**2.1 Dual phase model**

The unique properties of nanocrystalline materials are associated with very fine grain size, whereby, depending upon the grain size, interfaces can include up to 50% of the atoms in the material [2-5]. Therefore determination of the structure and associated properties of individual features of a nanocrystalline structure becomes very important. Various models representing the structure of nanocrystalline materials, such as "gas like" model as suggested by Birringer et al. [5] and a "frozen gas like" model suggested later [1,50], are proposed in the literature. However, the structure of nc-materials, in general, may be described as a composition of two components: a crystalline component (CC), which is formed by small equiaxed single crystals each with random crystallographic orientations and the intercrystalline component (IC), which is formed by the interfaces between the crystallites (grain boundaries) and intersection points of these interfaces (triple junctions). The second component may be characterized by the reduced atomic density and interatomic spacing deviating from those in the perfect crystal lattice. The IC surrounds the

the grain size is 60 nm [26]. This promotion effect is also evident for the K38G alloy containing 3.5-4 wt% Al and 16% Cr, which forms external Cr2O3 scale and internal Al2O3 precipitates in the cast form (large grains) but only Al2O3 when in the form of sputtered

The unique structure and high grain boundary fraction, enhances diffusion of impurities and alloying elements, and changes materials thermodynamic properties [31-33] which are expected to cause a considerable difference in the resistance of nanocrystalline materials to environmental degradation (oxidation) at high temperatures. For practical application of these nanocrystalline materials, an acceptable level of resistance to environmental degradation is required. However, the effect of the nanocrystalline structure on the hightemperature oxidation resistance has attracted only a limited research attention. Oxidation resistance of nanocrystalline Ni-Cr-Al [34-36], Fe-Cr [37-39], and Zr [40-43] based alloys have been mainly investigated and in most of the cases, oxidation resistance has been

The properties of oxides (Al2O3, SiO2 or Cr2O3) formed during oxidation [44,45,46] also depend upon the grain size of the alloy and nanocrystalline structure alters the properties of oxide. For example, more uniform oxide scale with finer grain size and higher Cr or Al content is formed on the nanocrystalline alloys [34-36]. The oxide scales formed from nanocrystalline materials exhibit enhanced plastic deformation (due to fine grain size of formed oxide), which can release the stresses accumulated in the scales, and therefore the scale spallation tendency is reduced. It was reported that cyclic and long-time oxidation resistance was significantly improved by applying nanocrystalline coatings on type 304

In order to investigate the possible differences in oxidation resistance along with any underlying mechanisms, understanding the nanocrystalline structure of a material is essential. This chapter will therefore first describe the structure of nanocrystalline materials, their thermodynamic properties and the possible effects of changes in the material structure (caused by such fine grain size) that may influence the oxidation resistance of a material.

The unique properties of nanocrystalline materials are associated with very fine grain size, whereby, depending upon the grain size, interfaces can include up to 50% of the atoms in the material [2-5]. Therefore determination of the structure and associated properties of individual features of a nanocrystalline structure becomes very important. Various models representing the structure of nanocrystalline materials, such as "gas like" model as suggested by Birringer et al. [5] and a "frozen gas like" model suggested later [1,50], are proposed in the literature. However, the structure of nc-materials, in general, may be described as a composition of two components: a crystalline component (CC), which is formed by small equiaxed single crystals each with random crystallographic orientations and the intercrystalline component (IC), which is formed by the interfaces between the crystallites (grain boundaries) and intersection points of these interfaces (triple junctions). The second component may be characterized by the reduced atomic density and interatomic spacing deviating from those in the perfect crystal lattice. The IC surrounds the

stainless steel [47,48], Ni-Cr-Al [27], Co-Cr-Al [49], and Ni-(Co)-Cr-Al [28-30].

**2. Structure and properties of nanocrystalline alloys** 

**2.1 Dual phase model** 

nano-crystalline structure [27-30].

reported to improve due to nanocrystalline structure.

nanometer-sized crystals and forms a network between them [1,21]. As grain size reduces, the IC increases and it may even exceed CC.

