Investigation of Magnetite Oxidation Kineticsat the Particle Scale

T.K. SANDEEP KUMAR, N.N. VISWANATHAN, H. AHMED, A. DAHLIN,C. ANDERSSON, and B. BJORKMAN

The induration of magnetite pellets is a complex physico-chemical process that involvesoxidation, sintering, and heat transfer. The thermal- and gas-composition profile that isexperienced by the pellet in an induration reactor could result in the formation of a homogenousor heterogeneous pellet structure, which could affect the pellet quality. The oxidation kinetics ofmagnetite pellets from sintering studies have been studied at two levels, namely, the pellet scaleand at the particle scale, and the findings of the latter are presented here. The rate of oxidationof the magnetite concentrate depends primarily on temperature, oxygen content in the oxidizinggas, and particle size. These factors are investigated in this study. It was found that theoxidation of the magnetite concentrate is comprised of two distinct stages, a primary stage withhigh rates followed by a secondary stage where rates decrease significantly. The isothermaloxidation behavior as analyzed by the Avrami kinetic model was found to fit better than theshrinking-core model. The partially oxidized particles were examined microstructurally tosupplement the experimental and model results. The Avrami kinetic model for isothermaloxidation was extended to non-isothermal profiles using the superposition principle, and themodel was validated experimentally.

https://doi.org/10.1007/s11663-018-1459-5� The Author(s) 2018

I. INTRODUCTION

THE pelletization of iron-ore fines is one of thewidely practiced agglomeration techniques in iron andsteel making because it enables the use of a very fineconcentrate. Iron-ore pellets offer several advantagesover other ferrous burdens in terms of strength,reducibility and uniformity of shape (spherical), chem-istry, and porosity. Magnetite pelletization provides anadded benefit in terms of energy, owing to the exother-mic nature of its oxidation to hematite.[1] Magnetite orethat is excavated from mines is crushed, beneficiated,and ground into fines concentrate. The concentrate isballed into green pellets with the addition of moistureand additives, such as flux and binder. Thereafter, greenpellets are fired in an induration furnace to impart

sufficient strength and to attain the desired properties.During induration, green pellets that are laid as apacked bed undergo updraft and downdraft drying[room temperature to 523 K (250 �C)] followed byoxidation [573 K to 1023 K (300 �C to 750 �C)] andfinally sintering [> 1273 K (1000 �C)].[2] The hot gasesare allowed to flow in the counter-current directionacross the furnace for efficient heat transfer.To achieve and enhance stability in the production of

homogeneous and good-quality pellets, a model isrequired to predict the optimum thermal and gaseousprofile for pellets during induration. Therefore, it isnecessary to understand and estimate the kinetics of thephenomena involved in magnetite pellet induration. Themethodology used was to investigate each of thephenomena (oxidation, sintering, and heat transfer) ona single pellet in isolation, and subsequently integratethese to develop the overall induration model. Sinteringmodels at the single-pellet scale have already beendeveloped on the basis of their kinetics, and have beendemonstrated in previous studies.[3,4] The oxidationkinetic model for magnetite pellets has been developedin two parts. We investigated the oxidation phenomenonof magnetite concentrate from the Luossavaara-Ki-irunavara Aktiebolag (LKAB) mine in Malmberget,Sweden at the particle scale; estimated the oxidationkinetics; and determined the responsible mechanisms.

T.K. SANDEEP KUMAR, C. ANDERSSON, and B.BJORKMAN are with the Lulea University of Technology (LTU),97187 Lulea, Sweden. Contact e-mail: kamesh.sandeep@ltu.se N.N.VISWANATHAN is with the Indian Institute of Technology Bombay(IITB), Mumbai 400076, India. H. AHMED is with the LuleaUniversity of Technology (LTU) and also with the Center ofMetallurgical Research and Development Institute, Cairo 11421,Egypt. A. DAHLIN is with the Luossavaara-KiirunavaraAktiebolag (LKAB), 98381 Malmberget, Sweden.

Manuscript submitted February 24, 2018.

METALLURGICAL AND MATERIALS TRANSACTIONS B

The kinetics that were estimated in this study will help toestablish the oxidation behavior of magnetite at thepellet scale, which will be communicated in future.

