Posted 20-July-1994 to sci.techniques.xtallography
and the Rietveld mailing list
Updated 15-October-1996 (Updated
parts are in dark-blue)
Updated 3-December-1998 and 14-January-1999 (in
red-brown)
Updated 15-June-1999 for NAC with variable
slits
Updated May-2002 with Philips X'Celerator
data
A. Le Bail
It was intended to buy the best powder diffractometer of the moment, according to the above requirements. A very difficult task. Another requirement was that any sample could be studied without any modification of the experimental conditions (avoid fluorescence problem). Several combinations were tested mainly by Siemens, Philips and Rigaku (not all combinations by all manufacturers):
SRM standards were particularly designed for this quest, and particularly LaB6 SRM 660 which is the recommended standard for calibration by the JCPDS-ICDD (Powder Diffraction 3, 209-218, 1988). However, tests were also on Al2O3 SRM 1976, quartz and Na5Cr3F14 choosen for medium fluorescence problems with a copper target in the absence of back monochromator.
Those who have pushed their diffractometer to their limits (for instance using 0.018 scattering slit or so on) know that very low FWHM may be obtained but that correspondingly, at the Rietveld refinement stage, Rp (background subtracted) may be > 20%. In such a case, the figure showing Iobs, Icalc and intensity difference in a manuscript submitted for publication may not be esthetically acceptable. So one may prefer to use, say 0.05 scattering slit, and have Rp<13% or less. A good equilibrium between FWHM and Rp is essential not only to refine a structure but also to determine a structure ab initio from powder diffraction data. What interest to have minimal FWHM < 0.04 (2-theta degrees) if your data cannot be reasonably fitted. Of course, to decide for a given compromise is subjective. My own quest was for the best resolution authorizing Rp<10% (Of course, Rp may be a function of the Rietveld program used, so this may be considered as a curious combination of criteria for selection of equipment that concern the hardware and the software).
Among various tests, the best results according to these requirements
corresponded to the data presented in the original posting. No need to
say that several days were generally necessary to obtain one pattern with
good statistics (step 0.02 to 0.01 2-theta or less; time>10sec/step).
Finally, the results on FWHM and Rp proposed in the posting were from data measured on a Siemens D5000 with variable incident and scattering slits set to V6/V6 (6mm), Peltier cooled Si(Li) detector. Note that these measurements were made for me by Siemens with the objective to have both "low FWHM and Rp". I have not the material, my intention was to buy the best one...
definitions : THX=TAN(THETA) ; COX=COS(THETA)
- FULLPROF : All fits with pseudo-Voigt.
3 parameters refined for the width : U V W.
FWHM = ( U*THX**2 + V*THX + W )**(1/2).
- GSAS : All fits with the Thompson, Cox, Hastings formula.
Eventually 6 parameters refined: GU, GV, GW, LX, LY, GP.
FG = [( GU*THX**2 + GV*THX + GW + GP/COX**2) * 8Ln2]**(1/2)
FL = LY*THX + LX/COX
FWHM = (FG**5+2.69269*FG**4*FL+2.42843*FG**3*FL**2+4.47163*FG**2*FL**3+0.07842*FG*FL**4+FL**5)**0.2
With FG, FL and FWHM in 0.01 degrees 2-Theta being the Gaussian, Lorentzian and full widths at half maximum. FWHM/100 are given below accordingly.
Note: These FWHMs may not well reflect the reality if Rps are high.
J. Cline furnished the FWHMs obtained for LaB6 measured with the D500-PSD, fitting the lines one by one, they are listed below.
J. Kaduk gave approximate formulae:
normal PAD V : FWHM = 0.006 + 0.065/COX
narrow PAD V : FWHM = -.065 + 0.1042/COX
X3B1 : FWHM = 0.000 + 0.0626*THX
results according to these formulae are also given.
A) CeO2 and m-ZrO2 data treated with FULLPROF
in Fobs extracting mode:
Lachlan's comments about his data:
> While the PW1710 had the traditional fixed slits. At the time the m-ZrO2 data was collected, the X'Pert had a ADS (automatic divergence slit) installed but was emulating a fixed 1 degree slit. We dumped it later as the Sollers slits inside the ADS assembly did not have as good beam collimation as the tradition Philips Sollers.
All data with CuKa1-a2 and diffracted beam monochromator. The Siemens D501 data are for the same ZrO2 sample in conditions not optimized for the best resolution (0.15 slit), because of line broadening intrinsic to the sample.
CeO2 (SRM 674a) m-ZrO2
PW1710 X'PERT PW1710 X'PERT Siemens D501 0.15 Slit
U 0.00995 0.01517 0.01403 0.02193 0.03303 V -.01241 -.02747 0.01493 -.00537 -.02084 W 0.01154 0.02397 0.01921 0.03311 0.05315
Rp % 13.5 12.9 7.35 7.39 5.99 Background Rwp % 22.7 20.5 9.39 9.65 8.23 subtracted Re % 6.88 3.44 4.08 4.51 2.51 Rp % 12.5 11.3 5.64 5.65 4.90 Background Rwp % 21.8 18.9 7.54 7.74 6.94 not Re % 6.60 3.18 3.28 3.61 2.11 subtracted 2-Theta 25-140 15-150 15-143 15-154 10-150 range 2-Theta 0.1481 0.1811 0.2251 18 FWHM values 0.1515 0.1816 0.2241 24 in 2-Theta 0.0945 0.1330 0.1556 0.1823 0.2235 30 degrees 0.0890 0.1202 0.1709 0.1881 0.2250 50 0.0879 0.1103 0.1912 0.2003 0.2340 70 0.0953 0.1080 0.2195 0.2229 0.2556 90 0.1188 0.1252 0.2630 0.2649 0.3013 110 0.1752 0.1866 0.3402 0.3499 0.4005 130 0.3105 0.5002 0.5817 146Note that the m-ZrO2 of the RRRR is not a very good choice for looking for low FWHM because of its mean grain size estimated to be 620 Angtroems.
B) For memory, the results posted originally to sci_tech_xtal :
Also with FULLPROF in Fobs extracting mode. D5000, variable slits V6/V6, Peltier cooled Si(Li) detector.
LaB6 Al2O3
NIST SRM 660 NIST SRM 1976
U 0.00310 0.00444 V 0.00112 0.00149 W 0.00112 0.00156
Rp 8.9% 8.1% (background subtracted, Rwp 12.6 10.7 peak only) Re 7.0 6.8
Rp 7.9% 5.9% (background not Rwp 11.5 8.5 subtracted, peak only) Re 6.4 5.4
2-Theta range 18-148 24-147.5 2-Theta Degrees FWHM values : 0.0381 0.0452 24 in 2-Theta 0.0405 0.0480 30 degrees 0.0481 0.0569 50 0.0585 0.0693 70 0.0731 0.0867 90 0.0951 0.1130 110 0.1333 0.1589 130 0.1948 0.2327 146
No formula combining FWHMs and Rp was given, so that a winner having
both "low FWHM and Rp" could be hard to designate.
If the definition is now "lowest FWHMs first and then Rp at least <10%",
the winner is LaB6 cited just above, up to now.
