Chemistry 1000 Lecture 10: Metals and crystal structures Marc R. Roussel October 3, 2018 Marc R. Roussel Metals and crystal structures October 3, 2018 1 / 17
Classification of the elements Classification of the elements Element Appearance Resistivity / Ω m Fluoride(s) 4 . 2 × 10 − 8 Na silvery solid ionic NaF 3 . 9 × 10 − 8 Ca silvery solid ionic CaF 2 6 . 8 × 10 − 8 Ni silvery solid ionic NiF 2 2 . 7 × 10 − 8 Al silvery solid molecular Al 2 F 6 9 . 8 × 10 − 7 Hg silvery liquid ionic Hg 2 F 2 and HgF 2 4 . 6 × 10 − 2 Ge grey solid molecular GeF 4 and GeF 2 3 . 9 × 10 − 7 Sb silvery solid molecular SbF 3 and SbF 5 1 . 8 × 10 4 B black solid molecular BF 3 1 . 0 × 10 9 P white solid molecular PF 3 , PF 5 and P 2 F 4 Marc R. Roussel Metals and crystal structures October 3, 2018 2 / 17
Classification of the elements Metal: malleable, ductile, good conductor of heat and electricity, shiny, resistivity increases with increasing T Nonmetal: brittle when solid, poor conductor of heat and electricity (insulator) Metalloid: intermediate between metal and nonmetal, often semiconducting Semiconductor: electrical conductivity is between that of a conductor and insulator, resistivity decreases with increasing T Marc R. Roussel Metals and crystal structures October 3, 2018 3 / 17
Classification of the elements Q& A about bonding in metals Question: Why do metals conduct electricity? Answer: They must have free electrons. Question: On an atomic level, what distinguishes metals from nonmetals? Answer: Metals give up their electrons relatively easily (low ionization energies). Marc R. Roussel Metals and crystal structures October 3, 2018 4 / 17
Classification of the elements Quasi-free-electron model of metals "valence" electrons + + + + + + + Explains metal + + + + heat and electrical conductivity + + + + deformability (ductility, + + + malleability) + + + + + + + + + + + + Marc R. Roussel Metals and crystal structures October 3, 2018 5 / 17
Metal crystal structures Crystal structure of metals Metals typically are (poly)crystalline. Crystal lattice: repeating arrangement of points in space Polycrystal: a material composed of many microscopic crystals (grains) stuck together in different orientations Grain boundary: surface where two grains meet Single crystal: a material composed of a single, (nearly) perfectly ordered crystalline material without grain boundaries Even in a polycrystal, relatively few atoms are at the grain boundary so most are surrounded by a well-organized crystal environment. Marc R. Roussel Metals and crystal structures October 3, 2018 6 / 17
Metal crystal structures Unit cells The lattice can be generated by sliding a unit cell along lattice vectors. No rotation or reflection of unit cells is allowed, only sliding. The smallest unit cell is the primitive unit cell. Marc R. Roussel Metals and crystal structures October 3, 2018 7 / 17
Metal crystal structures Some lattices and unit cells in two dimensions a) square b a Marc R. Roussel Metals and crystal structures October 3, 2018 8 / 17
Metal crystal structures b) rectangular b a Marc R. Roussel Metals and crystal structures October 3, 2018 9 / 17
Metal crystal structures c) hexagonal φ b a b’ a’ Marc R. Roussel Metals and crystal structures October 3, 2018 10 / 17
Metal crystal structures Possible crystal lattices In three dimensions, there are exactly 14 distinct crystal lattices known as Bravais lattices. https: //en.wikipedia.org/wiki/Bravais_lattice#In_3_dimensions Marc R. Roussel Metals and crystal structures October 3, 2018 11 / 17
Metal crystal structures Possible crystal lattices (continued) Almost all metals crystallize in a cubic or hexagonal lattice. Li Be Na Mg Al K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Nh Nh Fl Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Nh Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr : body−centered cubic : face−centered cubic : simple cubic : simple cubic : simple cubic : simple cubic : hexagonal close packed : double HCP : rhombohedral : orthorhombic : tetragonal : monoclinic Marc R. Roussel Metals and crystal structures October 3, 2018 12 / 17
Metal crystal structures Cubic structures simple cubic body-centered cubic face-centered cubic Marc R. Roussel Metals and crystal structures October 3, 2018 13 / 17
Structure statistics Counting atoms in a rectangular unit cell A corner atom is shared between 8 unit cells ∴ 1 8 of an atom is inside any given cell. A facial atom is shared between 2 unit cells ∴ 1 2 of an atom is inside any given cell. Simple cubic: 8 × 1 8 = 1 atom per unit cell bcc: 8 × 1 8 + 1 = 2 atoms per unit cell fcc: 8 × 1 8 + 6 × 1 2 = 4 atoms per unit cell Marc R. Roussel Metals and crystal structures October 3, 2018 14 / 17
Structure statistics Closest packing Some structures are packed more efficiently (leave less empty space) than others. fcc is also known as cubic closest packed (ccp) because it has the minimum empty space. 74% of the space is occupied by atoms. An identical packing fraction is obtained for the hexagonal closest packed (hcp) structure. Marc R. Roussel Metals and crystal structures October 3, 2018 15 / 17
Structure statistics Closest packing (continued) hcp and fcc structures are closely related. hcp structure described as ABAB. . . fcc structure described as ABCABC. . . Marc R. Roussel Metals and crystal structures October 3, 2018 16 / 17
X-ray diffraction X-ray diffraction X−ray sample beam scattered detector X−rays From this experiment, we get crystal structure (bcc, hcp, etc.) positions of atoms within unit cell dimensions of unit cell Marc R. Roussel Metals and crystal structures October 3, 2018 17 / 17
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