TOWARDS A Fundamental Rate Equation for Gibbsite Growth in Bayer Liquors
Christopher Vernon1, Gordon Parkinson2 & Daniel Lau1
AJ Parker CRC for Hydrometallurgy
1CsIRo Division of Minerals, PO Box 90, Bentley 6982, WA.
2Curtin University of Technology, PO Box U1987, Perth 6001, WA.
Equations for the growth of gibbsite from Bayer liquors have, until recently, been based on simple functions of supersaturation and temperature. Where necessary, these equations have made allowance for factors such as free caustic concentration, but none are satisfactory over a broad range of conditions. This is hardly surprising, as most approaches have been data fitting exercises and have paid little attention to the fundamental chemical processes.
The present work draws on the results of a number of techniques, ranging from the microscopic (Atomic Force Microscopy) to macroscopic (bulk batch crystallization) and recognises that a comprehensive growth model cannot be derived without knowledge of the crystal growth process, solution speciation and the effects of the liquor on the surface chemistry of gibbsite.
Microscopy suggests that crystal growth occurs on the basal face by a Birth & Spread mechanism at high supersaturation, but by spiral dislocation on all faces at the moderate supersaturations encountered in most of the precipitation circuit. For the purpose of growth rate calculations, supersaturation is better expressed as a relative (dimensionless) quantity (i.e. ) rather than . In any case, supersaturation is not the best expression of driving force, as other chemical factors including the activities of water, cations and participating aluminate species play an important role in determining growth rate. The present work offers an insight into recent developments in the field and future directions in kinetic modelling.
crystal growth, kinetics, gibbsite, precipitation, spiral, birth & spread
TOWARDS A Fundamental Rate Equation for Gibbsite Growth in Bayer Liquors
Christopher Vernon, Gordon Parkinson & Daniel Lau
The literature contains a number of equations (e.g. Brown, 1972; King, 1973; Misra, 1971; White & Bateman, 1988) that describe the growth rate of gibbsite (hydrate) from Bayer liquors. Despite the apparent utility of all of these equations, each is an empirical fit, not derived from a theoretical or chemical consideration. The main pitfalls with the empirical approach are a reduced ability to extrapolate beyond the fitted data, the inability to account for changing liquor chemistries and a lack of portability between refinery systems. Often, it is clear that the different equations have been tailored for different operating parameters (e.g. caustic concentration).
Veesler & Boistelle (1993) make a good attempt to reconcile the differences between the equations. They point out that some of the kinetic effects perceived to be due to different caustic concentrations are actually due to the use of absolute supersaturation, S:
They normalized the effect by using relative supersaturation, s , instead:
where Al2O3 can be any measure of dissolved aluminium and Al2O3* refers to the equilibrium solubility. Despite the advantage offered by using s , it is still an empirical factor, only loosely associated with the true "driving force" for the precipitation reaction.
The precipitation of gibbsite is usually written as some variant of:
and it is assumed that all dissolved aluminium is present as a single species, whether that is Al(OH)4- or AlO2- (e.g. McCoy & Dewey). If this were the case, simple representations of solubility would suffice. For over thirty years, it has been suspected that speciation in caustic aluminate liquors is far from simple. In 1964, Dibrov et al. suggested the existence of Al(OH)4-, AlO(OH)2- and AlO2-. In 1970, Moolenaar et al. proposed that the dimer Al2O(OH)62- is formed and in 1986, Zámbó proposed a large variety of poly-aluminium species. Of these works, the only one that has stood the test of more recent investigations is that of Moolenaar et al.
- The implication from the data of all of these authors is that driving force for crystal growth is not a simple function of measured supersaturation because speciation is not a simple function of concentration.
In order to arrive at a fundamental (i.e. mechanistic) understanding of gibbsite growth from sodium aluminate solutions, it is necessary to understand; 1) how solution composition affects speciation; 2) which species are involved in the growth of gibbsite; 3) how those species attach to the crystal surface and undergo a transition. Hence, the AMIRA P380B project "Fundamentals of Precipitation" has worked towards an understanding of Bayer liquor speciation, interfacial phenomena and mechanisms of gibbsite crystal growth. The present paper calls on data from all of these areas, but especially microscopic and bulk measurements of the growth of gibbsite crystals, in order to form a preliminary hypothesis for the fundamental mechanism, and therefore a rate equation form.