C) from posts of Cline and Kaduk using GSAS on LaB6 SRM 660 :
All refinements with the structure constraint, Cu Kalpha with the exception of X3B1.
Comments of J. Cline about his data:
> I have refined data from SRM 660 which were collected on: 1) a Siemens
D500 with an IBM and PSD, the incident slit was .7 degrees and the PSD
window was set to 4.6 degrees, there were no incident sollar slits (the
beam path is 550mm long and 8mm wide (.83 degrees divergence), the receiving
sollar were of 1.5 degrees divergence, and 2) a Siemens 5000 with automated
slits, incident sollars of unknown divergence (probably about 1 degree),
a .05 degree receiving slit, and a radius of 217 mm. I used GSAS to obtain
the following:
..........
> From the D5000 with the inc. slit set at "small" (6mm widrh), the
data were then corrected with a 1/sin(theta) function:
..........
> The second two data sets compare the results from data collected
with and without the use of the variable slits on our D5000. Both these
data are acceptable. However, one notes the difference in the temperature
and LP factors. The application of the correction to data collected at
a constant area of illumination to yield that would result from a constant
volume of illumination is predicated by an assumption of uniform flux density
with respect to the angle the beam makes with the tube anode. This is not
a reliable assumption; as the tube ages the flux density with respect angle
will most certainly change. Problems with this approach will appear in
the temperature and LP factors. Owing to their large impact on the scale
factor, I do not use the method unless the shape or size of the specimen
demand it. I have additional data collected on SRM 1976, using NBS*QUANT,
during its certification which also indicates problems with the use of
"corrected" data from theta compensating slits.
.......
LaB6 RESULTS from Cline and Kaduk with GSAS: -------------------------------------------- Cline Kaduk D500 D5000 D5000 Scintag PAD V X3B1 PSD .85 slit V6 .05 slit normal Brookhaven
GU 4.780 1.110 2.815 0.000 0.000 7.479 GV -8.727 -8.704 -7.244 0.000 0.000 -.676 GW 8.342 3.477 6.360 2.877 7.432 0.000 LX 1.461 3.744 2.625 0.000 0.000 0.375 LY 1.351 .5854 2.136 4.454 5.098 0.000 trns -3.195 -2.081 -.6622 asym 0.000 0.000 0.000 0.000 0.749 1.171 shft 7.088 8.151 6.689 GP 0.000 2.846 0.000 stec 0.000 0.000 0.000 ptec 0.000 0.000 0.000 sfec 0.000 0.000 0.000 Rp % 2.48 12.38 11.52 not given Rwp % 5.16 16.93 16.38 37.50 13.02 17.62 (R determined without background subtraction in all cases)
Special very fixed variable very peak Comment high slit slit weak splitting background peaks
2-Theta FWHM values 0.0708 0.0749 0.0709 0.0451 0.0700 0.0125 24 in 2-Theta 0.0697 0.0735 0.0702 0.0465 0.0716 0.0162 30 degrees 0.0669 0.0698 0.0688 0.0520 0.0775 0.0292 50 0.0663 0.0683 0.0693 0.0590 0.0850 0.0445 70 0.0699 0.0716 0.0737 0.0687 0.0954 0.0643 90 0.0833 0.0868 0.0879 0.0836 0.1114 0.0925 110 0.1191 0.1278 0.1254 0.1107 0.1402 130 0.1878 0.2045 0.2284 0.1564 0.1896 146 FULLPROF results on D500-PSD, fit in Fobs extracting mode : U=0.00532 V=-0.00621 W=0.00611 Rp=11.0 Rwp=10.7 Re=3.36 background subtracted, peak only Rp=3.36 Rwp=5.18 Re=1.63 background not subtracted, peak only
2-Theta Degrees FWHM values : 0.0709 24 in 2-Theta 0.0695 30 degrees 0.0661 50 0.0661 70 0.0722 90 0.0900 110 0.1314 130 0.2067 146 FWHM values obtained from individual profile refinements on the D500-PSD LaB6 data by J. Cline (with split Pearson 7, via Diffrac AT): ------------------------------------------------------------- 2-Theta FWHM 21.3046 0.077 30.341 0.065 37.4027 0.063 43.4692 0.06 48.9189 0.06 53.9535 0.06 63.1821 0.061 67.5124 0.062 71.7101 0.062 75.8138 0.064 79.8405 0.067 83.8193 0.067 87.7679 0.07 95.6475 0.072 99.6208 0.075 103.6339 0.078 107.7257 0.083 111.9135 0.087 116.2258 0.089 120.705 0.098 130.393 0.112 135.782 0.123 141.7594 0.138 148.6659 0.162 From the approximate equations given by J. Kaduk : --------------------------------------------------
Scintag PAD X3B1 .05 slit normal Brookhaven 2-Theta FWHM values 0.0415 0.0724 0.0133 24 in 2-Theta 0.0428 0.0733 0.0168 30 degrees 0.0500 0.0777 0.0292 50 0.0622 0.0854 0.0438 70 0.0824 0.0979 0.0626 90 0.1167 0.1193 0.0894 110 0.1816 0.1598 130 0.2913 0.2283 146To compare results with and without the structure constraint may be difficult. The Rp and Rwp values may decrease 2-3% in the Fobs extracting mode. Also, the conventional Rietveld Rp and Rwp (background subtracted) are generally much higher than the R calculated without subtracting the background (the more the bacground is high, the more the non-conventional Rp or Rwp are lower than the conventional ones).
The case of Al2O3 SRM 1976 poses some problems for Rietveld refinement with structure, because of a strong preferred orientation (although there is no problem in "Fobs" extracting mode). This may be the reason why nobody has shown any data on this sample up to now.
> 1- One can hear sometimes that variable slits lead to irreproducible measurements, is that true ?
About the suspicion of irreproducibility, there are some comments in the well known book "Modern Powder Diffraction", Chapter 3 from Ron Jenkins (Reviews in Mineralogy, Vol. 20, Bish & Post, editors, 1989) :
"Significant intensity differences are apparent among users of variable
divergence slit diffractometers. This problem can likely be corrected by
proper alignement of the divergence slit."
One response was obtained from Bob Snyder: X-rayX-press<SNYDER@xray.alfred.edu>
> Just a few words on variable slits and Rietveld refinement: Using
a 1 degree incident slit will cause the incident beam to splash over the
ends of most sample holders at two theta angles somewhat less than twenty
degrees (for example it is 17 degrees in the old vertical Philips diffractometers).
The conventional intensity equation for a diffractometer assumes a constant
volume of sample is illuminated and this is the equation implemented in
all of the Rietveld codes with which I am familiar. Therefore peaks below
the splash over angle will have less incident beam on them and will fail
the constant volume of irradiation assumption resulting in their observed
intensities being systematically too low. To use these peaks in a Rietveld
refinement the pattern must be run with a narrower incident slit and/or
a longer sample holder. If, on the other hand, you wish to use a variable
incident slit to ensure that the beam never splashes over the sides of
your sample holder, then you must modify the intensity equation in the
Rietveld program to allow for the now variable volume of diffracting material
in the beam as a function of 2-theta. Since it is only relative intensities
we care about you can use a very simple routine like the one that Cam Hubbard
and I used in the AUTO/NBS*QUANT84 system years ago (included below). Or,
you can put in the more formally derived equation of the effect of variable
receiving slit on intensity.
