Chapter 10 Phase Transformations

Kinetics and Phase Transformations Phase diagrams show which phases are in equilibrium under certain conditions, such as temperature –A change in the external conditions makes the phases unstable, and drives phase transformation A system cannot change instantaneously, i.e. phase transformations occur over a period of time. Kinetics deals with the rates of transformations –A diffusion controlled process involves the movement of atoms over “long” distances (more than a few lattice constant lengths) to form the new more stable phase(s)

Phase Transformations When the external conditions (e.g. temperature) is changed, the stable phase(s) may change Transformation typically occurs in two steps –Nucleation : Formation of stable nuclei of the more stable phase – Growth of nuclei : Increase in size of the nuclei to form a grain structure Nucleation can occur in one of two ways –Homogeneous nucleation occurs in the bulk –Heterogeneous nucleation occurs at grain boundaries and other defects

Phase Transformation: Solidification Homogenous Nucleation: –As temperature is reduced below the melting point, the liquid becomes more and more unstable –The atoms in the liquid, as they are moving around, may locally arrange themselves to form clusters of the solid and establish a solid-liquid interface The interface has a higher energy than the bulk The additional energy required to form the interface must be overcome by the energy released when the liquid changes to solid –The smallest viable particle of the solid phase is called a nucleus

Nucleation during Solidification Volume free energy G v Released by liquid to solid transformation. ΔG v is the change in free energy per unit volume between liquid and solid –ΔG v is negative –This is the energy that drives the transformation The free energy change for a spherical cluster of radius r is given by Surface energy Gs Required to form new solid surface ΔG s is energy needed to create a surface γ is the surface free energy per unit area, then ΔG s is a retarding energy

Homogeneous Nucleation As the size of the cluster of atoms increases, total free energy change increases up to a size r* Any further increase in size results in a decrease in free energy change A cluster of critical size is called a nucleus –Smaller clusters will redissolve into the liquid –Once a cluster reaches critical size it can grow At the critical cluster size Total free energy change is given by r + -ΔG v ΔG s ΔG T r* ΔG T

Homogeneous Nucleation The magnitude of  G V increases as temperature decreases below the melting point, while  does not change significantly It can be shown that the radius, r*, of the cluster of critical size at a transformation temperature T decreases as T decreases, i.e., with increasing undercooling where T m is the melting temperature in Kelvin, L is the latent heat of fusion and  T is the under-cooling As a result, it becomes easier to form nuclei, and the number of nuclei per unit volume increases as the temperature T drops further and further below the melting point

Effect of undercooling on nucleation Decrease in critical nucleus size Decrease in activation energy to form nuclei Increase in nucleation rate

Maximum observed undercooling during Homogeneous Nucleation

Heterogeneous Nucleation Occurs at a preexisting imperfection, such as a grain boundary (during solid state transformation) or the mold wall (during solidification of an ingot) During nucleation, two types of interfaces that require energy are formed –Solid-liquid ( SL ) and Solid-Imperfection ( SI ) One type of interface, the Liquid-Imperfection ( IL ) interface is removed. This provides additional energy to drive the transformation

Homo- and Heterogeneous Nucleation Rates At low under-cooling, the additional energy provided by the removal of the IL interfaces aids heterogeneous nucleation At higher under-cooling, the homogeneous nucleation rate becomes higher than heterogeneous nucleation rate because there are many more potential sites for homogeneous nucleation to occur At very high under-cooling, the nucleation rate drops off because atoms are not able to diffuse fast enough for nucleation to occur

Diffusion controlled growth Once stable nuclei have formed, they grow by diffusion of atoms to the interface, and their migration across the interface from the liquid to the solid phase It can be shown that the radius of a spherical particle will increase according to the equation below, where D is the diffusion coefficient As the temperature T decreases, the diffusion coefficient decreases exponentially. This results in a rapid decrease in growth rate

Overall Transformation Kinetics The overall rate of transformation depends on both nucleation and growth At low under-cooling, nucleation rate is low resulting in a low transformation rate At high under-cooling, the growth rate is low, also resulting in a low transformation rate The fastest transformation occurs at an intermediate temperature

Transformation rate and time The time that a transformation takes is proportional to the inverse of the transformation rate The figure above shows schematically, the rate and time for 50% of the transformation to complete –i.e., half of the liquid has solidified The time-temperature-transformation curve shows a characteristic “C” shape

Isothermal Transformation Diagram The isothermal transformation diagram has the typical “C” shape because –At high temperatures, close to the transformation temperature (melting point, solvus temperature, eutectoid temperature, etc) the nucleation rate is low because  T is small, while growth rate is high. Transformation is slow because there simply aren’t enough nuclei to grow –At low temperatures well below the transformation temperature, nucleation rate is very high, and a large number of small nuclei will form, but growth rate is low. The nuclei are generally too small to be observed, and the transformation is therefore sluggish –At an intermediate temperature, nucleation rate is high, and the growth rate is also sufficiently high that the overall transformation occurs rapidly

Diffusion controlled transformation The extent of transformation varies with time in a sigmoidal fashion Avrami equation is often used to describe such transformations where k and n are time independent constants that depend on the temperature and geometry of the transformation process.

