The atomic displacement factor or the Debye-Waller factor has been introduced to account for the reduction of the intensities of the diffracted X-rays due to the atomic vibrations. The reduction in intensity is more for higher Q or higher Bragg angles. When you refine a crystal structure you will not get good agreement unless you introduce the Debye -Waller factor in the intensity equation. If you are just interested in the crystal structure, i.e; the mean atomic positions then the atomic displacement factors are not so much interesting for you. However in order to be sure that your structure model is right you must check first whether the R-factor is small enough and at the same time the Debye-Waller or atomic displacement factors are not negative; they are all positive. But if your experiment is accurate then you can determine the important information about atomic motions. But if your data are not good (yours are not definitely good because you have ppreferred orientations) then B_iso values are of no use. Please remember in the least squares refinement process (you do it by the magic box program) is such that any error in intesities will pop up in these B-iso values and make them useless. In your case you just check wether you get some small positive values for these factors.

     But the B values if determined properly can give you a wealth of information. Its temperature variation can tell you something about the phase transition if you have any. It can tell you about the atomic disorder. It can tell you that your structure model is not quite right etc. etc.

Atomic displacement parameters can also be obtained from other techiques like Moessbauer spectroscopy and XAFS and specific heat measurements. But each experiment may give a slightly different quantity but are closely related. From theoretical point of view once you know the phonon density of states then you can calculate all these quantities.

   If you can do an accurate single crystal experiments preferabkly with neutrons up to a large value of Q or sintheta/lambda then you can get anisotropic values of the atomic displacement tensors Uij. This is represented by a three by three matrix. And if your data are of excellent quality then you may be able to go further and say something about the anharmonicity of the atomic motion.

  This is the maximum what the traditional crystallography can lead you to. If you you wish to go further you can extend the study by the pair distribution analysis. But the best would be to investigate the atomic dynamics by inelastic neutron scattering experiments supplimed by ab initio phonon calculations.

  You can read some of the papers we recently published on topically interesting substances like ReO3, LaMnO3 and GeTe. Some new results will soon come out on thermoelectric SnSe.

Thank you for you response Tapan. Is it better to let the Uiso values refine or to fix them at some reasonable value in order to get a more accurate phase fraction.

Thanks

Dan

Now coming to the topic of anisotropic tensor Uij. You must note that Uij although has nine components the main information is in the diagonal elements Uii. Also you must know that the local symmetry of the atomic positions restricts severly the components of the tensor. These have been amply discussed in Interanational Tables of crystallography and also in the excellent text book by Pryor and Willis, Thermal motions in crystallography (Oxford). Please read all these instead of using blindly the black box program like Fullprof or GSAS. Since is no fun unless you understand the basics.

Daniel, refine all other parameters, especially preferred orientation, with fixed Uiso values (that you get from a database or literature, similar to you analytical conditions?), and see afterwards if you need to refine thermal parameters...

It all depends on what exactly you wish to get out of your diffraction data. I guess Ni-Ti system is quite well studied and structures of the intermetallic phases are known. If your aim is to check whether you have got the right phase then you do not have bother about the atomic displacement parameters. But if the atomic displacemebnt parameters are your desired quantities then you have do very accurate measurements of intensity and correct for all the known effects. As I told you the atomic displacement parameters are related with the dynamical properties. Ni and Ti are well studied elements. So look to the literature whether someone has already measured carefully atomic displacement parameters. What are the intermetallic phases in the Ti-Ni system? Which phases are you really looking at? What are your objectives? Unless you tell us your problem in detail we cannot help you much.

Thanks Ferenc and Tapan,

A little more detail... I sintered in situ from elemental powders so the diffraction pattern I have is that of a solid. Ideally I am looking for phase progression. The data I have will not allow me to determine Uij values. I have runs where certain phases are the primary phases such that I can get Uiso data for the phase I have present, however since it is not a proper powder sample (and it can not be and still give me the information I need) the Usio values differ from the reported values (when they are available). In most cases the data is not available so I have to either use my experimental data or find some other way to determine a reasonable value. The problem I have is that when one of the experimental values gives me a result that it either way too high or too low but I have nothing to compare it to I am unsure if I should put a reasonable value in  (although knowing what a reasonable value is is tricky) and stop it from refining. I have seen people quote ranges but I have not seen over what temperature range the Uiso range applies.

Thanks

Dan 

As "Ferenc Kristály" suggested, start with refining all other parameters with fixed literature/known temperature factor. After, get a decent fit or the quality of the fit does not change with refinement, then, refine temperature factor. In the end, change isotropic temperature factor to an-isotropic temperature factor and try to to refine it only while fixing all other parameters.  

 I want to thank all who have answered I certainly appreciate the feedback. Tuerdi, I feel that given that I only have data up to 95° that I can not use anisotropic factors. I have refined my patterns where each phase I am looking for is the majority phase to obtain an 'experimental' Uiso. For the phases I have where I can not find Uiso or Biso data for I will use these as a starting point for the temperature and then when all else is refined I will adjust my Uiso value. 

