Inorganic Materials Chemistry: Crystal Structures, Defects, and Diffusion

Comprehensive practice flashcards covering crystal structures, unit cells, close-packing, Miller indices, 0D-2D lattice defects, and diffusion kinetics from Lectures 1 and 2 of Inorganic Materials Chemistry.

What are the five structural length scales in materials chemistry, listed from smallest to largest?

Atomic structure (elements + bonding), crystal arrangement (unit cells + symmetry), phases (composition domains), micro/nano structure (grains + defects), and macro structure (shape + function).

How do covalent, ionic, and metallic bonding differ in electron interaction and resulting physical properties?

Covalent bonds share electrons (strong, directional, often brittle); ionic bonds involve electron transfer forming charged ions (hard, brittle); metallic bonds consist of an electron sea (electrically conductive, ductile, malleable).

According to the Ketelaar-Van Arkel triangle shown below for Period 2 compounds, what are the ionic character percentages of $LiF$ and $BF_3$?

$LiF$ has an ionic character of $80\%$ and $BF_3$ has an ionic character of $44\%$.

What is the distinction between allotropy and polymorphism?

Allotropy is when the same element exists in different crystal structures (e.g., carbon as diamond, graphite, graphene, fullerenes, nanotubes). Polymorphism is when the same compound exists in different crystal phases (e.g., $Al_2O_3$ as $\alpha$-, $\gamma$-, and $\theta\text{-}Al_2O_3$).

What temperature intervals define the stable solid allotropic phases of pure iron at atmospheric pressure?

$\alpha$-iron (BCC) is stable up to $910\,^\circ\text{C}$; $\gamma$-iron (FCC) is stable from $910\,^\circ\text{C}$ to $1394\,^\circ\text{C}$; and $\delta$-iron (BCC) is stable from $1394\,^\circ\text{C}$ up to its melting point at $1538\,^\circ\text{C}$.

What are the three levels of atomic ordering used to classify materials?

No order (random atoms), short-range order (local neighbours), and long-range order (repeating crystal lattice).

How many crystal systems and Bravais lattices exist in three-dimensional crystallography?

There are $7$ crystal systems and $14$ Bravais lattices.

What are the five unit-cell centering types and their corresponding symbols?

Primitive ($P$), body-centered ($I$), face-centered ($F$), base-centered ($C$), and rhombohedral ($R$).

What are the coordination number, atoms per unit cell, and lattice parameter relation for a Simple Cubic (SC) lattice?

Coordination number = $6$; atoms per unit cell = $1$; lattice parameter $a_0 = 2r$, where atoms touch along the cube edge.

What are the coordination number, atoms per unit cell, and lattice parameter relation for the Body-Centered Cubic (BCC) structure depicted below?

Coordination number = $8$; atoms per unit cell = $2$; lattice parameter $a_0 = \frac{4r}{\sqrt{3}}$, where spheres touch along the body diagonal.

What are the coordination number, atoms per unit cell, and lattice parameter relation for a Face-Centered Cubic (FCC) lattice?

Coordination number = $12$; atoms per unit cell = $4$; lattice parameter $a_0 = \frac{4r}{\sqrt{2}}$, where spheres touch along the face diagonal.

What stacking sequences distinguish Hexagonal Close-Packed (HCP) from Face-Centered Cubic (FCC / CCP) structures?

HCP exhibits an $ABAB\dots$ stacking sequence, while FCC / CCP exhibits an $ABCABC\dots$ stacking sequence.

What are the coordination numbers and maximum interstitial radius ratios ($r_i/R$) for tetrahedral and octahedral voids?

Tetrahedral voids have a coordination number of $4$ and $r_i = 0.225 R$; octahedral voids have a coordination number of $6$ and $r_i = 0.414 R$, where $R$ is the host atom radius.

What is the procedure for determining the Miller indices $(hkl)$ of a crystallographic plane?

1) If the plane passes through the origin, shift the origin; 2) Determine the axis intercepts $(x, y, z)$; 3) Take reciprocals $(\frac{1}{x}, \frac{1}{y}, \frac{1}{z})$; 4) Clear fractions to obtain the lowest integer ratio $(hkl)$.

What do the crystallographic notations $(hkl)$, $(hkl)$, $[uvw]$, and $\langle uvw \rangle$ designate?

$(hkl)$ designates a single specific plane; $(hkl)$ (written as $\{hkl\}$) designates a family of symmetry-equivalent planes; $[uvw]$ designates a single direction; and $\langle uvw \rangle$ designates a family of symmetry-equivalent directions.

What are the close-packed planes and directions in FCC and HCP crystal structures?

In FCC, close-packed planes are $\{111\}$ and directions are $\langle 110 \rangle$. In HCP, the close-packed plane is $(001)$ and directions are $\langle 100 \rangle$.

What equation gives the equilibrium number of vacancies $n_v$ in a crystal lattice?

$n_v = N e^{(-Q_v/RT)}$, where $N$ is the total number of atomic sites, $Q_v$ is the activation energy for vacancy formation, $R$ is the gas constant, and $T$ is temperature in Kelvin.

What is the difference between intrinsic and extrinsic point defects?