Kinetics of transformation  Rate of a transformation occurs depends upon temperature  Q = activation energy for transformation  T = absolute temperature (in Kelvin)  R = universal gas constant t 0.5 Recrystallization of rolled copper Arrhenius Equation

Kinetics of Phase Transformation Typically, phase transformations do not start immediately after the temperature crosses a phase boundary (solidus, liquidus or solvus line) on the phase diagram For example, when a liquid solidifies under normal conditions, undercooling or supercooling of several degrees below the freezing temperature may occur before nuclei of the solid are observed. In solid state transformations, both supercooling and superheating can occur.

Isothermal transformation Diagram The Iron-Carbon system is very significant for industrial applications, and has been widely studied. The formation of pearlite from austenite has been extensively investigated under both isothermal transformation and continuous cooling conditions –Isothermal transformation: samples are held at constant temperature below the eutectoid temperature and the transformation is observed –Continuous cooling: samples are allowed to cool continuously from a temperature above the eutectoid temperature

Isothermal Transformation Diagram Several samples are first austenitized above eutectoid temperature, quickly transferred to a salt bath held at the desired temperature and then quenched in water after different time intervals. Repeat procedure at progressive lower temperatures 727ºC 0.76% Quenching stops any diffusional transformation that is occurring, and the extent of transformation can be observed under a microscope

Isothermal Transformation Diagram Also called Time Temperature Transformation or T-T-T diagrams Diffusion Controlled Processes Nucleation – rate increases as T decreases Growth – rate decreases as T decreases

Isothermal Transformation Diagram Diffusion Controlled Processes Nucleation – rate increases as T decreases Growth – rate decreases as T decreases

Bainite Bainite forms below the “nose” or “knee” Very rapid cooling produces Martensite Martensite Diffusion Controlled Processes Nucleation – rate increases as temperature drops below T eutectic Growth – rate decreases as T decreases Initially the transformation rate increases due to increased nucleation rate, but then slows down due to decreased growth rate giving the TTT curve a characteristic “C” shape

Formation of Martensite Very fast cooling results in the formation of a new phase called Martensite For the eutectoid composition, 0.76wt% C is dissolved in the fcc austenite phase. Limit of solid solubility in the bcc ferrite phase is 0.022wt%C Upon “slow cooling” below the eutectoid temperature, the excess carbon forms Fe 3 C or cementite in a diffusion controlled process During quenching, the carbon does not have time to get out of the fcc matrix, and the alloy transforms to Martensite in a diffusion-less or athermal transformation

Formation of Martensite The carbon position remains unchanged Instead of the bcc ferrite phase, a new phase with a body centered tetragonal (bct) structure is formed This can be thought of as a bcc structure that has been stretched in one direction by the trapped carbon atoms During quenching, austenite starts changing to martensite at the M(start) temperature and the extent of transformation depends on how far below this temperature the sample is quenched and not on how long it is held at a particular temperature Martensite is a very hard phase Austenite unit cell Ferrite unit cell Martensite unit cell

TTT curves for different steels Hypereutectoid steel Alloy steel type 4340

Microstructure can be controlled by changing the heat treatment process A = Austenite P = Pearlite B = Bainite M = Martensite F = Ferrite C = Cementite

Continuous Cooling Transformation The sample is withdrawn from the furnace and allowed to cool continuously The cooling rate depends upon the cooling medium –Furnace cooling –Air cooling (still air or forced air) –Oil quenching –Water quenching –Iced brine quenching –… –The start and finish lines for pearlite transformation get shifted to lower temperatures and longer times Bainite transformation is not observed for eutectoid PC steel because it occurs below the “nose” or “knee”

Continuous Cooling Transformation Slow to moderate cooling produces coarse or fine pearlite Fast cooling produces martensite Quenching at rates > than critical cooling rate of 140ºC/s produces 100% Martensite

Continuous Cooling of Alloy Steel 4340 Two “noses” or “knees” makes the transformation behavior more complex Critical cooling rate is smaller. Air cooling will produce 100% martensite

Mechanical Properties of plain carbon steels (PC Steels)

Mechanical Properties of PC steels

Eutectoid Steel Martensite

Tempering of Martensite Martensite is an extremely hard and brittle phase It is thermodynamically unstable phase. Upon reheating and holding over extended periods of time, the carbon atoms diffuse out of the bct lattice and form Fe 3 C This process is called tempering, and the resultant structure consisting of the a (bcc) phase and Fe 3 C is called tempered martensite

Effect of tempering temperature and time Strength and hardness decrease while ductility increases This is a diffusional process, and properties also depend upon tempering time

Summary of phase transformations in PC Steels

Shape Memory Alloys Ordered Cubic Complex Monoclinic