ME 330 Engineering Materials Lecture 4 Atomic Structure and Interatomic Bonding Chemistry review Interatomic bonding in solids Crystalline vs. Amorphous Crystals and crystallographic planes Read Chapters 2 and 3

Why Atomic Structure? Atomic level structure can strongly influence material performance –Modulus, melting point, coefficient of expansion all depend on interatomic forces Will now demonstrate how to understand properties based on bonding potentials Different bond types have different potentials Constructionist approach –Look at most basic level to begin our understanding –Today we’ll look (in detail) at: How atoms pack together How atoms bond together See how these effect macroscopic properties

ATOMIC STRUCTURE AND BONDING Why study it? Carbon (Diamond & Graphite) Many properties of materials depend on (i)bonds between atoms (ii)atomic packing (arrangement) NUCLEUS = PROTONS + NEUTRONS + ELECTRONS ( = no. of protons for neutrality) ATOM Protons: + charge, neutrons: neutral charge, electrons: negative charge

Quantum mechanics – establishment of a set of principles and laws that govern systems of atomic and subatomic entities. Models of atomic behavior: Bohr atomic model – electrons revolve around atomic nucleus in discrete orbitals. Wave-mechanical model – electron exhibits both wave-like and particle-like behavior. Position of electron is defined by probability of electron’s being at various locations around nucleus.

Nucleus  m. diameter surrounded by electron cloud. Atomic diameter  m ~ 99.98% of mass is in nucleus & most of volume is electron cloud. Bohr atomic model – electrons are assumed to revolve around nucleus in discrete orbitals

Electrons in ORBITALS or shells, characterized by four QUANTUM numbers – Size (K,L,M…) (shells; specified by a principal quantum number n=1,2,3,…) - Shape (s,p,d,f) (subshells – different shapes of electron orbits in a shell; second quantum numbers) - Spatial orientation (ml) (number of energy states for each subshell; third quantum number) - Spin (ms) (spin moment, oriented either up or down; fourth quantum number) See Table 2.1

Outermost shell contains VALENCE electrons (bonding, chemical, electrical and thermal properties). These are of most importance to us. If outer shell is complete, i.e. the S & P orbitals are full (S 2 P 6 = 8 electrons) then element is very stable and very un-reactive - Noble gases (helium, neon, argon, krypton). Some other elements gain or lose electrons to try and attain this stable configuration through bonding. Note: s, p, d, f subshells can accommodate the total of 2, 6, 10, and 14 electrons, respectively

Why? Valence (outer) shell usually not filled completely. Most elements: Electron configuration not stable. SURVEY OF ELEMENTS

PERIODIC TABLE Table of elements (types of atoms) Atomic Number - number of protons Hydrogen 1 proton Helium 2 “ etc. Atomic Mass - relative atomic mass - mass of x atoms of that element (6.023 x of something is 1 mole) 1 mole of aluminium atoms (i.e x atoms) has a mass of g etc.

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

Most elements in Periodic Table are METALS. e.g. Mg, Zn, Fe, Ti, Pd. Few gases and non-metals and some in between. CERAMICS are usually compounds based on mixtures of elements Cr 2 O 3, Al 2 O 3, Si 3 N 4, SiC. POLYMERS are usually based on CARBON chains / networks. Sizes of atoms can be important, i.e. Diffusion in Solids. ELECTROPOSITIVE -metallic elements give up outer electrons to form positive ions CATIONS Mg  Mg e -

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

ATOMIC BONDING ATOMS bond to each other to reduce their overall energy, i.e. to become more stable. Everything tends towards a state of lower free energy. Bonding Forces and Energies Inter-atomic spacing is caused by balance between REPULSIVE and ATTRACTIVE forces. Attractive force depends on type of bond trying to form between atoms; Repulsive force occurs when atoms get close together. Net force between atoms is balance of two forces and depends on inter-atomic distance.

F N = F A + F R F N = 0 when F A = F R F N : net force

F N = F A + F R Equilibrium is reached when: F A + F R = 0 Atoms happily sit this distance apart (r 0 ) (often r o  0.3nm) Also considered in energy terms: E N = E A + E R In this case, equilibrium is reached when overall energy is a minimum. Bonding energy, E 0 (binding energy) is the energy required to break the bond (separate two atoms). Higher bonding energy  Stronger bonds  higher strength & Melting point, (T m ) Also Stiffness (slope (dF/dr) at r 0 and thermal expansion (trough of E curve)

PRIMARY ATOMIC BONDS (Chemical) - STRONG IONIC COVALENT METALLIC SECONDARY BONDS (Physical) - WEAK Van Der Waals bonds/forces Fluctuating + permanent dipoles

IONIC BONDS Form between electropositive (metallic) and electronegative (non-metallic) elements, eg. CERAMICS NaCl, Al 2 O 3,MgO Na looses outer electron to be more stable  Na +. Chlorine accepts extra electron to be more stable  Cl - (Note: there is a size change when atoms form ions.) After such a transfer, the chlorine atom has net negative charge, while sodium atom has net positive charge. In sodium chloride (NaCl), all sodium and chloride atoms exist as ions.

