T7008T Phase Transformations in Metals and AlloysJohn Ion Division of Engineering Materials E-mail: [email protected] Office: E316 Phone: 491249 T7008T Phase Transformations 2010 John C. Ion Lecture 3 Crystal Interfaces and Microstructure T7008T Phase Transformations 2010 John C. Ion Issues to address... What are the most important interfaces in metallic systems? Why are crystal interfaces and microstructure important in phase transformations? How do we achieve equilibrium in polycrystalline materials? How do interfaces control kinetic transformations such as grain growth? What are interphase interfaces in solids? How do we classify the different types of phase transformation? T7008T Phase Transformations 2010 John C. Ion Count Alois von Beckh Widmanstätten 13 July 1753 – 10 June 1849 Austrian printer and scientist Director of the Imperial Porcelain works in Vienna In 1808 Widmanstätten was flame heating iron meteorites and noticed special patterns… The discovery was acknowledged by Carl von Schreibers, director of the Vienna Mineral and Zoology Cabinet, who named the structure after Widmanstätten However, the discovery should be assigned to the Englishman G. Thomson, as four years earlier he was using nitric acid to clean the rust off meteorites, noticed the same patterns, but published his findings in Italian (he was living in Naples at the time) T7008T Phase Transformations 2010 John C. Ion http://www.facebook.com/pag es/Count-Alois-von-BeckhWidmanstatten/14342953900 3005 André Guinier George Dawson Preston 1911 - 3 July 2000 French physicist, born in Nancy 8 August 1896 – 22 June 1972 British physicist, born in Oundle Simultaneously discovered Guinier-Preston (GP) zones in age hardening aluminium copper alloys in 1938 T7008T Phase Transformations 2010 John C. Ion Ion Studied metallurgy at the University of Birmingham (BSc) and at the Massachusetts Institute of Technology (Sc. 1952: Smith is holding a small glass capsule full of soap bubbles that he used to illustrate how surface forces control the growth of grains in solid materials T7008T Phase Transformations 2010 John C.D) Perhaps most famous for his work on the Manhattan Project where he was responsible for the production of fissionable metals . England Renowned metallurgist and historian of science c.Cyril Stanley Smith 4 October 1903 – 25 August 1992 Born in Birmingham. the total surface Gibbs free energy of formation should be a minimum for a constant volume of crystal In 1953 the American Conyers Herring gave a proof of the theorem and a method for determining the equilibrium shape of a crystal T7008T Phase Transformations 2010 John C. Ion Wulff (1901): “The length of a vector drawn normal to a crystal face will be proportional to its surface energy“ (the Gibbs-Wulff theorem) . Gibbs proposed that for the equilibrium shape of a crystal.Georg (Yuri Viktorovich) Wulff Russian mineralogist In 1878. Types of interface in metallic systems Three types are important in metallic systems: 1. Ion . α/γ) All crystals possess the first type The second type separates crystals with essentially the same composition and crystal structure. but a different orientation in space The third separates two different phases that may have different crystal structures and/or compositions (and therefore includes solid/liquid interfaces) The majority of phase transformations in metels occur by the growth of a new phase (β) from a few nucleation sites within the parent phase (α) T7008T Phase Transformations 2010 John C. free surfaces of a crystal (solid/vapour interface) 2. grain boundaries (α/α interfaces) 3. interfaces between phases (interphase interfaces. Interfacial free energy The free energy of a system containing an interface of area A and free energy γ per unit area is: 𝐺 = 𝐺0 + 𝐴𝛾 where 𝐺0 is the free energy of the bulk system Consider a wire frame suspending a liquid film with a movable bar: If a force F moves a small distance dA. the work done is FdA The free energy of the system is increased by dG: 𝑑𝐺 = 𝛾𝑑𝐴 + 𝐴𝑑𝛾 = 𝐹𝑑𝐴 𝑑𝛾 ∴ 𝐹 = 𝛾 + 𝐴 𝑑𝐴 Assuming T7008T Phase Transformations 2010 John C. 