Introduction material changes from one state to another

A phase transition occurs when one material changes from one state to another state at a specific combination of temperature and pressure. In fact, there are three states in every substances in this world, which are solid, liquid and gas.
A phase can be defined as a portion of the system whose properties and composition are homogeneous and which is physically distinct from other parts of the system. A change in a feature of a physical system, often involving the absorption or emission of energy from the system, resulting in a transition of that system to another state is known as phase transformation. (Phase Transformation, 2018)
Generally, there are some of the example of the process which will lead to a phase transition such as solidification, melting, evaporation, condensation and so on. The reason why a transformation occurs is because the initial state of the substance is unstable relative to the final state when it is subjected to change in temperature. The stability of a system for transformation occurs at constant temperature and pressure is determined by its Gibbs Free Energy (G).
In this assignment, a liquid to solid phase transformation solid to solid phase transformation as well as factors that affecting the transformation will be studied.

Liquid-Solid Transformation
The process of a substance change from liquid to solid state during cooling is known as solidification. Solidification is a transformation between crystallographic and non-crystallographic state of a metal or alloy. These transformations are basic to such technological applications as ingot casting, foundry casting, continuous casting, single-crystal growth for semiconductors and directionally solidified composite alloys. Generally, solidification process is affected by such parameters as temperature distribution, cooling rate and alloying.
The solidification of metals and alloys is an important industrial process since most metals are melted and then cast into a semi-finished or finished shape. In general, the solidification of metal or alloy can be divided into the following steps:
The formation of stable nuclei in the melt which is also known as nucleation;
The growth of nuclei into crystal;
The formation of grain structure by joining together of crystals to form grains and associated grain boundaries.

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Figure 1: Stages of solidification: (a) Nucleation, (b) Growth of nuclei into crystals, (c) Formation of grain structure.
In comparison with solid-solid transformation, liquid-solid transformation is more easily to be formed as the atoms in liquid is more freely to move from one place to another place compared with atoms in solid. Other than that, the undercooling needed for liquid-solid transformation is lesser compared to solid-solid transformation. Hence, liquid-to-solid transformation is more common than solid-to-solid transformation.

The driving force for solidification
In dealing with phase transformation, it is often concerned with the difference in free energy between two phases at temperatures away from the equilibrium temperature. For instance, if a liquid metal is undercooled by ?T below melting temperature, T_m before it solidifies, solidification will be accompanied by a decrease in free energy, ?G (J/mol) as shown in Figure 2 below. This free energy decrease provides the driving force for solidification.

Figure 2: Molar free energy as a function of temperature for liquid and solid.
Solidification of pure metal
In the case of solidification in pure metal, the cooling curve is shown in Figure 3 below.

Figure 3: Solidification of a pure metal.
In fact, for pure metal, the liquid is stable above the freezing point as the energy of liquid is less than solid above the freezing point. In other words, the energy of liquid becomes higher than solid when it is below the freezing point causing the solid more stable than the liquid. Hence, the liquid converted into solid at the freezing point during cooling. Thermodynamically, both liquid and solid have equal energy at freezing point, thus, both are equally stable at freezing point. During this stage, there is no solidification will take place at the freezing point. (Solidification of material, 2013)
Nucleation in pure metal
Nucleation is the appearance at points in the liquid of centres upon which further atoms can be deposited for the growth of solid crystal. At the solidification temperature, atoms from the liquid metal begin to cluster together by driving force and start to form crystals. The moment when a crystal begins to grow, it is known as nucleus and the point where it occurs is the nucleation point. When the metal begins to solidify, multiple crystals begin to grow in the liquid. The two main mechanisms by which the nucleation of solid particles in liquid metal occurs are homogeneous nucleation and heterogeneous nucleation.
Homogeneous nucleation
Homogeneous nucleation is a process of formation of a critically size solid from the liquid by clustering together of a large number of atoms at a high undercooling without an external interface. For a nucleus to be stable so that it can grow into a crystal, it must reach a critical size. A cluster of atoms bonded together that is less than critical size, r^* is called an embryo, and one that is larger than the critical size is called a nucleus.
In the homogeneous nucleation of a solidifying pure metal, two kinds of energy changes must be considered. First is the volume free energy released by the liquid-to-solid transformation and the surface energy required to form the new solid surfaces of the solidified particles as shown in Figure 4.

