Читать книгу Crystallography and Crystal Defects - Anthony Kelly - Страница 4

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1 Chapter 1Figure 1.1 (a) The arrangement of the atoms in graphene, a single sheet of g...Figure 1.2 Definition of the smallest separations a, b and c of the lattice ...Figure 1.3 The numbers give the elevations of the centres of the atoms, alon...Figure 1.4 A rectangular mesh of a hypothetical two‐dimensional crystal with...Figure 1.5 Demonstration of the law of constancy of angles between faces of ...Figure 1.6 A vector r written as the sum of translations along the x‐, y‐ an...Figure 1.7 Examples of various lattice vectors in a crystal Figure 1.8 The plane (hkl) in a crystal making intercepts of a/h, b/k and c/Figure 1.9 Examples of various lattice planes in a crystal. The indices of t...Figure 1.10 The plane (hkl) in a crystal making intercepts of a/h, b/k and c Figure 1.11 Translation symmetry in a crystal Figure 1.12 Reflection symmetry Figure 1.13 Diagram to help determine which rotation axes are consistent wit...Figure 1.14 The five symmetrical plane lattices or nets. Rotational symmetry...Figure 1.15 Restrictions placed on two‐dimensional lattices through the impo...Figure 1.16 The two possible arrangements of nets consistent with mirror sym...Figure 1.17 Examples of possible allowed combinations of rotational symmetri...Figure 1.18 Stacking of nets to build up a space lattice. The triplet of vec...Figure 1.19 Unit cells of the 14 Bravais space lattices. (a) Primitive tricl...Figure 1.20 Lattice points in the net at height zero are marked as dots, tho...Figure 1.21 A three‐dimensional view of the staggered arrangement of nets in...Figure 1.22 Lattice points in the net at height zero are marked with dots. T...Figure 1.23 The stacking of rhombus nets vertically above one another to for...Figure 1.24 The three possible stacking sequences of rectangular nets. In th...Figure 1.25 The staggered stacking of rhombus nets. This form of stacking ge...Figure 1.26 The stacking of triequiangular nets of points in a staggered seq...Figure 1.27 Lattice points in the net at level zero are marked with a dot, t...Figure 1.28 The relationship between a primitive cell of the trigonal lattic...Figure 1.29 Plan view of the alternative triply primitive hexagonal unit cel...Figure 1.30 The four 〈111〉 three‐fold axes with acute angles of 70.53° betwe...Figure 1.31 The relationship between the primitive unit cell and the convent...Figure 1.32 The relationship between the primitive unit cell and the convent...
2 Chapter 2Figure 2.1 The basic operation of repetition by a rotation axis. In this exa...Figure 2.2 Stereograms representing the operation of one‐, two‐, three‐, fou...Figure 2.3 The repetition of an object by a mirror plane, (a) and (b), and b...Figure 2.4 The operation of the twofold rotoinversion axis, Figure 2.5 The operation of the various rotoinversion axes that can occur in...Figure 2.6 Stereograms of the poles of equivalent general directions and of ...Figure 2.7 A stereogram of an orthorhombic crystal of point group 222 centre...Figure 2.8 (a) General location of a hk0 pole on the stereogram of an orthor...Figure 2.9 The cubic point group of lowest symmetry: 23 Figure 2.10 Stereograms centred on 001 of (a) mirror planes parallel to {100...Figure 2.11 Stereogram of a cubic crystal.Figure 2.12 (a) Stereogram of the holosymmetric class of the hexagonal syste...Figure 2.13 Geometry to show that in Miller−Bravais indices (hkil), i = −(h ...Figure 2.14 Indices of various directions in the hexagonal system specified ...Figure 2.15 Geometry to determine the angle θ between the (0001) pole a...Figure 2.16 A stereogram of a trigonal crystal of class m with a rhombohedr...Figure 2.17 The same crystal as in Figure 2.16 indexed using a hexagonal cel...Figure 2.18 The relationship between the special forms {101} and {011} in ...Figure 2.19 Monoclinic stereogram centred on [001] for the 2nd setting Figure 2.20 A diagram from which the angle φ in Figure 2.19 between 010...Figure 2.21 Diagrams relevant to drawing stereograms of triclinic crystals. ...Figure 2.22 (a) A twofold rotation axis. (b) A 2₁ screw axis. (c) A glide pl...Figure 2.23 Screw axes 3₁ and 3₂: these are screw axes of opposite hand, as ...Figure 2.24 The 17 two‐dimensional space groups arranged following the Inter...Figure 2.25 An example of a space group.Figure 2.26 The 10 black‐and‐white plane lattices: (a) parallelogram (obliqu...Figure 2.27 The effect of antiferromagnetic coupling on the size of the unit...
