Chapter 2: Atomic Structure and Interatomic Bonding These notes have been prepared by Jorge Seminario from the textbook material

ISSUES TO ADDRESS... • What promotes bonding? • What types of bonds are there? • What properties are inferred from bonding?

Basic idea … properties of materials are a consequence of Identity of the atoms Spatial arrangement of the atoms Interactions between the atoms Thus, we need to study atomic structure/bonding! End of lecture 1

Atomic Structure Changes as you move around the periodic table! Atomic number Number of electrons/electronic configuration e.g. you might expect electronic properties to depend on the number of electrons an atom has (i.e. open v closed shells) Type of bonding (ionic versus covalent) Changes as you move around the periodic table! End of lecture 1

2.2 Fundamental Concepts Atoms consist of a small nucleus containing Protons +1.60 x 10-19 C = e 1.67 x 10-27 kg Neutrons 0 C (neutral) Electrons (which circle the nucleus) -1.60 x 10-19 C = -e 9.11 x 10-31 kg

2.2 Fundamental Concepts Atomic Number (Z) Atomic Mass (A) Isotopes Number of protons in the nucleus Electrically neutral or complete atom: Z = # electrons Atomic Mass (A) Sum of the masses of protons and neutrons; atomic mass unit = amu = 1/12 mass of 12C Isotopes Atoms of the same element with different atomic masses due to varying number of neutrons (e.g. 12C, 13C, 14C

Atomic Structure 2.2 Fundamental Concepts Atomic weight is the weighted average of the element based on the relative amounts of its isotopes (e.g. 1 mol/carbon = 12.0107 g/mol, NOT 12 g/mol!)   Atomic wt = wt of NA molecules, atoms, etc. and NA = 6.022 x 1023   1 amu/atom = 1g/mol C 12.011 g/mol H 1.008 g/mol, etc. Mole Quantity of a substance corresponding to 6.022X1023 atoms, molecules, … 1 amu/ atom (or molecule) = 1g/mol

Basic concepts Atoms are made of protons, neutrons and electrons me = 0.00091094x10-27 = 9.1094x10-31 kg = 0.511 MeV mp = 1.6726 x 10-27 kg = 938.272 MeV mn = 1.6749 x 10-27 kg = 939.566 MeV = mp + 1.293 MeV Charge of a proton and electron are the same: 1.6022x10-19 C However p are +’ve and e are –’ve Since J = C x V (1 joule = 1 coulomb x 1 volt), 1 eV = 1.6022x10-19 J mass is related to energy by E = mc2 End of lecture 1

Examples How many grams are there in one amu of a material? The two major isotopes of carbon: 98.93% of 12C with an atomic weight of 12.00000 amu, and 1.07% of 13C with an atomic weight of 13.00335 amu. Confirm that the average atomic weight of C is 12.011 amu. Sum the product of the isotope atomic weight and the percent abundance. (12 amu)*(.9893)+(13.00335 amu)*(.0107) = 12.011 amu

2.3 Electrons In Atoms Bohr Atomic Model Early outgrowth of quantum mechanics Electrons revolve around nucleus in discrete orbitals Electrons closer to nucleus travel faster then outer orbitals Principal quantum number (n); 1st shell, n=1; 2nd shell, n=2; 3rd shell, n=3

c02f02 Quantum Numbers For the H atom Scaled for hydrogen-like atoms Degenerate states Same energy c02f02

c02f03 Bohr Atom Wave-mechanical atom c02f03

Atomic Models Wave-Mechanical Model Electron exhibits both wave-like and particle-like characteristics Position is now considered to be the probability of an electron being at various locations around the nucleus, forming an electron cloud

Electron Configuration Pauli Exclusion Principle Stipulates that electron states (orbital) can have no more than two electrons, must have opposite spins Ground state All electrons occupy the lowest energies Electrons can move to higher states Filled shells are more stable

