The Structures Of Simple Solids

Flashcards covering the description of solid structures, types of solids, unit cells, close packing, and the characteristics of metallic and ionic solids based on Dr. Disah Mpadi's lecture notes.

What is the definition of the solid state according to the text?

The state of matter whose melting point is above room temperature, characterized by a definite shape and volume, high density, and strongly held constituent particles.

How are crystalline solids and amorphous solids distinguished by their melting points and nature?

Crystalline solids have a sharp melting point and are anisotropic, while amorphous solids have no sharp melting point and are isotropic.

What is anisotropy in the context of crystalline solids?

Anisotropy means physicochemical properties (such as hardness, electric/thermal conductivity, and magnetization) show different values when measured along different directions.

Name the four categories of solids based on their bonding types.

Ionic, metallic, molecular (held by van der Waals or hydrogen bonds), and framework/network compounds (held by covalent bonds).

According to the text, what are the characteristic properties of network covalent solids?

Most are very hard, either sublime or melt at very high temperatures, and are generally non-conductors of electricity (e.g., Diamond, $SiC$).

What is the difference between an 'Ideal Crystal' and a 'Real Crystal'?

An Ideal Crystal is an infinite single crystal with $100\%$ order and purity, whereas a Real Crystal is never perfect and contains violations of long-range order known as imperfections.

How is a unit cell defined in crystallography?

A unit cell is the smallest repeating building unit in a crystal lattice that, when stacked together following translations, reproduces the three-dimensional crystal.

What components make up a crystal structure?

Crystal structure = Bravais lattice + motif (Basis).

What are the 'lattice parameters' or 'the metric' of a unit cell?

The lengths ($a, b, c$) and the angles ($\alpha, \beta, \gamma$) used to define the size and shape of a unit cell relative to an origin.

What does the Correspondence Principle state?

It states that there is a connection or relationship between the outer shape (morphology) of a crystal and its inner structure.

Define the fractional coordinates of an atom site.

The atomic site parameters given as a coordination triple $(x, y, z)$ which are fractional amounts of the lattice constants ($a, b, c$), where $0 \le x, y, z \le 1$.

What are the rules for counting lattice points in a 3-D unit cell?

A point in the body counts as $1$; a point on a face counts as $\frac{1}{2}$; a point on an edge counts as $\frac{1}{4}$; and a point at a corner counts as $\frac{1}{8}$.

What is the total number of lattice points in a face-centred cubic (fcc) unit cell?

$$8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$$

Describe the stacking sequences for hexagonal close-packed (hcp) and cubic close-packed (ccp) structures.

Hcp follows an $ABA$ arrangement, while ccp follows an $ABC$ arrangement.

What is the coordination number (CN) of a sphere in a close-packed arrangement?

$$12$$

What is the ratio of spheres to octahedral holes to tetrahedral holes in a close-packed structure?

$$1:1:2$$

What is the formula for Atomic Packing Factor (APF)?

$$APF = \frac{V_{atoms}}{V_{unit\,cell}}$$

What is the packing efficiency (occupied space) for a face-centred cubic (fcc) and a body-centred cubic (bcc) unit cell?

Fcc (or ccp) has a packing efficiency of $74\%$, and bcc has a packing efficiency of $68\%$.

Provide the general formula for calculating the density ($\rho$) of a substance from its crystal structure.

$\rho = \frac{nA}{V_c N_A}$ where $n$ is the number of atoms, $A$ is the molar mass, $V_c$ is the unit cell volume, and $N_A$ is Avogadro's constant.

What is polymorphism in metals?

The ability of a metal to adopt different crystal forms or phases under different conditions of temperature and pressure.

Which crystal structure is generally favored at high temperatures compared to low temperatures?

Less closely packed structures (such as bcc) are favored at high temperatures, while closely packed phases are favored at low temperatures.

What is the Goldschmidt correction used for?

It converts atomic radii of metals to the value they would have in a close-packed structure with $12$-fold coordination.

What are the three criteria for forming substitutional solid solutions (alloys)?

1. Atomic radii are within $15\%$ of each other; 2. Crystal structures of the pure metals are the same; 3. Electropositive characters are similar.

How does the rock-salt structure fill its holes?

It is based on a ccp array of anions with cations in all the octahedral holes, resulting in $(6,6)$-coordination.

Describe the characteristic of the perovskite structure ($ABX_3$).

It is typically cubic with the $A$ cation surrounded by $12$ $X$ anions and the $B$ cation surrounded by $6$ $X$ anions.

State the radius ratio ($\gamma$) formula used to predict coordination numbers in binary compounds.

$\gamma = \frac{r_{small}}{r_{large}}$, where $r_{small}$ is usually the cation and $r_{large}$ is commonily the anion.

What is the limiting radius ratio range for an octahedral geometry with a coordination number of $6$?

$0.414$ to $0.732$