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Lecture_2 - NE 125: Lecture 2 NE Interatomic Bonding...

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Unformatted text preview: NE 125: Lecture 2 NE Interatomic Bonding Instructor: William K. O’Keefe, P.Eng. wkokeefe@engmail.uwaterloo.ca “Office Hours”: Mondays 1:30 to 2:20 RCH 106 Week 1 Teaching Assistant (TA): Hua (Leanne) Wei h6wei@engmail.uwaterloo.ca Reading: Shackelford 6th Ed, Chapters 1 & 2 Assignment 1 (handout) problem set due: 14 January 2007 Suggested (extra) problems: Shackelford 6th Ed ( 2-2, 2-5, 2-10, 2-11) NE 125: NE Introduction to Materials Science and Engineering Introduction Review (From Monday) Review • Performance depends on material properties • Macroscopic material properties are governed by the microstructure • The microstructure is determined by crystal structure and processing history • Crystal structure is determined by atomic bonding • Classification of solids by atomic bonding and elemental constituents Metals, ceramics, semiconductors, polymers, composites • Classification of materials by inherent molecular disorder crystalline, amorphous, semicrystalline, liquid crystal, fractal Band Theory: • explains thermal and electrical conductivity in solids • explains light transmission in insulators • intrinsic semiconductors (silicon and germanium) • n and p type extrinsic semiconductors NE 125: NE Introduction to Materials Science and Engineering Introduction Primary Interatomic Bonding Primary Recall Lewis’ octet rule: (except H, Li and Be) An atom will combine with one or more atoms to (except try to achieve a complete octet (i.e. a closed shell or kernel) kernel Lowers the total energy of the system Lowers Atoms with incompletely filled octets can achieve a closed shell Atoms configuration like the noble gases by either sharing electrons with other atoms or transferring electrons completely to other atoms. Ionic bonding and covalent bonding represent these two extremes. Ionic NE 125: NE Introduction to Materials Science and Engineering Introduction Primary Interatomic Bonding Primary Covalent Bonding (Friday’s Lecture; Text section 2.3 ) Covalent - Electrons are shared between atoms by overlap of orbitals → form hybrid sp, sp2 and sp3 molecular orbitals form - Covalent bonding is directional; distinct bond angles; coordination numbers coordination low Ionic Bonding (Textbook section 2,2) - Complete electron transfer between atoms occurs due to significant difference in electronegativities difference - Bonding is due to electrostatic forces (Coulomb’s law) Bonding Metallic Bonding (Monday’s Lecture, textbook section 2.4) -Valence electrons are free to move through lattice as “sea of electrons” Valence or “electron clouds” or - stationary ion cores stationary NE 125: Introduction to Materials Science and Engineering Introduction Ionic Character and Covalent Character Ionic Generally interatomic bonds are not purely ionic or purely covalent in character The greater the difference in electronegativity between atoms, the greater the ionic character The more similar the electronegativities, the greater the covalent character The percentage ionic character can be calculated from the following equation from the electronegativites XA and XB equation % = 100% 1 − exp ( − 0.25) ( X A− X B) 2 [ { }] Bonds with less than 20% ionic character are classified as covalent Bonds Sometimes bonding of intermediate ionic character less than 50% are referred to as covalent with partial ionic character or polar covalent covalent Similarly, intermediate bonding with > 50% ionic character are sometimes referred to as Similarly, ionic with partial covalent character NE 125: NE Introduction to Materials Science and Engineering Introduction 1 Interatomic Bonding in Engineering Materials Interatomic Many ceramics have partial ionic character Many liquids and gases have covalent character (Eg. CH4, H2O, N2) Secondary bonding occurs between molecules (Friday’s Lecture; Textbook Sec. 2.5) - Van der Waals bonding; hydrogen bonding [1] Illustration from Shackelford, J.F. “Introduction to Materials Science and Engineering”, 6th Edition,; used by permission NE 125: NE Introduction to Materials Science and Engineering Introduction Ionic Bonding Ionic ClNa+ ClNa+ ClCl- Cl- Cl- Ionic bonding is Non-directional The electric field E created by a particle at rest with The charge q is a conservative force field Charged particles with the same net charge and with the same magnitude of displacement away from the point charge experience the same force of attraction regardless of direction The potential energy about the surface of an imaginary sphere a distance r from the point charge due to its electric field is the same at all points on the surface (i.e. an equipotential surface) the EA = q/ε 0 [1] Illustration from Shackelford, J.F. “Introduction to Materials Science and Engineering”, 6th Edition,; used by permission Electron transfer in NaCl1 Na: 1s2 2s2 2p6 3s1 Na+: 1s2 2s2 2p6 (neon) Cl: Cl-: 1s2 2s2 2p6 3s2 3p5 1s2 2s2 2p6 3s2 3p6 (argon) NE 125: NE Introduction to Materials Science and Engineering Introduction Ionic Bonding: Forces (F) and Potential Energy (E) Ionic F attraction r0 FN 0 E r0 E0 (Bonding Energy) r r EN repulsion FN = Σ F = FA + F R At the equilibrium bond length (r0) E N = EA + ER ∑F = 0 dE N =0 dr NE 125: NE Introduction to Materials Science and Engineering Introduction Ionic Bonding: Forces (F) and Potential Energy (E) Ionic kq1 q 2 F A= F c= − 2 r F R = λe −r (Coulomb’s Law) ρ empirical models of ionic repulsion, parameters λ , ρ , kR are determined experimentally kR F R= − n r E = ∫ Fdr E N = EA + ER NE 125: NE Introduction to Materials Science and Engineering Introduction Ionic Bonding: Forces (F) and Potential Energy (E) Ionic Electrostatic forces are very strong. The ionic bond is a long range interaction that extends beyond the nearest neighbour interaction To determine precise bond lengths and bonding energy, need to consider the contributions of all electrostatic forces By the Principle of Superposition, the net force acting on a reference ion is the vector sum of all forces E ij = kq i q j a ij r EN= ∑ i≠ j kq i q j k ( Z ) 2 (e) 2 A M =− a ij r r 1 a ij (Madelung constant, AM) A is characteristic of crystal structure Closely related to lattice energy Coulombic Potential energy between two interacting charged particles AM = ∑ i≠ j Sample Problems Shackelford 6th Ed 2-16, 2-27, 2-28 ...
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This note was uploaded on 10/08/2010 for the course NE 125 taught by Professor Simon during the Spring '10 term at Waterloo.

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