Standard Silicon refinement - BB geometry

srraju

Hi All,

I was trying to do calibrate the Bragg-Brentano geometry using fundamental parameters approach in TOPAS. After refining the axial divergence using Simple Axial model, tube tails, divergence, slit wdith, sample displacement and zero error, I managed to refine the lattice parameter of silicon to 5.43123, the standard value. However, when I plotted the Delta 2theta (2theta exp - 2theta standard) against the 2theta, the plot have a negative slope with Delta 2theta varying from -0.01 to -0.06.

Ideally when the lattice parameter is refined to the standard, the Delta 2theta plot should be horizontal. Can anyone please advise me what went wrong with my refinement. Here is my input file.

Thanks

'-------------------------------------------------------------------
/*
Scan date: 28/9/12
Sample: NIST Silicon with a= 5.43123
scan step size = 0.01
Fixed Div slit = 1 deg
Receiving slit = 0.1 mm
Irradiated length = 10 mm
Soller slits on both the incident and diffracting beam side = 0.04 rad
*/
Rs 420
Rp 420
CuKa2 (0.001)

''Instrument function
Simple_Axial_Model(!SAM, 23.73366_0.21599) 'Axial divergence
Divergence(1) 'Fixed divergence slit width = 1 degree
Slit_Width(!swidth,0.1) ''Width of the receiving slit
LP_Factor(26.4) ''for graphite monochromator
Tube_Tails(, 0.4, ,-0.85476_0.07893, , 1.90683_0.02922, , 0.01580_0.00514)
''End of instrument

xdd "...\Si-28912.xy"
x_calculation_step 0.01
bkg @ ...

Specimen_Displacement(!sd, 0.02318_0.00544) 'Specimen displacement
Zero_Error(!zero, 0.01955_0.00139)

hkl_Is
phase_name Si
Cubic(Si_a 5.43123`_0.00001)
space_group "Fd-3m"
load hkl_m_d_th2 I
{
...
}

Create_hklm_d_Th2_Ip_file("Si-28912-4.txt")

PV_Peak_Type(@, 0.00012`_0.01013,@, 0.05564`_0.00877,@, 0.00696`_0.01295,@, 0.90257`_0.46235,@, 0.12523`_0.46235,@, 0.10850`_0.46235)

'--------------------------------------------------------------

alancoelho

Best to leave tube tails out for the initial refinements and to then include it if there are misfits; unless of course you are sure the your tube is old and has tube tails.

Also, probably best to use the Full_Axial_Model macro instead of the Simple_Axial_Model; ie.

Full_Axial_Model(12, 10, 12, 2.3, 2.3)

Refine the second Soller angle after initial refinements; if the Rwp does not change much then leave it fixed.

I would not use the PV_Peak_Type. For the Silicon there should be:

CS_L(@, 1000)
' Strain_L(@, 1000) ' Include after initial refinement

>Ideally when the lattice parameter is refined to the standard, the
>Delta 2theta plot should be horizontal

Typically Zero error and Specimen displace are difficult to determine (you can use an extrapolation plot) from a single scan. Best to align the diffractometer such only one is used. Temperature could also be the reason why the lattice parameter is not corresponding to the standard.

Set absorption to the expected (and approximate) linear absorption coefficient; ie.

str...
prm ab = 0.4 Phase_LAC_Eqn_1_on_cm;
Absorption( !ab )

where 0.4 is the packing density of the sample.

djurdjijadzodan

Dear scientists,

I am having questions regarding the code lines for fixing the linear absorption coef. (LAC) to the expected value mentioned by Alan above.

The packing density value of 0.4 could be a characteristic of what kind of samples (beside powders in capillaries at instruments of transmission geometry) at diffractometers of BB geometry - backloaded powders?

Do we consider the packing density value to be 1 (or what other value would be optimal) in case of powders dispersed on zero-background holders at the diffractometers of BB geometry?

       str...
       prm ab = Phase_LAC_Eqn_1_on_cm;                                                      
       Absorption( !ab )

The same question as under 2. regarding samples in the form of discs ?

I am sorry for the super basic questions.

Kind regards,
Djurdjija

rowlesmr

0.4 is a packing density that is "about right". Random packing of monodisperse spheres 1s about 0.635, so it's probable that randomly packing micronised particles would be lower. If you really want to know, you can figure out the volume of your specimen holder, and weigh it before and after loading to figure out a packing density.

I don't generally worry too much about the value of the absorption correction. I get the mixture LAC, multiply it by a packing density (which I allow to refine between about 0.2 and 1), and just let it float. At least for quant, it's just there to fit peak profiles. If you want to extract fine detail from the peak profiles, you'll have to be more careful.

djurdjijadzodan

Dear Matthew,

Thanks so much for the kind reply and especially for the reference [1] (in another post). After taking a close look at the paper content and references cited in that work, I have realized how much my questions in this post were non-sense (I thought that packing density of 1 could be a property of any single phase powder if not packed in capillaries).

Additionally, I finally have a nice ''recipe" to follow regarding the parameter refinement order, which to me as a novice in the field means a lot.

Kind regards,
Djurdjija

[1] Rowles, Matthew R. "The effect of data quality and model parameters on the quantitative phase analysis of X-ray diffraction data by the Rietveld method." Journal of Applied Crystallography 54.3 (2021): 878-894.