concepts of crystal geometry
Download
Skip this Video
Download Presentation
Concepts of Crystal Geometry

Loading in 2 Seconds...

play fullscreen
1 / 17

Concepts of Crystal Geometry - PowerPoint PPT Presentation


  • 99 Views
  • Uploaded on

Concepts of Crystal Geometry. X-ray diffraction analysis shows that the atoms in a metal crystal are arranged in a regular, repeated three-dimensional pattern. The most elementary crystal structure is the simple cubic lattice (Fig. 9-1). Figure 9-1 Simple cubic structure.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Concepts of Crystal Geometry' - holmes-pate


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

X-ray diffraction analysis shows that the atoms in a metal

  • crystal are arranged in a regular, repeated three-dimensional
  • pattern.
  • The most elementary crystal structure is the simple cubic lattice
  • (Fig. 9-1).

Figure 9-1 Simple cubic structure.

slide3

We now introduce atoms and molecules, or “repeatable

  • structural units”.
  • The unit cell is the smallest repetitive unit that there are 14
  • space lattices.
  • These lattices are based on the seven crystal structures.
  • The points shown in Figure 9-1 correspond to atoms or groups
  • of atoms.
  • The 14 Bravis lattices can represent the unit cells for all
  • crystals.
slide4

Figure 9-2 (a) The 14 Bravais space lattices (P = primitive or simple; I = body-centered cubic; F = face-center cubic; C = base-centered cubic

slide11

Figure 9-4 Hexagonal

close-packed structure

Figure 9-5 Stacking of

close-packed spheres.

slide12
Three mutually perpendicular axes are arbitrarily placed through one of the corners of the cell.
  • Crystallographic planes and directions will be specified with

respect to these axes in terms of Miller indices.

  • A crystallographic plane is specified in terms of the length of its intercepts on the three axes, measured from the origin of the coordinate axes.
  • To simplify the crystallographic formulas, the reciprocals of these intercepts are used.
  • They are reduced to a lowest common denominator to give the Miller indices (hkl) of the plane.
slide13

For example, the plane ABCD in Fig. 9-1 is parallel to the

  • x and z axes and intersects the y axis at one interatomic
  • distance ao. Therefore, the indices of the plane are
  • , or (hkl)=(010).

Figure 9-1 Simple cubic structure.

slide14

There are six crystallographically equivalents planes of

  • the type (100).
  • Any one of which can have the indices (100), (010),
  • (001), depending upon the choice of
  • axes.
  • The notation {100} is used when they are to be considered
  • as a group,or family of planes.
slide15
Figure 9.6(a)shows another plane and its intercepts.

Figure 9-6(a) Indexing of planes by Miller indices rules in the cubic unit cell

slide16
As usual, we take the inverse of the intercepts and multiply them by their common denominator so that we end up with integers. In Figure 9.6(a), we have
slide17
Figure 9.6(b) shows an indeterminate situation. Thus, we have to translate the plane to the next cell, or else translate the origin.

Figure 9-6(b) Another example of indexing of planes by Miller rules

in the cubic unit cell.

ad