From the early 1950s, several researchers have studiedthe oxidation of magnetite pellets and investigated theeffect of different sources of concentrate, pellet, andparticle-size distribution with respect to various thermalatmospheres.[2,5–12] Many experimental studies havecaptured the oxidation behavior of magnetite at thepellet scale, although limited studies have been con-ducted at the particle scale to understand their behaviorand estimate their kinetics to develop and validate themodel.[2,5–7,9,13–15] Magnetite oxidation proceeds withhigh initial rates and plateaus at the later stages ofoxidation at a significantly slower rate. Magnetite-con-centrate oxidation can be simulated for non-catalyticheterogeneous gas–solid reactions. Several models havebeen proposed to follow the gas–solid reaction sequence,which provides insight into the dominant mechanism inthe range of variables studied.[12,13,16–20]

One of the gas–solid reaction models, the shrink-ing-core model (SCM), postulates that the oxidation ofmagnetite concentrate proceeds topo-chemically fromthe surface towards the center of the particle in anisothermal atmosphere, as described in Eq. [1].[21] Itpostulates that the mass transfer of the oxidizing gasfrom the bulk to the particle surface is rate determininginitially. When oxygen gas reaches the particle surface,the interfacial chemical oxidation reaction of magnetiteto hematite becomes dominant with a release ofexothermic energy. Thereafter, oxygen diffuses into theparticle through the grain boundaries or via micro-cracks in the hematite product layer because of theconcentration gradient, and proceeds concentricallytowards the center of the particle. This results in ahigher degree or rate of oxidation at the beginning, anda plateau at the later stage.

r

3kmfþ r

kR1� 1� fð Þ

13ð Þ

h iþ r2

6kS3� 2f� 3 1� fð Þ

23ð Þ

h i

¼ CM

qBt;

½1�

where f is the fraction of conversion for a concentratethat comprises particles with an average radius r foran isothermal time t and kM, kR, and kS are the rateconstants for the mass transfer of oxidizing gas to theparticle surface, chemical reaction at the interface, anddiffusivity, respectively. M and qB are the molar massand density of the reactant concentrate, respectively,and C is the oxygen concentration in the reacting gas.

Forsmo[1] studied the oxidation and sintering phe-nomena for magnetite pellets prepared from magnetiteconcentrates of varying fineness to understand themechanisms and to optimize the particle-size distribu-tion or fineness desired to achieve good-quality productpellets. Thereafter, Cho investigated the isothermaloxidation kinetics of magnetite and developed thepellet–particle model.[22] Monsen et al.[15] investigatedthe kinetics of magnetite oxidation at the particle scale

for a narrow-size-fraction concentrate from differentmines. They hypothesized that magnetite-particle oxi-dation proceeds in a topo-chemical manner with growthof the hematite product layer. They found that themagnetite oxidizes at a rapid rate initially, probablybecause of the fine particles in the concentrate, and aplateau is reached during the later stages owing tosolid-state diffusion in larger particles, according to theSCM. It was inferred that the plateau behavior can becontrolled by the concentrate particle-size distributionand, thus, the fraction of particles oxidized. However, itwas observed that the needle-like structure of thehematite grew ahead of the reaction front, whichindicates that the reaction may proceed by anothermechanism. Monazam et al.[23] examined the oxidationof secondary magnetite (i.e., reduced-hematite) particlesduring chemical-looping combustion to understand thereaction mechanisms by applying several gas–solidreaction-kinetic models. They found that the oxidationof magnetite particles follows a two-step kinetics phe-nomenon in parallel, which can be described by theAvrami kinetic model (AKM). The AKM describes thekinetics of isothermal phase transformation in materials,represented by Eq. [2]. The phase-transformation kinet-ics often follow a sigmoidal (S-shaped) profile withinitial slow rates owing to the formation of a sufficientnumber of nuclei (nucleation). Thereafter, the rateincreases at a rapid rate as the nuclei grow into particles(growth) and cease slowly when complete transforma-tion is approached.[24,25]

f ¼ 1� e�atn� �

; ½2�

where f is the conversion or transformation that isachieved in isothermal t, and the coefficients of theAKM are a, the rate constant, and n, the time expo-nent that provides insight into the type of nucleationand growth mechanism.The isothermal oxidation mechanisms for LKAB’s

