The Muppet’s Guide to: The Structure and Dynamics of Solids 6. Crystal Growth & Defects

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Heterostructures Dislocation/ Disorder

Lattice Match through Rotations Pt[100]//FeCo[110] 45° Rotation of unit cells a Pt =3.9242Å a Fe =2.8665Å

Disorder in crystalline materials No such thing as a perfectly ordered material Many materials are technologically of value because they are disordered/imperfect in some way: silicon devices – controlled levels of deliberate impurity additions (ppb)p-type : BSi  B + h n-type : PSi  P + e steels – additions of 0.1 to 1 at.% other metals to improve mechanical properties and corrosion resistance

Vacancy atoms Interstitial atoms Substitutional atoms Point defects Types of Imperfections Dislocations Line defects Grain Boundaries Area defects

Imperfections in Solids Linear Defects (Dislocations) –Are one-dimensional defects around which atoms are misaligned Edge dislocation: –extra half-plane of atoms inserted in a crystal structure –b  to dislocation line Screw dislocation: –spiral planar ramp resulting from shear deformation –b  to dislocation line Burger’s vector, b: measure of the magnitude and direction of lattice distortion.

Dislocations – linear defects Source: -growth -stress -temperature Evidence: -metals more deformable than predicted (but can be strengthened by impurities) -spiral growths on surface of some crystals -reactions occur at active surface sites Types: edge, screw, intermediate Transmission electron micrograph of Ti alloy – dark lines are dislocations (Callister: Materials Science and Engineering)

Edge dislocation – partial plane of atoms – lattice distorted where plane ends Dislocations characterised by the Burgers vector, b -for metals, b points in a close-packed direction and equals the interatomic spacing (Callister: Materials Science and Engineering)

Heterostructures ┬

Buffer Layers ┬ ┬ ┬

Screw dislocation partial slip of a crystal on one side of dislocation line, crystal has undergone slip; on other side, crystal is normal continued application of shear stress causes dislocation to move through crystal Shear stress (Callister: Materials Science and Engineering)

Edge, Screw, and Mixed Dislocations Edge Screw Mixed (Callister: Materials Science and Engineering)

Interfacial (planar) defects boundaries separating regions of different crystal structure or crystallographic orientation –External surfaces (see final section of module) –Internal boundaries Layer Interfaces (2D) Region Interfaces (3D)

Freezing - result of casting of molten material –2 steps Nuclei form Nuclei grow to form crystals Crystals grow until they meet each other –grain structure Planar Defects in Solids nuclei crystals growing grain structure liquid (Callister: Materials Science and Engineering)

Polycrystalline Materials Grain Boundaries regions between crystals transition from lattice of one region to that of the other slightly disordered low density in grain boundaries –high mobility –high diffusivity –high chemical reactivity Adapted from Fig. 4.7, Callister 7e.

Grain boundaries D = b/  b Internal surfaces of a single crystal where ideal domains (mosaic) meet with some misalignment: high-angle and small(low)-angle. NB – in polycrystalline materials, grain boundaries are more extensive and may even separate different phases Small-angle grain boundary equivalent to linear array of edge dislocations bonding not fully satisfied  region of higher energy, more reactive, impurities present. (Callister: Materials Science and Engineering)

Planar Defects in Solids 2 Another case is a twin boundary (plane) –Essentially a reflection of atom positions across the twin plane. Stacking faults –For FCC metals an error in ABCABC packing sequence –Ex: ABCABABC (Callister: Materials Science and Engineering)

Point Defects small substitutional atom All of these defects disrupt the perfect arrangement of the surrounding atoms – relaxation effects Schottky and Frenkel normally v low conc. since formation energy high vacancy interstitial large substitutional atom Frenkel defect Schottky defect

Found in ionic crystals Oppositely charged ions leave their lattice sites, creating vacancies anion and cation vacancies balance such that charge neutrality is preserved Schottky Defects