IONIC BONDS (cont) Form between electropositive (metallic) and electronegative (non-metallic) elements, Na loses outer electron to be more stable  Na +. Chlorine accepts extra electron to be more stable  Cl - Opposite charges attract so get: ELECTROSTATIC (coulombic) BONDING E A = Attractive energy, E R = Repulsive energy, A, B and n are constants that depend on system (n  8).

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

Example: NaCl

Ionic Bonding Na + Cl - Ions Ionic Bond NaCl NaCl Atomic Structure Metal Nonmetal

Notes on Ionic Bonding To be stable, all positive ions must be near negative ions Bond strength is equal in all directions (nondirectional) Energy considerations –Coulombic attractive force –Repulsive force: Generally, very high bonding energies Typically hard, brittle, thermally and electrically insulative Ceramics Cl - Na + Cl - Na + Cl - Separate Ions Atoms 0 r Energy  (r) “Stable” Electrostatic Attraction Repulsion Curve

Predominant bonding in Ceramics Give up electronsAcquire electrons EXAMPLES: IONIC BONDING

NON-DIRECTIONAL, electrical neutrality is most important. IONS pack to maintain neutrality. Eg. For NaCl For each Na + ion there must also be a Cl - ion. Likewise, for MgCl 2 there must be two Chlorine ions for every magnesium ion. Ionic bonds tend to be strong bonds - high bonding energy. (Table 2.3) Ceramics are usually ionically bonded and have high melting points, high hardness, brittle and electrically and thermally insulative (atoms and electrons cannot move easily).

COVALENT BONDING Atoms SHARE outer electrons with each other to attain noble gas electron configurations. Atoms close to each other in periodic table and in electronegativities (X) tend to form covalent bonds Covalent bonds do not distort very easily - so can be very strong (Diamond) but appear in "weak" materials as well (polyethylene - covalently bonded carbon chain) Some materials show mixed Ionic/Covalent bonding. X A, X B electronegativities for respective elements

Requires shared electrons Example: CH 4 C: has 4 valence e, needs 4 more H: has 1 valence e, needs 1 more Electronegativities are comparable. COVALENT BONDING Because atoms in covalent bonds have to share electrons with other atoms, Direction is very important. DIRECTIONAL BONDING e.g. DIAMOND

Covalent Bonding Two atoms share electrons - extra electron belongs to both Bonding is directional - between atoms being bonded Many interatomic bonds are partially ionic and covalent –Wider separation in periodic table  more ionic Ceramics, Metals, Polymer backbones CH 4 H C HH H ClCl 2

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

Covalent Potential Widely variable properties –Diamond Hardest substance known Very stiff, strong T melt = 3550 ºC –Bismuth Very soft Weak T melt = 270 ºC –Based on m & n Atoms Electron Overlap Attraction Repulsion Curve 0 r Energy  (r)

METALLIC BONDING- Found in metals and alloys. Atoms of metal pack relatively closely together in ordered arrangement - Ion cores Valence electrons form "sea" in between cores - "electron gas or cloud" These electrons can move/drift - thermal/electrical conduction. FREE electrons. Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).

Primary bond for metals and their alloys METALLIC BONDING Non-directional Not many restrictions on metallic bond (no charge neutrality - ionic, or electron-pair sharing - covalent) so if metal deformed, atom positions can move relatively large amounts without breaking bonds. (Ductility) Bonding energies affect melting points and vary from low (-39  C) to high (3410  C) values.

Metallic Bonding Ion Cores (M + )- net positive charge equal to total valence Valence electrons (e - ) drift through metal in “electron cloud” –Electrically shield ion cores –Physically hold cores together Nondirectional bond Metallic bonding potential similar to covalent (use same eqn.) Wide variety of bonding energies and hence properties Excellent conductors due to mobility of electron cloud Metals and metallic alloys M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+ M+M+

SECONDARY BONDING - Van Der Waal's forces (in biological systems) Low energy - weak bonds kJmol -1 (Primary 100  1500 kJmol -1 ) Based on DIPOLES When -ve and +ve charges are separated, an electric dipole moment is set up. FLUCTUATING INDUCED DIPOLE BONDS Asymmetrical distribution of electron cloud (vibrations etc) e.g. noble gases - boiling, melting.

