PPT UNIT CELL

• Unit Cell - A unit cell is the basic structural (repeating) unit of a crystalline solid.

  It acts as a building block for the entire crystal lattice.
• Lattice - Used in the context of crystal structures; in this sense lattice means a three- dimensional array of points coinciding with atom positions or sphere centers.
• Lattice Point - For each sphere, it denotes an atom, ion, or molecule and it is called a lattice point.
• Unit Cells

  
• Seven Types of Unit Cells

  
• Seven types of Unit Cells

  
• Seven types of Unit Cells

  
• Seven types of Unit Cells

  
• Face-Centered Cubic Crystal Structure

  • The face-centered cubic (FCC) is a crystal structure with atoms located at each of the corners and the center of all the cube faces.
  • Some familiar metals having this crystal structure are copper, aluminum, silver, and gold.
• Face Centered Cubic Crystal Structure

  
• Face Centered Cubic

  
• Formulas FCC

  
• Face-Centered Cubic Crystal Structure

  
• In determining the number of atoms associated with each unit cell

  that depends on an atom’s location, shared with adjacent unit cells

  may be considered.

  The number of atoms per unit cell, N, can be computed using the

  following formula:

  
• FCC Solution Set

  
• Characteristics of Crystal Structure

  a.Coordination number (for metals) wherein each atom has the same

  number of nearest-neighbor or touching atoms.

  Example: For FCCs, the coordination

  number is 12.

  
• Atomic Packing Factor (APF) which is the sum of the sphere

  volumes of all atoms within a unit cell divided by the unit cell volume.

  From the definition of APF, the formula is:

  
• Body-Centered Cubic Crystal Structure

  
• The BCC structure is a common metallic crystal arrangement where atoms are positioned at the eight corners of a cube, with one atom at the center.

  Some common metals under this crystal structure are Iron (Fe) and Chromium (Cr).
• BCC Equation no. 4

  
• Body-Centered Cubic Crystal Structure

  
• Hexagonal Close-Packed Crystal Structure

  Hexagonal Close-Packed(HCP) is a common metallic crystal

  structure where atoms are packed closely in a hexagonal

  pattern.

  The unit cell has six atoms forming hexagons on the top and

  bottom faces, surrounding one atom in the center. A middle

  layer adds three more atoms, creating a compact, dense

  structure.

  
• HCP Equation no. 5

  
• HCP Calculation

  
• Density - refers to mass per unit volume, and it tells us how closely packed the atoms or molecules are in a substance.
• Theoretical Density - the calculated density based on its atomic structure and molecular weight, helps us understand the ideal structure of a crystal and compare it with actual density to identify defects.
• Density Computations

  
• X-Ray Diffraction by Crystals

  X-ray diffraction refers to the scattering of X-rays by the units of a crystalline solid. The patterns produced by scattering, or diffraction are used to deduce the particle arrangement in the solid lattice.
• X-Ray Diffraction by Crytals (Image)

  
• In 1912, Max von Laue, a German physicist recommended that since the wavelength of X-rays is comparable in magnitude to the distances between lattice points in a crystal, then the lattice should be able to diffract X-rays. Interference in the waves associated with X-rays produced an X-ray diffraction pattern.

  Figure 6. Constructive interference (a) and destructive interference (b)

  of two waves of the same wavelength and amplitude (Chang &

  Goldsby, 2017).
• X-Ray Diffraction Setup

  
• X-Ray Diffraction

  
• Bragg Law - a special case of Laue diffraction, which determines the angles of coherent and incoherent scattering from a crystal lattice.

  
• Electron-Density Contour Map

  It tells us the relative electron densities at various locations in a

  molecule. The densities reach a maximum near the center of each

  atom and in this manner, we can determine the positions of the

  nuclei and thus the molecular geometric parameters. Chemists can

  construct an electron-density contour map from the diffraction

  patterns because X-rays are scattered by electrons but it is with the

  use of a complex mathematical procedure.
• Types of Crytals

  In determining the structures and properties of crystals,

  it is important to consider the kinds of forces that hold

  the particles together.

  The classification of any crystal has four types: ionic,

  covalent, molecular, or metallic.
• Ionic Crystals

  • composed of charged species
  • anions and cations are generally quite different in size
  • radii of the ions must be known because it is helpful in understanding the structure and stability of these compounds
• Ionic Crystals

  For example, the NaCl crystal shows that the edge

  length of the unit cell of NaCl is twice the sum of the

  ionic radii of Na⁺ and Cl⁻.

  We calculate the length of the edge to

  2(95 + 181) pm = 552 pm
• Ionic Crystals

  The edge length shown in the figure was determined by X-ray diffraction which has a value of 564 pm.

  The difference between these two values tells us that the radius of an ion actually varies slightly from one compound to another.
• Ionic Crystals

  
• Ionic Crystals