Stephens Peakshapes for TOF NPD

rowlesmr

So you have defined a macro

macro TOF_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H4 s400 + K4 s040 + L4 s004 +
H2 K2 s220 + H2 L2 s202 + K2 L2 s022 +
H K2 L s121 +
H L3 s103 + H3 L s301;

prm pp = D_spacing2 * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
}

which you are then calling in your input file as

TOF_Stephens_monoclinic(eta, 0.5, s400, 200, s040, 200, s004, 200, s220, 200, s202, 200, s022, 200, s121, 200, s103, 200, s301, 200)

Is that correct?

Well, there's your problem. You've defined a macro with 10 arguments and are calling it with 20. TOPAS then complains that it can't find a macro definition with 20 arguments because you haven't provided one.

You need to call it with 10 arguments.

prm eta 0.5
prm s400 200
prm s040 200
prm s004 200
prm s220 200
prm s202 200
prm s022 200
prm s121 200
prm s103 200
prm s301 200
TOF_Stephens_monoclinic(eta, s400, s040, s004, s220, s202, s022, s121, s103, s301)

jmas5

Hi Both, thanks again for your help and patience with me on this!

johnsoevans For John's comment, I think that's correct, but for some reason that macro works just fine for the xray xdds and has never had an issue. I think possibly because it is defined in the "Stephens_lor_gauss" macro that it calls? For consistency, I have tried making the below macro, where I have replaced references to tan Th with D_spacing:

Macro:

macro TOF_Stephens_lor_gauss(etac, etav, mhkl)
{
#m_argu etac If_Prm_Eqn_Rpt(etac, etav, min 0 max 1)
local #m_unique pp_ = D_spacing² * Sqrt(Max(mhkl,0)) D_spacing 0.0018/3.1415927;
gauss_fwhm = pp_ (1-CeV(etac, etav));
lor_fwhm = pp_ CeV(etac, etav);
}

macro TOF_Stephens_monoclinic
(
etac, etav,
s400c,s400v,
s040c,s040v,
s004c,s004v,
s220c,s220v,
s202c,s202v,
s022c,s022v,
s121c,s121v,
s103c,s103v,
s301c,s301v
)
{
#m_argu s400c If_Prm_Eqn_Rpt(s400c, s400v,)
#m_argu s040c If_Prm_Eqn_Rpt(s040c, s040v,)
#m_argu s004c If_Prm_Eqn_Rpt(s004c, s004v,)
#m_argu s220c If_Prm_Eqn_Rpt(s220c, s220v,)
#m_argu s202c If_Prm_Eqn_Rpt(s202c, s202v,)
#m_argu s022c If_Prm_Eqn_Rpt(s022c, s022v,)
#m_argu s121c If_Prm_Eqn_Rpt(s121c, s121v,)
#m_argu s103c If_Prm_Eqn_Rpt(s103c, s103v,)
#m_argu s301c If_Prm_Eqn_Rpt(s301c, s301v,)
TOF_Stephens_lor_gauss(
etac, etav,
CeV(s400c,s400v) H⁴ +
CeV(s040c,s040v) K⁴ +
CeV(s004c,s004v) L⁴ +
CeV(s220c,s220v) H² K² +
CeV(s202c,s202v) H² L² +
CeV(s022c,s022v) K² L² +
CeV(s121c,s121v) H K² L +
CeV(s103c,s103v) H L³ +
CeV(s301c,s301v) H³ L
)
}

This yields the below error, when called like this (with the 20 arguments):

Call:

TOF_Stephens_monoclinic
(
etac, 0.5,
s400c, 200,
s040c, 200,
s004c, 200,
s220c, 200,
s202c, 200,
s022c, 200,
s121c, 200,
s103c, 200,
s301c, 200
)

Error:

" Uninitialized_Variable in equation: m672c9d7a_1b"

rowlesmr Taking Matt's approach for the below macro, is also resulting in a different error currently:

Macro:

macro TOF_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H4 s400 + K4 s040 + L4 s004 +
H2 K2 s220 + H2 L2 s202 + K2 L2 s022 +
H K2 L s121 +
H L3 s103 + H3 L s301;

prm pp = D_spacing2 * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
}

Call:

prm eta 0.5
prm s400 200
prm s040 200
prm s004 200
prm s220 200
prm s202 200
prm s022 200
prm s121 200
prm s103 200
prm s301 200
TOF_Stephens_monoclinic(eta, s400, s040, s004, s220, s202, s022, s121, s103, s301)

