We know that crystal orientation will affect the mobility Mobility Dependence on Crystal Orientation and Strain Engineering. What is crystal orientation? Is there a basic textbook/lecture explaining this concept?

For 3d crystals, it seems to be about sectioning (crystal planes http://www.crystal-scientific.com/xtal_orientation.html) and rotation of the crystal (for cut, etc.) of the 3d lattice, in various directions.

it is often necessary to precisely cut the ingot, either to obtain a section with the correct orientation and finished size for the final crystal, or to provide a specific crystal orientation (e.g. a <311> cut). Crystal Scientific use an X-ray diffraction system to identify the planes in the crystal structure and to check the precise orientation of the crystals for machining to an accuracy of 0.05 degrees.

But below we study 2d materials, what is crystal orientation of 2d materials? Is it because metal dichalcogenides can form 3d (bulk) crystal, and 2d metal dichalcogenides can be regarded as a section of the 3d crystal? (This doesn't make much sense, for example, graphene's structure is very different from 3d carbon structure, we cannot simply section a 3d crystal to get the corresponding 2d crystal.)

Orientation is often used in relevant literature to describe angles or directions:

the relative orientation between the layers
control over the growth orientation of MX2 layers with respect to the substrate surface

Possibly crystal orientation is to describe the growth direction (dynamic instead of static) of the crystal layer, or the relative angle of lattice with respect to the substrate, while random orientation is to say that the direction of crystal growth or lattice has random direction.

control over the crystal orientation of deposited MX2 films by control of the deposition rate.
second harmonic imaging microscopy, has been recently employed as a powerful tool for determining the grain boundaries and crystal orientations within monolayer nanosheets, especially those grown uniformly over a large area by bottom-up methods, such as CVD.

[Remaining question:] But if so, why certain crystal orientation will result in special properties? In other words, why the orientation matters?
Is it because when we apply for example an electrical field to the 2d material, due to the heterogeneity of a crystal, the relative directions of the electrical field and the crystal lattice will result in different behaviors. For example, in a lattice direction where adjacent points (of the lattice) are nearest to each other, it is easier to apply an electrical field to polarize the electrons and significantly change the electron density distribution and the property of the crystal, e.g. we could make the crystal metallic (electons easily transit from a point to another). (Such behavior can be modeled using ab initio like DFT.)

In other words, by considering the directions of external field (electrical or light-induced ones) and the (induced change of) electron density distribution of lattice (relative to points), the significance of the crystal orientation seems to make sense to me.

(Similarly, since the substrate might be heterogeneous too, and therefore has certain electron distribution, it is possible that relative orientation of the crystal ('MoS$_2$ domains' below) and the substrate (e.g. SiO$_2$ below) might cause varied interactions of the two, and crystals of different properties; in particular, the (field-effect) mobility, which should be largely affected by the strength of the crystal-substrate interaction.
As a summary, the relative orientations of the different layers, layer-substrate, layer(s)-external field might matter for the properties of the crystal, which could be explained by electron/nucleus/external field interaction, and computed using quantum. Growth is about forming new bonds/polarization etc. of electrons.)

Original question: How to understand field-effect mobility and lattice orientation of 2-dim metal dichalcogenides?

I am reading a paper (Sajedeh Manzeli, 2017, 2D transition metal dichalcogenides) about metal dichalcogenides and chemical vapour deposition.


Q1 What is field-effect mobility? Is it a mono/multi-layer crystal moving with light/voltage created electric field? Does it enable us to design photoelectric devices that control the motions by light/electrical signals? ..

(added: both seem yes. Usually multi-layer crystal is less exposed to the environment and has higher mobility. The design of such devices seems to be called mobility engineering (another important material technique of such crystals is strain engineering.) See 2D transition metal dichalcogenides, Mobility engineering, doi:10.1038/natrevmats.2017.33.)

..Can light create an electric field?

Q2 why MoS2 layer has random lattice orientation and form boundaries of different types? [Remaining question:] What are (grain) boundaries of different types? What is lattice orientation? Are they something about the entire crystal, or something about the local unit cell? (According to https://kees.cc/tuning/lat_perbl.html, it seems to be the latter. ..

(Correction: the former, the link is more about linear (and in the final example there, non-linear) transformation between lattices of various shapes.)

.. https://chempedia.info/info/lattice_orientation/ is also relevant but I don't quite understand it.) Why does lattice orientation cause boundaries of different types and different electrical and optical properties?

Lattice orientation seems to be the orientation of the bonds (e.g. angles between bonds). Random orientation percolation (Grimmett model) from the viewpoint of statistical mechanics.

randomly assign an orientation for every bond of the lattice in the following way

How can I calculate the opacity of a crystal as function of its lattice orientation?

orientation ...the tilt angle 𝜃 from 0∘ to 90∘.

  • $\begingroup$ physics.stackexchange.com/q/158532/273056 chaos, fractal geometry, bonding, and growth orientation $\endgroup$ May 30, 2022 at 9:20
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    $\begingroup$ Simply said, the mobility is $\mu = e \frac{\tau} {m^*}$, where e is a particle charge, $m^*$ is effective mass $\tau$ is average scattering time. The effective mass changes according to the potential (which is a consequence of a crystal orientation). Thus the mobility depends on the crystal orientation. Chick this links out en.wikipedia.org/wiki/Effective_mass_(solid-state_physics) en.wikipedia.org/wiki/Electron_mobility $\endgroup$ May 30, 2022 at 11:37
  • $\begingroup$ Thanks. the mobility is 'the ratio of the velocity to the electric field'. Drift velocity $v_d = \mu E$. The particle charge / effective mass will increase / decrease $a$ of the particle. But why scattering time is proportional to $\mu$; it seems to me the longer the time, the less the mobility? $\endgroup$ May 30, 2022 at 11:56
  • $\begingroup$ I read the wiki ('...how long the carrier is ballistically accelerated by the electric field'), it seems scattering time is $t$ in $v = at$, where $a=e\frac E {m^*}$ is defined above, so the longer the acceleration is, the larger $v_d$. \\So basically $\mu$ describes the behavior of a charged particle, but it seems a 2d crystal (domain) has no net charge? $\endgroup$ May 30, 2022 at 12:07
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    $\begingroup$ The average scattering time is a sort of time between collisions, so you can say that if the time is higher, the charge will have less collisions and will be, consequently, more "mobile" $\endgroup$ May 30, 2022 at 12:10


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