Frenkel Defect Tend to be found in ionic solids with large size difference between the anion and cation The defect forms when an atom or cation leaves its place in the lattice, creating a vacancy, and becomes an interstitial. occur due to thermal vibrations occurrence depends on –size of ion –charge on ion –electronegativity –temperature Ag

Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -"extra" atoms positioned between atomic sites. Point Defects Vacancy distortion of planes self- interstitial distortion of planes (Callister: Materials Science and Engineering)

Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random dist. of point defects) OR Substitutional solid soln. (e.g., Cu in Ni) Interstitial solid soln. (e.g., C in Fe) Point Defects in Alloys (Callister: Materials Science and Engineering)

Solid Solutions Solid state mixture of one or more solutes in a solvent Crystal structure remains unchanged on addition of the solute to the solvent Mixture remains in a homogenous phase Generally composed on metals close in the periodic table Ni/Cu, Pb/Sn etc. Otherwise compounds tend to form NaCl, Fe 2 O 3 etc.

Solid Solutions Solute atoms create strain fields which can inhibit dislocations propagating in a material changing its properties

Hume-Rothery Rules – Substitutional Solutions 1.The solute and solvent should be of a similar size. (<15% difference) 2.The crystal structures must match. 3.Both solute and solvent should have similar electronegativity 4.The valence of the solvent and solute metals should be similar. Rules to describe how an element might dissolve in a metal. Stable composition in equilibrium (thermodynamics) Metals – Ni/Cu, Pd/Sn, Ag/Au, Mo/W

Hume-Rothery Rules – Interstitial Solution 1.The solute must be smaller than the interstitial sites in the solvent lattice 2.Solute and Solvent should have similar electro- negativities Rules to describe how an element might dissolve in a metal. Stable composition in equilibrium (thermodynamics) Light elements – H,C, N and O.

Phase Equilibria – Example Crystal Structure electroneg r (nm) KBCC NaBCC Both have the same crystal structure (BCC) and have similar electronegativities but different atomic radii. (W. Hume – Rothery rules) suggest that NO solid solution will form. K-Na K and Na sodium are not miscible.

Phase Equilibria – Example Crystal Structure electroneg r (nm) NiFCC CuFCC Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility. Simple solution system (e.g., Ni-Cu solution) Ni and Cu are totally miscible in all proportions.

Material Properties Dislocations & plastic deformation Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations). If dislocations don't move, deformation doesn't occur! Adapted from Fig. 7.1, Callister 7e.

Edge Defect Motion

Dislocations & Materials Classes Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) bonding Ionic Ceramics (NaCl): Motion hard. -need to avoid ++ and - - neighbours Metals: Disl. motion easier. -non-directional bonding -close-packed directions for slip. electron cloudion cores (Callister: Materials Science and Engineering)

Dislocation Motion Dislocation moves along slip plane in slip direction perpendicular to dislocation line Slip direction same direction as Burgers vector Edge dislocation Screw dislocation Adapted from Fig. 7.2, Callister 7e. (Callister: Materials Science and Engineering)

Pinning dislocations dislocations make metals easier to deform to improve strength of metals, need to stop dislocation motion trap with: - impurity atoms; - other dislocations (work hardening; - grain boundaries. atom trap (Callister: Materials Science and Engineering)

Modify Material Properties Grain boundaries are barriers to slip. Barrier "strength" increases with Increasing angle of miss-orientation. Smaller grain size: more barriers to slip. Increase material strength through reducing Grain size (Callister: Materials Science and Engineering)

Impurity atoms distort the lattice & generates stress. Stress can produce a barrier to dislocation motion. Modify Material Properties Smaller substitutional impurity Impurity generates local stress at A and B that opposes dislocation motion to the right. A B Larger substitutional impurity Impurity generates local stress at C and D that opposes dislocation motion to the right. C D Increase material strength through substitution (Callister: Materials Science and Engineering)