Back in the old days, a Rietveld fit was a one-to-one thing. You had sample that was composed of a single phase, you collected a set of powder diffraction data and one fit the structure (and all the other parameters this book discusses) to the data. So, one dataset and one phase: one refinement. The first change in that was that the software was expanded to handle fitting a second phase, so binary mixtures could then be fit. In the 1980s, the original GSAS came along, which could handle what then seemed to be an infinite number of phases – nine.1 GSAS also allowed you to read in 99 histograms (two digits!) and GSAS could fit your 9 phases simultaneously to all the datasets as you had loaded. This allowed something quite new. One could simultaneously fit a single crystal structure to more than one type of data. I can recall a structure containing both vanadium and deuterium, where V is pretty much invisible to neutrons, and x-rays have real difficulty with H (or D) atom positions. We had single-crystal x-ray data and I collected a neutron powder diffraction patterns, and did a combined fit to the two datasets. It worked great and an excellent fit was obtained to both sets of measurements. This was much better than what would have been done before GSAS came along, which would have been to fix some of the structural information in the Rietveld fit to results from the single-crystal fit. The quality of the combined fit was much better. Another example from my own work of the revolution wrought by GSAS is discussed in §25, where I used a synchrotron x-ray and neutron dataset together for a “simple” zeolite sample.
Since the 1990’s there has been a second revolution, and that is in the speed that one can collect powder diffraction data. A typical neutron powder diffraction pattern required at least a 12 hour measurement, likewise about the same for a high-resolution synchrotron powder diffraction pattern. Use of a PSD brought that down to 3-4 hours. Now, under the best circumstances, one can collect a neutron diffraction pattern in fraction of an hour and a medium-resolution synchrotron dataset in a fraction of a second; a high-resolution pattern in minutes. This allows for parametric measurements, where large numbers of diffraction patterns are collected while changes are made to the sample: different samples can be used or the temperature, pressure, chemical environment, electrostatic potential,... are varied. For non-equilibrium conditions, cycling the conditions may show systematic changes. A single experiment can result in thousands of powder diffraction patterns. To plan for this data deluge, with GSAS-II we designed a mechanism called sequential fitting for refinements for fitting similar models to large numbers of datasets. The original approach, where one model is fit simultaneously to all datasets, I will call a combined refinement, even if the model is a single phase and the data are a single histogram.