INFLUENCE OF THERMODYNAMICS AND DIFFUSION ON REACTION

MECHANISMS DURING GAS/SOLID REACTIONS

Peter C. Hayes

Pyrometallurgy Innovation Centre (PYROSEARCH), School of Chemical Engineering, The

University of Queensland, St Lucia Campus, Brisbane, Australia. p.hayes@uq.edu.au

Keywords: gas reduction, reaction kinetics, mechanisms, phase transformations

Abstract

The direct link between microstructure and material properties is the core principle underpinning

modern material science and engineering. Phase transformations in solids and solidification of

melts have been extensively studied to the point where the key elementary processes, process steps

and process variables are well understood. Less well investigated and less well understood are the

changes taking place during gas/solid reactions. Most studies have focussed determining the rates

of overall reactions rather than the structures of the solid products and the reaction mechanisms at

the gas/solid interface.

Recent research has shown that the reaction mechanisms in these fluid/solid systems and the solid

microstructures formed have direct analogies to those observed in solidification and solid/solid

transformation systems. Establishing the fundamental conceptual link between these different

classes of systems opens the opportunity to utilise these established theoretical frameworks to

improve existing process technologies and to develop and manufacture new material structures.

Introduction

Through the control of microstructure, it is possible to control the physical and chemical properties

of condensed phase materials. For this fundamental reason extensive research efforts have been,

and continue to be, devoted to understanding the mechanisms and kinetics of the transformations

in condensed phase structures. The driving force for change in a system is the difference in Gibbs

Free Energy between the initial and final states. This driving force acts on the system as whole,

and influences the association and movement of atoms in the system.

Christian [1] examined in detail the characteristics of homogeneous and heterogeneous

transformations taking place in metals and alloys. He argued that there were two types of

transformation. In a heterogeneous transformation, the material is divided microscopically into

regions that have transformed and those that have not. This means there must be an interface

dividing these regions; as the transformation proceeds changes take place at, or transfer of species

occurs across, interfaces between these different regions. In contrast, in the case of homogeneous

transformations, there is effectively no energy barrier to change and no identifiable boundary and

the reaction can take place in all parts of the material simultaneously. The majority of systems

used in practical applications involve heterogeneous transformations.

It has been established that phase transformations in solid materials, whether polymorphic or phase

formation, can take place through a variety of mechanisms; these have been categorised in a

number of ways. Transformations in crystalline solids can take place by displacive mechanisms,

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involving cooperative movement of atoms, or diffusion mechanisms involving the movement and

re-arrangement of individual atoms [2].

Christian [1] proposed a more detailed classification of phase transformations observed in metals

and alloys based on the growth processes taking place during these transformations; he identified

three principal categories;

Thermally activated growth, involving movement of individual atoms by diffusional

processes,

Athermal processes, which are associated with glissile interfaces that do not require

thermal activation to proceed and can propagate under mechanical stress, and

Growth controlled by heat transport, such as solidification and melting.

Inherent in this classification is the assumption that in each case the transformation is occurring

by one of these mechanisms. There are several points can be made here. To achieve the structural

and compositional changes taking place during heterogeneous transformations a number of

transport processes and chemical reactions must take place simultaneously. The relative

contributions of these processes taking place during these transformations and the proportion of

the available driving force associated with each of these processes change depending on the

material characteristics and the process conditions in the reaction system. In the case of cellular

solid/solid reactions these processes these material characteristics have been shown [1,3,4] to

include, chemical compositions of the initial and final phases, crystal structures, coherence,

interfacial energy, solute drag, curvature, interfacial diffusion, volume diffusion. The process

conditions include, temperature, processing history (e.g. mechanical working, thermal pre-

treatment).

In solidification processes heat transfer is essential to maintain the thermodynamic driving force

for transformation. In metal alloy systems the mass transfer of solute in the melt is a major

consideration; this leads to changes in the geometries of the interface and product structure, such

as, planar, cellular and dendritic morphologies and massive transformations [5-7]. The additional

material characteristics influencing the growth processes and relative rates of transformations

include the roughness of the interface at the atomic level, reflected in the presence of facetted or

non-facetted interfaces. The process conditions include interface velocity, temperature gradient

and cooling rate. The general principles underlying solidification theory have been shown to

describe the kinetic behaviour and microstructures formed on the solidification of melts of non-

metal systems.

Building on these well-established phenomena, and the theoretical understanding of solid/solid

and liquid/solid transformations, there is the opportunity to extend this fundamentally based

approach to fluid/solid systems in general, i.e. to gas/liquid/solid systems. As part of this broader

view, an alternative approach to classification of these heterogeneous reaction systems has been

proposed [8]. Rather than classifying transformations and chemical reactions in terms of the

dominant growth processes, the focus here is placed on the stability of the reaction interface, the

phases formed and product microstructures obtained as a result of the transformations. The

advantage of this classification approach is that it inherently acknowledges that there are many

different elementary processes and process steps taking place in these heterogeneous

transformation processes, involving transfers of species between gas, liquid, and solid phases, and

necessarily include chemical reactions occurring at interfaces in addition to transport across and

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within individual phases. The classification shown in Figure 1 was developed to explain some of

the interface structures and product microstructures formed during gas/solid reactions. Whilst not

perfect, the intention is to use this initial classification as a basis for exploring further analogies

between reactions taking place in these heterogeneous reaction systems, and to demonstrate the

range of related product structure outcomes depending on the relative contributions of the mass

transfer and chemical reaction processes taking place at the interface.

