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A topic from the subject of Inorganic Chemistry in Chemistry.

  • 1 year ago
  • 15 min read
Crystal Lattices and Unit Cells
Introduction

A crystal lattice is an arrangement of atoms, molecules, or ions in a repeating pattern. The unit cell is the smallest repeating unit of a crystal lattice. It is the building block from which the entire lattice is constructed. Crystal lattices are important in many areas of chemistry, including solid-state chemistry, materials science, and mineralogy.

Basic Concepts

Crystal structure: The arrangement of atoms, molecules, or ions in a crystal lattice.

Unit cell: The smallest repeating unit of a crystal lattice.

Lattice parameter: The distance between two adjacent atoms, molecules, or ions in a crystal lattice.

Space group: The symmetry operations that describe the arrangement of atoms, molecules, or ions in a crystal lattice.

Equipment and Techniques

X-ray diffraction: A technique used to determine the crystal structure of a material.

Electron diffraction: A technique used to determine the crystal structure of a material.

Neutron diffraction: A technique used to determine the crystal structure of a material.

Types of Experiments

Single-crystal X-ray diffraction: A technique used to determine the crystal structure of a single crystal.

Powder X-ray diffraction: A technique used to determine the crystal structure of a powder sample.

Electron diffraction: A technique used to determine the crystal structure of a thin film.

Neutron diffraction: A technique used to determine the crystal structure of a material that is not sensitive to X-rays.

Data Analysis

Indexing: The process of determining the lattice parameters and space group of a crystal lattice.

Structure refinement: The process of determining the atomic positions and thermal parameters of a crystal lattice.

Applications

Solid-state chemistry: Crystal lattices are used to understand the structure and properties of solids.

Materials science: Crystal lattices are used to develop new materials with desired properties.

Mineralogy: Crystal lattices are used to identify and classify minerals.

Conclusion

Crystal lattices are important in many areas of chemistry. They provide a fundamental understanding of the structure and properties of solids. Crystal lattices are also used to develop new materials with desired properties.

Lattices and Unit Cells in Chemistry

A lattice is a regular, three-dimensional pattern of points that extends throughout space. In a lattice, the points represent the locations of molecules, ions, or other small, repeating units. A unit cell is the basic repeating unit of a lattice. It is the simplest portion of a lattice that can be repeated to generate the entire lattice. The unit cell is also the basis for calculating the lattice's density.

Key points and Main Concepts: 1. Lattices
  • Lattices are three-dimensional, regular patterns of points that extend throughout space.
  • The points represent the locations of molecules, ions, or other small, repeating units.
  • The size and shape of the unit cell determine the properties of the lattice.
2. Unit Cells
  • Unit cells are the basic repeating units of lattices.
  • The unit cell is the simplest portion of a lattice that can be repeated to generate the entire lattice.
  • The unit cell is also the basis for calculating the lattice's density.
  • There are 14 types of Bravais lattices (unit cells when considering symmetry):
1. Simple Cubic

The simplest of all three-dimensional lattices is the simple cubic lattice. In this structure, each lattice point is at the corner of a cube, and the points are connected by lines to form a continuous framework. The simple cubic structure is not common among the elements. Polonium (α-polonium) crystallizes in this lattice.

2. Body-Centered Cubic (BCC)

This differs from the simple cubic structure in that it has an additional lattice point in the center of each cube. The body-centered cubic structure is found for many common metals such as alkali and transition elements like sodium, potassium, and chromium.

3. Face-Centered Cubic (FCC)

The FCC structure is very common among metallic elements, including copper (Cu), silver (Ag), gold (Au), platinum (Pt), nickel (Ni), palladium (Pd), and many more. In this structure, in addition to the eight corner lattice points of the cube, there is one lattice point in the center of each of the six square faces.

4. Hexagonal Close-Packed (HCP)

This lattice generally forms the crystal structure of elements with six valence electrons. The shape is not a perfect rectangular cuboid but slightly distorted. The first layer is made up of three close-packed spheres. The gap between the close-packed spheres on the first layer is covered by another set of three close-packed spheres to form the second layer. The third layer is similar to the first layer, and they are placed on top of each of the three depressions of the second layer. Thus, each sphere in the third layer lies directly above one of the spheres in the first layer.

5. Cesium Chloride (CsCl)

The structure of CsCl differs from other structures in that the two types of ions are of opposite sizes. The corner positions are filled by one type of ion, and the body-centered position is filled by the other type of ion.