Various researchers support the view of the two phase model of nanocrystalline metals. For example, extended x-ray-adsorption fine structure (EXAFS) and Mössbauer spectroscopy of ball-milled iron indicated the presence of two phases as characterized by significantly different atomic arrangements. These different atomic arrangements can be attributed to the presence of interfacial region and crystalline region [51]. Similarly, EXFAS investigation of nanocrystalline Fe and Pd indicated a large reduction in the atomic coordination number, supporting the idea of a very disordered structure at the interfaces [52-56]. Positron-lifetime spectroscopy measurements showed a large density of vacancy-like defects in grain boundaries and relatively large free volume at the triple points arising from misorientationinduced atomic instability of these sites [57]. Elastic relaxation of the interfaces occurred with a very different parameter than conventional coarse grain size polycrystalline materials. Modelling of thermoplastic properties and structure demonstrates that two phase model is an appropriate mean to account for the vibrational density of states and excess energy density in terms of grain boundary [58]. Similar to experimental findings, computer simulation of nanocrystalline iron has shown that grain boundary component in nanocrystalline material is very high and is a strong function of grain size [59,60].

In discussing the structure of nanocrystalline materials further, the following terminology will be used in the text. Three types of grain contacts are possible in a polycrystalline material. They include, a) contact surfaces, b) contact lines and c) contact points. Surfaces of two grains which contact one another are called as contact interfaces. A contact line may represent a common line for three or more adjacent grains. A contact line of three grains is called triple junction. The boundary of grain is its surfaces. Grain boundaries which are seen in the metallographic slides are the section of interfaces by slide plane. A triple point is a section of triple junction by a plane. A detailed description of the terminology used here can be found elsewhere [61].

#### **2.2 Volume fraction of crystalline and intercrystalline regions**

Mutschele and Kirchheim [62] proposed following relation to evaluate the volume fraction (*Cic*) of nanocrystalline materials associated with intercrystalline regions,

$$\mathbf{C}\_{ic} = \mathfrak{ad} \, \mathcal{J} \, \mathrm{d} \tag{1}$$

where, is the average grain boundary thickness and *d* is the average diameter of the grains and grains are considered to be cubes. Later, Palumbo et. al. [2] have shown that equation 1 was not suitable for the calculation of volume associated with triple points and to make it more general (to account for the triple points associated with the intercrystalline component) they proposed following relationship for the calculation of the intercrystalline component ( *ic Vt* ):

$$V\_t^{ic} = 1 - \left[\frac{d - \delta}{d}\right]^3 \tag{2}$$

where, *d* is the maximum diameter of an inscribed sphere. This yields the following relation for grain boundary volume fraction ( *gb Vt* ),

Oxidation Resistance of Nanocrystalline Alloys 217

Based on Figure 1, properties which are influenced by the grain boundary and triple points are expected to be altered significantly when grain size is refined to, or below, 100 nm. The effect of triple points is more pronounced when the grain size is less than 10 nm; consequently material properties with grain size less than 10 nm would be significantly

Many researchers have described grain boundaries in nanocrystalline materials as more disordered than those in conventional microcrystalline materials [64-67]. For example, investigations on nanocrystalline Fe have demonstrated that grain boundaries in nanocrystalline Fe differ significantly from the grain boundaries in conventional polycrystalline Fe [64-69]. Thermodynamic properties (specific heat at constant pressure, heat of fusion and stored enthalpy) of ball-milled Fe and other nanocrystalline materials, investigated by Fecht suggested [64-69] that the grain boundaries' energy in nanocrystalline materials to be considerably greater than in the case of equilibrated grain boundaries in microcrystalline materials. In conventional polycrystalline materials, grain boundary energy, as determined by experiments, as well as static and dynamic simulations, is approximately 1 J/m2, whereas, this value soars to 4 J/m2 in nanocrystalline materials [70-

Significantly different thermodynamic properties of nanocrystalline materials are expected to increase the Gibbs free energy of the materials alloys which can be represented as per

G= *gb Vt* .Ggb+ *tp Vt* .Gtp+ *cc Vt* .Gcc (5)

where, Ggb, Gtp and Gcc are the standard gibbs free energies of grain boundaries, triple points

Increases in the interfacial energy may lead to a significant increase in the free energy which can be described simply as (neglecting second order contributions due to specific heat

Enthalpy difference, ΔH, is shown to be quite higher in nanocrystalline materials than conventional microcrystalline materials. For example it has been shown that ΔH of nanocrystalline Fe increases with decrease in grain size [64-67,76]. Similar behaviour was reported for nanocrystalline copper as well. For example, nanocrystalline Cu, prepared as a powder by vapour deposition followed by compaction releases 300 J/mol at 430K when analysed immediately after compaction and 53 J/mol at 450K when analysed five days after preparation. Such values of enthalpy release have also been confirmed by a study on nanocrystalline Cu prepared by electrodeposition and cold rolling [77-79]. Comparison of these data show that nanocrystalline materials are far from equilibrium, not only because they contain a large amount of interfaces but also because these interfaces are not equilibrated. Therefore, these materials should have high value of free energy which may

result in higher reaction rate at the nanocrystalline surfaces.