magnetite concentrate have been investigated experi-mentally to estimate the kinetic parameters. Isothermalexperiments were performed by considering three mainparameters as variables, namely, temperature [773 K to1073 K (500 �C to 800 �C)], the partial pressure ofoxygen in the oxidizing gas (0.05 to 0.21 atm), and anaverage concentrate particle size (45.5 to 68.5 lm). Theresults were analyzed with the two kinetic models, SCMand AKM, and compared with the experimental obser-vations to identify the oxidation mechanisms. Thenon-isothermal behavior was validated by performingnon-isothermal experiments.Isothermal thermogravimetric analysis (TGA) studies

can be conducted in two ways: (1) by allowing thesample to reach the isothermal temperature in an inertgas atmosphere and then switching from an inert to areactive gas[7,9,22] and (2) by inserting the sample for ashort duration into the reactor zone at a desiredtemperature and gas composition.[2] Both methodsexhibit disadvantages in terms of initial transients. Inthe former method, depending on the reactor volumeand gas flow rates, it would take some time for the gascomposition to reach a stable value. In the latter case,

METALLURGICAL AND MATERIALS TRANSACTIONS B

depending on the thermal capacity of the crucible andthe sample, time is required for the crucible–sampleassembly to reach the desired steady temperature. Mostexperiments reported in the literature have used theformer method. In this study, the latter method has beenchosen.

II. METHODS AND MATERIALS

A. Raw Materials

The magnetite concentrate was from LKAB’s mine inMalmberget, Sweden. The concentrate was collectedcarefully by coning and quartering and contained96.32 pct Fe3O4, 0.4 pct SiO2, and 0.23 pct Al2O3 withminor proportions of CaO, MgO, MnO, and TiO2. Theconcentrate is wet-sieved into three narrow size frac-tions, 38 to 53 lm (mesh #400), 53 to 63 lm (mesh#270), and 63 to 74 lm (mesh #230), with averageparticle diameters (dp) of 45.5, 58, and 68.5 lm,respectively. This enabled us to capture the effect ofparticle size on the inherent oxidation behavior. Thesieved concentrates were collected and dried in an ovenat 423 K (150 �C) overnight. Thereafter, to ensure theefficiency of sieving, the particle-size distribution of thesieved particles was determined by a laser-based method(CILAS 1190, France).

B. Oxidation Experiments

Isothermal oxidation of the magnetite particles wasstudied using TGA (Setaram 92, Setaram, France). TheTGA consisted of a platinum crucible that was sus-pended from a weighing balance at the top and loweredinto a graphite tube furnace with the assistance of anelevator, as shown in Figure 1.

Approximately 27 mg of a narrow size fraction ofparticles (dp) was poured into a platinum crucible (8 mmin diameter and 5 mm in depth) to form a shallow layerof approximately 2 mm. An S-type thermocouple wasplaced beneath the sample to measure the temperature.Different proportions (5 to 21 pct) of oxygen in nitrogenwere used as the oxidizing gas, mixed with the help of adigital gas mixer. The oxidizing gas was allowed to flowfrom the bottom to the top of the furnace at 200 ml/min.This flow rate exceeded the optimized gas flow rateachieved by performing starvation tests to ensure thatthe resistance because of gas diffusion is negligible. Thethermal excursion designed for each of the experimentscomprises heating the furnace to the isothermal tem-perature at 20 K/min, holding it under isothermalconditions for 60 min, followed by cooling at 20 K/minunder the desired oxidizing atmosphere. Once the gasatmosphere had been established and isothermal tem-perature had been reached, the sample was lowered intothe furnace. It is reasonable to consider the non-isother-mal oxidation while lowering the sample to be negligi-ble, compared with the overall oxidation extent andtime. Isothermal oxidation experiments were conductedover a range of temperature, pO2

and size fraction asprovided in Table I. Background correction tests were

conducted for each TGA experiment using an emptyplatinum crucible by following the respective thermaland gas profiles. The weight gain was captured everysecond by the data logger, corrected using the back-ground tests, and then used for further analysis.Non-isothermal oxidation experiments were conductedat 20 K/min from room temperature to the set isother-mal temperature for 873 K to 1073 K (600 �C to800 �C).