𝐹 = 𝛾 . Ion 𝑑𝛾 𝑑𝐴 = 0. Solid/vapour interfaces Assume that the structure of solids may be discussed in terms of a hard sphere model The atomic configurations on the three closes packed planes in fcc crystals are: Atoms in the layers nearest the surface are without some of their neighbours Atoms on a {111} surface. for example. Ion . are missing three of their twelve nearest neighbours This may be used to calculate the energy of a surface T7008T Phase Transformations 2010 John C. 25 𝐿𝑠 /𝑁𝑎 T7008T Phase Transformations 2010 John C. then each bond may be 𝜀 considered to lower the internal energy of each atom by 2 Every surface atom with three ”broken bonds” has an excess internal 3𝜀 energy of compared with atoms in the bulk 2 For a pure metal.Surface energy If the bond strength of the metal is ε. Ion . ε may be estimated from the latent heat of sublimation 𝐿𝑠 (the sum of the latent heats of fusion and vaporisation): 𝜀 𝐿𝑠 = 12𝑁𝑎 2 for an fcc structure in which 12𝑁𝑎 broken bonds are formed The energy of a {111} surface 𝐸𝑠𝑣 is therefore approximately 𝐸𝑠𝑣 = 0. taking a minimum corresponding to the orientation of a close packed plane T7008T Phase Transformations 2010 John C.Variation of surface energy with plane orientation The energy E of different planes in a crystal varies systematically with the orientation of the plane θ. Ion . Wulff construction Possible section through the plane energy plot of an fcc crystal Length OA represents the free energy of a surface plane whose normal lies in the direction OA OB = 𝛾 001 OC = 𝛾 111 T7008T Phase Transformations 2010 John C. Ion . Boundaries in single-phase solids The grains in a single-phase polycrystalline specimen are generally in many different orientations and many different types of grain boundary are therefore possible The lattices of any two grains may be made to coincide by rotating one of them about a single axis Pure tilt boundary T7008T Phase Transformations 2010 John C. Ion Pure twist boundary . Ion .Grains Metallographic specimens are two dimensional sections of a three dimensional structure Two grains meet in a plane (a grain boundary) Three grains meet in a line (a grain edge) Four grains meet at a point (a grain corner) T7008T Phase Transformations 2010 John C. Ion .Low and high angle grain boundaries Lower density of atoms means: high mobility high diffusivity high chemical reactivity T7008T Phase Transformations 2010 John C. Soap bubble analogy: several grains of varying misorientation row of dislocations (low angle) disordered structure (high angle) T7008T Phase Transformations 2010 John C. Ion . Twins The stacking sequence across a coherent twin boundary in the fcc lattice is: ABCABACBA The twin plane is a plane of mirror symmetry (the crystals on either side of it are twins) The nearest neighbour packing is correct through the twin plane. Ion . only the second nearest neighbours lie in the wrong sites T7008T Phase Transformations 2010 John C. g. {111} plane in FCC incoherent grain boundary energy γ as a function of grain boundary misorientation φ T7008T Phase Transformations 2010 John C. Ion .Twin boundaries coherent e. Measured boundary free energies for twin crystals Crystal Coherent (mJ m-2) 21 8 19 Incoherent (mJ m-2) 498 126 209 Grain boundary (mJ m-2) 623 377 835 Cu Ag Fe-Cr-Ni Al Al tilt parallel to <100> T7008T Phase Transformations 2010 John C. Ion tilt parallel to <110> . Ion .Equilibrium in polycrystalline materials (I) How do different grain boundary energies affect the microstructure of a polycrystalline material? high angle grain boundary incoherent annealing twin boundary coherent annealing twin boundary low angle grain boundary Annealed (recrystallized) austenitic stainless steel T7008T Phase Transformations 2010 John C. Ion .Single crystal and polycrystalline materials Turbine blades in jet engines may: • be polycrystalline • have a columnar grain structure • be a single crystal Polycrystalline blades are formed using a ceramic mould Columnar grain structured blades are created using directional solidification techniques and have grains parallel to the major stress axes Single-crystal superalloys are formed as a single crystal using a modified version of the directional solidification technique. so