3 Chapter 3Figure 3.1 (a) The conventional unit cell of the c.c.p. crystal structure. (...Figure 3.2 Close packing of equal spheres. (a) Cubic close‐packed (c.c.p.). ...Figure 3.3 Plan view of the ABCABCABC… stacking sequence of (111) planes in ...Figure 3.4 The stacking of closest‐packed planes in (a) the c.c.p. structure...Figure 3.5 The largest interstice in the c.c.p. structure: the octahedral in...Figure 3.6 The second largest interstice in the c.c.p. structure: the tetrah...Figure 3.7 The unit cell of the h.c.p. structure Figure 3.8 Interstices in the h.c.p. arrangement. The octahedral interstices...Figure 3.9 The b.c.c crystal structure Figure 3.10 Tetrahedral (X) and octahedral (O) interstices in the b.c.c crys...Figure 3.11 The crystal structure of mercury, showing the primitive rhombohe...Figure 3.12 The crystal structure of diamond Figure 3.13 The stacking of (111) planes in the diamond and sphalerite struc...Figure 3.14 (a) The crystal structure of graphite. (b) The crystal structure...Figure 3.15 The crystal structure of As, Sb and BiFigure 3.16 The crystal structure of sodium chloride, NaClFigure 3.17 The crystal structure of caesium chloride, CsClFigure 3.18 The crystal structures of (a) sphalerite (α‐ZnS) and (b) wu...Figure 3.19 The crystal structure of nickel arsenide, NiAsFigure 3.20 The crystal structure of calcium fluoride, CaF₂Figure 3.21 (a) The crystal structure of rutile, TiO₂. (b) The rutile crysta...Figure 3.22 The crystal structure of perovskite, PmmFigure 3.23 The structure of sapphire (α‐Al₂O₃ or corundum). The large ...Figure 3.24 One‐eighth of the unit cell of spinel, MgAl₂O₄Figure 3.25 Coordination about the oxygen ions (solid black circles) in a ga...Figure 3.26 The structure of calcite (CaCO₃). The primitive rhombohedral uni...Figure 3.27 A c.c.p. crystal showing (a) a substitutional solid solution and...Figure 3.28 (a) A (111) plane of the disordered form of Cu₃Au. (b) A (111) p...Figure 3.29 Structures of ordered solid solutions: (a) B2, (b) D0₃, (c) D0₁₉Figure 3.30 Molecular models of (a) polyethylene (–CH₂–)_n and (b) polytetraf...Figure 3.31 (a) Unit cell of polyethylene viewed along [001]. The unit cell ...Figure 3.32 Illustration of a continuous polymer chain running through neigh...
4 Chapter 4Figure 4.1 (a) Construction of a Voronoi polygon in two dimensions. (b) A po...Figure 4.2 Para‐azoxyanisole (PAA)Figure 4.3 A sketch of the molecular arrangements in the three classes of li...Figure 4.4 Schematics of the three types of distortion of a nematic mesophas...Figure 4.5 The five Platonic solids. Left‐hand column: the solids. Centre co...Figure 4.6 Packing of equal‐sized spheres into an icosahedral arrangement. T...Figure 4.7 The crystal structure of MoAl₁₂. This figure is derived from Figu...Figure 4.8 The microstructure of a foam made from an Al − 9 wt% Si alloy con...
5 Chapter 5Figure 5.1 The relationship between a set of orthonormal axes (Ox₁, Ox₂, Ox₃Figure 5.2 The general tensorial relationship between an electrical field E ...Figure 5.3 Derivation of the magnitude of the conductivity in a particular d...Figure 5.4 The representation ellipsoid.Figure 5.5 The radius–normal property of a representation ellipsoid.
