1. The estimated site density of calcite was�1970 lmol of surface Ca atoms kg�1 (i.e., 7.94 lmol -Ca m2). Thus, the linearity of the LF isotherm up to�2000 lmol Cd kg�1 suggests a uniform sorption processthat remains unaffected by the extent of Cd sorption. Totest this assumption further, the effect of initial Cd concen-tration on the fitting of the KM model was tested by formu-

lating a combination model that combines five sub-models—as was described in Ahmed et al. (2006). The re-sult of this test showed that the initial Cd concentrationhad an insignificant effect on the values of adjustableparameters of the KM model, at the range of Cd loadingsused in these experiments (data not shown). The qualityof prediction achieved by the KM model is shown in

Kinetics of Cd sorption, desorption & fixation by calcite 1507

Fig. 9 for CdLS against {Cd2+}. The fitting error (expressedas ±1 SD) was very small with an error in adjustableparameters of less than 1.5%.

3.6.1.1. Rates of Cd sorption. The fitted values of the appar-ent rate coefficients describing transfer between labile andnon-labile pools, k1 and k2, were 37.8 (±0.4) � 10�3 and3.97 (±0.05) � 10�3 d�1, respectively, indicating that the fi-nal equilibrium position favors Cd residence in a non-labileform. The modeled and measured distribution of Cd be-tween the solution, labile and non-labile phases are pre-sented in Fig. 10. After 210 d, only 9% and 4% of Cdremained in the labile sorbed and solution phases, respec-tively, whereas the remaining Cd (87% of total) was in thenon-labile phase. Bailey et al. (2005) measured the propor-tion of radio-labile Cd on powdered calcite, following acontact time of 171 d to be 20.6% of total Cd. This valueis very close to the proportion of total labile Cd estimatedin this study after 171 d which corresponds to �16% of to-tal Cd.

As depicted in Fig. 10, CdNL approaches an asymptoteafter a contact time of �120 d. The two-pool model pre-sented in Fig. 1 may be a simplification of a continuumof sorption pools. However, the shallow slope of the CdNL

curve after �120 d in Fig. 10 suggests that the introductionof further (conceptual) metal pools to the model would re-quire very precise data to be collected over a very long con-tact time (years) for effective model parameterization. Thetwo-pool KM model described in this study is certainly ade-quate to describe Cd sorption and desorption by calciteover the time scale studied.

3.6.1.2. Rates of Cd desorption. During desorption, if a‘zero-sink’ in solution is assumed such that non-labile Cd

KM Model

{Cd2+} μ

Lab

ile

Sorb

ed C

d (μ

mol

kg-1

)

0.1 0.2 0.3 0.4 0.5 0.6 0.10

20

30

4050

70

100

200

300

400500

700

1000

2000

Fig. 9. The effect of contact time (5–210 d) on the equilibrium of labile somodel based on the LF model; the dotted lines represent the fitting error�68% confidence in the normal distribution of errors.

is continuously transferred to the labile form with a rateconstant, k2 = 3.97 � 10�3 d�1, then the predicted half-lifefor Cd desorption is �175 d. Slow desorption rateshave been reported by several authors (McBride, 1980;Papadopoulos and Rowell, 1988). Davis et al. (1987)reported only limited desorption of Cd from calcite evenafter just 24 h sorption but with more complete desorptionif contact times were shortened. Zachara et al. (1991, 1988)reported that while largely desorbable, approximately 20%of sorbed Zn2+, Co2+ and Ni2+ was irreversibly bound tocalcite. These authors attributed this to the incorporationof metal ions into calcite lattice through recrystallizationprocess.

3.6.2. Analysis of the DM model

Bratter et al. (1972) studied the movement of 45Ca intocalcite at elevated temperature and estimated the diffusioncoefficient to be less than 5 � 10�16 cm2 s�1

(1.8 � 104 A2 h�1) at 800 �C. A much smaller diffusion coef-ficient of 8 � 10�20 cm2 s�1 (2.88 A2 h�1) for the diffusionof 45Ca in calcite at low temperature was reported by Lahavand Bolt (1964). Cd2+ and Ca2+ have similar ionic radii andhydration enthalpies and thus it seems reasonable to as-sume that solid-state diffusion rates may be similar. Themean diffusion distance (�d; cm) traveled by Cd2+ ions in acalcite matrix can be estimated from Einstein’s equation(1905):

�d ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi2Dappt

pð12Þ

where Dapp is the apparent solid-state diffusion coefficient(cm2 s�1), and t is the time of diffusion (s).

