Lab 5: Solids and Unit Cells Overview

Crystalline Solid

Solid with a regular atomic arrangement.

Unit Cell

Simplest repeating unit in a crystalline structure.

Coordination Number

Number of nearest neighbors around an atom.

Simple Cubic Structure

Atoms arranged in layers directly above each other.

Body-Centered Cubic

Unit cell with an atom at the center.

Face-Centered Cubic

Unit cell with atoms at each face center.

Atomic Radius

Half the distance between two adjacent atoms.

Density Calculation

Mass of unit cell divided by volume.

X-ray Diffraction

Technique to determine crystalline structures.

Lattice Points

Positions representing atoms in a unit cell.

Polonium

Only metal crystallizing in simple cubic structure.

Edge Length

Distance between corners of a unit cell.

Volume of Unit Cell

Calculated as edge length cubed.

Intermolecular Energy

Total energy due to interactions between particles.

Metallic Properties

Malleability and ductility due to atomic arrangement.

Cubic Lattice Types

Includes simple, body-centered, and face-centered.

Mass of Unit Cell

Total mass of atoms within the unit cell.

Crystalline Structure

Regular arrangement of atoms in solids.

Packing Efficiency

Percentage of volume occupied by atoms.

Atomic Diameter

Twice the atomic radius.

Nickel Density

Actual density of nickel is 8.90 g/cm³.

Polonium Density Calculation

Density derived from unit cell mass and volume.

Lattice Structure

Arrangement of atoms in a crystalline solid.

Crystalline Arrangement

Maximizes attractive interactions between particles.

Metal Crystal Geometries

Common types include simple, body-centered, face-centered.

Eight Corners

Each corner atom contributes one-eighth to unit cell.

Layer Arrangement

Spheres in layers directly above or below.

Volume Units

Converted from pm to cm for density.

Density of Polonium

Calculated using unit cell dimensions and mass.

Crystalline Solids

Over 90% of naturally occurring solids.

Body-Centered Cubic (BCC)

Cubic unit cell with atoms at corners and center.

BCC Atom Count

Contains two atoms per unit cell.

BCC Packing Efficiency

Atoms occupy about 68% of total volume.

Isomorphous Metals

Metals crystallizing in the same structure.

Face-Centered Cubic (FCC)

Cubic unit cell with atoms at corners and faces.

FCC Atom Count

Contains four atoms per unit cell.

FCC Packing Efficiency

Atoms occupy about 74% of total volume.

Cubic Closest Packing (CCP)

Another name for face-centered cubic arrangement.

Coordination Number in FCC

Each atom contacts 12 nearest neighbors.

Hexagonal Closest Packing (HCP)

Consists of two alternating layers of atoms.

Layer Arrangement in HCP

Stacking follows ABABAB pattern.

Layer Arrangement in CCP

Stacking follows ABCABC pattern.

Atomic Radius Calculation (FCC)

Diagonal equals four atomic radii.

Calcium Unit Cell Edge Length

558.8 pm for face-centered cubic structure.

Silver Unit Cell Edge Length

409 pm for face-centered cubic structure.

Total Atoms in FCC Unit Cell

Includes 1 from corners and 3 from faces.

Density of Calcium

Density calculated from unit cell mass and volume.

Density of Silver

Density calculated from unit cell mass and volume.

Face Diagonal in FCC

Connects atoms at corners and face centers.

Hexagonal Layer Contact

Atoms in second layer touch three in first.

Metallic Crystallization

Most metals crystallize in closest-packed arrays.

Examples of Isomorphous Metals

K, Ba, Cr, Mo, W, Fe in BCC.

Examples of HCP Metals

Cd, Co, Li, Mg, Na, Zn.

Examples of CCP Metals

Ag, Al, Ca, Cu, Ni, Pb, Pt.

Axes of Unit Cell

Lengths a, b, and c define unit cell dimensions.

Angles of Unit Cell

Angles α, β, and γ between unit cell axes.

Lattice Systems

Seven distinct arrangements of crystal lattices.

Ionic Crystals

Crystals formed from different sized ions.

Monatomic Ions

Single charged ions behaving as spheres.

Stable Ionic Structures

Formed by surrounding opposite charge ions.

Cations

Positively charged ions in ionic compounds.

Anions

Negatively charged ions in ionic compounds.

Tetrahedral Hole

Space surrounded by four anions in tetrahedron.

Octahedral Hole

Space surrounded by six anions in octahedron.

Closest-Packed Array

Maximized packing of ions in crystal structure.

Cation:Anion Ratio

Proportion of cations to anions in compounds.

Zinc Sulfide

ZnS, zinc occupies half tetrahedral holes.

Lithium Selenide

Li3Se, lithium occupies all tetrahedral holes.

Stoichiometry

Ratio of elements in a compound.

Aluminum Oxide

Al2O3, aluminum occupies two-thirds octahedral holes.

Titanium Oxide

TiO2, titanium occupies half octahedral holes.

Simple Cubic Array

One cubic hole per anion in structure.

Cubic Holes

Spaces in cubic arrays for cation occupancy.

Ionic Compound Structure

Determined by ion sizes and stoichiometry.

HCP Structure

Hexagonal close-packed arrangement of ions.

CCP Structure

Cubic close-packed arrangement of ions.

Vacant Tetrahedral Holes

Unoccupied spaces in tetrahedral arrangements.

Octahedral Hole Ratio

1:1 ratio of octahedral holes to anions.

Cation Size Influence

Cation size determines hole type occupancy.

Ionic Compound Examples

Li2O, Na2O, Li2S, Na2S in tetrahedral holes.

Cation Occupancy

Cations occupy holes based on size.

Ionic Compound

A compound formed by cations and anions.

Cation

Positively charged ion, e.g., Cs+.

Anion

Negatively charged ion, e.g., Cl−.

Cesium Chloride (CsCl)

Example of ionic compound with simple cubic structure.

Body Diagonal

Diagonal line connecting opposite corners of a cube.

1:1 Stoichiometry

Equal ratio of cations to anions in a compound.

FCC Structure

Face-centered cubic arrangement of ions.

Sodium Chloride (NaCl)

Example of ionic compound with FCC structure.

Octahedral Holes

Spaces in FCC structure occupied by smaller cations.

Zinc Sulfide (ZnS)

Ionic compound with FCC structure and tetrahedral holes.

Tetrahedral Holes

Spaces in FCC structure occupied by smaller ions.

Calcium Fluoride (CaF2)

Ionic compound with FCC structure and 1:2 ratio.

Ionic Radii

Size of ions in an ionic compound.

Pythagorean Theorem

Mathematical relation used for calculating distances.

X-ray Crystallography

Technique to determine crystal structure using X-rays.

Diffraction

Change in direction of waves encountering barriers.

Constructive Interference

Waves combine to increase amplitude.

Interatomic Distance

Distance between atoms in a crystal.

Wavelength (λ)

Distance between successive peaks of a wave.