Materials Science and Engineering

1. Atomic Structure & Bonding Dictate Material Behavior

Atomic mass is the mass of an individual atom, whereas atomic weight is the average (weighted) of the atomic masses of an atom's naturally occurring isotopes.

Fundamental building blocks. Materials science begins with understanding atoms and how they bond. Atomic structure, including electron configuration and quantum numbers, determines an atom's chemical behavior and bonding preferences. Atomic mass and weight are key descriptors, with atomic weight being the average mass considering isotopes.

Primary bonds. Atoms form primary bonds to achieve stable electron configurations, like those of inert gases.

• Ionic bonding: Electrostatic attraction between oppositely charged ions (e.g., NaCl). Occurs between metals and nonmetals with large electronegativity differences.
• Covalent bonding: Sharing of electrons between atoms (e.g., diamond). Directional bonds, common in nonmetals.
• Metallic bonding: A "sea" of valence electrons shared among positively charged ion cores (e.g., copper). Non-directional, explaining metal ductility and conductivity.

Secondary bonds. Weaker van der Waals bonds arise from temporary or permanent dipoles. Hydrogen bonding is a stronger type involving hydrogen atoms bonded to highly electronegative atoms. These bonds influence properties like boiling points, especially in polymers and some ceramics.

2. Crystal Structures Define Atomic Arrangement

Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the constituent electrons. On the other hand, crystal structure pertains to the arrangement of atoms in the crystalline solid material.

Ordered arrangements. Crystalline solids feature atoms arranged in repeating, three-dimensional patterns called crystal structures. The smallest repeating unit is the unit cell, which defines the overall lattice. Common metallic structures include Face-Centered Cubic (FCC), Body-Centered Cubic (BCC), and Hexagonal Close-Packed (HCP).

Packing efficiency. Different crystal structures have varying atomic packing factors (APF), representing the volume occupied by atoms within the unit cell.

• FCC and HCP have high APFs (0.74).
• BCC has a slightly lower APF (0.68).
• Simple Cubic (SC) has the lowest APF (0.52).
  This packing influences density and mechanical properties.

Crystallographic directions and planes. Specific directions and planes within a crystal lattice are described using Miller indices. These indices are crucial for understanding anisotropic properties and deformation mechanisms like slip. Different planes and directions have different atomic densities, affecting surface energy and other properties.

3. Imperfections & Diffusion Drive Atomic Movement

Although each individual grain in a polycrystalline material may be anisotropic, if the grains have random orientations, then the solid aggregate of the many anisotropic grains will behave isotropically.

Real materials aren't perfect. Crystalline solids contain imperfections, or defects, which significantly influence their properties. Point defects include vacancies (missing atoms) and interstitials (extra atoms). Linear defects are dislocations, which are line imperfections crucial for plastic deformation in metals. Planar defects include grain boundaries (interfaces between crystals) and twin boundaries.

Atomic motion. Atoms move within solids through diffusion, driven by concentration gradients or thermal energy.

• Vacancy diffusion: Atoms move into adjacent vacant lattice sites.
• Interstitial diffusion: Smaller atoms move between interstitial sites. Interstitial diffusion is generally faster due to smaller atom size and more available sites.

Diffusion kinetics. Diffusion rate is quantified by the diffusion flux (Fick's first law for steady-state) and is temperature-dependent (Arrhenius equation). Nonsteady-state diffusion involves concentration changes over time and position, described by Fick's second law. Diffusion is vital for processes like heat treatments, doping semiconductors, and creep.

4. Materials Respond to Stress: Elasticity & Plasticity

The elastic modulus is the slope in the linear elastic region...

Deformation behavior. When subjected to external forces (stress), materials deform (strain). Elastic deformation is temporary and reversible; the material returns to its original shape upon load removal. The relationship between stress and strain in this region is linear for many materials, defined by the elastic modulus (Young's modulus).

Permanent deformation. Plastic deformation is permanent and occurs when stress exceeds the yield strength. In crystalline materials, this involves the movement of dislocations (slip). The stress-strain curve beyond the yield point shows strain hardening, where the material becomes stronger as it deforms plastically.

Anisotropy. Material properties, including elastic modulus and yield strength, can vary with crystallographic direction in single crystals (anisotropy). Polycrystalline materials, made of many randomly oriented grains, often behave isotropically on a macroscopic scale, averaging the anisotropic behavior of individual grains.

