On the Relationships between the Kinetics and Mechanismsof Gaseous Hydrogen Reduction of Solid Nickel Oxide

T. HIDAYAT, M.A. RHAMDHANI, E. JAK, and P.C. HAYES

Analysis has been undertaken on the kinetics of gaseous hydrogen reduction of solid nickeloxide by considering elementary steps commonly found in gas-solid reactions, i.e., gas-film masstransfer, gas pore diffusion, and chemical reaction. It is demonstrated that these reaction stepsalone cannot account for the observed rates. The analysis has therefore been extended to includerecently obtained microstructural information on the reduction product. The study providesstrong evidence for direct links between the overall reduction kinetics and the changes to thereduction product microstructures generated at the Ni-NiO interface.

DOI: 10.1007/s11663-009-9239-x� The Minerals, Metals & Materials Society and ASM International 2009

I. INTRODUCTION

THE industrial application of the gaseous hydrogenof solid NiO is found in a number of metallurgicalprocesses. In the Caron process[1] carried out in the BHPBilliton Yabulu refinery (Townsville, QLD, Australia),the intermediate product of basic nickel carbonate(BNC) is decomposed to form NiO and, subsequently,the NiO is reduced at high temperature to obtain a high-grade nickel metal. In the Inco Goro process (Vale Inco,New Caledonia), NiO produced by the pyrohydrolysisof nickel chloride solutions is reduced by hydrogen.[2]

The overall reaction of the reduction process can beexpressed as

NiO sð Þ þH2 gð Þ ! Ni sð Þ þH2O gð Þ ½1�

In these processes, the reduction rates and residualoxygen concentrations are important factors that deter-mine the production rates and the value of the final Niproduct, respectively.[3]

The kinetics of reduction of NiO by hydrogen hasbeen studied over a wide range of temperatures,between 155 �C and 1000 �C, and reaction conditions.A review[4] of the literature on this topic has shown thatthere are disagreements between researchers on themagnitudes of the reduction rates, rate-limiting reactionmechanisms, and apparent temperature dependence.The review concluded that the values of the apparentactivation energies could be divided into four catego-ries, which, it was argued, corresponded to condi-tions from gas-phase mass transfer (17 to 22 kJÆmole�1)

to chemical reaction (98 to 133 kJÆmole�1) limitedprocesses.Those studies specifically designed to eliminate the

effects of gas-phase mass transfer from the bulk gas andporous diffusion have included (1) the direct observationof metal nuclei growth on the oxide,[5] (2) thermogravi-metric studies of thin NiO plates[6] and small-sizedspherical pellets,[2] and (3) metallographic studies ofinitial interface growth.[7] Even when the effects of gas-phase mass transfer have been eliminated, these mea-surements have shown that the kinetics of reductionexhibit a range of behaviors. In the temperature range227 �C to 300 �C, the reaction rate appears to beindependent of the hydrogen partial pressure; between300 �C and 400 �C, the rates are of variable order withrespect to the hydrogen partial pressure.[5] At temper-atures above approximately 400 �C, the rate of nickelgrowth varies from p0:5H2

[5] to pH2:[7] At temperatures

above approximately 700 �C, the rate of reduction isactually found to decrease with increasing temperature;above 800 �C, the reaction rate again increases withincreasing temperature.[2,7]

Several factors that contribute to the slowdown inreaction rates have been proposed. In developingmathematical models to describe these high-temperaturereduction rates, it was argued[8] that the slowdown in thenickel oxide reduction rate was associated with thesintering and densification of the product with increas-ing temperature and time. However, a comparison of therates of reduction of NiO that had been partiallyreduced and then subjected to high-temperature thermaltreatment in a neutral atmosphere demonstrated thatthere was no difference in rate with or without thistreatment.[2] This experiment[2] shows that sintering themetal product (or physical changes) alone cannotaccount for the observed rate slowdown. Separatemeasurements[9,10] of the pore sizes of the Ni producthave shown that, in the range 600 �C to 1000 �C, thechanges taking place in the nickel product structureresult in an increase in the pore size; the pore volumes,however, remained relatively constant. This indicates

T. HIDAYAT, Postgraduate Research Student, E. JAK, Director,and P.C. HAYES, Xstrata Professor of Metallurgical Engineering, arewith the Pyrometallurgy Research Centre, The University of Queens-land, Brisbane, QLD 4072, Australia. Contact e-mail: t.hidayat@uq.edu.au M.A. RHAMDHANI, formerly Postdoctoral Research Fellow,Pyrometallurgy Research Centre, The University of Queensland, isLecturer, Faculty of Engineering and Industrial Sciences, SwinburneUniversity of Technology, Melbourne, VIC 3122, Australia.

Manuscript submitted September 2, 2008.Article published online June 11, 2009.

474—VOLUME 40B, AUGUST 2009 METALLURGICAL AND MATERIALS TRANSACTIONS B

that the structural changes in the product took placewith relatively little densification. These findings supportthe argument that the slowdown in the rate of NiOreduction is not associated with the physical changesoccurring in the Ni product.

Other factors that have been proposed[2] as possiblereasons for the slowdown in reduction rates are thesurface segregation of sulfur to the nickel surface andthe decrease in available chemical reaction sites on thenickel surface, or the formation of a thin sulfide film thatcoats the oxide surface. Experiments using dense syn-thetic nickel oxide and pure reducing gas (no sulfurpresent) have shown that, even in sulfur-free systems, aslowdown in the rate at temperatures above approxi-mately 700 �C occurs.[7] The results clearly demonstratethat the cause of the slowdown is not from theinterference of impurities, such as sulfur, with thereduction process. It is interesting to note, however,that the slowdown in the reaction rate was found to beaccompanied by changes in the microstructure of thereduction product.[7]

A number of distinctly different types of nickelproduct structures developed during the gaseous reduc-tion of NiO have been characterized,[9] namely, a coarsefibrous nickel with fissures, a fine porous nickel-planarinterface, a coarse porous nickel-irregular interface, anda dense nickel layer. The conditions of the formation ofthese microstructures have been identified and theirevolution with temperature and time has been system-atically investigated.[10]

Although the reduction of nickel oxide appearssuperficially to be a simple reaction, the factors influ-encing the rates and extent of reduction are still notcompletely characterized. In the present article, thefundamental kinetics and mechanisms of nickel oxidereduction are examined. First, the observed rates of NiOare compared with the rates calculated assuming thatthe elementary process steps commonly found in a gas-solid reaction, i.e., the gas-film mass transfer, gas porediffusion, and chemical reaction, are rate limiting. Next,this analysis is integrated with microstructural observa-tions to provide further evidence of the mechanisms ofNiO reduction. The implications of the findings forindustrial practice are discussed in Section V of thisarticle.

