Crystallographic Directions And Planes
Crystallographic directions and planes OutlineCrystallographic directionsCrystallographic planesLinear and planar atomic densitiesClose-packed crystal structuresChapter 3 -
Point CoordinateszPoint coordinates for unit cellcenter are111ca/2, b/2, c/2000aybPoint coordinates for unit cellcorner are 111xz2cb½½½yTranslation: integer multiple oflattice constants identicalposition in another unit cellbChapter 3 - 2
Crystallographic DirectionsAlgorithmzy1. Vector repositioned (if necessary) to passthrough origin.2. Read off projections in terms ofunit cell dimensions a, b, and c3. Adjust to smallest integer values4. Enclose in square brackets, no commas[uvw]xex: 1, 0, ½ 2, 0, 1 [ 201 ]-1, 1, 1 [ 111 ]where overbar represents anegative indexfamilies of directions uvw Chapter 3 - 3
ExamplesSketch the following directions : [110], [-1-21], [-1 0 2]Chapter 3 -
HCP Crystallographic DirectionszAlgorithma2-a3a11. Vector repositioned (if necessary) to passthrough origin.2. Read off projections in terms of unitcell dimensions a1, a2, a3, or c3. Adjust to smallest integer values4. Enclose in square brackets, no commas[uvtw]a2ex:½, ½, -1, 0-a3a22Adapted from Fig. 3.8(a), Callister 7e. [ 1120 ]a3dashed red lines indicateprojections onto a1 and a2 axesa12a1Chapter 3 - 5
HCP Crystallographic Directions Hexagonal Crystals– 4 parameter Miller-Bravais lattice coordinates arerelated to the direction indices (i.e., u'v'w') asfollows.z[ u 'v 'w ' ] [ uvtw ]1(2 u ' - v ')31 v(2 v ' - u ')3t - (u v )u a2-a3a1Fig. 3.8(a), Callister 7e.w w'Chapter 3 - 6
Crystallographic Planes Miller Indices: Reciprocals of the (three) axialintercepts for a plane, cleared of fractions &common multiples. All parallel planes havesame Miller indices. Algorithm1. Read off intercepts of plane with axes interms of a, b, c2. Take reciprocals of intercepts3. Reduce to smallest integer values4. Enclose in parentheses, nocommas i.e., (hkl)Chapter 3 - 7
Crystallographic PlaneszcbaxyzcabyxChapter 3 - 8
Crystallographic PlaneszcabyxChapter 3 - 9
Crystallographic planes (continued) Construct planes by Miller indices of planes (0 -1 -1) and (1 1 -2)Chapter 3 -
Atomic arrangements The atomic arrangement for a crystallographic plane dependson the crystal structureFCC: (a) reduced sphere(b) atomic packing ofan FCC (110) planeBCC: (a) reduced sphere(b) atomic packing ofan BCC (110) planeChapter 3 -
Atomic arrangements A family of planes contains all the planes that arecrystallographically equivalent. In cubic system, planes with same indices, irrespectiveof order and sign, are equivalent– (111), (111), (111) belong to {111} family– (100), (100), (010), and (001) belong to {100} family– (123), (123), (312) in cubic crystals belong to {123} family In tetragonal, (001) (001) are not as same family as (100),(100)Chapter 3 -
Linear and planar atomic density Linear Density of Atoms LD Number of atomsUnit length of direction vectorAtomic planar density: number of atoms centered on aplane/area of plane#atomsPlanar Density Area(2D repeat unit)Chapter 3 -
Planar Density of (100) IronSolution: At T 912 C iron has the BCC structure.2D repeat unit(100)Adapted from Fig. 3.2(c), Callister 7e.Chapter 3 - 14
Close-packed crystal structuresClose-packed plane stackingsequence for HCPClose-packed plane stackingsequence for HCPChapter 3 -
Chapter 3 - Atomic arrangements A family of planes contains all the planes that are crystallographically equivalent. In cubic system, planes with same indices, irrespective of order and sign, are equivalent – (111), (111), (111) belong to {111} family – (100), (100), (010), and (001) belong to {100} family – (123), (123), (312)
2 Crystallographic directions (continue) denote the direction by [uvw] family direction u v w , defined by transformation material properties along any direction in a family are the same, e.g. [100],[010],[001] in simple cubic are same. for uniform crystal materials, all parallel directions have the same properties negative index: a bar over the index
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Figure 5 Default datum planes Figure 6 Datum planes as solid plates Select the Datum Plane button now. Since we currently have no features in the model, Wildfire rightly assumes that we want to create the three standard datum planes. The datum planes represent three orthogonal planes to be used as references for features that will be created later.
Introducir el concepto de la Competencia Universitaria de Planes de Negocios . Introducción a la mentalidad empresarial y generación de Planes de Negocios. Período de Preguntas y Respuestas. Presentación de la Competencia Nacional de Planes de Negocios 2011 y su vinculación con esta Competencia Universitaria.
Oct 20, 2016 · Two planes that do not intersect are parallel. 30. Two lines that lie in parallel planes are parallel. 31. Two lines in intersecting planes are skew. 32. A line and a plane that do not intersect are skew. 33. a. Connect Mathematical Ideas (1)(F) Suppose two parallel planes A and B are each intersected by a third plane C. Make a conjecture about .
is perpendicular to any two lines n and p in X, then m is perpendicular to X. In 6 9, draw a picture of the situation. 6. two intersecting planes that are not perpendicular 7. two perpendicular planes 8. two skew lines 9. two parallel planes 10. In this picture of a needle intersecting a plane, which angle seems to be the angle
March 10, 2014 The task of determining the net force acting upon an . in your Hilroy scribbler. P12 Inclined Planes.notebook 20 March 10, 2014. P12 Inclined Planes.notebook 21 March 10, 2014 Friction and Inclined Planes The force of friction must e
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