The present paper is part experimental report, part review, and aims to draw together many recent developments in the understanding of Bayer precipitation chemistry.
1.2 Unit conventions
Concentration measurements are made in a number of different ways in the literature. North American practice is to refer to aluminium concentration, A, as g/L Al2O3 equivalent, and sodium hydroxide concentration, C, as its Na2CO3 g/L equivalent. European practice uses the same aluminium units but prefers to measure sodium hydroxide in units of g/L Na2O. In the present paper, SI units will be used for aluminium (expressed as moles/L Al) and sodium hydroxide (expressed as moles/L NaOH). Where appropriate, North American units will be also be used.
2.1 Crystallizer design and kinetic measurement
Bulk kinetic data was obtained using a cylindrical, flat-bottomed stainless steel crystallizer with an aspect ratio close to 1:1. The volume of liquor added was 400.0 mL (the total crystallizer volume was approximately 480 mL). Agitation at 200 rpm was achieved using an overhead stirrer and a small impeller with blades inclined at 45° . Stirrer speed was chosen as being slightly above the minimum required to ensure suspension of all of the solids. An outer jacket allowed temperature control in the range 60 to 95° C, with stability generally better than ± 0.2° C.
The primary reference for measuring aluminium and caustic concentration was the gluconate-fluoride titration method. Aliquots were withdrawn three times during the course of each experiment to determine the aluminium and caustic concentrations. Conductivity was tracked continuously over time and was then correlated with the titrated concentrations to allow a continuous plot of concentration versus time. In each case, excellent linear correlation was observed. Numerous additional tests were carried out, involving more frequent titration, to ensure the quality of the correlation.
2.2 Seed preparation and seeding rate
Seed material was prepared by wet sieving commercially available C31 (Alcoa Chemicals, Arkansas), removing all of the >100 m m material and most of the <60 m m material. A final clean-up of fines in the sample was achieved by an agglomeration step in a large stirred tank, followed by slow growth. The resulting material was washed well, dried at 70° C, mixed and split. Seed so produced was low in <45 m m particles, had a smooth appearance by SEM, and a reproducible surface area (N2 BET method) of 0.10 m2/g. More importantly, the seed exhibited no agglomerating behaviour throughout the experiments, thus holding surface area more or less constant. A standard seeding rate of 100 g per litre of liquid was used.
3.1 Bulk kinetic measurements
Fig. 1 shows a typical desupersaturation curve, in this instance for a 3.77 mol/L NaOH (C 200), 2.83 mol/L Al (A/C 0.720) liquor, held at 70.0° C and seeded. It is obvious that there is an induction period which lasts, in this case, approximately 20 minutes. Kinetic measurements commence after this has passed and are based on d[Al]/dt, the tangent to the curve.
A typical desupersaturation curve. In this particular run, at 70° C, 3.77 mol/L NaOH, 2.83 mol/L Al, the induction time is approximately 20 minutes.
The initial desupersaturation rate plotted against NaOH concentration. Temperature was 70.0° C and the initial supersaturation ratio was maintained at 1.56± 0.08. The fitted model will be explained in the Discussion.
Fig. 2 shows a plot of growth rate against caustic concentration at an average supersaturation ratio of [Al]/[Al*]=1.56 and at 70.0° C for each run. Experiments were conducted so that the supersaturation over the first part of the desupersaturation curve was the same for each experiment (1.56± 0.08). Thus, even without using a constant composition apparatus, the data in Figure 2 can be considered to have been obtained at constant supersaturation. It is clear that caustic concentration (or some connected factor) plays a strong part in determining the rate of growth. In other experiments (not shown here) the addition of NaCl or NaClO4 had the same mole for mole effect as adding NaOH, implying an ionic strength, sodium ion or water activity effect, but not a hydroxide effect, as suggested in many of the empirical rate equations.