II. EXPERIMENTAL TECHNIQUES

The details of the experimental technique have beendescribed in a previous publication by the authors.[9]

Dense synthetic NiO samples with dimensions of2 9 2 9 1 mm were used. Pure H2, H2-N2, andH2-H2O with various compositions were used as reduc-tants. The reducing gas was injected into a quartzreaction tube with an approximately 10-mm internaldiameter at a total flow rate of 1 lÆmin�1 (25 �C, 1 atm).When the effective cross section of flowing gas aroundthe sample is 6.28 mm2, the linear flow rate of thereducing gas passing over the sample is approximately2.65 mÆs�1. Each sample was directly introduced into thehot zone of the reaction tube and was held in the tube

for selected reaction times. For all of the experiments,the extent of the reactions of NiO to Ni are small, i.e.,the product volume is small compared to the mass of thesample. Therefore, the amount of heat generated perunit total volume is quite small. The high gas velocityacross the surface will also ensure that there are no largetemperature excursions during the reaction. The samplewas then quenched into a bath of liquid nitrogen. As aresult, the morphology developed during the reductionprocess was preserved.Two techniques were used for the preparation of

samples for subsequent analysis of the reduction prod-ucts. The first preparation technique was used for theinternal kinetic measurement. The kinetic measurementswere conducted by measuring the progress of the Ni-NiOinterface on a cross section perpendicular to the samplesurface. This was achieved by using conventional metal-lographic preparation techniques, i.e., mounting thesamples in acrylic resin and polishing with SiC paperand diamond paste from 6 to 0.25 lm. The advantages ofselecting the present technique over a thermogravimetricanalysis approach have been presented in a previousarticle by the authors.[7] The second preparation tech-nique was used to enable observation of the product porestructure without destroying the structure. This wasachieved by fracturing the partially reduced samples inhalf by cutting them perpendicular to the sample surfaceusing a scalpel. The samples prepared from both tech-niques were sputter coated with Pt (Eiko IB-5 sputtercoater, Eiko Co. Ltd., Hitachinaka, Japan) before beinganalyzed using a scanning electron microscope (SEM).Two types of SEM, a PHILIPS* XL-30 and a

JEOL** 6400F, were used in the present work. The

PHILIPS XL-30 operating in backscattered electronmode was used for distinguishing the original nickeloxide and the nickel metal product; this is useful forobtaining information about the kinetics of the Niproduct advancement. The JEOL 6400F, a cold field-emission SEM, on the other hand, was used to acquirehigh-resolution images of the morphology of the frac-tured, partially reduced samples.

III. ANALYSIS OF KINETICSOF NiO REDUCTION

The NiO reduction by hydrogen gas takes placethrough a series of processes involving mass transport,chemical reactions, nucleation and growth. Each of theprocesses may be controlling the overall reductionprocess. In the case of the NiO reduction carried outat elevated temperatures and high hydrogen partial

*PHILIPS is a trademark of Philips Electronic Instruments Corp.,Mahwah, NJ.

**JEOL is a trademark of Japan Electron Optics Ltd., Tokyo.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—475

pressures, the process of the nucleation of the Ni metalproceeds rapidly. The high nucleation frequency resultsin the uniform coverage of the NiO surface by the Niproduct. As the reducing gas constantly consumes theNiO, the Ni metal product layer is observed to contin-uously grow in a direction perpendicular to the solidsurface; the Ni-NiO interface moves toward the NiObulk. The measurements of the kinetics of the NiOreduction in various temperature and gas conditionshave been presented in detail in a previous study by theauthors.[7]

Under conditions inwhich themetal nucleation processtakes place relatively rapidly, a variety of mass transportor chemical reactions may become rate-limiting steps inthe overall reduction process (Figure 1). Figure 1(a)shows a reduction process that is controlled by mass-transfer of hydrogen gas from the gas bulk to the outersurface of the solid through a stagnant boundary layer orgas film surrounding the solid particle. In Figure 1(b), thestagnant gas-film layer does not impose any significantbarrier for the reducing gas; however, the porous productlayer limits the rate of transport of the reducing gas to thereaction interface. In cases in which the mass transport ofthe reducing and product gases are rapid, the rate-limitingsteps of the overall process may be associated with thevarious chemical reactions at the metal-oxide interfaceand mass transfer in the condensed phases, as shown inFigure 1(c).

It has been shown previously that it is valid toconsider that the thickness of the Ni product resulting

from the reduction process is equal to the thickness ofthe NiO consumed by H2.

[7] Consequently, the rate ofthe reduction process is proportional to the rate of theNi product advancement. Because the synthetic oxidesamples with plate geometry have been used in thepresent study and considering a one-dimensional (1-D)analysis, the following relationships apply:

JO ¼1

s

dnOdt¼ qNiO

MNiO

1

s

dVNiO

dt½2a�

dx

dt¼ JO

MNiO

qNiO

½2b�

where JO is the flux of oxygen removal (moleÆm�2Æs�1);nO represents the moles of oxygen (mole); t is time (s);s is the surface area of oxide (m2); x is depth ofpenetration (m), which equates to the thickness of thenickel oxide that is consumed by hydrogen gas, closelyapproximated with the thickness of the Ni product; andMNiO, qNiO, WNiO, and VNiO represent the molecularweight, density, sample weight, and sample volume,respectively, of NiO.In this section, a detailed 1-D kinetic analysis is

carried out. It is assumed that the oxide sample is aninfinite plate and that only one side of the plate isconsidered for the analysis. Using this technique ofanalysis, advancements in the Ni product thicknessunder the influence of various controlling steps areevaluated. It is further assumed that each controlling

Fig. 1—Schematic of the gas profiles under possible limiting conditions in the reduction of metal oxide by hydrogen, including those controlledby (a) gas-film mass transfer, (b) pore diffusion, and (c) chemical reaction.

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step operates individually without the influences of othercontrolling step. The results of the analysis can be usedto determine the rate-controlling processes of the NiOreduction for the conditions investigated in the presentstudy. Several rate-limiting processes considered in thepresent analysis are summarized in Table I.

The partial pressure of hydrogen in equilibrium withNi-NiO approaches zero (e.g., 0.51 pct H2-99.49 pctH2O at 700 �C); hence, it can be assumed that pH2;eq

equals 0. The mass-transfer coefficient (km) for a gasflowing over a sphere can be calculated using the Rantz–Marshall formula.[11] A characteristic dimension, e.g.,an equivalent diameter for a nonspherical particle, isused for the Rantz–Marshall formula in the presentcalculations.

In the calculation of the effective binary diffusivitycoefficient DH2-H2O;eff

� �; the porosity-to-tortuosity ratio

(e/s) of approximately 0.06, as reported by DebRoy andAbraham,[12] is used in the calculation with the assump-tion that the value is independent of temperature. Fromthe measurement of pore sizes,[10] it was found that theNiO reduction carried out in the present study takesplace in the transition region between Knudsen andmolecular diffusion.[13] In the transition region, both ofthe diffusion mechanisms are operative and the com-bined diffusivity of the Knudsen and molecular diffu-sions has been considered.

