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What determines the bonding and properties of materials?

Valence electrons determine chemical, electrical, thermal, and optical properties.

What are the primary types of atomic bonds?

Ionic, covalent, metallic, and secondary (van der Waals).

What forces exist between atoms that lead to bonding?

Attractive and repulsive forces; bonding energy is minimized at equilibrium distance r₀.

What is E₀ in a bonding energy graph?

Bond energy at the minimum point of the potential energy curve.

What is the relationship between melting temperature and bonding energy?

Larger Tₘ generally indicates deeper energy wells and stronger bonding.

What type of bonding do metals exhibit and what properties arise from it?

Metallic bonding; high electrical/thermal conductivity, ductility, opacity.

What type of bonding do polymers exhibit?

Covalent (and some van der Waals); they are soft, insulating, low-density.

What type of bonding do ceramics exhibit?

Ionic and covalent; ceramics are brittle, non-conducting, inelastic.

What are the four main classes of engineered materials?

Metals, ceramics, polymers/plastics, and semiconductors.

How do semiconductors differ in bonding and properties?

Mixed ionic/covalent bonding; engineered electrical conductivity, typically brittle.

What is the difference between crystalline and noncrystalline solids?

Crystalline solids have a periodic 3D arrangement of atoms; noncrystalline (amorphous) solids lack long-range order.

What causes ordered structures to be more stable?

They are nearer the minimum in bonding energy and tend to have lower energy states.

What are common crystal structures of metals?

Simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP).

What is atomic packing factor (APF)?

APF = Volume of atoms in unit cell / Volume of unit cell; indicates how tightly atoms are packed.

What are the APF values for common crystal structures?

SC = 0.52, BCC = 0.68, FCC = 0.74, HCP = 0.74.

What is the coordination number in a crystal structure?

The number of nearest neighbor atoms around a central atom.

Why are metals generally dense?

They have nondirectional metallic bonds, small nearest-neighbor distances, and efficient packing (e.g., FCC/BCC).

What is the relationship between structure and density?

Denser packing (e.g., FCC) leads to higher density; atomic mass and unit cell volume also factor in.

What is a unit cell?

The smallest repeating unit of a crystal lattice that fully describes the crystal structure.

What does it mean for a material to be anisotropic?

Material properties vary with crystallographic direction; common in single crystals.

What does it mean for a material to be isotropic?

Properties are direction-independent; typical in polycrystalline materials with random grain orientation.

What is allotropy (polymorphism)?

The existence of two or more different crystal structures for the same element (e.g., iron: BCC and FCC).

What is a single crystal?

A material with a continuous and uninterrupted crystal structure throughout the entire specimen.

What is a polycrystalline material?

A material made of many small crystals or grains, each with its own orientation.

How are crystallographic directions specified?

By using [uvw] format derived from vector coordinates normalized by unit cell dimensions.

How are crystallographic planes specified?

Using Miller indices (hkl), determined by taking reciprocals of plane intercepts and reducing to smallest integers.

What is a family of directions?

A set of directions that are crystallographically equivalent, denoted by ⟨uvw⟩.

What is a family of planes?

A group of equivalent planes, denoted by {hkl}, that have the same atomic arrangement and spacing.

How is linear density (LD) calculated?

LD = Number of atoms centered on a direction vector / Length of that direction vector.

How is planar density (PD) calculated?

PD = Number of atoms centered on a plane / Area of that plane.

What is X-ray diffraction used for in crystallography?

Determining crystal structure and interplanar spacing using Bragg’s Law: nλ = 2d sinθ.

What does Bragg’s Law relate?

The X-ray wavelength, interplanar spacing, and diffraction angle: nλ = 2d sinθ.

What factors influence the theoretical density of a material?

Atomic mass, number of atoms per unit cell, and unit cell volume.

How does structure impact material properties?

Denser structures (FCC) tend to have higher strength and conductivity than less dense ones (SC).

What are the four main types of defects in solids?

Point defects, line defects, planar defects, and volume defects.

What are the common point defects?

Vacancies, interstitial atoms, and substitutional atoms.

What is a vacancy?

A missing atom in a normally occupied lattice site; increases entropy and affects diffusion.

How does temperature affect the number of vacancies?

The number of vacancies increases exponentially with temperature.

What is a self-interstitial defect?

An atom occupies a normally unoccupied interstitial site; less common in metals.

What is a substitutional impurity atom?

An atom that replaces a host atom in the crystal lattice.

What is an interstitial impurity atom?

An atom that occupies a space between regular lattice atoms; usually much smaller in size.

What are the Hume-Rothery rules for forming a substitutional solid solution?

<15% atomic radius difference, same crystal structure, similar electronegativity, same valence.

What is a solid solution?

A homogeneous mixture where the solute atoms occupy regular lattice positions or interstitial sites.

What is an edge dislocation?

A line defect caused by the insertion of an extra half-plane of atoms; Burgers vector is perpendicular to the dislocation line.

What is a screw dislocation?

A helical distortion caused by shear stress; Burgers vector is parallel to the dislocation line.

What is a mixed dislocation?

A combination of edge and screw components along the same dislocation line.

What is a Burgers vector?

A vector that describes the magnitude and direction of lattice distortion caused by a dislocation.

What is plastic deformation?

Irreversible deformation caused by dislocation motion.

What are grain boundaries?