Electronic Structure Electrons have wave-like and particle-like properties (old view) We can better say that the wave-particle nature is the real thing; individual wave and particle states are limiting cases, observed in measurements (collapse of the wave function) To better understand electronic structure, we assume Electrons “reside” in orbitals. Each orbital, at a discrete energy level, is determined by quantum numbers. c Quantum numbers Designation n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.) l = angular (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1) ml = magnetic 1, 3, 5, 7 (-l to +l) ms = spin ½, -½

Quantum Numbers c02f04 Relative electrons energies (E) for shells and subshells if n↓ then E↓ Within each shell E↑ with quantum number Overlapping in energy of a state in one shell with states in adjacent shells, true of d and f states c\2f04

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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

Atomic Models Quantum numbers Principal quantum number n, represents a shell K, L, M, N, O correspond to n=1, 2, 3, 4, 5.... Quantum number l, signifies the subshell Lowercase italics letter s, p, d, f; related to the shape of the subshell Quantum number ml , represents the number of energy states s, p, d, f have 1, 3, 5, 7 states respectively Quantum number ms, is the spin moment Each electron is a spin moment (+1/2) and (-1/2)

Electron Configuration Silicon (Si) Electron configuration represents the manner in which the states are occupied Valence electrons Occupy the outermost shell Available for bonding Tend to control chemical properties

Electron Configurations - Pauli Exclusion Principle c02f05 Na Atom Z = 11 c02f05

c02tf02 When some elements covalently bond, they form sp hybrid bonds, e.g., C, Si, Ge c02tf02

Examples Give the electron configurations for the following: C 1s2 2s2 2p2 Br 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 Mn+2 1s2 2s2 2p6 3s2 3p6 3d5 F- 1s2 2s2 2p6 Cr 1s2 2s2 2p6 3s2 3p6 4s1 3d5

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 & Rethwisch 3e. Notice that 2s and 2p do not have the same energy

Electron Configuration “Stable electron configurations” States within the outermost or valence electron shell are completely filled Some atoms of elements with unfilled shells assume stable electron configurations by gaining or losing electrons to form charged ions Sometimes s and p orbitals form hybrid spn orbitals 3A, 4A, and 5A group elements typically Lower energy state for the valence electrons

SURVEY OF ELEMENTS • Most elements: Electron configuration not stable. ... 1s 2 2s 2p 6 3s 3p 3d 10 4s 4p Atomic # 18 36 Element 1 Hydrogen Helium 3 Lithium 4 Beryllium 5 Boron Carbon Neon 11 Sodium 12 Magnesium 13 Aluminum Argon Krypton Adapted from Table 2.2, Callister & Rethwisch 3e.

STABLE ELECTRON CONFIGURATIONS • have complete s and p subshells • tend to be unreactive. Adapted from Table 2.2, Callister 6e. 4

2.4 Periodic Table Elements classified according to electron configuration Elements in a given column or group have similar valence electron structures as well as chemical and physical properties Group 0 – inert gases, filled shells and stable Group VIIA – halogen Group IA and IIA - alkali and alkaline earth metals Groups IIIB---IIB – transition metals Groups IIIA, IVA and VA – characteristics between the metals and nonmetals

2.4

c02f07 Electropositive: Electronegativity Values Electronegative: Capable of giving up their valence electrons to become positively charged Electronegative: Readily accept electrons to form negatively charged ions Sometimes share electrons with other atoms

Atomic Bonding Valence electrons determine all of the following properties Chemical Electrical Thermal Optical Deteriorative etc.

