31-03-2014, 03:58 PM
Estimating Crystallite Size Using XRD
Goals of Today’s Lecture
Provide a quick overview of the theory behind peak profile analysis
Discuss practical considerations for analysis
Demonstrate the use of lab software for analysis
empirical peak fitting using MDI Jade
Rietveld refinement using HighScore Plus
Discuss other software for peak profile analysis
Briefly mention other peak profile analysis methods
Warren Averbach Variance method
Mixed peak profiling
whole pattern
Discuss other ways to evaluate crystallite size
Assumptions: you understand the basics of crystallography, X-ray diffraction, and the operation of a Bragg-Brentano diffractometer
Instrument and Sample Contributions to the Peak Profile must be Deconvoluted
In order to analyze crystallite size, we must deconvolute:
Instrumental Broadening FW(I)
also referred to as the Instrumental Profile, Instrumental FWHM Curve, Instrumental Peak Profile
Specimen Broadening FW(S)
also referred to as the Sample Profile, Specimen Profile
We must then separate the different contributions to specimen broadening
Crystallite size and microstrain broadening of diffraction peaks
Contributions to Peak Profile
Peak broadening due to crystallite size
Peak broadening due to the instrumental profile
Which instrument to use for nanophase analysis
Peak broadening due to microstrain
the different types of microstrain
Peak broadening due to solid solution inhomogeneity and due to temperature factors
How is Crystallite Size Defined
Usually taken as the cube root of the volume of a crystallite
assumes that all crystallites have the same size and shape
For a distribution of sizes, the mean size can be defined as
the mean value of the cube roots of the individual crystallite volumes
the cube root of the mean value of the volumes of the individual crystallites
Scherrer method (using FWHM) gives the ratio of the root-mean-fourth-power to the root-mean-square value of the thickness
Stokes and Wilson method (using integral breadth) determines the volume average of the thickness of the crystallites measured perpendicular to the reflecting plane
The variance methods give the ratio of the total volume of the crystallites to the total area of their projection on a plane parallel to the reflecting planes
What Instrument to Use?
The instrumental profile determines the upper limit of crystallite size that can be evaluated
if the Instrumental peak width is much larger than the broadening due to crystallite size, then we cannot accurately determine crystallite size
For analyzing larger nanocrystallites, it is important to use the instrument with the smallest instrumental peak width
Very small nanocrystallites produce weak signals
the specimen broadening will be significantly larger than the instrumental broadening
the signal:noise ratio is more important than the instrumental profile
Qualifying your Macrocrystalline Standard
select powder for your potential macrocrystalline standard
if not already done, possibly anneal it to allow crystallites to grow and to allow defects to heal
use internal calibration to validate that macrocrystalline specimen is an appropriate standard
mix macrocrystalline standard with appropriate NIST SRM
compare FWHM curves for macrocrystalline specimen and NIST standard
if the macrocrystalline FWHM curve is similar to that from the NIST standard, than the macrocrystalline specimen is suitable
collect the XRD pattern from pure sample of you macrocrystalline specimen
do not use the FHWM curve from the mixture with the NIST SRM