............
Followed the SUBROUTINE TCSLIT
...........
> 2- Has anybody better results with an in-laboratory apparatus (eventually Kalpha1) on both aspects (FWHM and Rp) for these well known standards ?
From the FWHM and Rp listed above, there was no better results on both aspects than those I gave.
The winner according to FWHMs is undoubtedly x3b1 (synchrotron) but is not an in-laboratory apparatus and has Rwp quite high. Moreover, near 110 2-theta degrees, the FWHMs are larger than with a lab instrument.
For in-lab results, none of the FWHM curves as a funtion of two-theta is the best in the whole 2-theta domain. Concerning the samples, the best results are for LaB6 (other recommended compound with similar quality, provided it has been correctly annealed is BaF2, according to D. Louer).
Selecting the three possible winners :
Posting Cline Kaduk Siemens Siemens Scintag V6/V6 D500 PSD .05 slit 2-Theta Degrees FWHM values : 0.0381 0.0708 0.0451 24 in 2-Theta 0.0405 0.0697 0.0465 30 degrees 0.0481 0.0669 0.0520 50 0.0585 0.0663 0.0590 70 0.0731 0.0699 0.0687 90 0.0951 0.0833 0.0836 110 0.1333 0.1191 0.1107 130 0.1948 0.1878 0.1564 146 Rp 8.9% 11.0* (background subtracted, Rwp 12.6 10.7* peak only) Re 7.0 3.36*
Rp 7.9% 2.48 (background not Rwp 11.5 5.16 37.5 subtracted, peak only) Re 6.4 1.63**: with FULLPROF
Improvements due to variable slits are mainly at low angle where this can be interesting for indexation purpose. For structure determination and refinement, FWHMs at large angles that would be lower than those shown here would be of the highest interest. The Scintag results on the point of view of FWHM are fine, they are the best at large angle, however, Rwp is really too high (may be the reason is not only difficulties in profile fitting, very poor statistics may have also such a consequence).
Results obtained with a Philips X-Pert MPD equipped also with variable slits (presented below and compared with Siemens) were almost exactly identical with those given in the original posting for Al2O3, SRM 1976 (on both FWHM and Rp):
Results from fits without structure constraint (Le Bail method) by FULLPROF, Full data, base of peak=9*FWHM, 11 parameters refined (background estimated manually) Measurements on two different Al2O3 samples NIST SRM 1976
Philips Siemens X-Pert MPD D5000 Variable slits
a 4.75879(1) 4.75883(2) c 12.99245(2) 12.99301(4) zero 0.0215(2) 0.0051(4) TRANSP -.0239(4) -.0076(7) Asym1 0.185(5) -.069(9) Asym2 0.028(1) 0.007(1) X 0.0007(1) 0.0009(2) Eta(p-V) 0.621(9) 0.68(1) U 0.0046(1) 0.0044(1) V 0.0020(1) 0.0015(2) W 0.00096(5) 0.00157(8)
Rp 8.0% 8.1% (background subtracted, Rwp 10.8 10.7 peak only) Re 6.8 6.8
Rp 6.4% 5.9% (background not Rwp 9.3 8.5 subtracted, peak only) Re 5.8 5.4 2-Theta range 24-147.5 24-147.5 step 0.01 0.02 (measured:0.005) (mean of 2 points) 2-Theta Degrees FWHM values : 0.0400 0.0452 24 in 2-Theta 0.0427 0.0480 30 degrees 0.0537 0.0569 50 0.0679 0.0693 70 0.0869 0.0867 90 0.1148 0.1130 110 0.1625 0.1589 130 0.2382 0.2327 146Rigaku on Quartz
Finally, Rigaku (which has no variable slits to propose to date) presented data on quartz with low FWHMs (incident slit 0.05mm, scattering slit 0.05mm, receiving slit 0.15mm with CuKalpha1+2-60kV-300mA, goniometer radius 285mm). Without the complete pattern, a Rietveld fit was not possible, so the results are from separated fits on independent reflexions (as given by Rigaku):
hkl 2-theta FWHM
100 20.84 0.0450 101 26.83 0.0571 110 36.53 0.0574 112 50.12 0.0688 211 59.93 0.0805 302 75.64 0.0826 205 106.57 0.1076 412 122.57 0.1433 206 136.39 0.1813 413 137.85 0.1986So, the comments made by Lachlan Cranswick in an oldest posting : "all diffractometers are approximately the same so you can concentrate on going for the best price" may be true at least for Siemens/Philips latest XRD systems. However, not a lot of data coming from these variable slits new systems have been published up to now. Since the money to buy a new system is reported now to 1996-97 in Le Mans, I have some time for more reflexion... This seems to be also the Lachlan's position since he writes to me:
> I am not very trusting of computer controlled slits at the moment. How do you know that when you choose 1 degree it is one degree? And if/when the slits go out of whack - how much dodgy data will be collected before you find out? Until at least a few years in the future - I think I will be sticking to fixed slits as these are inherently reliable.
Manufacturers seem confident in the quality of their apparatus with variable slits (both Siemens and Philips). Yes the patterns may be well fitted with low FWHM and Rp at least with a Rietveld-type program in Fobs extracting mode. It is interesting now to compare refinements with structure constraint performed on LaB6 with and without variable slits :
fixed slits variable slits ------------------ ----------------- D500 D5000 D5000 D5000 PSD .85 slit V6 V6/V6 -----------------------GSAS----------------- FULLPROF B/U(La) 0.23(1) 0.30(1) 0.14(1) 0.202(9) z(B) 0.1896(7) 0.1906(8) 0.1939(8) 0.1911(8) B/U(B) 1.00(8) 1.10(8) 0.68(7) 0.34(6) a 4.15695(1) 4.15647(1) 4.15646(1) 4.15666(1) (100*Uiso) (100*Uiso) (100*Uiso) (B) RB(%) not given not given 4.89 RF(%) not given not given 2.93Large differences on B/U thermal parameters are detected. This is also the case when comparing different measurements made with fixed slits. The fact is that a satisfying fit on the point of view of the Bragg R-factor is obtained in the case of variable slits systems.
The fit with structure constraint is not possible with SRM 1976 (Al2O3). However, the "|Fobs|" extracted from the Siemens and Philips independent measurements were very similar (also the FWHM and Rp). So this allows to conclude that SRM 1976, in spite of strong preferred orientation, is a good standard, and that good alignment of the slits has been achieved by both manufacturers. May be variable slits will be the system for the future of powder diffractionists, after all.
New Cu-K-alpha-1 data from Philips
(X'Pert) on Al2O3 NIST SRM 1976
(more
information could be obtained on demand).