Van der Waals Bonding Sometimes called physical bonds to contrast with chemical (primary) Much lower energy than primary bonds Arise from electric dipoles - –Separation of + and - portions of atom - much weaker than ions –Bonding from attraction of + from one dipole to - of other dipole Hydrogen bonding is special case when hydrogen is present –Strongest secondary bonding type Polymeric interchain bonds O HH O HH O HH

POLAR MOLECULE-INDUCED DIPOLE BONDS Asymmetric charge distribution in some molecules (polar) Eg. HCl molecule. Can attract non-polar molecules. PERMANENT DIPOLE BONDS Van der Waals forces will also exist between adjacent polar molecules. H-F, H-O and H-N bonds Hydrogen end becomes very +ve. One of strongest secondary bonds. eg. H 2 O. (Hydrogen bonding - Reason for high boiling point of water.) Also between carbon chains in polymeric materials.

Permanent dipoles-molecule induced Fluctuating dipoles -general case: -ex: liquid HCl -ex: polymer

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

Elastic modulus, E E ~ curvature at r o E is larger if E o is larger. PROPERTIES FROM BONDING: E

Coefficient of thermal expansion,   ~ symmetry at r o  is larger if E o is smaller. PROPERTIES FROM BONDING: 

Ceramics (Ionic & covalent bonding): Metals (Metallic bonding): Polymers (Covalent & Secondary): Large bond energy large T m large E small  Variable bond energy moderate T m moderate E moderate  Directional Properties Secondary bonding dominates small T small E large  SUMMARY: PRIMARY BONDS

Summary - Atomic Bonding in Solids Primary –Ionic –Covalent –Metallic Secondary –Van der Waals –Hydrogen Interatomic potential energies –Function of separation, r –Attractive - depends on bond –Repulsive - atomic scale overlap Bonding energy (E o ) is strongly dependent on bond type –Effect on modulus ??? –Effect on thermal expansion ??? Energy  (r) roro Force r EoEo

Atomistic Origins of Properties Force F(r) Atomic separation, r r Energy  (r) Modulus –Proportional to slope of force-separation curve at equilibrium separation distance Melting Temperature –Large E o leads to high T melt Coefficient of thermal expansion –Large E o leads to small  –Deep narrow trough forces large energy change for small dimensional change E0E0

Potentials & Properties From Callister, p. 22 Relative differences in potential curves Assumes  &  are 1 - comparitive purposes only!

Crystalline: –3-D arrangement of atoms in which every atom has the same geometrical arrangement of neighbors –Long-range, periodic array over large length scales –Most solids are crystalline (metals, most ceramics, some polymers) Amorphous –Arrangement over which no long range order exists –Often clear - not enough order to diffract light –Rarely purely amorphous - have regions of crystallinity –Many polymers and some ceramics Atomic Packing

Crystal Structure Definitions Unit cell: Smallest repeating unit of the crystal. Lattice: 3–D framework of a crystal where atoms are located Lattice parameters: Dimensions (a,b,c) and angles ( , ,  ) of the lattice b c a   

Bravais Lattices French Crystallographer Bravais (1848) 7 crystal systems using primitive unit cells Primitive - one lattice point at origin 14 distinguishable point lattices –P - simple –F - face centered –I - body centered –C - base centered For now, interested in BCC, FCC, HCP –Metallic crystal structures –Metallic bond is non-directional –No restriction on nearest neighbors –Very dense packing First need to collect some definitions BCC FCC HCP CubicHexagonal Rhombohedral Tetragonal Orthorhomic Triclinic Monoclinic

Determining direction indices –Start vector at crystal axis –Draw to any point in the 3-D crystal –Project vector on each xyz axes measure a in x-direction measure b in y-direction measure c in z-direction –Multiply by common factor to achieve smallest integer value –Enclose in [ ] without commas Negative directions indicated with - Family of directions indicated by Hexagonal crystals have 4 indices x [100] y [010] z [001] In a cubic crystal, are all in the family. a = 1 b = ½ c = 0 [210] [110] [111] Crystallographic Directions

Crystallographic Planes Determining Miller indices –Look at plane in unit cell which does not pass through the origin –Determine length of planar intercept with each axes (again, a,b,c) –Take reciprocal of a,b,c –Reduce to smallest integer value –Enclose in ( ) without commas Any parallel planes are equivalent x [100] y [010] z [001] a = 1 c = 1/3 b = 1/2 (123) z x y z x z (012)