Learning Profiles

Site map
Up Standard Specimen Learning Profiles
There is available a large number of Y2O3 reflections. We follow the rule "Selection of isolated reflections with well defined background areas, which must span the whole angular range". Following this, we select reflections of partially low intensity as follows:

Y2O3 reflection rel. intensity measured angular range time per step
(2 1 1) 11% 19-22 deg 4 s
(2 2 2) 100% 27.5-30.5 deg 0.5 s
(4 0 0) 25% 32-35 deg 2 s
(4 4 0) 44% 47.5-49.5 deg 1 s
(6 2 2) 30% 56.7-58.8 deg 1.5 s
(6 5 1)/(7 3 2) 2.2% 67.5-70.3 deg 20 s
(8 4 0) 5.3% 80.2-81.7 deg 10 s
(8 7 1)/(8 5 5)/(7 7 4) 2.9% 100.5-102.3 deg 20 s
(10 4 4)/(8 8 2) 1.5% 111.4-113.8 deg 40 s

In general, the step size was 0.01°. While using a secondary monochromator, we may add the (431) reflection. This weak reflection is disturbed by the strong (4 4 0) Cu-Kß reflection, if we use a Ni filter. This is the case for our D 5000 set-up, so we have omitted this reflection.

For extracting the geometric part from the measured standard profiles, a high accuracy of the standard measurement must be achieved. Grain statistic errors should be minimised by appropriate sample preparation and sample illumination. Sufficient counting statistic can be achieved by large counting intervals. Many long-term intensity fluctuations restrict the accuracy capable by a single scan. Therefore, we have added all the nine partial ranges into a 6 hour scan, which was measured 20 times. This method was chosen to test the extracting procedure using different data quality by different scan counts. The reference measurements was done for a Siemens D 5000 device, with a Cu long fine focus tube, Ni filter, primary beam Goebel mirror without Soller collimator, 0.2 mm receiving slit and a scintillation detector. This configuration cannot be described by our raytracing FPA method.

Now, we must do some manual editing of the y2o3lprof.par result file of the Rietveld refinement mentioned on the site Standard Specimen. We delete the most of the lines. In following, we must unify some multiplet lines which VERZERR is unable to handle. For example the four lines 
4   1.991656E-02  7.4245083 0.00056098 0.00000031470 ... 7 3 2
4   3.284202E-03  7.4245083 0.00056098 0.00000031470 ... 7 2 3
4   1.191584E+00  7.4245083 0.00056098 0.00000031470 ... 6 5 1
4   1.309926E+00  7.4245083 0.00056098 0.00000031470 ... 6 1 5
must be unified to one: 
4   2.524711E+00 7.4245083 0.00056098 0.00000031470 ... 732 ... 723 ... 651 ... 615
This is done by adding the intensities (second column) and buiding weighted averages of B1 (fourth column) and B2 (fifth column). In this case no averaging is needed, the fourth and fifth columns do contain identic values between all the multiplet lines. As a final action, set the header entry PEAKZAHL (german for line count) to the remaining count of lines. In following, only the heading line plus the nine selected reference lines remain: 
PEAKZAHL=9 TITEL=y2o3t3d1502 LAMBDA=CU ...
4   9.464530E+00  2.3096569 0.00056098 0.00000031470 ... 2 1 1
4   8.971993E+01  3.2663482 0.00056098 0.00000031470 ... 2 2 2
4   2.296439E+01  3.7716540 0.00056098 0.00000031470 ... 4 0 0
4   4.405558E+01  5.3339242 0.00056098 0.00000031470 ... 4 4 0
4   3.174841E+01  6.2545805 0.00056098 0.00000031470 ... 6 2 2
4   2.524711E+00  7.4245083 0.00056098 0.00000031470 ... 7 3 2 ... 7 2 3 ... 6 5 1 ... 6 1 5
4   6.138161E+00  8.4336747 0.00056098 0.00000031470 ... 8 4 0 ... 8 0 4
4   2.615395E+00 10.0675612 0.00056098 0.00000031470 ... 8 7 1 ... 8 5 5 ... 8 1 7 ... 7 7 4
4   1.062661E+00 10.8332513 0.00056098 0.00000031470 ... 10 4 4 ... 8 8 2
Now we have prepared the y2o3lprof19.sav file as follows: 
STANDARDPAR=y2o3lprof
VAL[1]=val\y2o3a2.raw
VAL[2]=val\y2o3a3.raw
VAL[3]=val\y2o3a4.raw
VAL[4]=val\y2o3a5.raw
VAL[5]=val\y2o3a6.raw
VAL[6]=val\y2o3a7.raw
VAL[7]=val\y2o3a8.raw
VAL[8]=val\y2o3a9.raw
VAL[9]=val\y2o3a10.raw
VAL[10]=val\y2o3a11.raw
VAL[11]=val\y2o3a12.raw
VAL[12]=val\y2o3a13.raw
VAL[13]=val\y2o3a14.raw
VAL[14]=val\y2o3a15.raw
VAL[15]=val\y2o3a16.raw
VAL[16]=val\y2o3a17.raw
VAL[17]=val\y2o3a18.raw
VAL[18]=val\y2o3a19.raw
VAL[19]=val\y2o3a20.raw
VERZERR=y2o3lprof
pi=2*acos(0)
POL=sqr(cos(26.6*pi/180))
WMIN=20.6
WMAX=113
WSTEP=3*sin(pi*zweiTheta/180)
We have excluded the first scan. This scan shows some very poor grain statistics.

Now we start the VERZERR program by selecting
Run→Verzerr
browsing to the y2o3lprof.sav file and open it.

In following, we must interpolate the nine reference lines in the file y2o3lprof.ger by
Run→MakeGEQ

Here follow some exemplary plots of the geometric part G of the line profiles:
25deg90deg
Plots of the learnt geometric part for the two exemplary angles 25° and 90°.

These learnt geometric profile parts are less acurate than those simulated by raytracing. The main reason: Learnt profiles require an extraction procedure which gives deconvolution oscillations. Raytracing simulates the geometric part itself.

However, the asymmetry of the flanks is more critical than the sharp oscillations which will be predominated by the spectral part of the profile. Therefore, no significant differences in Rietveld refinement are visible.