With the use of the value of Dapp (Ca2+) given by Lahavand Bolt (1964), Eq. (12) suggests that Ca2+ (and Cd2+) re-quire �2 h to diffuse beyond the first surface CaCO3 mono-

+1SD

-1SD

mol L-1

7 0.8 1 2 3 4 5

LS: 5dLS: 10dLS: 20dLS: 30dLS: 40dLS: 60dLS: 80dLS: 105dLS: 130dLS: 210d

rbed Cd with {Cd2+} on calcite. The solid line represents the kineticexpressed as ±1 standard deviation (±1 SD) which corresponds to

Contact Time (day)

Cad

miu

m D

istr

ibut

ion

(%)

0 25 50 75 100 125 150 175 200 225 2500

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

CdSoln :C1-C5CdTS : C1-C5CdLS : C1-C5CdNL : C1-C5

Total Sorbed Cd

Non-Labile Cd

Labile Sorbed Cd

Total Dissolved Cd

Fig. 10. The distribution of Cd among labile sorbed, non-labile sorbed, total dissolved and total sorbed forms in a calcite-CaCl2 suspension.The solid lines represent the fit of the kinetic model (KM); the symbols (h, M, *, s) represent experimental data for CdSoln, CdLS, CdNL andCdTS, respectively, at five Cd concentration levels collected after contact times between 5 and 210 days.

1508 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

layer (assuming that the sum of the thickness of the ad-sorbed layer and the distance traveled, �d, by diffused ionsequal to the thickness of one calcite unit cell �3.2 A, Liangand Baer, 1997). This implies that the solid-state diffusionof Cd2+ through the calcite surface is possible.

Using time-resolved XPS (X-ray Photoelectron Spec-troscopy) and LEED (Low Energy Electron Diffraction),Stipp and co-workers (1992, 1994, 1998) reported loss ofCd2+ and Zn2+ ions from the surface of freshly cleaved cal-cite (1014) faces. Solid-state diffusion into the calcite struc-ture was suggested, to depths of tens of angstroms throughexchange with Ca2+ over time periods of weeks to months.Using a similar approach, Hoffmann and Stipp (2001) didnot find any evidence for Ni2+ solid-state diffusion intothe bulk structure of calcite. Using stirred flow-throughreactor experiments, Martin-Garin et al. (2003) estimatedDapp (Cd2+) of 8.5 � 10�21 cm2 s�1 which is roughly an or-der of magnitude lower than that estimated by Stipp et al.(1992). Xu et al. (1996) studied the uptake of Co2+ by agedcalcite powder and cleaved calcite crystals using XPS sput-tering depth profiling. They showed that Co2+ had pene-trated the calcite to depths in excess of 50–100 A in1 week or less. Assuming that Co2+ ions diffuse at a ratesimilar to 45Ca, these authors concluded that solid-state dif-fusion model cannot explain their results. The above studiessuggest the importance of ion diffusion at low temperaturebut with these experiments carried out at short reactiontimes it is not clear if diffusion coefficients are absolute min-imum estimates.

The concentric shell diffusion model (DM model) wastested as described in Section 2.2.5.2; the model fit is com-pared to the KM model in Fig. 11 and Table 1. The KMmodel provided a markedly better fit to experimental data

(i.e., CdNL and CdTL) (R2 = 0.992) than the DM model(R2 = 0.959) with lower MDL and RSD values. Moreover,the diffusion depth estimated by Stipp and co-workers(1998, 1992) by direct measurement is much lower than thatestimated by the DM model. This large difference in diffu-sion depth (and diffusion coefficient) may suggest that theDM model is mechanistically inappropriate to predictCd2+ movement into calcite. However, all the sorptionstudies mentioned earlier such as that of Stipp (1994,1998) were carried out using single freshly cleaved crystalsexposed to metal-bearing solutions that were not in equilib-rium with calcite. Such non-equilibrated solutions mayhave caused calcite dissolution and subsequent co-precipi-tation. In support of this, in their XPS and AFM (AtomicForce Microscopy) experiments, Chada et al. (2005) foundno evidence to imply solid-state diffusion mechanism ofCd2+ or Pb2+ sorbed at single crystal calcite ð10�14Þ surfacesthat were brought in contact with pre-equilibrated solutionswith calcite. The current study used pre-equilibrated pow-dered calcite samples and it may be un-realistic to compareresults with the sorption experiments using single crystals.