4.1 Crystal growth mechanism - A brief review of kinetic and AFM evidence
Only the broad results of such work will be summarised here; the detail has been covered extensively in recent dissertations by both Lee and Friej and will be treated in other publications.
Lee's interpretation of optical observations of the growth of single crystals is based on theoretical rate equations derived for different mechanisms of growth (e.g. in Mullin, 1994). Lee found that, at low to moderate relative supersaturations, a spiral growth mechanism was the most appropriate description of gibbsite growth:
where values of n are not necessarily whole numbers, but in the case of a spiral growth at a moderate rate, n is expected to be 2.0. Lee checked this for growing gibbsite crystals by fitting a power curve and found n=1.98, close enough to the theoretical value of 2.0.
For the basal (e.g. hexagonal) face, Lee found that above a relative supersaturation of 1.69 at 80oC ([Al]=2.38 mol/L, [NaOH]=3.77 mol/L; A/C 0.607, C 200), growth occurs by a birth and spread mechanism.
The birth and spread mechanism has been observed using AFM (Friej, 1999) but only on the basal face and only at high supersaturations. Furthermore, the existence of emergent spirals on the prismatic faces have been observed, indicative that they may be involved in their growth mechanism (Friej, 1999).
- It can therefore be concluded that a growth equation of a similar form to (4) should represent the kinetics of gibbsite growth for most of the Bayer precipitation circuit. Only at high supersaturations does an equation describing Birth & Spread need to be considered (i.e. in the first tank of the precipitation circuit).
4.2 Crystal growth mechanism - bulk kinetic evidence
While measurements in bulk slurries may seem crude compared to optical and AFM observations of single crystals, bulk studies provide methods of more rapidly examining the effects of solution composition and provide a method for statistically screening out spurious effects. As Lee points out, growth rate dispersion can cause a scatter of one order of magnitude in growth rate depending on which crystal is chosen, whereas bulk studies return values representing the average of all processes.
Fig. 2 showed a plot of growth rate against caustic concentration. While authors such as Veesler and Boistelle have accounted for the well-known "caustic effect" by plotting growth rate against [Al]/[Al*] or ([Al]-[Al*])/[Al*], this does not appear to solve the present caustic dependence, as shown in Fig. 2. Veesler & Boistelle (1993) used a range of concentrations between 2.7 and 5.3 mol/L NaOH (C=138 to 271). The range is not broad and much of their data lies around the peak of Fig. 2. This might explain why they did not readily observe the effect shown in the present work.
4.3 A brief review of speciation in synthetic Bayer liquors
In the past 6 years, there have been significant developments in the understanding of speciation in caustic aluminate liquors. Much of this has arisen from the work of Sipos et al. (e.g. Sipos, 1997; Sipos, 1998; Radnai, 1998). Briefly, the conclusions of this work are that:
- A low concentration of an oligomeric species is formed.
- Considerable Na-OH and Na-Al(OH)4 ion pairing occurs.
- A species similar to Moolenaar's dimer, (OH)3Al-O-Al(OH)32-, exists in caustic aluminate solutions and its concentration is in more or less direct proportion with aluminate concentration.
Additionally, a computational simulation by Gale et al. (Gale, 1998) suggests that a more hydrated, but structurally similar, dimer forms with close coordination of two or more water molecules, (OH)3Al-(OH)2-Al(OH)32-. On an experimental level, it may be difficult to distinguish between the Moolenaar dimer and the Gale dimer. Buvári-Barcza et al. suggest that a cyclic hexamer forms readily in caustic aluminate solutions and is a precursor to precipitation of Al(OH)3, although no such species is found in the work of Sipos et al. or suggested by Gale et al. Gale's work is, however, in agreement with Buvári-Barcza's prediction of a double hydroxy-bridged dimer.