Pattern 1 Pattern 2 DivergenceSlit, Fixed,1, Automatic, 7, ReceivingSlit, 0.05, MonochromatorUsed, YES , GeneratorVoltage, 37, TubeCurrent, 55, FileDateTime, 27-apr-1996 7:44, 1-may-1996 6:45, DataAngleRange, 20.0000, 157.0000, ScanStepSize, 0.010, ScanType, STEP, ScanStepTime, 10.00,
Results from fits without structure constraint (Le Bail method) by FULLPROF, Full data, base of peak=5*FWHM, 17 parameters refined (6 for background):
Pattern 1 Pattern 2 a 4.75868(2) 4.75883(1) c 12.99240(4) 12.99283(4) zero -0.0200(8) -0.0046(8) TRANSP -0.0084(8) -0.0228(8) Asym1 0.234(8) 0.264(9) Asym2 0.057(2) 0.056(3) X 0.016(2) 0.0015(1) Eta(p-V) 0.087(11) 0.097(12) U 0.0058(2) 0.0048(1) V -0.0015(3) 0.0013(2) W 0.028(1) 0.00144(9) Rp 10.8 11.0 (background subtracted, Rwp 15.0 14.4 peak only) Re 11.3 10.8 Rp 8.9 8.5 (background not Rwp 13.3 12.2 subtracted, peak only) Re 10.0 9.2
2-Theta range 22-157 step 0.01 2-Theta Degrees FWHM values : 0.0524 0.0440 24 in 2-Theta 0.0531 0.0462 30 degrees 0.0580 0.0556 50 0.0678 0.0686 70 0.0843 0.0868 90 0.1112 0.1144 110 0.1620 0.1622 130 0.1956 0.1934 138 0.2448 0.2388 146 0.3242 0.3117 154These results remain similar with those obtained two years before on the point of view of the FWHMs. However, this time we cope with Alpha-1 instead of Alpha-1+2. The reliability factors appear a bit higher by nearly 2%. In fact, the counting time was slightly too small (10sec/point) for ensuring sufficient statistics. In order to demonstrate this, intensities were summed, two points giving one and the fit was repeated this time with a 0.02 step. Reliabilities were considerably improved without large modification of the fit parameters :
Pattern 1 Pattern 2 a 4.75876(2) 4.75882(2) c 12.99292(5) 12.99307(4) zero -0.0481(11) -0.0356(9) TRANSP 0.0162(9) -0.0001(8) Asym1 -0.045(17) -0.123(13) Asym2 0.033(4) 0.032(4) X 0.020(2) 0.0022(2) Eta(p-V) 0.022(11) 0.0009(112) U 0.0054(2) 0.0047(1) V -0.0010(3) 0.0010(2) W 0.029(1) 0.00204(9) Rp 8.3 8.0 (background subtracted, Rwp 11.4 10.6 peak only) Re 8.1 7.8 Rp 6.8 6.1 (background not Rwp 10.0 9.0 subtracted, peak only) Re 7.1 6.5
2-Theta range 22-157 step 0.02 (two points 0.01 apart summed) 2-Theta Degrees FWHM values : 0.0542 0.0495 24 in 2-Theta 0.0550 0.0514 30 degrees 0.0601 0.0594 50 0.0696 0.0710 70 0.0854 0.0880 90 0.1117 0.1143 110 0.1600 0.1606 130 0.1922 0.1912 138 0.2396 0.2358 146 0.3160 0.3075 154It is not excluded that you could obtain a better fit with another Rietveld program or even with FULLPROF by selecting other profile shapes and so on. Have a look at the fits as GIF files for Pattern 1 (parts 20-80 and 80-157) and Pattern 2 (parts 20-80 and 80-157).
Try by yourself : download Pattern 1 and Pattern 2.
Note that if you use DMPLOT (shareware), you should contact the author (Henryk Marciniak) for obtaining the program version allowing to plot more than 9600 points...
Conclusions : if your synchrotron can't do really better, stay at home !
However, staying at home you may have fluorescence problems with this configuration (monochromator in the incident beam). Joke apart, the definite synchrotron advantage remains the possibility to tune the wavelenght and to obtain really low FWHMs (Full Width at Half Maximum in 2-Theta degrees <0.01 recently at ESRF). The time needed, if calculated on the basis of 20 sec/point would have been 76 hours for the 13700 points of pattern 1. This remains manageable and may be compared to not so low counting times needed at some synchrotron sources. For low symmetry samples, I had been unable to obtain good patterns at Daresbury on station 2.3 by counting less than 12 to 24 hours (3 shifts) for 7000 points.
New data coming soon, maybe next month.
The diffractometer, whatever it is (D8 - Bruker), is there.
Fortunately, the contract was mentioning that a test on NIST 1976 should be presented before and after delivering, and should be as satisfying as above (background subtracted Rp lower than 10% - and why not near of 8% -, minimal FWHM lower than 0.045 2-theta degrees)...
I would recommend you to do the same ! Do not buy any diffractometer without those tests.
NIST-1976
If you are insterested in the test pattern, you
may download it here (it is a zipped .uxd file).
Recording conditions are : Bragg Brentano geometry, Cu-Kalpha, graphite
monochromator in the diffracted beam, Soller 2°, divergence slit 0.3°,
antiscatter slit 0.3°, Soller 2°, receiving slit 0.1mm. And the
summary of the Le Bail fit (without structure) by using the FULLPROF program
is below :
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 12/01/1999 Time: 10:07:42.560 => Title:Al2O3 ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 8.00 ==> Angular range, step and number of points: 2Thmin: 20.0000 2Thmax: 140.0000 Step: 0.0100 No. of points: 12001 => Pattern Matching (fixed scale) for phase: 1 => Scor: 1.5788 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 14 ------------------------------------------------------------------------------ => Phase No. 1 Al2O3 R -3 C ------------------------------------------------------------------------------ => No. of reflections: 115 ==> PROFILE PARAMETERS: => Cell parameters : 4.75881 0.00002 4.75881 0.00002 12.99295 0.00005 90.00000 0.00000 90.00000 0.00000 120.00000 0.00000 => overall scale factor : 0.000000100 0.000000000 => Eta(p-v) or m(p-vii) : 0.39955 0.00988 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00458 0.00017 0.00037 0.00022 0.00171 0.00007 => Preferred orientation: 0.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.02931 0.01305 0.03607 0.00158 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00190 0.00014 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00407 0.00025 0.00255 0.00034 0.00100 0.00010 ==> GLOBAL PARAMETERS: => Zero-point: 0.0054 0.0009 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : -0.0077 0.0006 ==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS: => Cycle: 30 => MaxCycle: 30 => N-P+C: 11987 => Rp: 7.33 Rwp: 11.1 Rexp: 9.88 Chi2: 1.27 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 10.5 Rwp: 13.8 Rexp: 12.24 Chi2: 1.27 => Deviance: 0.154E+05 Dev* : 1.278 => DW-Stat.: 1.6624 DW-exp: 1.9458 => N-sigma of the GoF: 21.204 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 6698 => Rp: 6.08 Rwp: 9.49 Rexp: 8.09 Chi2: 1.38 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 7.34 Rwp: 10.8 Rexp: 9.19 Chi2: 1.38 => Deviance: 0.914E+04 Dev* : 1.358 => DW-Stat.: 2.7548 DW-exp: 1.9285 => N-sigma of the GoF: 21.747 => Phase: 1 => Bragg R-factor: 2.65 Vol: 254.821( 0.002) Fract(%): 0.00( 0.00) => Rf-factor= 1.58 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 12/01/1999 Time: 10:08:01.730NAC
% RP RWP RB
Fixed slits Le Bail method 10.1 11.9 Rietveld with structure constrained : 10.6 12.4 5.4 Rietveld with structure refined : 10.0 12.0 4.5 Variable slits V6/V6 Le Bail method 9.28 11.1 uncorrected by 1/sin(theta) Rietveld with structure constrained : 10.1 12.8 5.5 corrected by 1/sin(theta) Rietveld with structure refined : 8.75 11.1 4.2 corrected by 1/sin(theta)From these results, it seems that no preferred orientation occurs with NAC. Seems that the thermal parameters, as estimated by the Rietveld method from these Bruker D8 data, are quite similar to those produced by the previous single crystal study. The slightly high RP and RWP values are probably due to the presence of a few percent of impurities, the step too large (0.02) regarding the minimal FWHM (0.05) and the statistics slightly too low, needing to increase the counting time (was 3 days already !).