3.7. Mechanisms of Cd sorption

At low initial Cd loadings, Cd2+ ions can replace Ca2+

ions in accessible surface sites of calcite and, in this case,the dominant reaction mechanism is chemisorption ofCd2+; during this process, changes in pH are likely to bevery small. By contrast, if a precipitate of CdCO3 wasformed then pH would be expected to decrease (McBride,1980; Papadopoulos and Rowell, 1988), due to reactionwith dissolved HCO3

�. In the present study, minimal pHchanges of calcite suspension (<0.15 pH units) were

DM model

Contact time (day)

Non

-Lab

ile

Cd

(m

ol C

d kg

-1)

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 2400

300

600

900

1200

1500

1800

2100

2400

2700CdNL: C1CdNL: C2CdNL: C3CdNL: C4CdNL: C5

KM model

Fig. 11. A comparison between the kinetic model (solid lines) and the diffusion model (dotted lines) both fitted to experimental values of CdNL

and CdTL. Closed symbols represent experimental data at five increasing Cd concentrations.

Table 1Goodness of fit and parameter values generated by the optimiza-tion of the DM and the KM models fitted to experimental data ofCdNL and CdTL

KM model DM model

R2 0.992 0.959RSD 0.000757 0.00381MDL 4.65 7.94Dapp � 10�16 (cm2 s�1) — 1.17 ± 0.0694�dðlm yr�1Þa — 2.95

a Estimated using Eq. (12) and optimized value of Dapp.

Kinetics of Cd sorption, desorption & fixation by calcite 1509

observed during the course of sorption experiments. How-ever, it is difficult to tell if a change from chemisorption(at short reaction time) to surface precipitation of individ-ual Cd phases (e.g., CdCO3) has occurred especially atthe Cd loadings used. A number of authors suggested thatmetal ions (especially Mn2+ and Cd2+) exhibit a continuumbetween adsorption and co-precipitation in the calcite ma-trix via the formation of a mixed CanCdmCO3(n+m) solid-solution phase at the calcite surface (Chang and Brice,1971; Davis et al., 1987; Fuller and Davis, 1987; Papadopo-ulos and Rowell, 1988). Alternatively, Stipp et al. (1992)proposed the formation of an CdCO3–CaCO3 solid-solu-tion by solid-state diffusion of Cd2+ into the calcite struc-ture. According to Stipp et al. (1992), Zachara et al.(1991) and Davis et al. (1987), the formation of a solid-solu-tion does not necessarily require saturation of sorption sitesbut may form at low surface loadings. In studies with highCd loadings and at short reaction times, a slow sorptionreaction over time was ascribed to co-precipitation (Daviset al., 1987; Zachara et al., 1991), with surface sorption sitesregenerated by the incorporation of dehydrated Cd2+ ions

within the calcite structure. Because most of the Cd load-ings used in this study are almost within the range of theapparent site density of the calcite (1970 lmol surfaceCa kg�1) then co-precipitation is a possible mechanismespecially at high Cd loadings. However, the fit of theKM model, with single rate constants, was very consistentacross the concentration range used which suggests themechanism of fixation was not concentration-dependent.

Bailey et al. (2005) studied the effect of extended reactiontimes (up to �6 months) on Cd fixation by calcite using acombination of isotopic dilution and EXAFS techniques.The calcite EXAFS data were fitted to a four-shell otavitemodel (i.e., three atoms of each carbonate group and thenearest Cd atoms 3.934 A) and refined the partial substitu-tion of the Cd shell with Ca atoms to see if this improvedthe fit. Their results showed replacement of Cd in the fourthshell with Ca indicating diffusion between the two phases.They also reported an increase in Ca in the fourth shell sug-gesting that incorporation of Cd2+ within the calcite struc-ture increased with time (up to 256 days), results were inqualitative agreement with 109Cd isotopic exchange data.In the current study, continuing incorporation of Cd over210 days was evident which is in agreement with the studyof Bailey et al. (2005). It seems that the formation of octa-hedral Cd-calcite complexes (the favored surface geometry)permits transformation of Cd2+ ions from a labile state atthe surface to a less labile state in the bulk structure of cal-cite; it would be interesting to investigate if this argumentapplies to Mn2+ ions. Cheng et al. (1998) studied the incor-poration of Zn2+ from Zn-bearing solution on freshlycleaved single calcite ð10�14Þ surface using X-ray StandingWave Triangulation and Surface EXAFS and found thatZn2+ incorporation occurs as an octahedral complex atthe calcite ð10�14Þ surface by direct substitution for Ca2+