ΔG= ΔH –TΔS (6)

different than those with grain size > 10 nm.

75].

following relationship:

and grains.

differences):

**2.3 Thermodynamic properties of nanocrystalline materials**

$$V\_t^{\mathcal{S}^b} = \left[\frac{3\delta (d-\mathcal{S})^2}{d^3}\right] \tag{3}$$

The volume fraction associated with triple points (Vt tp) is then given by,

$$V\_t^{tp} = V\_t^{ic} - V\_t^{gb} \tag{4}$$

Using above equations and applying a boundary thickness () of l nm [2, 62,63], the effect of grain size (*d*), in the range of 2 nm to 1000 nm, on the calculated volume fractions corresponding to intercrystalline regions, grain boundaries, and triple junctions, is shown in Figure 1. The intercrystalline component increases from a value of 0.3% (at a grain size of l000 nm) to a maximum value of 87.5% at a 2 nm grain size (Figure 1). The volume fractions associated with intercrystalline regions and perfect crystal are equivalent (i.e., 50%) at a grain size of ~ 5 nm. In assessing the individual elements of the intercrystalline fraction, it is noted that the triple junction volume fraction displays greater grain size dependence than that of the grain boundaries. In the range 100 nm to 2 nm, the triple junction volume fraction increases by three orders of magnitude, while the grain boundary volume fraction increases by little over one order of magnitude. In the nanocrystalline range (i.e., d ~ 10 nm), the grain boundary fraction only increases from ~27% at 10 nm, to a maximum value of ~ 44% at 3 nm. Over the same range of grain sizes, the triple junction fraction increases from ~3% to a value of 50%.

Fig. 1. The effect of grain size on the volume fractions of intercrystalline region, grain boundaries and triple points; calculated from equations 2-5 and assuming the grain boundary thickness to be 1 nm [2].

 

*t <sup>d</sup> <sup>V</sup>*

The volume fraction associated with triple points (Vt

value of 50%.

boundary thickness to be 1 nm [2].

1E-4

1E-3

0.01

Volume Fraction

0.1

1

2

tp) is then given by,

*tp g ic <sup>b</sup> V VV t tt* (4)

 Viv t Vgb t Vtp t

(3)

3 *gb* 3( )

 

*d*

Using above equations and applying a boundary thickness () of l nm [2, 62,63], the effect of grain size (*d*), in the range of 2 nm to 1000 nm, on the calculated volume fractions corresponding to intercrystalline regions, grain boundaries, and triple junctions, is shown in Figure 1. The intercrystalline component increases from a value of 0.3% (at a grain size of l000 nm) to a maximum value of 87.5% at a 2 nm grain size (Figure 1). The volume fractions associated with intercrystalline regions and perfect crystal are equivalent (i.e., 50%) at a grain size of ~ 5 nm. In assessing the individual elements of the intercrystalline fraction, it is noted that the triple junction volume fraction displays greater grain size dependence than that of the grain boundaries. In the range 100 nm to 2 nm, the triple junction volume fraction increases by three orders of magnitude, while the grain boundary volume fraction increases by little over one order of magnitude. In the nanocrystalline range (i.e., d ~ 10 nm), the grain boundary fraction only increases from ~27% at 10 nm, to a maximum value of ~ 44% at 3 nm. Over the same range of grain sizes, the triple junction fraction increases from ~3% to a

Fig. 1. The effect of grain size on the volume fractions of intercrystalline region, grain boundaries and triple points; calculated from equations 2-5 and assuming the grain

1 10 100 1000

Grain size (nm)

Based on Figure 1, properties which are influenced by the grain boundary and triple points are expected to be altered significantly when grain size is refined to, or below, 100 nm. The effect of triple points is more pronounced when the grain size is less than 10 nm; consequently material properties with grain size less than 10 nm would be significantly different than those with grain size > 10 nm.