Planar defects where crystals of different orientations meet; reduce electrical and thermal conductivity.

What is a twin boundary?

A special grain boundary where atomic positions are mirror images across the twin plane.

What is a stacking fault?

A defect in the stacking sequence of atomic planes (e.g., FCC ABCABC → ABCABABC).

How do defects affect material properties?

They influence strength, ductility, conductivity, and diffusion.

How are dislocations observed experimentally?

They appear as dark lines in transmission electron microscopy (TEM) images.

Why are dislocations important?

They enable plastic deformation in crystalline solids and determine mechanical strength.

What is diffusion in materials science?

Mass transport by atomic motion from regions of high concentration to low concentration.

What are the two main types of diffusion in solids?

Interstitial diffusion and vacancy diffusion.

What is vacancy diffusion?

Atoms exchange with adjacent vacancies; applies to host and substitutional atoms.

What is interstitial diffusion?

Small atoms move between interstitial sites; faster than vacancy diffusion.

What is interdiffusion?

Atoms of one material diffuse into another.

What is self-diffusion?

Atoms migrate within a pure material.

What factors influence diffusion rate?

Number of vacancies, temperature, diffusion mechanism, and activation energy.

What is diffusion flux (J)?

The rate of mass transfer per unit area per unit time; J = M / At.

What is Fick’s First Law (steady-state diffusion)?

J = -D (dC/dx), where D is the diffusion coefficient, and dC/dx is the concentration gradient.

What is Fick’s Second Law (non-steady-state diffusion)?

∂C/∂t = D ∂²C/∂x²; describes time-dependent concentration changes.

How does temperature affect the diffusion coefficient (D)?

D increases exponentially with temperature.

What is the Arrhenius equation for diffusion?

D = D₀ exp(-Qd/RT), where Qd is activation energy, R is gas constant, and T is temperature in K.

How can diffusion be measured experimentally?

By measuring mass transfer through a membrane under a concentration gradient.

What is case hardening?

An interstitial diffusion process where carbon atoms diffuse into steel to harden the surface.

Why is case hardening useful?

It increases wear resistance and creates compressive surface stress that prevents fatigue failure.

What is doping in semiconductors?

Introduction of impurity atoms (e.g., phosphorus into silicon) by diffusion to alter electrical properties.

How is diffusion used in semiconductors?

Impurities are deposited and heat-treated to diffuse into the silicon lattice.

What is the Hume-Rothery rule for atomic radius?

Atomic radii must differ by less than 15% for substitutional solid solution formation.

What are the four Hume-Rothery rules?

Atomic radius <15%, similar electronegativity, same crystal structure, and similar valence.

How does valence affect solubility in alloys?

A metal tends to dissolve metals of higher valence more easily than those of lower valence.

What is the continuity equation in diffusion?

dJ/dx + dC/dt = 0; describes conservation of mass in a diffusing system.

What is stress?

Force applied per unit area; σ = F / A.

What is strain?

Deformation per unit length; ε = ΔL / L₀.

What is the difference between elastic and plastic deformation?

Elastic deformation is reversible; plastic deformation is permanent.

What is Hooke’s Law?

σ = Eε, where E is Young’s modulus (stiffness).

What does Young’s modulus (E) represent?

A material's stiffness; the slope of the linear elastic region on a stress-strain curve.

What does a steeper slope in a stress-strain curve indicate?

Higher stiffness (greater resistance to deformation).

What is Poisson’s ratio (ν)?

The ratio of lateral strain to axial strain; ν = -εlateral / εaxial.

What are typical values of Poisson’s ratio?

Metals ≈ 0.3, ceramics ≈ 0.25, polymers ≈ 0.4.

What does it mean if a material is auxetic?

It has a negative Poisson’s ratio; it expands laterally when stretched.

What is yield strength (σy)?

The stress at which a material begins to deform plastically (defined at 0.2% offset strain).

What is ultimate tensile strength (UTS)?

The maximum stress a material can withstand before necking begins.

What is necking?

Localized reduction in cross-sectional area after UTS, leading to fracture.

What is ductility?

The degree of plastic deformation at failure; measured by % elongation or % area reduction.

What is resilience?

The ability of a material to absorb energy in the elastic region; Ur = ½ σy ε_y.

What is toughness?

Total energy absorbed before fracture; represented by the area under the entire stress-strain curve.

What is true stress and true strain?

σT = σ (1 + ε), εT = ln(1 + ε); account for changing dimensions during deformation.

What is hardness?

A measure of a material’s resistance to localized plastic deformation (indentation).

What are common hardness tests?

Rockwell, Brinell (HB), and Vickers.

How is hardness related to tensile strength? (Numerical relationship)

TS ≈ 3.45 × HB.

What is the safety factor (N)?

A design margin; σworking = σyield / N.

Why do we use safety factors?

To account for uncertainties in loading, material properties, and processing; typical values range from 1.2–4.

What is the significance of modulus of resilience?

It quantifies the energy stored per unit volume up to the yield point.

What is the difference between stiffness and strength?

Stiffness is resistance to elastic deformation (E); strength is resistance to permanent deformation (σ_y, UTS).

How does strain hardening affect a material?

Increases strength due to dislocation interactions during plastic deformation.

What are the stages of a tensile stress-strain curve?

Elastic region → yield point → strain hardening → necking → fracture.