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Materials Science and Engineering 405/572
Analysis of Powder Diffraction Patterns and Vegard`s Law
Dr. Who’s timey wimey is getting overly wibbly wobbly and the TARDIS is missing his targets. He believes that overlapping dimensions have caused a ferroelectric in the TARDIS mainframe to fail and that it has experienced a solid-state reaction during travel. Visual inspection shows that the ceramic is cracked, and The Doctor believes that the -Ba-Sr solid solution is varying across the piece. He has taken three powder samples from the failed ferroelectric;
-one of which he has a good guess of the composition.
-Barium and strontium form a solid solution in the perovskite structure as: BaxSr1-xTiO3.
-Literature shows that where x=0.4-0.8 the solid solution of BaxSr1-xTiO3 is cubic.
-If x is varied across the ferroelectric there will be a lattice parameter mismatch, which may cause mechanical failure.
-The Doctor needs you to determine the lattice parameter and composition of each sample via Rietveld refinements on each data set.
-Vegard’s law will be applied to the refined lattice parameters to determine the solid solution composition for each sample.
The known samples were identified using HighScore. The ratios provided are meant to be a starting guess. Use either BaTiO3 or SrTiO3 as a starting model, add in a partial occupancy of the other part by adding another atom into the structure. The .CIF files provided for SrTiO3 (MyBaseFileName_23076_SrTiO3.cif) and BaTiO3 (MyBaseFileName_67518_BaTiO3) differ slightly. Enter phase peak and phase data manually.
Laboratory Write Up:
Since this is only a mini-lab you are not required to write up a report, however we
will hone your results and discussion skills through a series of short answers. Some may ask
you for plots, tables, or diagrams with a written observation of trends or inconsistencies
(Results), while others may ask you to answer theoretical questions or to connect the dots of
your observations (Discussion).
For this report you need to answer/report the following. Simply create a document
which has these in order and labelled. You will still need to follow the proper formatting
(figure captions, table titles etc.). When you are discussing refining the pattern, remember
that you are modifying a calculated pattern generated from complex equations handled by
GSAS, the measured pattern doesn’t change, and incorrect usage will be marked off. This
should effectively look like a standard lab report, but with less in it:
Briefly discuss (keep it short- introduce these things but don’t go into all of the detail) :
Experimental: You may assume that the data was obtained with the normal set-up used for all of the other laboratories; however, do NOT use your own parameter file (.prm) when going through GSAS, there should be a .prm file in the data provided. You do not need to write an experimental section.
Address and discuss any deviations between refined composition (via occupancies) and composition from Vegard’s law.
Overview: You are provided with The CIFs for BaTiO3 and SrTiO3 to use as starting models for GSASII refinements. Full refinements will provide composition via occupancy, lattice parameter, etc. In this lab you will use the refined lattice parameter in Vegard’s law to calculate the solid solution composition of four samples and you will compare these results with refinements.