Solution X-ray diffraction studies (Radnai, 1998) and molecular dynamics simulations (Fleming, 1998) are indicative that some form of ordering occurs between sodium and aluminate species. Radnai et al. found that as concentration increased, a diffraction distance of 0.33 to 0.39 nm appeared. Fleming's work, an ab initio simulation of a periodic cell of a liquor, found that ion clustering occurred readily at normal Bayer concentrations and temperatures. This clustering involved sodium and aluminate ions in varying proportions, with a distribution from single sodium ions shared by many aluminates, to a number of sodium ions around a single aluminate. Although the system remained dynamic throughout the simulation, the mean sodium-aluminate distance remained stable at approximately 0.4 nm. It is important to note that Fleming's work involved only physical interactions and is unable to predict any chemical changes, such as dehydration, formation of contact ion pairs etc. It can, however, be used with the other evidence to indicate that:
- "Clustering" occurs in sodium aluminate solutions and this clustering may also take place with the formation of dimeric or oligomeric species.
Evidence for the formation of pre-crystalline clusters may be also be found in the work of Gerson et al. (Gerson, 1998), where pockets of increased density were found in Bayer liquors which had been cryovitrified. These pockets, of the order of 20 nm across, were interpreted as a densified region of polymerized aluminate species but the data could equally be interpreted as the formation of clusters/associates as predicted in Fleming's work.
4.4 Interpretation of kinetic data in terms of crystal growth theory and speciation
The kinetic data presented so far stands alone as a phenomenological study of gibbsite growth kinetics under the influence of a number of solution parameters. When coupled with the growing evidence in solution speciation and clustering, AFM and optical growth observations together with crystal growth theory, this data allows the formulation of a mechanistic model for gibbsite growth.
4.4.1 Speciation and kinetics
There is good evidence for the formation of an oligomeric species, responsible for Raman sidebands, which is formed in proportion with aluminium concentration (Watling, 1997; Sipos, 1997; Buvári-Barcza, 1998). The growth rate shows a similar increase at low to moderate concentrations and it is highly likely that the growth mechanism involves this species.
At high ionic strengths, the kinetics of growth decrease. This effect would appear to be due to either a marked decrease in the activity of water, a high population of cations, and possibly any effects that these have on the formation of the dimeric species. The rate appears to correlate well with water activity in this range, which shows a monotonic decrease with [NaOH] (Sipos et al.) and also with the concentration profile that Buvári-Barcza assign to the dimer. While the cation is no doubt intimately related to the growth mechanism, the present paper will concentrate on correlations with water activity. When better information is available on relative activities of all of the species present, it will be possible to better distinguish between the effects.
4.4.2 Direct AFM evidence
AFM observations show that in the absence of gross crystal defects, nucleation occurs on the basal (hexagonal) face, but only a spreading (spiral) growth occurs on the prismatic faces. This is in general agreement with the work of Lee, which indicated a birth and spread type of growth could occur only on the basal face. The smallest nucleation feature appears to be in the range 20-50 nm. This is in general agreement with the denser features in Gerson's 1998 cryovitrification work and with Fleming's predicted clustering.
4.4.3 Physical Growth Mechanism
From the combined evidence above, a growth mechanism should describe the following:
- Slow growth by addition of aluminate or polyaluminate units at steps in the prismatic or basal planes.
- Rapid growth by the addition of pre-crystalline clusters at step sites on the basal plane.
- Nucleation by pre-crystalline clusters at the basal plane (at high s ).
The following diagram proposes a physical growth mechanism, based on the evidence:
where the species referred to in reactions 1 to 3 may be any simple aluminate or oligomer, whether ion paired or not, and n , participating in 4 and 5, is a clustered or otherwise pre-ordered species.
An equation for growth, based on this physical evidence, might therefore be similar to:
Where reaction 4 is the basal nucleation step, described by a Birth & Spread mechanism, and the other reactions are governed by a spiral growth type mechanism. It is important to note that each growth reaction has its own area term, A and activation term, E. Eq. (5) is no doubt an oversimplification of the rate equation required to represent the true mechanism.
