In this article we will discuss about:- 1. Introduction to Allotropy of Iron 2. Thermodynamics of Allotropy in Iron 3. Effect of Pressure 4. Geometry of BCC and FCC Crystal Structures of Pure Iron 5. Solubility of Carbon in Alpha and Gamma Irons.
Contents:
- Introduction to the Allotropy of Iron
- Thermodynamics of Allotropy in Iron
- Effect of Pressure on Allotropy of Iron
- Geometry of BCC and FCC Crystal Structures of Pure Iron
- Solubility of Carbon in Alpha and Gamma Irons
1. Introduction to the Allotropy of Iron:
Many of the metallic elements (even some compounds such as SiO2, quartz) exist in more than one crystal structure form depending on the external conditions of temperature and pressure, though only one crystal structure is stable under a given set of conditions. A crystal structure may transform into another by the phenomenon of phase transformation if, say, temperature is changed with the evolution/absorption of heat, called latent heat of transformation.
ADVERTISEMENTS:
Almost all the properties are changed when one modification changes to another. This phenomenon of materials to have more than one crystal structure is called allotropy or polymorphism, the former term is reserved for this behaviour in pure elements like metals, whereas polymorphism is a more general term, and the different phases are called allotropes, or polymorphs. For example, titanium and zirconium change from CPH to BCC at temperatures of 802°C and 815°C respectively on heating.
The best known example of allotropy is exhibited by iron which (at normal one atmospheric pressure) is BCC at temperatures below 910°C and above 1394°C, but FCC between 910°C and 1394°C as is illustrated in Fig. 1.11 in the form of free energy versus temperature curve for pure iron, illustrating that γ-iron (FCC) has lower energy between 910°C and 1394°C, and is thus stable in that range.
When pure iron is cooled from the molten state from temperature above its freezing temperature to room temperature, heat is evolved as a phase change takes place, leading to arrest of fall of temperature and the arrest lasts as long as the phase transformation is taking place, that is, the temperature remains constant during the phase change as illustrated by a horizontal line in the thermal analysis curve. The first arrest takes place at the freezing temperature of pure (1539°C) iron.
When all the liquid iron has changed to solid δ-iron (BCC), the temperature starts falling again, and then the thermal arrest takes place when δ -Fe changes to γ-Fe (1394°C). After freezing of pure iron, there are three thermal arrest temperatures (excluding freezing temperature), also called critical temperatures, and are designated as A4 (where the letter ‘A’ being taken from the French word ‘arret’-meaning arrest), A3 and A2, associated with the δ-iron → γ-Fe, γ-Fe → α-Fe (paramagnetic) and α-paramagnetic to α-ferromagnetic transformations respectively.
At A2 temperature (768°C) also called Curie temperature (named after Madam Curie), the heat change is not very conspicuous as it occurs over a range of temperatures with a maximum in the vicinity of 768°C, that is, while heating pure iron from room temperature, the transformation of α-iron ferromagnetic into α-iron paramagnetic is spread over a range of temperatures and is not completely isothermal unlike the transformations taking place at A3 or A4.
The temperature range of Curie transformation is unaffected by the variations in cooling, or heating rate and always occurs over the same temperature range. The Curie change is not regarded as an allotropic transformation as there is no change in either the crystal structure or lattice parameter. The iron existing between 768°C to 910°C, i.e., α-Fe paramagnetic is sometimes called beta-iron. Gamma iron as well as δ-iron are also paramagnetic.
Alpha and delta-irons are not independent modifications of iron as they have the same crystal structure, and the physical properties of delta-iron are the high temperature version of those of α-Fe, and can be extrapolated from the temperature dependence of the properties of α-Fe. Fig. 1.13 illustrates temperature dependence of mean volume per atom in iron crystal.
ADVERTISEMENTS:
If the curve for α-Fe is extrapolated as shown by dotted line in Fig. 1.13, it ends in value for δ-Fe. Delta-Fe is a high temperature manifestation of α-Fe. Fig. 1.13 also illustrates that when γ-Fe transforms to α-Fe (on cooling), expansion takes place by approximately 1%, which leads to the generation of internal stresses during transformation.
The transformation of α phase to γ phase and γ phase to α phase or/and other transformations are largely responsible for the heat treatment of steels. Fig. 1.12 (b) illustrates how the grain size can be made smaller (grain refinement) by phase transformation if it takes place by nucleation and growth.
