Material Science - CEEM110/MEC281 - 2nd Edition 2023

Atomic Structure & Interatomic Bonding

All matter is made up of tiny particles called atoms.
Scientists use models to understand atoms because they are too small to be seen, even with powerful microscopes.
The model includes:
- Nucleon or Nucleus
- Shell
- Electron

What does an ATOM look like?

Atoms are made of a nucleus (protons + neutrons) and electrons that orbit the nucleus in shells.
Particles' properties:
- Proton: Positive (+ve) charge, located in the nucleus, mass of 1.0073 amu.
- Neutron: Neutral charge, located in the nucleus, mass of 1.0087 amu.
- Electron: Negative (-ve) charge, located in orbitals/shells/energy levels, mass of 0.000549 amu.
Atomic mass unit (amu) is used to describe the mass of an atom.
The number of protons, neutrons, and electrons determines an atom's properties.

Why are all ATOMS electrically neutral?

Most atoms are electrically neutral, having an equal number of protons and electrons.
Positive and negative charges cancel each other out.

ION

If an atom gains or loses electrons, it becomes electrically charged and is called an ION.
CATION: Ion with a positive charge (loses electrons).
- Cations are smaller than their parent atoms due to less electron-electron repulsion.
ANION: Ion with a negative charge (gains electrons).
- Anions are larger than their parent atoms because of more electron-electron repulsion.

PERIODIC TABLE (P.T.)

Arrangement of elements in order of atomic number.
Elements with similar properties are in the same group.
Basics of the Periodic Table:
- Periods: Horizontal rows (designate electron energy levels).
- Groups or Families: Vertical columns.

ATOMIC NUMBER and ATOMIC MASS

Atom described by:
- Atomic Number (Z) = number of protons.
- Atomic Mass (A) = number of protons (Z) + number of neutrons (N).

ISOTOPES

Atoms with the same number of protons but different numbers of neutrons.
Atoms with the same atomic number but different atomic mass.
Example: Hydrogen has 3 isotopes:
- Hydrogen 1 (hydrogen): 1 proton, 0 neutrons, atomic mass 1.
- Hydrogen 2 (deuterium): 1 proton, 1 neutron, atomic mass 2.
- Hydrogen 3 (tritium): 1 proton, 2 neutrons, atomic mass 3.

ELECTRON SHELLS

Electron cloud divided into 7 shells (energy levels): K, L, M, N, O, P, Q.
Each shell holds a limited number of electrons.
- K (2 electrons), L (8 electrons), M (18 electrons), N (32 electrons).
Maximum number of electrons in a shell: Electron Capacity = $2n^2$

ORBITAL

Electrons occupy subshells (energy sublevels) within each shell: s, p, d, f, g, h, i.
- Each subshell holds different types of orbitals.
- Each orbital holds a maximum of 2 electrons.
- Each orbital has a characteristic energy state and shape.
  - s-orbital: Spherical shape, closest to the nucleus, max 2 electrons.
  - p-orbital: Dumbbell shape, 3 distinct p-orbitals (px, py, pz), max 6 electrons.
  - d-orbital: 5 distinct d-orbitals, max 10 electrons.

ELECTRON CONFIGURATIONS

Electron configuration: arrangement of electrons around the nucleus.
Representation:
- $1s^2$
- Energy level (Principal quantum number).
- Orbital.
- Number of electrons in the orbital.
Aufbau principle: electrons enter orbitals of lowest energy first.

Transition Element

Cr [Z = 24]: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5$ (correct – half filled)
Mo [Z = 42]: …5s1 4d5 (correct – half filled)
Cu [Z = 29]: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}$ (correct – completely filled)
Ag [Z = 47]: …5s1 4d10 (correct – completely filled)
Au [Z = 79]: …6s1 5d10 (correct – completely filled)

INTERATOMIC BONDING

Forces of attraction that hold atoms together are either:
- Primary Interatomic Bonding
  - Metallic, ionic, and covalent.
- Secondary Atomic Bonding
  - Van der Waals.
Chemical reactions involve releasing/receiving or sharing electrons.

