Nucleation is as a physical process in which there is change of state —liquid to solid —around certain focal points which are called nuclei.
Examples-
• When tiny water droplets nucleate from the supersaturated wet air and cools it forms clouds.
• Shortly after the pressure from a container containing carbonated liquid is released small bubbles are nucleated
Nucleation can be
Heterogeneous – the new phase appears on the walls of the containers, and at impurity particles, etc.
Homogeneous – solid nuclei appears spontaneously within the undercooled phase.
Nucleation nuclei act as template to grow crystals for nucleus to form because rate of addition of atoms to nucleus must always be faster than rate of loss . The force driving nucleation increases as we increase ∆ T – supercooling ( that is eutectic, eutectoid) – superheating (peritectic).
(“source: Phase Diagrams and Kinetics, Leonid Zhigilei”)
Homogenous Nucleation
Nucleation without any preferential nucleation sites is homogeneous nucleation . It only occurs in controlled environment spontaneously, but it always requires superheating or supercooling of the medium. Homogeneous nucleation occurs with difficulty in the interior of uniform substance compared to heterogeneous nucleation .
needs to be calculated to find out if reaction is fast or slow. According to classical theory of nucleation free energy of a droplet of microscopic nucleii of the new phase, is written as the sum of the bulk term proportional to the volume of nucleus, and a surface term proportional to the surface area of nucleus.
For small surface term dominates and . The free energy is the sum of and terms. varies more rapidly with than , so at small , dominates and the free energy is on the whole positive while for large , term dominates and the free energy is on the whole negative. There is an intermediate value of for which the free energy goes through to a maximum value because of which the probability of formation of a nucleus becomes a minimum. There is a least-probable nucleus which occurs with the highest value of where
This is critical nucleus and occurs at a critical nucleus radius which is
Heterogenous nucleation
Heterogeneous nucleation is nucleation which occurs on a surface , is more common than homogeneous nucleation . Heterogeneous nucleation is usually faster than homogeneous nucleation because the nucleation barrier ΔG * is much lower on a surface . This happens because the nucleation barrier which comes from the positive term in ΔG . However, for homogeneous nucleation approach the core through an area and so a free energy equal to the area of the region , 4πr2 , once the surface tension σ . But drops on the surface is not completely spheres and therefore part of the interface between the droplet and the surrounding liquid is always less than . This geometric factor reduces the boundary surface and thus also the interfacial free energy, which in turn also reduces the nucleation barrier .
Considering the heterogeneous nucleation of the nucleus which is in the form of a spherical cap on the wall of the container . There are three energies o : γLC – interface liquid container , γLS – and solid- liquid interface , γSC – interface and solid container. And achieve a balance between all interfaces tensions in the plane of the wall of the container to give γLC = γSC + γLS cos (θ) and θ is defined by urinating angle (θ) = cos (γLC – γSC) / γLS
In the schematic the contact angle that is between the droplet surface and the surface decreases from left to right (A to C), and the surface area of the droplet reduces as the contact angle decreases. This reduces the barrier and results in faster nucleation on surfaces with smaller contact angles. Also, of the surface discussed curves towards the fluid, then this also reduces the interfacial of area and so the nucleation barrier.
Kinetics of Phase Transformation
Grain nucleation and growth are very important phenomena in polycrystalline materials like metals and also in most ceramics. They govern the kinetics of several phase transformations and many recrystallization processes that take place during the processing. The final and average grain size after the transformation is directly related to the strength of the material that is chosen. In general a smaller average grain size will results into a stronger material.
A phase diagram is a representation of the regions where a substance is said to be stable in a given phase. External control variables such as pressure, temperature, chemical potential or an external field are represented on the axes or sometimes just the one extensive variable such as volume, magnetisation, etc.) The different phases are separated by lines,which are indicative of phase transitions, or regions where the system is said to be unstable.
Growth theories of transformations of vapour to liquid, liquid to solid and solid to solid
The three coexistence lines are:
1) Sublimation line: here the solid will coexists with the gas. This line exists from zero up to the triple-point temperature. When we lowering the temperature at constant pressure starting from gas side, the gas will reach the sublimation line, at which crystallites would start forming until the whole system becomes one bigger crystal. On the other hand when crossing the line from the crystal side, gas would sublimate from the crystal until the system has passed to gas entirely.
2) Melting line, is also called fusion line: it is here the solid coexists with the liquid. On crossing this line from the liquid side the system would begin to crystallise; On the other hand, the crystal would melt in the opposite direction. This line exists from T3 up to an infinite temperature (since there is no upper limit in the melting line). This means that we cannot pass from liquid to crystal without crossing the transition line, a result that comes essentially from the essentially different symmetries of these phases.
3) Condensation line, which is also called vapour-pressure line: here the gas coexists with the liquid phase. On crossing the line from the gas side the system begins to form droplets of 50 liquid on the condensation line, which can grow and coalesce until all the material has passed on to the liquid phase. On the other hand, from the liquid side, gas bubbles form at the line, which do grow and coalesce until all the material has transformed into the gaseous phase. This is called vapour-pressure line as it gives the maximum pressure the system can stand as gas for the given temperature. The line just begins at the triple point and ends at the critical point, C, with Tc the critical temperature and pc which is the critical pressure. Above this point C there is no distinction between gas phase and liquid, and one may continually pass from gas phase to liquid, without crossing the transition line, by going to the supercritical region. This indicates that there is basically only one fluid phase, which can be understood due to symmetry since both phases, that is liquid and gas, have the same symmetries
Sources
• Phase diagrams and
kinetics, Leonard Zhiegler
• Brittanica Encyclopedia
• Fundamentals of material science and engineering- Callister