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

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

Chapter 2- –Atoms are made of protons, neutrons and electrons m e = x = x kg = 0.511MeV m p = x kg = MeV m n = x kg = MeV = m n = m p MeV proton & electron charge x C However p are +’ve and e are –’ve –Atomic number (Z) describes the number of protons in the nucleus –Atomic mass (A) of an element is approximately equal to the number of neutrons and protons the element has Remember elements have isotopes – elements can have different numbers of neutrons (e.g. 12 C, 13 C, 14 C) –Atomic weight is the weighted average of the element based on the relative amounts of its isotopes (e.g. 1 mol/carbon = g/mol, NOT 12 g/mol!) Basic concepts

Chapter Fundamental Concept Atomic Weight Weighted average of the atomic masses of an atom's naturally occurring isotopes Atomic Mass Unit (amu) Measure of atomic mass 1/12 the mass of C 12 atom Mole Quantity of a substance corresponding to 6.022X10 23 atoms or molecules 1 amu/ atom (or molecule) = 1g/mol

Chapter 2- How many grams are there in one amu of a material? The two major isotopes of carbon: 98.93% of 12 C with an atomic weight of amu, and 1.07% of 13 C with an atomic weight of amu. Confirm that the average atomic weight of C is amu. Sum the product of the isotope atomic weight and the percent abundance. (12 amu)*(.9893)+( amu)*(.0107) = amu Examples

Chapter Electrons In Atoms Bohr Atomic Model (old view) 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); 1 st shell, n=1; 2 nd shell, n=2; 3 rd shell, n=3

Chapter 2- c02f02 Quantum Numbers—Hydrogen atom

Chapter 2- c02f03 Bohr Atom Wave-mechanical atom

Chapter 2- 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

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

Chapter 2- Electron Configuration 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 Ex. Silicon (Si)

Chapter 2- Energy

Chapter 2- c02tf02 When some elements covalently bond, they form sp hybrid bonds, e.g., C, Si, Ge

Chapter 2- Examples Give the electron configurations for the following: C 1s 2 2s 2 2p 2 Br 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5 Mn +2 1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 F - 1s 2 2s 2 2p 6 Cr 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5

Chapter Electronic Structure Electrons have wave-like and particle-like (old view) properties. We can better say that the wave-particle nature is the real thing; individual wave and particle states are limiting cases; usually observed in measurements (collapse of the wave function) To better understand electronic structure, we assume –Electrons “reside” in orbitals. –Each orbital at discrete energy level is determined by quantum numbers. c Quantum # 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) m l = magnetic1, 3, 5, 7 (- l to + l ) m s = spin½, -½

Chapter 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) 1s 2 2s 2 2p 2 valence electrons

Chapter Electronic Configurations ex: Fe - atomic # = 26 valence electrons Adapted from Fig. 2.4, Callister & Rethwisch 3e. 1s1s 2s2s 2p2p K-shell n = 1 L-shell n = 2 3s3s 3p3p M-shell n = 3 3d3d 4s4s 4p4p 4d4d Energy N-shell n = 4 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2

Chapter 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 and IIB – transition metals Groups IIIA, IVA and VA – characteristics between the metals and nonmetals

Chapter

Chapter Atomic Bonding Valence electrons determine all of the following properties 1)Chemical 2)Electrical 3)Thermal 4)Optical 5)Deteriorative 6)etc.

Chapter 2- Atomic Bonding in Solids

Chapter Bonding Forces and Energies F N = F A + F R E N = E A + E R When 0 = F A + F R, equilibrium exists. The centers of the atoms will remain separated by the equilibrium spacing r o. 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 E o Figure 2.8

Chapter Bonding Forces and Energies A number of material properties depend on E o, the curve shape, and bonding type –Material with large E o 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 shapeof its E o vs. r o curve

Chapter 2- Bonding in Solids 2.5 Bonding forces and energies –Far apart: atoms don’t know about each other –As they approach one another, exert force on one another Forces are –Attractive (F A ) – slowly changing with distance –Repulsive (F R ) – typically short-range –Net force is the sum of these F N = F A + F R –At some point the net force is zero; at that position a state of equilibrium exists

