1、Lattice Defects/Imperfections in Crystalline MaterialsA scanning probe micrograph(generated using a scanning-tunneling microscope)that shows a(111)-type surface plane for silicon.The arrow points to the location of a silicon atom that was removed using a tungsten nanotip probe.This site from which a
2、n atom is missing is the surface analogue of a vacancy defectthat is,a vacant lattice site within the bulk material.Approximately20,000,000X.Defect types:-0-D:point defects-1-D:dislocations-2-D:interfaces,grain boundaries-3-D:pores Lattice defect is meant a lattice irregularity having one or more of
3、 its dimensions on the order of an atomic diameter.Importance of Lattice Defects for Properties of Materialsu Show some examples:-Learning Objectives1.Describe both vacancy and self-interstitial crystalline defects.2.Calculate the equilibrium number of vacancies in a material at some specified tempe
4、rature,given the relevant constants.3.Name the two types of solid solutions,and provide a brief written definition and/or schematic sketch of each.4.For each of edge,screw,and mixed dislocations:(a)describe and make a drawing of the dislocation.(b)note the location of the dislocation line,and(c)indi
5、cate the direction along which the dislocation line extends.Point defects-Vacancies and Self-interstitialsThe simplest of the point defects is a vacancy,or vacant lattice site,one normally occupied from which an atom is missing.Vacancies are a type of equilibrium lattice defects.The necessity of the
6、 existence of vacancies is explained using principles of thermodynamics;in essence,the presence of vacancies increases the entropy(i.e.,the randomness)of the crystal.Calculation of equilibrium vacancy concentrationNv:number of equilibrium vacanciesN:total number of atomic sitesQv:formation energy of
7、 a vacancyk:Boltzmann constantT:temperatureuA self-interstitial is an atom from the crystal that is crowded into an interstitial site.uIn metals,a self-interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial posit
8、ion in which it is situated.Consequently,the formation of this defect is not highly probable,and it exists in very small concentrations,which are significantly lower than for vacancies.Point defects-ImpuritiesThe addition of impurity atoms to a metal will result in the formation of a solid solution
9、and/or a new second phase,depending on the kinds of impurity,their concentrations,and the temperature of the alloy.In a solid solution,the impurity atoms are randomly and uniformly dispersed within the solid.Q:Under what conditions a solid solution/a new second phase forms?There are two types of sol
10、id solution,i.e.,substitutional and interstitial,depending the sites the impurity atoms situated.uSolubility of substitutiional atoms is influenced by atomic size difference,crystal structure,electronegativity,and valences.uFor metallic materials that have relatively high atomic packing factors,thes
11、e interstitial positions are relatively small.Therefore,the interstitial solute atoms must be substantially smaller than the host atoms.Linear defects-DislocationsA dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned.extra half-plane of atomsEdge dislocati
12、onScrew dislocationSchematic representation of a dislocation that has edge,screw,and mixed character.Top view,where open circles denote atom positions above the slip plane.Solid circles,atompositions below.At point A,the dislocation is pure screw,while at point B,it is pure edge.For regions in betwe
13、en where there is curvature in the dislocation line,the character is mixed edge and screw.Dislocations in cold-rolled palladium observed by TEM.Y.Z.Chen et al.,Scripta Materialia,2013,Vol.68:743-746Interfacial defectsInterfacial defects are boundaries that have two dimensions and normally separate r
14、egions of the materials that have different crystal structures and/or crystallographic orientations.external surfacesgrain boundariestwin boundariesstacking faultsphase boundariesInterfacial defects-External surfaceu Surface atoms are not bonded to the maximum number of nearest neighbors.u Energy hi
15、gher than the atoms at interior positions.uTends to reduce the total surface area to reduce the energy.-Essentially important for catalysts applicationsHigh-resolution transmission electronmicrograph that shows single crystals of(Ce0.5Zr0.5)O2;this material is used in catalytic converters for automo
16、biles.Schematic representations of surfacedefects that are potential adsorption sites for catalysis.Interfacial defects-Grain boundariesThe boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials.The atoms are bonded less regularly
17、 along a grain boundary(e.g.,bond angles are longer),and consequently,there is an interfacial or grain boundary energy similar to the surface energy.A larger misorientation leads to larger GB energy.Photomicrograph of the surface of a polished and etched polycrystalline specimen of an iron-chromium
18、alloy in which the grain boundaries appear dark.Interfacial defects-Twin boundariesA twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry;that is,atoms on one side of the boundary are located in mirror-image positions of the atoms on the other si
19、deAnnealing twin,often observed in fccDeformation twin,often observed in bcc and hcpAtoms bonded regularly and close packed.Low energy and stable.Observation of lattice defectsExercise1.Calculate the number of vacancies per cubic meter in gold at 900C.The energy for vacancy formation is 0.98 eV/atom
20、.Furthermore,the density and atomic weight for Au are18.63 g/cm3(at 900C)and 196.9 g/mol,respectively.2.Explain the relative orientation between Burgers vector and dislocation line for edge dislocation,screw dislocation,and mixed dislocation.3.For both FCC and BCC crystal structures,there are two di
21、fferent types of interstitial sites.In each case,one site is larger than the other,and is normally occupied by impurity atoms.For FCC,this larger one is located at the center of each edge of the unit cell;it is termed an octahedral interstitial site.On the other hand,with BCC the larger site type is found at positions 0 ;it is termed a tetrahedral interstitial site.For both FCC and BCC crystal structures,compute the radius r of an impurity atom that will just fit into one of these sites in terms of the atomic radius R of the host atom.