4.4.4 Chemical Growth Equation
Eq. (5) is a simple description of the proposed physical reaction mechanism. It is also important to describe the chemical dependence of the growth rate (i.e. speciation and surface chemistry dependence) on solution conditions. This is partially accomplished already, by recognising a minimum of two participating species and up to five significant reaction pathways. Any growth equation ought to account for the following:
- Dependence on pre-crystalline cluster formation on the concentration of aluminium, sodium and hydroxide.
- Dependence on cation concentration, water activity or associated effects on speciation.
It would be relatively simple to develop an equation which described the region below or above 3 M NaOH, but the foundation of an equation which will work under a wide range of conditions must account for the whole data set in a single expression.
A speculative (and simplified) model might concentrate on the relatively easily calculated variables: total aluminium concentration and water activity. Dependence on water activity is easily accounted for if a bimolecular reaction, between aluminium containing species and water, occurs at the gibbsite surface. This is in fact partially supported by isotope substitution results (unpublished work, this laboratory) that suggest the gibbsite surface must be re-protonated before growth can occur. Since the pKa of gibbsite is usually in the range 8-9, a largely deprotonated gibbsite surface is expected to exist in Bayer liquors. There is no doubt that cation activity and speciation also have a role to play in determining growth rate, but in the absence of data for species activities, and water activity strongly influencing or being influenced by the other factors, the present work uses water activity alone as an overall measure of these variables.
Cluster or active species formation should be a direct function of aluminium concentration and possibly a function of hydroxide, sodium and water activities. Unfortunately, this demands a statistical fit of a model to the data and is further complicated in that the reaction pathway is unknown and difficult to guess, even with semi empirical molecular modelling (Soar, 1999). Therefore, the concentration of a pre-crystalline cluster or active species was expressed as an appropriate function of [Al] and [H2O]. Assuming unit activity, both of these are converted into true driving forces, m :
The isothermal data in Fig. 2 was therefore fitted to the simplified model:
assuming that growth at the supersaturations used in Fig. 2 resulted in only spiral growth (although close to the s =1.69 limit found by Lee, the majority of growth should be spiral) and assuming that the A and k terms for spiral growth in Eq. (5) are similar and can be averaged.
The fit (shown as the dotted line in Fig. 2) gave good correlation and low, uncorrelated residuals with the data from Fig. 2 for the following equation (assuming unit activity):
which implies a relationship between the "active species", supersaturation and gibbsite formation which involves water:
where water is involved in either a speciation reaction or surface reprotonation, or both. Solvation requirements during the production of an active species (as suggested by Raman spectroscopy and by ab initio QM calculations) may also account for this sensitivity to water activity. Factors other than water activity (e.g. the formation of ion pairs and surface-solute or surface-cation interactions) cannot be ruled out, but water activity would seem to be an important factor which is at least related to these other phenomena. In particular, the effect of water activity on the formation of a key "precipitation pathway" species such Gale's dimer or Moolenaar's dimer, should be considered further.
Equation 8 does not show any temperature dependence because it was generated using isothermal data. Lee suggests an activation energy of 99-105 kJ/mol is appropriate for the spiral growth mechanism on gibbsite, depending on the face being studied. Estimates from this laboratory suggest a value 100± 8 kJ/mol.
Recent progress in understanding the speciation and growth kinetics of gibbsite is beginning to make possible the application of fundamental knowledge to derive a growth rate equation, rather than being restricted to the traditional empirical data fitting methods. While the study is incomplete at this time, such an approach promises the ability to compare kinetic data from different experiments on a common footing, now that the important solution parameters are becoming better understood. The equation presented here requires much refinement, especially when the consequences of impurities on speciation and the transition from spiral to birth-and-spread mechanism are better understood.
The authors would like to thank the sponsors of the AMIRA P380B Fundamentals of Precipitation project: Alcoa of Australia, Billiton, Comalco, MERIWA, Nabalco, Queensland Alumina and Worsley Alumina. The financial assistance of the Australian Federal Government through its Cooperative Research Centres program is gratefully acknowledged.
Brown, N. (1972). Kinetics of crystallization of aluminium trihydroxide from seeded caustic aluminate solutions of industrial composition, Proc. Conf. ICSOBA (Czech).