5. Failure Modes: Fracture, Fatigue, and Creep

Creep becomes important at about 0.4 T_m, T_m being the absolute melting temperature of the metal.

Material breakdown. Materials can fail under stress through various mechanisms. Fracture is the separation of a body into pieces. Brittle fracture occurs suddenly with little plastic deformation, often initiated by flaws. Ductile fracture involves significant plastic deformation before failure. Fracture toughness quantifies a material's resistance to brittle fracture in the presence of cracks.

Time-dependent failures.

• Fatigue: Failure under cyclic stress, even below the yield strength. Characterized by an S-N curve (stress amplitude vs. cycles to failure). Fatigue limit is the stress below which fatigue doesn't occur.
• Creep: Time-dependent plastic deformation under constant stress at elevated temperatures. Occurs significantly above 0.4 times the absolute melting temperature. Characterized by primary, secondary (steady-state), and tertiary stages leading to rupture.

Influencing factors. Temperature, stress level, stress history (cyclic vs. static), and the presence of flaws or corrosive environments all influence failure behavior. Understanding these modes is critical for designing reliable components.

6. Phase Diagrams Map Material States

A “phase” is a homogeneous portion of the system having uniform physical and chemical characteristics, whereas a “microconstituent” is an identifiable element of the microstructure (that may consist of more than one phase).

Equilibrium states. Phase diagrams are graphical maps showing the equilibrium phases present in a material system as a function of temperature, pressure, and composition. They represent the state where the system's free energy is minimized. The Gibbs phase rule relates the number of phases, components, and degrees of freedom.

Binary systems. For two-component (binary) systems at constant pressure, phase diagrams show phase fields (regions where specific phases exist) and phase boundaries.

• Liquidus line: Above this, only liquid exists.
• Solidus line: Below this, only solid exists.
• Isomorphous systems: Components are completely soluble in both liquid and solid states (e.g., Cu-Ni).
• Eutectic systems: Feature a specific composition (eutectic) that melts/solidifies at a single temperature, forming a mixture of two solid phases.

Lever rule. For two-phase regions, the lever rule is used to calculate the relative mass fractions of each phase present at a given temperature and overall composition. This is crucial for understanding microstructure development.

7. Phase Transformations Control Microstructure

The two stages involved in the formation of particles of a new phase are nucleation and growth.

Changing states. Phase transformations involve changes in the number or type of phases present, often driven by temperature changes. These transformations occur via nucleation (formation of small, stable particles of the new phase) and growth (increase in size of these particles).

Transformation kinetics. The rate of transformation is time-dependent and often follows the Avrami equation, which describes the fraction transformed over time. Transformation rates are also highly temperature-dependent, typically increasing with temperature above the transformation start temperature, but decreasing at very high temperatures due to reduced driving force.

Iron-carbon transformations. The Fe-Fe3C phase diagram is critical for steels. Austenite (γ) transforms upon cooling.

• Pearlite: Lamellar mixture of ferrite (α) and cementite (Fe3C). Forms at higher temperatures.
• Bainite: Acicular mixture of α and Fe3C. Forms at intermediate temperatures.
• Spheroidite: Spheroidal Fe3C particles in an α matrix. Forms after long times at elevated temperatures.
• Martensite: Metastable, body-centered tetragonal structure formed by rapid quenching of austenite. Very hard and brittle.

TTT and CCT diagrams. Isothermal Transformation (TTT) diagrams show transformation kinetics at constant temperatures. Continuous Cooling Transformation (CCT) diagrams show transformations during continuous cooling, more relevant to heat treatments like quenching. These diagrams guide the selection of heat treatments to achieve desired microstructures and properties.

8. Metals: Versatile Structures and Properties

Ferrous alloys are used extensively because: (1) Iron ores exist in abundant quantities. (2) Economical extraction, refining, and fabrication techniques are available. (3) The alloys may be tailored to have a wide range of properties.

Metallic characteristics. Metals are known for their high strength, stiffness, ductility, electrical and thermal conductivity, and toughness. These properties arise from their metallic bonding and crystalline structures (FCC, BCC, HCP). Alloying metals allows for tailoring properties.

Ferrous alloys. Steels (Fe-C alloys) and cast irons are the most common metals.

