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? 1

Ch 2 Callister – Atomic Structure and Bonding in Solids Before we get started … This should be a review of what you saw in general chemistry Basic idea … many properties of materials are a consequence of Identity of the atoms that comprise them Spatial arrangement of the atoms that comprise them Interactions between the atoms that comprise them So, we need to talk about atomic structure/bonding! End of lecture 1

Atomic Structure and Bonding in Solids So what do I mean by atomic structure? 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) And how these things change as you move around the periodic table! Last chance … have any of you not taken general chemistry? End of lecture 1

BOHR ATOM Nucleus: Z = # protons = 1 for hydrogen to 94 for plutonium Adapted from Fig. 2.1, Callister 6e. Nucleus: Z = # protons = 1 for hydrogen to 94 for plutonium N = # neutrons Atomic mass A ≈ Z + N 2

Atomic Structure and Bonding in Solids Basic concepts Atoms are made of protons, neutrons and electrons me = 9.11 x 10-31 kg, mp = mn = 1.67 x 10-27 kg Charge of a proton and electron is the same: 1.60 x 10-19 C 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 (why do I say approximately) Remember elements have isotopes – elements can have different numbers of neutrons (e.g. 12C, 13C, 14C) Atomic weight is the weighted average of the element based on the relative amounts of its isotopes (e.g. 1 mol/carbon = 12.011 g/mol, NOT 12 g/mol!) pp 11,12 – definition of atomic mass unit (amu), mole End of lecture 1

Atomic Structure and Bonding in Solids Electrons in atoms Why do we care about electrons? Turns out to understand properties of materials need to have at least a basic appreciation for electrons! A rigorous description – quantum mechanics! An early outgrowth of quantum mechanics was the Bohr atomic model Basic idea – electrons revolve around the nucleus Nucleus Orbital electrons Adapted from Fig 2.1 Callister End of lecture 1

Atomic Structure and Bonding in Solids Electrons in atoms Turns out the Bohr model has some significant shortcomings! That’s ok though … it is a useful starting point Few other implications of quantum mechanics Energies are quantized – electrons are only permitted to have specific values of energy Adjacent energy states are separated by finite energy (i.e. the energy states are not continuous) 1kT, 2kT, … Bohr model was an early attempt to describe electrons in terms of position and energy Turns out electrons have both particle and wave properties (wave-mechanical model) Position is described by probability distribution (Figure 2.3; you’ll learn more about this in quantum mechanics) End of lecture 1

ELECTRON ENERGY STATES Electrons... • have discrete energy states • tend to occupy lowest available energy state. Adapted from Fig. 2.5, Callister 6e. 3

Atomic Structure and Bonding in Solids Quantum numbers Using wave mechanics the electrons in atoms can be characterized using quantum numbers Principal quantum number n – refers to shells (distance of an electron from the nucleus) n = 1, 2, 3, 4, 5 … or K, L, M, N Second quantum number l – signifies the subshell s, p, d, f Third quantum number ml – denotes number of energy states in the s, p, d, f subshells s subshell (orbital) – 1 state p subshell – 3 states d subshell – 5 states f subshell – 7 states Spin moment – fourth quantum number Spin up or spin down Table 2.1, Figure 2.4 summarize all this! End of lecture 1

Atomic Structure and Bonding in Solids Electronic configurations That is all well and good, but how are the various states filled? Where do the electrons actually go? Pauli exclusion principle – Each electron state can hold no more than 2 electrons, and they must have opposite spins Take home – s, p, d, f subshells can hold 2, 6, 10, and 14 electrons respectively (does this make sense based on what I said before?) But there is more … not all possible states are always filled! Electrons fill the lowest energy states in the shells/subshells first (makes sense) and do not violate the Pauli exclusion principle! This is said to be the ground state of the atom Electron configuration describes this – hydrogen (1s1), helium (1s2), sodium (1s2, 2s2, 2p6,3s1) End of lecture 1

Atomic Structure and Bonding in Solids Okay, hopefully no surprises so far. Key points regarding electronic configuration Valence electrons are extremely important Valence electrons are those that occupy the outermost shell These participate in chemical bonding “Stable electron configurations” - states where the outermost electron shell is filled These were probably referred to as “closed shell” in your chemistry course Typically means s and p shells are full Explains inertness of Ar, Kr (noble gases) This also has implications for bonding/coordination/oxidation states of metals End of lecture 1

Atomic Structure and Bonding in Solids Periodic table (pp 18 – 19) Read it! I know you have seen this before Note trends in electronegativity as one moves across the periodic table Which elements are metals, intermediate, and non-metals and where are they in the periodic table? End of lecture 1

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

SURVEY OF ELEMENTS • Most elements: Electron configuration not stable. Adapted from Table 2.2, Callister 6e. • Why? Valence (outer) shell usually not filled completely. 5

THE PERIODIC TABLE • Columns: Similar Valence Structure Adapted from Fig. 2.6, Callister 6e. Electropositive elements: Readily give up electrons to become + ions. Electronegative elements: Readily acquire electrons to become - ions. 6