1) IONIC BONDING

Found in compounds of electropositive (metals) and electronegative elements (non-metals).
Electrons are transferred to form a bond.
Large difference in electronegativity required.
Properties:
- Solid at room temperature (made of ions).
- High melting and boiling points.
- Hard and brittle.
- Poor conductors of electricity in solid state.
- Good conductors in solution or when molten.
Predominant bonding in Ceramics.
Example: NaCl, CsCl, MgO, CaF2

2) COVALENT BONDING

Electrons are shared to form a bond.
Occurs between atoms with similar electronegativities.
Found in:
- Molecules with nonmetals.
- Molecules with metals and nonmetals (Aluminum phosphide (AlP)).
- Elemental solids (diamond; C, silicon; Si, germanium; Ge).
- Compound solids (about column IVA) – (gallium arsenide - GaAs, indium antimonide - InSb and silicone carbide - SiC).
- Nonmetallic elemental molecules ( $H2, Cl2, F_2$ etc).
Properties:
- Gases, liquids, or solids (made of molecules).
- Poor electrical conductors in all phases.
- Variable properties (hardness, strength, melting temperature, boiling point).

3) METALLIC BONDING

Electrons in the valence shell separate and exist in a cloud surrounding positively charged atoms.
Valence electrons form a ‘sea of electrons’.
Found for group IA and IIA elements.
Found for all elemental metals and their alloys.
Properties:
- Good electrical conductivity.
- Good heat conductivity.
- Ductile.
- Opaque.

SECONDARY INTERATOMIC BONDING - VAN DER WAALS

Arises from atomic or molecular dipoles.
Three hydrogen bonding mechanism:
- Fluctuating Induced Dipole Bonds
 - Eg: Inert gases, symmetric molecules ( $H2, Cl2$ )
- Polar molecule-Induced Dipole Bonds
 - Asymmetrical molecules such as HCl
- Permanent Dipole Bonds
 - Hydrogen bonding
 - Between molecules.
 - H-F, H-O, H-N
Molecule is considered the smallest particle of a pure chemical substance that still retains its composition and chemical properties.
Most common molecules are bound together by strong covalent bonds.
E.g. : $F2, O2, H_2$ .
Smallest molecule : Hydrogen molecule .

Summary of BONDING

Directional bonding – Strength of bond is not equal in all directions.
Nondirectional bonding – Strength of bond is equal in all directions.
Type, Bond energy, Melting point, Hardness, Conductivity, Comments.
Ionic bonding, Large (150-370kcal/mol), Very high, Hard & brittle, Poor (required moving ion), Nondirectional (ceramic).
Covalent bonding, Variable (75-300 kcal/mol), Large -Diamond Small – Bismuth, Variable Highest – diamond (>3550) Mercury (-39), Very hard (diamond), Poor, Directional (Semiconductors, ceramic, polymer chains).
Metallic bonding, Variable (25-200 kcal/mol), Large- Tungsten Small- Mercury, Low to high Soft to hard Excellent Nondirectional (metal).
Secondary bonding, Smallest, Low to moderate, Fairly soft, Poor, Directional inter-chain (polymer) inter-molecular.
Ceramics (Ionic & covalent bonding): Large bond energy large Tm large E small $alpha$ .
Metals (Metallic bonding): Variable bond energy moderate Tm moderate E moderate $alpha$ .
Polymers (Covalent & Secondary): Secondary bonding dominates small T small E large $alpha$ .

CRYSTAL STRUCTURES, APF & DENSITY COMPUTATION

CRYSTAL STRUCTURE

Crystalline Material: atoms pack in periodic, 3D arrays (metals, many ceramics, some polymers).
Non-crystalline Material (Amorphous): atoms have no periodic packing (complex structures, rapid cooling).
Single Crystal.
Polycrystal: comprised of many single crystal or grain.