• Steels: Classified by carbon content (low, medium, high) and alloying elements (stainless, tool). Properties vary widely with composition and heat treatment.
• Cast Irons: Higher carbon content than steels, often containing graphite. Types include gray, ductile (nodular), white, and malleable iron, differing in graphite shape and matrix structure, affecting ductility and strength.

Nonferrous alloys. Include aluminum, copper, titanium, refractory metals, superalloys, and noble metals. Chosen for specific properties like low density (Al, Ti), high conductivity (Cu), high temperature strength (refractory metals, superalloys), or corrosion resistance (noble metals, stainless steel).

9. Ceramics: Ionic/Covalent Structures & Brittle Behavior

The two characteristics of component ions that determine the crystal structure of a ceramic compound are: 1) the magnitude of the electrical charge on each ion, and 2) the relative sizes of the cations and anions.

Strong, brittle bonds. Ceramics are inorganic, nonmetallic solids, often compounds of metals and nonmetals. Bonding is typically ionic or covalent, leading to high hardness, stiffness, melting points, and chemical stability, but also brittleness. Crystal structures are complex, determined by ion size ratios and charge neutrality (e.g., rock salt, cesium chloride, zinc blende, perovskite, spinel).

Silicates. A major class based on the SiO4 tetrahedron. Structures range from simple silicates to complex networks (glasses). Bonding is mixed covalent-ionic.

Imperfections. Point defects (vacancies, interstitials) exist, but must maintain charge neutrality (e.g., Schottky, Frenkel defects). Impurities also introduce defects to balance charge.

Mechanical behavior. Ceramics are strong in compression but weak in tension due to crack propagation from flaws. Fracture strength shows significant scatter and increases with decreasing size. Plastic deformation is difficult due to limited slip systems. Elastic modulus decreases with porosity.

10. Polymers: Molecular Chains and Diverse Properties

Thermoplastic polymers soften when heated and harden when cooled, whereas thermosetting polymers, harden upon heating, while further heating will not lead to softening.

Long chain molecules. Polymers are large molecules (macromolecules) formed by repeating structural units (repeat units) linked by covalent bonds. Molecular weight varies, influencing properties. Degree of polymerization is the number of repeat units per chain.

Structure and architecture.

• Linear, branched, crosslinked, network structures.
• Stereoisomerism (isotactic, syndiotactic, atactic) and geometric isomerism (cis, trans) affect chain packing.
• Copolymers combine different repeat units (random, alternating, block, graft).

Thermal behavior.

• Thermoplastics: Soften upon heating, solidify upon cooling (linear/branched). Recyclable.
• Thermosets: Harden irreversibly upon heating (network/heavily crosslinked). Not recyclable.
• Elastomers: Lightly crosslinked, rubbery polymers used above their glass transition temperature.

Crystallinity. Polymers can be crystalline, amorphous, or semicrystalline. Crystallinity depends on chain regularity, stereochemistry, and branching. Influences density, stiffness, and strength. Melting temperature (Tm) for crystalline regions, glass transition temperature (Tg) for amorphous regions.

11. Electrical Properties: Conduction and Semiconductors

For metallic materials, there are vacant electron energy states adjacent to the highest filled state; thus, very little energy is required to excite large numbers of electrons into conducting states.

Charge transport. Electrical conductivity is a material's ability to conduct electric current, the flow of charge carriers (electrons or ions). Conductivity is the reciprocal of resistivity. Ohm's law relates voltage, current, and resistance.

Band theory. Explains conductivity based on electron energy levels in solids.

• Metals: Overlapping valence and conduction bands or partially filled valence bands allow easy electron movement. High conductivity.
• Insulators: Large band gap between filled valence band and empty conduction band. High energy needed for conduction. Low conductivity.
• Semiconductors: Smaller band gap than insulators. Conductivity is intermediate and highly temperature-dependent.

Semiconductors.

• Intrinsic: Conductivity depends on thermally generated electron-hole pairs. Concentration increases exponentially with temperature.
• Extrinsic: Conductivity dominated by impurities (dopants). Donors (e.g., P in Si) create excess electrons (n-type). Acceptors (e.g., B in Si) create excess holes (p-type). Conductivity depends on dopant concentration and mobility.
• Mobility: Carrier velocity per unit electric field. Influenced by temperature and impurity scattering.

Devices. p-n junctions form the basis of diodes (rectification) and transistors (amplification, switching). Ionic conduction occurs in ceramics and polymers via ion migration.

Last updated: May 18, 2025