It seems also that the correction in 1/sin(theta) for variable slits works in a satisfying way, at least for this pattern (however, the F3 B factor is a bit small when the structure is refined - anyway the F3 weight is small due to the special position occupied). Of course it would be better to use the raw data and to fit by calculating a pattern multiplied by sin(theta) rather than to use a modified observed pattern divided by sin(theta). At least one Rietveld software can do that : WinMProf (the example is exactly the pattern shown here). The interest is to obtain more counts at large angles, improving statistics (but less at small angle...).
If you are interested in the test patterns, you may download here (zipped .uxd file) the fixed slit pattern. Recording conditions are : Bragg Brentano geometry, Cu-Kalpha, graphite monochromator in the diffracted beam, Soller 2°, divergence slit 0.5°, antiscatter slit 0.5°, Soller 2°, receiving slit 0.1mm.
The variable slits patterns are there (nac-test-5.uxd = uncorrected data ; nac5stru3.dat = corrected data).
And the summaries of the 6 above fits by using
the FULLPROF program are below :
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 12/01/1999 Time: 12:01:44.410 => PCR file code: NACtest2 => DAT file code: NACtest2 => Title: Na2Ca3Al2F14 NAC-test-2 sur D8 fentes 0.5 0.5 0.1 ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 8.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 140.0000 Step: 0.0200 No. of points: 6501 => Pattern Matching (fixed scale) for phase: 1 => Scor: 1.8653 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 19 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 400 ==> PROFILE PARAMETERS: => Cell parameters : 10.25197 0.00005 10.25197 0.00005 10.25197 0.00005 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.010000000 0.000000000 => Eta(p-v) or m(p-vii) : 0.54614 0.01238 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00516 0.00027 -0.00264 0.00030 0.00298 0.00008 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.07488 0.00526 0.04089 0.00097 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00277 0.00024 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00497 0.00044 -0.00141 0.00049 0.00276 0.00013 ==> GLOBAL PARAMETERS: => Zero-point: 0.0234 0.0007 => Background Polynomial Parameters ==> 96.7082 0.523397 -43.0679 2.25469 226.432 10.3165 306.700 14.4346 -692.570 38.0027 -872.613 39.6150 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : 0.0137 0.0009 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4373 => Rp: 6.59 Rwp: 8.86 Rexp: 5.70 Chi2: 2.41 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 10.1 Rwp: 11.9 Rexp: 7.63 Chi2: 2.41 => Deviance: 0.109E+05 Dev* : 2.489 => DW-Stat.: 1.3072 DW-exp: 1.9150 => N-sigma of the GoF: 65.961 => Phase: 1 => Bragg R-factor: 3.59 Vol: 1077.510( 0.009) Fract(%): 0.00( 0.00) => Rf-factor= 2.39 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 12/01/1999 Time: 12:02:07.370
VARIABLE
SLITS
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 17/05/1999 Time: 14:34:21.150 => PCR file code: NACtest5 => DAT file code: NACtest5 => Title: Na2Ca3Al2F14 NAC-test-5 sur D8 fentes V6-V6 ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 8.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 140.0000 Step: 0.0200 No. of points: 6501 => Pattern Matching (fixed scale) for phase: 1 => Scor: 1.8857 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 19 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 408 ==> PROFILE PARAMETERS: => Cell parameters : 10.25308 0.00004 10.25308 0.00004 10.25308 0.00004 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.010000000 0.000000000 => Eta(p-v) or m(p-vii) : 0.51346 0.01321 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00181 0.00017 0.00195 0.00022 0.00146 0.00007 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.05549 0.00904 0.03697 0.00118 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00405 0.00021 0.00000 0.00000 => Strain parameters : 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 => Size parameters : 0.00000 0.00000 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00219 0.00030 0.00286 0.00039 0.00144 0.00011 ==> GLOBAL PARAMETERS: => Zero-point: 0.0675 0.0009 => Background Polynomial Parameters ==> 116.591 0.575055 7.36134 2.31746 189.861 10.0476 356.360 13.0238 -493.454 32.8539 -613.677 32.6398 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : 0.0011 0.0008 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4384 => Rp: 6.04 Rwp: 8.18 Rexp: 5.31 Chi2: 2.38 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 9.28 Rwp: 11.1 Rexp: 7.17 Chi2: 2.38 => Deviance: 0.107E+05 Dev* : 2.438 => DW-Stat.: 1.3091 DW-exp: 1.9151 => N-sigma of the GoF: 64.462 => Phase: 1 => Bragg R-factor: 3.38 Vol: 1077.862( 0.007) Fract(%): 0.00( 0.00) => Rf-factor= 2.04 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 17/05/1999 Time: 14:35:03.600
Rietveld
with structure constrained :
FIXED SLITS
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 12/01/1999 Time: 12:02:50.480 => PCR file code: NACstru2 => DAT file code: NACstru2 => Title: Na2Ca3Al2F14 NAC-test-2 sur D8 fentes 0.5 0.5 0.1 ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 8.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 140.0000 Step: 0.0200 No. of points: 6501 => Crystal Structure Refinement for phase: 1 => Scor: 2.0467 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 20 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 408 ==> ATOM PARAMETERS: Name x sx y sy z sz B sB occ. socc. CA 0.46670( 0) 0.00000( 0) 0.25000( 0) 0.660( 0) 0.120( 0) AL 0.24820( 0) 0.24820( 0) 0.24820( 0) 0.600( 0) 0.080( 0) NA 0.08470( 0) 0.08470( 0) 0.08470( 0) 2.160( 0) 0.080( 0) F1 0.13870( 0) 0.30620( 0) 0.12060( 0) 0.970( 0) 0.240( 0) F2 0.36400( 0) 0.36270( 0) 0.18730( 0) 1.140( 0) 0.240( 0) F3 0.46140( 0) 0.46140( 0) 0.46140( 0) 0.820( 0) 0.080( 0) ==> PROFILE PARAMETERS: => Cell parameters : 10.25199 0.00005 10.25199 0.00005 10.25199 0.00005 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.003888535 0.000008927 => Eta(p-v) or m(p-vii) : 0.52535 0.01303 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00451 0.00028 -0.00197 0.00030 0.00281 0.00008 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.07579 0.00587 0.04019 0.00101 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00377 0.00026 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00429 0.00045 -0.00059 0.00049 0.00253 0.00013 ==> GLOBAL PARAMETERS: => Zero-point: 0.0238 0.0008 => Background Polynomial Parameters ==> 95.6832 0.552610 -41.8855 2.35543 175.038 10.7676 275.914 15.0733 -466.592 39.6650 -653.621 41.3530 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : 0.0135 0.0009 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4365 => Rp: 6.94 Rwp: 9.27 Rexp: 5.70 Chi2: 2.64 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 10.6 Rwp: 12.4 Rexp: 7.61 Chi2: 2.64 => Deviance: 0.119E+05 Dev* : 2.734 => DW-Stat.: 1.1910 DW-exp: 1.9154 => N-sigma of the GoF: 76.783 => Phase: 1 => Bragg R-factor: 5.35 Vol: 1077.517( 0.010) Fract(%): 0.00( 0.00) => Rf-factor= 4.02 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 12/01/1999 Time: 12:03:15.690VARIABLE SLITS