1510 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

in the surface layer. However, in a recent study by Elzingaet al. (2006), it has been shown that Cu2+, Zn2+ and Pb2+

ions form a non-octahedral configuration with respect totheir first oxygen shell on the calcite surface and thus noevidence for slow formation of a metal-calcite solid wasprovided. These authors ascribed Zn2+ incorporation via

the formation of octahedral surface complexes in the studyof Cheng et al. (1998) to experimental condition where Zn-solutions were not in equilibrium with calcite.

4. CONCLUSION

Our work suggests that it is vital to age the calcite sus-pension prior to undertaking sorption and desorptionexperiments to enable ‘healing’ of superficial wounds inthe surface morphology in order to stabilize the solubilityproduct. We also found that it preferable to carry outdesorption experiments using calcite-equilibratedelectrolyte.

This study has shown that time-dependent Cd sorptionand desorption hysteresis are consistently described usinga reversible first-order kinetic model; fits to a diffusion mod-el were relatively poor. Results have demonstrated that theslow assimilation of Cd by calcite continues even after 200days, in agreement with recent EXAFS studies.

The rate-limiting step for Cd2+ sorption may be an en-ergy barrier required to break the bond between CO3

2�

and Ca2+ at the calcite surface in order to allow for Cd2+

replacement of Ca2+. Desorption occurred at slower ratethan sorption implying the presence of a greater energy bar-rier. With the relatively slow release rate of Cd2+ from cal-cite (half-life �175 d assuming zero-sink situation) calcite isan efficient sorbent in environmental systems subject tominor fluctuations in pH and metal concentration. How-ever, acid dissolution of calcite remains the main limitationfor its use in remediation of wastewater and slightly acidicsoils.

ACKNOWLEDGMENTS

This research was supported by the University of Nottingham.The authors also gratefully acknowledge Altajir Trust for the finan-cial support during the course of this project. Moreover, theauthors wish to thank Dr. Elizabeth Bailey for the useful discussionespecially in relation to her previous work on calcite. Moreover, wethank the Associated Editor Dr. Karen Johannesson and the anon-ymous reviewers for their useful comments and the time they in-vested into our manuscript.

REFERENCES

Ahmed I. A. M. (2006) Measuring cadmium fixation in zeolites andcalcite. Ph.D. Thesis, The University of Nottingham.

Ahmed I. A. M., Young S. D. and Crout N. M. J. (2006) Time-dependent sorption of Cd2+ on CaX zeolite: experimentalobservations and model predictions. Geochim. Cosmochim. Acta

70, 4850–4861.

Ainsworth C. C., Pilon J. L., Gassman P. L. and van der Sluys W.G. (1994) Cobalt, cadmium, and lead sorption to hydrousiron-oxide: residence time effect. Soil Sci. Soc. Am. J. 58,

1615–1623.

Amacher M. C., Selim H. M. and Iskandar I. K. (1990) Kinetics ofmercuric-chloride retention by soils. J. Environ. Qual. 19, 382–

388.

Backes E. A., McLaren R. G., Rate A. W. and Swift R. S. (1995)Kinetics of cadmium and cobalt desorption from iron andmanganese oxides. Soil Sci. Soc. Am. J. 59, 778–785.

Bailey E. H., Mosselmans J. F. W. and Young S. D. (2005) Time-dependent surface reactivity of Cd sorbed on calcite, hydroxy-apatite and humic acid. Mineral. Mag. 69, 563–575.

Bratter P., Rosick U. and Moller P. (1972) Equilibrium ofcoexisting sedimentary carbonates. Earth Planet. Sci. Lett. 14,

50–54.

Brecevic L. and Nielsen A. E. (1989) Solubility of amorphouscalcium carbonate. J. Cryst. Growth 98, 504–510.

Chada V. G. R., Hausner D. B., Strongin D. R., Rouff A. A. andReeder R. J. (2005) Divalent Cd and Pb uptake on calcitecleavage faces: an XPS and AFM study. J. Colloid Interface Sci.

288, 350–360.