ELECTRONEGATIVITY • Ranges from 0.7 to 4.0, • Large values: tendency to acquire electrons. Smaller electronegativity Larger electronegativity 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. 7

Bonding in Solids Bonding forces and energies Start with simple picture … forces and energies experienced by two atoms as a function of their separation distance (Remember: Energy is the integral of the force over the length) End of lecture 1

Bonding forces and energies Bonding in Solids Bonding forces and energies Explain in words/equations what I just showed pictorially Far apart: atoms don’t know about each other As they approach one another, start to exert force on one another In general terms two types of forces Attractive (FA) – can vary 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 (who has taken thermo? Ever hear of equilibrium before?) End of lecture 1

Bonding forces and energies 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 (ro) corresponds to the potential energy at that minimum (Eo, it is also the bonding energy) The physical interpretation is that it is the energy needed to separate the atoms infinitely far apart End of lecture 1

Bonding forces and energies Bonding in Solids Bonding forces and energies Ok, things are more complicated in real solids But the picture above is extremely insightful Why? Can describe interactions between atoms/molecules using pair interatomic potentials (e.g. Lennard-Jones potential, etc..) Many material properties will depend on the shape of the potential energy surface Position of ro, depth of potential well, etc. Why is that? Can you give me a simple example of how a physical property might be related to the bonding energy? End of lecture 1

Types of chemical bonds found in solids Bonding in Solids 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!!!

IONIC BONDING • Occurs between + and - ions. • Requires electron transfer. • Large difference in electronegativity required. • Example: NaCl 8

Ionic bonding Prototype example – sodium chloride (NaCl) Bonding in Solids 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 bonding – few other points Bonding in Solids Ionic bonding – few other points 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 End of lecture 1

EXAMPLES: IONIC BONDING • Predominant bonding in Ceramics Give up electrons Acquire electrons 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. 9

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. Adapted from Fig. 2.10, Callister 6e. 10

Bonding in Solids Covalent bonding Saw this in general chemistry (Molecular orbital theory) Sharing of electrons between adjacent atoms Most nonmetallic elements and molecules containing dissimilar elements have covalent bonds Polymers! Here bonding is highly directional! Number of covalent bonds possible is determined by the number of valence electrons Typically is 8 – N, where N is the number of valence electrons Work? Carbon has 4 valence e’s – 4 bonds (ok!) Read p 24 – I am assuming you are already very familiar with covalent bonds End of lecture 1

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

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

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 You can guess which type of matter exhibits this type of bonding Simple idea: 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 ER) Metallic bonding is also non-directional Free electrons also act to hold structure together Wide range of bonding energies, typically good conductors (why?) End of lecture 1

SECONDARY BONDING Arises from interaction between dipoles • Fluctuating dipoles Adapted from Fig. 2.13, Callister 6e. • Permanent dipoles-molecule induced Adapted from Fig. 2.14, Callister 6e. -general case: -ex: liquid HCl Adapted from Fig. 2.14, Callister 6e. -ex: polymer 13

Secondary (van der Waals), physical bonding Bonding in Solids Secondary (van der Waals), physical bonding Hallmark of this: interactions are much weaker (~10 kJ/mol) as compared to chemical bonds (> 100 kJ/mol) Secondary bonding is almost always present Secondary bonding is a consequence of atomic/molecular dipoles What is a dipole? Electric dipole exists whenever there is a separation of positive and negative charges These dipoles can interact with one another Hydrogen bonding is another type of secondary bonding End of lecture 1

Dipoles Fluctuation induced dipoles Bonding in Solids Even molecules/atoms that symmetrically charged can have dipoles Why? Displacements of electron cloud can lead to short-lived asymmetries Very weak interaction (liquefaction of inerts, diatomics) End of lecture 1

Dipoles Polar molecule induced dipoles Bonding in Solids Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H2O, HCl) These molecules can induce dipoles in adjacent, non-polar molecules Interaction stronger than fluctuating dipoles End of lecture 1

Permanent dipoles (hydrogen bonds) Bonding in Solids Permanent dipoles (hydrogen bonds) Van der Waals interactions between polar molecules Best known example – hydrogen bonding See picture below These interactions are fairly strong, very complex, and surprisingly not well understood! End of lecture 1

SUMMARY: BONDING Type Bond Energy Comments Ionic Large! Nondirectional (ceramics) Variable Directional Covalent large-Diamond semiconductors, ceramics small-Bismuth polymer chains) Variable Metallic large-Tungsten Nondirectional (metals) small-Mercury Directional Secondary smallest inter-chain (polymer) inter-molecular 14

PROPERTIES FROM BONDING: TM • Bond length, r • Melting Temperature, Tm • Bond energy, Eo Tm is larger if Eo is larger. 15

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

PROPERTIES FROM BONDING: a • Coefficient of thermal expansion, a • a ~ symmetry at ro a is larger if Eo is smaller. 17

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 T small E large a (Covalent & Secondary): 18

ANNOUNCEMENTS Reading: All Chapter 2