One of the problems is that the 'apparent sizes' don't correspond to physical dimensions at all. They correspond to what is known as an average column length. If you imagine a crystallite cut into rectangular strips (or a series of stacked unit cells), these are the columns. A simple analogy would be chips cut from a potato. The numbers derived from XRD analysis are mean column lengths. The only example where the column length equals the physical dimension of the crystallite is when the crystallite is a cube. If the crystallite is spherical, then a simple correction will yield the diameter. Should the crystallite have another shape, e.g. needle-like, then anisotropic broadening can be apparent in nanoscale particles, to add another headache (roll-on the aspirin).
Volume and area weighting are quite important to consider when trying to compare results from different techniques. Volume weighting (as given by most integral-breadth methods) simply means that the mean value is weighted by the volume of the column. Area weighting (as given by the Warren-Averbach method) weights the mean column length by surface area as opposed to volume. What this means is that the values you obtain are simply on different parts of the size distribution curve - similarly TEM gives number-weighted values. Integral breadth and WA also give different measures of strain. As different methods give different points on the distribution curve, direct comparisons are tricky. Consequently using TEM to verify XRD results as commonly published is very shaky indeed unless the size distribution is very narrow. Of course the ideal situation is to obtain a full size distribution, so as to avoid these problems. If one assumes a log-normal distribution (quite a serious assumption, but there is some experimental basis) then with values for <DA> and <DV> you can calculate the distribution. It's a widely published area and I'd strongly suggest reading up on it. There is quite a bit of information on the various methods for obtaining size information and what it means. Alot of it appeared in J.Appl.Cryst. at various times. Pam Dr Pamela Whitfield CChem MRSC Energy Materials Group Institute for Chemical Process and Environmental Technology Building M12 National Research Council Canada 1200 Montreal Road Ottawa ON K1A 0R6 CANADA Tel: (613) 998 8462 Fax: (613) 991 2384 Email: <mailto:[EMAIL PROTECTED]> ICPET WWW: http://icpet-itpce.nrc-cnrc.gc.ca -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Sent: June 7, 2004 1:09 PM To: [EMAIL PROTECTED] Dear Dr Pamela Whitfield , Thank you very much for your detail replies on this particular topic.Yours replies were quite benificial for me. Please write something about what do (physically) volume weighted and area weighted domain size mean. Thanking you. Regards, Apu **************************************************** Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA **************************************************** ----- Original Message ----- From: "Whitfield, Pamela" <[EMAIL PROTECTED]> Date: Monday, June 7, 2004 10:04 pm > > Domain size work is a bit of a can of worms. It's something I > looked at > more carefully a while back for nanoparticle work, and the deeper > I got into > it the worse it got. > Peak broadening methods tend to give 'apparent' sizes, either area > or volume > weighted, and require corrections (usually not done) to a give a > physicallymeaningful value, e.g. for a spherical particle D = > 4/3<Dvol>. Langford > and Louer published quite a bit on crystallite shape effects on peak > broadening of nanoparticles. I've never quite looked at published > crystallite size results in the same way again, especially direct > comparisons to TEM data. > > As far as size distributions (yet another can of wriggly things) are > concerned there are people far more qualified than myself to > comment. For > the double-Voigt, Davor Balzar's various publications are worth > looking at, > if a little difficult to follow at times for a poor > experimentalist like > myself :-) > There is a full chapter in IUCr monograph "Defect and Microstructure > Analysis by Diffraction". You'll find it on Davor's publication page > http://www.boulder.nist.gov/div853/balzar/selpublic.htm > I can't remember where I got it from, but there is an Excel > spreadsheet that > will directly convert GSAS profile parameters to double-Voigt size- > strainresults. > > Pam > > Dr Pamela Whitfield CChem MRSC > Energy Materials Group > Institute for Chemical Process and Environmental Technology > Building M12 > National Research Council Canada > 1200 Montreal Road > Ottawa ON K1A 0R6 > CANADA > Tel: (613) 998 8462 Fax: (613) 991 2384 > Email: <[EMAIL PROTECTED]> > ICPET WWW: http://icpet-itpce.nrc-cnrc.gc.ca > > > -----Original Message----- > From: Nandini Devi Radhamonyamma [EMAIL PROTECTED] > Sent: June 7, 2004 11:33 AM > To: [EMAIL PROTECTED] > > > > Dear All, > > Following the discussion about fundamental parameters > approach (which was very helpful), I have a few more > questions regarding the profile functions and their > refining. I apologise if they seem very trivial (or > plain stupid). > > We have a Philips PW3040 X'celerator running in a flat > plate Bragg-Brentano geometry. My interest would be to > calculate the domain size. The X'pert suit of programs > includes a Scherrer calculator. Is it but better to > use other programs like Breadth (double voigt) for > more accurate results ? Or GSAS suit will do the job? > > While profile fitting, how does one choose which > profile to fit? Is it by trial or does it in anyway > depend on the instrument or geometry. For eg. while > trying XFit, I could see that the options run to > fundamental parameters also and previous discussions > pointed to a dependency of fundamental parameters > approach to the geometry. > > For using Double Voigt, how can I obtain the > Lorentzian and Gaussian contributions? > > Any advice in this matter will be highly appreciated > since I am in the woods so to speak in getting > accurate size distributions in our samples. > > Thanks in advance, > Nandini > > N. Radhamonyamma > School of Chemistry > Queen's University Belfast > Belfast BT9 5AG > > > > > > __________________________________ > Do you Yahoo!? > Friends. Fun. Try the all-new Yahoo! Messenger. > http://messenger.yahoo.com/ > >
