To the best of my knowledge, the best method for studying crystalline
defects forming
or increasing in concentration due to plastic deformation in metals is
the Warren-Averbach
method. Of course, excluded from this are point defects, provided no
vacancy coalescence
occurs whereby an edge dislocation line is formed.
Indeed, the said method was specifically developed in the late 40s,
early 50s for the analysis of such
defects in work-hardened (a.k.a cold worked) metals and alloys. A good
account of the said
method is given in several chapters of Ray Young's Rietveld Method
book, wherein one may find
a rather comprehensive list of references as well. Single line
Warren-Averback analysis is very well
discussed in Young's book. Further details can be found in the book by
Warren himself, although it is
mostly a book on X-ray scattering and such. However, therein one would
find the derivation of the said method.
Warren's book is re-published by Dover Publications, and is available at
a reasonable cost ($20 or so).
A quick reminder: In my humble opinion, the term crystallite size is not
only misleading but also outdated
in the era of nano-materials, technology, _______(fill in the blanks as
you see fit) :-). First and foremost,
what is really measured in the Warren-Averbach method is the so-called
coherently diffracting domain size, which
is nothing but the volume element in a given crystalline material which
is free from defects (excluding point defects).
Hence, the comparison of this domain size with the characteristic
physical dimension of the specimen in question provide
one with some insight into the level of crystalline perfection of the
same. For instance, the comparison of particle size, as measured
by FESEM or TEM, with the crystallite size is a good measure of the said
crystalline perfection in that particle.
Especially for materials with cubic symmetry, which is the closest point
group to the spherically symmetric Curie Group,
the <111> crystallite size has traditionally been used as the <111>
planes (total 8) mimic the spherical symmetry well.
However, in systems such as perovskites, it might be interesting to
measure the <110> crystallite size as the dislocation
slip system (although disclocations in perovskites are sessile) is
{110}<110>.
And finally...I believe it is time to replace the term "crystallite
size" with "crystal size" in the literature since what has been
deemed very small (hence the term crystallite) in the 1950s is now
considered "massive" in the 2000s, and anything larger
than 100 nm in size is not even considered part of the nano-realm.
Best wishes,
Koray
Angel L. Ortiz wrote:
Dear All:
I have the following question.
Which is a proper definition of the crystallite size measured by XRD
(line-broadening methods) in metals and alloys deformed plastically where
there are abundant faults, twins and dislocations? In other words, from the
XRD viewpoint, the boundaries of the crystallites are what (twin boundary,
high density dislocation wall, and what)? May I ask for a list of your
understanding of the boundaries for XRD crystallites?.
I guess that most of you will say that the size provided by X-ray
diffraction corresponds to the average of the regions in the material
diffraction coherently. But, such domains are undistorted, distorted or
what?. Can such domain contains dislocations in their interior, or point
defects, or what?
Thanks in advanced
Angel
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E. K. Akdogan, Ph.D.
Research Associate
Electroceramics Research Group
IEEE Senior Member 2005
Chair, Education Committee
IEEE Ultrasonics, Ferroelectrics, Frequency Control Society
Web Page : www.ieee-uffc.org
Dept. of Materials Science & Engineering
Rutgers University,
607 Taylor Road, Piscataway,
New Jersey 08854-8065
Telephone : 732-445 5614
Facsimile : 732-445 5577
E-mail : [EMAIL PROTECTED]
Web Page : www.rci.rutgers.edu/~ecerg
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