Here, γ-Fe transforms to α-Fe. When, γ-Fe is cooled slowly such as in furnace, small number of nuclei of α-Fe form at the grain boundaries of γ-Fe [Fig. ‘1.12 (b) 2]. These nuclei grow to impinge on the neighbouring grains to complete the transformation. The grain size of α- Fe [Fig. 1.12 (b) 4] is smaller than of γ- Fe [Fig. 1.12 (b) 1].
If the γ-Fe is cooled a bit faster, such as in air, the transformation temperature Ar3 gets lowered, which increases the rate of nucleation, but lowers the rate of growth due to lesser diffusion at low temps. As the number of nuclei is much more, which grow slowly to a lesser extent, because the neighbouring growing grains impinge on each other earlier.
ADVERTISEMENTS:
The resulting number of grains of α-Fe is much more when the transformation is completed, [Fig. 1.12 (b) 4]. Whenever phase transformation takes place, a grain refinement takes place which becomes more if the amount of super-cooling (or heating) is more (If it takes place by nucleation and growth process).
Fig. 1.12 (a) illustrates that the phase changes in iron are reversible but do not ordinarily take place at the same temperature during cooling and heating cycles. These transformations occur below the equilibrium temperature during cooling and above it during heating, and that is why the temperature of transformation during cooling is designated by the symbol, Ar (‘A’ letter is for arrest), where the letter V being taken from the French ‘refroidissement’ meaning ‘cooling’.
Thus, the critical temperatures in pure iron during cooling are designated as Ar4, Ar3 and Ar2. The critical temperature observed on heating is designated as Ac, where the letter ‘c’ being taken from the French ‘chauffage’-meaning ‘heating’. And, thus, the critical temperatures are designated as Ac2, Ac3 and Ac4. This, difference in temperatures during heating and cooling, called the thermal hysteresis, is because at the equilibrium temperature, the free energies of the two phases, one the parent phase and second the product phase, are equal.
The parent phase may transform if its temperature is changed where the product phase has lower free energy. Moreover, the creation of an interface between the parent and the product phase, when the product phase forms, needs surface energy for its creation and which is met by the difference in the free energies of the two phases.
ADVERTISEMENTS:
Thus, super-cooling during cooling cycle and superheating during heating cycle, become necessary to bring about the changes resulting in the thermal hysteresis, which can be reduced by slow heating and cooling rates and increased with faster rates of heating and cooling.
The phase transformations which take place by nucleation and growth are affected more by the variations in rates of cooling than of heating as an increase in the rate of cooling tends to depress the transformation to lower temperatures where the diffusion of atoms become lesser and lesser, whereas during heating, the diffusion of atoms increases during superheating. That is also the reason that transformation referring to A3 temperature shows more hysteresis than that to the A4 temperature. Also, higher is the starting temperature of cooling, lower is the Ar temperature.
2. Thermodynamics of Allotropy in Iron:
The variation of free energies of different crystal structures of pure iron with temperatures may now be considered. The relative magnitude of the free energy value governs the stability of a phase, that is, the phase having lowest free every in any temperature range is the stable phase. (Fig.1.11).
The free energy, G, of a system at a temperature T can be given as:
Equation 1.2 indicates that the stability of a phase, that is, the low value of the free energy, G, requires lowest value of H0 and high value of specific heat, particularly at high temperatures, because the factor Cp/T should be as high as possible so that free energy of a given phase decreases with the rise of temperature if larger is its specific heat. Specific heat is primarily contributed by the lattice vibration of atoms and partly by the vibrations of electrons.
A phase may be stable at low temperatures if it has smaller specific heat than the high temperature phase. Actually at low temperatures, the second term in the equation (1.2) is less significant and the phase having lowest value of H0 is the stable phase. The phase having close packed crystal structure has strong bonding of atoms, and thus has low H0 value. But a strongly bonded phase has high elastic constants, which means higher vibrational frequency and thus, has smaller specific heat.
On the other hand, more weakly bonded crystal structure, which has a higher H0 at low temperatures, is likely to be a stable phase at high temperatures, as the second term now becomes important. Thus, it can be generalised that whenever a phase change occurs, the more close-packed structure usually exists at low temperatures, whereas the more open structure is stable at the higher temperatures.
That is why all metals must melt at sufficiently high temperatures, because the liquid has no long-range structure and has higher entropy than any solid phase, that is, the term ‘T.S’ overcomes the H0 term in the normal free energy equation. But the phase changes in iron, (i.e., BCC, the open structure is stable at low temperatures and changes at 910°C to a more close packed FCC structure, which again changes at 1394°C to BCC, the less close packed structure), is an exception to this rule, because the low temperature BCC structure is stable due to its ferro-magnetic properties, which requires, and this structure has just the right interatomic distances for the electrons to have parallel spins to give magnetism.
