MSE 440/540: Processing of Metallic Materials Instructors: Yuntian Zhu Office: 308 RBII Ph: 513-0559 ytzhu@ncsu.edu Lecture 2: Solidification Theory Homework: Problem from notes, Text book, Office hour, by appointment Department of Materials Science and Engineering 1

Solidification Nearly every metal product started as a liquid at some point in time. What is Solidification What is the Melting Point? What’s composition? Quiz: how about the solidification of an alloy? Why is there a thermal arrest? What is the equilibrium temperature? Department of Materials Science and Engineering 2

Nucleation and Growth During solidification, solid nuclei form in the liquid and subsequently grow until the entire volume is a solid. What is the driving force for nucleation and growth? Quiz Department of Materials Science and Engineering 3

Homogeneous Nucleation Consider free energy change when small spherical nuclei of solid is formed in a liquid G = H – TS L S ΔG = ΔH – TΔS At Tm, ΔG = 0, ΔH = L ΔS = L/Tm ΔGv(T) = L – T(L/Tm) = L(1-T/Tm) Quiz: is L positive or negative? Department of Materials Science and Engineering 4

Homogeneous Nucleation There is a critical radius r*, at a given undercooling ΔT where embryos can grow and reduce the free energy. r* occurs at HOMEWORK: Show that: r* =-2g/ΔGv ΔG at r* , If ΔGv = LΔT/Tm, then = thermodynamic barrier to nucleation or work of nucleation Quiz: What is the physical origin of energy barrier for nucleation? Department of Materials Science and Engineering 5

Homogeneous Nucleation Note that r* and ΔGv* decrease with increasing undercooling Quiz: The effect of ΔT on solidification speed and microstructure. https://www.youtube.com/watch?v=-kIOXusTgoU Freeze beer/2:22 Quiz: What does this mean in terms of solidification speed and microstructure? Department of Materials Science and Engineering 6

Heterogeneous Nucleation r* is the same as the homogeneous nucleation Department of Materials Science and Engineering 7

Heterogeneous Nucleation Rate Innoculants (seeds): C1 is # of atoms in contact with hetergeneous nucleation sites, Quiz: Seeds requirement: 1. Low interfacial energy, 2. The seeds makes nucleation easier because ? Nucleation of Melting: Low undercooling is needed for heterogeneous nucleation gSL + gLV < gSV Department of Materials Science and Engineering 8

Commercial Practice Dynamic Nucleation - Vibrate melt to collapse internal cavities - Fragmentation of existing solids; breaking of dendrite arms (crystal multiplication) - Electromagnetic mixing and stirring Nucleation during Melting - Why does melting usually occur at Tm, even at high heating rates? Most liquid metals wet their own solid, so the wetting angle Θ = 0  no energy barrier for nucleation Department of Materials Science and Engineering 9

Commercial Practice Characteristics of a good inoculant - low interfacial energy, γSP, between nucleant and growing solid - γSP decreases with decreasing lattice mismatch between solids and nucleant with increasing chemical affinity (coherent interface) Should be as stable as possible in the liquid melt Tminoc > Tmmelt possess a high surface area (rough or pitted) Smaller particles Department of Materials Science and Engineering 10

Growth: Practical Results Crystals grow in two ways after nucleating Planar growth – heat extraction through the solid phase and a smooth solid/liquid interface Dendritic growth – formation of branched skeleton structures. http://www.youtube.com/watch?v=S07fPo45BvM Department of Materials Science and Engineering 11

Reading Assignment Read Chapter 5 HW: 1. Calculate the volume change from fcc γ-iron to bcc α-iron. Hint: the atom radius is R, which does not change during phase transformation. Department of Materials Science and Engineering 12