Figure 1. Examples of interface structures that can be formed during reaction between fluid (1)

and solid (2) phases. Phase 3 is the new solid formed as a result of the chemical reaction (Hayes,

2013). Vo refers to the velocity of the interface between 1 and 2, the fluid and original phase. Vm

velocity or rate of growth of the new phase M across the interface [8].

Some Characteristics of Gas Solid Reactions

All transformations require a thermodynamic driving force for change. For systems under constant

pressure, this is expressed in the form of a change in the Gibbs Free energy between the initial and

final states. In the case of solute transfer within or between phases two solvent phases 1 and 2 in

which there is no phase change, then this chemical thermodynamic driving force is directly related

to the difference in chemical potential of the species. For a species i, the chemical thermodynamic

driving force, ΔG = RTln(ai1/ai2). For dilute solutions, ai is commonly approximated to the

concentration ci of the species i. In the case of gas/solid oxide reactions, in which there is a change

in composition of the condensed phase, this can alternatively be expressed as ΔG = RTln(PO2 initial/

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PO2 final) J mol-1 O2, where PO2 is the effective oxygen partial pressure. This equivalence can be

seen from inspection of Figure 4. The driving force for change ΔG per mole of element in

solidification processes is in most cases described in terms of the undercooling, ΔT; the

undercooling is directly linked to the Gibbs Free Energy through the relation, ΔG = (-ΔHfusion /TL).

ΔT where ΔHfusion is the enthalpy of solidification, TL the melting temperature and ΔT the

undercooling of the melt.

Figure 4. Phase relations in the system FeO-Fe2O3 as a function of temperature and weight percent

FeO-Fe2O3. Phase boundaries are represented by the solid lines. Oxygen isobars (atm.) are

represented by the dashed lines. Heavy dashed phase boundaries at high temperatures represent

approximations for the hematite liquidus and solidus regions [9].

In gas/solid reactions the rate of isothermal chemical reactions can be controlled by adjusting not

only the thermodynamic driving force for reaction but also the concentration of the reactant species

in the gas phase. This can be clearly seen in the rate equation for removal of oxygen, RO from a

pure MeO condensed phase by carbon monoxide as the reducing agent, expressed in the form,

MeO(s) + CO(g) → Me(s) + CO2(g) (1)

when to described by the first-order rate equation of the form

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RO = kf.PCO_- kr.PCO2 (mol O m-2 s-1) (2)

where kf and kr are the apparent chemical reaction rate constants for the forward and reverse

reactions, respectively (mol O m-2 s-1 atm-1); PCO and PCO2 are the partial pressures of CO and CO2

in the reaction gas (atm.). At chemical equilibrium rearranging kf /kr = (PCO/PCO2)eq, substitution

in equation 2 and rearranging gives

RO = kf.PCO(1- [PCO2/PCO].[PCO/PCO2])eq) = kf.PCO(1- [expΔGreaction/RT]) (mol O m-2 s-1 ) (3)

where ΔGreaction is the Gibbs Free Energy change associated with reaction given in equation (1),

R is the Gas constant and T the temperature in Kelvin.

Another distinguishing feature of fluid/solid reactions is that transport of reactant species in the

phase occurs in phase that is growing rather than the one that is decomposing or being transformed.

In gas/solid reactions, in order for the reaction at the gas/solid interface to continue, and the

thermodynamic driving force for reaction maintained, gas species must be continually supplied

from the bulk gas. This involves transfer from the bulk gas to the outer surface of the particle and

transfer from the outer surface to the reaction interface. This mass transfer step can be through

existing pores, pores created as a result of the chemical reaction or through dense product layer

[10], and involve gas film mass transfer, porous and Knudsen gas diffusion, and transfer of

dissolved species in the solid state [8].

The surface roughness of the interface between gas and solid at an atomic level can be described

by the Jackson factor, α =ΔSfη1/RZ, where ΔSf is the entropy difference between the two phases

at the interface, η1 is the number of nearest neighbours in the surface layer and Z is the maximum

number of atom nearest neighbours for each atom in the crystal [6]. Solid oxides have high entropy

of formation and, based on the Jackson factors, it is expected that they will form atomically smooth

surfaces having faceted surfaces and interfaces. These characteristics, and how they might

influence the reaction interface geometry and reaction kinetics, have been discussed in more detail

in a previous publication [11].