Structure of SOLID

Amorphous: Atoms are disordered, no lattice.
Crystal: All atoms arranged on a common lattice.
Polycrystalline: Different lattice orientation for each grain.

Lattice, Unit Cell, Crystal Structure

Crystal Structure = Lattice + Motif.
Lattice: The three-dimensional array formed by the unit cells of a crystal.
Unit Cell: smallest unit that demonstrates the full symmetry of a crystal.. + =.
Crystal structure may be present with any of the four types of atomic bonding.
The atoms in a crystal structure are arranged along crystallographic planes designated by Miller indices.
The crystallographic planes and Miller indices are identified by X-ray diffraction.

BRAVAIS LATTICE - Describe the geometric arrangement of the lattice points.

CRYSTAL SYSTEM AND CRYSTALLOGRAPHY

Cubic, hexagonal, tetragonal, rhombodhedral, orthorhombic, monoclinic, triclinic.

7 crystal systems.
14 Bravais lattices (by adding additional lattice point to 7 basic crystal systems).

Crystal Structure of Metals

Simple Cubic (SC) - Manganese
Body-centered cubic (BCC) - alpha iron, chromium, molybdenum, tantalum, tungsten, and vanadium.
Face-centered cubic (FCC) - gamma iron, aluminum, copper, nickel, lead, silver, gold and platinum.

SIMPLE CUBIC (SC)

Atoms lie on a grid: layers of rows and columns sitting at the corners of stacked cubes.
Number of atoms at corner = 8 x 1/8 = 1 atom.
Total number of atoms in one unit cell = 1 atom.
Example: Manganese.

BODY CENTERED CUBIC STRUCTURE (BCC)

Cubic unit cell with 8 atoms located at the corner & single atom at cube center.
Example: Chromium, Tungsten, Molybdenum, Tantalum, Vanadium.
Number of atoms at corner = 8 x 1/8 = 1 atom
Number of atoms at center = 1 atom
Total Number of atoms in one unit cell = 2 atoms.

FACE CENTERED CUBIC STRUCTURE (FCC)

Atoms are located at each of the corners and the centers of all the cube faces.
Each corner atom is shared among 8 unit cells, face centered atom belong to 2.
Example : Cu,Al,Ag,Au, Ni, Pt.
Number of atoms at corner = 8 x 1/8 = 1 atom
Number of atoms at face = 6 x 1/2 = 3 atoms
Total Number of atoms in one unit cell = 4 atoms.

ATOMIC PACKING FACTOR

Atomic packing factor (APF) is defined as the efficiency of atomic arrangement in a unit cell.
Used to determine the most dense arrangement of atoms.
Atoms are assumed closely packed and treated as hard spheres.
$APF = "(no. of atoms, (n) x volume of atom in unit cell, (Vs)) / volume of unit cell, (Vc)"$
Simple cubic (SC): a = 2R, 1 atom, 52%.
BCC: a = $4R/[3]$ , 2 atoms, 68%.
FCC: a = $2R*[2]$ , 4 atoms, 74%.

DENSITY COMPUTATIONS

$rho = (nA) / (Vc NA)$
- $rho$ = density.
- n = number of atoms associated with each unit cell.
- A = atomic weight.
- Vc = volume of the unit cell/cube.
- $N_A$ = Avogadro’s number ( $6.023 x 10^{23}$ atoms/mol) – Fixed value.
- a = edge length / lattice parameter/lattice constant.

CRYSTALLOGRAPHIC POINT, DIRECTIONS & PLANES

MILLER INDICES

Used to label the planes and directions of atoms in a crystal.
Important to determine the shapes of single crystals, the interpretation of X-ray diffraction patterns, and the movement of a dislocation.
- Shapes of single crystals.
- The interpretation of X-ray diffraction patterns and the movement of a dislocation.
(h k l): specific crystal plane or face.
{h k l}: family of equivalent planes.
[h k l]: specific crystal direction.
: family of equivalent directions.