The data used to obtain the apparent chemicalreaction rate constants were obtained for the NiOreduction in pH2

¼ 100 pct and 1 atm pressure in therange 227 �C to 700 �C, as measured using the cross-sectional analysis technique,[7] the direct observation ofnuclei growth,[5] and thermogravimetric studies of thinfoils.[6] All of these experiments are specifically designedto eliminate any limitation associated with gas-transferprocesses; all give very similar rate data in this temper-ature range. The initial rates shown in Figure 2 wereobtained using the cross-sectional analysis technique fortimes as short as 5 seconds. These initial rates, when theproduct layer is very thin, are the least likely to beinfluenced by gas-phase mass transfer or porous gasdiffusion.

It has therefore been assumed that the low-tempera-ture data represent the ‘‘chemical reaction rate’’ and aredescribed by the Arrhenius equation:

kc ¼ k exp � Q

RT

� �½6�

where k is the frequency factor (mÆs�1), Q is the activa-tion energy (JÆmole�1), R is the gas constant(JÆmole�1ÆK�1), and T is temperature (K). Using theArrhenius law, the rates of NiO reduction above700 �C are calculated using the activation energy mea-sured from experiments between 500 �C and 700 �C(Q = 66.6 kJÆmole�1). The results of the calculationare shown as a dashed line in Figure 2. Finally, theprogress of the Ni product thickness (x) as a functionof time in the present analysis is determined from theinitial reaction rates (ki):

x ¼ kit ½7�

where ki (mÆs�1) equals MNiOkcpH2;bulk

�qNiORT;

obtained under the assumption that the rate of theoverall process is controlled by chemical reaction.A summary of the parameters and data used in the

present analysis of the reaction kinetics is provided inthe Appendix (Tables II and III). A kinetic analysis ofthe oxygen removal during the NiO reduction at variouslimiting conditions may give an indication as to whichstep controls the overall rate of the reduction process.To determine which subprocess is controlling the overallNiO reduction process, a comparison of the extent ofthe NiO reduction under several limiting conditions iscarried out. By substituting Eq. [2] into each equation inTable I, a kinetic model of the Ni product thickness as afunction of time for each individual controlling processcan be acquired. Comparisons of Ni product thicknessesas a function of time in the NiO reduction using 100 pctH2 (1 atm) obtained from the actual experiments, andfrom kinetic models at various limiting conditions andtemperatures are provided in Figure 3.The thicknesses of the Ni product as a function of

time in Figure 3 are presented in log-log scale. Usingthis presentation, the magnitude of each subprocessrelative to others can be seen clearly. In all temperatures,it can be seen that the extent of the reduction under theinfluence of the gas-film mass transfer would be far

Table I. Rate-Limiting Processes in Gas-Solid Reactions

Process Equation for 1-D Analysis

gas-film mass transfer JO ¼ kmRT pH2;bulk � pH2;eq

� �3½ �

gas pore diffusion JO ¼DH2�H2O;eff

xRT pH2;bulk � pH2 ;eq

� �4½ �

chemical reaction JO ¼ kcRT pH2;bulk � pH2;eq

� �5½ �

where km is the gas-phase mass-transfer coefficient (mÆs�1); R is the gasconstant (m3ÆatmÆmole�1ÆK�1); T is the temperature (K); pH2 ;bulk andpH2 ;eq are the partial pressures of hydrogen in the bulk and at metal-oxide equilibrium (atm), respectively; DH2�H2O;eff is the effective binarydiffusion coefficient for H2 and H2O mixtures (m2Æs�1); x is the productlayer thickness (m); and kc is the interfacial chemical rate constant(mÆs�1).

Fig. 2—Measured initial rates of NiO reduction between 0 and 5 susing 100 pct H2 (1 atm) between 500 �C and 1000 �C.[7]

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—477

greater than the extent of the reductions carried outunder the influence of the gas pore diffusion or chemicalreaction. This confirms the view that the presentexperimental technique is able to eliminate the limita-tions introduced by the stagnant gas film surroundingthe solid sample. Hence, it is acceptable to rule out gas-film mass transfer from the list of processes that may

limit the overall reduction process. Further discussionwill be focused on the influence of the gas pore diffusionand chemical reaction.At low temperatures, between 500 �C and 600 �C, the

plots of the Ni thickness obtained from the actualmeasurements are identical to those from the results ofthe analysis assuming that the process is chemically

Fig. 3—Comparisons of Ni product thickness as a function of time in NiO reduction using 100 pct H2 (1 atm) obtained from experiments andcalculated from kinetic analyses at various limiting conditions: (a) 500 �C, (b) 600 �C, (c) 700 �C, (d) 800 �C, (e) 900 �C, and (f) 1000 �C.

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controlled. This is because the chemical rate in theanalysis was derived from the initial reaction rates of theactual measurements (Eq. [7]). It is also observed thatthe extent of the NiO reduction to any thickness up toapproximately 100 lm under the rate of the gas porediffusion is higher than the extent of the NiO reductionunder the influence of a chemical reaction. The differ-ences in the Ni thicknesses of both of the limitingconditions become less as the reaction temperature isincreased.

Between 500 �C and 600 �C, the increase in the timeof the reduction results in a decrease in the difference inthe extent of the predicted reductions for the porediffusion and chemical reaction limiting conditions. Astemperatures approach 700 �C, the relative rates of thechemical reaction and gas pore diffusion become com-parable in magnitude. It can be seen that, at 700 �C, theplot of the Ni thickness of the chemical-reaction-controlled reduction approaches that of gas-pore-diffusion-controlled reduction. Figure 3(c) shows thatthe extent of the NiO reduction for both mechanisms, ifthey are operating independently, will be equal atapproximately 1 minute or a 292-lm product thickness.As the temperature increases, the time required for bothlimiting conditions to have the same extent of reductionbecomes shorter. It can also be seen that, above 700 �C,the plots of the Ni thickness obtained from the actualmeasurement are all lower than those obtained from thetheoretical calculations. It appears that 700 �C is thetemperature at which changes in the rate-controllingreaction mechanism of the NiO reduction take place.From this analysis, it might be reasonably expected,based on observation in analogous systems, that thechanges in the rate-controlling process takes placegradually, i.e., from chemical control at low tempera-tures and small product thickness, to mixed control atintermediate temperatures, and to gas-pore-diffusioncontrol at high temperatures and large productthicknesses.