#### **2.3 Thermodynamic properties of nanocrystalline materials**

Many researchers have described grain boundaries in nanocrystalline materials as more disordered than those in conventional microcrystalline materials [64-67]. For example, investigations on nanocrystalline Fe have demonstrated that grain boundaries in nanocrystalline Fe differ significantly from the grain boundaries in conventional polycrystalline Fe [64-69]. Thermodynamic properties (specific heat at constant pressure, heat of fusion and stored enthalpy) of ball-milled Fe and other nanocrystalline materials, investigated by Fecht suggested [64-69] that the grain boundaries' energy in nanocrystalline materials to be considerably greater than in the case of equilibrated grain boundaries in microcrystalline materials. In conventional polycrystalline materials, grain boundary energy, as determined by experiments, as well as static and dynamic simulations, is approximately 1 J/m2, whereas, this value soars to 4 J/m2 in nanocrystalline materials [70- 75].

Significantly different thermodynamic properties of nanocrystalline materials are expected to increase the Gibbs free energy of the materials alloys which can be represented as per following relationship:

$$\mathbf{G} = \, V\_t^{\circ \flat} \, \mathbf{.} \mathbf{G} \mathfrak{d} + \, V\_t^{\sharp \flat} \, \mathbf{.} \mathbf{G} \mathfrak{d} + \, V\_t^{\mathrm{cc}} \, \mathbf{.} \mathbf{G} \mathfrak{c} \tag{5}$$

where, Ggb, Gtp and Gcc are the standard gibbs free energies of grain boundaries, triple points and grains.

Increases in the interfacial energy may lead to a significant increase in the free energy which can be described simply as (neglecting second order contributions due to specific heat differences):

$$
\Delta \mathbf{G} = \Delta \mathbf{H} \text{ -T} \Delta \mathbf{S} \tag{6}
$$

Enthalpy difference, ΔH, is shown to be quite higher in nanocrystalline materials than conventional microcrystalline materials. For example it has been shown that ΔH of nanocrystalline Fe increases with decrease in grain size [64-67,76]. Similar behaviour was reported for nanocrystalline copper as well. For example, nanocrystalline Cu, prepared as a powder by vapour deposition followed by compaction releases 300 J/mol at 430K when analysed immediately after compaction and 53 J/mol at 450K when analysed five days after preparation. Such values of enthalpy release have also been confirmed by a study on nanocrystalline Cu prepared by electrodeposition and cold rolling [77-79]. Comparison of these data show that nanocrystalline materials are far from equilibrium, not only because they contain a large amount of interfaces but also because these interfaces are not equilibrated. Therefore, these materials should have high value of free energy which may result in higher reaction rate at the nanocrystalline surfaces.

Oxidation Resistance of Nanocrystalline Alloys 219

surface of the alloy. Oxide scale should possess mechanical properties as close possible to the base material and most importantly it should be adherent to the substrate even in the presence of large thermal shocks. These parameters largely depend upon the alloy composition and microstructure and can be optimized choosing the right combination of the two. The development of the nanocrystalline structure has provided a large scope of modification of the microstructure and to investigate the effect of nanocrystalline structure on the properties of oxide scale formed and therefore the resultant oxidation resistance. Since nanocrystalline materials are thought to be very reactive due to presence of large fraction of defects, it was supposed that they may possess poor oxidation resistance. Here both the possibilities of improvement and deterioration of oxidation resistance due to a

**3.1 Deterioration of oxidation resistance caused by nanocrystalline structure** 

The following are possibilities which may lead to a higher oxidation rate in a nanocrystalline

1. It was described in the previous section that free energy of a nanocrystalline alloy is increased as the atoms residing at the grain boundaries are more reactive than the atoms at grains. This increased free energy of nanocrystalline materials would accelerate the reactions occurring upon them and therefore oxidation rate of nanocrystalline structure is expected to increase, leading to poor resistance to

2. Increase in oxide nucleation sites and, therefore, formation of oxide scale with comparatively finer grain size through which diffusion of oxygen and metal would be faster because of enhanced diffusion through the grain boundaries. Such phenomenon occurring in Ni-Cr-Al alloy accelerates diffusion of Al through the oxide which facilitates the formation of Al oxide [34] and leads to substantial improvement in oxidation resistance. However, such diffusion in a pure metal may lead to a significant higher oxidation rate if a non-protective oxide scale forms. For example in cause of pure Ni, nanocrystalline structure has reported to increase the oxidation rate because of increased diffusion of Ni and oxygen through the grain boundaries of oxide formed on

3. In the case of alloys where the concentration of solute atoms is lower than a critical value for external oxide scale formation, internal oxidation occurs. The oxidation rate is enhanced because of increased diffusivity of oxygen through grain boundaries leading to severe internal oxidation near the surface. Rapid oxidation occurs for these alloys.

