DM308 Production Techniques 2 Lecture 2 - 2021 Lecture Notes PDF

DM308 Production Techniques 2 Lecture 2 – Crystals, defects and interfaces Dr. Vassili Vorontsov Department of Design, Manufacture and Engineering management, Faculty of Engineering, University of Strathclyde [email protected] What is a crystal? A crystal is a combination of a lattic...

DM308 Production Techniques 2 Lecture 2 – Crystals, defects and interfaces Dr. Vassili Vorontsov Department of Design, Manufacture and Engineering management, Faculty of Engineering, University of Strathclyde [email protected] What is a crystal? A crystal is a combination of a lattice (a spatial grid of points) and a basis (object or objects that sit/s on those points). The two elements comprise a crystal structure. Basis Lattice Crystal + a The crystal is formed by placing atom(s) or molecule(s) (the basis) on each lattice point. The unique minimal spacings between the lattice points are known as the lattice parameters. Not all materials are crystalline Some materials are only partly crystalline (semi-crystalline) while others have completely no crystal structure at all and are amorphous. Amorphous e.g. glasses e.g. bulk metallic glasses Semi-crystalline e.g. polymers/elastomers such as polyethylene (Pd43Cu27Ni10P20) www.tf.uni-kiel.de/matwis www.chm.bris.ac.uk Polymer crystallites Organic (carbon-based) polymers can form semi-crystalline structures known as spherulites. This greatly increases the polymer density, opaqueness and strength. Semi-crystalline lamella Amorphous polymer between lamellae Spherulites in polyester and polylactic acid viewed under cross-polarised light Ivanov and Rosenthal, Polymer Crystallization II pp 95-126 polymerdatabase.com Unit cells Crystals are usually described using repeat elements that can be tessellated in space. These elements are known as unit cells. The smallest possible unit cell is known as a primitive unit cell. How many 3D lattices are there? There are 14 non-equivalent Bravais lattices that can fill the entirety of space when repeatedly translated. These are the simplest unique lattice structures from which more complex ones can be formed. They are described by their lattice parameters a, b and c as well as their unit cell axis angles a, b, and g. Example crystal structures Face-centred cubic e.g. Cu, Al, Ni, Au, g-Fe Rock salt e.g. NaCl, TiC, TiO Body-centred cubic e.g. Cr, Nb, Ta, W, a-Fe , b-Ti Hexagonal close-packed e.g. Zn, Co, Mg, a-Ti Diamond Perovskite e.g. diamond, Si, Ge e.g. BaTiO3, CaTiO3, SrTiO3 Close packed crystals When arranging spheres/circles in two dimensions we the closest packing is obtained with a hexagonal arrangement. We can then stack these hexagonal layers in two possible ways: Hexagonal close-packed (HCP) Stacking alternates every 2 layers (…ABABAB….) Face-centred cubic (FCC) Stacking alternates every 3 layers (…ABCABC….) Both arrangements give the highest possible packing fraction for a crystal of 74%. This means that only 26% is empty space. i.e. cubic unit cell https://chem.libretexts.org Crystallographic directions Directions in a crystal are indexed using the corresponding vectors using indices [uvw]. Square brackets are used to denote crystallographic directions. Crystallographic planes Planes are usually described by their normal vector. (i.e. one of the two directions that are perpendicular to the plane) To determine the indices (hkl) of a plane, we need to see where it intercepts each of the three coordinate axes and take the reciprocal of the values. Round brackets are used to denote planes. Crystallographic defects A crystallographic defect is a location in a crystal where the periodicity (or symmetry) is disrupted. The following types of defects are possible: • Point defects (“0-dimensional”) • Line defects (“1-dimensional”) • Planar defects (“2-dimensional”) A crystal that has no defects is called perfect or ideal. Defects can play a significant role in determining the properties of a crystalline material, both functional and structural. The effect of defects can be both detrimental and beneficial to the properties of a material. Therefore, it is important to understand them and hence control their effect on the material properties. Point defects Defects featuring only atoms from the original crystal are called intrinsic, whilst defects from impurity atoms are called extrinsic. E.g. semiconductor doping Small proportion of dopant impurities can be used to control the electronic properties of semiconductors. P and N-type doping is used to increase the number of free charge carriers (electrons or holes) in these materials. pure silicon n-type p-type E.g. solid oxide fuel cells Solid oxide fuel cells are reactors in which a fuel (e.g. hydrogen or hydrocarbons) is oxidised to produce an electric current. The devices rely on ionic conductivity of a solid oxide ceramic, which is usually heated to around 1000 Celsius. At this temperature the oxygen vacancies in the ceramic lattice are very mobile and allow the ionisation and transport of oxygen from the air in the cathode. mobile oxygen ion + fuel = oxidised fuel + oxygen vacancy + 2 electrons oxygen atom + oxygen vacancy + 2 electrons = mobile oxygen ion Line defects - dislocations Dislocations are by far the most common type of line defect, which can be viewed as lines of extra or missing atoms. There are three possible types: edge, screw and mixed