Inorganic Chemistry: Structures and Properties of Solids

This flashcard set covers the fundamental concepts of inorganic chemistry regarding crystalline solids, including crystal systems, unit cells, lattice structures, defects, band theory, semiconductors, alloys, and calculations for lattice enthalpy and density.

Unit Cell

The smallest repeating unit of a crystalline solid that contains specific positions (corners, edges, faces, and body) where lattice points are located.

Lattice Points

The locations of atoms, ions, or molecules within a crystalline solid represented in a unit cell structure.

Simple Cubic (SC)

A crystal structure where lattice points are located only at the corners, having an edge length $a = 2r$ and a packing efficiency of $52\%$. Example: Polonium ($Po$).

Body-centered Cubic (BCC)

A crystal structure with lattice points at the corners and the center of the body, having an edge length $a = \frac{4r}{\sqrt{3}}$ and a packing efficiency of $68\%$. Examples: $Ba$, $Cr$, $Fe$, $W$, and alkali metals.

Face-centered Cubic (FCC)

Also known as cubic close-packed ($CCP$), this structure has lattice points at the corners and the centers of faces, an edge length $a = \frac{4r}{\sqrt{2}}$, and a packing efficiency of $74\%$. Examples: $Ag$, $Al$, $Au$, $Pb$, $Ni$.

Hexagonal Close-packed (HCP)

A structure where atoms are arranged in hexagonal layers with an $ABABAB$ layering sequence, achieving a packing efficiency of $74\%$. Examples: $Mg$, $Ti$, $Zn$, $Be$.

Packing Efficiency

The percentage of space occupied by atoms in a crystal structure.

Octahedral Hole

A void in a close-packed structure surrounded by six nearest neighbor atoms positioned at the corners of an octahedron; they are larger than tetrahedral holes.

Tetrahedral Hole

A void in a close-packed structure surrounded by four nearest neighbor atoms forming a tetrahedral shape.

Radius Ratio ($r_{+}/r_{-}$)

A calculation used to predict coordination numbers and the specific type of lattice structure based on the relative sizes of ions.

Intrinsic Defects

Structural imperfections that occur within a pure substance, such as Schottky or Frenkel defects.

Schottky Defect

A point defect characterized by a missing cation and a corresponding missing counter anion within a perfect lattice, which decreases the density of the solid.

Frenkel Defect

A point defect occurring when an ion is displaced from its normal site and placed into an interstitial hole, leaving the overall density unchanged.

Metallic Bond

A bond between metal atoms where valence electrons are delocalized, forming a "sea" or "swarm" that surrounds the metal cations.

Valence Band

In band theory, the energy band that contains the valence electrons.

Conduction Band

The next higher energy band above the valence band which is partially filled or empty, allowing for the movement of electrons.

Band Gap

The energy difference between the valence band and the conduction band; a large gap results in an insulator, while a small/zero gap exists in conductors.

n-type Semiconductor

An extrinsic semiconductor created by doping a material with elements from Group 15, resulting in a surplus of electrons.

p-type Semiconductor

An extrinsic semiconductor created by doping a material with elements from Group 13, resulting in a lack of electrons (holes).

Substitutional Alloy

An alloy where some host metal atoms are replaced by other metal atoms of similar size. Examples: Brass, Bronze.

Interstitial Alloy

An alloy where small atoms occupy the interstices or holes in the closest packed metal structure. Example: Steel (Carbon in Iron).

Molecular Solids

Solids consisting of discrete molecules held by weak intermolecular forces but strong internal covalent bonds, typically resulting in softness and low melting points. Examples: $H_{2}O$, $S_{8}$, $P_{4}$.

Covalent Network Solids

Atomic solids composed of atoms bonded to nearest neighbors via strong covalent bonds in a continuous network. Examples: Diamond, Graphite.

Lattice Enthalpy ($U$ or $\Delta H^{\circ}$)

The change in energy that occurs when separated gaseous ions are packed together to form an ionic solid or to form a gas of ions from the solid.

Born-Haber Cycle

A thermochemical cycle that breaks down the formation of an ionic compound into hypothetical steps (sublimation, ionization, dissociation, electron affinity, and lattice enthalpy) to apply Hess's Law.

Hydration Enthalpy (\Delta H_{hydration})

The energy released when gaseous ions are surrounded by water molecules; more negative values indicate stronger ion-water interactions and greater solubility.

Born-Land Equation

A theoretical equation used to calculate lattice enthalpy based on an electrostatic model using crystal charges, internuclear distance, and the Madelung constant.

Kapustinskii Equation

A semi-empirical formula used to estimate lattice enthalpy when the Madelung constant and structural data of the crystal are unavailable.

Madelung Constant ($M$)

A value used in the calculation of lattice energy that accounts for the geometric arrangement of ions in a crystal lattice structure.