Buvári-Barcza, Á., Rózsahegyi, M., Barcza, L. (1998). Hydrogen bonded associates in the Bayer process (in concentrated aluminate lyes): the mechanism of gibbsite nucleation, J. Mater. Chem., 8, 451-455.
Dibrov, I.A., Mal'tsev, G.J., Mashovets, V.P. (1964). Saturated vapour pressure of caustic soda and sodium aluminate solutions in the 25 - 350° temperature range over a wide range of concentrations, J. Appl. Chem. USSR, 37, 1907-1915.
Fleming, S., Rohl, A.L., Gale, J.D. (1998) Personal communication.
Friej, S. (1998). AFM measurements of crystal growth, Thesis (PhD) Curtin University of Technology
Friej, S., Lee, M-Y, Parkinson, G.M. (1999). AFM and optical measurements of gibbsite growth, 5th Int. Alumina Quality Workshop (Bunbury, WA).
Gale, J.D., Rohl, A.L., Watling, H.R., Parkinson, G.M. (1998). Theoretical investigation of the nature of aluminium-containing species present in alkaline solution (submitted for publication).
Gerson, A., Addai-Mensah, J., Counter, J., Soar, T., Watson, J (1998). Nucleation mechanism of gibbsite from Bayer liquors, Light Metals , 167-172.
King, W.R. (1973). Some studies of alumina trihydrate precipitation kinetics. Light Metals, 551-563.
Lee, M.-Y. (1998). Growth of gibbsite from caustic aluminate solutions. Thesis (Ph.D) The University of Western Australia.
McCoy, B.N., Dewey, J.L. (1982). Equilibrium Composition of Sodium Aluminate Liquors. Light Metals, 173-185.
Misra, C., White, E.T. (1971). Kinetics of crystallization of aluminium trihydroxide from seeded caustic aluminate solutions, AICHE Symposium series, 67, (116), 53-65.
Moolenaar, R.J., Evans, J.C., McKeever, L.D. (1970). The structure of the aluminate ion in solutions at high pH, J. Phys. Chem., 74, 3629-3636.
Mullin, J.W. (1994). Crystallization, Butterworth-Heinemann (Oxford), 3rd Ed.
Radnai, T., May, P.M., Hefter, G., Sipos,P. (1998). Structure of aqueous sodium aluminate solutions: a solution X-ray diffraction study (submitted to J. Phys. Chem.).
Sipos, P., Capewell, S.G., May, P.M., Hefter; G., Laurenczy, G., Lukács, F., Roulet, R. (1998). Spectroscopic Studies of the chemical speciation in concentrated alkaline aluminate solutions, (submitted to J. Chem. Soc. Dalton).
Sipos, P., Capewell,S.G., May, P.M., Hefter; G.T., Laurenczy, G., Lukács, F., Roulet, R. (1997). 205Tl-NMR and UV-Visible spectroscopic determination of the formation constants of aqueous thallium(I) hydroxo-complexes, J. Solution Chem., 26, 419-431.
Soar, T., Gerson, A. (1999). Nucleation Mechanisms of Gibbsite as suggested by Computational Molecular Modelling, 5th Int. Alumina Quality Workshop (Bunbury, WA).
Veesler, S., Boistelle, R (1993). About supersaturation and growth rates of hydragillite Al(OH)3 in alumina caustic solutions, J. Crystal Growth, 130, 411-415.
Veesler, S., Boistelle, R (1994). Growth kinetics of hydragillite Al(OH)3 from caustic soda solutions, J. Crystal Growth, 142, 177-183.
Watling, H. (1998). Spectroscopy of concentrated aluminate solutions, Appl. Spectrosc., 52, 250-258.
White, E.T., Bateman, S.H. (1988) Effect of caustic concentration on the growth rate of Al(OH)3 particles. Light Metals,157-162.
Zámbó, J. (1986). Structure of sodium aluminate liquors: molecular model of the mechanism of their decomposition. Light Metals, 199-215.