Intrinsic point defects involve host lattice atoms only (vacancies, self-interstitials, antisite defects), whereas extrinsic point defects involve foreign impurity atoms or dopants (substitutional solutes, interstitial dopants).

What type of ionic point defect is shown in the diagram below, and how does it maintain electrical neutrality?

A Schottky defect, which consists of a paired cation vacancy and anion vacancy; mass leaves the lattice while overall charge neutrality is preserved.

What type of ionic point defect is shown in the diagram below, and how does it affect composition and disorder?

A Frenkel defect, where an ion shifts from a lattice site into an interstitial void; overall chemical composition remains unchanged while crystal disorder increases.

What structural feature defines an edge dislocation as shown in the diagram below?

An edge dislocation is formed by an extra half-plane of atoms inserted into the crystal lattice.

What structural feature defines a screw dislocation as shown in the diagram below?

A screw dislocation is characterized by a spiral slip step produced by lattice shear around the dislocation line.

What does the Burgers vector $\mathbf{b}$ specify for a dislocation?

The Burgers vector $\mathbf{b}$ defines the magnitude and direction of lattice distortion produced by the dislocation.

How do dislocation slip, obstacles, and lack of slip govern mechanical behavior?

Dislocation slip gives rise to ductility; obstacles blocking dislocation movement produce strengthening; the complete inability of dislocations to slip leads to brittle fracture.

Why do surfaces and grain boundaries act as planar defects that alter physical properties?

Surface atoms suffer broken periodicity, dangling bonds, and lower coordination numbers; grain boundaries represent structural misorientation between adjacent crystals. Both scatter electrons and phonons and block dislocation slip.

How does grain boundary density correlate with material yield strength?

Smaller grains generate more grain boundaries per unit volume, which impede dislocation slip more effectively, resulting in higher yield strength.

What distinguishes an intrinsic stacking fault from an extrinsic stacking fault in close-packed crystals?

An intrinsic stacking fault is caused by a missing layer (e.g., $\dots ABCACABCA \dots$), whereas an extrinsic stacking fault is caused by an inserted extra layer (e.g., $\dots ABCACBCABC \dots$).

What is diffusion, and what role does it typically play in solid-state reactions?

Diffusion is the net transport of atoms or ions via thermal motion; it is frequently the rate-limiting step in solid-state reactions and phase transformations.

How is diffusion flux $J$ defined mathematically, and what are its typical units?

$J = \frac{dn}{A\,dt}$, measuring the number of atoms or moles crossing a reference plane per unit area per unit time, expressed in units of $\text{s}^{-1}\,\text{cm}^{-2}$ or $\text{atoms}\,\text{m}^{-2}\,\text{s}^{-1}$.

What is Fick's First Law, and what is the physical significance of the minus sign?

$J = -D \frac{\partial c}{\partial x}$, where $J$ is the diffusion flux, $D$ is the diffusion coefficient (diffusivity), and $\frac{\partial c}{\partial x}$ is the concentration gradient. The minus sign signifies that net atomic flux proceeds down the concentration gradient (from higher to lower concentration).

What does the diagram below illustrate regarding the activation energy barriers for solid-state diffusion?

It illustrates that substitutional (vacancy) diffusion requires a higher activation energy barrier ($Q_v$) because it depends on vacant sites, whereas interstitial diffusion has a lower activation barrier ($Q_i$) because small solute atoms move directly through lattice gaps.

How is the temperature dependence of diffusivity $D$ expressed in the Arrhenius equation, and what do the slope and intercept represent on an Arrhenius plot?

$D = D_0 \exp\left(-\frac{Q}{RT}\right)$. On a plot of $\ln(D)$ versus $1/T$, the slope equals $-\frac{Q}{R}$ and the y-intercept equals $\ln(D_0)$, with a steeper slope indicating a stronger temperature dependence.

Why is carbon diffusion approximately $40\times$ faster in $\alpha\text{-Fe}$ (BCC) than in $\gamma\text{-Fe}$ (FCC) at $900\,\text{K}$?

Although FCC iron has a higher pre-exponential factor ($D_0 = 2.3 \times 10^{-5}\,\text{m}^2\,\text{s}^{-1}$ vs $1.1 \times 10^{-6}\,\text{m}^2\,\text{s}^{-1}$), BCC iron has a significantly lower activation energy ($Q = 87.5\,\text{kJ\,mol}^{-1}$ vs $137.7\,\text{kJ\,mol}^{-1}$), and the exponential barrier term dominates diffusivity ($9.2 \times 10^{-12}\,\text{m}^2\,\text{s}^{-1}$ vs $2.3 \times 10^{-13}\,\text{m}^2\,\text{s}^{-1}$).

How do the activation energy $Q$ and diffusivity $D$ compare among volume (bulk), grain-boundary, and surface diffusion?

Activation energy: $Q_{\text{bulk}} > Q_{\text{GB}} > Q_{\text{surf}}$; Diffusivity: $D_{\text{bulk}} < D_{\text{GB}} < D_{\text{surf}}$. Diffusivity increases as atomic coordination decreases and crystal disorder increases from bulk to free surfaces.