: Atomic Systems and Bonding : R. R. Lindeke, Ph.D. ME 2105– Lecture Series 2

ISSUES TO ADDRESS... The Structure of Matter What Promotes Bonding? A Quick Review from chemistry What Promotes Bonding? What type of Bonding is Possible? What Properties are Inferred from Bonding?

Their FINAL PROPERTIES Just as before: How the atoms are arranged & how they bond GREATLY AFFECTS Their FINAL PROPERTIES & therefore use ATOMIC Structure Electron configurations Primary & secondary BONDING

Structure of Matter: Atoms are the smallest particle in Nature that exhibits the characteristics of a substance The radius of a typical atom is on the order of 0. 0.0000000001 meter and cannot be studied without very powerful microscopes Pictured here is an “Electron Microscope” It can greatly magnify materials but can’t resolve individual atom – we need a TEM or STP for that

Structure of Matter: A molecule consists of 2 or more atoms bound together In a common glass of water “upon closer examination” we would find a huge number of Water “Molecules” consisting of 1 atom of Oxygen and 2 atoms of hydrogen

Atomic Structure (Freshman Chem.) atom – electrons – 9.11 x 10-31 kg  protons neutrons atomic number = # of protons in nucleus of atom = # of electrons of neutral species   A [=] atomic mass unit = amu = 1/12 mass of 12C   Atomic wt = wt of 6.023 x 1023 molecules or atoms   1 amu/atom = 1g/mol C 12.011 H 1.008 etc. (.000911x 10-27 kg) } 1.67 x 10-27 kg Atomic Weight is rarely a whole number – it is a weighted average of all of the natural isotopes of an “Element”

What is this in weight or mass in “Real Terms” Example 1:

What is this in weight or mass in “Real Terms”

Structure of Matter – an Element Any material that is composed of only one type of atom is called a chemical element, a basic element, or just an element. Every element has a unique atomic structure. Scientists know of only about 109 basic elements at this time. (This number has a habit of changing!) All matter is composed of combinations of one or more of these elements. Ninety-one of these basic elements occur naturally on or in the Earth (Hydrogen to Uraninum). These elements are pictured in the “Periodic Table”

The Periodic Table of the Elements

Structure of Matter Each of the “boxes” in the periodic table help us to understand the details of a given elements Here we see atomic Number (# of Electrons or Protons) and Atomic Weight Some tables provide information about an elements “Valance State” or the ability to gain or shed their outermost electrons when they form molecules or “Compounds”

Structure of Matter These outermost or Valence electrons determine all of the following properties concerning an element: Chemical Electrical Thermal Optical

Schematic Image of Atoms: Atomic number is 29

Electronic Structure Electrons have wavelike and particulate properties. This means that electrons exist in orbitals defined by a probability. – Boer coupled w/ Schrödinger models Each orbital is located at a discrete energy level determined by quantum numbers. Quantum # Designation n = principal (energy level/shell) K, L, M, N, O (1, 2, 3, etc.) l = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1) ml = magnetic 1(s), 3(p), 5(d), 7(f) ms = spin ½, -½

Electron Energy States • have discrete energy states • tend to occupy lowest available energy state. 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 Can hold up to 32 electrons Can hold up to 18 Electrons Can hold up to 8 electrons Can hold up to 2 electrons Adapted from Fig. 2.4, Callister 7e.

More exhaustively:

SURVEY OF ELEMENTS • For Most elements: This Electron configuration not stable. Electron configuration (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 • Why? Valence (outer) shell usually not filled completely so the electrons can ‘move out’!

Lets Try one: Here we have Iron ‘Fe’ (w/ Atomic Number 26) ex: Fe - atomic # = 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 1s2 2s2 2p6 3s2 3p6 3d 6 4s2

Electron Configurations Valence electrons – those in unfilled shells Filled shells are 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

Matter (or elements) Bond as a result of their Valance states give up 1e give up 2e give up 3e 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.

Molecular/Elemental Bonding Bonding is the result of the balance of the force of attraction and the force of repulsion of the electric nature of atoms (ions) Net Force between atoms: FN = FA + FR and at some equilibrium (stable) bond location of separation, FN = 0 or FA = FR From Physics we like to talk about bonding energy where:

Bonding Energy r A B EN = EA + ER = Equilibrium separation (r0) is about .3 nm for many atoms 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 n is 7-9 for most ionic pairs

Here: A, B and n are “material constants” EN = EA + ER = -

Figure 2.7 Net bonding force curve for a Na+−Cl− pair showing an equilibrium bond length of a0 = 0.28 nm.