To investigate the possibility of changes in theapparent rates due to the transition in the rate-control-ling process, kinetic analysis is carried out with respectto the NiO reduction process in 100 pct H2 (1 atm) at800 �C; the influence of the mixed control of thechemical reaction and gas pore diffusion on the extentof the NiO reduction is considered. It has been shownthat, in the mixed-control processes, the time required toreach certain stages of conversion will be equal to thesum of the times that would be needed if each resistanceacted alone.[14] By using Eqs. [2], [4], and [7], the relationbetween the total time (ttotal) and the Ni thickness underthe mixed control of the chemical reaction and gaspore diffusion can be determined from the followingequation:

ttotal ¼x

kiþ qNiORTx2

MNiODH2-H2O;effpH2;bulk

½8�

Based on Eq. [8], the nickel thickness resulting fromthe NiO reduction, using 100 pct H2 (1 atm) at varioustimes under the mixed control of the chemical reactionand gas pore diffusion, can be calculated. The resultsof the calculations for the NiO reduction carried outat 800 �C using 100 pct H2 (1 atm) is provided inFigure 4(a). It can be seen that, when the mixed-controlcondition is considered, the rate of reaction under thiscondition is lower than each of the independent limitingsteps. However, the measured extent of the reduction atall times is still much lower than was predicted assumingmixed-control conditions. The relative rates of the mass-transfer and chemical reaction steps for the NiOreduction have been calculated for a range of hydrogenpartial pressures. The example of a calculation carriedout for the NiO reduction at 600 �C using 26 pct H2-N2

(1 atm) is shown in Figure 4(b). The analyses of all thesecases show that none of the limiting processes consid-ered in the present analysis contributes to the slowdown

Fig. 4—Comparisons of Ni product thickness as a function of time obtained from experiments and kinetic analyses at various limiting condi-tions indicated (a) NiO reduction at 800 �C using 100 pct H2 and (b) NiO reduction at 600 �C using 26 pct H2-N2.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—479

in the apparent rate. The results of the calculationsindicate that the anomalous behavior in the NiOreduction above 700 �C is not due to factors related tothe influence of the chemical reaction and gas porediffusion, or their combination.

IV. FORMATION MECHANISMSOF MICROSTRUCTURE DEVELOPEDDURING GASEOUS NiO REDUCTION

Four types of nickel product structures developedduring the reduction process were identified,[9] namely:(1) a coarse fibrous nickel with fissures, (2) a fine porousnickel-planar interface, (3) a coarse porous nickel-irregular interface, and (4) a dense nickel layer. Theconditions for the formation of these structures havebeen identified and described in a previous study.[10] Inthis section, an investigation of the formation mecha-nisms of each product is carried out by considering theformation conditions, microstructural information, andelementary processes involved.

A. Coarse Fibrous Nickel with Fissures

The surface appearance of the coarse fibrous nickelwith fissures resulting from a NiO reduction carried outat 300 �C using a pure H2 atmosphere is shown inFigure 5(a). It can be seen that circular, isolated Ninuclei are formed with a star-shaped cracking patterndevelop from the middle of the nucleus. The Ni nucleiappear to grow at the same rate in all directions,independent of the presence of fissures. A carefulexamination of the cross sections shows that thestructure consists of nickel in the form of fibrous metalseparated by fissures that appear to follow the directionof the growth of the metal nuclei (Figure 5(b)). Theformation of a fissured structure has also been observedin other metal oxide systems. In the reduction of CoO inH2-N2 mixtures,[5] the Co nucleus with a star-shapedcracking pattern was observed after the CoO wasreduced at 210 �C using 97 pct H2-N2. A similar

structure was also found in the reduction of magnetiteand tungsten oxide. Large radial fissures were observedat the middle of the iron nuclei during the reduction ofmagnetite below approximately 550 �C; in addition tothe large radial fissures, the iron nuclei containedextensive micropores.[15,16] In the reduction of tungstenoxide,[17] it was found that, when the WO2.96 wasreduced to metal with hydrogen gas between 500 �C and700 �C, a star-shaped cracking pattern was formed onthe solid surface. It was suggested that the star-shapedcracking pattern is formed due to a local contraction ofthe product during the reduction process.Examination of the metal-metal oxide interface of

partially reduced NiO (300 �C using 100 pct H2) wascarried out using an SEM; the results of these observa-tions are provided in Figure 6. An example of thestructure of the Ni-NiO interface and Ni product isshown in Figure 6(a). A number of structures can be seenon this fractured interface. At locations 1 and 2 inFigure 6(a), the internal structure of the Ni product isexposed by the fracturing technique. Location 3, on theother hand, shows a portion of the surface of the Niproduct adjacent to the large cracks or fissures in theproduct. The detail of location 1, shown in Figure 6(b),reveals the presence, at the Ni-NiO interface, of thin Niplates approximately 10-nm thick oriented perpendicularto the interface, with a spacing of 15 to 50 nm. Thepresence of thin, aligned Ni plates within the product hasbeen reported in a previous study.[10] It appears that thethin platelike Ni found in the coarse fibrous nickel withfissures is the initial structure developed by the reductionprocess. The formation of a platelike metal structure hasalso been observed in the gaseous reduction of solidcalciowustites.[18] Since the edges of the platelike Niproducts have a high curvature and the plates haverelatively close spacing, they join/sinter together duringthe reduction process; this results in the geometry shownin location 2 (Figure 6(c)). In location 2, the thicker Niproduct is apparently formed as a result of sintering ofneighboring Ni plates. In order to reduce their surfaceenergy, the edges of the Ni plates become rounded andprogress to form equiaxed nickel particles/grains 0.02 to

Fig. 5—SEM secondary electron images of reduction product resulting from NiO reduction at 300 �C using 100 pct H2 (1 atm): (a) surface ofreduction product (1-min reduction) and (b) cross section of reduction product (30-min reduction).

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0.1 lm as found in location 3 (Figure 6(d)). The rate ofthe NiO reduction at 300 �C using pure hydrogen wasmeasured. It was found that the rate of the Ni-NiOinterface advancement at this condition is approximately1.9 lmÆmin�1. The distance between locations 1 and 2,that is, approximately 1.5 lm, indicates that the struc-ture at location 2 has been exposed at 300 �C forapproximately 1 minute. It appears that this relativelyshort holding time at this temperature is sufficient tosinter the thin Ni plates (location 1) to formNi structuressuch as those at location 2. The rearrangement toward amore stable structure, in this case a nearly equiaxed grainstructure, can be seen clearly near the Ni surface(Figure 7). The area close to the Ni surface has beenexposed to heating for a longer time, i.e., 30 minutes.The grain size at 300 �C after the extensive holding timehas increased to 0.1 to 0.2 lm diameter.

The sintering of the nickel during the course ofreduction at these low temperature leads to a nickelproduct with a lower volume compared to the mainoxide and also leads to the formation of fissures/cracksto compensate for the difference in volume. Althoughthe agglomerates appear at low magnification to bedense, analysis by transmission electron microscopy[10]

has shown that these structures are actually composedof fine loosely bound polycrystalline nickel. As a result,the fissures may propagate easily throughout this fragilemetal product. The evidence appears to support the

hypothesis[17] that the mechanism of the formation ofstarlike fissures is the result of local contraction in themetal product. The fissures were not observed in theNiO reduction at temperatures above 400 �C. It appearsthat, at high temperatures, nickel products are createdwith wider spacing. In this structure, the difference in thevolume between the metal and the oxide is compensatedby the formation of a porous network structure.

Fig. 6—Details of nickel product structure resulting from reduction at 300 �C using 100 pct H2 for 30 min.

Fig. 7—Cross-section of the coarse fibrous nickel with fissures in thesurface region (300 �C, 100 pct H2, 30 min).