6 Chapter 6Figure 6.1 (a) Definition of extension. (b) Definition of shearFigure 6.2 Distortion of a body in two dimensions. Points P and Q move to P′...Figure 6.3 Distortion in two dimensions of a rectangular element at P. Two s...Figure 6.4 Imposition of a rigid body rotation ω to enable a relative d...Figure 6.5 The geometrical interpretation of Eq. (6.9) for e₁₂ and e₂₁Figure 6.6 Distortion of a unit cube whose edges are parallel to the princip...Figure 6.7 The force f acting on a small area δA in a plane surrounding...Figure 6.8 Definition of stress components (a) in Cartesian coordinates and ...Figure 6.9 Calculation of the stress acting on the plane ABCFigure 6.10 Stresses acting on one face of a cube of side 2δ in a varyi...Figure 6.11 A shear stress at the point PFigure 6.12 If σ₃ is the largest principal stress and σ₁ is the smallest, th...Figure 6.13 Orthonormal ‘old’ and ‘new’ sets of axes related to one another ...Figure 6.14 Orthonormal ‘old’ and ‘new’ sets of axes related to one another ...Figure 6.15 Orthonormal ‘old’ and ‘new’ sets of axes related to one another ...
7 Chapter 7Figure 7.1 Illustration of the process of glide. Blocks 1, 2 and 3 in a crys...Figure 7.2 Schematic diagram of glide occurring in the direction β in a...Figure 7.3 Schematic diagram of the fine structure observed in slip lines in...Figure 7.4 Macroscopic measurement of the amount of glide in a crystalFigure 7.5 Illustration of the inherent centrosymmetric nature of the simple...Figure 7.6 Pencil glide, also known as wavy glide. Here, the slip direction Figure 7.7 Illustration of simple shear in two dimensions: (a) before shear ...Figure 7.8 Simple shear in three dimensions. Here, a point P relative to O m...Figure 7.9 A small simple shear deformation e_ij is equivalent to a pure stra...Figure 7.10 The strains produced by the physically different slip systems [Figure 7.11 Schematic diagram to illustrate that the cubic crystal in (a) sl...Figure 7.12 Deformation in tension of a single crystal. Glide is presumed to...Figure 7.13 Standard stereogram of a c.c.p. metal crystal which glides on {1...Figure 7.14 A unit triangle of the standard stereogram of a hexagonal crysta...Figure 7.15 The 001–011– stereographic triangle for a b.c.c. metal crystal ...Figure 7.16 Nomenclature for the various {111} slip planes for a c.c.p. sing...Figure 7.17 Change in orientation during a glide operation if there is no la...Figure 7.18 Changes in orientation of c.c.p. metal crystals during glide. Th...Figure 7.19 Compression of a single crystal between plates
8 Chapter 8Figure 8.1 A screw dislocation in a primitive cubic latticeFigure 8.2 Primitive cubic lattice after the screw dislocation in Figure 8.1...Figure 8.3 An edge dislocation in a primitive cubic latticeFigure 8.4 A mixed dislocation, DD′, in a primitive cubic latticeFigure 8.5 Atom positions around an edge dislocation in a simple cubic cryst...Figure 8.6 Schematics of a screw dislocation in a simple cubic crystal (a) l...Figure 8.7 A Burgers circuit around an edge dislocation in a simple cubic cr...Figure 8.8 Schematic of a closed dislocation loop in a simple cubic crystal...Figure 8.9 The motion of a dislocation DD' in the direction represented ...Figure 8.10 The dislocation loop shown in (a) can glide so that its area pro...Figure 8.11 (a) Production of a prismatic dislocation loop by punching. (b) ...Figure 8.12 An edge dislocation in a region of general stress σ showing...Figure 8.13 Strain due to a screw dislocation lying along the z‐axisFigure 8.14 Stress due to a screw dislocation along the z‐axis acting on a s...Figure 8.15 The relationship between the x₁‐ and x₂‐axes, r and θ for a...Figure 8.16 Schematic of a screw dislocation in a simple cubic crystal looki...Figure 8.17 Plot of Eq. (8.28)Figure 8.18 A screw dislocation of twice the width of the one shown in Figur...Figure 8.19 Dislocation multiplicationFigure 8.20 Force between parallel edge dislocations on slip planes a distan...Figure 8.21 Orthogonal screw dislocations, a perpendicular distance d apart...Figure 8.22 A jog QR on a dislocation PQRS where PQ and RS have screw disloc...