One last question is there a database of Uiso values out there like there are for other material properties (i.e. like Touloukian's thermophysical porperties of matter)?

@Daniel, I now checked he Ni-Ti phase diagram from Hansen's book and now I know that there are three intermetallic phases: Ti2Ni, TiNi and TiNi3. Ti2Ni has a fcc space group with a = 11.333 Å and has 96 atoms per cell. TiNi has CsC type structure with a = 3.013 Å. TiNi3 has a hexagonal structure with a = 5.1010 and c = 8.3067 Å. Are these correct? I guess you are talking about the end phases of Ti and Ni. Now which intermetallic phase are you talking about? If you tell me that then Igive you better answer for your queries.

Hi Daniel, check this paper "Debye-Waller Factors and Absorptive Scattering Factors of Elemental Crystals,   http://scripts.iucr.org/cgi-bin/paper?S010876739600089X".  If you do not find your interested element from that paper or any where else, then, I suggest to use the neighboring(or similar) element's values as a reference or starting point.  

I have found the Debye-Waller factors of Ti and Ni from the literature:

B_Ni = 0.37(1), B_Ti = 0.52(3) Å^2.

Thanks Tuerdi and Tapan.

Tuerdi, I have found that paper as well. The main problem with it is that it only has HCP Ti and I need both HCP and BCC Ti values. 

Tapan it looks like you have a different source than I have (your values are slightly different than mine). Where did you find those numbers if you do not mind me asking? And do they give values at high temperatures as well?

1) how much variation in Uiso is acceptable.

• There's no general answer, it'll vary depend on ur material as long as it not negative, besides the instrument settings. (Accuracy in Temperature Factor Determination in Powder Diifractometry, G. KimmelA and W. N. Schreiner)

2) what are acceptable values of Uiso for metals and intermetallics at room temperature and at high temperatures? (I am going up to 1473K)

Same as above. Here 2 examples from my Ni database:

• BNi = 0.517 Å2 (298K) to 1.12 Å2 (598k). Andreas Leineweber, Herbert Jacobs, Steve Hull, Inorganic Chemistry, 40, 5818 - 5822, (2001)
• BNi = 1.9739 Å2, Angel, R. J., Bismayer, U., Marshall, W. G., Acta Crystallographica Section B, 60, 1 - 9, (2004)

3) Is it preferable to use the experimentally determined values over the given that due to the nature of my experiment it is not an ideal powder diffraction experiment. ( I have sintered in situ so I have a solid polycrystalline piece -not a powder- that could have some texture).

• Mostly at room temperature Biso set to 0.5 (0.08 Å) as starting value.
• Refine the texture before u refine the temperature factors

 Thanks Maykel for your answer.

Based on all the feedback I have refined my workflow where I adjust Uiso only at the very end. I also keep the data from before Uiso is refined to comapare it later. 

Tapan I must have missed your previous message. During sintering I form all the intermetallic phases. At one point (~ 780 °C) I have Alpha-Ti, Beta-Ti, Ti2Ni, NiTi, Ni3Ti and Ni all present at the same time in my microstructure. I have some interrupted sintering specimens mounted for microstructural analysis where I will be able to verify my phase fraction values.

Thanks

Dan 

If you have all phases present at the same time then I do not see how can you refine the structures successfully. How many phases did you put in the refinements? I do not understand what exactly is your goal. Why don't you try to prepare phase pure samples?

My main goal is phase fraction. I am sintering in situ, in other words I am doing neutron diffraction while my specimens are sintering. During sintering I go from the two elemental phases to ideally a singular NiTi phase but in between I get all the phases as you would expect based on the phase diagram. These phases appear and disappear. My goal is to track the changes with time and changing temperature. What I am after is the most accurate phase fractions I can get and not necessarily a refinement of the structure (although I clearly need an accurate idea of what my structure is if I am to get accurate phase fractions).

Given the problems getting a Uiso from the data I am worried that if I get one that is too small it throws off the phase fraction values. The same can be said if it goes too high. So what I am looking for is how do I make sure I get phase fraction data I can trust (given that it is for sequential patterns, i.e. I am watching the phases appear and disappear over time) I do not need to know the phase fraction down to 1% if my errors are of the order of 4 % I can handle that as I will have a phase fraction value on each side of that point to determine if it fits the trend or if it is an outlier.

Also I have some runs where I have relatively pure phases (or almost singular where the phase id >93 %). But given that I am only going to 95° the values I am getting do always match the literature (it does not help I an having trouble finding values in the literature for 1473 K). I have been refining everything with my best guess Uiso values based on some of those high phase fraction runs and then letting the Uiso refine at the end (only for phases that have sufficient phase fraction to allow it). I am just not sure this is the correct and/or the best way I can do it.

Not sure that is clear, if not let me know and I will try to clear it up a bit more