When you determine the particle size from TEM you have to make some assumptions about it's 3D shape since you are just seeing a projection of its shape. If it is not spherical and has an irregular shape which extends in the direction of the projection then the actual particle volume could be much large than what you have calculated. What shape do you use to calculate the 3D volume of the particle?

How did you measure the particle size in TEM? And which particle size do you get from the XRD? Maybe you can give some more details.

From the Scherrer equation, you calculate the particle size for every reflection and these single values can vary a little bit, depending on the shape of the particles (better: the crystallites). So, if you have elongated particles in one crystallographic direction, then the value calculated from this specific peak can of course be greater than the average value determined by other methods. But the average value, using all possible reflections, should give a similar result than TEM (assuming it is calibrated correctly). This is for single crystalline particles. If you have polycrystalline particles, the value from the Scherrer equation will of course be smaller than the value from TEM because every particle consists of several (smaller) crystallites.

This assumes that the particles are oriented randomly, i.e. they do not have a strong  predominant direction on the TEM substrate. In case they are standing all "upright" on the TEM substrate, you will not get the correct size because you get only 2D-information. From XRD, you get 3D information in case of enough material randomly arranged. So, your result could indicate a preferred orientation on the TEM-substrate, so that the height of the particles is much larger that the width.

So, XRD will result usually in smaller particle sizes than TEM for polycrystalline particles, but vice versa I have not seen yet.

This discussion has already been done in RG as indicated by Volker.

As said by other contributers, normally the mean size of the crystalline domains calculated by Scherrer equation should not be higher then the size of the particles observed by TEM.

But you probably performed your TEM observations on a few particle (a tenth of particles, or if your are courageous over hundred) however the XRD measurements have been realized on several thousand or million particles. Then the average number is not the same.     

Yes, I am agree with Aladin, and Karthikeyan. Crystallite size and particle size are two different two different things, at suitable condition (Thin film) they may be same. You may plz. follow the reference suggested by Volker.

ok

I agree with my predecessors. One should additionally take into account the fact that in general stress (including internal) can change the value calculated from the Scherrer formula. One should also remember that procedure of calculating average value of the particles also can influence results (distribution of particle sizes is asymmetric so arithmetic average isn't good measure of the most common size). Any way the situation you described is strange to me.

When you determine the particle size from TEM you have to make some assumptions about it's 3D shape since you are just seeing a projection of its shape. If it is not spherical and has an irregular shape which extends in the direction of the projection then the actual particle volume could be much large than what you have calculated. What shape do you use to calculate the 3D volume of the particle?

Thanks to all of you

you're welcome.

I went through the references. Let me clarify a little further so that you all can guide me better. 

Sample S1: TEM size: 4.4nm; XRD: 8.6nm

Sample S2: TEM size: 4.9nm; XRD: 9.5nm

Sample S3: TEM size: 7.5nm; XRD: 7.4nm (GOOD MATCH)

I have used different biomolecular templates (biomimetic templates) to synthesize the nanoparticles. All XRD was done at identical conditions. TEM particle sizes were averaged on 50 particles. The XRD pattern was fitted using Philips Analytical X-Ray Profile Fitting software using Pearson VII function, instrumental broadening was deducted. 

I was expecting at least the sizes would be matching, if not less. The deviation is far too greater for S1 and S2.

1) CAN NON UNIFORM STRAIN BE A FACTOR. 

2) CAN SURFACE FUNCTIONALIZATION RESULT IN NON UNIFORM STRAIN. 

3) WILL I GO FOR WILLIAMSON-HALL ANALYSIS AND CALCULATE THE CRYSTALLITE SIZE AND STRAIN

With regards

Dear Dr. Bhattacharya,

I want to add two points in this regard. 1. From your XRD diffractogram, I found Increasing peak intensity due to decreasing particle size mostly due to microstrain (positive or negative). Strain increases due to reducing the particle size in crystalline materials, and 2. TEM gives the particle size and XRD gives the crystallite dimension, both are two different entities. In specific, process or form they may be same, usually not. Try to correct the strain using W-H analysis to reduce the strain contribution.

SEM = number average determination of particle size

XRD = volume average determination of crystallite size

Its extremely unlikely the the number values you get out from these techniques will agree. Hence several 'large' particles not picked up in the SEM analysis but measured in the XRD will totally skew the volume weighted XRD figure to a number greater than that of the SEM. I know it is bad form to self cite but the article in Platinum Metals Review. 2008; 52:129-130. DOI: 10.1595/147106708X299547 which is freely downloadable covers this topic.

Use SAXS. Problem solved.

XRD gives you the volume weighted average, where as SEM/TEM and other 'counting' techniques give the results which are number weigted. And very rarely will they match. (A good reference for understanding various aspects of particle size determination is: Particle Size Measurements by Merkus)

You will definately need to remove the strain component when dealing with XRD data for the nano-sized powders before you get the accurate (volume weighted) particle size. Williamson-Hall as well as double-Voigt are both good methods.