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

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

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 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 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 12 C Atomic wt = wt of x molecules or atoms 1 amu/atom = 1g/mol C H etc. } 1.67 x kg Atomic Weight is rarely a whole number – it is a weighted average of all of the natural isotopes of an “Element” ( x kg)

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: 1)Chemical 2)Electrical 3)Thermal 4)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) m l = magnetic1(s), 3(p), 5(d), 7(f) m s = spin½, -½

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

More exhaustively:

Why? Valence (outer) shell usually not filled completely so the electrons can ‘move out’! For Most elements: This Electron configuration not stable. SURVEY OF ELEMENTS Electron configuration (stable)... 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 6 (stable)... 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 6 3d3d 10 4s4s 2 4p4p 6 (stable) Atomic # Element 1s1s 1 1Hydrogen 1s1s 2 2Helium 1s1s 2 2s2s 1 3Lithium 1s1s 2 2s2s 2 4Beryllium 1s1s 2 2s2s 2 2p2p 1 5Boron 1s1s 2 2s2s 2 2p2p 2 6Carbon... 1s1s 2 2s2s 2 2p2p 6 (stable) 10Neon 1s1s 2 2s2s 2 2p2p 6 3s3s 1 11Sodium 1s1s 2 2s2s 2 2p2p 6 3s3s 2 12Magnesium 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 1 13Aluminum... Argon... Krypton Adapted from Table 2.2, Callister 7e.

Lets Try one: Here we have Iron ‘Fe’ (w/ Atomic Number 26) ex: Fe - atomic # = 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

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) 1s 2 2s 2 2p 2 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 1eaccept 2e O Se Te PoAt I Br He Ne Ar Kr Xe Rn F ClS LiBe H NaMg BaCs RaFr CaKSc SrRbY 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: F N = F A + F R and at some equilibrium (stable) bond location of separation, F N = 0 or F A = F R  From Physics we like to talk about bonding energy where:

Bonding Energy  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 7e. n is 7-9 for most ionic pairs Equilibrium separation (r 0 ) is about.3 nm for many atoms

Here: A, B and n are “material constants” r A n r B E N = E A + E R = 

Figure 2.7 Net bonding force curve for a Na + −Cl − pair showing an equilibrium bond length of a 0 = 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 = r 0 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 E 0 versus r 0 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: 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] Note: after exchange we have a stable (albeit ionic) electron structure for both Mg & O!

Predominant bonding in Ceramics 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. Examples: Ionic Bonding Give up electronsAcquire electrons NaCl MgO 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, ‘r 0 ’ 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  similar electronegativity  share electrons  bonds determined by valence – s & p orbitals dominate bonding  Example: 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. shared electrons from carbon atom shared electrons from hydrogen atoms H H H 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. The bond angle is °.

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

Primary Bonding Ionic-Covalent Mixed Bonding % ionic character = where X A & X B are ‘Pauling’ electronegativities %)100( x Ex: MgOX Mg = 1.2 X O = 3.5

“Electro-negativity” Values for determining Io vs. Co Bond Character Give up electronsAcquire electrons

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.

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

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

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

Coefficient of thermal expansion,   ~ symmetry 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 larger  smaller  Energy unstretched length EoEo EoEo

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