C. Optical Microstructures

The partially oxidized magnetite particles were coldmounted in epoxy, vacuum impregnated, and polishedto a fineness of 1 lm with diamond paste to obtain a flatreflecting surface for examination under the microscope.Microstructures were captured using a light opticalmicroscope (Zeiss Imager.M2m, Germany) at a magni-fication of 1000 times to examine the pattern of theoxidation interface and hematite needle growth.

III. RESULTS AND DISCUSSIONS

A. Oxidation Fraction and Oxidation Rate

Magnetite oxidation is accompanied by weight gain.For the Fe3O4 content of the concentrate used, thetheoretical or maximum weight-gain percentage(DWmax) that the magnetite particles can achieve during

Fig. 1—Schematic of Setaram TG92-16 TGA.

METALLURGICAL AND MATERIALS TRANSACTIONS B

its oxidation to hematite was found to be 3.33 pct. Thefraction of conversion during oxidation was normalizedwith respect to the theoretical weight gain. Therefore,the oxidation fraction (f) or degree of oxidation wasdetermined as the ratio of the weight gain captured byTGA to the maximum weight gain of the magnetiteparticles during oxidation according to Eq. [3]. There-after, the oxidation rate that corresponded to theoxidation fraction was calculated for the given thermalprofile.

f ¼Wf�Wi

Wi

� �� 100

DWmax¼ DWTGA

DWmax; ½3�

where DWTGA is the percentage weight change mea-sured during oxidation in TGA between the initial(Wi) and final (Wf) particle weight.

The profiles of oxidation fraction and oxidation ratefor the magnetite particles at different temperatures, thepartial pressure of the oxidizing gas, and the particle sizewith respect to the isothermal time are shown inFigure 2. The oxidation fraction increases initially at arapid rate, and thereafter plateaus where the oxidationincreases gradually at a constant oxidation rate. Thisimplies that magnetite oxidation at the particle scale is atwo-step phenomenon, which is in line with the findingsreported by several researchers.[2,7,15,22,23] The degree ofoxidation (fraction) increases with isothermal tempera-ture (Figure 2(a)) from 773 K to 1073 K (500 �C to800 �C) and with increasing pO2

in the oxidizing gasfrom 0.05 to 0.21 (Figure 2(b)). Finer particle-sizefractions (Figure 2(c)) with a larger surface area achievea higher degree of oxidation compared with relativelycoarser particle-size fractions, in the order of 38 to 53 lm> 53 to 63 lm > 63 to 74 lm. However, there is amarginal difference in the oxidation profiles for the twolarger particle-size fractions. This could be because ofthe agglomeration of some of the finer particles onto the

large particles observed by optical-microscopy analysis.This could be because of the limitations in the capabilityof available size-distribution techniques (wet-sieving) toseparate very fine magnetite particles. The authors willaim to develop a quantitative analysis for size distribu-tion by optical microscopy.

B. Kinetic Models

1. SCMThe isothermal oxidation results were analyzed using

the SCM to evaluate the kinetics. According to theSCM, the conversion proceeds by mass transfer of thegaseous phase, chemical reaction, and solid-state diffu-sion kinetics, as mentioned in Eq. [2]. In general, themass transfer of the oxidizing gas to the particle surfaceis not rate limiting, even when the gas flow rate isoptimized with the help of starvation tests in TGA. Ifthe chemical reaction is the dominant step, the fractionof conversion for the spherical particles with respect totime proceeds according to Eq. [4], whereas, if diffusionthrough the product layer is the rate-controlling mech-anism, the same is represented by Eq. [5].[21,22]

Chemical reaction at the interface;

FR ¼ 1� 1� fð Þ13ð Þ

h i¼ kRtR

½4�

Diffusion through the product layer;

FS ¼ 3� 2f� 3 1� fð Þ23ð Þ

h i¼ kStS;

½5�

where FR and FS are conversion fractions that corre-spond to chemical reactions and diffusion in theisothermal time tR and tS with the rate constants kRand kS, respectively.