This state has low entropy as well as minimum internal energy, which makes BCC structure stable in iron at low temperatures. Contribution of lattice vibrations to the specific heat of metals is greater for the phase with lower Debye characteristic temperature, which is associated with lower vibrational frequency and lower binding energy. The Debye characteristic temperature of γ-iron (FCC) is lower than that of α-iron (BCC) and this is mainly responsible for the α-Fe to γ-iron transformation.
The occurrence of BCC iron structure above 1394°C is due to large electronic specific heat of iron in general (on heating). The electronic specific heat of BCC iron is greater than FCC iron above about 300°C and becomes sufficiently greater at higher temperatures to make it stable again above 1394°C.
3. Effect of Pressure on Allotropy of Iron:
As the pressure is increased, the α-Fe → γ-Fe transition temperature is lowered, whereas γ-Fe δ→ Fe transition temperature is raised. This is true to Le Chateliers principle. As γ-Fe (FCC) is a close-packed structure, it resists the pressure more than α-Fe, or δ-Fe (BCC) which are more open structures (less densely packed), and that is why the area of stabilisation of γ-Fe increases with the increase of pressure. This is also the reason that the pressure of 15 GPa (~ 150,000 atmospheres), or more changes the α-Fe to HCP (ε) phase.
4. Geometry of BCC and FCC Crystal Structures of Pure Iron:
Pure iron has essentially two crystal structures, one BCC and the other FCC. It is relevant to study the geometry of unit cells of a-iron and γ-iron crystals. The body centered cubic crystal structure and icrystal structure of face centered cube.
Gamma-iron unit cell has greater lattice parameter than α-iron unit cell, but atomic packing factor of FCC is 0.74, that is, 26% of the volume of unit cell is unoccupied by atoms; and is 0.68 in BCC, that is, 32% of the volume of unit cell is unoccupied by atoms. FCC unit cell has 4 atoms per unit cell as compared to BCC having 2 atoms per unit cell. Thus, BCC structure of a-iron is more loosely packed than that of FCC γ-iron, and that is why density of FCC γ-iron is 8.14 g/cm3 at 20°C and 7.87 g/cm3 for α-iron.
In any crystal structure, there are small holes in between the usual atoms into which smaller interstitial atoms may sit to form interstitial solid solution. These holes or voids are called interstitial holes, or sites, or voids. An interstitial atom has a co-ordination number equal to the number of atoms of parent lattice (here iron) it touches. The non-metallic elements like carbon, nitrogen, oxygen, hydrogen, boron in iron sit in these sites to form their interstitial solid solutions.
There are two main types of interstitial holes called octahedral and tetrahedral holes in FCC and BCC irons. These two types of holes derive their names from the number of sides of the polyhedron formed by the iron atoms that surround a given interstitial hole. A carbon atom has six nearest neighbour iron atoms if in an octahedral hole and four in a tetrahedral hole.
Fig. 1.15 (a) illustrates one octahedral hole in FCC structure which is at the centre u. the cube. Fig. 1.15 (b) illustrates location of other octahedral holes in FCC structure by solid spheres which are at the centres of cube edges [also Fig. 1.15 (c)].
There are eight in number per unit cell. The octahedral hole in FCC-γ- iron is the largest hole and the largest diameter of sphere which can be accommodated here without elastic distortion is of 0.052 nm in radius, whereas largest diameter of sphere which can be accommodated in tetrahedral hole in FCC-γ-iron is 0.028 nm in radius.
In FCC structure, there are 4 atoms per unit cell. Thus, there is one octahedral hole per iron atom in FCC-γ-iron. Fig. 1.16 illustrates that there are 8 tetrahedral holes per unit cell. And, thus there are 2 tetrahedral holes per atom in FCC structure.
The two types of interstitial holes in BCC structure are illustrated in Fig. 1.17. The largest holes are tetrahedral holes of radius 0.036 nm. The unsymmetrical octahedral holes in BCC structure have a size of radius 0.019 nm. Note that centre of this hole is at a distance of a/2 from two atoms and at a distance of a/√2 from four atoms.
5. Solubility of Carbon in Alpha and Gamma Irons:
Carbon steels are essentially alloys of iron and carbon containing up to roughly 2.0% carbon, but invariably contain some elements like manganese, silicon, sulphur and phosphorous due to the industrial practice of making steels. Most of the elements when dissolved in iron form substitutional solid solutions such as manganese, nickel, chromium, etc. as their atomic sizes are nearer in size to that of iron.
