ENGN 0410: Materials Science - Bonding, Structure, Defects, and Diffusion

Comprehensive practice vocabulary flashcards covering atomic structure, primary and secondary bonding, crystal systems, Miller indices, X-ray diffraction, point and extended defects, and diffusion in materials.

Percent Ionic Character (%IC)

The degree of ionic character of an interatomic bond between elements A and B, computed using the expression $f = [1 - \exp(-0.25(X_A - X_B)^2)] \times 100\%$, where $X_A$ and $X_B$ are the respective electronegativities.

Bonding Energy ($E_0$)

The potential energy value at the equilibrium interatomic separation spacing $r_0$, representing the minimum energy in the potential well and the energy required to completely separate two bonded atoms to an infinite distance.

Bond Stiffness (Spring Constant, $k$)

The curvature of the interatomic potential evaluated at the equilibrium atomic spacing, defined mathematically by the second derivative $k = \left.\frac{\partial^2 E(r)}{\partial r^2}\right|_{r_0}$, which directly relates to a material's elastic modulus and resistance to mechanical compression.

Coefficient of Thermal Expansion ($\alpha$)

A parameter defining the fractional dimensional change of a solid per degree change in temperature ($L = L_0(1 + \alpha\Delta T)$), physically originating from the asymmetry or anharmonicity of the interatomic potential well as atomic vibrational amplitude increases with temperature.

Materials Science vs. Materials Engineering

Materials science investigates the relationships between the internal structures and properties of materials, whereas materials engineering designs or engineers the structure of a material to produce a predetermined set of properties based on these structure-property correlations.

Bohr Atomic Model

An early quantum-mechanical atomic model in which electrons are assumed to revolve around the dense atomic nucleus in discrete, circular orbitals with quantized energy levels.

Wave-Mechanical Atomic Model

A modern quantum model where electrons exhibit both wave-like and particle-like characteristics, treating electron position not as a fixed orbital path, but as a spatial probability distribution or electron cloud specified by four quantum numbers ($n$, $l$, $m_l$, $m_s$).

Pauli Exclusion Principle

A quantum-mechanical principle stating that each electron energy state can hold no more than two electrons, which must possess opposite spin quantum numbers ($m_s = +\frac{1}{2}$ and $m_s = -\frac{1}{2}$).

Valence Electrons

The electrons that occupy the outermost filled electron shell of an atom, which actively participate in interatomic bonding and determine most of the physical, chemical, and electrical properties of solids.

Metallic Bonding

A primary interatomic bonding mechanism found in metals and alloys where valence electrons are delocalized to form a non-directional 'sea of electrons' that shields and holds together positively charged ion cores.

Covalent Bonding

A primary, directional interatomic bond formed when adjacent atoms achieve stable, inert-gas electronic configurations by sharing pairs of valence electrons in localized overlapping orbitals.

Ionic Bonding

A non-directional primary chemical bond occurring between electropositive metallic elements and electronegative nonmetallic elements, characterized by the transfer of valence electrons and mutual coulombic electrostatic attraction between the resulting ions.

Van der Waals Bonding (Fluctuating Induced Dipoles)

A weak secondary physical bond arising from instantaneous, short-lived fluctuations in electron density that create temporary electric dipoles, which subsequently induce attractive dipoles in adjacent symmetric atoms or molecules.

Hydrogen Bond

A strong form of permanent dipole-dipole secondary bonding occurring when hydrogen is covalently bonded to a highly electronegative atom (fluorine, oxygen, or nitrogen), exposing a bare proton that electrostatically attracts the negative end of an adjacent molecule.

Crystal Structure

The specific spatial and geometric arrangement of atoms, ions, or molecules in a crystalline solid, defined by the translational periodicity of an underlying lattice populated with an atomic basis.

Unit Cell

The fundamental structural repeating entity or parallelepiped block of a crystal structure whose translational replication across space along its edge vectors completely reconstructs the macroscopic crystal.