Figure 4: Schematic diagram of the energies involved in homogeneous nucleation.

In equation form, the total free energy change for the formation of a spherical embryo or nucleus of radius, r formed in a freezing pure metal is
?G_T=4/3 ?r^3 ?G_v+4?r^2 ?
where, ?G_T= total free-energy change,
r= radius of embryo or nucleus,
?G_v= volume free energy,
?= specific surface free energy.

Heterogeneous nucleation
Heterogeneous nucleation is a process of formation of a critically sized solid from the liquid on an impurity surface. It occurs in a liquid on the surface of its container, insoluble impurities and other structural materials that lower the critical free energy required to form a stable nucleus.

Figure 5: Comparison between ?G_het and ?G_homo.
Based on Figure 5, the free energy needed for heterogeneous nucleation is lower than the homogeneous nucleation. This is because the surface energy to form a stable nucleus is lower when nucleation takes place on the nucleation agent rather than in the pure liquid itself. Since the surface energy is lower for heterogeneous nucleation, the total free-energy change for the formation of stable nucleus will be lower, and the critical size of the nucleus will be smaller. Hence, a much smaller amount of undercooling is required to form a stable nucleus produced by heterogeneous nucleation.
Solid-Solid Transformation
Solid–solid transformation between different crystalline structures are possibly the most numerous of nature’s phase transitions. Among them are common transformations exhibited by elemental crystals, alloys and minerals with broad implications in earth science, diamond and steel production, and the synthesis of ceramic materials. The majority of phase transformation that occur in the solid state take place by thermally activated atomic movements. The transition from graphite to diamond, the property design of steels or the formation of metastable phases to strengthen aluminium are just a few well-known examples of solid–solid transitions in crystalline materials. Another typical example of solid-solid transformation is martensitic transformation.
Solid-solid transformation can be generally subdivided into two stages: nucleation and growth. It also has two main mechanisms which are homogeneous nucleation and heterogeneous nucleation that similar with liquid-solid transformation. In fact, there are some factors affecting the transformation such as the presence of impurities, dislocation, grain boundary and so on.
Martensitic transformation
When a sample of a plain carbon steel in the austenitic condition is rapidly cooled to room temperature by quenching it in water, its structure will change from austenite (FCC) to martensite (BCT). Martensite is a metastable phase consisting of a supersaturated interstitial solid solution of carbon in BCC iron or body centred tetragonal (BCT) iron. Tempering will be carried out to reduce the hardness and brittleness of martensite as tempering process allow the carbon to diffuse out from BCT and form a stable structure. Hence, it is one of the examples of solid-solid transformation. Figure 6 shows a crystal structure of austenite and martensite.

Figure 6: FCC austenite and BCT martensite.
Factors affecting solid-solid transformation
Nucleation in solid, as in liquids, is almost always heterogeneous. Suitable nucleation sites are non-equilibrium defects for example dislocations, grain boundaries and inclusions, which increase the free energy of material. If the creation of a nucleus results in the destruction of a defect, some free energy (?G_d) will be released thus reducing the activation energy barrier.
Nucleation on grain boundaries
A grain boundary is a general planar defect that separates regions of different crystalline orientation within a polycrystalline material. Grain boundaries are usually the result of uneven growth when the solid is crystallizing. During nucleation, the nucleus shape will be the one that minimizes the interfacial energy by ignoring misfit strain energy effects. For incoherent grain boundary nucleus, this shape will be two spherical caps joined at the grain boundary.