Error:
"Uninitialized_Variable in equation: K2"

I wonder if the error is the same between them both, just that it is named in the second macro and not in the first? Thanks again for your help!

rowlesmr

jmas5 Checking the stephens_monoclinic macro in our topas.inc (V7) actually shows it is a bit different to that on the topas website:

macro Stephens_monoclinic
...
}

I am a little confused, as this seems to entirely remove reference to the tan Th, which we thought was causing the TOF incompatibility to begin with.

It just abstracts away the Tan(Th) to the Stephens_lor_gauss macro, which is

macro Stephens_lor_gauss(etac, etav, mhkl)
{
   #m_argu etac  If_Prm_Eqn_Rpt(etac, etav, min 0 max 1)   
               local #m_unique pp_ = D_spacing^2 * Sqrt(Max(mhkl,0)) Tan(Th) 0.0018/3.1415927;
               gauss_fwhm =  pp_ (1-CeV(etac, etav));
               lor_fwhm   =  pp_ CeV(etac, etav);
}

jmas5

(Edit: re-posting with correct formatting)

Hi Both, thanks again for your help and patience with me on this!

Macro:

macro TOF_Stephens_lor_gauss(etac, etav, mhkl)
{
#m_argu etac If_Prm_Eqn_Rpt(etac, etav, min 0 max 1)
local #m_unique pp_ = D_spacing2 * Sqrt(Max(mhkl,0)) D_spacing 0.0018/3.1415927;
gauss_fwhm = pp_ (1-CeV(etac, etav));
lor_fwhm = pp_ CeV(etac, etav);
}

macro TOF_Stephens_monoclinic
(
etac, etav,
s400c,s400v,
s040c,s040v,
s004c,s004v,
s220c,s220v,
s202c,s202v,
s022c,s022v,
s121c,s121v,
s103c,s103v,
s301c,s301v
)
{
#m_argu s400c If_Prm_Eqn_Rpt(s400c, s400v,)
#m_argu s040c If_Prm_Eqn_Rpt(s040c, s040v,)
#m_argu s004c If_Prm_Eqn_Rpt(s004c, s004v,)
#m_argu s220c If_Prm_Eqn_Rpt(s220c, s220v,)
#m_argu s202c If_Prm_Eqn_Rpt(s202c, s202v,)
#m_argu s022c If_Prm_Eqn_Rpt(s022c, s022v,)
#m_argu s121c If_Prm_Eqn_Rpt(s121c, s121v,)
#m_argu s103c If_Prm_Eqn_Rpt(s103c, s103v,)
#m_argu s301c If_Prm_Eqn_Rpt(s301c, s301v,)
TOF_Stephens_lor_gauss(
etac, etav,
CeV(s400c,s400v) H4 +
CeV(s040c,s040v) K4 +
CeV(s004c,s004v) L4 +
CeV(s220c,s220v) H2 K2 +
CeV(s202c,s202v) H2 L2 +
CeV(s022c,s022v) K2 L2 +
CeV(s121c,s121v) H K2 L +
CeV(s103c,s103v) H L3 +
CeV(s301c,s301v) H3 L
)
}

This yields the below error, when called like this (with the 20 arguments):

Call:

TOF_Stephens_monoclinic
(
etac, 0.5,
s400c, 200,
s040c, 200,
s004c, 200,
s220c, 200,
s202c, 200,
s022c, 200,
s121c, 200,
s103c, 200,
s301c, 200
)

Error:

" Uninitialized_Variable in equation: m672c9d7a_1b"

rowlesmr Taking Matt's approach for the below macro, is also resulting in a different error currently:

Macro:

macro TOF_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H4 s400 + K4 s040 + L4 s004 +
H2 K2 s220 + H2 L2 s202 + K2 L2 s022 +
H K2 L s121 +
H L3 s103 + H3 L s301;

prm pp = D_spacing2 * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
}

Call:

prm eta 0.5
prm s400 200
prm s040 200
prm s004 200
prm s220 200
prm s202 200
prm s022 200
prm s121 200
prm s103 200
prm s301 200
TOF_Stephens_monoclinic(eta, s400, s040, s004, s220, s202, s022, s121, s103, s301)