dislocations. A dislocation is described by its Burgers vector (b)– the displacement vector that is needed to close a circuit around the dislocation line. respectively. (Edge = b ┴ dislocation line , Screw = b || dislocation line) Dislocation glide When a shear stress is applied to the dislocation, it is able to move through the crystal by the breaking and re-forming of inter-atomic bonds. This phenomenon is known as dislocation glide and is responsible for the plastic deformation of crystalline material. N.B. Plastic deformation in crystals is also possible via other less-common mechanisms. t t Glide/slip plane Slip step The minimum stress required to initiate the glide of a dislocation is called the critical resolved shear stress (CRSS). It ultimately determines the yield strength of a material. E.g. dislocations in FCC crystals The most likely dislocations to form will have their Burgers vector aligned with one of the close-packed directions in a crystal. These dislocations will move along a glide plane in which the Burgers vector lies. In an FCC crystal there are 4 unique (non-equivalent) close-packed {111}-type planes. Each of these planes hosts three unique close-packed slip directions linking the lattice sites. These are of ½<110>-type directions. Thus, there are at least twelve possible lattice dislocations that can form. As a result, FCC crystals are comparatively plastic due to this high number of slipsystems. Stress field at dislocation core Let us create an edge dislocation by inserting an extra half-plane of atoms. This compresses the crystal above the dislocation line. It also stretches the crystal below the dislocation line. This creates tensile and compressive stress fields around the dislocation core. These stress fields can interact with other stress fields in the crystal, such as those around other dislocations, solute atoms, interfaces, etc. Dislocation interactions The stress fields around dislocations can give rise to attractive and repulsive forces. Like Burgers vectors repel and opposite ones attract. When dislocations with opposing Burger’s vectors meet, they annihilate. +i.e. The net Burgers vector becomes zero. Dislocation sources A crystal may contain intrinsic dislocations, from when it formed. A dislocation segment in which the ends are immobilised (“pinned”) will act a source for multiple new dislocations via the Frank-Read mechanism. The segment bows out under applied stress until it forms a dislocation loop and a newly reformed segment. The cycle repeats generating more loops. Dislocation sources Electron microscope image of a Frank-Read source in silicon Computer simulation of a Frank-Read source pierrehirel.info Dislocation glide = plasticity The generation and multiplication of dislocations is responsible for the plastic deformation of a material. (i.e. dislocations are the carriers of plastic deformation) If a material is capable of sustaining dislocation glide, it will be ductile. The stress will continue to gradually rise after the yield of some materials. This is known as work hardening or strain hardening and occurs because the dislocations that are continually generated act as obstacles to one another. As their number increases with progressive deformation, so does the number of obstacles. v Elasticity = stretching of bonds by the applied force Plasticity = breaking and reforming of bonds by dislocation movement due to an applied force Strain hardening Work hardening can therefore be exploited to strengthen ductile materials. Unloading the material after yielding recovers the elastic strain, and the yield strength is increased to approximately the highest sustained plastic stress. However, this strengthening occurs at loss in the overall ductility. Yielding and plastic deformation increases the dislocation number density. The retained dislocations strengthen the material the next time it is loaded. Planar defects Interfaces between dissimilar crystals Regions with different crystal structures and chemical composition can co-exist in the same material. These regions with distict chemistry and crystal structure are known as phases. Three types of inter-phase interfaces are possible: Coherent The two lattices mesh perfectly, but the difference in lattice parameters results in a misfit strain. Semi-coherent The two lattices mesh well, but some dislocations are formed between coherent areas. Incoherent The two lattices do not mesh and the interface between them comprises a dense network of geometrically necessary dislocations. Solute strengthening If a dissolved impurity (i.e. solute) atom has a different size to the atoms of the host lattice, a stress field will be generated. This stress field will interact with the stress field around a dislocation and will inhibit its glide through the lattice. This is another example of beneficial point defects. The critical resolved shear stress due to a dissolved impurity is given by: shear strength of solute square of atom/particle radius solute concentration shear modulus of solute E.g. solute hardening in Al alloys Below we see an example of solution strengthening in aluminium. By alloying aluminium with 5 weight % magnesium, its strength is significantly improved relative to pure aluminium. Order strengthening A dislocation moving through and chemically ordered crystal may create an antiphase boundary. The creation of energetically unfavourable “wrong” bonds