Figure 7: incoherent grain boundary nucleus.
Nucleation on dislocations
The lattice distortion in the area of dislocation can help in nucleation process. The main effect of dislocations is to reduce the strain energy of the nucleus. A coherent nucleus with a negative misfit, in other words, a smaller volume than the matrix, can reduce its energy barrier by forming in the region of compressive strain above an edge dislocation, whereas of the misfit is positive, it is energetically favorable for it to form below the dislocation. Dislocations are not very effective in reducing interfacial energy. This means that the nucleation on dislocations usually requires formation of a low energy coherent or semi-coherent interface can be formed between precipitate and matrix.
Nucleation on excess vacancies
For those alloy that quenched from a high temperature, there are excess vacancies trapped in it. Those excess vacancies assist in nucleation by increasing the diffusion rate and relieving the misfit strain energy. These vacancies can either influence as individual vacancies or by clustering. Free energy for vacancies is very small, hence, they are effective only when a combination of low interfacial energy, small volume strain energy and high driving force conditions are met.
Compare and contrast between Liquid-solid and Solid-solid Transformation
L?S Transformation S?S Transformation
Both required energy.
Both involved two stages: nucleation and grain growth.
Both have two main mechanisms: heterogeneous and homogeneous nucleation.
Both temperature dependent.
Both changed their atomic arrangement/crystal structure after transformation.
Between crystallographic and non-crystallographic state Process Between crystallographic and crystallographic state
More easily to form due to freely moving atoms Transformation process Difficult to form
Changed Physical appearance Remain unchanged
Form crystal lattice Crystal structure Lattice distorted
Low amount is needed Undercooling High amount is needed
Lower energy needed Energy Higher energy needed
4/3 ?r^3 ?G_v+4?r^2 ? Total free energy change for the formation of a spherical embryo (Homogeneous) 4/3 ?r^3 (?G_v-?G_s)+4?r^2 ?
Temperature distribution, cooling rate and alloying Factor affecting the transformation Presence of impurities, dislocations, grain boundary
Casting; Eutectic transformation Examples Martensitic transformation; Eutectoid transformation; Transition from graphite to diamond

Most of the materials shrink during solidification and cooling. This may be due to the contraction of the liquid as it cools prior to its solidification as well as contraction during phase change from a liquid to solid. In addition, shrinkage also is the results of contraction of the solid as it continues to cool to ambient temperature. In fact, shrinkage can cause cracking to occur in component as it solidifies. If the solid surface is too rigid and will not deform to accommodate the internal shrinkage, the stress can become high enough to exceed the tensile strength of material causing the crack to form. Besides, shrinkage cavities can also occur when there is not enough atoms present to fill the available space and a void is left. (Solidification of material, 2013)
In order to reduce shrinkage, it is encouraged to work within a delineated temperature range. Furthermore, shrinkage cavities can be reduced by ensuring the flow of liquid metals are under high pressure during solidification phase. (Fagnani, 2017) During casting, a properly sized sprue attached directly to the heavy section can fill the cavity and provide the feed material necessary to counteract shrinkage as cooling occurs. In addition, using a rounded, rather than a flat or square, gate on the sprue can further reduce the risk of forming defects. (Shrinkage in Casting: Causes and Solutions, 2018)
Martensitic transformation is one of the examples of solid-solid transformation. Martensite only can be formed from austenitic conditions. In order to get martensite, the specimens should be quenched very fast in a quenching medium. In other words, the cooling rate should be high. However, if the temperature of the quenching medium is higher than the MS and MF, then it is unable to get martensite structure. Furthermore, martensite has a very high hardness compared to the others structure. This is due to the internal strain within the lattice as a result of presence of excess carbon contents as well as plastic deformation of parent austenite surrounding the martensitic plate. Therefore, to reduce the high hardness, tempering is carried out to relieve the stress of the specimen.

In conclusion, liquid-to-solid transformation and solid-to-solid transformation have many similarities and also differences. Furthermore, there are also some factors that affecting the transformation. For instance, factors affecting the liquid-to-solid transformation are temperature distribution, cooling rate and alloying while solid-to-solid transformation are presence of impurities, grain boundaries and so on. Hence, precautions have to be carried out to prevent the transformation failed.
In addition, liquid-to-solid transformation are more easily to carried out and it is more easily to be formed as compared to solid-solid transformation. This is because the atoms in liquid state are freely moving around, hence, the transformation is easy to occur. Meanwhile, only a little amount of undercooling as well as low energy is needed for this transformation.
Last but not least, solid-to-solid transformation are more difficult to occurred as it is a transition between crystallographic and crystallographic state. The solid atoms within the crystal lattice is not easy to move compare with liquid atoms. Hence, higher amount of undercooling is needed to generate larger driving force and energy to support the transformation.

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