w.d. callister, materials science and engineering an introduction, 5 th edition, chapter 3
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MM409: Advanced engineering materials. W.D. Callister, Materials science and engineering an introduction, 5 th Edition, Chapter 3. Crystallography. Crystal structure. - PowerPoint PPT PresentationTRANSCRIPT
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W.D. Callister, Materials science and engineering an introduction, 5th Edition, Chapter 3
MM409: Advanced engineering materials
Crystallography
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Crystal structure
• The solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another
• A crystalline materials is one in which the atoms are situated in a repeating or periodic array over large atomic distances
• In crystalline structures, atoms are thought of as being solid spheres having well-defined diameters
• This is termed the atomic hard sphere model in which spheres representing nearest-neighbor atoms touch one another
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An example of the hard sphere model
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Unit cells• The atomic order in crystalline solids indicates that small
groups of atoms form a repetitive pattern.
• Unit cells subdivide the structure into small repeated entities.
• A unit cell is chosen to represent the symmetry of the crystal structure.
• Unit cell is chosen to represent the symmetry of the crystal structure
• Thus, the unit cell is the basic structural unit or building block of the crystal structure.
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Metallic crystal structure
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BCC
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FCC
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Density computations
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Crystal systems
The unit cell geometry is completely defined in terms of six
parameters:
3 edge lengths, a, b and c
3 interaxial angles , and These are termed as ‘lattice parameters’
of the crystal structure.
Fig: A unit cell with x, y, and z coordinate axes, showing axial lengths (a, b, and c) and interaxial angles (, , and )
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Crystallographic directions and planes
When dealing with crystalline materials, it is often becomes necessary to specify some particular crystallographic plane of atoms or a crystallographic direction.
3 integers or indices are used to designate directions and planes.
The basis for determining index values is the unit cell. Coordinate system consists of three (x, y and z) axes.
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Crystallographic directionsA crystallographic direction is defined as a line
between two points, or a vector.Steps:1. A vector of convenient length is positioned
such that it passes through the origin of the coordinate system
2. The length of the vector projection on each of the 3 axes is determined; a, b & c
3. Reduce them to the smallest integer values; u, v & w
4. The 3 indices are enclosed in square brackets, thus: [uvw].
The [100], [110], and [111] directions with in a unit cell.
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Crystallographic planesCrystallographic planes are specified by three Miller indices as (hkl).Any two planes parallel to each other are equivalent and have identical indices.
A unit cell with x, y, and z coordinate axes, showing axial lengths (a, b, and c) and interaxial angles (, , and ).
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Steps in determining (hkl)1. Define origin of axis
2. At this point the crystallographic plane either intersects or parallels each of the 3 axes; the length of the planar intercepts for each axis is determined in terms of the lattice parameter a, b and c
3. Reciprocal of these numbers are taken
4. These numbers are changed to set of smallest integers
5. Enclose integer indices within parentheses (hkl)
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Fig: Representations of a series each of (110) and (111) crystallographic planes.
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Atomic arrangementsAtomic arrangement depends on crystal structure
Fig: (a) Reduced-sphere FCC unit cell with (110) plane. (b) Atomic packing of an FCC (110) plane. Corresponding atom positions from (a) are indicated
Fig: (a) reduced-sphere BCC unit cell with (110) plane. (b) Atomic packing of a BCC (110) plane. Corresponding atom positions from (a) are indicated
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Closed-packed crystal structures
ABC, ABA, ACB, ACA
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Figure: Close-packed plane staking sequence for hexagonal close-packed.
Figure: Close-packed plane staking sequence for FCC.
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Noncrystalline solids
Fig: Two-dimensional schemes of the structure of (a) crystalline silicon dioxide and (b) noncrystalline silicon dioxide.