**3.2 Improvement in oxidation resistance caused by the nanocrystalline structure** 

Improvement in oxidation resistance of some engineering alloys where protective oxide scales are formed at high temperatures is noticed in their nanocrystalline forms. Improved oxidation resistance of FeBSi [87], Ni-based alloys [88-93], Zr and its alloys [40-43], Cr-33Nb [94], Fe-Co based alloys [95,96] and Cu-Ni-Cr alloys [97] is reported in their nanocrystalline form (in comparison to their microcrystalline counterparts). The mechanistic role of a nanocrystalline structure leading to the improved oxidation resistance is discussed below:

nanocrystalline structure are discussed:

environmental degradation.

the metal [86].

structure:

The total free energy also depends upon entropy term (equation 1), however, evaluation ΔS is not straightforward since there is a little reported in the literature on the entropy contribution from grain boundaries and interfaces for crystals of any size. Although it is expected that this entropy contribution is small and it can also be conceived that nonequilibrated grain boundaries have higher entropy. A value of 0.36 mJ/m2 K has been estimated for as-prepared nanocrystalline Pt, in contrast to the value for conventional grain boundaries of 0.18 mJ/m2 K [80]. In fact, the excess entropy per atom sitting in a grain boundary is a substantial part of the entropy of fusion, but the overall entropy per mole of substance sums up to a limited amount even for materials with very small grains. Using this knowledge of enthalpy and entropy, the free energy of nanocrystalline copper has been reported to be higher than that of coarse grain copper [80,81].

#### **2.4 Diffusion in nanocrystalline materials**

In general, atomic transport in nanocrystalline materials differs substantially from that in coarse-grained material, due to the crystallite interfaces providing paths of high diffusivity. In conventional microcrystalline materials, crystal volume self-diffusion or substitutional diffusion dominates, at least at temperatures higher than approximately half of the melting temperature. Interface diffusion, in combination with a high fraction of atoms in interfaces, gives rise to modified physical properties of nanocrystalline solids. Furthermore, diffusion processes may control the formation of nanocrystalline materials, for example, by means of crystallization of amorphous precursors, as well as the stability of nanocrystalline materials (relaxation, crystallite growth), their reactivity, corrosion behaviour, or interaction with gases. The relevance of diffusion-controlled processes demands a comprehensive understanding of atomic diffusion in nanocrystalline materials. Detailed discussion of the diffusion processes in the nanocrystalline material is out of the scope. For the readers interest it could be found elsewhere [82-85]. A recent study on nanocrystalline Fe has shown that the diffusion coefficient of Cr in Fe can be enhanced by several orders of magnitude by reducing the grain size to nanometer level [11].

Diffusion in a material can be expressed as the combined effect of diffusion through the grain boundaries and lattice diffusion and can be written as:

$$D\_{\rm B} = fD\_{g\rm b} + (1 - f)D\_{\rm b} \rightarrow D\_{\rm B} = f\{D\_{g\rm b} - D\_{\rm b}\} + D\_{\rm b} \tag{7}$$

where, *f* is the grain boundary fraction, *Dgb* is the grain boundary diffusion coefficient and *Db* is the bulk diffusion coefficient of B in the alloy. Assuming the cubic shape of grains, the grain boundary area fraction (*f)* can be calculated as per equation (1). Because Dgb is much larger than Db, the effective diffusion coefficient of nanomaterials increases significantly by their high area proportion of grain boundaries.

