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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.

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## 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, 5th Edition, Chapter 3 Crystallography**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**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.**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 )**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.**Crystallographic directions**A crystallographic direction is defined as a line between two points, or a vector. Steps: • A vector of convenient length is positioned such that it passes through the origin of the coordinate system • The length of the vector projection on each of the 3 axes is determined; a, b & c • Reduce them to the smallest integer values; u, v & w • The 3 indices are enclosed in square brackets, thus: [uvw]. The [100], [110], and [111] directions with in a unit cell.**Crystallographic planes**Crystallographic 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 ).**Steps in determining (hkl)**• Define origin of axis • 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 • Reciprocal of these numbers are taken • These numbers are changed to set of smallest integers 5. Enclose integer indices within parentheses (hkl)**Fig: Representations of a series each of (110) and (111)**crystallographic planes.**Atomic arrangements**Atomic arrangement depends on crystal structure 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 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**Closed-packed crystal structures**ABC, ABA, ACB, ACA**Figure: Close-packed plane staking sequence for hexagonal**close-packed. Figure: Close-packed plane staking sequence for FCC.**Noncrystalline solids**Fig: Two-dimensional schemes of the structure of (a) crystalline silicon dioxide and (b) noncrystalline silicon dioxide.

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