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ME 330 Engineering Materials Lecture 4 Atomic Structure and Interatomic Bonding Chemistry review Interatomic bonding in solids Crystalline vs. Amorphous Crystals and crystallographic planes Read Chapters 2 and 3 Why Atomic Structure? • Atomic level structure can strongly influence material performance – Modulus, melting point, coefficient of expansion all depend on interatomic forces • Will now demonstrate how to understand properties based on bonding potentials • Different bond types have different potentials • Constructionist approach – Look at most basic level to begin our understanding – Today we’ll look (in detail) at: • How atoms pack together • How atoms bond together • See how these effect macroscopic properties ATOMIC STRUCTURE AND BONDING Why study it? Carbon (Diamond & Graphite) Many properties of materials depend on (i) bonds between atoms (ii) atomic packing (arrangement) ATOM NUCLEUS = PROTONS + NEUTRONS + ELECTRONS ( = no. of protons for neutrality) Protons: + charge, neutrons: neutral charge, electrons: negative charge Quantum mechanics – establishment of a set of principles and laws that govern systems of atomic and subatomic entities. Models of atomic behavior: Bohr atomic model – electrons revolve around atomic nucleus in discrete orbitals. Wave-mechanical model – electron exhibits both wave-like and particle-like behavior. Position of electron is defined by probability of electron’s being at various locations around nucleus. Nucleus 10-14m. diameter surrounded by electron cloud. Atomic diameter 10-10 m ~ 99.98% of mass is in nucleus & most of volume is electron cloud. Bohr atomic model – electrons are assumed to revolve around nucleus in discrete orbitals Electrons in ORBITALS or shells, characterized by four QUANTUM numbers – Size (K,L,M…) (shells; specified by a principal quantum number n=1,2,3,…) - Shape (s,p,d,f) (subshells – different shapes of electron orbits in a shell; second quantum numbers) - Spatial orientation (ml) (number of energy states for each subshell; third quantum number) - Spin (ms) (spin moment, oriented either up or down; fourth quantum number) See Table 2.1 Outermost shell contains VALENCE electrons (bonding, chemical, electrical and thermal properties). These are of most importance to us. If outer shell is complete, i.e. the S & P orbitals are full (S2P6 = 8 electrons) then element is very stable and very un-reactive - Noble gases (helium, neon, argon, krypton). Some other elements gain or lose electrons to try and attain this stable configuration through bonding. Note: s, p, d, f subshells can accommodate the total of 2, 6, 10, and 14 electrons, respectively SURVEY OF ELEMENTS • Most elements: Electron configuration not stable. Electron configuration 1s1 1s2 (stable) 1s22s1 1s22s2 1s22s22p1 1s22s22p2 ... 1s22s22p6 (stable) 1s22s22p63s1 1s22s22p63s2 1s22s22p63s23p1 ... 1s22s22p63s23p6 (stable) ... 1s22s22p63s23p63d10 4s246 (stable) • Why? Valence (outer) shell usually not filled completely. PERIODIC TABLE Table of elements (types of atoms) Atomic Number - number of protons Hydrogen 1 proton Helium 2 “ etc. Atomic Mass - relative atomic mass - mass of 6.023 x 1023 atoms of that element (6.023 x 1023 of something is 1 mole) 1 mole of aluminium atoms (i.e. 6.023 x 1023 atoms) has a mass of 26.98 g etc. THE PERIODIC TABLE • Columns: Similar Valence Structure Adapted from Fig. 2.6, Callister 6e. Electropositive elements: Readily give up electrons to become +ve ions. Electronegative elements: Readily acquire electrons to become -ve ions. Most elements in Periodic Table are METALS. e.g. Mg, Zn, Fe, Ti, Pd. Few gases and non-metals and some in between. CERAMICS are usually compounds based on mixtures of elements Cr2O3 , Al2O3, Si3N4, SiC. POLYMERS are usually based on CARBON chains / networks. Sizes of atoms can be important, i.e. Diffusion in Solids. ELECTROPOSITIVE metallic elements give up outer electrons to form positive ions CATIONS Mg Mg2+ + 2e- ELECTRONEGATIVITY • Ranges from 0.7 to 4.0, • Large values: tendency to acquire electrons. Smaller electronegativity Larger electronegativity