Chapter 2- Bonding in Solids Bonding forces and energies –We are more accustomed to thinking in terms of potential energy instead of forces – in that case The point where the forces are zero also corresponds to the minimum potential energy for the two atoms (i.e. the trough in Figure 2.8), which makes sense because dE/dr = F =0 at a minimum. The interatomic separation at that point (r o ) corresponds to the potential energy at that minimum (E o, it is also the bonding energy) The physical interpretation is that it is the energy needed to separate the atoms infinitely far apart Setting our ZERO ENERGY reference at infinite

Chapter 2- Examples Calculate the force of attraction between ions X + and an Y -, the centers of which are separated by a distance of 2.01 nm. &

Chapter 2- Types of chemical bonds found in solids –Ionic –Covalent –Metallic As you might imagine, the type of bonding influences properties – why? Bonding involves the valence electrons!!! 2.6 Primary Interatomic Bonds

Chapter 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 E A = -A/r E R = -B/r n –Bonding is nondirectional: the magnitude of the bond is equal in all directions around an ion –Properties: generally large bonding energies ( kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally insulative A, B, and n are constants Na + Cl - Coulombic bonding Force

Chapter 2- c02f Primary Interatomic Bonds

Chapter 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 –The repulsive term is given by

Chapter 2- IONIC BONDING –Ionic bonding is non-directional – magnitude of the bond is equal in all directions around the ion –Many ceramics have an ionic bonding characteristic –Bonding energies typically in the range of 600 – 1500 kJ/mol –Often hard, brittle materials, and generally insulators

Chapter Ionic bond: metal + nonmetal donates accepts electrons electrons Dissimilar electronegativities ex: MgOMg 1s 2 2s 2 2p 6 3s 2 O 1s 2 2s 2 2p 4 [Ne] 3s 2 Mg 2+ 1s 2 2s 2 2p 6 O 2- 1s 2 2s 2 2p 6 [Ne] [Ne]

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

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

Chapter Predominant bonding in Ceramics 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. Examples: Ionic Bonding Give up electronsAcquire electrons NaCl MgO CaF 2 CsCl

Chapter 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 electron s %ionic character = {1 – exp[-(0.25)(X A -X B ) 2 ]} x 100 X A and X B are electronegatives

Chapter 2- 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!)

Chapter 2-11 Molecules with nonmetals Molecules with metals and nonmetals Elemental solids (RHS of Periodic Table) Compound solids (about column IVA) 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. EXAMPLES: COVALENT BONDING

Chapter 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. Covalent Bonding similar electronegativity  share electrons bonds determined by valence – s & p orbitals dominate bonding Example: CH 4 shared electrons from carbon atom shared electrons from hydrogen atoms H H H H C CH 4

Chapter 2- 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: X A, X B are the electronegativities of atoms A and B involved Notice: this is a very very very empirical formula

Chapter Primary Bonding Ionic-Covalent Mixed Bonding % ionic character = where X A & X B are Pauling electronegativities %)100( x Ex: MgOX Mg = 1.3 X O = 3.5

Chapter 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

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

Chapter 2- 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” –Free electrons shield positive core of ions from one another (reduce E R ) –Metallic bonding is also non- directional –Free electrons also act to hold structure together –Wide range of bonding energies, typically good conductors (why?)

Chapter 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

Chapter 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 Electron cloud Electron cloud Instantaneous Fluctuation

Chapter 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 + - Polar Molecule Induced Dipole Atomic nucleus Electron Cloud

Chapter 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 HClH Hydrogen Bond

Chapter 2- Bonding in Solids Permanent dipoles (hydrogen bonds) –Van der Waals interactions between polar molecules –Best known example – hydrogen bonding These interactions are fairly strong, very complex, and surprisingly not well understood!

Chapter 2- c02tf03

Chapter 2- c02f16 Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H 2 O, HCl) MATERIAL OF IMPORTANCE Water

Chapter 2- c02uf01

Chapter Bond length, r Bond energy, E o Melting Temperature, T m T m is larger if E o is larger. Properties From Bonding: T m r o r Energy r larger T m smaller T m EoEo = “bond energy” Energy r o r unstretched length

Chapter Coefficient of thermal expansion,   ~ symmetric at r o  is larger if E o is smaller. Properties From Bonding :  =  (T 2 -T 1 )  L L o coeff. thermal expansion  L length,L o unheated, T 1 heated, T 2 r o r smaller  larger  Energy unstretched length EoEo EoEo

Chapter 2-16 Elastic modulus, E PROPERTIES FROM BONDING: E E ~ dF/dr| ro elastic modulus

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

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