Crystal Defects

1. Crystal Defects • Perfect crystals do not exist; even the best crystals have 1ppb defects. • defects are imperfections in the regular repeating pattern and may be classified in terms of their dimensionality (Point vs. Extended). • Point Defects • Vacancies • given a perfect crystal (e.g. of Cu), an atom can be placed on the outside of the cell to produce a vacancy (≡ □); remember atom migration. • e.g. TiO has 1:1 stoichiometry and NaCl structure, but has 15% vacancies on the Ti sites and 15% vacancies on the O sites. Both sets of vacancies are disordered.

2. Crystal Defects • driving force? movement of the atom requires breaking (endothermic) and making (exothermic) of bonds. Because the atom is moving from an internal site (w/say 6 bonds) to an external site (w/say 3 bonds), there are more bonds broken than being made, so this is an overall endothermic process. • counteracting this is an obvious large increase in disorder (from perfect crystal to defect); in addition, atoms around the vacated site can vibrate more, further increasing the disorder. ΔG(n) = nΔH –nTΔS n= #defects • Implications: • n≠ 0; ΔG = 0, so no driving force. • there is some min value of n which is most stable. • there is some minimum n after which ΔG becomes positive. • as T↑ nminand nmax will also increase. ΔG(n) max min n →

3. Crystal Defects • Ionic Crystal Defects • in pure metal compounds, don’t need to worry about electroneutrality. • in an ionic crystal, the interior and surface must remain ≈ neutral. • Shottky Defect • take anions and cations and place them on surface in equal numbers. • stoichiometric effect: equal numbers of anion and cation vacancies. • may be randomly distributed, but tend to cluster because of oppositely charged vacancies. • most important with alkali halides. • at room temp, ~1 in 1015 pairs vacant in NaCl, so 1mg sample has ~10,000 Shottky Defects.

4. Crystal Defects • Frenkel Defect • take cation out of position and cram it into an interstitial site (void between normal atomic position). • Ag+ surrounded by 4Cl- stabilizes this defect. • tendency for vacancy and interstitial to form nearby pair. • also a stoichiometric deffect (vacancies = interstitials).

5. Crystal Defects • Color Centers (aka F-center; Ger: farbenzentre) • electron trapped in an anion vacancy. • possible mechanism: high energy radiation (x-ray, γ-ray) interacts with alkali halide, causing halide to lose an electron. The electron moves through the crystal until it encounters a halide vacancy. It is trapped there by strong electrostatic forces (i.e. 6 cations!). • a series of energy levels are available for the electron within the vacancy; often in the visible region (deep purple in KCl; smoky quartz; amethyst). • found for a series of alkali halides: • absorption energy, Emax α a-1.8 a= cubic lattice parameter (length of the edge of the cubic unit cell). Note: E is inversely proportional to a.

6. Crystal Defects Large E; little a. Emax α a-1.8 Large a; little E.

7. Crystal Defects • Extended Defects. • have seen that many vacancies are initially random, but can cluster • when vacancy density gets high, the material will try to do something to get rid of them. • Sheer Planes • e.g. ReO3: bright red, Re Oh h.s. d7, conducting. • “normal” crystal (cut through face); note metal-containing Oh’s with shared corners. • when heated, the compound starts losing O atoms; these vacancies tend to line up in a plane through the center of a unit cell. • the structure sheers itself (½ unit cell length) so that the octahedrons now have shared edges. There are more and more sheer planes as O’s are lost.

8. Crystal Defects • Dislocations. • important class of defect; responsible for the malleability of metals; explains the process of work hardening of metals. • dislocations are line-defects; instead of the loss of atoms (as with point defects), they can be looked at as an extra partial line or plane of atoms. • looks like a perfect crystal, but if you look at the figure from a low angle, you see an extra partial line.

9. Crystal Defects • edge dislocations are easily moved by slipping; like a carpet: too heavy to drag, but can move small wrinkle. • the presence of a distortion relaxes the requirement that entire planes of interatomic bonds must distort and break simultaneously for plastic* deformation to occur. Instead, plastic deformation can accompany the motion of a dislocation through a crystal. *plastic = irreversible elongation (e.g. pulling wire) by movement of planes.

10. Crystal Defects • can get rid of dislocations; this gets rid of maleability and material becomes brittle (e.g. bend Cu wire). • movement of dislocations is key to plastic deformation, therefore, increasing resistance to deformation (strengthening the metal) requires either eliminating the distortions or preventing them from moving (pinning them). • dislocations are often pinned by other defects in the crystal; new dislocations are created during deformation and become pinned by the initial dislocation. • the build-up of pinned dislocations leads to the hardening of the metal in a process known as work hardening.

11. Crystal Defects • e.g. moving an entire rug requires lots of energy. A single wrinkle serves as a dislocation in facilitating the movement of the rug; at any time only a small part of the rug moves, so little energy required. • work hardening is like having multiple tangled wrinkles in the rug---one wrinkle pins the other. • a work-hardened metal can be softened again by annealing (heating) at high temperatures; increased thermal motion allows atoms to rearrange and go to lower energy states. • so, work hardening adds edge dislocations so that planes no longer slip.

12. Crystal Defects • can strengthen materials with sheer planes by adding impurities. if impurity prefers shorted bond lengths, then this is a stable situation. Cu + Zn → bronze Cu + Sn → brass edge dislocation strains bond lengths, etc.

13. Stress & Strain some materials, e.g. glass break after a certain point; brittle fracture. linear portion reversible. • Experiment: measure width and length of wire; pull and re-measure; repeat. • initial = • pull = • breaks at = • σ = stress = force/unit area • ε = strain = Δl/lo • yield strength increases as dislocations increase. • distortions get tangled up like spaghetti; too many cause material to become brittle. • e.g. Fe sword: add impurities and pound; becomes hard; dislocations climb to surface; anealing makes material soft by getting rid of distortions. σ ~0.1% ε cross-sectional area (larger diameter would require more force to break). again, linear portion reversible, so below yield point no permanent elongation occurs = elastic deformation change in length/ initial length σ σo ~20% ε above yield point plastic elongation occurs.

14. Burger’s Vectors (Berger’s Circuit) 4 3 3 4 • Way to describe dislocation. 4 3 3 4 Above: Burger’s circuit for dislocation-free material. note “compressed bonds” and “elongated bonds.” To Right: Do same with dislocation and end up “past” starting point. Vector b = distance to get back to curcuit.

15. Burger’s Vectors • Screw dislocation with Berger’s vector. Note direction is direction of screw axis. • Crystals often will grow along screw dislocation.

16. Impurities and Doping • Impurities are elements present in the material that are different from those in the compound formula. • Dopants are intentionally added impurities (to make alloys or affect changes in properties). Alloy formation most likely when dopant anions and cations are close in size to original material. • Isovalentdopants: substitution species have the same charge. NaCl:AgCl → Na1-xAgxCl (alloy on cation site) AgBr:AgCl → AgBr1-xClx (alloy on anion site) • Aleovalentdopant: substitution species has different charge. NaCl:CaCl2 could be either Na1-2xCax□xCl or Na1-xCaxClClxi • either could happen; experimentally, first is found. vacancy interstitial