Atomic Bonding in Solids

2.5 Bonding Forces and Energies When 0 = FA + FR, equilibrium exists. The centers of the atoms will remain separated by the equilibrium spacing ro. This spacing also corresponds to the minimum of the potential energy curve. The energy that would be required to separate two atoms to an infinite separation is Eo FN = FA + FR EN = EA + ER Figure 2.8

2.5 Bonding Forces and Energies A number of material properties depend on Eo, the curve shape, and bonding type Material with large Eo typically have higher melting points Mechanical stiffness is dependent on the shape of its force vs. interatomic separation curve A material’s linear coefficient of thermal expansion is related to the shape of its Eo vs. ro curve

Bonding in Solids 2.5 Bonding forces and energies Far apart: atoms don’t know about each other As they approach one another, start to exert force on one another two types of forces Attractive (FA) – slowly changing with distance Repulsive (FR) – typically short-range Net force is the sum of these FN = FA + FR At some point the net force is zero; at that position a state of equilibrium exists End of lecture 1

Bonding in Solids Bonding forces and energies & setting our ZERO ENERGY reference at ∞ The point where the forces are zero also corresponds to the minimum potential energy for the two atoms, which makes sense because -dE/dr = F = 0 at a minimum. End of lecture 1 The interatomic separation at that point (ro) corresponds to the potential energy at that minimum Eo, it is also the bonding energy Eo is the energy needed to separate the atoms

Examples (assume the book wrong sign of the F) Calculate the force of attraction between ions X+ and an Y-, the centers of which are separated by a distance of 2.01 nm. &

2.6 Primary Interatomic Bonds Types of chemical bonds found in solids Ionic Covalent Metallic As you might imagine, the type of bonding influences properties – why? End of lecture 1 Bonding involves the valence electrons!!!

2.6 Primary Interatomic Bonds Ionic Bonding Compounds composed of metallic and nonmetallic elements Coulombic Attractive Forces: positive and negative ions, by virtue of their net electrical charge, attract one another EA = -A/r ER = B/rn Bonding is nondirectional: the magnitude of the bond is equal in all directions around an ion Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally insulative A, B, n are constants Coulombic bonding Force Cl- Na+

2.6 Primary Interatomic Bonds c02f09 c02f09

2.6 Primary Interatomic Bonds Ionic bonding Prototype example – sodium chloride (NaCl) Sodium gives up one its electrons to chlorine – sodium becomes positively charged, chlorine becomes negatively charged The attraction energy is electrostatic in nature in ionic solids (opposite charges attract) The attractive component of the potential energy (for 2 point charges) is given by End of lecture 1 The repulsive term is given by

Ionic bond: metal + nonmetal donates accepts electrons electrons   Dissimilar electronegativities   ex: MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4 [Ne] 3s2  Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 [Ne] [Ne]

Ionic Bonding - + • Occurs between + and - ions. • Requires electron transfer. • Large difference in electronegativity required. • Example: NaCl Na (metal) unstable Cl (nonmetal) electron + - Coulombic Attraction Na (cation) stable Cl (anion)

Ionic Bonding Energy – minimum energy most stable A B EN = EA + ER = r Energy balance of attractive and repulsive terms A B EN = EA + ER = - + r r n Attractive energy EA Net energy EN Repulsive energy ER Interatomic separation r Adapted from Fig. 2.8(b), Callister & Rethwisch 3e.

Examples: Ionic Bonding • Predominant bonding in Ceramics NaCl MgO Give up electrons Acquire electrons CaF 2 CsCl Adapted from Fig. 2.7, Callister & Rethwisch 3e. (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.

2.6 Primary Interatomic Bonds Covalent Bonding Stable electron configurations are assumed by the sharing of electrons between adjacent atoms Bonding is directional: between specific atoms and may exist only in the direction between one atom and another that participates in electron sharing Number of covalent bonds for a particular molecule is determined by the number of valence electrons Bond strength ranges from strong to weak Rarely are compounds purely ionic or covalent but are a percentage of both. Sharing 4 electrons Sharing 2 electrons %ionic character = {1 – exp[-(0.25)(XA-XB)2]} x 100 XA and XB are electronegatives

Covalent bonding Sharing of electrons between adjacent atoms Most nonmetallic elements and molecules containing dissimilar elements have covalent bonds Polymers! Bonding is highly directional! Number of covalent bonds possible is guessed by the number of valence electrons Typically is 8 – N, where N is the number of valence electrons Carbon has 4 valence e’s – 4 bonds (ok!) End of lecture 1

EXAMPLES: COVALENT BONDING Adapted from Fig. 2.7, Callister 6e. (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. • Molecules with nonmetals • Molecules with metals and nonmetals • Elemental solids (RHS of Periodic Table) • Compound solids (about column IVA) 11

Covalent Bonding 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 & Rethwisch 3e.