ATOMIC BONDING ATOMS bond to each other to reduce their overall energy, i.e. to become more stable. Everything tends towards a state of lower free energy. Bonding Forces and Energies Inter-atomic spacing is caused by balance between REPULSIVE and ATTRACTIVE forces. Attractive force depends on type of bond trying to form between atoms; Repulsive force occurs when atoms get close together. Net force between atoms is balance of two forces and depends on inter-atomic distance. FN = FA + FR FN = 0 when FA = FR FN : net force FN = FA + FR Equilibrium is reached when: FA + FR = 0 Atoms happily sit this distance apart (r0) (often ro 0.3nm) Also considered in energy terms: EN = EA + ER In this case, equilibrium is reached when overall energy is a minimum. Bonding energy, E0 (binding energy) is the energy required to break the bond (separate two atoms). Higher bonding energy Stronger bonds higher strength & Melting point, (Tm) Also Stiffness (slope (dF/dr) at r0 and thermal expansion (trough of E curve) PRIMARY ATOMIC BONDS (Chemical) - STRONG IONIC COVALENT METALLIC SECONDARY BONDS (Physical) - WEAK Van Der Waals bonds/forces Fluctuating + permanent dipoles IONIC BONDS Form between electropositive (metallic) and electronegative (non-metallic) elements, eg. CERAMICS NaCl, Al2O3,MgO • Na looses outer electron to be more stable Na+. • Chlorine accepts extra electron to be more stable Cl(Note: there is a size change when atoms form ions.) After such a transfer, the chlorine atom has net negative charge, while sodium atom has net positive charge. In sodium chloride (NaCl), all sodium and chloride atoms exist as ions. IONIC BONDS (cont) Form between electropositive (metallic) and electronegative (non-metallic) elements, • Na loses outer electron to be more stable Na+. • Chlorine accepts extra electron to be more stable Cl- Opposite charges attract so get: ELECTROSTATIC (coulombic) BONDING A B EA and ER n r r EA = Attractive energy, ER = Repulsive energy, A, B and n are constants that depend on system (n 8). THE PERIODIC TABLE • Columns: Similar Valence Structure Adapted from Fig. 2.6, Callister 6e. Electropositive elements: Readily give up electrons to become +ve ions. Electronegative elements: Readily acquire electrons to become -ve ions. Example: NaCl Ionic Bonding Metal Nonmetal Na Cl Atomic Structure Cl- Na+ Ions Ionic Bond NaCl Notes on Ionic Bonding Repulsion Curve • • A 1 r – Repulsive force: R • • • ER To be stable, all positive ions must be near negative ions Bond strength is equal in all 0 directions (nondirectional) Energy considerations – Coulombic attractive force 1 (n 8) n r Generally, very high bonding energies Typically hard, brittle, thermally and electrically insulative Ceramics Energy (r) • r8 Separate Ions Atoms Electrostatic Attraction EA “Stable” r r8 r r Cl- Na+ Cl- Na+ Cl- Na+ Cl- Na+ Cl- EXAMPLES: IONIC BONDING • Predominant bonding in Ceramics H 2.1 Li 1.0 Be 1.5 Na 0.9 Mg 1.2 K 0.8 Ca 1.0 Sr 1.0 Rb 0.8 Cs 0.7 Fr 0.7 NaCl MgO CaF2 CsCl Ti 1.5 Cr 1.6 Ba 0.9 Fe 1.8 Ni 1.8 O F 3.5 4.0 Cl 3.0 Zn 1.8 As 2.0 Br 2.8 I 2.5 At 2.2 Ra 0.9 Give up electrons Acquire electrons He Ne Ar - Kr Xe Rn - NON-DIRECTIONAL, electrical neutrality is most important. IONS pack to maintain neutrality. Eg. For NaCl For each Na+ ion there must also be a Cl- ion. Likewise, for MgCl2 there must be two Chlorine ions for every magnesium ion. Ionic bonds tend to be strong bonds - high bonding energy. (Table 2.3) Ceramics are usually ionically bonded and have high melting points, high hardness, brittle and electrically and thermally insulative (atoms and electrons cannot move easily). COVALENT BONDING Atoms SHARE outer electrons with each other to attain noble gas electron configurations. Atoms close to each other in periodic table and in electronegativities (X) tend to form covalent bonds Covalent bonds do not distort very easily - so can be very strong (Diamond) but appear in "weak" materials as well (polyethylene - covalently bonded carbon chain) Some materials show mixed Ionic/Covalent bonding. % ionicity 1 exp 0.25( X A X B ) 2 x100 XA, XB electronegativities for respective elements