#### **3. Factors effecting the oxidation behavior of a nanocrystalline alloy**

An effective protection of metallic materials against high temperature oxidation is based on the protective oxide scale which acts as diffusion barrier, isolating the material from the aggressive atmosphere. The principle is simple, however its application is complex; to act as a real barrier the oxide film needs to be dense and homogenous and has to cover entire

The total free energy also depends upon entropy term (equation 1), however, evaluation ΔS is not straightforward since there is a little reported in the literature on the entropy contribution from grain boundaries and interfaces for crystals of any size. Although it is expected that this entropy contribution is small and it can also be conceived that nonequilibrated grain boundaries have higher entropy. A value of 0.36 mJ/m2 K has been estimated for as-prepared nanocrystalline Pt, in contrast to the value for conventional grain boundaries of 0.18 mJ/m2 K [80]. In fact, the excess entropy per atom sitting in a grain boundary is a substantial part of the entropy of fusion, but the overall entropy per mole of substance sums up to a limited amount even for materials with very small grains. Using this knowledge of enthalpy and entropy, the free energy of nanocrystalline copper has been

In general, atomic transport in nanocrystalline materials differs substantially from that in coarse-grained material, due to the crystallite interfaces providing paths of high diffusivity. In conventional microcrystalline materials, crystal volume self-diffusion or substitutional diffusion dominates, at least at temperatures higher than approximately half of the melting temperature. Interface diffusion, in combination with a high fraction of atoms in interfaces, gives rise to modified physical properties of nanocrystalline solids. Furthermore, diffusion processes may control the formation of nanocrystalline materials, for example, by means of crystallization of amorphous precursors, as well as the stability of nanocrystalline materials (relaxation, crystallite growth), their reactivity, corrosion behaviour, or interaction with gases. The relevance of diffusion-controlled processes demands a comprehensive understanding of atomic diffusion in nanocrystalline materials. Detailed discussion of the diffusion processes in the nanocrystalline material is out of the scope. For the readers interest it could be found elsewhere [82-85]. A recent study on nanocrystalline Fe has shown that the diffusion coefficient of Cr in Fe can be enhanced by several orders of magnitude by

Diffusion in a material can be expressed as the combined effect of diffusion through the

where, *f* is the grain boundary fraction, *Dgb* is the grain boundary diffusion coefficient and *Db* is the bulk diffusion coefficient of B in the alloy. Assuming the cubic shape of grains, the grain boundary area fraction (*f)* can be calculated as per equation (1). Because Dgb is much larger than Db, the effective diffusion coefficient of nanomaterials increases significantly by

An effective protection of metallic materials against high temperature oxidation is based on the protective oxide scale which acts as diffusion barrier, isolating the material from the aggressive atmosphere. The principle is simple, however its application is complex; to act as a real barrier the oxide film needs to be dense and homogenous and has to cover entire

**3. Factors effecting the oxidation behavior of a nanocrystalline alloy** 

ܦ ൌ ݂ܦ ሺͳെ݂ሻܦ ՜ ܦ ൌ ݂൫ܦ െ ܦ൯ܦ) 7 (

reported to be higher than that of coarse grain copper [80,81].

**2.4 Diffusion in nanocrystalline materials** 

reducing the grain size to nanometer level [11].

their high area proportion of grain boundaries.

grain boundaries and lattice diffusion and can be written as:

surface of the alloy. Oxide scale should possess mechanical properties as close possible to the base material and most importantly it should be adherent to the substrate even in the presence of large thermal shocks. These parameters largely depend upon the alloy composition and microstructure and can be optimized choosing the right combination of the two. The development of the nanocrystalline structure has provided a large scope of modification of the microstructure and to investigate the effect of nanocrystalline structure on the properties of oxide scale formed and therefore the resultant oxidation resistance. Since nanocrystalline materials are thought to be very reactive due to presence of large fraction of defects, it was supposed that they may possess poor oxidation resistance. Here both the possibilities of improvement and deterioration of oxidation resistance due to a nanocrystalline structure are discussed:

### **3.1 Deterioration of oxidation resistance caused by nanocrystalline structure**

The following are possibilities which may lead to a higher oxidation rate in a nanocrystalline structure:


### **3.2 Improvement in oxidation resistance caused by the nanocrystalline structure**

Improvement in oxidation resistance of some engineering alloys where protective oxide scales are formed at high temperatures is noticed in their nanocrystalline forms. Improved oxidation resistance of FeBSi [87], Ni-based alloys [88-93], Zr and its alloys [40-43], Cr-33Nb [94], Fe-Co based alloys [95,96] and Cu-Ni-Cr alloys [97] is reported in their nanocrystalline form (in comparison to their microcrystalline counterparts). The mechanistic role of a nanocrystalline structure leading to the improved oxidation resistance is discussed below:

30,47].

structure.

oxidise, respectively.