Chang L. L. Y. and Brice W. R. (1971) Subsolidus phase relationsin the system calcium carbonate–cadmium carbonate. Am.

Mineral. 56, 338–341.

Cheng L., Sturchio N. C., Woicik J. C., Kemner K. M., Lyman P.F. and Bedzyk M. J. (1998) High-resolution structural study ofzinc ion incorporation at the calcite cleavage surface. Surf. Sci.

415, L976–L982.

Coleman N. T., Williams D. E., Nielsen T. R. and Jenny H. (1950)On the validity of interpretations of potentiometrically mea-sured soil pH. Soil Sci. Soc. Am. Proc. 15, 106–114.

Coppin F., Castet S., Berger G. and Loubet M. (2003) Microscopicreversibility of Sm and Yb sorption onto smectite and kaolinite:experimental evidence. Geochim. Cosmochim. Acta 67, 2515–

2527.

Davis J. A., Fuller C. C. and Cook A. D. (1987) A model for trace-metal sorption processes at the calcite surface: adsorption ofCd2+ and subsequent solid-solution formation. Geochim. Cos-

mochim. Acta 51, 1477–1490.

de Brauwere A., de Ridder F., Pintelon R., Elskens M., SchoukensJ. and Baeyens W. (2005) Model selection through a statisticalanalysis of the minimum of a weighted least squares costfunction. Chemomet. Intell. Lab. Syst. 76, 163–173.

Degryse F., Buekers J. and Smolders E. (2004) Radio-labilecadmium and zinc in soils as affected by pH and source ofcontamination. Eur. J. Soil Sci. 55, 113–122.

Dromgoole E. L. and Walter L. M. (1990) Iron and manganeseincorporation into calcite: effects of growth kinetics, tempera-ture and solution chemistry. Chem. Geol. 81, 311–336.

Eick M. J., Peak J. D., Brady P. V. and Pesek J. D. (1999) Kineticsof lead adsorption/desorption on goethite: residence time effect.Soil Sci. 164, 28–39.

Einstein A. (1905) The motion of elements suspended in staticliquids as claimed in the molecular kinetic theory of heat.Annalen der Physik 17, 549–560.

Elzinga E. J. and Reeder R. J. (2002) X-ray absorption spectros-copy study of Cu2+ and Zn2+ adsorption complexes at thecalcite surface: implications for site-specific metal incorporationpreferences during calcite crystal growth. Geochim. Cosmochim.

Acta 66, 3943–3954.

Elzinga E. J., Rouff A. A. and Reeder R. J. (2006) The long-termfate of Cu2+, Zn2+, and Pb2+ adsorption complexes at thecalcite surface: an X-ray absorption spectroscopy study. Geo-

chim. Cosmochim. Acta 70, 2715–2725.

Franklin M. L. and Morse J. W. (1982) The interaction of copperwith the surface of calcite. Ocean Sci. Eng. 7, 147–174.

Fuller C. C. and Davis J. A. (1987) Processes and kinetics of Cd2+

sorption by a calcareous aquifer sand. Geochim. Cosmochim.

Acta 51, 1491–1502.

Kinetics of Cd sorption, desorption & fixation by calcite 1511

Gerth J., Bruemmer G. W. and Tiller K. G. (1993) Retention of Ni,Zn and Cd by Si-associated goethite. Zeitschrift fur Pflanzen-

ernahrung und Bodenkunde 156, 123–129.

Gray C. W., McLaren R. G., Roberts A. H. C. and Condron L. M.(1998) Sorption and desorption of cadmium from some NewZealand soils: effect of pH and contact time. Aust. J. Soil Res.

36, 199–216.

Grunwald P. (2000) Model selection based on minimum descrip-tion length. J. Math. Psychol. 44, 133–152.

Hamon R. E. and McLaughlin M. J. (2002) Interferences in thedetermination of isotopically exchangeable P in soils and amethod to minimise them. Aust. J. Soil Res. 40, 1383–1397.

Hamon R. E., McLaughlin M. J., Naidu R. and Correll R. (1998)Long-term changes in cadmium bioavailability in soil. Environ.

Sci. Technol. 32, 3699–3703.

Hoffmann U. and Stipp S. L. S. (2001) The behavior of Ni2+ oncalcite surfaces. Geochim. Cosmochim. Acta 65, 4131–4139.

Hogg D. S., McLaren R. G. and Swift R. S. (1993) Desorption ofcopper from some New-Zealand soils. Soil Sci. Soc. Am. J. 57,

361–366.

