Chemistry 1000 Lecture 10: Metals and crystal structures Marc R. - - PowerPoint PPT Presentation

Chemistry 1000 Lecture 10: Metals and crystal structures

Marc R. Roussel October 3, 2018

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Classification of the elements

Classification of the elements

Element Appearance Resistivity/Ω m Fluoride(s) Na silvery solid 4.2 × 10−8 ionic NaF Ca silvery solid 3.9 × 10−8 ionic CaF2 Ni silvery solid 6.8 × 10−8 ionic NiF2 Al silvery solid 2.7 × 10−8 molecular Al2F6 Hg silvery liquid 9.8 × 10−7 ionic Hg2F2 and HgF2 Ge grey solid 4.6 × 10−2 molecular GeF4 and GeF2 Sb silvery solid 3.9 × 10−7 molecular SbF3 and SbF5 B black solid 1.8 × 104 molecular BF3 P white solid 1.0 × 109 molecular PF3, PF5 and P2F4

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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

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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).

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Classification of the elements

Quasi-free-electron model of metals

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

"valence" electrons

Explains metal heat and electrical conductivity deformability (ductility, malleability)

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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.

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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.

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Metal crystal structures

Some lattices and unit cells in two dimensions

a b a) square

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Metal crystal structures

a b b) rectangular

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Metal crystal structures

a b b’ c) hexagonal a’ φ

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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

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Metal crystal structures

Possible crystal lattices (continued)

Almost all metals crystallize in a cubic or hexagonal lattice.

: simple cubic Bi Sm Eu Tm Er Ho Dy Tb Gd : body−centered cubic : face−centered cubic Ce Pr Nd Pm U Np Cm Bk Cf Am Lr : simple cubic : simple cubic : simple cubic Mg Be Fr K Rb Cs Cr Mn Tc Bh Re Hs Ti Li Ds Y Sc Ga Cd Zn Nh Nh Nh Hg La Db Nh : hexagonal close packed : double HCP : rhombohedral : orthorhombic : tetragonal : monoclinic Na Ra Ba V Nb Ta Mo W Sg Fe Ru Os Co Rg Cn Zr Rf Hf Tl Fl Ag Sr Fm Pb Ac Sn Th Po Rh Ir Mt Al Au Yb Pa No In Ni Pd Pt Md Pu Es Ca Cu

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Metal crystal structures

Cubic structures

simple cubic body-centered cubic face-centered cubic

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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

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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.

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Structure statistics

Closest packing (continued)

hcp and fcc structures are closely related. hcp structure described as ABAB. . . fcc structure described as ABCABC. . .

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X-ray diffraction

X-ray diffraction

X−ray beam sample scattered X−rays detector From this experiment, we get crystal structure (bcc, hcp, etc.) positions of atoms within unit cell dimensions of unit cell

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