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B. Microporous Structure

A transition in the microstructure from a structure ofcoarse fibrous nickel with fissures to a porous structuretakes place as the reduction temperature is increasedabove 400 �C in pure hydrogen. The transition is alsofound to be dependent on the hydrogen partial pressure.In this porous structure, the metallic product consists ofcontinuous networks of pores that provide directcontact between the gaseous reactant and the solidoxide. To investigate the mechanisms of formation ofthe porous structure, reduction experiments were carriedout in low chemical driving force gas mixtures, in orderto create a condition in which the reduction process isrelatively slow and the progress of the experiment can bereadily followed. The surface of the reduction productresulting from the reduction at 600 �C using 14.5 pctH2-H2O (equal to a Gibbs energy driving force of�53 kJÆ(mole O2)

�1) for 30 seconds is shown inFigure 8. Figure 8(a) shows the SEM secondary electronimage of the product surface, while Figure 8(b) showsthe SEM backscattered electron image of the sameproduct surface. The SEM backscattered electron imageis more sensitive to differences in the mean atom numberof the phases, thus increasing the contrast between theNiO and Ni. It can be seen that two different types

of instabilities are formed on the NiO surface, namely,instabilities that are surrounded by nickel metal andinstabilities that are formed without nickel metal. Theresults suggest that the instabilities are initially formedon the NiO before the nickel metal starts to nucleate.The formation of a porous structure that is initiated

by the formation of instabilities has been proposedpreviously.[19] The mechanisms of the formation ofinstabilities themselves have been explained.[20,21] It wasargued that, under conditions in which the chemicalreaction rates are higher relative to the mass transportrates, the extensive removal of oxygen from the oxidesurface takes place; this creates a high gradient of Niions between the surface and the bulk of the solid(Figure 9(a)). Because the rates of mass transport arerelatively lower than the rates of chemical reaction, anyperturbations on the oxide surface will result in a localvariation in the mass transport process and, eventually,in differences in rates of Ni cation removal at thatlocation. This condition leads to a nonplanar decom-position resulting in small tunnels or instabilities priorto the nucleation process (Figure 9(b)). Because theoxide surface surrounding the instabilities is supersatu-rated with Ni cations, nucleation of the Ni metal willoccur (Figure 9(c)). The geometry of the tip of the

Fig. 8—Surface of reduction product resulting from the reduction of dense synthetic nickel oxide at 600 �C using 14.5 pct H2-H2O (1 atm) for30 s: (a) SEM secondary electron image and (b) SEM backscattered electron image.

Fig. 9—Initiation of porous structure during the reduction of dense metal oxide: (a) gradient between the surface and bulk solid is established,(b) instability is formed, and (c) instability develops into small tunnel with metal product nucleating at the wall of the tunnel.[20,21]

482—VOLUME 40B, AUGUST 2009 METALLURGICAL AND MATERIALS TRANSACTIONS B

instability provides a high flux of Ni removal andprevents the supersaturation of Ni ions at the tip.Consequently, direct contact between gaseous reactantand oxide phase will be maintained at the tip of theinstability.

1. Instability CriteriaThe critical conditions for the growth of instabilities

on the oxide surface can be derived using the perturba-tion analysis approach. This approach has been used todescribe the relative stabilities of solid surfaces duringthe solidification of metal alloys.[22] In alloy solidifica-tion, it is possible to obtain a planar solidification frontor, cellular or dendritic growth morphologies. Thepossibilities for the growth and elimination of pertur-bations are examined by considering the degree ofconstitutional undercooling of the melt, which is directlyrelated to the solute concentration, and the effect of thecurvature of the solid interface. In the present study, asimilar analysis can be undertaken by consideringanalogous parameters that are applicable to gas-solidreaction processes.

Figure 10 shows a schematic example of a perturbedsolid surface developed after exposure to a reactive gasmixture for a particular reduction period. As a result ofthe different rates of mass transport and elementaryreactions in the interface region, the tip of the concaveinstability contains a lower concentration of cationsrelative to that at the unperturbed surface. For thepurpose of analyzing this phenomenon, it is assumedthat the geometry (height (z)) of the perturbed surfacefollows a simple sinusoidal function:[22]

z ¼ e sin2pky

� �½9�

where e is the amplitude of the perturbation and 2p/k isthe wave number.

The Gibbs free energy of the oxide at any point on theinterface (G*), can be deduced from the assumption oflocal equilibrium:

G� ¼ Gb þ C�dG

dC

� �

ox

þ �VrK � ½10�

where Gb is the Gibbs free energy of the bulk oxide, C*is the difference in chemical composition between any

given point on the interface and the bulk phase,dG=dCð Þox is the change in Gibbs free energy of theoxide associated with change in composition ofthe oxide, �V is the molar volume of the oxide, r is thesurface energy of the oxide, and K* is the curvature ofthe solid surface. In this equation, the second term onthe right describes the change in Gibbs free energy of theoxide associated with compositional differences on theinterface, the last term of the equation is the effect ofshape of the interface on the Gibbs free energy of theoxide (Gibbs–Thompson effect[23]).Considering the difference of the Gibbs free energy of

the oxide between the tips (t) and depressions (d) of theinterface, the following equation is obtained:

Gt � Gd ¼dG

dC

� �

ox

ðCt � CdÞ þ �VrðKt � KdÞ ½11�

Assuming the Gibbs free energy of the oxide and con-centration gradients in the oxide are unaffected by thepresence of small perturbations, the difference ofGibbs free energy of the oxide between the tips anddepressions can be expressed as follows:

Gt � Gd ¼ 2edG

dz

� �

g

½12�

where dG=dzð Þg is the Gibbs free energy gradient in theoxide generated by the presence of the reactant gas. Asimilar analysis can be used to describe the differenceof concentration between the tips and depressions:

Ct � Cd ¼ 2edC

dz

� �½13�

The curvatures at the surface perturbation extrema canbe determined from the second derivative of theEq. [9] at y = k/4 and 3k/4:[22]

Kt ¼ �Kd ¼4p2e

k2½14�

Note that the curvature is positive when the centers ofits radii lie on the side of the solid (convex surface)and vice versa. By substituting Eqs. [12], [13], and [14]into Eq. [11], the following relationship is obtained:

2edG

dz

� �

g

¼ dG

dC

� �

ox

2edC

dz

� �þ 2 �Vr

4p2e

k2

� �½15a�

and rearranging

dG

dz

� �

g

� dG

dz

� �

ox

¼ 4p2 �Vr

k2½15b�

where UI ¼ dG=dzð Þg� dG=dzð Þox is the difference in

thermodynamic gradients imposed by: i) the Gibbs freeenergy differences between the reacting gas and thesolid, and ii) the composition differences in the solid.Consequently:

k ¼ 2p

ffiffiffiffiffiffiffi�VrUI

s

½16�

Fig. 10—Idealized model of interface perturbations at gas-solidinterface.[22]

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—483

By using an analogous approach to instability formation

to that adopted in solidification systems,[22] it can beshown that Eq. [16] describes the critical wavelength (kc)below which the curvature effect will dominate; as aresult, any perturbations will be eliminated and theplanar decomposition of oxide will result. If the wave-length is greater than this critical value, the interface willbecome unstable and the perturbation will grow inmagnitude, i.e., the amplitude (e) of the perturbationwill progressively increase with time.

