There might be a correlation, but not necessarily, because you don't measure the same thing. By XRD, you measure a crystallite size, which may be independant from the size that is probed by a gas like CO. If the outer surface of the metal particles is available, and if these particles are both crystallised (not amorphous) and monocrystalline, then a correlation should exist.

Alain

In theory, you are measuring the thing. However, the measurment mechanism is very different and both procedures are effected by very different factors (purity of the phase in XRD, behaviour of the support, which can modify the adsorption mechanism)....chemical and geometrical assumptions, etc....Therefore, values measured by both methods can largely diverge.

With Pd you have to be careful with CO chemisorption as, depending on the pressure and particle size, the binding stoichiometry may be somewhere between 1 and 2 and you have to base the result on a significant assumption of bridged versus linear bound CO. It's best to use a combination of techniques for particle size analysis if you really need to know it exactly, or rely on relative values based on the same measurement technique. 

Not necessary a correlation. I think there is a confusion between particle size and grain size (ordered domain). A particle can have several grains with different cristal orientation. I don't think that we can calculate the particle size directly from XRD, but    we can estimate the mean grain size from the Scherrer formula.

Be carefoul,  the CO coverage depends on the adsorption conditions (pressure, temperature,..) and cristallographic orientation of Pd atoms (for exemple (111) or (110) surface would not have the same adsoprtion properties). It is not necessary that you have Pd/CO =1 (bridge or on top, or repulsive interactions between adsorbed CO molecules).

Even if we suppose that you have Pd/CO=1, as the adsoprtion of CO on Pd occurs between top most Pd atoms and CO, you can just probe the number of avaliable Pd atoms on the surface of your Pd particles for CO adsoprtion.

May be then you can find a correlation between these two parameters, if you know the shape of your Pd particles and number of grains in a particle...

I think it is not obvious...          

Thanks for all replays. Pd particle shape nearly spherical and poly crystalline (TEM). From CO chem. Avg. Pd particle size was about a micron. Where from TEM, its  varied; some time less than 500 nm. From XRD, the peak intensity was very small so I didn't calculate. Pd loading was 1 to 2%. I am correlating TEM, CO chem, XRD particle size pattern to compare all same time measure samples, still some time Its a problem. Please let me know any suggestions. Once gain thanks

As far as I understand, you have a Pd supported (probably on a ceramic) catalyst. The difference of results between TEM and CO chemisorption  is may be normal. Because in TEM, you probably analyzed a few Pd particles and you just calculated a mean size. However on CO chemisorption, you probe all your particles.

In TEM, you can deduce the mean diameter (2r) after your measurements (see attached figure). In CO chemisorption, as Pd particles are polycrystalline, you can suppose in a first approximation a square lattice with a lattice parameter of a.

Total area of a spherical particle is : 4. Pi. r2 

 The area of a square lattice (in 2D) is : a2

If we suggest a Pd atom in a square lattice  Then

the ratio 4. Pi. r2  / a2 will give you the number of Pd atoms on the surface of a spherical Pd particle.

If r=500 nm and a=0,3 nm, this ratio is  around 3.107 atoms. This value should correspond to the value calculated from CO chemisorption if all the surface Pd atoms are reactive and you have Pd/CO=1

Coming to the XRD measurement, you calculate from Scherrer law, the mean size of crystallites (or grains) over all your particles probed by XRD (see attached figure , different colors correspond to different crystallite). Normally, the size of crystallites should be smaller then the mean size of Pd particles. From the intensity of XRD patterns corresponding to each crystallite, you may be deduce the relative number of each crystallite....  

You told that you found 1 micron from CO chemisoption for the Pd particle size and from TEM it is around 500 nm. I think, these results are not too bad.     

For relationship between XRD and chemisorption in Pd catalysts pls refer to the many papers of our group. Mail to [email protected] to get list of them. Certainly the widely adopted Pd/CO = 1 is wrong.

Read my book -- it's discussed there.

Dear Atilla Atli, Thank you very, I got better understanding. Once again thanks for your picture and explanation.

M. Albert Vannice: Is this the same book "Kinetics of Catalytic Reactions--Solutions Manual by M. Albert Vannice" 

No, it's "Kinetics of Catalytic Reactions", not the solutions manual.