POINT COORDINATES

Position of any point located within a unit cell may be specified in terms of its coordinates (x, y, z).

MILLER INDICES OF A DIRECTION

Determine the length of the vector projection on each of the three axes.
Express these three numbers as the smallest integers; negative quantities are indicated with an overbar.
Label the direction [h k l].
Axis, X, Y, Z
Head (H), x2, y2, z2
Tail (T), x1, y1, z1
Head (H) – Tail (T), x2-x1, y2-y1, z2-z1
Reduction (if necessary)
Enclosed, [h k l]

MILLER INDICES OF A PLANE

Determine the points at which a given crystal plane intersects the three axes (a,0,0), (0,b,0), and (0,0,c). If the plane is parallel to an axis, it is given an intersection ∞.
Take the reciprocals of the three integers from step i).
Label the plane (hkl).
Express these three numbers as the smallest integers with negative quantities indicated with an overbar.
Axis, X, Y, Z
Interceptions
Reciprocals
Reduction (if necessary)
Enclosed (h k l)

NOTE (for plane and direction):

PLANE: Enclose in brackets (…) with no separating commas → (hkl).
DIRECTION: Enclose in brackets […] with no separating commas → [hkl].
FOR BOTH PLANE AND DIRECTION: Negative number should be written with overbar above integer. Eliminate fractions by multiplying by a common factor.

MECHANICAL PROPERTIES OF MATERIALS

PHYSICAL PROPERTIES OF METALS

Solid at room temperature (mercury is an exception).
Opaque.
Conducts heat and electricity.
Reflects light when polished.
Expands when heated, contracts when cooled.
Crystalline structure.
Responses of materials to forms of energy such as heat, light, electricity, and magnetism.

MECHANICAL PROPERTIES OF METALS

Dimensional changes in response to applied external or internal mechanical forces.

Tensile Test

Tensile stress, $"sigma = Ft/A0"$
- Ft = tensile force
- Ao = original area before loading
Engineering Strain, $"\varepsilon = \Delta L / L_o"$
- Stress is in N/m2 or lb/in2.
- Strain is dimensionless.

Stress-Strain Diagram

Elastic Region (Point 1 – 2):
- Material returns to its original shape after unloading.
- Stress is linearly proportional to strain:
  - $"\sigma=E\varepsilon"$
  - E = Elastic modulus (Young’s Modulus).
- Point 2: Yield Strength:
  - Permanent deformation occurs. Material doesn't return to original length.
Strain Hardening
- Reloading from Point 4 follows the same Elastic Modulus.
- Material now has a higher yield strength of Point 4.
- Raising yield strength by permanently straining the material is Strain Hardening.
Tensile Strength (Point 3)
- Largest value of stress on the diagram.
- Maximum stress a material can support without breaking.
Fracture (Point 5)
- Stress decreases as necking and non-uniform deformation occur.
- Fracture will finally occur at Point 5.

Important Properties from Tensile Test

Young's Modulus: Slope of the linear portion of the stress-strain curve.
Yield Strength: Value of stress at the yield point, calculated by plotting Young's modulus at a specified percent of offset (usually offset = 0.2%).
Ultimate Tensile Strength: Highest value of stress on the stress-strain curve.
Percent Elongation: Change in gauge length divided by the original gauge length.

Elastic Deformation

Atomic bonds are stretched but not broken.
Object returns to its original shape when forces are removed.
Elastic means reversible.

Plastic Deformation (Metals)

Atomic bonds are broken and new bonds are created.
Plastic means permanent.
Permanent deformation for metals is accomplished by slip, involving the motion of dislocations.
Structures are designed to ensure only elastic deformation results.
A structure that has plastically deformed may not function as intended.

