The Scherrer equation is a widely used tool to determine the crystallite
size of polycrystalline samples. However, it is not clear if one can
apply it to large crystallite sizes because its derivation is based on
the kinematical theory of X-ray diffraction. For large and perfect
crystals, it is more appropriate to use the dynamical theory of X-ray
diffraction. Because of the appearance of polycrystalline materials with
a high degree of crystalline perfection and large sizes, it is the
authors' belief that it is important to establish the crystallite size
limit for which the Scherrer equation can be applied. In this work, the
diffraction peak profiles are calculated using the dynamical theory of
X-ray diffraction for several Bragg reflections and crystallite sizes
for Si, LaB6 and CeO2. The full width at half-maximum is then extracted
and the crystallite size is computed using the Scherrer equation. It is
shown that for crystals with linear absorption coefficients below 2117.3
cm(-1) the Scherrer equation is valid for crystallites with sizes up to
600 nm. It is also shown that as the size increases only the peaks at
higher 2 theta angles give good results, and if one uses peaks with 2
theta > 60 degrees the limit for use of the Scherrer equation would go
up to 1 mu m.
%0 Journal Article
%1 WOS:000375147400013
%A Muniz, Francisco Tiago Leitao
%A Miranda, Marcus Aurelio Ribeiro
%A dos Santos, Cassio Morilla
%A Sasaki, Jose Marcos
%C 2 ABBEY SQ, CHESTER, CH1 2HU, ENGLAND
%D 2016
%I INT UNION CRYSTALLOGRAPHY
%J ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES
%K X-ray diffraction; dynamical equation; powder theory} {Scherrer
%N 3
%P 385-390
%R 10.1107/S205327331600365X
%T The Scherrer equation and the dynamical theory of X-ray diffraction
%V 72
%X The Scherrer equation is a widely used tool to determine the crystallite
size of polycrystalline samples. However, it is not clear if one can
apply it to large crystallite sizes because its derivation is based on
the kinematical theory of X-ray diffraction. For large and perfect
crystals, it is more appropriate to use the dynamical theory of X-ray
diffraction. Because of the appearance of polycrystalline materials with
a high degree of crystalline perfection and large sizes, it is the
authors' belief that it is important to establish the crystallite size
limit for which the Scherrer equation can be applied. In this work, the
diffraction peak profiles are calculated using the dynamical theory of
X-ray diffraction for several Bragg reflections and crystallite sizes
for Si, LaB6 and CeO2. The full width at half-maximum is then extracted
and the crystallite size is computed using the Scherrer equation. It is
shown that for crystals with linear absorption coefficients below 2117.3
cm(-1) the Scherrer equation is valid for crystallites with sizes up to
600 nm. It is also shown that as the size increases only the peaks at
higher 2 theta angles give good results, and if one uses peaks with 2
theta > 60 degrees the limit for use of the Scherrer equation would go
up to 1 mu m.
@article{WOS:000375147400013,
abstract = {The Scherrer equation is a widely used tool to determine the crystallite
size of polycrystalline samples. However, it is not clear if one can
apply it to large crystallite sizes because its derivation is based on
the kinematical theory of X-ray diffraction. For large and perfect
crystals, it is more appropriate to use the dynamical theory of X-ray
diffraction. Because of the appearance of polycrystalline materials with
a high degree of crystalline perfection and large sizes, it is the
authors' belief that it is important to establish the crystallite size
limit for which the Scherrer equation can be applied. In this work, the
diffraction peak profiles are calculated using the dynamical theory of
X-ray diffraction for several Bragg reflections and crystallite sizes
for Si, LaB6 and CeO2. The full width at half-maximum is then extracted
and the crystallite size is computed using the Scherrer equation. It is
shown that for crystals with linear absorption coefficients below 2117.3
cm(-1) the Scherrer equation is valid for crystallites with sizes up to
600 nm. It is also shown that as the size increases only the peaks at
higher 2 theta angles give good results, and if one uses peaks with 2
theta > 60 degrees the limit for use of the Scherrer equation would go
up to 1 mu m.},
added-at = {2022-05-23T20:00:14.000+0200},
address = {2 ABBEY SQ, CHESTER, CH1 2HU, ENGLAND},
author = {Muniz, Francisco Tiago Leitao and Miranda, Marcus Aurelio Ribeiro and dos Santos, Cassio Morilla and Sasaki, Jose Marcos},
biburl = {https://www.bibsonomy.org/bibtex/288c21489e08301e211cfad49841e1987/ppgfis_ufc_br},
doi = {10.1107/S205327331600365X},
interhash = {c1b719ea5f4676903dca1819d4929921},
intrahash = {88c21489e08301e211cfad49841e1987},
issn = {2053-2733},
journal = {ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES},
keywords = {X-ray diffraction; dynamical equation; powder theory} {Scherrer},
number = 3,
pages = {385-390},
publisher = {INT UNION CRYSTALLOGRAPHY},
pubstate = {published},
timestamp = {2022-05-23T20:00:14.000+0200},
title = {The Scherrer equation and the dynamical theory of X-ray diffraction},
tppubtype = {article},
volume = 72,
year = 2016
}