Table I. Experimental Design for the Oxidation of Magnetite Particles in TGA

Particle Experiment T, K (�C) pO2(atm) Size Fraction, dp (lm) H.R., (K/min)

Isothermal Oxidation P1 773 (500) 0.21 38 to 53 —P2 823 (550) 0.21 38 to 53 —P3 873 (600) 0.21 38 to 53 —P4 923 (650) 0.21 38 to 53 —P5 973 (700) 0.21 38 to 53 —P6 1023 (750) 0.21 38 to 53 —P7 1073 (800) 0.21 38 to 53 —

P8 873 (600) 0.05 38 to 53 —P9 873 (600) 0.10 38 to 53 —P10 873 (600) 0.15 38 to 53 —P3 873 (600) 0.21 38 to 53 —

P3 873 (600) 0.21 38 to 53 —P11 873 (600) 0.21 53 to 63 —P12 873 (600) 0.21 63 to 74 —

Non-isothermal Oxidation P13 873 (600) 0.21 38 to 53 20P14 973 (700) 0.21 38 to 53 20P15 1073 (800) 0.21 38 to 53 20

METALLURGICAL AND MATERIALS TRANSACTIONS B

The oxidation fraction ðfÞ of magnetite particles asobtained experimentally for different isothermal tem-peratures has been rearranged and plotted accordingto Eqs. [5] and [6] with respect to the isothermal time,respectively, as shown in Figure 3. The conver-sion–time plots for the initial oxidation (Figure 3(a))and the later stages (Figure 3(b)) fit a straight-line

equation. This implies that the oxidation of magnetiteparticles proceeds by the SCM and is initially domi-nated by chemical reaction and thereafter bydiffusion through the hematite product layer. Theslopes of the curves that fit Eqs. [4] and [5] deter-mine the rate-constant terms (kR and kS),respectively.

Fig. 2—Oxidation fraction and oxidation rate for magnetite particles with respect to (a) isothermal temperatures, (b) pO2in oxidizing gas, and (c)

size fraction.

METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 3—Isothermal oxidation by SCM with respect to different isothermal temperatures, pO2; and size fraction with (a) chemical reaction and (b)

diffusion as dominant mechanisms.

Fig. 4—Arrhenius equation plots to estimate activation energy for (a) chemical reaction and (b) solid-state diffusion-controlling mechanism.

METALLURGICAL AND MATERIALS TRANSACTIONS B

Because oxidation is a thermally activated phe-nomenon, the variation in rate constant with respectto the isothermal temperature is expressed by theArrhenius equation (Eq. [6]) and is plotted as shownin Figure 4 for each of the mechanisms independently.

ln TKð1=nÞ� �

¼ lnK0 �Q

RT; ½6�

where n is the time exponent, Q is the activationenergy (J/mol), K is the rate constant (s�1) of the dom-inant mechanism, K0 is the pre-exponential factor (s�1)for the first-order reaction, T is the temperature in K,and R is the gas constant in J/mol/K.

The respective slope and intercept of Eq. [6] determi-nes the activation energies and pre-exponential factor.The activation energies for the initial and later stages ofthe magnetite-particle oxidation were found to be 31and 76.5 kJ/mol, respectively. This implies that theoxidation of magnetite particles at the initial stage maynot only occur because of the chemical reaction. Instead,it can be postulated that the initial oxidation isdominated by the mixed influence of gas-phase masstransfer and chemical reaction, whereas, during the laterstages, oxidation proceeds by diffusion.

2. AKMThe AKM hypothesizes that the isothermal conver-

sion or phase transformation of particles proceeds bynucleation and growth, represented by Eq. [2]. Theresults for the isothermal oxidation from experiments onmagnetite concentrate have been analyzed with theAKM by rearranging Eq. [2] to a straight line as shownin Eq. [7]. The isothermal oxidation results plottedaccording to Eq. [7] with respect to time for magnetiteparticles exposed to different temperatures, pO2

and sizefraction are shown in Figure 5.

ln � ln 1� fð Þð Þð Þ ¼ n ln tð Þ þ ln að Þ; ½7�

Two straight lines with different slopes for the initialand later stages of oxidation result for the experimentswith all variables. This result implies that the isothermaloxidation of magnetite concentrate investigated in thisstudy satisfies the AKM. The Avrami rate constant (a)for different isothermal experiments is related to theArrhenius rate constant ðKÞ according to Eq. [8].Thereafter, the Arrhenius Equation (Eq. [6]) is plottedfor the nucleation and growth mechanisms, as shown inFigure 6, to estimate activation energies (Q) and pre-ex-ponential factors ðK0Þ by evaluating the respectiveslopes and intercepts.