9 Chapter 9Figure 9.1 An edge dislocation formed by making a cut in a cylinder and then...Figure 9.2 A dislocation reaction in which two dislocations combine to form ...Figure 9.3 Forces on a small segment of a dislocation loop in equilibriumFigure 9.4 A dislocation line being extruded between obstacles a distance l ...Figure 9.5 Forces acting on a small curved segment of a dislocation when acc...Figure 9.6 A perfect dislocation on a (111) plane of a c.c.p. metal which ha...Figure 9.7 (a) Faulted vacancy loop in a c.c.p. metal, showing traces of the...Figure 9.8 Thompson's tetrahedron. (After Thompson [15]).Figure 9.9 The vector relationship between the Burgers vectors of a Shockley...Figure 9.10 The dissociation of a perfect dislocation CB into two partial di...Figure 9.11 Reaction of two dislocations on a common slip plane. The disloca...Figure 9.12 Same reaction as Figure 9.11 but showing splitting into partials...Figure 9.13 Lomer–Cottrell lockFigure 9.14 Formation of a stacking fault tetrahedron from a Frank vacancy l...Figure 9.15 Hirth lockFigure 9.16 Relation between slip planes and directions in {110} or {110} Figure 9.17 Edge dislocation in NaCl. The slip plane and the two sheets of i...Figure 9.18 Edge dislocation in NaCl viewed in a different section to that s...Figure 9.19 Atoms and lattice vectors in a hexagonal metalFigure 9.20 Two possible structures for a vacancy loop in a hexagonal metal...Figure 9.21 A slip systemFigure 9.22 Relation between slip planes and directions in slipFigure 9.23 A ball model of the {110} planes in a b.c.c. metalFigure 9.24 Double kink in a dislocation line. The dotted lines represent po...Figure 9.25 A 60° dislocation in sphalerite. The structure of a 60° dislocat...Figure 9.26 Stacking fault in a silicon film. Point O lies at the bottom sur...Figure 9.27 Atoms and lattice vectors in the basal plane of graphiteFigure 9.28 A schematic side view of a split 60° dislocation in graphite. At...Figure 9.29 Reaction between partial dislocations on adjacent planes in grap...
10 Chapter 10Figure 10.1 Crystal surface acting as a vacancy source. In (a) an atom jumps...Figure 10.2 {100} plane of NaCl, showing the sense of the displacements of t...Figure 10.3 Hypothetical split interstitial in a c.c.p. metal. The plane of ...Figure 10.4 Hypothetical split interstitial in a b.c.c. metal. The plane of ...Figure 10.5 Crowdion in an alkali metal, as postulated by Paneth [23]. The l...Figure 10.6 H‐centre in a KCl crystal. The plane of the diagram is (001). (N...Figure 10.7 Path followed by an atom jumping into a vacant nearest‐neighbour...Figure 10.8 Path followed by an atom jumping into a vacant nearest‐neighbour...Figure 10.9 Effects of changes in length and lattice parameter with temperat...Figure 10.10 Schematic conductivity plot for a NaCl crystal containing a sma...Figure 10.11 Effect of CdBr₂ additions on the electrical conductivity of AgB...Figure 10.12 Annealing out of the quenched‐in resistivity ρ of a metal ...Figure 10.13 Isochronal recovery of electron‐irradiated copper containing an...Figure 10.14 Interstitial sites occupied by C or N atoms in ferrite, α‐Fe. T...Figure 10.15 Effect of relaxation on the strain caused by a constant stress Figure 10.16 Hypothetical tetravacancy in a c.c.p. metal. The dotted lines s...