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 17/05/1999 Time: 15:53:09.410 => PCR file code: NAC5stru => DAT file code: NAC5stru => Title: Na2Ca3Al2F14 NAC-test-5 sur D8 V6-V6 corrected 1/sin(theta) ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 10.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 140.0000 Step: 0.0200 No. of points: 6501 => Crystal Structure Refinement for phase: 1 => Scor: 2.3955 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 20 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 408 ==> ATOM PARAMETERS: Name x sx y sy z sz B sB occ. socc. CA 0.46670( 0) 0.00000( 0) 0.25000( 0) 0.660( 0) 0.120( 0) AL 0.24820( 0) 0.24820( 0) 0.24820( 0) 0.600( 0) 0.080( 0) NA 0.08470( 0) 0.08470( 0) 0.08470( 0) 2.160( 0) 0.080( 0) F1 0.13870( 0) 0.30620( 0) 0.12060( 0) 0.970( 0) 0.240( 0) F2 0.36400( 0) 0.36270( 0) 0.18730( 0) 1.140( 0) 0.240( 0) F3 0.46140( 0) 0.46140( 0) 0.46140( 0) 0.820( 0) 0.080( 0) ==> PROFILE PARAMETERS: => Cell parameters : 10.25336 0.00005 10.25336 0.00005 10.25336 0.00005 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.010537170 0.000027404 => Eta(p-v) or m(p-vii) : 0.60831 0.01411 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00369 0.00025 -0.00038 0.00025 0.00195 0.00007 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.15396 0.00337 0.03526 0.00098 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00331 0.00027 0.00000 0.00000 => Strain parameters : 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 => Size parameters : 0.00000 0.00000 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00321 0.00042 0.00196 0.00043 0.00150 0.00010 ==> GLOBAL PARAMETERS: => Zero-point: 0.0785 0.0004 => Background Polynomial Parameters ==> 159.758 1.24920 -161.811 5.48362 421.106 22.3883 654.290 37.4726 -868.236 72.8059 -1396.62 87.0274 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : -0.0056 0.0007 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4690 => Rp: 7.29 Rwp: 10.2 Rexp: 3.76 Chi2: 7.37 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 10.1 Rwp: 12.8 Rexp: 4.72 Chi2: 7.37 => Deviance: 0.334E+05 Dev* : 7.123 => DW-Stat.: 1.0588 DW-exp: 1.9181 => N-sigma of the GoF: 308.408 => Phase: 1 => Bragg R-factor: 5.48 Vol: 1077.951( 0.009) Fract(%): 0.00( 0.00) => Rf-factor= 3.58 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 17/05/1999 Time: 15:54:08.840
Rietveld
with structure refined :
FIXED SLITS
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 12/01/1999 Time: 14:41:44.450 => PCR file code: NACstru3 => DAT file code: NACstru3 => Title: Na2Ca3Al2F14 NAC-test-2 sur D8 fentes 0.5 0.5 0.1 ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 8.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 136.8000 Step: 0.0200 No. of points: 6341 => Crystal Structure Refinement for phase: 1 => Scor: 1.9465 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 36 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 400 ==> ATOM PARAMETERS: Name x sx y sy z sz B sB occ. socc. CA 0.46574( 13) 0.00000( 0) 0.25000( 0) 0.747( 25) 0.120( 0) AL 0.24841( 25) 0.24841( 25) 0.24841( 25) 0.799( 39) 0.080( 0) NA 0.08448( 21) 0.08448( 21) 0.08448( 21) 2.069(118) 0.080( 0) F1 0.13911( 27) 0.30639( 25) 0.12159( 37) 0.884( 73) 0.240( 0) F2 0.36297( 37) 0.36250( 25) 0.18818( 27) 1.344( 81) 0.240( 0) F3 0.46175( 19) 0.46175( 19) 0.46175( 19) 0.608(113) 0.080( 0) ==> PROFILE PARAMETERS: => Cell parameters : 10.25201 0.00005 10.25201 0.00005 10.25201 0.00005 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.003919237 0.000014435 => Eta(p-v) or m(p-vii) : 0.55900 0.01349 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00437 0.00027 -0.00173 0.00030 0.00273 0.00008 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.07963 0.00568 0.04008 0.00097 => X and y parameters : 0.00307 0.00028 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00411 0.00044 -0.00027 0.00048 0.00243 0.00012 ==> GLOBAL PARAMETERS: => Zero-point: 0.0244 0.0008 => Background Polynomial Parameters ==> 96.4012 0.578133 -40.2696 2.34532 182.282 10.6013 284.332 14.7851 -493.580 39.1065 -685.849 40.6327 => Sin(2theta)-shift parameter : 0.0131 0.0009 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4349 => Rp: 6.51 Rwp: 8.97 Rexp: 5.69 Chi2: 2.48 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 9.97 Rwp: 12.0 Rexp: 7.60 Chi2: 2.48 => Deviance: 0.112E+05 Dev* : 2.572 => DW-Stat.: 1.2606 DW-exp: 1.9228 => N-sigma of the GoF: 69.171 => Phase: 1 => Bragg R-factor: 4.45 Vol: 1077.523( 0.009) Fract(%): 0.00( 0.00) => Rf-factor= 3.98 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 12/01/1999 Time: 14:42:24.490VARIABLE SLITS
******************************************************** ** PROGRAM FULLPROF.98 (Version 0.2 - Mar98-LLB JRC) ** ******************************************************** Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 17/05/1999 Time: 15:57:24.980 => PCR file code: NAC5stru3 => DAT file code: NAC5stru3 => Title: Na2Ca3Al2F14 NAC-test-5 sur D8 V6-V6 corrected 1/sin(theta) ==> CONDITIONS OF THIS RUN: => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format => Wavelengths: 1.54056 1.54439 => Cos(Monochromator angle)= 0.7998 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 10.00 ==> Angular range, step and number of points: 2Thmin: 10.0000 2Thmax: 140.0000 Step: 0.0200 No. of points: 6501 => Crystal Structure Refinement for phase: 1 => Scor: 2.1577 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 36 ------------------------------------------------------------------------------ => Phase No. 1 Na2Ca3Al2F14 I 21 3 ------------------------------------------------------------------------------ => No. of reflections: 408 ==> ATOM PARAMETERS: Name x sx y sy z sz B sB occ. socc. CA 0.46570( 11) 0.00000( 0) 0.25000( 0) 0.635( 21) 0.120( 0) AL 0.24735( 21) 0.24735( 21) 0.24735( 21) 0.623( 34) 0.080( 0) NA 0.08451( 20) 0.08451( 20) 0.08451( 20) 2.125(105) 0.080( 0) F1 0.13627( 25) 0.30508( 23) 0.12097( 33) 0.940( 65) 0.240( 0) F2 0.36309( 32) 0.36031( 22) 0.18728( 24) 1.060( 68) 0.240( 0) F3 0.46193( 17) 0.46193( 17) 0.46193( 17) 0.139( 90) 0.080( 0) ==> PROFILE PARAMETERS: => Cell parameters : 10.25335 0.00004 10.25335 0.00004 10.25335 0.00004 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.010484128 0.000037432 => Eta(p-v) or m(p-vii) : 0.52325 0.01215 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00266 0.00022 0.00085 0.00022 0.00165 0.00006 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.09947 0.00569 0.03949 0.00092 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00460 0.00024 0.00000 0.00000 => Strain parameters : 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 => Size parameters : 0.00000 0.00000 0.00000 0.00000 => U,V,W for Lambda(2) : 0.00274 0.00037 0.00228 0.00039 0.00150 0.00009 ==> GLOBAL PARAMETERS: => Zero-point: 0.0688 0.0006 => Background Polynomial Parameters ==> 157.592 1.17995 -161.154 4.98089 445.652 20.0857 657.984 33.5124 -940.810 65.4198 -1464.48 78.0686 => Cos( theta)-shift parameter : 0.0000 0.0000 => Sin(2theta)-shift parameter : 0.0033 0.0007
==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => N-P+C: 4673 => Rp: 6.35 Rwp: 8.84 Rexp: 3.76 Chi2: 5.54 L.S. refinement => Conventional Rietveld R-factors ==> => Rp: 8.75 Rwp: 11.1 Rexp: 4.70 Chi2: 5.54 => Deviance: 0.260E+05 Dev* : 5.565 => DW-Stat.: 1.2730 DW-exp: 1.9249 => N-sigma of the GoF: 219.395 => Phase: 1 => Bragg R-factor: 4.18 Vol: 1077.946( 0.008) Fract(%): 0.00( 0.00) => Rf-factor= 3.28 ATZ: 0.000 Brindley: 1.0000 => Run finished at: Date: 17/05/1999 Time: 15:58:53.840
Philips X'Celerator data
Refinements performed by using FULLPROF, in the |F| extraction mode (no structure). Using pseudo-Voigt profiles and asymmetry by using the classical asy1 and asy2 parameters (in FULLPROF). The main problem seems to be due to asymmetry. Improved reliabilities would probably be obtained with an approach that would better take account of this asymmetry at low angle.
Some reliabilities :
Al2O3 - step 0.004 - plot ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => R-factors (not corrected for background) for Pattern: 1' => Rp: 8.20 Rwp: 12.1 Rexp: 11.16 Chi2: 1.17 => Conventional Rietveld R-factors ==> => Rp: 11.0 Rwp: 14.3 Rexp: 13.22 Chi2: 1.17 Al2O3 : step 0.008 - plot (summation of 2 points in one). This improves statistics, and gives better R values : ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1 => R-factors (not corrected for background) for Pattern: 1 => Rp: 7.46 Rwp: 10.7 Rexp: 7.89 Chi2: 1.83 => Conventional Rietveld R-factors for Pattern: 1 => Rp: 10.0 Rwp: 12.7 Rexp: 9.38 Chi2: 1.83 And some FWHM (=Hw below) No. Code H K L Mult Hw ETA/M 2theta/TOF 1 1 0 1 2 6 0.045745 0.104477 25.577 2 1 1 0 4 6 0.047820 0.117819 35.150 3 1 1 1 0 6 0.048575 0.121483 37.778 4 1 0 0 6 2 0.049844 0.126915 41.675 5 1 1 1 3 12 0.050448 0.129256 43.355 6 1 2 0 2 6 0.051540 0.133193 46.180 7 1 0 2 4 6 0.054368 0.142075 52.552 8 1 1 1 6 12 0.056927 0.148970 57.499 9 1 2 1 1 12 0.058197 0.152098 59.744 10 1 1 2 2 12 0.059019 0.154034 61.133 11 1 0 1 8 6 0.059120 0.154268 61.300 12 1 2 1 4 12 0.062472 0.161544 66.520 13 1 3 0 0 6 0.063648 0.163903 68.213 14 1 1 2 5 12 0.065248 0.166976 70.418 15 1 2 0 8 6 0.068263 0.172386 74.300 16 1 1 0 10 6 0.070407 0.175970 76.871 17 1 1 1 9 12 0.070720 0.176476 77.234 18 1 2 1 7 12 0.073573 0.180915 80.419 19 1 2 2 0 6 0.073838 0.181312 80.704 20 1 0 3 6 6 0.076251 0.184817 83.219 22 1 2 2 3 12 0.077392 0.186408 84.360 23 1 1 3 1 12 0.078193 0.187502 85.145 24 1 3 1 2 12 0.079458 0.189191 86.356 25 1 1 2 8 12 0.079614 0.189395 86.503 26 1 0 2 10 6 0.082336 0.192869 88.996 27 1 0 0 12 2 0.084294 0.195251 90.704 28 1 1 3 4 12 0.084867 0.195931 91.192 29 1 3 1 5 12 0.089343 0.200991 94.823 30 1 2 2 6 12 0.089898 0.201589 95.252 31 1 0 4 2 6 0.094147 0.205975 98.399 32 1 2 1 10 12 0.098026 0.209704 101.074 33 1 1 1 12 12 0.100702 0.212139 102.821 34 1 4 0 4 6 0.101492 0.212837 103.322 35 1 1 3 7 12 0.103624 0.214678 104.643 36 1 3 2 1 12 0.112232 0.221514 109.548 37 1 1 2 11 12 0.112819 0.221948 109.859 38 1 2 3 2 12 0.114690 0.223309 110.835 39 1 3 1 8 12 0.114996 0.223528 110.992 40 1 2 2 9 12 0.121284 0.227819 114.071 41 1 3 2 4 12 0.125763 0.230656 116.106 42 1 0 1 14 6 0.126887 0.231340 116.597 43 1 4 1 0 12 0.129853 0.233099 117.859 44 1 2 3 5 12 0.135726 0.236388 120.219 SRM 660a, step 0.004 - plot : ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS: => R-factors (not corrected for background) for Pattern: 1 => Rp: 7.54 Rwp: 10.1 Rexp: 5.21 Chi2: 3.78 => Conventional Rietveld R-factors ==> => Rp: 14.4 Rwp: 14.6 Rexp: 7.53 Chi2: 3.78 SRM 660a step = 0.008 - plot : ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1 => R-factors (not corrected for background) for Pattern: 1 => Rp: 7.11 Rwp: 9.70 Rexp: 3.69 Chi2: 6.91 => Conventional Rietveld R-factors for Pattern: 1 => Rp: 13.6 Rwp: 14.1 Rexp: 5.34 Chi2: 6.91 And some FWHM (=Hw below) No. Code H K L Mult Hw ETA/M 2theta/TOF 1 1 1 0 0 6 0.040438 0.178903 21.357 2 1 1 1 0 12 0.040657 0.207317 30.384 3 1 1 1 1 8 0.041144 0.229530 37.440 4 1 2 0 0 6 0.041805 0.248619 43.505 5 1 2 1 0 24 0.042607 0.265777 48.956 6 1 2 1 1 24 0.043538 0.281613 53.987 7 1 2 2 0 12 0.045772 0.310664 63.216 8 1 3 0 0 6 0.047083 0.324291 67.545 10 1 3 1 0 24 0.048534 0.337504 71.742 11 1 3 1 1 24 0.050138 0.350405 75.841 12 1 2 2 2 8 0.051910 0.363076 79.866 13 1 3 2 0 24 0.053872 0.375590 83.842 14 1 3 2 1 48 0.056049 0.388010 87.787 15 1 4 0 0 6 0.061190 0.412811 95.666 16 1 4 1 0 24 0.064251 0.425310 99.637 18 1 3 3 0 12 0.067730 0.437958 103.655 20 1 3 3 1 24 0.071723 0.450826 107.743 21 1 4 2 0 24 0.076362 0.463995 111.927 22 1 4 2 1 48 0.081837 0.477564 116.237 23 1 3 3 2 24 0.088426 0.491657 120.715 24 1 4 2 2 24 0.106956 0.522141 130.399 25 1 5 0 0 6 0.120900 0.539107 135.789 26 1 4 3 0 24 0.120901 0.539107 135.789 27 1 5 1 0 24 0.141032 0.557909 141.762 29 1 5 1 1 24 0.173952 0.579630 148.662 These results are not better than previous ones above, nor really worst. However, I repeat that a better account of asymmetry would probably lead to better reliabilities.