K ¼ a1n: ½8�

The activation energies that were estimated for thenucleation and growth mechanisms are 15 and 226kJ/mol, respectively. Therefore, it can be postulated thatduring oxidation, hematite (Fe2O3) needles grow bysolid-state diffusion of oxygen anions into a matrix ofmagnetite (Fe3O4) particles.

[23] Some uncertainties mayexist during the first few seconds of the initial stagebecause too few data points exist and too little stabi-lization of experimental data occurs or because of aresponse of the weighing balance to the weight gain.Therefore, further analysis was focused primarily on thelater stage of the oxidation reaction to determine thekinetics.The pre-exponential factor ðK0Þ and time exponent (n)

determined from the Arrhenius equation (Eq. [6]) andthe slopes of Eq. [7], respectively, are tabulated inTable II. The pre-exponential factor ðK0Þ is found tovary with pO2

and dp according to Eqs. [9] and [10],respectively. The time exponent (n) increases linearlywith respect to the temperature, and decreases with pO2

in the oxidizing gas as per Eqs. [11] and [12], respec-tively, whereas it does not vary with the particle-sizefraction.

Fig. 5—Isothermal oxidation by AKM for different (a) isothermal temperatures, (b) pO2; and (c) size fractions.

METALLURGICAL AND MATERIALS TRANSACTIONS B

K0 ¼ 2:81� 109pO2þ 7:511� 108 ½9�

K0 ¼ �6:054� 1013dp þ 4:024� 109 ½10�

n ¼ 4:938� 10�4T� 0:197 ½11�

n ¼ �0:428pO2þ 0:3231: ½12�

C. Predicting Isothermal Oxidation—ComparisonBetween SCM and AKM

The derived kinetic parameters have been used topredict the isothermal oxidation behavior of the mag-netite concentrate. The oxidation fraction of the con-centrate is predicted according to the SCM and AKMkinetic models using Eq. [1] for the SCM (assumingmass transfer is not rate limiting) and Eq. [2] for theAKM. The predicted profiles of the oxidation fractionðfÞ for different isothermal temperatures with respect totime are validated with the respective experimentalbehavior, as shown in Figure 7.

Fig. 6—Arrhenius plots for AKM for (a) nucleation and (b) growth mechanisms during oxidation of magnetite concentrate.

Table II. Pre-exponential (K0) and Time Exponent (n) Determined by AKM for Magnetite-Particle Oxidation Experiments

Particle Experiment T, K (�C) pO2(atm) Size Fraction, dp (lm) K0 9 108 (s�1) n

P1 773 (500) 0.21 38 to 53 6.3 0.16P2 823 (550) 0.21 38 to 53 0.21P3 873 (600) 0.21 38 to 53 0.23P4 923 (650) 0.21 38 to 53 CI = (1.9, 21.3) 0.29P5 973 (700) 0.21 38 to 53 0.28P6 1023 (750) 0.21 38 to 53 0.29P7 1073 (800) 0.21 38 to 53 0.32

P8 873 (600) 0.05 38 to 53 9.9 0.30P9 873 (600) 0.10 38 to 53 9.4 0.28P10 873 (600) 0.15 38 to 53 10.6 0.24P3 873 (600) 0.21 38 to 53 14.3 0.23

P3 873 (600) 0.21 38 to 53 14.3 0.23P11 873 (600) 0.21 53 to 63 2.0 0.24P12 873 (600) 0.21 63 to 74 0.7 0.22

METALLURGICAL AND MATERIALS TRANSACTIONS B

The oxidation profiles that are predicted from theAKM (Figure 7(b)) agree significantly better with theexperimental observations compared with those pre-dicted from the SCM (Figure 7(a)). Optical microstruc-tures of magnetite particles (38 to 53 lm) that wereoxidized at isothermal temperatures of 873 K and 1073K (600 �C and 800 �C) for 60 min were examined, asshown in Figure 8. The oxidation proceeds inwardsfrom the magnetite-particle surface by nucleation ofneedle-like hematite crystals that begin to grow alongthe preferred planes in the magnetite at the lowertemperature [873 K (600 �C)]. Similar findings havebeen observed by Monazam et al.[23] As the extent orfraction of oxidation increases at higher temperature[1073 K (800 �C)], a sharp reaction interface appearsthat progresses inwards somewhat in an anisotropic