Bonding in Solids Many materials have bonding that is both ionic and covalent in nature (very few materials actually exhibit pure ionic or covalent bonding) Easy (empirical) way to estimate % of ionic bonding character: End of lecture 1 XA, XB are the electronegativities of atoms A and B involved Notice: this is a very very very empirical formula

Primary Bonding Ionic-Covalent Mixed Bonding % ionic character = where XA & XB are Pauling electronegativities %) 100 ( x Ex: MgO XMg = 1.3 XO = 3.5

Example Compute the percentage ionic character of the interatomic bond for zinc oxide (ZnO). Refer to the periodic Table for electronegativity values. Note: Electronegativity values in slides differ slightly from those in book. % ionic character = {1-exp[-(0.25)*(XZn-XO)2]}*100 = {1-exp[-(0.25)*(1.7-3.5)2]}*100 = 55.51%

2.6 Primary Interatomic Bonds Metallic Bonding Found in metals and their alloys 1 to 3 valence electrons that form a “sea of electrons” or an “electron cloud” because they are more or less free to drift through the entire metal Nonvalence electrons and atomic nuclei form ion cores Bonding energies range from weak to strong Good conductor of both electricity and heat Most metals and their alloys fail in a ductile manner Ion Cores + + + - - + + + - - + + + Sea of Valence Electrons

METALLIC BONDING • Arises from a sea of donated valence electrons (1, 2, or 3 from each atom). Adapted from Fig. 2.11, Callister 6e. • Primary bond for metals and their alloys 12

Bonding in Solids Metallic bonding Most metals have one, two, or at most three valence electrons These electrons are highly delocalized from a specific atom – have a “sea of valence electrons” End of lecture 1 Free electrons shield positive core of ions from one another (reduce ER) Metallic bonding is also non-directional Free electrons also act to hold structure together Wide range of bonding energies, typically good conductors (why?)

2.7 Secondary Bonding or van der Walls Bonding Also known as physical bonds Weak in comparison to primary or chemical bonds Exist between virtually all atoms and molecules Arise from atomic or molecular dipoles bonding that results from the coulombic attraction between the positive end of one dipole and the negative region of an adjacent one a dipole may be created or induced in an atom or molecule that is normally electrically symmetric

2.7 Secondary Bonding or van der Waals Bonding Fluctuating Induced Dipole Bonds A dipole (whether induced or instantaneous) produces a displacement of the electron distribution of an adjacent molecule or atom and continues as a chain effect Liquefaction and solidification of inert gases Weakest Bonds Extremely low boiling and melting point Atomic nucleus Atomic nucleus Instantaneous Fluctuation Electron cloud Electron cloud

2.7 Secondary Bonding or van der Waals Bonding Polar Molecule-Induced Dipole Bonds Permanent dipole moments exist by virtue of an asymmetrical arrangement of positively and negatively charged regions Polar molecules can induce dipoles in adjacent nonpolar molecules Magnitude of bond greater than for fluctuating induced dipoles Atomic nucleus - Electron Cloud + Polar Molecule Induced Dipole

2.7 Secondary Bonding or van der Waals Bonding Permanent Dipole Bonds Stronger than any secondary bonding with induced dipoles A special case of this is hydrogen bonding: exists between molecules that have hydrogen as one of the constituents Hydrogen Bond H Cl H Cl

van der Waals interactions between polar molecules Permanent dipoles Hydrogen-bonds These interactions are fairly strong, very complex, and surprisingly not well understood! 2.82 Å 109.47° van der Waals interactions between polar molecules Best known example hydrogen bonding

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MATERIAL OF IMPORTANCE Water c02f16 Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H2O, HCl) c02f16

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Properties From Bonding: Tm • Bond length, r • Melting Temperature, Tm r o Energy r • Bond energy, Eo Eo = “bond energy” Energy r o unstretched length smaller Tm larger Tm Tm is larger if Eo is larger.