2. Transition between Fine Porous-Planar Interfaceand Large Porous-Irregular Interface

In the current study, two types of porous Ni prod-uct structures were observed, namely, a fine porousnickel-planar interface (Figure 11(a)) and large porousnickel-irregular interface structures (Figure 11(b)). Theinitiation of both structures may take place through thesame process, which is schematically shown in Figure 9.The transition from one structure to the other isdependent on the characteristics and properties of theoxide and metal, and on the reduction parameters,namely, temperature, gas composition, and time.

The transition from the planar to the irregular growthinterface during the gaseous reduction of nickel oxidecan be explained as follows. The planar growth mor-phology corresponds to a reaction mechanism thatinvolves a cooperative/coupled growth of the nickelmetal product and the simultaneous decomposition ofthe oxide surface. The interface and the various sub-processes active during this reaction are shown inFigure 12. Oxygen is removed by chemical reactionfrom the surface of the oxide and from the nickel metal.The rate of oxygen removal is a function of the gascomposition and temperature. The resulting excess of Nications at the oxide surface diffuses by surface and bulkdiffusion mechanisms to the existing nickel metal thatforms the metal pore walls.

Under steady-state conditions, the rate of oxygenremoval by the chemical reaction at the interface will beequal to the diffusive flux of nickel cations to the pore

wall; these are related directly to the interface velocity, V(mÆs�1):

V ¼MNiO

qNiO

k1pH2� k2pH2Oð Þ ¼ D

RT

Dld=2ð Þ ½17�

where MNiO=qNiO is the molar volume of the NiO(m3Æmole�1); k1 and k2 are the chemical reaction rateconstants (moleÆm�2Æatm�1Æs�1); Dl is the chemicalpotential driving force for diffusion (JÆmole�1); D isthe diffusion coefficient of Ni cations (m2Æs�1); R is thegas constant (JÆmole�1ÆK�1); T is the absolute temper-ature (K); and d/2 is the radius of the pores (m) formedat the interface, assuming cylindrical pores are formed.A similar equation of the growth mechanism of thissteady-state situation has been proposed earlier by otherresearchers.[24] It can be seen that, for a given thermo-dynamic driving force, the rate of the chemical reactionwill determine the pore size at the Ni-NiO interface. It isnow possible to apply the previously described stabilitycriteria to this situation.Consider the situation for a fixed value of Dl, in

which the partial pressure of hydrogen in the gasmixture is decreased. Because in cooperative growth thechemical reaction rate and the cation diffusive flux arelinked through Eq. [17], a reduction in the chemical rate

Fig. 11—Types of porous structure formed during the reduction of dense synthetic nickel oxide: (a) fine porous nickel-planar interface and(b) large porous-irregular interface.

Fig. 12—Schematic of metal-oxide interface geometry during cou-pled/cooperative porous growth.

484—VOLUME 40B, AUGUST 2009 METALLURGICAL AND MATERIALS TRANSACTIONS B

will result in an increase in the pore diameter d. At somevalue of pH2

; the pore diameter will exceed kc, the criticalwavelength for stability of the interface given byEq. [16]. At pore sizes greater than this critical value,the oxide surface is inherently unstable, i.e., the planaroxide surface will spontaneously move at differentvelocities at different points on the surface. The resultwill be the formation of instabilities or tunnels in theoxide; the resulting interface geometry is illustratedschematically in Figure 13. The onset of instabilities atthe interface signals the end of the cooperative/coupledgrowth mechanism; the geometries of the instabilitiesbecome independent of the presence of the nickel metal.

The departure from the cooperative growthmechanismcan also be the result of the increasing temperature of thereduction process. The activation energy of the solid-statediffusion processes is considerably greater than thechemical reaction. For example, the activation energy ofthe self-diffusion of Ni in NiO was found to be 191 kJ,[25]

while the apparent activation energy of the chemicalreaction obtained in this experimental work was 66.6 kJ.As a result, the changes in temperature will, in relativeterms, affect the solid-state diffusion process to an extentgreater than the chemical reaction. Based on Eq. [17], fora given interface velocity, an increase in the diffusion raterelative to the chemical rate will be compensated for by anincrease in the pore diameter (d); the increase in the porediameter will eventually lead to the oxide surface becom-ing unstable, as explained earlier. The metallographicevidence demonstrating the increasing pore size of theplanar coupled interface with increasing temperature andthe transition from a fine porous nickel-planar interfaceto large porous nickel-irregular interface structures withincreasing temperature is provided in previous work onthis topic by the authors.[10]

The rate of growth of the pore tip of the perturbationor instability will, in each case, be determined by thediffusive flux of Ni2+ cations away from the free oxidesurface and into the bulk oxide. Because the oxidesurface is no longer planar, the diffusive fluxes move inall directions (three dimensions), depending on localconcentration gradients. The pores may resemble linear

or columnar tunnels or, if the tip of the perturbationbecomes more distant from the nickel product, it ispossible that the pore walls may also become unstable,forming side arms to the main instability. This latterstructure closely resembles the analogous ‘‘dendritic’’structures formed during alloy solidification.[22] In thesescenarios, depending on the pore geometry, an increas-ing proportion of the available thermodynamic drivingforce for reaction is expended in driving the masstransport in the bulk solid oxide phase rather than thechemical reaction at the gas-solid interface. It is to beexpected, therefore, that the overall rate of the reductionof the oxide will actually decrease relative to thatexpected from a purely ‘‘chemically controlled’’ rate asthe result of the formation of interface instabilities at theoxide interface. In qualitative terms, this explains theobserved slowdown in the apparent growth rate between700 �C to 800 �C in 100 pct H2. In these cases, the nickelmetal product is still formed on the oxide surface, butfollows behind the tip of the perturbation.

C. Dense Nickel Layer

It has been shown[10] that, at low thermodynamicdriving forces represented by gas mixtures containinglow H2-H2O gas ratios, the oxide surface can becomecovered by a dense metallic nickel layer. If the condi-tions are maintained such that the dense Ni metalpersists, then direct contact between the reducing gasmixtures and the oxide is lost and a catastrophicreduction in the overall rate of reduction of the oxidesample occurs. The detailed reaction mechanisms occur-ring in these situations are discussed in the followingparagraphs.A series of reduction experiments was carried out

close to the limiting conditions between porous anddense Ni structures. Experiments were carried out at800 �C using 12.5 pct H2-H2O. The micrographs of thereduction products are provided in Figures 14(a)through (d). It can be seen that, under this condition,the nickel nuclei are formed preferentially at the ledgesof the faceted surface (Figures 14(b) and (c)). As thetime progresses, the number of nuclei increase until theoxide surface is completely covered by nickel nuclei(Figure 14(d)).The formation of a dense metal layer in the gaseous

reduction of the metal oxide has been explained previ-ously.[19] It was stated that, under atmospheres that havea low chemical driving force and in the presence of metalnuclei, chemical reaction rates on the metal surface arerelatively faster than on the oxide surface. This condi-tion promotes the removal of oxygen via the metalsurface and, because this process is followed by theattachment of metal ions at the perimeter of metalnucleus, the growth of the metal nucleus predominantlyoccurs at the perimeter of the metal nucleus. If thiscontinues to happen, the metal nucleus will spread onthe surface of the original solid and the entire surface ofthe original solid will be covered by a dense metalproduct layer.The experimental investigations carried out in the

present study confirm that an individual metal nucleus

Fig. 13—Schematic of instability formation at the oxide surface dur-ing gas reduction.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—485

may grow across the oxide surface by the attachment ofcations at the perimeter of the nucleus; the evidencefor this is shown by the circular nuclei observed inFigure 14. Apart from the lateral growth of metalnuclei, the results also suggest that the dense metal layeris promoted by a planar decomposition of oxide. As theplanar decomposition of oxide slowly takes place, anumber of metal nuclei are created (Figures 14(b) and(c)); the nuclei grow laterally and join together until theoxide surface is completely covered (Figure 14(d)).