Hardness

Measure of a material’s resistance to localized plastic deformation (a small dent or scratch).
Quantitative hardness techniques:
- Small indenter is forced into the surface of a material.
- Depth or size of the indentation is measured, and corresponds to a hardness number.
- Softer material, larger and deeper indentation and lower hardness number.
Overall bulk hardness of materials measured using loads >2 N.
Hardness Tester
Hardness of materials typically measured using loads less than 2 N using such test as Knoop (HK).
Hardness of materials measured at 1– 10 nm length scale using extremely small (~100 µN) forces.
Standard Hardness Conversion Tables for Metals relationship among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness.
*Hardness value in Vickers e.g.: 440HV30 (440 is the hardness number, HV gives the hardness scale (Vickers), 30 indicates the load used in kgf).

Correlation between Hardness and Tensile Strength

Both hardness and tensile strength are indicators of a metal’s resistance to plastic deformation.
For cast iron, steel, and brass, the two are roughly proportional.
Tensile strength (psi) = 500 * HBR.

Summary Mechanical Properties

Stress and strain: Size-independent measures of load and displacement, respectively.
Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G).
Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy.
Toughness: The energy needed to break a unit volume of material.
Ductility: The plastic strain at failure.

CHAPTER 2 - METALLIC MATERIALS

Terminology and Basic Concepts
- Solution.
- Metal Solid Solution.
- Types of Solid Solution.
  - Substitutional Solid Solution.
    - Hume-Rothery Rules.
  - Interstitial Solid Solution.
- The Solubility Limit.
Solidification.
Cooling Curve.
- Cooling Curve of Pure Metal.
- Cooling Curve of Alloys.
Development of Phase Diagram.
- Cooling Curve for Binary Isomorphous.

TERMINOLOGY

Solvent - element or compound present in greater amount.
Solute - element or compound present in lesser amount.
Solution - When two components combine to form a single phase.
Solubility - Degree to which the two components mix.
Solubility limit - maximum concentration of a solute that may be added without forming a new phase.
Note that solid, gas, and liquid is a phase.
Components: The elements or compounds which are mixed initially (e.g., Al and Cu).
Phases: The physically and chemically distinct material regions that result (e.g., a and b).

SOLUTION

When 2 components combined they can either remain separate or combine to form a single phase.

METALLIC SOLID SOLUTION

Most metals are combined to form alloy in order to impart specific characteristic.
An alloy is a combination of two or more elements (added impurity atoms), at least one of which is a metal.
The addition of impurity atoms to a metal will result in the formation of a solid solution.
A solid solution is a solid-state solution of one or more solutes in a solvent.
E.g : Steel/Cast Iron (Iron base alloys), Bronze/Brass (Copper base alloys), Al alloys, Ni base alloys, Mg base alloys, Ti alloys.
Characteristic of solid solution:
- Form when solute atoms are added to the host material.
- Crystal structure is maintained.
- No new structure formed.
- Compositionally homogeneous.
- Solute Used to denote an element/compound present in a minor concentration.
- Solvent Element / compound that is present in the greatest amount (host atoms).

TYPES OF SOLID SOLUTION

i. Substitutional solid solution.
ii. Interstitial solid solution.

Known as point defects (where an atom is missing or is in an irregular place in the lattice structure).

Substitutional Solid Solution - Hume -Rothery Rules

Substitutional solid solution with complete solubility exists when:

Atomic radius Less than about ± 15% difference in atomic radii.
Crystal structure Same crystal structure (e.g : BCC, FCC or HCP).
Electronegativity Similar electronegativity/ smaller diff.
Valence electron Similar valance electron
Host atoms are replaced/substitute with solute/ impurity atoms.