COVALENT BONDING • Requires shared electrons • Example: CH4 C: has 4 valence e, needs 4 more H: has 1 valence e, needs 1 more Electronegativities are comparable. Because atoms in covalent bonds have to share electrons with other atoms, Direction is very important. DIRECTIONAL BONDING e.g. DIAMOND Covalent Bonding Cl H H C H CH4 Cl2 H • Two atoms share electrons - extra electron belongs to both • Bonding is directional - between atoms being bonded • Many interatomic bonds are partially ionic and covalent – Wider separation in periodic table more ionic • Ceramics, Metals, Polymer backbones EXAMPLES: COVALENT BONDING H2 H 2.1 Li 1.0 Na 0.9 K 0.8 Be 1.5 Mg 1.2 Ca 1.0 Rb 0.8 Cs 0.7 Sr 1.0 Fr 0.7 Ra 0.9 • • • • Ba 0.9 column IVA H2O C(diamond) SiC Ti 1.5 Cr 1.6 Fe 1.8 Ni 1.8 Zn 1.8 Ga 1.6 C 2.5 Si 1.8 Ge 1.8 F2 He O 2.0 As 2.0 Sn 1.8 Pb 1.8 GaAs Molecules with nonmetals Molecules with metals and nonmetals Elemental solids (RHS of Periodic Table) Compound solids (about column IVA) F 4.0 Cl 3.0 Ne - Br 2.8 Ar Kr - I 2.5 Xe - At 2.2 Rn - Cl2 • Widely variable properties – Diamond Energy (r) Covalent Potential Repulsion Curve • Very soft • Weak • Tmelt = 270 ºC – Based on m & n rn 0 Atoms • Hardest substance known • Very stiff, strong • Tmelt = 3550 ºC – Bismuth ER Electron Overlap Attraction EA r m r n r m n rm METALLIC BONDING- Found in metals and alloys. Atoms of metal pack relatively closely together in ordered arrangement - Ion cores Valence electrons form "sea" in between cores "electron gas or cloud" These electrons can move/drift - thermal/electrical conduction. FREE electrons. • Arises from a sea of donated valence electrons (1, 2, or 3 from each atom). METALLIC BONDING Non-directional Not many restrictions on metallic bond (no charge neutrality - ionic, or electron-pair sharing covalent) so if metal deformed, atom positions can move relatively large amounts without breaking bonds. (Ductility) Bonding energies affect melting points and vary from low (-39 C) to high (3410C) values. • Primary bond for metals and their alloys Metallic Bonding e- M+ e M+ ee- e e M+ M+ M+ ee- eM+ M+ M+ e e- M+ • • • • • • • M+ M+ M+ M+ M+ M+ M+ M+ M+ Ion Cores (M+)- net positive charge equal to total valence Valence electrons (e-) drift through metal in “electron cloud” – Electrically shield ion cores – Physically hold cores together Nondirectional bond Metallic bonding potential similar to covalent (use same eqn.) Wide variety of bonding energies and hence properties Excellent conductors due to mobility of electron cloud Metals and metallic alloys SECONDARY BONDING - Van Der Waal's forces (in biological systems) Low energy - weak bonds 4 - 40 kJmol-1 (Primary 100 1500 kJmol-1) Based on DIPOLES When -ve and +ve charges are separated, an electric dipole moment is set up. FLUCTUATING INDUCED DIPOLE BONDS Asymmetrical distribution of electron cloud (vibrations etc) e.g. noble gases - boiling, melting. Van der Waals Bonding H H • • • • • O H O H H O r 6 r n (n 12) H Sometimes called physical bonds to contrast with chemical (primary) Much lower energy than primary bonds Arise from electric dipoles – Separation of + and - portions of atom - much weaker than ions – Bonding from attraction of + from one dipole to - of other dipole Hydrogen bonding is special case when hydrogen is present – Strongest secondary bonding type Polymeric interchain bonds POLAR MOLECULE-INDUCED DIPOLE BONDS Asymmetric charge distribution in some molecules (polar) Eg. HCl molecule. Can attract non-polar molecules. PERMANENT DIPOLE BONDS Van der Waals forces will also exist between adjacent polar molecules. H-F, H-O and H-N bonds Hydrogen end becomes very +ve. One of strongest secondary bonds. eg. H2O. (Hydrogen bonding - Reason for high boiling point of water.) Also between carbon chains in polymeric materials. • Fluctuating dipoles • Permanent dipoles-molecule induced -general case: -ex: liquid HCl -ex: polymer PROPERTIES FROM BONDING: TM • Bond length, r F • Melting Temperature, Tm F r • Bond energy, Eo Tm is larger if Eo is larger. PROPERTIES FROM BONDING: E • Elastic modulus, E Elastic modulus F L =E Ao Lo • E ~ curvature