The dense metal layer that covers the NiO surfaceprevents direct contact between the gaseous reactantand the oxide interface. The subsequent reduction ofthe oxide may only take place if the reactants (H or O)can diffuse through the dense metal product. If the Odiffuses out through the dense layer from the metal-oxide to the metal-gas interface, there will not be anyproblem disposing of the gaseous H2O product fromthe reaction interface; however, when the H is thediffusing component, there will be issue with thedisposal of steam produced from the reaction atthe metal-oxide interface.

A two-stage reduction that involved both an initialreduction of NiO at 1000 �C in atmosphere thatcontains 5 pct H2-H2O for 30 minutes to form an initialdense nickel product on the surface (Figure 15(a)) and asubsequent reduction using 100 pct H2 (1 atm) was

carried out to check the possibility of a subsequentreduction of NiO with a dense Ni product. It can be seenin Figure 15(b) that the introduction of pure hydrogengas (1 atm) at the second stage of the reduction for15 seconds results in the formation of bubbles on themetal surface. As the accumulation of steam under thedense metal layer proceeds, the rupture of the denselayer may occur, providing access for the reducing gas(Figures 15(c) and (d)). If the chemical driving force ofthe reducing gas is in the range of that required for theformation of porous structure, a secondary porousstructure may be formed below the dense nickel layer. InFigure 16, it can be seen that the secondary porousstructure develops extensively under the dense nickellayer. It appears that the passage for the reducing gasprovided by the bursting of the dense metal layer issufficient to create this extensive pore structure.It has been demonstrated in the present study that the

transitions in reaction mechanisms as a function of gascomposition, temperature, and time are the result ofrelative changes in contributions from the elementaryprocesses steps. Transitions in the reaction mechanismlead to changes in the reaction interface geometry andmay influence the overall reduction rate. The presentstudy shows that knowledge of the elementary processesis important in understanding the gaseous reduction ofmetal oxide.

Fig. 14—Sequence of reactions showing the formation of dense nickel on NiO during reduction at 800 �C using 12.5 pct H2-H2O (1 atm) for(a) 2, (b) and (c) 5, and (d) 7 s.

486—VOLUME 40B, AUGUST 2009 METALLURGICAL AND MATERIALS TRANSACTIONS B

V. IMPLICATIONS FOR INDUSTRIALPRACTICE

A slowdown in the rate identified at temperaturesabove approximately 700 �C was observed during the

reduction of Inco Goro NiO.[2] From the observationsmade in the present study, it appears likely that theslowdown in the reaction rate is associated withthe large porous nickel-irregular interface structure.The transition from a continuous cooperative/coupledgrowth mechanism, in which simultaneous chemicalreaction and mass transport processes occur, to a pore(instability) growth mechanism, in which the growth ofits tips is determined by the rate of the solid-statediffusion of cations, appears to be the most likelyexplanation for the observed slowdown.The entrapment of NiO by a dense Ni metal product

during the reduction of BNC/NiO carried out in theBHP Billiton Yabulu refinery was reported by Rhamdhaniet al.[26] The mechanism of formation of the dense metallayers is not straightforward. It was demonstrated thatisothermal reduction at a high temperature and for along time on its own was not sufficient to form the densemetal morphologies.[9,10] What was different about thestudies carried out on the industrial BNC/NiO sampleswas that the reduction was carried out in nonisothermalconditions. It was shown by Rhamdhani et al.[3] that,under the conditions used, the reduction of NiO to Nistarted at temperatures as low as 300 �C; it was onlywhen temperatures reached 700 �C to 800 �C that thereaction was halted by the formation of a dense Niproduct. The reason why the formation of this dense

Fig. 15—Surface of nickel product showing a development of bubbles and subsequent breakdown of Ni layer at 1000 �C: (a) initial samplereduced using 5 pct H2-H2O for 30 min, (b) sample reduced subsequently in 100 pct H2 (1 atm) for 15 s, and (c) and (d) subsequent reduction in100 pct H2 (1 atm) for 1 min.

Fig. 16—Fractured section showing secondary porous Ni growthobtained following initial formation of dense layer structure at1000 �C (initial reduction under 5 pct H2-H2O (1 atm) for 30 min,followed by reduction in 100 pct H2 (1 atm) for 15 s).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—487

metal layer only occurs on nonisothermal reduction isnow clearer, as a result of the present study. At lowtemperatures, the product microstructures are very fine,with nickel metal sheets of spacing 10 to 20 nm beingformed. These structures are highly unstable and, as thetemperature is progressively increased, they undertake aseries of transformations driven by the high surfaceenergy, curvatures, and defect concentrations in theproduct. The evolution of the microstructure leads tothe densification of the Ni product and results in theencapsulation of the oxide.

The phenomenon explained here should not beconfused with the dense nickel layer that can be formedat all temperatures as a result of the reduction processbeing carried out with a weakly reducing atmosphere.The coverage of the oxide surface with metal will, in thiscase, lead to the drastic lowering of the reduction rate,but the origins of these microstructures are verydifferent.

The present study shows that there are many param-eters that need to be considered in order to obtain ahigh-quality nickel product in the hydrogen reduction ofNiO. As identified by Rhamdhani et al.[3,26] for acomplete removal of oxygen at a relatively fast rate, itis recommended that the reactions are carried out by thefollowing:

(a) reducing at temperatures below 700 �C;(b) maintaining high concentrations of hydrogen in the

atmosphere and ensuring the delivery of freshreducing gas to the reaction interface; and

(c) avoiding a slow heating rate in reducing atmo-spheres.

VI. SUMMARY

A detailed analysis has been undertaken on thekinetics of the reduction of dense nickel oxide byhydrogen in the temperature range between 500 �C and1000 �C. It has been shown that the gas-film masstransfer and gas diffusion through the porous productcannot account for the observed anomalous low reac-tion rates in the temperature range 700 �C to 1000 �C. Itis argued that the decrease in the rate in these conditionsis associated with a breakdown in the cooperative/coupled growth mechanism. The transitions in theproduct microstructures between a coarse fibrous nickelwith fissures, a porous planar (cooperative) growth, a

porous-irregular interface, and a dense metal productare explained in terms of the relative rates of thechemical reactions and mass transport processes at theNi-NiO interface.