Bravais Lattice

An infinite periodic array of geometric points in three-dimensional space wherein each point possesses an identical surrounding environment and orientation regardless of the lattice point from which it is viewed.

Atomic Basis (Motif)

The group or cluster of one or more atoms associated with each Bravais lattice point that, when repeated at every lattice point throughout space, builds the complete physical crystal structure.

Coordination Number

The number of nearest-neighbor touching atoms or oppositely charged ions in direct contact with a given central atom or ion in a crystal structure.

Atomic Packing Factor (APF)

The fraction of solid sphere volume occupied within a unit cell, defined by the formula $\text{APF} = \frac{\text{Volume of atoms in unit cell}}{\text{Total unit cell volume}}$.

Face-Centered Cubic (FCC) Structure

A cubic crystal structure with atoms positioned at each corner and the center of all six faces, having $4$ atoms per unit cell, coordination number $12$, an APF of $0.74$, and unit cell edge length $a = 2R\sqrt{2}$.

Body-Centered Cubic (BCC) Structure

A cubic crystal structure featuring atoms located at all eight unit cell corners and a single central atom, possessing $2$ atoms per unit cell, coordination number $8$, an APF of $0.68$, and edge length $a = \frac{4R}{\sqrt{3}}$.

Hexagonal Close-Packed (HCP) Structure

A close-packed crystal structure characterized by an $ABABAB\dots$ stacking sequence of close-packed atomic planes, with $6$ atoms per unit cell, coordination number $12$, an APF of $0.74$, and an ideal axial ratio of $\frac{c}{a} = 1.633$.

Diamond Cubic Structure

A crystal structure characteristic of carbon, silicon, and germanium consisting of an FCC Bravais lattice with a two-atom basis at $(0,0,0)$ and $(\frac{1}{4},\frac{1}{4},\frac{1}{4})$, exhibiting tetrahedral covalent bonding with coordination number $4$, $8$ atoms per unit cell, and an APF of $0.34$.

Rock Salt (NaCl) Structure

An AX-type ionic crystal structure consisting of two interpenetrating FCC sublattices of cations and anions, where both ion species exhibit an octahedral coordination number of $6$.

Cesium Chloride (CsCl) Structure

An AX-type ionic crystal structure built upon a simple cubic Bravais lattice with a two-ion basis ($A$ at $(0,0,0)$ and $B$ at $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$), giving each ion a coordination number of $8$.

Perovskite Structure

An $ABX_3$ ceramic crystal structure, exemplified by $\text{BaTiO}_3$, where $A$ cations occupy the cube corners, a $B$ cation sits at the unit cell center, and $X$ anions reside at the centers of all six faces, producing coordination numbers of $12$ for $A$ and $6$ for $B$.

Polymorphism (Allotropy)

The capability of a material to exist in more than one distinct crystal structure depending on ambient temperature and pressure; the term allotropy is specifically used when this occurs in elemental solids.

Miller Indices

A set of three smallest integers, denoted $(hkl)$, that identify the orientation of a crystallographic plane, calculated from the reciprocals of the fractional axial intercepts made by the plane with the unit cell axes.

Interplanar Spacing ($d_{hkl}$)

The perpendicular distance separating adjacent, parallel crystallographic planes with Miller indices $(hkl)$, given for cubic crystal systems by the formula $d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$.

Bragg's Law

The relationship governing constructive interference in X-ray diffraction: $n\lambda = 2d_{hkl}\sin(\theta)$, where $n$ is the diffraction order, $\lambda$ is the radiation wavelength, $d_{hkl}$ is the interplanar spacing, and $\theta$ is the diffraction angle.

Systematic Absences (Diffraction Selection Rules)

Diffraction peak extinction rules resulting from destructive interference caused by centering atoms in non-primitive unit cells; allowed reflections require $h, k, l$ to be all odd or all even for FCC crystals, and $h + k + l$ to sum to an even number for BCC crystals.

