11.7 Structures of Solids

Unit Cells The Crystal Structure of Sodium Chloride Close Packing of Spheres

Cara Barskey, Brendan Degnan, Courtney Gregor

Crystalline SolidsAtoms, ions, or molecules are ordered in well-

defined arrangements

Amorphous Solids Greek – “without form”, particles

have no orderly structure

Quartz When melted, converted from crystalline amorphous

Unit CellRepeating unit of a solid, the crystalline “brick”Shows symmetry characteristic of entire pattern (2-dimensional)Described by lengths of edges and angles

Crystal lattice - represented by 3-D array of points

Types of Unit Cells7 basic types - simplest is cubic unit cell3 types of cubic unit cell

Primitive: lattice points at CORNERS ONLYBody-centered: at corners and at center of unit cellFace-centered: lattice points at corners and at center of each face

Simple crystal structuresCubic unit cells with only ONE ATOM centered at each lattice point – as seen in metals

3-D Solids

Nickel atom on each of the eight corners of the cell Simple cubic structure:

8 corners x 1/8 = 1 atomBody-centered cubic structure = two atoms per unit cell

Body-centered cubic structure:(8 corners x 1/8) + 1 body = 2 atoms

Six atoms on the faces of the unit cell = three nickel atoms, for a total of four atoms per unit cell

Face-centered cubic structure:(8 corners x 1/8) + (6 faces x 1/2) = 4 atoms

Crystal Structure of Sodium ChlorideParticles at corners, edges, and faces are shared by other unit cells (fractions)Total cation : anion ratio must be SAME for entire crystalEqual number of Na+ ions and Cl- ionsEx: Unit cell of CaCl21 Ca+2 for every 2 Cl-

Fraction of an atom that occupies a unit cell

Position in Unit Cell Fraction in Unit Cell

Center 1

Face 1/2

Edge 1/4

Corner 1/8

PracticePlan : Find total number of ions of each typeSolve : There is 1/4 of an Na+ on each edge, a whole Na+ in the center, 1/8 of a Cl- on each corner, and 1/2 of a Cl- on each face.

Close Packing of SpheresClose contact, maximize forcesMost efficient arrangement equal-sized spheresEach sphere has six others in layerPossible to have second and third layer

Two Depression Types of 3rd LayerHexagonal Close Packing

3rd layer spheres are placed in line with 1st layer

1,3 & 2,4 repeat = ABAB

Cubic Close Packing3rd layer spheres are placed as staggered in relation to 1st layer

1,4 repeat = ABCA Face-centered cubic

Coordination NumberEach sphere 12 equidistant neighborsCoordination number = 12

Number of particles immediately surrounding a particle in the crystal structure

Body-centered has coordination number of 8Simple cubic-centered has coordination number of 6Unequal-sized spheres: large particles take close-packed arrangements, small particles occupy cavities between larger spheres

Section QuestionsHow does an amorphous solid differ from a crystalline one? Give an example of an amorphous solid

In a crystalline solid, particles are arranged in a regularly repeating pattern. An amorphous solid is one whose particles show no such order. An example of an amorphous solid is rubber or glass.

Amorphous silica has a density of about 2.2 g/cm3, whereas the density of crystalline quartz is 2.65 g/cm3. Account for this difference in densities

Something has an effect on something that causes one thing to be more dense than the other thing

What is a unit cell? What properties does it have?

The unit cell is the smallest part of the crystal than can reproduce the three-dimensional structure, which can also be represented by its crystal lattice. The simplest unit cells are cubic; these cubic unit cells can be primitive, body-centered, or face-centered.

Perovskite, a mineral composed of Ca, O, and Ti has the cubic unit cell shown in the drawing. What is the chemical formula of this mineral?

TiCa8O6

The elements xenon and gold both have solid-state structures consisting of cubic close-packed arrangements of atoms. Yet Xe melts at -112 °C and gold melts at 1064 °C. Account for these greatly different melting points.

It requires more kinetic energy to overcome the delocalized metallic bonding in gold than to overcome the relatively weak London dispersion forces in xenon.

Rutile is a mineral compound of Ti and O. It’s unit cell, shown in the drawing, contains Ti atoms at each corner and a Ti atom at the center of the cell. Four O atoms are on the opposite face of the cell, and two are entirely with-in the cell. A.) What is the chemical formula. B.) What is the nature of the bonding that holds the solid together?

Ti3O2 Electrostatic attractions because its ionic bonding (see Table 11.7 on page 435)

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 Angstroms. The atom in the center of the face is in contact with the corner atoms, as shown in the drawing. A.) Calculate the atomic radius of an iridium atom. B.) Calculate the density of the iridium metal.

4(192.2 amu)=768.8 amu

22.7 g/cm3

768.8 amu

(3.833 Å)3

1 g

6.02 x 1023 amu (10^-8 cm)3

(1 Å)3

Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, Figure 11.34). A.) How many aluminum atoms are in a unit cell? B.) What is the coordination number of each aluminum atom? C.) Assume that the aluminum atoms can be represented as spheres, as shown in the drawing fro Exercise 11.59. If each Al atom has a radius of 1.43 Å, what is the length of a side of the unit cell? D.) Calculate the density of aluminum metal.

½(6)+1/8(8)=4 atoms of Al 12, it’s a face-centered cubic cell unit1.43 Å x 4=5.72 Å2x2=5.72x=1.69 Å (10^-8 cm)3

4(27.0) amu

(1.69 Å)3

1 g

6.02x1023 amu

(1 Å)3

37.2 g/cm3