Properties From Bonding : a • Coefficient of thermal expansion, a coeff. thermal expansion D L length, o unheated, T 1 heated, T 2 D L = a ( T - T ) 2 1 L o • a ~ symmetric at ro r o smaller a larger a Energy unstretched length Eo a is larger if Eo is smaller.

PROPERTIES FROM BONDING: E • Elastic modulus, E E ~ dF/dr|ro elastic modulus 16

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

JIC, additional vg’s

Electron Configurations of Cations and Anions Of Representative Elements Na [Ne]3s1 Na+ [Ne] Atoms lose electrons so that cation has a noble-gas outer electron configuration. Ca [Ar]4s2 Ca2+ [Ar] Al [Ne]3s23p1 Al3+ [Ne] H 1s1 H- 1s2 or [He] Atoms gain electrons so that anion has a noble-gas outer electron configuration. F 1s22s22p5 F- 1s22s22p6 or [Ne] O 1s22s22p4 O2- 1s22s22p6 or [Ne] N 1s22s22p3 N3- 1s22s22p6 or [Ne] 8.2

Na+, Al3+, F-, O2-, and N3- are all isoelectronic with Ne Na+: [Ne] Al3+: [Ne] F-: 1s22s22p6 or [Ne] O2-: 1s22s22p6 or [Ne] N3-: 1s22s22p6 or [Ne] Na+, Al3+, F-, O2-, and N3- are all isoelectronic with Ne What neutral atom is isoelectronic with H- ? H-: 1s2 same electron configuration as He 8.2

Electron Configurations of Cations of Transition Metals When a cation is formed from an atom of a transition metal, electrons are always removed first from the ns orbital and then from the (n – 1)d orbitals. Fe: [Ar]4s23d6 Mn: [Ar]4s23d5 Fe2+: [Ar]4s03d6 or [Ar]3d6 Mn2+: [Ar]4s03d5 or [Ar]3d5 Fe3+: [Ar]4s03d5 or [Ar]3d5 8.2

Cation is always smaller than atom from which it is formed. Anion is always larger than atom from which it is formed. 8.3

8.3

I1 first ionization energy Ionization energy is the minimum energy (kJ/mol) required to remove an electron from a gaseous atom in its ground state. I1 + X (g) X+(g) + e- I1 first ionization energy I2 + X (g) X2+(g) + e- I2 second ionization energy I3 + X (g) X3+(g) + e- I3 third ionization energy I1 < I2 < I3 8.4

8.4 Filled n=1 shell Filled n=2 shell Filled n=3 shell

Electron affinity is the negative of the energy change that occurs when an electron is accepted by an atom in the gaseous state to form an anion. X (g) + e- X-(g) F (g) + e- X-(g) DH = -328 kJ/mol EA = +328 kJ/mol O (g) + e- O-(g) DH = -141 kJ/mol EA = +141 kJ/mol 8.5

Group 2A Elements (ns2, n  2) M M+2 + 2e- Be(s) + 2H2O(l) No Reaction Mg(s) + 2H2O(g) Mg(OH)2(aq) + H2(g) M(s) + 2H2O(l) M(OH)2(aq) + H2(g) M = Ca, Sr, or Ba Increasing reactivity 8.6

Group 3A Elements (ns2np1, n  2) 4Al(s) + 3O2(g) 2Al2O3(s) 2Al(s) + 6H+(aq) 2Al3+(aq) + 3H2(g) 8.6

Group 7A Elements (ns1np5, n  2) X + 1e- X-1 X2(g) + H2(g) 2HX(g) Increasing reactivity 8.6