Dear Sachin Kumar ,

First of all, be sure that crystallite is nothing but tiny crystal and the crystallite boundaries are nothing behind the grain boundaries.

Let's talk about tetragonal BaTiO3, Please note that:

1- It has lattice parameters of a=3.992 Å, c=4.036 Å.

2- The reason behind its ferroelectricity is the off-centered Ti/O ions.

3- The length of the off-centering is about 6-9 pm, which is about 1.5-2.25% of the lattice parameters.

Based on that, it is easy to imagine a crystal, or crystallite if you like, with single or multi-domains as the change in the direction of the polarization vector, in the case of multi-domains, does not coincide with a change in the crystallographic direction and, hence, the crystal will keep its identity.

The question now, can a ferroelectric domain extends from one crystal to another across the grain boundary between them? the answer is:

It is NOT possible when the grain boundary thickness, which is typically 2–20 Å, is equal/higher than the domain wall thickness (∼2–3 Å). However, hypothetically, we can imagine a very low angle grain boundary or a special high angle grain boundary, with very low thickness, across which the domain is extended due to the various directions that the off-centering ions can have.

In my view

Crystalite size and domain size in magnetic material is same.. Almost same

The relationship between crystalite size and the magnetic properties, such as the coercivity (Hc), of Fe3O4 NPs has been widely reported. Te critical size of magnetic NPs, which indicates the transition from a single- to multi-domain structure, was evaluated by the change in Hc with respect to the particle size. However, the critical size for Fe3O4 NPs has not yet been systematically demonstrated because this value depends on the crystal structure, which can have spherical, cubic, or multiple phases. Terefore, investigation of the critical size on the basis of the crystal structure is necessary. The crystalite size required to achieve superparamagnetism in Fe3O4 NPs is widely estimated to be below 20nm.

below article may be benificial for you

Optical, dielectric and magnetic properties of Mn doped SnO2 diluted magnetic semiconductors

N Ahmad, S Khan, MMN Ansari

Ceramics International 44 (13), 15972-15980

Hello all! my question is a little bit more fundamental than applied.

Let a polarization or magnetization vector is along z-axis and here is a domain wall in which the vector changes its orientation. But in crystallites there is no wall and the orientation of crystal lattice changes abruptly. So how these two things co-exist. I want a physical picture of how polarization vector behaves when it passes over from one crystallite to another crystallite.

Dear Sachin Kumar ,

First of all, be sure that crystallite is nothing but tiny crystal and the crystallite boundaries are nothing behind the grain boundaries.

Let's talk about tetragonal BaTiO3, Please note that:

1- It has lattice parameters of a=3.992 Å, c=4.036 Å.

2- The reason behind its ferroelectricity is the off-centered Ti/O ions.

3- The length of the off-centering is about 6-9 pm, which is about 1.5-2.25% of the lattice parameters.

Based on that, it is easy to imagine a crystal, or crystallite if you like, with single or multi-domains as the change in the direction of the polarization vector, in the case of multi-domains, does not coincide with a change in the crystallographic direction and, hence, the crystal will keep its identity.

The question now, can a ferroelectric domain extends from one crystal to another across the grain boundary between them? the answer is:

It is NOT possible when the grain boundary thickness, which is typically 2–20 Å, is equal/higher than the domain wall thickness (∼2–3 Å). However, hypothetically, we can imagine a very low angle grain boundary or a special high angle grain boundary, with very low thickness, across which the domain is extended due to the various directions that the off-centering ions can have.

Imad Disher Thanks for your fruitful reply.

You said that the dislocation along c-axis decides the direction of polarization vector. We are talking about a single grain and not jumping out any grain boundary.

A crystallite (in terms of XRD) is the part of crystal which coherently diffracts when X-Rays fall on them. So the c-axis must be aligned in a particular direction. and hence the polarization vector.

There can be some problem with my picture of understanding. but the question is the order of the size of crystallite and ferroelectric domain is different. their boundaries (within single grain) have different properties. this should not happen according to above states definitions.

So there must be any additional feature or piece of information which i am missing or misunderstanding?

PFA-picture of crystallites from a book on XRD by B D Cuilty.

Dear Sachin Kumar ,

I said nothing regarding dislocation.

I was talking about off-centering of Ti/O ions in the BaTiO3. The off-centering means the "very small" shift of a cation/anion from its equilibrium site in the perfect unit cell. The values of such shift in BaTiO3 is only about 1.5-2.5% of the lattice parameter.

To clarify my point, let's imagine a crystal of BaTiO3 that contains two domains only; the first domain has polarization vector along the c-axis and the second domain has a polarization vector in the opposite direction, i.e. the polarization vectors in the adjacent domains are anti-parallel. The question now, when such crystal is subjected to x-ray beam, will the two domains have the same diffraction response? You agree with me that the answer will be "yes" or "no" depending on the values of the d-spacing of the two domains. To compare the d-spacing of the two domains and deiced the answer, please have a look at the attached image that shows a sketch for the [100] projections of the domains.