dear Sadegh Mojahedfar

see, please,  a similar Question in ref.

ref : https://www.researchgate.net/post/What_is_the_difference_between_grains_and_crystals_They_are_interchangeably_used_in_a_few_texts_I_came_across

Grains are single crystals. In a polycrystalline microstructure (obtained by nucleation and growth of the grains as explained in the RG post quoted above) there are multiple grains together. Each one has a different 3-D orientation of planes compared to its neighbours. Therefore, the presence of grain boundaries with a « twisted » microstructure to allow the grains to join together in the polycrystal.

....In the figure shown (« polycrystalline »), there are 3 grains each one with a different 3-D plane orientation : one of 5 atomic unit cells above left, one with 18 atomic unit cells above right and one with 17 atomic unit cells below. One immediately sees that the plane orientations of the 3 grains are different. This is just a schematic example as there are no grain boundaries represented. 

In crystallography, a domain of unit cells with the same crystalline lattice and orientation is a grain. A material which is composed of more than one such domain is called a poly crystalline material.

Yes, this is correct. A domain of unit cells with the same crystalline lattice and orientation is a single crystal. If there are more than one such domain, it's a polycrystal. Same for metals.  

Dear Sedighe Pirsalami

How are you my friend?

What is the difference between crystallite size, grain size, and particle size? How can we measure these sizes?

 Some respondents consider crystallite and grain size to be the same. It is important to note that a grain consists of a single material, but may be crystalline, or polycrystalline. An individual crystallite consists of a single phase.

The agglomeration of many crystallite size gives the grain size, while The agglomeration of many particles gives the grain size.  

Their measuring Tools are: 

Crystalline size can be determined by using XRD. Grain size is determined by SEM and Particle size is determined using TEM.

I hope this help you.

Yours,

Ahmed Saeed Hassanien

I think the terms "grain" was first used in metallurgy with microscopic /SEM evaluation. Those were in multi-micron size and often different in either crystallographic phase or chemical composition, some phases segregating in the grain boundaries of others. When we got to the TEM evaluation with atomic resolution we can see individual crystals that differ from each other only by orientation, sometimes only by a few degrees. Some people still call these crystals grains. All togother I would say "grain" is not a scientific term.

The meaning of terms can change over the time. Sometimes it is necessary to readjust them since over the time people start to mix them. In so far it is useful to discuss this from time to time. For me grain is a scientific term. It describes a volume of exactly the same orientation, and in so far it is a very theoretical definition since we know the existence of crystal or lattice defects. Of course, it preassumes a chemical homogeneity which is also quite theoretical. A grain has grain boundaries and this is a difference to the definition of a crystal. I know, crystals are also macroscopically not endless but the model of a crystal is a three-dimensional, periodic and infinitely expanded arrangement of atome, ions or molecules. Again, this is a model and only required to make some mathematical simplifications like the structure factor calculations as sum over the content of the usit cell in contrast to complicated integrals but we shouldn't forget that this formula is only exact for an endless crystal dimension. In practice crystal and grain are often used in the same way, although crystals are also described as objects with a polyhedral form, i.e. they are free.-grown. The term crystallite is from my point of view a more technical and commonly used for small grains or crystals.

Terms like "crystalline lattice" are from my point incorrect and shouldn't be used since crystalline points out a physical property, i.e. a solid which is not amorphous. On the other hand, a lattice is a mathematical abstraction which describes the regular arrangement of mathematical points which do not have any dimension. The points may represent one atom but can stand for thousands of atoms like in polymers or proteins. The lattice only describes the translation symmetry of a crystal. In very special cases like hcp the lattice point even does not coincide with the single atomic position. The first is described by [0,0,0] as primitive lattice, the hcp structure however has positions at [1/2,2/3,1/3] and [2/3,1/3,2/2] only.

Totally different I see the term particle since it only explain a solid volume which might be crystalline bit also can be amorphous. It can contain many grains since it only expresses a volume with a specific surface to a solid, liquid or gas. Therefore particle size does not has anything to do with crystal size. Crystal size in diffraction is defined by a coherently scattered volume which contributes to an excess intensity caused by diffraction. Minimally misoriented volumes still contribute to the signal or are even discussed as major reason why we can observe intensity (mosaic structure) but these deviations are extremely small and usually clearly below a degree, mostly caused by dislocations and other lattice defects.

Nature is much more complicated to match a simple definition so that we have to accept somehow deviations with respect of the chemical homogeneity or lattice defect density (when stacking faults form a new phase?) These are often more philosophical questions and only underline that boundaries as often fluid ...        

grain is like a single crystal. Over the grain size, the three  axes x, y and z keep the same directions. v