there are no grain boundaries in the material T7008T Phase Transformations 2010 John C. Ion .Equilibrium in polycrystalline materials (II) Consider the factors that control grain shapes in a recrystallised polycrystal Why do grain boundaries exist at all in annealed materials? Boundaries are all high energy regions that increase the free energy of a polycrystal relative to a single crystal Therefore a polycrystalline material is never a true equilibrium structure Grain boundaries in a polycrystal can adjust themselves during annealing to produce a metastable equilibrium at the grain boundary intersections The conditions for equilibrium at a grain boundary junction may be obtained by considering the forces that each boundary exerts on the junction T7008T Phase Transformations 2010 John C. there will be no torque forces acting since the energy is a minimum in that orientation The grain boundary then behaves like a soap film For metastable equilibrium the boundary tensions must balance: 𝛾23 𝛾 𝛾 + 13 = 12 sin 𝜃1 sin 𝜃2 sin 𝜃3 T7008T Phase Transformations 2010 John C. Ion .Equilibrium in polycrystalline materials (III) If the boundary energy is independent of orientation. Thermally activated migration of grain boundaries A cylindrical boundary is acted 𝛾 on by a force 𝑟 Tension forces balance in three dimensions if the boundary is planar or if it is curved with equal radii in opposite directions In real metals there are always grain boundaries with net curvature in one direction Consequently a random grain structure is inherently unstable: boundaries will tend to migrate towards ther centre of curvature T7008T Phase Transformations 2010 John C. Ion . Two dimensional grain boundary configurations Arrows indicate directions of boundary migration during grain growth T7008T Phase Transformations 2010 John C. Ion . Ion .S. Smith) Numbers are time in minutes The higher pressure on the concave side of the films induces air molecules in the smaller cells to diffuse through the film into the larger cells. so that the smaller cells eventually dissolve T7008T Phase Transformations 2010 John C.Grain growth in a soap solution (C. Grain growth in a polycrystalline metal If atom Ⓒ jumps from grain 1 to grain 2 the boundary locally advances a small distance The effect of the pressure difference caused by a curved boundary is to create a difference in free energy ∆𝐺 or chemical potential ∆𝜇 In a pure metal ∆𝐺 = ∆𝜇: 2𝛾𝑉 𝑚 ∆𝐺 = = ∆𝜇 𝑟 T7008T Phase Transformations 2010 John C. Ion . The kinetics of grain growth Assume that the mean radius of curvature of grain boundaries is proportional to the mean grain diameter 𝐷 The mean driving force for grain growth is proportional to 2𝛾 d𝐷 𝜈 = 𝛼𝑀 = d𝑡 𝐷 2𝛾 𝐷 giving: where: 𝜈 = average grain boundary velocity 𝛼 = proportionality constant of the order 1 𝑀 = grain boundary mobility (strongly dependent on temperature) Integrating. Ion . taking 𝐷 = 𝐷0 when 𝑡 = 0: 𝐷 2 = 𝐷0 2 + 𝑘𝑡 where: 𝑘 = 4𝛼𝑀𝛾 T7008T Phase Transformations 2010 John C. the mean 3𝑓 number of particles intersecting unit area of a random plane is such 2𝜋𝑟 2 that the restraining force 𝑃 per unit area of grain boundary is 3𝑓 3𝑓𝛾 𝑃 = .Pinning of grain boundaries by precipitates (I) Second phase particles pin grain boundaries (precipitation hardening) A grain boundary is attached to a particle along a length 2𝜋𝑟 cos 𝜃 It feels a pull of (2𝜋𝑟 cos 𝜃 γ) sin 𝜃 If there is a volume fraction 𝑓 of particles all with a radius 𝑟. 𝜋𝑟𝛾 = 2𝜋𝑟 2 2𝑟 T7008T Phase Transformations 2010 John C. Ion . but as 𝐷 increases the 2𝛾 driving force decreases until 𝐷 2𝛾 3𝑓𝛾 = 2𝑟 𝐷 when the driving force becomes insufficient to overcome the drag. Ion . giving: 4𝑟 𝐷max = 3𝑓 T7008T Phase Transformations 2010 John C.Pinning of grain boundaries by precipitates (II) The force 𝑃 opposes the driving force for grain growth 2𝛾 𝐷 When 𝐷 is small 𝑃 is relatively insignificant. Effect of second phase particles on grain growth A large volume fraction of stable small particles is required to stabilise a fine grain grain size during heating at high temperatures T7008T Phase Transformations 2010 John C. Ion . Ion .Interphase interfaces in solids So far we have considered