Bonding Energy, the Curve Shape, and Bonding Type Properties depend on shape, bonding type and values of curves: they vary for different materials. Bonding energy (minimum on curve) is the energy that would be required to separate the two atoms to an infinite separation. Modulus of elasticity depends on energy (force) versus distance curve: the slope at r = r0 position on the curve will be quite steep for very stiff materials, slopes are shallower for more flexible materials. Coefficient of thermal expansion depends on E0 versus r0 curve: a deep and narrow trough correlates with a low coefficient of thermal expansion

Bonding Types of Interest: Ionic Bonding: Based on donation and acceptance of valance electrons between elements to create strong “ions” – CaIONs and AnIONs due to large electro-negativity differences Covalent Bonding: Based on the ‘sharing’ of valance electrons due to small electro negativity differences Metallic Bonding: All free electrons act as a moving ‘cloud’ or ‘sea’ to keep charged ion cores from flying apart in their ‘stable’ structure secondary bonding: van der wahl’s attractive forces between molecules (with + to – ‘ends’) This system of attraction takes place without valance electron participation in the whole Valence Electrons participate in the bonding to build the molecules not in ‘gluing’ the molecules together

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] Note: after exchange we have a stable (albeit ionic) electron structure for both Mg & O!

Examples: Ionic Bonding • Predominant bonding in Ceramics NaCl MgO Give up electrons Acquire electrons CaF 2 CsCl

Ionic Bonding – a Closely held Structure of +Ions and –Ions (after this Valence exchange) These structure a held together by Coulombic Bonding forces after the Atoms exchange Valance Electrons to form the stable ionic cores: It the solid state these ionic cores will sit at highly structured “Crystallographic Sites” We can compute the coulombic forces holding the ions together – it is a balance between attraction force (energy) due to the ionic charge and repulsion force (energy) due to the nuclear cores of the ions These forces of attraction and repulsion compete and will achieve a energy minimum at some inter-ion spacing

Figure 2.10 Formation of an ionic bond note effect of ionization on atomic radius. The cation (Na+) becomes smaller than the neutral atom, while the anion (Cl−) becomes larger than the neutral atom

Example: Using these energy issues Here, ‘r0’ equals the sum of the ionic radii of each and represents the r in the energy balance equations!

Another Example (working backward with Coulomb’s Law):

The largest number of ions of radius R that can coordinate an atom of radius r is 3 when the radius ratio r/R = 0.2. (Note: The instability for CN = 4 can be reduced, but not eliminated, by allowing a three-dimensional, rather than a coplanar, stacking of the larger ions.) – to keep the ionic characteristic in balance!

The minimum radius ratio, r/R, that can produce threefold coordination is 0.155

Covalent Bonding CH 4 C: has 4 valence e-, needs 4 more similar electronegativity  share electrons bonds determined by valence – s & p orbitals dominate bonding 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 7e. shared electrons from carbon atom from hydrogen atoms H C CH 4

Three-dimensional structure of bonding in the covalent solid, carbon (diamond). Each carbon atom (C) has four covalent bonds to four other carbon atoms. Note, the bond-line schematic of covalent bonding is given a perspective view to emphasize the spatial arrangement of bonded carbon atoms.

Tetrahedral configuration of covalent bonds with carbon Tetrahedral configuration of covalent bonds with carbon. The bond angle is 109.5°.

During Polymerization, We break up one “double bond” (must supply 162 kcal/mole) and add two single bonds (releases 2*88 = 176 kcal/mole) which requires a catalyst to start but will be self-sustaining (releasing heat!) once the process begins

“Electro-negativity” Values for determining Ionic vs “Electro-negativity” Values for determining Ionic vs. Covalent Bond Character Give up electrons Acquire electrons

Primary Bonding %) 100 ( x Ex: MgO XMg = 1.2 XO = 3.5 Ionic-Covalent Mixed Bonding % ionic character =   where XA & XB are ‘Pauling’ electronegativities %) 100 ( x Ex: MgO XMg = 1.2 XO = 3.5

Metallic Bonding: In a metallic bonded material, the valence electrons are “shared” among all of the ionic cores in the structure not just with nearest neighbors!

Considering Copper: It valance electrons are far from the nucleus and thus are not too tightly bound (making it easier to ‘move out’) outside shell had only one electron When the valence electron in any atom gains sufficient energy from some outside force, it can break away from the parent atom and become what is called a free electron Atoms with few electrons in their valence shell tend to have more free electrons since these valence electrons are more loosely bound to the nucleus. In some materials like copper, the electrons are so loosely held by the atom and so close to the neighboring atoms that it is difficult to determine which electron belongs to which atom! Under normal conditions the movement of the electrons is truly random, meaning they are moving in all directions by the same amount. However, if some outside force acts upon the material, this flow of electrons can be directed through materials and this flow is called electrical current in a conductor.

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

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

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

Summary: Primary Bonds Large bond energy large Tm large E small a Ceramics (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