Oxidation Resistance of Nanocrystalline Alloys 221

depends upon their physical properties (e.g., crystal size, morphology and crystallographic orientation of oxides formed, lattice mismatch with the base metal, adhesion of oxide layer) of oxide [105,106]. For example, fine grained oxide scales often show a fast creep rate at high temperatures, releasing the stresses accumulated in the scales and, therefore, decrease in scale spallation tendency. This may have important implication in reducing the spallation of oxides at high temperature. Since nanocrystalline materials provide several orders of magnitude more nucleation sites than the microcrystalline materials therefore grain size of the oxide developed on nanocrystalline materials is expected to be finer. This finer grain size of oxide suppresses oxide scale spallation in nanocrystalline form. This effect has been demonstrated in high temperature oxidation tests of several nanocrystalline alloys [27-

It was also proposed that fine nano-sized oxide structure reduces conductivity which suppresses the transport of the oxidizing species, enhancing oxidation resistance. This proposal was successfully used to explain improved oxidation resistance of Zr and Zr based

It is important to note that the above factors can operate both indifferently and in combination [12]. The nature of the influence of nanostructure on the diffusion-assisted corrosion (viz., high temperature oxidation) depends on the role of the predominantly diffusing species in a given alloy. For example, oxidation resistances of an ironaluminide and an Fe-B-Si alloy in the nanocrystalline state are reported to be superior to that in their microcrystalline state [87,108]. This behaviour is attributed to Al and Si, the well-known protective oxide film formers, being the predominantly diffusing species respectively in the two alloys, and the nanostructure facilitating their diffusion and expedited formation of protective films (of Al/Si oxide). Therefore, it is important to consider all the factors effecting the oxidation resistant, and the net effect of all the parameters would determine the change in the oxidation rate caused by nanocrystalline

**4. Critical concentration of solute required for the transformation of internal** 

Oxidation of engineering alloys is very complex as the components of the alloys has different affinities for the oxygen, and reacting atoms do not diffuse at the same rates in the oxides or alloy substrates. Various types of oxides can be formed on and in the alloy. Atomic ratios of the elements in the oxide scale may differ significantly from those in the alloy. When oxygen and metal atoms diffuse and react at the surface of an alloy, an external oxide layer is formed on the surface and this is termed as the "external oxidation". For external oxidation, outward flow of metal atoms must exceed the inward flow of oxygen, whereas, when inward flow of oxygen exceeds the outward flow of the metal atoms, oxygen diffuses inside the metal and oxidation takes places within the alloy. This process is termed as "internal oxidation" which leads to catastrophic loss in the material property [44,45,109]. Figures 2 and 3 schematically show internal and external oxidation for alloy A-B under the conditions where only B oxidises and both A and B

**to external oxidation as a function of grain size** 

alloys [107]. However, it is not clear if this model also applies for other alloys.

## **3.2.1 Enhanced diffusivity and oxidation resistance**

Certain alloys can develop a continuous layer of the protective oxide of more reactive alloying elements which forms basis for the development of oxidation resistanct alloys. Such alloys are Fe, Ni, Co based, with Al, Cr or Si as the reactive alloying additives. For example, Iron-chromium alloys (such as stainless steels) are the most commonly employed oxidation resistant materials. It has been established that when time-dependent inward flux of oxygen is less than the time-dependent outward flux of solute (Cr), a continuous layer of Cr-oxide is formed at or very near the surface. Formation of such oxide layer and therefore oxidation resistance of Fe-Cr alloys depend upon the supply of solute from the alloy to alloy/oxide scale. It was established in the literature that a fine grain (~17 µm or less) stainless steel easily developed a uniform layer of Cr2O3. For an alloy with grain sizes greater than ~40 *µ*m, this protective layer of Cr2O3 was difficult to form due to insufficient grain boundary diffusion and inadequate chromium supply [98-100]. In nanocrystalline materials where grain size is very fine and diffusion coefficients are high, such Cr oxide formation should be facilitated by a large extent. Since enhanced diffusion of alloying elements in the nanocrystalline structure facilitates the formation of protective oxides, therefore alumina, chromia and/or silica forming alloys should have improved oxidation resistance in their nanocrystalline form.