Interstitial Solid Solution

The atoms of the parent or solvent metal are bigger than the atoms of the alloying or solute metal.
In this case, the smaller atoms fit into spaces between the larger atoms.
Interstitial Solid Solution exists when:
- Impurity atoms fill the voids in the solvent atom lattice.
- It interstice among the host atoms.
- Atomic diameter of an interstitial impurity must be smaller than host atoms.
- Normal max. allowable concentration of interstitial impurity atom is low (<10%).
Solubility Limit: Max concentration for which only a solution occurs.

SOLIDIFICATION & COOLING CURVE

Solidification is the most important phase transformation because most of metals/alloys undergo this transformation before becoming useful objects.
Solidification involve liquid-solid phase transformation, e.g : casting process.
The solidification process differs depending on whether the metal is a pure element or an alloy.
Solidification of Pure Metal and Alloys.
- The formation of stable nuclei in the melt (nucleation).
- The growth of nuclei into crystal.
- The formation of a grain structure.
Cooling Curve: Used to determine phase transition temperature.
Temperature and time data of cooling molten metal is recorded and plotted.
Produce a graph known as phase diagram.
Pure Metal solidifies at a constant temperature equal to its freezing point, which is the same as its melting point.

PHASE DIAGRAM

A graphical representations of what phases are present in a materials system at various temperature (T), pressure (P), and composition (C).
Besides, development of alloy microstructure is related to the characteristics of its phase diagram.
Applications: Casting, Soldering

Types of PHASE DIAGRAM

1. Unary – Consists of One components in an alloy.
2. Binary – Consists of two components in an alloy.
3. Ternary - Consists of three components in an alloy.

What do I need to know about BINARY PHASE DIAGRAM?

Definition: Consists two components in an alloy.
Types:
- Complete solid solution (e.g. Cu and Ni are completely soluble).
- No solid solution (e.g. Pb insoluble in copper).
- Limited solid solution (e.g. Sn has limited solubility in Pb).

Complete solid solution, no solid solution, limited solid solution.

Alcohol and water Oil and water, Salt and water.
- Complete solubility in liquid and solid Result in single phase, Result in multi phase.
- Often soluble up to limit Result in multi phase, Cu and Ni, Pb and Copper, Zinc and Copper, Sn and Pb.

BINARY ISOMORPHOUS

Complete liquid & solid solubility.
Only one solid phase forms.
Same crystal structure.
Liquid above, solid bellow Liquid.
Solidus is line below which all of alloy is solid.

Rules

Rule 1:
- # and types of phases present.
Rule 2:
- Composition of each phase (weight percent, wt%).
Rule 3:
- Amount of each phase.

The Lever Rule

Let WL = fraction of liquid and Wa = fraction of solid (unknown).
\begin{equation}
WL + W\alpha = 1
\end{equation}
Let CL = composition of liquid and C $alpha$ = composition of . W = WLCL + WCa.
- \begin{equation}
  WLR = W\alphaS (A geometric interpretation)
  \end{equation}

Binary Eutectic Diagram

Region above line ced = liquid solution, Line ce and ed = liquidus, Line cfegd = solidus, Region below line feg = mixture of solid A & B, Point e = eutectic point (the lowest temp. at which a liquid solution can exist).

Eutectic and three phases in equilibrium. From the Greek 'eutektos', meaning 'easily melted'.
Composition of a mixture that has lowest melting point where phases crystallize from molten solution.

Binary Eutectic Diagram (Limited Solid Solution)

Where the components are completely soluble in the liquid state but limited solubility in the solid state.
Example: Sn-Pb system, Cu-Ag systems.
alpha, beta = solid solution ae, be = liquidus ac, cd, bd = solidus cf, dg = solvus.
There are three single phase region alpha, beta, L.
Liquid above, Solid bellow 1587227001957 ,1: 14 PM Page 63 of 569
Three number make phase diagrams

Invariant Equilibrium

Different systems have different types of alloy transformation at zero degrees of freedom (temperature is fixed).
1. Eutectic L alpha + beta.
2. Eutectoid, L + alpha beta, alpha beta gamma.