Dear All,
Here I have an interesting question that comes to me about crystallographic planes and growth rate. The literature survey shows, the (100)-oriented crystals the crystallographic plane (100) has higher growth rate as compare to other planes such as (110), (111). Generally speaking, a possible reason is, the crystallographic plane (100) has lower planer density (Number of atoms accumulated per unit area) compare to other planes. This is reasonable as it accumulates lesser number of atoms per unit area. Now the question is, the (100)-oriented unit cell contains all the planes (111), (110), (100) etc. then how one can say (that is extensively stated in literature) that (100) planes has higher growth rate compare to others? If (100) planes are growing, likewise the other planes are also showing growth, to make a complete unit cell, so how can we assume that this planes (100) has higher growth rate?
Your comments/suggestions and opinions are highly appreciated.
Hi
As far as I know, the facet with the lowest energy grows preferably. One important condition to satisfy this condition is the influx rate. If the influx of reactive species is limited, preferential-one-dimensional growth occurs. In contrast, with the high flux rate (at high temperature, high concentration etc) the simultaneous growth of multiple planes is possible.
If the growth is homogeneous (in the solution), then the above postulate works, however in heterogeneous film growth, the lattice spacing of substrate is important as well. The heterogeneous film/particle/rod will nucleate on the substrate with the least lattice mismatch with the substrate.
Best regards.
Crystallographic planes with lower indexes have higher density of units (atoms or molecules) and, correspondingly, lower free energy. For this reason they grow preferentially.
There is no " crystallographic planes growth" There is growth in the crystallographic direction (for example dendrite for the normal mechanism of growth, 100 prefered direction for metals with cubic symmetry) or growth of facets (layer-by-layer growth mechanism) formed by proper plane. What is it about?
@all According to Bravais law growth rate of crystalline plane is inversely proportional to the lattice density (L.D) in the plane
As: L.D(111)>L.D(110)>L.D(100)
In both attached (100 and 110-oriented) unit cells the number of atoms are equal. I am wondering how can we say that (100)-oriented crystals have higher growth rate than (110)-oriented crystal or (110)-oriented crystals have higher growth rate than (111)-oriented crystals (as proposed in the paper in the link ).
Article Orientation-dependent growth rate of crystalline plane study...
Of course, literature is right if we are speaking of growth on "exposed faces" of the crystal. In other words, if you have a macroscopic fcc crystal , cleave it normal to the 100 direction and apply the growth process, you will get a growth rate larger than in the case you would have cleaved the crystal normal to 110 direction, just because of a different atom density of the exposed face. That would be the case for multifaceted nanowires, for example.
The point is the difference between rate of growth and probability to actually obtain a given crystal orientation. High lattice density, i.e. crystal faces with low Miller indexes, indeed correspond to lower growth rate (Bravais law), and this implies their preferential growth, given to their lower free energy. This is generally accepted. The actual case raised by Waseem Abbas deals with two orientations with an equal number of atoms (a situation... too close to call). My guess is that here you should manage with different methods of growth to get either orientation. Probably...
What is "rate of growth of crystalline plane"?
Stуp on crystal facet is growing paraдlel to it!!
what I think, the crystal planes having lower planer density (P.D) grow faster than the planes of higher P.D due to lager attraction ability to outside atoms during deposition. Thus the growth rate depends upon the exposed faces (100, 110 or 111) which are different in different orientations.
am I right?
Dear @all, thanks for your time and useful comments and suggestions. Still, one thing is not clear to me, for that your opinions are highly appreciated.
Why is the attraction ability to outside atoms higher for the crystal planes having lower planer density (P.D)?
I think that you are referring to a cubic cell. In that case you must also take into account the type of Bravais cell, P, F
or I and other present symmetry elements such as screw axis and glide planes. Application of the X-ray extinction rules about the confitions for h,k and l learn about the largest interplanar spacing dhkl, and thus the slowest growth rate of the face (hkl).
See also:
Canadian Mineralogist
Vol. 16, pp. 387-391 (1978)
ON the validity of the Donnay-Harker law
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