Tutorial 6 - Structural Disorder

Overview

In this tutorial you will model data from a material which displays short-range structural order (barium titanate, BaTiO₃), but this ordering is confined to very short length scales and so the average, long-range structure is actually an ensemble average of all orientations of the short-range ordering. We will use very simple modelling techniques to simultaneously model the low-r and high-r regions. 

Dependencies

Naturally leads on from the correlated motion tutorial.

Required Files

Instrument Parameters

Tutorial Instructions

These PDF data of BaTiO₃ are collected using neutrons at room temperature on the POWGEN instrument at the SNS, Oak Ridge National Lab. It is known that the average structure of BaTiO₃ is tetragonal at room temperature, crystallising in space group P4mm. This structure is polar, with the Ti cation displaced along the z direction.  

1. Start by performing a Rietveld refinement (against x-ray reciprocal space data) to confirm the average structure. Start with the BaTiO3_11_BM.inp input file (these data from 11-BM at the APS require a few bespoke macros which are included in this file) to model the long-range structure and confirm the space group. Inspect the fit and the output structure to confirm you are happy with this model.  

2. Start a fresh inp file to perform the PDF refinement. Use the structure you just refined from the 11-BM data as a starting point, replacing the beq's with beq_sphericals. Start at r = 1. Make a note of the r_wp, and inspect the fit. Does this model work for the whole r-range? The overall fit looks rather good, but take a closer look at the first peak. Although the average structure model fits most of the PDF, it does not explain the first peak. 

3. At lower temperatures, BaTiO3 adopts a rhombohedral average structure, with the Ti cations displaced along the body diagonal (111) directions. At room temperature, there is no long-range rhombohedral order, but locally the structure could adopt the rhombohedral distortion. We will test this by modelling the data with a rhombohedral structure. Remove the tetragonal structure from the input file by enclosing it with an #ifdef / #endif pair, and add a second #ifdef section containing the rhombohedral structure as described in the BaTiO3_R3m_Kwei.cif file. Only refine up the low-r region by including a finish_X command. You should see that this fits the first peak and the low r region better. Think about how it might be possible for the local structure and the average structure to differ in this way. What disordering is required to make the structure look rhombohedral locally, but tetragonal on average? 

4. Since the rhombohedral structure looks better at low r, lets test this model for the whole PDF. Extend the range of the refinement by removing the finish_X command and inspect the fit to the data. Do you think that the rhombohedral model is good over the whole range? What has happened to the fit of the first peak now you've increased the range? Why has this happened? 

5. Now we want to combine the two models over different length scales. The simplest method of doing this is to pick a radius, and use the rhombohedral model below this radius, and the tetragonal model above. To do this, we need to utilise a scale_phase_X command. scale_phase_X applies a scale factor to the current phase, and we can choose the function to utilise. Later we will see macros which utilise this function in more complex ways, but for the moment let's just scale the rhombohedral structure by 1 if X is below the radius, and 0 if it's above; and vice versa for the tetragonal phase. Warning! the keyword "radius" is reserved for use by the beq_spherical macro, so call it something else! The syntax for this is as follows:

   prm phase_radius 5 ' rhombohedral phase scale_phase_X = If(X<phase_radius, 1, 0 ); ' tetragonal phase scale_phase_X = If(X>phase_radius, 1, 0 );

6.  You should be able to get an improvement in the r_wp. Can you use the r_wp to make an estimate of the ordering length-scale of the rhombohedral distortion? What are the limitations of using this approach to estimate the ordering length-scale?

7. Look back at your average structure Rietveld refinement from the 11-BM data. Were there any indications in this refinement that there was some short-range ordering? 

References

This tutorial is based on that provided by the MMRRSA-17 workshop organised by Peter Khalifah & Katharine Page. 

11-BM data

If data from this beamtime are used in a publication, the following Acknowledgement should be used: “Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Data were collected as part of the 2017 Modern Methods in Rietveld Refinement and Structural Analysis School with support from its sponsors”. You may also wish to acknowledge the beamline staff that collected your data, “We thank Saul H. Lapidus for his assistance with synchrotron powder diffraction data collection at 11-BM.”