Vacancy

A zero-dimensional point defect in a crystal consisting of a vacant atomic site normally occupied in a perfect crystal, whose equilibrium concentration increases exponentially with temperature according to $N_v = N\exp(-\frac{Q_v}{kT})$.

Self-Interstitial

A point defect created when a host atom becomes crowded into an interstitial site (a normally unoccupied void between lattice atoms), inducing large surrounding compressive lattice strains.

Frenkel Defect

A point defect pair in an ionic ceramic consisting of a cation vacancy and a displaced cation interstitial, preserving crystal electroneutrality without altering stoichiometry.

Schottky Defect

An electroneutral point defect pair in an AX ceramic material created by removing one cation and one anion from the interior of the crystal to external surfaces, creating both a cation vacancy and an anion vacancy.

Hume-Rothery Rules

A set of four empirical conditions governing extensive solid solubility in substitutional alloys: atomic radius mismatch within $\pm 15\%$, identical crystal structures, similar electronegativities, and matching or greater solute valence.

Vegard's Law

An empirical rule stating that the lattice parameter ($a_{\text{alloy}}$) of a substitutional solid solution varies linearly with the atomic fraction ($x$) of its components according to $a_{\text{alloy}} = x a_A + (1 - x) a_B$.

Burgers Vector ($\mathbf{b}$)

A vector specifying the magnitude and direction of the lattice distortion associated with a dislocation; it is perpendicular to the dislocation line for an edge dislocation, parallel for a screw dislocation, and oriented at an intermediate angle for a mixed dislocation.

Grain Boundary

A two-dimensional interfacial defect that separates adjacent crystals (grains) having different crystallographic orientations in a polycrystalline material, characterized by localized atomic mismatch and excess interfacial energy.

Twin Boundary

A special planar grain boundary across which there is a mirror-image lattice symmetry, formed either during plastic deformation (mechanical twins) or subsequent annealing heat treatments (annealing twins).

Diffusion Flux ($J$)

The rate of atomic mass transfer across a unit cross-sectional area per unit time, expressed mathematically as $J = \frac{M}{A t}$ in units of $\text{kg}/(\text{m}^2\cdot\text{s})$ or $\text{atoms}/(\text{m}^2\cdot\text{s})$.

Fick's First Law

The law governing steady-state diffusion stating that diffusion flux is directly proportional to the negative of the concentration gradient: $J = -D \frac{dC}{dx}$, where $D$ is the diffusion coefficient.

Fick's Second Law

The differential equation governing nonsteady-state diffusion where concentration varies with both time and position, expressed for a position-independent diffusion coefficient as $\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$.

Activation Energy for Diffusion ($Q_d$)

The energy barrier required to activate the motion of one mole of diffusing atoms between lattice or interstitial sites, governing the temperature dependence of the diffusion coefficient through the Arrhenius relation $D = D_0 \exp(-\frac{Q_d}{RT})$.

Carburizing

A nonsteady-state industrial diffusion heat treatment in which carbon atoms diffuse from a carbon-rich environment into the outer surface of a steel component to increase surface hardness, wear resistance, and fatigue endurance.

Degree of Polymerization ($n$)

The average number of repeating mer units linked within a polymer chain molecule, calculated as the ratio of average molecular weight to repeat unit molecular weight ($n_n = \frac{M_n}{m}$).

Thermoplastic Polymer

A polymer composed of linear or branched molecular chains that reversibly softens and liquefies upon heating and solidifies upon cooling, without forming permanent chemical crosslinks.

Thermosetting Polymer

A network or heavily crosslinked polymer that permanently hardens during initial heat treatment and crosslinking, resisting softening upon subsequent heating and degrading only at excessive temperatures.

Spherulite

A spherical, polycrystalline aggregate structure formed during the crystallization of bulk polymers from a melt, comprising radiating ribbon-like, chain-folded lamellar crystallites separated by amorphous regions.