ACKNOWLEDGMENTS

The authors thank the BHP Billiton Yabulu refineryand the Australian Research Council Linkage program(Grant number: LP0562201) for financial support, andAusAid for providing a scholarship. The authors alsoacknowledge Mr. John Fittock and Dr. Joy Morgan(BHP Billiton Yabulu) for their valuable help and crit-ical discussions.

APPENDIX

In the present study, the combined diffusivity of themolecular and Knudsen diffusion is calculated from thefollowing relationship:[13]

Di;eff ¼es

Di�iiDiK

Di�ii þDiK½18�

The Knudsen diffusivity of H2 is determined based onthe following equation:[13]

DH2K ¼ 97r

ffiffiffiffiffiffiffiffiffiffiT

MH2

s

½19�

where r is the radius of pores in the metal product, Tis the temperature, and MH2

is the molecular weight ofhydrogen gas. While the binary diffusion coefficient ofgases DH2K�H2Oð Þ is calculated using the Chapman–Enskog relation:[13]

DH2�H2O ¼1:858:10�7T3=2 1

MH2

þ 1MH2O

� �1=2

Pr2H2-H2O

XH2-H2O

½20�

where DH2-H2O is the binary gas diffusion coefficient(m2Æs�1), MH2

and MH2O are the molecular weights ofthe two species, P is the total pressure (atm), XH2-H2O isthe collision integral, and r is the force constant in theLennard–Jones potential function (A). The parametersused in the calculation are provided in Tables II and III.

Table II. Force Constants in Lennard–Jones Potential Function and Collision Integral for H2-H2O Mixtures

Individual Gas e/j (K) r (A) M

H2 38.00[27] 2.92* 2H2O 498.18* 3.51* 18Mixture ei�ii/j = [(ei/j)(eii/j)]

1/2 ri�ii = (ri+ rii)/2 Xi�iiH2-H2O 137.59 3.21 5.8Æ10�3(jT/ei�ii)

2 � 1.01Æ10�1T(jT/ei�ii)+1.2148�

*Estimated using e/j = Tc/1.3 and r = 1.18Vb1/3 (Tc and Vb are critical temperature and molar volume at the normal boiling temperature,

respectively.)[13].�Extrapolated from data provided by C.N. Satterfield (valid for jT/ei�ii < 10).[13]

Other experimental parameters used in the calculations are provided in Table III.

488—VOLUME 40B, AUGUST 2009 METALLURGICAL AND MATERIALS TRANSACTIONS B

REFERENCES1. J.G. Reid and J.E. Fittock: Int. Laterite Nickel Symp., TMS,

Warrendale, PA, 2004, pp. 599–618.2. T.A. Utigard, M. Wu, G. Plascencia, and T. Marin: Chem. Eng.

Sci., 2005, vol. 60 (7), pp. 2061–68.3. M.A. Rhamdhani, E. Jak, and P.C. Hayes: Metall. Mater. Trans.

B, 2008, vol. 39B, pp. 218–33.4. J.T. Richardson, R. Scates, and M.V. Twigg: Appl. Catal. A-Gen.,

2003, vol. 246, pp. 137–50.5. W. Pluschkell and B.V.S. Sarma: Arch. Eisenhuttenwes., 1974,

vol. 45 (1), pp. 23–31.6. A.H. Rashed and Y.K. Rao: Chem. Eng. Commun., 1996, vol. 156,

pp. 1–30.7. T. Hidayat, M.A. Rhamdhani, E. Jak, and P.C. Hayes: Metall.

Mater. Trans. B, 2009, vol. 40B, pp. 1–16.8. J. Szekely and J.W. Evans: Chem. Eng. Sci., 1971, vol. 26,

pp. 1901–13.9. T. Hidayat, M.A. Rhamdhani, E. Jak, and P.C. Hayes: Miner.

Eng., 2008, vol. 21 (2), pp. 157–66.10. T. Hidayat, M.A. Rhamdhani, E. Jak, and P.C. Hayes: Metall.

Mater. Trans. B, 2009. doi:10.1007/s11663-009-9247-x.11. J. Szekely, J.W. Evans, and H.Y. Sohn: Gas-Solid Reactions,

Academic Press, Inc., New York, NY, 1976, pp. 10–22.12. T. DebRoy and K.P. Abraham: Physical Chemistry of Process

Metallurgy: The Richardson Conf., Institute of Mining and Met-allurgy, London, 1973, pp. 85–93.

13. C.N. Satterfield: Mass Transfer in Heterogeneous Catalysis, MITPress, London, 1970, pp. 12–46.

14. O. Levenspiel: Chemical Reaction Engineering, John Wiley & Sons,Inc., New York, NY, 1999, p. 579.

15. W. Pluschkell and B.V.S. Sarma: Arch. Eisenhuttenwes., 1973,vol. 44 (1), pp. 161–66.

16. S.P. Matthew and P.C. Hayes: Metall. Trans. B, 1990, vol. 21B,pp. 153–72.

17. T.R. Wilken, W.R. Morcom, C.A. Wert, and J.B. Woodhouse:Metall. Trans. B, 1976, vol. 7B, pp. 589–97.

18. D.H. St. John, F. Nakiboglu, and P.C. Hayes: Metall. Trans. B,1986, vol. 17B, pp. 383–93.

19. S.P. Matthew, T.R. Cho, and P.C. Hayes: Metall. Trans. B, 1990,vol. 21B, pp. 733–41.

20. D.H. St. John, S.P. Matthew, and P.C. Hayes: Metall. Trans. B,1984, vol. 15B, pp. 709–17.

21. K.R. Lilius: Acta Polytech. Scand., 1974, vol. 118, pp. 1–17.22. W. Kurz and D.J. Fisher: Fundamentals of Solidification, Trans

Tech Publications, Aedermannsdorf, Switzerland, 1998, pp. 45–58.

23. C.H.P. Lupis: Chemical Thermodynamics of Materials, ElsevierScience Publishing Co., Inc., New York, NY, 1983, pp. 347–84.

24. B. Ilschner: Z. Metallkd., 1964, vol. 55, pp. 153–62.25. J.S. Choi and W.J. Moore: J. Phys. Chem., 1962, vol. 66 (7),

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B, 2008, vol. 39B, pp. 234–45.27. O. Hirschfelder, C.F. Curtiss, and R.B. Bird: Molecular Theory of

Gases and Liquids, John Wiley & Sons, Inc., New York, NY, 1967,p. 1110.

Table III. Summary of Experimental Parameters used in the Present Study

Number Parameter Value

1 flow rate (f) 1 (LÆmin�1)2 area of tube cross section near sample (A) 6.28Æ10�6 (m2)3 linear flow rate (U = f/A) 2.65 (mÆs�1) at NTP (normal

temperature and pressurei.e., 25 �C and 1 atm, respectively)

4 characteristic dimension of NiO

L ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisurface area of plate sample=p

p� � 2.26Æ10�3 (m)

5 molecular weight of NiO MNiOð Þ 74.7 gÆmole�1

6 density of NiO qNiOð Þ 6.55Æ106 gÆm�3

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 40B, AUGUST 2009—489