at ro Energy unstretched length ro r E is larger if Eo is larger. smaller Elastic Modulus larger Elastic Modulus PROPERTIES FROM BONDING: • Coefficient of thermal expansion, coeff. thermal expansion L = (T2-T1) Lo • ~ symmetry at ro is larger if Eo is smaller. SUMMARY: PRIMARY BONDS Ceramics (Ionic & covalent bonding): Metals (Metallic bonding): Polymers (Covalent & Secondary): Large bond energy large Tm large E small Variable bond energy moderate Tm moderate E moderate Directional Properties Secondary bonding dominates small T small E large Summary - Atomic Bonding in Solids • Primary – Ionic – Covalent – Metallic • Secondary – Van der Waals – Hydrogen Force F( r ) d dr ro Energy (r) r • Interatomic potential energies – Function of separation, r – Attractive - depends on bond – Repulsive - atomic scale overlap • Bonding energy (Eo) is strongly dependent on bond type – Effect on modulus ??? – Effect on thermal expansion ??? Eo Atomistic Origins of Properties dF E dr r r•o Modulus – Proportional to slope of force-separation curve at Atomic separation, r equilibrium separation distance Force F(r) • Melting Temperature – Large Eo leads to high Tmelt Energy (r) • Coefficient of thermal expansion E0 – Large Eo leads to small r – Deep narrow trough forces large energy change for small dimensional change Potentials & Properties Atomic Separation 0 0 2 4 6 8 -0.1 Ceramics ~~Potential -0.2 -0.3 Material E (GPa) Silicon Carbide 475 Alumina 375 Glass 70 Steel Brass 210 97 Aluminum 69 PVC 3.3 Epoxy 2.4 LDPE 0.23 10 Ionic n=2,m=8 n = 2, m = 6 Secondary Metals -0.4 -0.5 Polymers -0.6 Material (C-1x10-6) Silicon Carbide 4.1-4.6 Alumina 7.6 Glass 9.0 Steel Brass 12.0 20 Aluminum 23. PVC 90-180 Epoxy 81-117 LDPE 180-400 -0.7 Relative differences in potential curves Assumes & are 1 - comparitive purposes only! Ceramics Metals Polymers From Callister, p. 22 Atomic Packing • Crystalline: – 3-D arrangement of atoms in which every atom has the same geometrical arrangement of neighbors – Long-range, periodic array over large length scales – Most solids are crystalline (metals, most ceramics, some polymers) • Amorphous – – – – Arrangement over which no long range order exists Often clear - not enough order to diffract light Rarely purely amorphous - have regions of crystallinity Many polymers and some ceramics Crystal Structure Definitions • Unit cell: Smallest repeating unit of the crystal. • Lattice: 3–D framework of a crystal where atoms are located • Lattice parameters: Dimensions (a,b,c) and angles (,,) of the lattice c b a Bravais Lattices • • • • • • French Crystallographer Bravais (1848) 7 crystal systems using primitive unit cells Primitive - one lattice point at origin 14 distinguishable point lattices – P - simple – F - face centered – I - body centered – C - base centered For now, interested in BCC, FCC, HCP – Metallic crystal structures – Metallic bond is non-directional – No restriction on nearest neighbors – Very dense packing First need to collect some definitions Tetragonal FCC Monoclinic Rhombohedral BCC Cubic Hexagonal Orthorhomic HCP Triclinic Crystallographic Directions • Determining direction indices z – Start vector at crystal axis – Draw to any point in the 3-D crystal – Project vector on each xyz axes • • • measure a in x-direction measure b in y-direction measure c in z-direction [001] [111] a=1 b=½ c=0 – Multiply by common factor to achieve smallest integer value x – Enclose in [ ] without commas • • • y [010] [100] [210] [110] Negative directions indicated with Family of directions indicated by < > Hexagonal crystals have 4 indices [100], [ 1 00], [010], [0 1 0], [001], [00 1 ] In a cubic crystal, all in the <100> family. are Crystallographic Planes • Determining Miller indices – Look at plane in unit cell which does not pass through the origin – Determine length of planar intercept with each axes (again, a,b,c) – Take reciprocal of a,b,c – Reduce to smallest integer value – Enclose in ( ) without commas • Any parallel planes are equivalent z z y x -1 z [001] c = 1/3 b = 1/2 a=1 x y [010] [100] (123) z 1 Intercepts : , 1, 2 Re ciprocals: 0 , 1,2 Plane : 01 2 x (012)