11 Chapter 11Figure 11.1 Structure of a twin in a c.c.p. metal. The plane S in (a) is the...Figure 11.2 Formation of a twin in a c.c.p. metal by shear. The dotted lines...Figure 11.3 Displacements produced by a twin lamella. The traces PQ and QR d...Figure 11.4 The elements of deformation twinning. O is an origin, K₁ is the ...Figure 11.5 (a) Type I twin. (b) Type II twin. In (a) the lattice vector l₃ ...Figure 11.6 Twin in a b.c.c. metal. The scheme of the figure is the same as ...Figure 11.7 Twin in sphaleriteFigure 11.8 Twin in calcite. The scheme of the figure is the same as that of...Figure 11.9 The (102) twin in zirconium. The scheme of the figure is the sa...Figure 11.10 The (102) twin in zincFigure 11.11 Plan view of the (100) plane in graphite, showing the structur...Figure 11.12 The formation of a twin in graphite by a partial dislocation on...Figure 11.13 Shear and the geometry of deformation twinning: a vector l₃ par...Figure 11.14 (a) Twin lamella intersecting a surface AB. (b) Dislocation mod...Figure 11.15 Dislocation model of a thin twin lamellaFigure 11.16 Emissary dislocations. The dislocations shown by a single line ...Figure 11.17 Pole mechanism for the growth of a twinFigure 11.18 (a) Projection of 2 × 2 unit cells of pyrite projected onto (00...Figure 11.19 Structures for Type II twinning with stable twin modes for devi...
12 Chapter 12Figure 12.1 Scratched surface intersected by a martensite plate MM′Figure 12.2 The square lattice within the plate outlined in (a) is strained ...Figure 12.3 The three possible 〈211〉 vectors in a (111) planeFigure 12.4 (a) Unit cell of the b.c.c. lattice, drawn with (011) in the x‐y...Figure 12.5 A section through a sphere of zirconium and the ellipsoid develo...Figure 12.6 Undistorted planes of the strain S′Figure 12.7 Rotation suffered by the undistorted planes of the strain S′Figure 12.8 Approximate crystallography of a plate of martensite in titanium...Figure 12.9 Schematic of a partly transformed In–Tl alloy single crystal. Th...Figure 12.10 The twin relationship of the lamellae shown in Figure 12.9Figure 12.11 Three parallel plates of martensite with alternating shear stra...Figure 12.12 The c.c.p. lattice with a b.c.t. cell picked out of it. (After ...Figure 12.13 Lattice parameters of austenite and martensite as a function of...Figure 12.14 Habit plane normals of martensite in various steels plotted on ...Figure 12.15 The (011) plane of a b.c.c. metal (a) before and (b) after a di...Figure 12.16 The one‐way shape memory effect. (a) a sample annealed in its a...Figure 12.17 The two‐way shape memory effect. (a) a sample annealed in its a...
13 Chapter 13Figure 13.1 The two alternative {100} surfaces of a hexagonal metal. The su...Figure 13.2 The four alternatives for a surface parallel to (0001) in wurtzi...Figure 13.3 Surface at a small angle θ to a {111} plane of a c.c.p. met...Figure 13.4 A schematic of energy E as a function of angle θ away from ...Figure 13.5 Possible (10) section through the γ‐plot of a c.c.p....Figure 13.6 A fine wire with a bamboo‐like grain structure to which a load WFigure 13.7 Splitting of a crystal of width w with a pre‐existing crack of l...Figure 13.8 Low‐angle symmetrical tilt boundary in a simple cubic lattice. T...Figure 13.9 Energy of a tilt boundary as a function of the tilt angle θ. Val...Figure 13.10 Schematic of a high‐angle tilt boundary of good fit between one...Figure 13.11 An asymmetrical tilt boundary where the misorientation across t...Figure 13.12 A low‐angle twist boundary in a simple cubic lattice. The bound...Figure 13.13 (a) Generation of grains 1 and 2 by opposite rotations of θ/...Figure 13.14 Twist boundary of good fit in a simple cubic lattice. The bound...Figure 13.15 Part of the CSL produced from a c.c.p. lattice by a rotation of...Figure 13.16 Twin boundary in a monoclinic lattice. The boundary is normal t...Figure 13.17 Graphical representation of the total Burgers vector B of the d...Figure 13.18 Maximum disorientation angles as a function of angle/axis descr...Figure 13.19 Grain boundary groove, seen in cross‐sectionFigure 13.20 A segment of an interface, OE, held in equilibrium by forces F_xFigure 13.21 Two boundaries of the same twin joining at right angles to one ...Figure 13.22 The junction of the interfaces between three grains. Each inter...Figure 13.23 Twin boundary grooving, seen in cross‐sectionFigure 13.24 The γ‐plot of Figure 13.5, showing the equilibrium s...Figure 13.25 Construction due to Herring [43]Figure 13.26 The same equilibrium shape as shown in Figure 13.24, arising fr...Figure 13.27 A surface that has reduced its energy by breaking up into facet...Figure 13.28 The instability of four interfaces meeting along a line through...Figure 13.29 (a) Truncated octahedron and (b) distorted truncated octahedron...Figure 13.30 The Weaire–Phelan foam structure. The individual cells within t...