acts to oppose the motion of the dislocation. Thus effect acts to increase the strength since dislocations have to travel in pairs – one that creates the APB and one that removes it from the crystal. The increase in the CRSS to move the dislocation is given by: gAPB – is the APB energy per unit area b – is the magnitude (length) of the Burgers vector Precipitation hardening Some materials are processed in a such way that numerous fine particles (precipitates) with a stronger/harder crystal structure are formed within the prior parent crystal. Such particles can also act as obstacles to dislocation glide. Depending on the particle size and volume fraction, the dislocations must either cut through the particles or bypass them via the Orowan bowing mechanism. Either way, this increases the strength of the material. Precipitate cutting Bypass by Orowan bowing Precipitation hardening Precipitates sheared by dislocations in Al alloys Bowing and Orowan loops in a Ni-based alloy Polycrystalline materials Most manufactured materials are polycrystalline. (i.e. they consist of multiple crystals (or grains) which are mis-oriented relative to one another) This is not only because single crystals can be difficult to produce, but because polycrystalline materials are stronger. Grains in an aluminium alloy Grain boundaries in a bubble raft viewed under polarised light Crystal orientation map in a titanium alloy <= obtained using electron backscatter diffraction in an electron microscope. Similar colours are similar orientations relative to viewing direction. Grain boundary strengthening Grain boundaries are essentially networks of dislocations, which act as obstacles to dislocation glide limiting the transfer of plastic strain between the grains. Thus the smaller the size of the grains in the material, the higher its strength. Dislocation pile-ups at grain boundaries in stainless steel The Hall-Petch equation relates the yield strength to the grain size D in a material. - is the single crystal strength - is a proportionality constant specific to the material Controlling grain size Significant plastic deformation. (e.g. cold work) Dislocation tangles We can actually control the average grain size of a ductile material by a series of processing steps. Recovery Recrystallisation Grain growth Anneal the material (i.e. increase its temperature) Cell formation Annihilation of dislocations within cells Subgrain formation Subgrain growth Controlling grain size We can actually control the average grain size of a material by a series of processing steps. 1. First we need to plastically deform the material to increase the number density of dislocations in it. The more deformation, the greater the dislocation number. (E.g. cold rolling, cold extruding, cold forging, cold swagging) 2. Anneal the deformed material by raising its temperature and holding it in the heated state for a period of time. (I.e. put it in a furnace and let it sit there) • This will begin the process known as recovery. The dislocations will start to migrate and react with one another either annihilating or combining into dislocation networks. • The dislocation networks will start to form cells within the deformed grains, that will gradually evolve into finer sub-grains and eventually giving a grain structure that is finer that the original. This process is known as recrystallisation. • Once recrystallisation is complete, grain growth will follow. Larger grains will grow at the expense of while small ones which will shrink and disappear This process occurs to minimise the overall grain boundary area, which is thermodynamically unfavourable. If the material is not deformed prior to annealing, only grain growth will occur. Growing single crystals In certain cases the existence and accumulation of crystalline defects can lead to a deterioration of properties. In these cases, it is important to minimise their number or eliminate them entirely. We can grow single crystals and eliminate grain boundaries (and dislocations) in applications where their presence is undesirable. Directional solidification Czochralski process with a grain selector A rotating seed crystal is lifted out of the melt. With Si, Ge and GaAs the crystals are sliced into wafers for manufacturing integrated circuits. Dislocations and grain boundaries are low density regions that would accumulate the dopant atoms, which would alter the electronic properties. Grain boundaries allow the crystals to slide at high temperatures accelerating the rate of creep. Modern aero engine turbine blades are thus grown a single crystals. Molten blade alloy is poured into a mould which is slowly withdrawn from inside the furnace. A spiral grain selector ensures that growing crystals compete as they grow through it and ensures that only the one fastestgrowing crystal emerges out of it to grow into the mould. Summary • Solid materials are either crystalline, semi-crystalline or non crystalline. • Crystal = lattice + basis • Smallest repeat unit in a crystal is the Primitive Unit Cell • There are only 14 possible primitive unit cells in 3D • Defects are disruptions in the crystal symmetry • Crystal defects can be detrimental and beneficial • Crystal defects and interfaces between different crystals can be controlled by materials processing • Thus the processing of materials during manufacture controls the material properties and performance