Chapter 3: Crystal & Amorphous structure in materials Part 1 DMT125 Materials Science Chapter 3: Crystal & Amorphous structure in materials Part 1 26 November 2013 Copyright © MAMA

Contents Space lattice & unit cells Crystal systems & bravais lattices Principal metallic crystal structures BCC FCC HCP Atom positions & directions in cubic unit cells Miller indices Comparisons of FCC, HCP & BCC crystal structures Volume, planar & linear density unit cell calculations Amorphous materials 26 November 2013 Copyright © MAMA

Space lattice & unit cells Solids maybe categorized into: Crystalline solids Amorphous solids Crystalline solids due to orderly structure of their atoms, molecules or ions, possess well-defined shapes Metals are crystalline, composed of well-defined crystals or grains Amorphous solids have poor or no long-range order & do not solidify with symmetry & regularity of crystalline solids 26 November 2013 Copyright © MAMA

Space lattice & unit cells Crystalline solid Long range order (LRO) - Atoms or ions of a solid are arranged in a pattern that repeats itself in 3D, they form a solid Example Metals Alloys Some ceramics Short range order (SRO) – Atoms & ions are not arranged in a long-range, periodic & repeatable manner 1 oxygen atom is covalently bonded to 2 hydrogen atoms Amorphous – materials with only short-range order 26 November 2013 Copyright © MAMA

Space lattice & unit cells Atomic arrangements in crystalline solids can be described by referring the atoms to the points of intersection of a network of lines in 3D 26 November 2013 Copyright © MAMA

Space lattice & unit cells In an ideal crystal, the grouping of lattice points about any given point are identical with the grouping about any other lattice point in the crystal lattice Unit cell - Each space lattice can thus be described by specifying the atom positions in a repeating pattern Motif – a group of atoms organized in a certain arrangement relative to each other & associated with lattice points Lattice constants axial length a, b & c Interaxial angles alpha, beta & gamma 26 November 2013 Copyright © MAMA

Crystal systems & bravais lattices There are 4 basic types of unit cells: Simple Body centered Face-centered Base-centered In cubic system, there 3 types of unit cells Simple cubic Body-centered cubic Face-centered cubic 26 November 2013 Copyright © MAMA

Principal metallic crystal structures Most elemental metals (~90%) crystallize upon solidification into 3 densely packed crystal structures Body-centered cubic (BCC) Face-centered cubic (FCC) Hexagonal close-packed (HCP) Most metals crystallize in these dense-packed structures because energy is released as atoms come closer together & bond more tightly with each other Thus resulting in lower & more stable energy arrangements 26 November 2013 Copyright © MAMA

Principal metallic crystal structures 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: BCC Each cells has equivalent of 2 atoms/ unit cell Relationship between length of the cube side a & atomic radius R 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: BCC Atomic packing factor (APF) Many metals such as iron. Chromium, tungsten, molybdenum & vanadium have BCC crystal at room temperature 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: BCC Example 1 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: FCC Atoms in FCC crystal structure are packed as close together as possible APF = 0.74 Each cells has equivalent of 4 atoms/ unit cell Relationship between length of the cube side a & atomic radius R Many metals such as aluminium, copper, lead, nickel & iron at elevated temperatures crystallize with FCC crystal structure 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: FCC 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: HCP APF = 0.74 Atoms structures packed as tightly as possible Each cells has equivalent of 6 atoms/ unit cell Ratio c/a Ration of the height c of the hexagonal prism of HCP crystal structure to its basal side a Metals like cadmium & zinc have ratio higher than ideality Atoms in the structures are slightly elongated along the c axis Metals like magnesium, cobalt, zirconium, titanium & beryllium have ratio less than ideality Atoms in the structures are slightly compressed in the direction along c axis 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: HCP 26 November 2013 Copyright © MAMA

Atom positions & directions in cubic unit cells 26 November 2013 Copyright © MAMA

Atom positions & directions in cubic unit cells Crystallographically equivalent Atom spacing along each direction is the same 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: HCP APF = 0.74 Atoms structures packed as tightly as possible Each cells has equivalent of 6 atoms/ unit cell Ratio c/a Ration of the height c of the hexagonal prism of HCP crystal structure to its basal side a Metals like cadmium & zinc have ratio higher than ideality Atoms in the structures are slightly elongated along the c axis Metals like magnesium, cobalt, zirconium, titanium & beryllium have ratio less than ideality Atoms in the structures are slightly compressed in the direction along c axis 26 November 2013 Copyright © MAMA

Principal metallic crystal structures: HCP Example 2 Draw the following direction vectors in cubic unit cells: a) [100] & [110] b) [112] c) d) 26 November 2013 Copyright © MAMA

26 November 2013 Copyright © MAMA

Miller indices Reciprocals of the fractional intercepts (with fractions cleared) that the plane makes with the crystallographic x, y & z axes of the 3 nonparallel edges of the cubic unit cell Procedure 1) choose a plane that does not pass through the origin at (0,0,0) 2) determine the intercepts of the plane in terms of the crystallographic x, y & z axes for a unit cube. These intercepts maybe fractions 3) form the reciprocals of these intercepts 4) clear fractions & determine the smallest set of whole numbers that are in the same ration as the intercepts 26 November 2013 Copyright © MAMA

Miller indices 26 November 2013 Copyright © MAMA

Miller indices: Example 3 26 November 2013 Copyright © MAMA

Miller indices Interplanar spacing Dhkl, where h, k & l are the Miller indices of the planes 26 November 2013 Copyright © MAMA

Miller indices Example 4 Copper has an FCC crystal structure & a unit cell with a lattice constant of 0.361 nm. What is its interplanar spacing d220? 26 November 2013 Copyright © MAMA

Miller indices Solution = 0.128 nm 26 November 2013 Copyright © MAMA

End of Part 1 Copyright © Mr.Mohd. Azarulsani b. Md. Azidin 26 November 2013 Copyright © MAMA