I think single-crystal is easily defined as crystal that have no grain boundaries and other defects. Usually, single-crystal grows continuou continually with single crystal nucleus. Single-crystal silicon is a good example.

I hope the wiki can help you.

https://en.wikipedia.org/wiki/Single_crystal

Dear Xu:

The size of the nanoparticles is the thermodynamic parameter such as temperature, pressure. It needs to be added to the Gibbs phase rule. 2 should be changed to 3.  If the  properties of phase do not depend on this parameter (size), then the phase may be regarded as the single-crystal phase.

Regards

The single crystalline nature of the material can be analyzed from the SAED pattern, which is expected to show an array of dots.

You may get some details about finding out single-crystalline graphene in this paper.

http://pubs.acs.org/doi/abs/10.1021/nl300039a

Similar discussion can be found in the below link

https://www.researchgate.net/post/What_is_the_best_way_to_confirm_that_I_am_having_a_single_crystal_or_poly-crystalline_material_using_different_characterization_techniques

Actually, I know the definition of  single-crystal material and its distinct property. What i am really asking is how to check whether the material is single-crystal or not. Thanks for all your answers. However, to my knowledge, SAED may not be enough to confirm that, as the area SAED detects is too small, even polycrystal material can get bright dot patterns. what it can prove is just the area you detect has only one crystal type. It is true that researchers usually choose a lot of place to check whether the same pattern could be observed. Still, i think in that way the single crystal is not fully justified.

In this case, I am just wondering can we confirm its crystallinity using other characterization technique.  

Dear Xu,

This is very much depending on how pristine your samples is. If your sample is 2-3 layers you can pretty much assured it is of a single crystal in nature. So first, you need to determine the type of graphene (layers) you are producing.

Generally we use HRTEM image to measure the lattice spacing to determine if the structure is really single crystal in nature. The lesser the number of layers the easier for you to determine. If the sample is say 5-10 layers, we usually sample more locations within the same specimen and repeat it with several specimens to get a good statistical data. This is done as confirmation even if the SAED shows definite bright spots. This can be a really tedious job in the beginning. 

You can even use scanning tunneling microscope but again the number of sample/location has to be statistically sound.

For metals usually we use XRD to do a wide scan. XRD scans a larger area and would give us a quick response on the crystal structure. However, I'm not so sure if this really possible with pristine graphene with

Dear XU,

single crystal material is dependent on the material under description. There are many ways to check whether a material is pristine. For instance, Graphene which is single atomic layer can  be confirmed through AFM, SEM and the raman spectroscopy, check these techniques and the way their data is discussed and you will have a clear insight on the aspect of single crystal..

I have read all of the answers but still confused how to confirm the single crystalline nature of my sample. Is it the only way to check SAED pattern for many different positions on the sample?

Typical Diffraction Patterns: Single-crystal Versus Powder:

Upon irradiation of a crystal by X-rays, the radiation is diffracted upon interaction with electron density within the crystal. Just like water waves in the classic double-slit experiment from physics, the diffracted X-rays interact, resulting in constructive and destructive interference. In XRD, the diffraction pattern represents the electron density due to atoms and bonds within the crystal. A typical diffraction pattern for a single crystal is shown in (Figure 1). Notice that the diffraction pattern is comprised of spots instead of lines like in the double slit experiment. In fact, these “spots” are 2D slices of 3-dimensional spheres. Crystallographers use a computer program to integrate the resulting spots in order to determine the shape and intensity of the diffracted X-rays. In a powder sample, the X-rays interact with many tiny crystals in random orientations. Therefore, instead of seeing spots, a circular diffraction pattern is observed (Figure 2). The intensities of the diffracted circles are then plotted against the angles between the ring the beam axis (denoted 2θ) to give a 2 dimensional plot known as a powder pattern.

📷 Figure 1. Single Crystal Diffraction Pattern.

📷 Figure 2. Powder XRD: Circular Diffraction Pattern.

I think in XRD pattern you will get intense diffraction peaks of particular oriented plane.

Using XRD Laue pattern, SAED pattern one can confirm the material is single crystal. Also If we get intense diffraction peak and its higher order from XRD (theta-2theta scan) particular oriented plane of single crystal, one can confirm that the material is single crystal.

Dear Xu,

AS we know that XRD data will tell about the material is single crystal or polycrystalline. The single crystal will grow in particular plane direction so from the theta-2theta scan you can confirm it. As other researcher mentioned you the same.