1. Anandh Subramaniam & Kantesh Balani
Crystal Growth
Spiral growth
2D nucleation
MATERIALS SCIENCE
&
ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur
URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOK
Part of
A Learner’s Guide
Advanced Reading
Crystal Growth for Beginners
Ivan V Markov
World Scientific, Singapore (2017)

2. Click here to know more about
Crystal Growth
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Equilibrium shape of a crystal
We had noted that there are two shapes to consider for a ‘eumorphic’ (well formed) crystal: the equilibrium shape and the growth shape.
The growth of a crystal can take place by attachment of species (atoms, molecules, ions) from the liquid phase or the gas phase.
Deposition from the vapour phase can be via: physical vapour deposition (PVD) or chemical vapour deposition (CVD).
In the context of epitaxial growth, vapour phase deposition techniques take the names like: molecular beam epitaxy & liquid phase epitaxy.
Based on the capability to grow, crystal surfaces can be classified as:  close packed,  non-close packed (with ledges and kinks).
Non-close packed surfaces offer preferred site for atom attachment and thus circumvent the problem of 2D nucleation sites or the need for screw dislocations.
We have noted that (Surface energy and surface tension), there are three types of surfaces: (i) flat (F), (ii) with ledges (stepped) (L) & (iii) kinked (K).
E.g. in a simple cubic crystal: F(100), L(110), K(111).

3. Screw dislocation mediated crystal growth
Sir F.C. Frank realized that the growth of crystals from very dilute solutions is much faster than a computation involving attachment of atoms to flat surfaces (low index).
He postulated that the growth could be mediated by the step created by a screw dislocation terminating on the surface. The step acts like a preferred attachment site. The series of steps involved in the process are in F1-F9. During this process the step is not exhausted and provides ledge site for continued attachment of atoms.
Surface step F2
Screw dislocation
along ‘z’
The original step moves by one unit
in the direction of the arrow
(y-direction)
Attachment at ledge F1
Attachment of atoms in perpendicular direction
(x direction) F4 F3
Continued…

4. The ledge boundary forms the growth spiral
Growth along
y direction
Growth along
x direction
The story so far
Rotation of the ‘spiral arm’
F7’ F9 F7 F8
The ledge boundary forms the growth spiral

5. 2D Nucleation