Jeong H. C. and Williams E. D. (1999) Steps on surfaces:experiment and theory. Surf. Sci. Rep. 34, 171–294.

Lahav N. and Bolt G. H. (1964) Self-diffusion of 45Ca into certaincarbonates. Soil Sci. 9, 293–299.

Liang Y. and Baer D. R. (1997) Anisotropic dissolution at theCaCO3(1014)-water interface. Surf. Sci. 373, 275–287.

Lock K. and Janssen C. R. (2003) Influence of ageing on zincbioavailability in soils. Environ. Pollut. 126, 371–374.

Lombi E., Hamon R. E., McGrath S. P. and McLaughlin M. J.(2003) Lability of Cd, Cu, and Zn in polluted soils treated withlime, beringite, and red mud and identification of a non-labilecolloidal fraction of metals using isotopic techniques. Environ.

Sci. Technol. 37, 979–984.

Lorens R. B. (1981) Sr, Cd, Mn and Co distribution coefficients incalcite as a function of calcite precipitation rate. Geochim.

Cosmochim. Acta 45, 553–561.

Luth H. (1993) Surfaces and Interface of Solids. Springer-Verlag,Inc., Berlin.

Ma Y. B., Lombi E., Nolan A. L. and McLaughlin M. J. (2006a)Short-term natural attenuation of copper in soils: effects oftime, temperature, and soil characteristics. Environ. Toxicol.

Chem. 25, 652–658.

Ma Y. B., Lombi E., Nolan A. L. and McLaughlin M. J. (2006b)Determination of labile Cu in soils and isotopic exchangeabilityof colloidal Cu complexes. Eur. J. Soil Sci. 57, 147–153.

Marqusee J. A. and Ross J. (1983) Kinetics of phase transitions:theory of Ostwald ripening a. J. Chem. Phys. 79, 373–378.

Martin-Garin A., van Cappellen P. and Charlet L. (2003) Aqueouscadmium uptake by calcite: a stirred flow-through reactorstudy. Geochim. Cosmochim. Acta 67, 2763–2774.

McBride M. B. (1979) Chemisorption and precipitation of Mn2+ atCaCO3 surfaces. Soil Sci. Soc. Am. J. 43, 693–698.

McBride M. B. (1980) Chemisorption of Cd2+ on calcite surfaces.Soil Sci. Soc. Am. J. 44, 26–28.

McLaren R. G., Backes C. A., Rate A. W. and Swift R. S. (1998)Cadmium and cobalt desorption kinetics from soil clays: effectof sorption period. Soil Sci. Soc. Am. J. 62, 332–337.

Mucci A. and Morse J. W. (1990) Chemistry of low-temperatureabiotic calcites: experimental studies on coprecipitation, stabil-ity, and fractionation. Rev. Aquat. Sci. 3, 217–254.

Myung I. J. and Pitt M. A. (2004) Model comparison methods. InMethods in Enzymology: Numerical computer methods (Part

D), vol. 383 (eds. L. Brand and M. Johnson), pp. 351–366.Myung J. I., Navarro D. J. and Pitt M. A. (2006) Model selection

by normalized maximum likelihood. J. Math. Psychol. 50,

167–179.

Nakhone L. N. (1989) Factors affecting the lability of cadmium insoil. Ph.D. Thesis, The University of Nottingham, UK.

Nakhone L. N. (1997) Cadmium adsorption and desorption onhumic acid, montmorillonite, goethite, and calcareous clay.Discov. Innov. 9, 53–71.

Nakhone L. N. and Young S. D. (1993) The significance of (radio-)labile cadmium pools in soil. Environ. Pollut. 82, 73–77.

O’Connor G. A., O’Connor C. and Cline G. R. (1984) Sorption ofcadmium by calcareous soils: influence of solution composition.Soil Sci. Soc. Am. J. 48, 1244–1247.

Papadopoulos P. and Rowell D. L. (1988) The reactions ofcadmium with calcium-carbonate surfaces. J. Soil Sci. 39, 23–

36.

Paquette J. and Reeder R. J. (1995) Relationship between surface-structure, growth-mechanism, and trace-element incorporationin calcite. Geochim. Cosmochim. Acta 59, 735–749.

Parkhust D. L. and Appelo C. A. J. (1999) User’s guide toPHREEQC (Version 2): a computer program for speciation,batch-reaction, one-dimensional transport and inverse geo-chemical calculations. US Geological Survey, Denver,Colorado.