Error:
"Uninitialized_Variable in equation: K2"

I wonder if the error is the same between them both, just that it is named in the second macro and not in the first? Thanks again for your help!

rowlesmr

Its a copy/paste forum-formatting issue (at least for the error in my macro)

macro TOF_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 +
H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022 +
H K^2 L s121 +
H L^3 s103 + H^3 L s301;

prm pp = D_spacing^2 * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
}

You need the sysmbol in there to make a power.

jmas5

Thanks for this! That does seem to have been the issue with that macro. However, I'm now getting a different error (though I think this now means that the macro itself is working). The new fun error is "Negative FWHM encountered", which I have seen before when I accidentally leave these parameters refining with simulated annealing on. I'm wondering if perhaps the starting parameters that the macro for XRD uses will now need to be different for NPD? To confirm, I'm currently using:

Macro:

`macro TOF_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H⁴ s400 + K⁴ s040 + L⁴ s004 +
H² K² s220 + H² L² s202 + K² L² s022 +
H K² L s121 +
H L³ s103 + H³ L s301;

prm pp = D_spacing² * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
}
`

Input file:
prm eta 0.5 prm s400 200 prm s040 200 prm s004 200 prm s220 200 prm s202 200 prm s022 200 prm s121 200 prm s103 200 prm s301 200 TOF_Stephens_monoclinic(eta, s400, s040, s004, s220, s202, s022, s121, s103, s301)

Setting all the parameters to 1 (instead of 200) allowed the refinement to initialise, but after one run I encountered the negative FWHM error again. I was able to get around this with the below restrictions, however all the parameters do minimise. Is this physically meaningful?

prm eta_b5 0.5 min 0 max 1 prm s400_b5 0.01 min 0 max 1 prm s040_b5 0.01 min 0 max 1 prm s004_b5 0.01 min 0 max 1 prm s220_b5 0.01 min 0 max 1 prm s202_b5 0.01 min 0 max 1 prm s022_b5 0.01 min 0 max 1 prm s121_b5 0.01 min 0 max 1 prm s103_b5 0.01 min 0 max 1 prm s301_b5 0.01 min 0 max 1 TOF_Stephens_monoclinic(eta_b5, s400_b5, s040_b5, s004_b5, s220_b5, s202_b5, s022_b5, s121_b5, s103_b5, s301_b5)

Thanks again for your continued help!

jmas5

Apologies, macro was not formatted as code. Re-posted below:

`macro TOF_Matt_Stephens_monoclinic(s400, s040, s004, s220, s202, s022, s301, s121, s103, eta)
{
prm mhkl = H⁴ s400 + K⁴ s040 + L⁴ s004 +
H² K² s220 + H² L² s202 + K² L² s022 +
H K² L s121 +
H L³ s103 + H³ L s301;

prm pp = D_spacing² * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
} `

Also for reference, below are the refined values:

prm eta_b5 0.0625563.501034_LIMIT_MIN_0 min 0 max 1
prm s400_b5 0.87625_4709.88862_LIMIT_MIN_0 min 0 max 1 prm s040_b5 0.876254764.84687_LIMIT_MIN_0 min 0 max 1
prm s004_b5 0.12625_875.637423_LIMIT_MIN_0 min 0 max 1 prm s220_b5 0.626254261.83885_LIMIT_MIN_0 min 0 max 1
prm s202_b5 0.87625_4728.59797_LIMIT_MIN_0 min 0 max 1 prm s022_b5 0.876255195.35536_LIMIT_MIN_0 min 0 max 1
prm s121_b5 0.87625_4906.25752_LIMIT_MIN_0 min 0 max 1 prm s103_b5 0.37625_2631.16776_LIMIT_MIN_0 min 0 max 1
prm s301_b5 0.87625_2375.1912_LIMIT_MIN_0 min 0 max 1

jmas5

I do not know why it is not formatting correctly, but the "^" signs are in the macro as below

johnsoevans

The Max(mhkl, 0) should stop pp from going negative. Have you tried just putting the min/max on the eta Gaussian/Lorentzian broadening term? That should be the only term left that would allow a negative fwhm (unless you are also refining other peak shape parameters).