However, elements like boron, carbon, nitrogen, oxygen, and hydrogen form interstitial solid solutions in α-iron and γ-iron as their atomic sizes are sufficiently small relative to that of iron. The formation of interstitial solid solutions in iron, specially of carbon deserves special discussion. The solubility of carbon in iron essentially depends on the crystal structure in which iron exists (and also the temperature).
However, the comparison of atomic size of carbon with the available interstitial holes (these are much smaller) makes it clear that carbon forms interstitial solid solutions with γ-iron, called austenite and with α-iron called ferrite. As some lattice distortion must take place when carbon atoms enter the iron lattice and which thus, does not allow large solid solubility’s of carbon in iron.
In FCC γ-iron, octahedral holes are large sized than tetrahedral holes and thus carbon atoms sit in these symmetrical octahedral holes even though some uniform lattice expansion takes place. The effect of carbon on the lattice parameter of γ-iron (now also called austenite). The interstitial holes in BCC α-iron (also called ferrite) are much smaller, which explains the very limited solubility of carbon in it.
Although, in BCC-α-iron, the size of the tetrahedral hole is larger than of octahedral hole, it has been actually found that carbon atom does not sit in tetrahedral hole but in the smaller octahedral hole which are more favorably placed for the relief of strain caused by carbon atom, that is, as the octahedral holes in BCC α-iron are not symmetrical because the carbon atom has only two nearest iron atoms at a distance of a/2 (the other four iron atoms are at a larger distance of a/√2).
Each of these two nearest (neighbour) iron atoms is displaced by 0.053 nm in one of the <100> directions and the unsymmetrical octahedral hole becomes symmetrical but causes tetragonal distortion of the lattice, i.e. c-axis tries to become larger than α-axis. This strain does not allow large number of carbon atoms to be accommodated in BCC α-iron. In case, carbon atom tries to occupy the larger tetrahedral hole, then four iron atoms are its nearest neighbours, and the displacement of these would require more strain energy. Thus, tetrahedral holes are not preferred sites in α-iron (also ferrite) for carbon but prefer smaller octahedral holes.
As carbon (r = 0.077 nm) sits in octahedral hole in FCC phase of iron (r = 0.052 nm) and in octahedral hole (r = 0.019 nm) in BCC phase of iron (also ferrite), the size of the octahedral hole in FCC phase in much larger and thus the elastic strains are less, resulting in greater solubility of carbon in γ-phase FCC (austenite) than in BCC α-phase iron (ferrite) as in shown in table 1.8. The marked difference in solubility of carbon in austenite and in ferrite is of great importance in the heat treatment of steels.
The presence of carbon in octahedral hole in BCC α-iron causes tetragonal distortion of lattice, and this large strain permits ferrite to accommodate only a limited number of carbon atoms, and thus, the lattice remains essentially body centred cubic. The interstitial solute atoms prefer to segregate to point, line and surface lattice defects which are responsible for strain ageing in steels.
If a large number of carbon atoms present in dissolved state in γ-iron (austenite) are trapped to BCC octahedral holes by rapid cooling to temperatures below 727°C, when highly supersaturated solid solution of carbon in BCC forms, the cubic structure may actually become tetragonal, particularly when carbon is more than 0.2%, which is a typical crystal structure of martensite , whose formation is the object of hardening heat treatment. The tetragonal distortion of the lattice is able to block the motions of all types of dislocations and, which, probably, is the single most important cause of high hardness of martensite.
The lattice parameter of γ-iron increases with the increase of temperature due to increase of thermal vibrations, increase of vacancies etc., which also means increase in the size of the interstitial holes too. That is why the solid solubility of carbon in different crystal structures of iron increases with the increase of. It is also true of nitrogen in iron.
Nitrogen (r = 0.072 nm) too sits in octahedral holes in austenite and ferrite but causes lesser strains in the lattices as its atomic radius is smaller than carbon and thus, the solid solubility of nitrogen in iron is more than carbon as shown in table 1.8.
As γ-iron having FCC structure is a close-packed structure (APF = 0.74) and α-iron (BCC) is more loosely packed (APF = 0.68), the FCC structure has large sized interstitial holes but fewer in number as compared to BCC structure which has small sized interstitial holes but inter-connected large number of them, the diffusion of both substitutional and interstitial solute takes place faster in ferrite than in austenite, and that is why activation energy is less for a particular element diffusing in α-iron than it is for the same element diffusing in γ- iron. Also, at any temperature, the substitutional atoms in iron move (diffuse) several orders of magnitude more slowly than interstitial atoms.