Parkman R. H., Charnock J. M., Livens F. R. and Vaughan D. J.(1998) A study of the interaction of strontium ions in aqueoussolution with the surfaces of calcite and kaolinite. Geochim.

Cosmochim. Acta 62, 1481–1492.

Pingitore N. E. (1986) Modes of coprecipitation of Ba2+ and Sr2+

with calcite. In Geochemical Processes at Mineral Surfaces (eds.J. A. Davis and K. F. Hayes). American Chemical Society,

Washington, DC, pp. 574–586.

Pitt M. A. and Myung I. J. (2002) When a good fit can be bad.Trends Cogn. Sci. 6, 421–425.

Press W. H. et al. (2002) Numerical Recipes in C++: The Art of

Scientific Computing. Cambridge University Press, Cambridge,UK.

Rimstidt J. D., Balog A. and Webb J. (1998) Distribution of traceelements between carbonate minerals and aqueous solutions.Geochim. Cosmochim. Acta 62, 1851–1863.

Sibbesen E. (1981) Some new equations to describe phosphatesorption by soils. J. Soil Sci. 32, 67–74.

Sips R. (1948) On the structure of a catalyst surface. 1. J. Chem.

Phys. 16, 490–495.

Sposito G. (1982) On the use of the Langmuir equation in theinterpretation of adsorption phenomena-2: the two-surfaceLangmuir equation. Soil Sci. Soc. Am. J. 46, 1147–1152.

Stipp S. L. S. (1994) Understanding interface processes and theirrole in the mobility of contaminants in the geosphere: the use ofsurface sensitive techniques. Eclogae Geologicae Helvetiae 87,

335–355.

Stipp S. L. S. (1998) Surface analytical techniques applied tocalcite: evidence of solid-state diffusion and implications forisotope methods. Palaeogeogr. Palaeoclimatol. Palaeoecol. 140,

441–457.

Stipp S. L. S., Hochella M. F., Parks G. A. and Leckie J. O. (1992)Cd2+ uptake by calcite, solid-state diffusion, and the formationof solid-solution: interface processes observed with near-surfacesensitive techniques (XPS, LEED, and AES). Geochim. Cos-

mochim. Acta 56, 1941–1954.

Striegel J., Sanders D. A. and Veenstra J. N. (2001) Treatment ofcontaminated groundwater using permeable reactive barriers.Environ. Geosci. 8, 258–265.

Tesoriero A. J. and Pankow J. F. (1996) Solid solution partitioningof Sr2+, Ba2+, and Cd2+ to calcite. Geochim. Cosmochim. Acta

60, 1053–1063.

Tiller K. G., Gerth J. and Bruemmer G. W. (1984) The sorption ofCd, Zn and Ni by soil clay fractions: procedures for partition ofbound forms and their interpretation. Geoderma 34, 1–16.

1512 I.A.M. Ahmed et al. / Geochimica et Cosmochimica Acta 72 (2008) 1498–1512

Toran L. and Grandstaff D. (2002) PHREEQC and PHREEQCI:geochemical modeling with an interactive interface. Ground

Water 40, 462–464.

Toth J. (1995) Uniform interpretation of gas/solid adsorption. Adv.

Colloid Interface Sci. 55, 1–239.

Wang Y. and Reardon E. J. (2001) A siderite/limestone reactor toremove arsenic and cadmium from wastewaters. Appl. Geo-

chem. 16, 1241–1249.

Xu N., Hochella, Jr., M. F., Brown, Jr., G. E. and Parks G. A.(1996) Co(II) sorption at the calcite–water interface.1. X-rayphotoelectron spectroscopic study. Geochim. Cosmochim. Acta

60, 2801–2815.

Young S. D., Tye A. M., Carstensen A., Resende L. and Crout N.(2000) Methods for determining labile cadmium and zinc insoil. Eur. J. Soil Sci. 51, 129–136.

Zachara J. M., Cowan C. E. and Resch C. T. (1991) Sorption ofdivalent metals on calcite. Geochim. Cosmochim. Acta 55, 1549–

1562.

Zachara J. M., Kittrick J. A. and Harsh J. B. (1988) Themechanism of Zn2+ adsorption on calcite. Geochim. Cosmo-

chim. Acta 52, 2281–2291.

Associate editor: Karen Johannesson