Dear Andreas, Matthew and John,
I have had exactly the same dilemmas as Andreas regarding refining the parameters in the TCHZ peak type macro and thanks to your discussion I have narrowed down the number of my questions.
In the TOPAS software version that I use, the TCHZ peak type macro is being displayed in the following way: TCHZ_Peak_Type(pku, 0.00039,pkv, -0.00221,pkw, -0.00146,!pkz, 0.0000,pky, 0.00957,!pkxz, 0.0000) and the equations defining the macro (from the "topas.inc") are:
macro TCHZ_Peak_Type(u, v, w, z, x, y)
local #m_unique tch_p_l = x Tan(Th) + y / Cos(Th);
local #m_unique tch_p_g = Sqrt( Abs( u Tan(Th)2 + v Tan(Th) + w + z / Cos(Th)2) );
local #m_unique tch_p =
2.69269 tch_p_g4 tch_p_l +
2.42843 tch_p_g3 tch_p_l2 +
4.47163 tch_p_g2 tch_p_l3 +
0.07842 tch_p_g tch_p_l4 +
local #m_unique tch_q = tch_p_l / tch_p;
pv_lor = 1.36603 tch_q - 0.47719 tch_q2 + 0.1116 tch_q3;
pv_fwhm = tch_p;
macro TCHZ_Peak_Type(u, uv, v, vv, w, wv, z, zv, x, xv, y, yv)
If_Prm_Eqn_Rpt(u, uv, min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4)
If_Prm_Eqn_Rpt(v, vv, min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4)
If_Prm_Eqn_Rpt(w, wv, min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4)
If_Prm_Eqn_Rpt(z, zv, min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4)
If_Prm_Eqn_Rpt(x, xv, min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 )
If_Prm_Eqn_Rpt(y, yv, min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 )
TCHZ_Peak_Type(CeV(u, uv), CeV(v, vv), CeV(w, wv), CeV(z, zv), CeV(x, xv), CeV(y, yv))
Question 1. In the TCHZ macro that is, upon request, being automatically displayed in the JEdit software, the pkx term seems to "contain" (beside the x parameter) also the z parameter. However, according to the .inc file, the parameters x and z seem to be defined separately (if I am not mistaken?). I am trying to understand if the two parameters (x and z) are "coupled" in the displayed "pkxz" term of the TCHZ macro in the TOPAS version that I use in order to be able to decide if I need to initially set (and fix) the pkxz (beside the pkz) parameter to zero when refining the TCHZ parameters for XRD pattern of a standard of interest?
Question 2. In the book "Rietveld Refinement - Practical Powder Diffraction Pattern Analysis using TOPAS" by R. Dinnebier, A. Lienewber and J. Evans it is written that the z parameter shouldn't be refined together with the u and w parameters without additional constrains. What are those additional constrains in practice? I also haven't managed to find the answer in any TOPAS source available online so far.
I was thinking to refine first the v and w parameters for XRD pattern of a standard of interest (to refine both v and w parameters at the same time for example), then to fix the retrieved v and w values (which could be considered as "solely instrumental") while refining one by one the u, y , x parameters and at the end perhaps also the z parameter (if z parameter ever really need to be refined)? Actually, in some cases the TOPAS software instructs me to refine certain parameters together (and give me no opportunity to refine the parameters one by one). I assume it is because the parameters are correlated so I don't find it as a problem, but I still wonder how to proceed further with the refinements after refining the (u), v and w parameters (is the order at which those parameters are being refined important for the TOPAS software)?
Question 3. Regarding the signs in front of the u,v,w,x,y and z parameters, If I have understood your discussion well, considering the way at which (equations) the terms in the TCHZ macro in the TOPAS software are defined, we don't need to "force" the v parameter to be negative and the u and w parameters to be positive at the end of refinements (as mentioned to be needed for the case of u, v and w parameters in the "original" Caglioti function, the page 208 in the following publication: 10.6028/jres.120.013), but to accept any signs in front of all the parameters (including also the x, y and z parameter) that the software will display after refinement cycles (provided that the calculated pattern will match to a "satisfying degree" to the observed pattern)?
Question 4. Is there an unique combination of parameters' values in the TCHZ macro that provide the best fit for each example, or there could be more than one combination of parameters that provide the "satisfying or best" fit?
I am sorry for the long post and thank you in advance if you will have time to try to help me.