Introduction to Materials Science and Engineering Chapter 2 Atomic Structure and Interatomic Bonding ISSUES TO ADDRESS... • What promotes bonding? • What types of bonds are there? • What properties are inferred from bonding?

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Atomic Structure: As I mentioned in the first lecture, the property of material is not the property of atoms composed of the material, but is critically depends on the types of atomic bonding which, in turn, is critically dependent on the valence electrons (outermost electrons in an atom). In order to deduce the types of bonding, we have to understand the electronic structure of atoms.

Transmission Electron Atomic Force Microscope Atom – visibility: GaN Transmission Electron microscope Au, (111) surface Atomic Force Microscope

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Early Atomic Model: 1858 : cathode ray identified by Pluker 1869 : negative charge of cathode ray identified by Hittorf 1874 : momentum of cathode ray detected by Crookes 1876 : cathode ray named by Goldstein 1890 : electron named by Stony 1897 : properties of cathode ray  electron by J. J. Thomson 1906 electron

Bohr’s model: To resolve the discontinuous emission spectra... Bohr, Niels (1885-1962) To resolve the discontinuous emission spectra... Assumptions : Quantum condition Frequency condition

Bohr Atom: Nucleus ; Z = # protons = 1 for hydrogen to 94 for plutonium N = # neutrons Atomic mass A ~ Z + N

Bohr Atom: electrons & protons are electrically charged: 1.60 x 10-19 C mass-proton = mass-neutron = 1.67 x 10-27 kg mass-electron = 9.11 x 10- 31 kg atomic number (Z) = # protons atomic mass = mass-protons + mass-neutrons # of protons: same for all atoms of an element # of neutrons is variable  “isotopes” (elements with 2 or more atomic masses) atomic weight = weighted average of the atom’s isotopes the atomic weight of an element may be specified as mass/mole of material 1 amu = 1/12 atomic mass of carbon 12 (12C) 1 mole = 6.023 x 1023 (Avogadro’s number) atoms or molecules 1 amu/atom (or molecule) = 1 g/mol

Wave- Particle Duality of Electron: What is an electron? – we experience merely the actions of electrons, e.g., television screen (particle-like) or in an electron microscope (wave-like), showing particle-like and wave-like behavior of electrons, respectively. Light Electron 1887 Hertz: photoelectric effect 1905 Einstein: PE effect interpretation 1897 J.J. Thompson Proposed particle-like nature of electron m0 ~ 1/2000 H e = 1.6 x 10-19 C 1910 E. Rutherford Proposed atomic structure Tiny solar system Electrons moving around positive charge center 1924 De Brogile Proposed the idea that wave-like duality of electrons lp=h (Matter Wave) 1926 Schrodinger develops a mathmatical form 1927 Davisson and Germer Discover electron diffraction 1928 G.P. Thompson The concept of energy quanta for light is proposed.

Derivation of Schrodinger Equation: Matter wave equation is expressed as a harmonic wave form: Energy(E) Momentum(p) Particle: mv Wave: Since, E= (time-dependent Schrodinger equation)

Derivation of Schrodinger Equation: At stationary state – time independent state We are asking what energy states are allowed. We can write, Then, (time-independent Schrodinger equation) Solution: Choose desired potential energy V(x, y, z) Get the general solution of y(x, y, z) Retain only mathematically well behaved terms single valued not=0 continuous and continuous derivatives finite 4. Apply boundary condition - En

Wave Equation to Hydrogen Atom: 참고자료 Wave Equation to Hydrogen Atom: ... From the solution of the wave function, three quantum numbers result ...  n, l, ml

Quantum Numbers: n principal quantum number 1, 2, 3, 4, --- (K, L, M, N, ---) Determines the effective volume of an electron orbital Distance of an electron from the nucleus, position of an electron l azimuthal quantum number 0, 1, 2, 3, 4, ---, (n-1) (s, p, d, f) Determines the angular momentum of the electron Shape of electron subshell, shape of electron distribution ml magnetic quantum number 0, ±1, ±2, ---, ±l Determines the orientation of the orbital ms spin quantum number ½, -½ Pauli exclusion principle No two interacting entities can have the same set of the quantum numbers ...  Each orbital will hold up to two electrons There can never be more than one electron in the same quantum state Only one electron can be in a particular quantum state at a given time Each electron state cannot hold more than two electrons with opposite spins