14 Chapter 14Figure 14.1 A particle of a phase B situated at a grain boundary of the phas...Figure 14.2 Interface between two orthorhombic crystals. The interface is no...Figure 14.3 Energy of a boundary of the type shown in Figure 14.2, between t...Figure 14.4 Epitaxy of Ag deposited on (001) of NaCl: (a) observed orientati...Figure 14.5 Superposition of nets representing atoms in unrelaxed (110) b.c....Figure 14.6 A strained epitaxial layer in the (001) orientation. The in‐plan...Figure 14.7 The relaxed region with lateral dimension mh around a misfit dis...
15 Chapter 15Figure 15.1 The {111} pole figure of electrolytic copper rolled to 96.6% red...Figure 15.2 (a) Standard stereographic projection in the (110) orientation s...Figure 15.3 Spatial representation of the half‐maximum density of the ODF re...Figure 15.4 Definition of the orientation of a crystallite in rolled sheet b...
16 1Figure A1.1 The addition of two vectors, a and b, to produce a third resulta...Figure A1.2 The components a_x, a_y and a_z of a vector a referred to three axe...Figure A1.3 The vector product a × b = (|a||b| sin θ) of two vectors Figure A1.4 The definition of the reciprocal lattice vector a*: the directio...Figure A1.5 The plane (hkl) in the real crystal making intercepts of a/h, b/Figure A1.6 An anticlockwise rotation of θ about n carrying the point x
17 2Figure A2.1 (a) Sphere of projection. (b) The angle between two planes is eq...Figure A2.2 Projections of poles on the surface of a sphere onto a flat piec...Figure A2.3 (a) Stereographic projection. (b) A small circle projects as a c...Figure A2.4 (a) Poles of a cubic crystal. (b) Stereogram of a cubic crystal...Figure A2.5 Construction of a small circle about the centre of the primitive...Figure A2.6 Rotation of the sphere of projection in Figure A2.5 by 90° about...Figure A2.7 Construction of a small circle about a pole within the primitive...Figure A2.8 Construction of a small circle about a pole on the primitiveFigure A2.9 To find the opposite of a given poleFigure A2.10 An alternative view of the construction in Figure A2.9 to show ...Figure A2.11 To find the pole of a great circleFigure A2.12 To find the angle between two polesFigure A2.13 (a) Projection of lines of latitude and longitude to make the W...Figure A2.14 (a) Stereographic projection of two poles and . (b) Rotation...Figure A2.15 To find the trace of a pole using the Wulff net.Figure A2.16 Rotation of poles about an axis B lying on the primitive.Figure A2.17 Rotation of poles about an inclined axis.Figure A2.18 Two‐surface analysisFigure A2.19 The fundamental projectional geometry of the stereographic proj...Figure A2.20 Geometry to show that any sphere inverts into a sphereFigure A2.21 Geometry to show that a stereographic projection is angle true...
18 4Figure A4.1 Relationship between the conventional hexagonal unit cell with c...Figure A4.2 Unit cells in the rhombohedral lattice. (a) Obverse setting of r...
19 6Figure A6.1 Illustration of the relationship between a pure shear and a simp...

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