manner, albeit with hematite needles that grow signif-icantly ahead of the reaction interface into the mag-netite-particle matrix. A similar observation wasreported by Monsen et al.[15] Thus, it can be substan-tiated that magnetite-particle oxidation considered inthis study proceeds by nucleation and growth, wherehematite needle growth into the magnetite particlesoccurs via a solid-state diffusion mechanism. Thesefindings are also consistent for particles exposed todifferent pO2

and dp.The activation energy estimated by the SCM in this

study for the diffusion stage is 76.1 kJ/mol. Activationenergies in a similar range were found by Cho[22] usingthe SCM. The lower activation energies for thesolid-state diffusion is attributed to a short-circuit pathor grain-boundary diffusion. Significantly higher

Fig. 7—Predicted and experimental isothermal oxidation of magnetite concentrate (38 to 53 lm at pO2¼ 0:21 atm atm according to (a) the SCM

and (b) the AKM.

Fig. 8—Light optical microstructures (1000 times magnification) of magnetite particles (38 to 53 lm) oxidized at an isothermal temperature of(a) 873 K (600 �C) and (b) 1073 K (800 �C) showing hematite needles (H) growing into the magnetite matrix (M).

METALLURGICAL AND MATERIALS TRANSACTIONS B

activation energies, such as 242, 208, and 469 kJ/mol,have been reported by Himmel,[26] Paidassi,[27] andDavies,[28] respectively, for the solid-state diffusionmechanism. However, the activation energy determinedby the AKM for the growth stage was 226 kJ/mol, whichfalls in the range of values reported in the litera-ture.[26–28] This result is backed up by the predictedprofiles for the oxidation fraction by the AKM, whichmatches that obtained experimentally fairly well(Figure 7), as well as by the microstructural observationof hematite crystal growth ahead of the reactioninterface (Figure 8). Therefore, for the activation-energyvalues, predicted oxidation profiles, and microstructuralobservations, the AKM describes the oxidation mech-anisms of the magnetite concentrate suitably. Hence,AKM was used to predict the oxidation behavior of themagnetite concentrate.

D. Non-isothermal Oxidation Prediction Using KineticParameters

In industrial operations, magnetite-particle pellets areexposed to non-isothermal atmospheres, and therefore itis appropriate to predict the non-isothermal oxidationbehavior of the magnetite concentrate investigated inthis study. The kinetic parameters derived from isother-mal studies using AKM were extended to predict thenon-isothermal oxidation behavior of the magnetiteconcentrate. This has been done by discretizing theentire non-isothermal (time–temperature) plot withseveral small pseudo-isothermal steps. The variation inoxidation fraction ðfÞ can be obtained from the temporalvariation of temperature and the corresponding Avramicoefficients (a; n), using Eq. [2] by proceeding in time fora sufficiently small Dt.

To develop the oxidation model that should be able toconsider all three parameters as variables, the kineticparameters (n, K0) have been correlated with T, pO2

; anddp to have a combined effect in the range considered inthis study. The time exponent (n) is a function of T andpO2

, whereas the pre-exponential factor ðK0Þ is depen-dent on pO2

and dp. These coefficients are correlated totheir parameters in a bilinear way using the least-squaresfitting method according to Eqs. [13] and [14],respectively.

n ¼ 1:76� 10�4Tþ 0:1255 ln pO2ð Þ � 2:03� 10�4T

� lnðpO2Þ ½13�

log10 K0 ¼ 11:46þ 0:786pO2� 5:55� 10�4dp: ½14�

These predictions have been validated by thenon-isothermal oxidation experiments. The magnetiteconcentrate in the size fraction of 38 to 53 lm(dp = 45.5 lm) was oxidized non-isothermally fromroom temperature to different isothermal temperatures[873 K, 973 K and 1073 K (600 �C, 700 �C and 800 �C)]at 20 K/min with 21 pct oxygen in the oxidizing gas