Refinement with structure for LaB6 - plot
Doing fits with structure is not possible with SRM 1976 due to high preferred orientation. But this should be possible with LaB6 SRM 660a. Using CTHM=0.8247 in FULLPROF (2-theta for the Ge 111 reflection is 24.749), here is the .sum FULLPROF file :
********************************************************** ** PROGRAM FullProf.2k (Version 1.9c - May2001-LLB JRC) ** ********************************************************** M U L T I -- P A T T E R N Rietveld, Profile Matching & Integrated Intensity Refinement of X-ray and/or Neutron Data Date: 17/04/2002 Time: 09:28:42.510 => PCR file code: 660a-2s => DAT file code: 660a-2s -> Relative contribution: 1.0000 => Title: LaB6 NIST 660a Philips - X'celerator ==> CONDITIONS OF THIS RUN FOR PATTERN No.: 1 => Global Refinement of X-ray powder diffraction data => Global Refinement of X-ray powder diffraction data Bragg-Brentano or Debye-Scherrer geometry => The 5th default profile function was selected => Data supplied in free format for pattern: 1 => Wavelengths: 1.54056 1.54056 => Cos(Monochromator angle)= 0.8247 => Absorption correction (muR-eff): 0.0000 => Base of peaks: 2.0*HW* 20.00 ==> Angular range, step and number of points: 2Thmin: 18.0030 2Thmax: 151.9950 Step: 0.0080 No. of points: 16750 =>-------> Pattern# 1 => Crystal Structure Refinement for phase: 1 => Scor: 2.7954 ==> RESULTS OF REFINEMENT: => No. of fitted parameters: 19 ------------------------------------------------------------------------------ => Phase No. 1 La B6 NIST P M 3 M ------------------------------------------------------------------------------ => No. of reflections for pattern#: 1: 30 ==> ATOM PARAMETERS: Name x sx y sy z sz B sB occ. socc. Mult LA 0.00000( 0) 0.00000( 0) 0.00000( 0) 0.112( 7) 0.100( 0) 1 B 0.50000( 0) 0.50000( 0) 0.19850( 67) 0.131( 53) 0.600( 0) 6 ==> PROFILE PARAMETERS FOR PATTERN# 1 => Cell parameters : 4.15697 0.00001 4.15697 0.00001 4.15697 0.00001 90.00000 0.00000 90.00000 0.00000 90.00000 0.00000 => overall scale factor : 0.000572586 0.000001496 => Eta(p-v) or m(p-vii) : 0.11607 0.00572 => Overall tem. factor : 0.00000 0.00000 => Halfwidth parameters : 0.00257 0.00005 -0.00099 0.00007 0.00174 0.00002 => Preferred orientation: 1.00000 0.00000 0.00000 0.00000 => Asymmetry parameters : 0.02044 0.00464 0.04150 0.00109 0.00000 0.00000 0.00000 0.00000 => X and y parameters : 0.00299 0.00010 0.00000 0.00000 => Strain parameters : 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 => Size parameters (G,L): 0.00000 0.00000 0.00000 0.00000 ==> GLOBAL PARAMETERS FOR PATTERN# 1 => Zero-point: 0.0144 0.0002 => Background Polynomial Parameters ==> 330.888 0.801991 29.0268 4.14131 29.3728 10.0818 122.108 29.7537 171.935 23.0625 -384.967 49.7109 ==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS FOR PATTERN: 1 => Cycle: 20 => MaxCycle: 20 => N-P+C: 16731 => R-factors (not corrected for background) for Pattern: 1 => Rp: 6.42 Rwp: 8.69 Rexp: 4.30 Chi2: 4.09 L.S. refinement => Conventional Rietveld R-factors for Pattern: 1 => Rp: 18.1 Rwp: 15.3 Rexp: 7.59 Chi2: 4.09 => Deviance: 0.711E+05 Dev* : 4.250 => DW-Stat.: 0.5594 DW-exp: 1.9544 => N-sigma of the GoF: 282.495 ==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1 => N-P+C: 8320 => R-factors (not corrected for background) for Pattern: 1 => Rp: 7.30 Rwp: 9.82 Rexp: 3.69 Chi2: 7.06 L.S. refinement => Conventional Rietveld R-factors for Pattern: 1 => Rp: 14.0 Rwp: 14.2 Rexp: 5.36 Chi2: 7.06 => Deviance: 0.613E+05 Dev* : 7.362 => DW-Stat.: 0.6514 DW-exp: 1.9367 => N-sigma of the GoF: 390.956 => Global user-weigthed Chi2 (Bragg contrib.):8.22 => Phase: 1 => Bragg R-factor: 2.32 Vol: 71.834( 0.000) Fract(%): 100.00( 0.02) => Rf-factor= 1.18 ATZ: 203.770 Brindley: 1.0000 CPU Time: 15.928 seconds 0.265 minutes => Run finished at: Date: 17/04/2002 Time: 09:28:58.500
RBragg = 2.32%, that seems OK. The thermal parameters factors are a bit small. The CTHM value would have to be better estimated, Celeste Reiss suggests to use 0.88.
The main advantage of the X'Celerator is the gain in time with no loss of resolution. For the two data sets (the original with 0.004 step) the total times were:
SRM1976 16:00:34 h:m:s SRM660a 17:48:50 h:m:s
For those interested in the data, they are gathered together with the .pcr and .sum FULLPROF files in a file compressed by WinZip : x-celerator.zip