the structure and properties of boundaries between crystals of the same solid phase Now we will consider the boundaries between different solid phases We consider adjoining crystals that have: • different crystal structures • different compositions • both Interphase boundaries in solids may be divided on the basis of their atomic structure into: • coherent • semicoherent • incoherent T7008T Phase Transformations 2010 John C. Ion Different crystal structures Different compositions .Interface coherence A coherent interface arises when the two crystals match perfectly at the interface plane such that the two lattices are continuous across the interface Same crystal structure Different compositions T7008T Phase Transformations 2010 John C. Fully coherent interface (I) Consider Cu-Si alloys in which: the hcp Si-rich κ phase and the fcc Cu-rich α matrix have identical hexagonally close packed planes: (111)fcc : 0001hcp and identical interatomic distances Orientation relationship: 111 𝛼 // 0001 𝜅 110 𝛼 // 1120 𝜅 The only contribution to interfacial energy is a chemical component (1 mJ m-2 for the α-κ interface) T7008T Phase Transformations 2010 John C. Ion . Orientation relationships and habit planes Orientation relationship: Crystallographic texture is one of the main characteristics of a polycrystalline material: it determines its functional properties An orientation relationship between two crystals of the phases α and β defines the planes and directions that lie in a common plane between two crystals and is written: (hkl)α // (hkl)β . [uvw]α // [uvw]β Habit plane: The crystallographic plane or system of planes along which certain phenomena (such as twinning) occur The habit plane is a common plane between two crystals T7008T Phase Transformations 2010 John C. Ion . Fully coherent interface (II) When the distance between the atoms in the interface is not identical it is still possible to maintain coherency by straining one or both of the lattices T7008T Phase Transformations 2010 John C. Ion . it becomes energetically more favourable to replace a coherent interface with a semicoherent interface containing periodic misfit dislocations (200500 mJ m-2) When more than one dislocation is present for every four interplanar spacings. or interfacial area.Semicoherent interface Strains at a coherent interface raise the total energy of the system For sufficiently large atomic misfit. regions of poor fit around the dislocation cores overlap and the interface cannot be considered coherent any longer T7008T Phase Transformations 2010 John C. Ion . the interatomic distances may differ by more than 25% An incoherent interface then arises Incoherent interfaces have high energy (500-1000 mJ m-2) T7008T Phase Transformations 2010 John C.Incoherent interface When the interfacial plane has a very different atomic configuration in the two adjoining phases there is no possibility of good matching across the interface The pattern of atoms may either be very different in the two phases or. Ion . if it is similar. Ion .g.Second phase shape: interfacial energy effects In a two phase microstructure one of the phases is often dispersed within the other. e. and assume for simplicity that both the precipitate and matrix are strain-free Such a system will have a minimum free energy when the shape of the precipitate and its orientation relationship with the matrix are optimised to give the lowest total interfactial free energy How may this be achieved for different types of precipitate? T7008T Phase Transformations 2010 John C. β precipitates in an α matrix Consider for simplicity a system containing one β precipitate embedded in a single α crystal. Ion .Fully coherent precipitates A zone with no misfit e. ⃝ Al and ∙ Ag Ag-rich zones (GP) zones in an Al-4 at% Ag alloy (TEM) Since the two crystal structures match across all interfacial planes the zone may be any shape and remain coherent T7008T Phase Transformations 2010 John C.g. Partially coherent precipitates (I) Unit cell of θ’ precipitate in Al-Cu alloys Unit cell of matrix in AlCu alloys Coherent plate of θ’ in Al-3. Ion Orientation relationship: 001 𝜃′ // 001 𝛼 100 𝜃′ // 100 𝛼 .9wt%Cu alloy T7008T Phase Transformations 2010 John C. H = GP zone) T7008T Phase Transformations 2010 John C.Partially coherent precipitates (II) When the precipitate and matrix have different crystal structures it is usually difficult to find a lattice plane that is common to both phases Nevertheless for certain phase combinations there may be one plane that is common to both phases By choosing the correct orientation relationship orientation a low energy coherent or semicoherent interface to be formed Widmanstätten morphology of γ’ precipitates in Al-4at% Ag alloy (TEM. Ion . Widmanstätten morphologies Widmanstätten patterns (also called Thomson structures) are microstructural features characterised by a cross-hatched appearance due to one phase having formed along certain crystallographic planes Crystalline intergrowth of two Fe-Ni alloys. kamacite and taenite T7008T Phase Transformations 2010 John C. Ion . Incoherent precipitates When the two phases have completely different crystal structures. and the precipitates are said to be incoherent Incoherent precipitates of θ in an Al-Cu alloy (TEM) T7008T Phase Transformations 2010 John C. it is unlikely that any coherent or semicoherent interfaces form. or when the two lattices are in a random orientation. Ion . b) and c)) T7008T Phase Transformations 2010 John C. a)) • Atomically diffuse (transition over several atom layers.Solid / liquid interfaces Two types of atomic structure in solid / liquid interfaces: • Atomically flat close packed (as solid / vapour interfaces. Ion . Examples of solid / liquid interfaces in metallic systems Nonfaceted dendrites of silver in a Cu-Ag eutectic matrix T7008T Phase Transformations 2010 John C. Ion Faceted cuboids of β’ SnSb compound in a matrix of Sn-rich material . civilian) T7008T Phase Transformations 2010 John C. military) • non-glissile (migrate by random jumps of atoms. which migrates into the surrounding parent phase during growth Nucleation is important. but most of the transformation product is formed during the growth stage by the transfer of atoms across a moving parent/product interface There are two basic types of interface: • glissile (migrate by dislocation glide.Interface migration Many phase transformations occur by a process known as nucleation and growth The new phase (β) first appears at certain sites in the metastable parent (α) phase (nucleation). which grow into the surrounding matrix An interface is created during nucleation. Ion . athermal. thermal. Military transformations Nearest neighbours of any atom are essentially unchanged Parent and product phases have the same composition (no diffusion) Examples: martensite forming from austenite in steels formation of mechanical twins T7008T Phase Transformations 2010 John C. Ion . Ion .g. the new phase grows as fast as atoms cross the interface (interface controlled) If the parent and product phases have different compositions growth of the new phase will require long range diffusion: The growth of a B-rich β phase into an A-rich α phase can only occur if diffusion is able to transport A away from the interface. e.Civilian transformations Parent and product phases may or may not have the same composition If there is no change in composition. and B towards the advancing interface (diffusion controlled growth) T7008T Phase Transformations 2010 John C. ferrite (α) → austenite (γ) in pure iron. T7008T Phase Transformations 2010 John C. Ion . Summary The three most important interfaces in metals and alloys: free surfaces of a crystal (solid/vapour interface) grain boundaries (α/α interfaces) interfaces between phases (interphase interfaces. α/γ) Equilibrium in polycrystalline materials is achieved by minimising surface energy Coherent. semicoherent and incoherent interfaces may be formed between phases Atomic migration resulting from differences in free energy control kinetic transformations Phase transformations may be classified in many ways Military or civilian Diffusionless or diffusion-controlled Athermal or thermally activated Interfaces play an important role in all types of phase transformation T7008T Phase Transformations 2010 John C. Ion .