Meaning of Quantum Numbers: n determines the size: l determines the shape: ml=-1,0,1 ml=-2,-1,0,1,2 ml determines the orientation:

Additional Quantum Number: Electron spin : Therefore, complete description of an electron requires 4 quantum numbers Pauli exclusion principle: ... No two interacting entities can have the same set of the quantum numbers ...  Each orbital will hold up to two electrons

참고자료 The complete set of quantum numbers for each of the 11 electrons in sodium: © 2003 Brooks/Cole Publishing / Thomson Learning™

Electron Energy States: Electrons... have discrete energy states tend to occupy lowest available energy state.

Stable Electron Configurations: have complete s and p subshells tend to be unreactive.

Survey of Elements: Most elements: Electron configuration is not stable Why? Valence (outer) shell usually not filled completely

Electron Configurations: Valence electrons – those in unfilled shells Filled shells more stable Valence electrons are most available for bonding and tend to control the chemical properties example: C (atomic number = 6) 1s2 2s2 2p2 valence electrons

Electronic Configurations: ex: Fe - atomic # = 26 1s2 2s2 2p6 3s2 3p6 3d 6 4s2 valence electrons 1s 2s 2p K-shell n = 1 L-shell n = 2 3s 3p M-shell n = 3 3d 4s 4p 4d Energy N-shell n = 4 Adapted from Fig. 2.4, Callister 7e.

The Periodic Table: • Columns: Similar Valence Structure give up 1e inert gases accept 1e accept 2e O Se Te Po At I Br He Ne Ar Kr Xe Rn F Cl S Li Be H Na Mg Ba Cs Ra Fr Ca K Sc Sr Rb Y Electropositive elements: Readily give up electrons to become + ions. Electronegative elements: Readily acquire electrons to become - ions. Adapted from Fig. 2.6, Callister 7e.

Electronegativity: Smaller electronegativity Larger electronegativity • Ranges from 0.7 to 4.0, • Large values: tendency to acquire electrons. Smaller electronegativity Larger electronegativity Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

Bonding: primary bonding ionic bonding covalent bonding metallic bonding secondary bonding van der Waals hydrogen bonding

Atomic Bondings:  Metallic bonding  Covalent bonding When more than two atoms get closer ... Especially in case of atoms of the kind ... When atoms with less valence electrons are brought together, each atom tends to form ‘ closed shell ’ structure by abandoning less bound free electrons  Metallic bonding Free electron Shared electron When atoms with many valence electrons are brought together, each atom tends to form ‘ closed shell ’ structure by sharing electrons belonging to neighbor atoms  Covalent bonding

Atomic Bondings:  Ionic bonding When atoms of far- & near-closed shell structure are brought together ... Atoms of far-closed shell structure & near-closed one tend to lose & gain electrons, respectively  Electronegativity by L. Pauling Excess charge induced by the transfer of electrons are compensated by the presence of ions of opposite sign  Ionic bonding

Secondary Bonding: + - asymmetric electron clouds -general case: Arises from interaction between dipoles • Fluctuating dipoles asymmetric electron clouds + - secondary bonding H 2 ex: liquid H Adapted from Fig. 2.13, Callister 7e. • Permanent dipoles-molecule induced + - -general case: secondary bonding Adapted from Fig. 2.14, Callister 7e. Cl Cl -ex: liquid HCl secondary H H bonding secondary bonding -ex: polymer secondary bonding

Ionic Bonding: r A B EN = EA + ER = Energy – minimum energy most stable Energy balance of attractive and repulsive terms r A n B EN = EA + ER = - Attractive energy EA Net energy EN Repulsive energy ER Interatomic separation r Adapted from Fig. 2.8(b), Callister 7e.

