Periodic chain and nature of faces

Within a crystal, molecules are bonded between each other by forces that can be represented by a geometric vector sum of the bonds between the atoms of both neighboring molecules. These intermolecular bonds recur periodically in a direction parallel to the bond considered, forming what is known as a bond chain that is clearly periodic.

Typically, faces are categorized according to the number of periodic chains parallel to them and accounting only for chains that contain strong bonds (for instance, Hydrogen bonds). According to Hartmann and Perdok [HAR 55a, HAR 55b, HAR 55c], we can distinguish:

  • 1) K faces that are not parallel to any periodic chain (PC). K faces develop very quickly.
  • 2) F faces containing at least two PCs. These faces develop slowly and, as a consequence, are dominant from a morphological point of view.
  • 3) Faces containing only one PC whose growth is intermediate.

Note that by saying that a K face has no PC is the same as saying that the E cou energy is low, and consequently, the attachment energy Efix is strong.

A mnemonic illustration of this would be to consider the molecules as the tops of tightly packed cubes. Each molecule is bonded to six neighbors on six sides (more or less common) by the eight cubes sharing the same molecule:

  • 1) K faces: Each cube top is the meeting point of three edges joining the top to tops A, B and C. The plan of triangle ABC defines a K-type face. Each surface molecule of this face has only three bonds, unlike the molecules inside the crystal that have six bonds (which is known as a coordination number of 6). This is why the molecules on the K faces are known as half-sites.
  • 2) S faces: The surface is in steps. Each cube top has four bonds on six.
  • 3) F faces: The surface is flat and even. Each surface molecule has a coordination number equal to 5.
 
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