[The code formatting on the wiki isn't topas-specific. It's just something built in that "almost works". Sorry for hassle.]

jmas5

johnsoevans

Hi John,

Thanks for your message. Trying to use the standard values of 200 (Also happens for 20, 2) for the sx terms, with only min 0 max 1 (start 0.5) on eta, still results in the negative FWHM error. I can get it start the refinement by setting them all to 1 (or 0.5/0.05...), but I quickly encounter negative FHWM error on the first step. It seems the only way I can make the refinement happy is to give it min 0 max 1 for all parameters, below are my starting point and the refined values. If this seems physically reasonable I am happy to use this, but would like to avoid adding extra terms otherwise. Thanks again for your help!

Macro:

prm pp = D_spacing² * Sqrt(Max(mhkl,0)) / 1000;

gauss_fwhm = 1.8/3.1415927 pp (1-eta) D_spacing + 0.0001;
lor_fwhm = 1.8/3.1415927 pp eta D_spacing + 0.0001;
} `

Call:

prm eta_b5 0.5 min 0 max 1 prm s400_b5 0.05 min 0 max 1 prm s040_b5 0.05 min 0 max 1 prm s004_b5 0.05 min 0 max 1 prm s220_b5 0.05 min 0 max 1 prm s202_b5 0.05 min 0 max 1 prm s022_b5 0.05 min 0 max 1 prm s121_b5 0.05 min 0 max 1 prm s103_b5 0.05 min 0 max 1 prm s301_b5 0.05 min 0 max 1 TOF_Stephens_monoclinic(eta_b5, s400_b5, s040_b5, s004_b5, s220_b5, s202_b5, s022_b5, s121_b5, s103_b5, s301_b5)

Refined values:

prm eta_b5 0.0625561.686111_LIMIT_MIN_0 min 0 max 1
prm s400_b5 0.88125_4732.37809_LIMIT_MIN_0 min 0 max 1 prm s040_b5 0.881254789.89379_LIMIT_MIN_0 min 0 max 1
prm s004_b5 0.00625_562.368449_LIMIT_MIN_0 min 0 max 1 prm s220_b5 0.256253034.88555_LIMIT_MIN_0 min 0 max 1
prm s202_b5 0.88125_4752.97901_LIMIT_MIN_0 min 0 max 1 prm s022_b5 0.881255428.61298_LIMIT_MIN_0 min 0 max 1
prm s121_b5 0.88125_4917.87234_LIMIT_MIN_0 min 0 max 1 prm s103_b5 0.63125_3928.17146_LIMIT_MIN_0 min 0 max 1
prm s301_b5 0.88125_2386.28893_LIMIT_MIN_0 min 0 max 1

rowlesmr

Those large errors on the coefficients are concerning. They show that something not quite right is going on.

Other things to try are wrapping the gauss and lor equations in Abs(...) or 'Max(..., 0)`, but I can't really grep how those equations can be negative given all of the other constraints.

jmas5

rowlesmr
Updated macro:

Input 1:

Resultant output1 :

Result: Very large errors as before

Input 2:

Output 2:

Result: Quite large values (?), no large errors except for eta which is the only param with the min 0 max 1 left

Input 3:

Output 3:

Result: No large errors, I guess because they are now allowed to go to huge values which they seem to want to do. I don't know if this is physically meaningful.

I think, overall, the Abs(x) has eliminated the prior issues of negative FWHM, so that I don't need the min x max y restraints on the values. My question now then is, are the values it is refining to sensible? I have included the XRD stephens monoclinic parameters below for comparison, as they are quite different. My main concern is Eta, which I believed should be between 0 and 1? I don't know if this is different when working with TOF data?

Thanks again for your help!

rowlesmr

Caveat: Never used TOF, never seriously used Stephen's peak shape.

I have no intuition as to sensible magnitudes for the parameters.

eta really only makes sense in the range [0,1], as it is a mixing parameter between lorentzian and gaussian peakshapes.

I would posit that output 3 still shows large errors; 5000 +- 100000 is a large error.

As a final thought, do you have the correct functional form? I've worked through the paper and have derived eqn 4 by differentiating Bragg's Law. I assume that I could then follow through the separation into Lorentzian and Gaussian widths. The paper does say "A similar result for the peak-width as a function of s²(M_hkl) may be derived for TOF neutron diffraction.". Have you done this? It might be worth the trouble.