6. Sodium Chloride (NaCl)

The cuboidal box is filled with two types of ions by dividing it into two interpenetrating FCC lattices. In the first lattice, the corner positions are filled by one type of ion, and the face-centered positions are filled with the second type of ion.

7. Calcium Fluoride (CaF2) (Fluorite)

This is an important structure formed by the combination of divalent cations and monovalent anions. In this, Ca2+ ions occupy the corner positions. The six faces are filled with F- ions. In addition, there are four more F- ions, one in the center of each edge of the cube.

8. Rutile (TiO2)

In this structure, the positions of cations and anions are interchanged with respect to CaF2. Here, Ti4+ ions occupy the corner positions. The six faces are each filled with O2- ions. In addition, there are two more O2- ions, one in the center of each edge of the cube.

9. Cadmium Iodide (CdI2)

The Cd2+ ions are present at the corner positions, and the I- ions are present at the face-centered positions (and some other positions to achieve the layered structure).

10. Natron (Na2CO3·2H2O)

The corner positions are filled with Na+ ions. The center of each face is filled by CO32- ions. Two H2O molecules are associated with the two Na+ ions present at the corners, and these H2O molecules are located inside the cuboid.

11. β-Uranium

The positions of the corner and face-centered ions are interchanged with respect to Na2CO3·2H2O.

12. Zirconium Dioxide (ZrO2)

This is a common structure for oxides of trivalent cations. The Zr4+ ions occupy the corner positions, and the O2- ions occupy the face-centered positions (along with other positions to create the complex structure).

14. Periclase (MgO)

A simple structure with Mg2+ ions at the face centers and O2- ions at the corners (or vice-versa, depending on the focus). Note that the original description of Perichite (MgSiO3) was not a correct crystal structure description.

The three most common unit cell types are:

  • Simple Cubic: This unit cell is a cube with lattice points at each of the eight corners.
  • Body-centered Cubic: This unit cell is a cube with lattice points at each of the eight corners plus one in the center.
  • Face-centered Cubic: This unit cell is a cube with lattice points at each of the eight corners plus one in the center of each of the six faces.
Experiment: Observing Crystal Lattices and Unit Cells (NaCl)
Materials:
  • Salt (NaCl)
  • Distilled Water
  • Glass beaker (small)
  • Stirring rod
  • Microscope (with slide capability)
  • Microscope slides
  • Cover slips
  • Hot plate (optional, for faster evaporation)
Procedure:
  1. Dissolve a small amount of salt in a small volume of distilled water in a clean glass beaker. The solution should be saturated or nearly saturated for better crystal growth.
  2. Stir the solution gently with a stirring rod until the salt is completely dissolved.
  3. If using a hot plate, gently heat the solution to near boiling then remove from heat and allow it to cool slowly. If not using a hot plate, skip to step 4.
  4. Place a drop of the salt solution onto a clean microscope slide.
  5. Carefully cover the drop with a cover slip, avoiding air bubbles.
  6. Allow the slide to sit undisturbed for at least 30 minutes, or preferably several hours or overnight, to allow for crystal formation through evaporation.
  7. Observe the slide under a microscope, starting with low power. Locate areas with visible salt crystals.
  8. Gradually increase the magnification to observe the crystal shapes and arrangements more closely. Note the shapes and relative sizes of the crystals.
Key Concepts:

Crystallization: The process by which dissolved salt molecules come out of solution and arrange themselves into an ordered, repeating pattern, forming crystals. The rate of crystallization is affected by factors like temperature, concentration, and the presence of impurities.

Crystal Lattice: The regular, three-dimensional arrangement of atoms, ions, or molecules in a crystal. NaCl forms a cubic crystal lattice.

Unit Cell: The smallest repeating unit within a crystal lattice. Identifying the unit cell's structure helps to understand the overall crystal structure.

Microscopy: Microscopy allows visualization of the crystal structures, providing evidence for the ordered arrangement of particles predicted by crystal lattice theories.

Significance:

This experiment demonstrates the formation of crystals from solution and provides visual evidence of crystal lattices. While observing perfect unit cells might be challenging with this simple experiment, students can observe the overall crystalline structure and understand how the regular arrangement of ions gives rise to the macroscopic properties of a salt crystal. This experiment introduces fundamental concepts of crystallography and the relationship between microscopic structure and macroscopic properties.

Note: It may be difficult to observe individual unit cells with this basic technique. The experiment is designed to demonstrate the formation and overall crystalline structure of NaCl, leading to an understanding of crystal lattices and the concept of a unit cell.

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