Potential Energy E + Force F - Derivation of equilibrium distance of inter-atomic distance with A and B unknown Force F -

Bonding Forces & Energies: 참고자료 - Covalent bonding : nucleus to electrons : nucleus to nucleus : electrons to electrons - Ionic bonding : electrostatic attraction between unlike ions : closed shell overlapping

Potential Well Concept: Long-range attractive Short-range repulsive

Properties from Bonding: Thermal expansion  asymmetric nature of the energy well Broad well (generally more asymmetric)  larger expansion

Properties from Bonding: ... Temperature supplies thermal energy into solids ...  thermal vibration (phonon) Slope is related to the thermal expansion coefficient of materials

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Ionic Bonding: Occurs between + and - ions Requires electron transfer Large difference in electronegativity required An ionic bond is created between two unlike atoms with different electronegativities When sodium donates its valence electron to chlorine, each becomes an ion; attraction occurs, and the ionic bond is formed

Examples: Ionic Bonding: • Predominant bonding in Ceramics NaCl MgO Give up electrons Acquire electrons CaF 2 CsCl Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

Ionic Bonding:

Ionic Crystal: Na Cl N molecules each positive ion is surrounded by several negative ions and vice versa

Ionic Crystal: strong infrared absorption transparency in visible wavelength low electrical conductivity at low temp but good ionic conductivity at high temp non-directional in nature maximum number of neighbors (packing density)

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Covalent Bonding: shared electrons from carbon atom C H from hydrogen similar electronegativity  share electrons bonds determined by valence – s & p orbitals dominate bonding Example: CH4 shared electrons from carbon atom from hydrogen atoms H C CH 4 C: has 4 valence e-, needs 4 more H: has 1 valence e-, needs 1 more Electronegativities are comparable. Adapted from Fig. 2.10, Callister 7e.

Covalent Bonding: The tetrahedral structure of silica (Si02), which contains covalent bonds between silicon and oxygen atoms

Covalent Bonding: Calculation of bonding angle Covalent bonds are directional. In silicon, a tetrahedral structure is formed, with angles of 109.5° required between each covalent bond.

Example : Covalent Bonding: molecules with nonmetals molecules with metals and nonmetals elemental solids (RHS of Periodic Table) compound solids (about column IVA)

Covalent Bonding: bond energy curve strong directional nature of bonding high hardness High (Diamond) or low (Bismuth) melting point low electrical conductivities at low temperatures

Ionic vs. Covalent Bonding: many compounds-partially ionic and partially covalent degree of bond type - electronegativity a large difference in electronegativity  largely ionic similar electronegativity  largely covalent

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Metallic Bonding: Arises from a sea of donated valence electrons (1, 2, or 3 from each atom) Primary bond for metals and their alloys

Metallic Bonding: delocalized electron Free electrons act as a “glue” to hold the ion core

Metallic Bonding: The metallic bond forms when atoms give up their valence electrons, which then form an electron sea. The positively charged atom cores are bonded by mutual attraction to the negatively charged electrons.

Metallic Bonding: When voltage is applied to a metal, the electrons in the electron sea can easily move and carry a current.

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Van der Waals bonding:  van der Waals bonding Although electrons have tendency of being separated as far as possible due to e-e repulsion, electrons are constantly in motion It follows that electrons could get close enough to induce a “electric dipole moment” at atomistic level This tendency is expected to be more significant as the number of electrons increases Temporal bonding due to the induced electric dipole  van der Waals bonding

Van der Waals Bonding: induced dipole permanent dipole (polar molecule)

Van der Waals Bonding: dipole-dipole interaction

Contents Introduction 1 Atomic Structure 2 Bonds – Ionic, Covalent, and Metallic Secondary Bonds – Van der Waals and Hydrogen 3 1 2 4 Introduction

Hydrogen Bonding: When one of the components of covalent bonding is hydrogen ... Since hydrogen atom has only one electron, there is no electron left for the formation of closed shell  Bare proton is exposed without being shielded by electrons ...  Strong ionic character develops locally about hydrogen atom ... ... Strong bonding develops ...

Hydrogen Bonding: H2O H2S NH3 Strongest secondary bonding Positively charged Hydrogen ion forms a bridge between two negatively charged ions

Materials-Bonding Classification:

Summary: Primary Bonds: Ceramics Large bond energy large Tm large E small a (Ionic & covalent bonding): Metals Variable bond energy moderate Tm moderate E moderate a (Metallic bonding): Polymers Directional Properties Secondary bonding dominates small Tm small E large a (Covalent & Secondary): secondary bonding

Summary: Bonding: Type Bond Energy Comments Ionic Large! Nondirectional (ceramics) Covalent Variable Directional (semiconductors, ceramics polymer chains) large-Diamond small-Bismuth Metallic Variable large-Tungsten Nondirectional (metals) small-Mercury Secondary smallest Directional inter-chain (polymer) inter-molecular