Structures Observed on Gas/Solid Reactions

Most micromodels of heterogeneous fluid/solid chemical reactions assume a planar interface that

moves progressively into the bulk as the reaction proceeds. Whilst this appears to be the case on a

macroscopic scale, as indicated in the classification this does not necessarily reflect the reality at

the microscopic scale. There are many examples of the formation non-planar interfaces during

phase transitions in fluid/solid systems; the challenge is to describe these changes formally in a

robust quantitative models.

The formation of unstable reaction surfaces during the treatment of dense, single-phase wustite

(Fe1-yO) and magnetite (Fe3-δO4) materials in reactive gas atmospheres [12, 13] demonstrates that

these morphological changes can take place a result of changing solid stoichiometry; it is not

necessary to create a new phase for gas pore formation to occur.

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Dendritic pore formation can occur during thermal decomposition of solids, not requiring an active

reaction gas, is exemplified in CaCO3 [14] and FeS2 [15] decomposition.

Experiments on the reduction of iron oxides with reactive gas mixtures have revealed a number of

interesting features of these reaction systems. An example of the formation of dendritic gas pores

in originally dense iron oxide is shown in Figure 2; it can be seen that the gas pores exemplify the

classical dendritic structures with the formation of main stem and branching side arms. Close

inspection of the pore shows the facetted nature of the surfaces. Individual pores grow and sub–

divide provide there is a significant volume of material ahead of the interface that is unaffected by

the transformation essentially the pore growth continues as long as the critical conditions for

instability growth are satisfied. When the pores approach each other the pore growth stops leaving

regions of dense oxide between the individual dendritic pores; this observation indicates the

influence of intersecting bulk or volume diffusion fields from the adjacent pores on the pore

growth. The condition for instability growth in these circumstances has been discussed in detail

elsewhere [11].

Figure 2. Secondary electron micrograph demonstrating the formation of dendritic gas pores in

Fe3O4 on the reduction of Fe2O3 single crystal 1173K, 25%CO, 75%CO2 [17]

As the reaction temperatures are reduced the contribution of mass transfer in the initial phase,

ahead of the growing interface, to solute redistribution decreases since the activation energies for

bulk diffusion are generally higher than through other mechanisms. The contributions to volume

diffusion are also expected to be limited if the initial solids are highly stoichiometric solids with

low defect concentrations; the volume diffusion coefficients in these solids are generally low [18].

In these cases, it is expected that mass transfer contributions through alternative pathways, such

as, grain boundary and interfacial diffusion mechanisms will become more significant. At these

low temperatures and for low bulk diffusive fluxes the diffusion distances become small and the

scale of the resulting microstructure also become finer. At these fine scales the reaction interfaces

can cannot be distinguished using optical metallographic techniques and high resolution electron

microscope examination is essential to resolve the essential features of the interface geometry. An

example of the cellular growth of gas pores is shown in Figure 3 [19].

2 µm

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Figure 3. Transmission electron micrographs showing a) the cellular gas pores morphology, and

b) the Fe3O4 /Fe2O3 interface. Partially reduced hematite crystal 673K, 1 atm. CO [19].

As the thermodynamic driving force for transformation is reduced by changes to the composition

of the reactive gas atmosphere, conditions may be reached under which reconstructive reactions

can no longer be supported and interface growth takes place through other mechanisms. Displacive

transformations can take place in selected systems in which the initial and final solid crystal

structures are closely related. These have been observed in the transformation of hcp Fe2O3 to fcc

hcp Fe3O4 structures [17, 19, 20]. Examples of the dense product structures resulting from the

hematite to magnetite transformation are given in Figure 4.

Figure 4. Example of dense ‘lenticular’ or lath type magnetite formed on reduction of hematite

single crystals. 1273K, CO/CO2 = 0.125, a) optical micrograph of polished section [17], and b)

transmission electron micrograph of magnetite product [19].

a) b)

25 µm

a) b)

Fe2O3

25 µm

Fe3O4

Fe3O4

25 µm

500nm

Fe3O4

matrix

Fe2O3

25 µm

Fe3O4

25 µm

300nm 50nm

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Summary

In heterogeneous reaction systems many elementary processes and process steps are operating

simultaneously as the processes proceed. The relative rates of these elementary process steps

determine the structures of the reaction interfaces, the resultant product microstructures and rate

limiting reaction mechanisms. Many aspects of the phase transformations in gas/oxide systems are

analogous to those observed in melt solidification and solid-state transformations, and it is argued

that these all form a part of a general class of heterogeneous fluid/solid reaction systems.

Understanding these fundamental linkages points the way to the further development of a generic

theoretical framework that can be used to improve the design, control and optimisation of these

important reaction systems.

To be able to develop predictive models of the reduction processes fundamental information on

the thermodynamic, phase equilibria and transport properties in the initial and product phases is

required. Thanks to the pioneering work of Gunnar Eriksson in enhancing modern computer

capability, the vision of the development of predictive tools to predict the outcomes of these

complex reactions and phase transformations is already becoming a reality.

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