(pO2¼ 0:21 atm) at 200 ml/min. The predicted

non-isothermal oxidation profiles have been plottedwith the experimental profiles for validation in Figure 9.A kink exists in Figure 9 at approximately f = 0.55

to 0.65 pct and 723 K (450 �C). Similar observationshave been reported earlier,[2,13,29,30] and it has beenpostulated that this occurs because of the formation ofc-Fe2O3 (maghemite) at lower temperature, and furtherto a-Fe2O3 (hematite) at a higher temperature (~ 873 K(600 �C). However, the metastable nature of c-Fe2O3

makes it difficult to confirm by characterization. Thepredicted oxidation profiles follow the experimentaloxidation profiles with respect to the pattern or progressof the oxidation curves. It can also be inferred that aslight deviation from the model predictions results withregard to the absolute extent of oxidation fraction. Thevalues of n and K¢ that affect the oxidation behaviorsignificantly have been fine-tuned to estimate the rangewhere predictions are accepted statistically. An opti-mization of these by a least-squares fit enables us togenerate non-isothermal oxidation predictions for entirethermal profiles within a 90 pct confidence interval.Deviations from the experimental observations could

be attributed to the fact that the particle shape withineach narrow size fraction is not uniform and spherical.Another limitation could be the lack of experiments atdifferent temperatures for the range of pO2

and sizefractions while determining the kinetic parameters.Although these experiments were not within the scopeof this study, their incorporation will increase thewindow of experimental observations, which couldimprove the model efficiency, and can be considered infuture studies. Further, the particle kinetics modeldeveloped in this study will be used to upscale anddevelop the oxidation model for magnetite at the pellet

Fig. 9—Prediction and validation of non-isothermal oxidation formagnetite concentrate (38 to 53 lm) at pO2

¼ 0:21 atm by adaptingthe AKM.

METALLURGICAL AND MATERIALS TRANSACTIONS B

scale. This is communicated separately, and provides theoverall oxidation behavior of magnetite at the pellet andparticle scale.

IV. CONCLUSIONS

The oxidation behavior of magnetite has been inves-tigated quantitatively at the particle scale using TGA.The study focused on narrow size fractions of magnetite.Isothermal oxidation kinetics have been determinedexperimentally by considering the isothermal tempera-ture, the partial pressure of oxygen in an oxidizing gas,and the particle-size fraction as variables. Experimentalresults were analyzed by two kinetic models, namely, theSCM and the AKM. The isothermal oxidation of themagnetite concentrate was predicted and validated forboth kinetic models. Oxidation of the magnetite con-centrate was described best by the AKM, whichpostulates that oxidation at the particle scale proceedsby nucleation and growth in the initial and later stages,respectively, where growth occurs by diffusion mecha-nisms. A methodology has been developed to predict theoxidation behavior of magnetite concentrate undernon-isothermal conditions and validated experimentally.

ACKNOWLEDGMENTS

The authors thank the Hjalmar Lundbohm Re-search Centre (HLRC) for their financial support. Wealso thank Ola Eriksson and Daniel Marjavaara fromLKAB for their technical input. The authors wouldalso like to extend their sincere thanks to Professor N.B. Ballal and Professor M. P. Gururajan of the IndianInstitute of Technology (IIT) Bombay for valuable dis-cussions.

OPEN ACCESS

This article is distributed under the terms of theCreative Commons Attribution 4.0 International Li-cense (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, andreproduction in any medium, provided you giveappropriate credit to the original author(s) and thesource, provide a link to the Creative Commons li-cense, and indicate if changes were made.

LIST OF SYMBOLS

km Rate constant for mass transfer of gaskR Rate constant for chemical reaction at the

interfacekS Rate constant for diffusionDeS Diffusivityr Average radius of particles in the concentrate

dp Average diameter of particles in theconcentrate

pO2Partial pressure of oxygen in oxidizing gas

T Isothermal temperatureWi Initial weight of concentrate in TGAWf Final weight of concentrate in TGADWTGA Weight change during oxidation in TGAf Fraction of concentrate conversion by

oxidationC Concentration of oxidizing gas in the pelletM Molar massqB Bulk densityt Isothermal timea Avrami rate constantn Time exponentFR Fraction of conversion because of chemical

reaction at the interfaceFS Fraction of conversion because of diffusiontR Isothermal time to reach FR

tS Isothermal time to reach FS

K Arrhenius reaction rate constantK0 Pre-exponential factorQ Activation energyR Ideal gas constant

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