In the INS study of Pr1/2Ca1/2MnO3, crytal micro-twinning is THE MOST crucial issue of Neutron scattering studies (INS or diffraction)

However, in section II of the INS article, we read:
"In the analysis of our INS data we will account for the twinning in the modeling explained in Section IV"
but in section IV we read:
"We then fitted the calculated S(Q, ω), averaged with equal weight from each twin, to the data by least-squares refining the exchange constants Jij"

Then, there is a description of twinning, but it is so unclear I am sure it is false:
"Our analysis has up to this point has also assumed an equal population of the six structural twins that are possible in this system. It is simplest to describe the twins with respect to the pseudo-cubic perovskite unit cell. Twin 1 is the unrotated coordinate system, and twin 2 corresponds to a 90◦ rotation of this system about its pseudo-cubic c-axis." Up here it is correct because the pseudo-cubic c-axis of the orthorhombic twins, is one axis of the pseudo cubic perovskite cell. However all the the rest, do not make sense: "Twin 3 is a 90◦ rotation of twin 1 about its a-axis..." is wrong: other twins 3-4 and 5-6 have orthorhombic c- axes that are another axis of the pseudo-cubic lattice, which cannot be described wrt to rotations around the orthorombic axes of other twins like it is done here for twins 3-6.

And last, authors say "We now illustrate the validity of the approach of assuming an equal population of twins in two ways."

One way, is an incredibly unclear "analysis" that consists of producing simulations in Fig 9 of real data sets shown Fig 6, and which are energy cuts  mapping the same reciprocal space: no explanation is given to justify why you'd need to strangely select at different energies different twins that contribute to scattering, and nothing is said about the consistency of the twin fractions used to combine the arbittrarily selected twins. Given that the description of twin laws is dubious, I strongly suspect Fig9 is a FABRICATION (not a simulation of scattering using twins and twin laws, but a splitting/smoothing of real data in two componenents associated each to  arbitrary twin contributions)

The other way is, " Second, we repeated the entire fitting procedure with additional fit parameters of the relative contributions from each twin. We found that, irrespective of the initial values of the fit parameters chosen, within the error on the fit parameters the populations of all six twin were essentially equal". No agreement factor are given.

This extremely elusive description of twinnig and corresponding analysis should be compared to my on-goig unpublished neutron single crystral diffraction structural analysis on a cut from the same crystal, which accurately refines those twin fractions together with the model. At RT, bragg factors obtained are excellent Rb=2.87% and  I guess, the number coming from diffraction speak for themselves...

c-orth axis along

    a-cub                  b-cub                 c-cub

INS (essentially the same means...):
16.66% 16.66% 16.66% 16.66% 16.66% 16.66%

DIFF, experimentally "refined quantitatively" form the data
 8.72%  13.81%  9.9%  19.23%  25.43%  22.89%

Those fractions have been obtained I repeat on a cut FROM THE SAME rod (i.e much smaller than the INS sample) but twinning being microscopic, it would be a MIRACLE that the large disparity of twin population in the small diffraction sample averages to the advocated "essentially equal populations", in the bigger sample cut for INS from the same rod. Those twinn fraction speak for themselves, about being ALL, but "essentially equal"... from a serious Structural determination involving a least square Fit procedure giving Reliability factors, not on an "analysis" based on loose combination fiddling around between simulations and fits all made with hypotheses, but one solid & verifiable structural determination (most reliable at RT but also invaribly consitent with ~4 data collections at other temperatures AND consistent between two different 4-circle diffractometers!
 
The whole INS analysis therefore self-justify a LIE, and do not account in reality for the real twin fractions (I recall... WHICH the authors actually have access, through me!) and the final model discrimination is then "designed" to show only ONE single selected 1D fit that may represent <1% of the data (that seems to not account for twinning!...) to finish... That model discrimination is from this respect  unambiguous, in the STANDARD (except for twinning) analysis of the competing SYMMETRIES, in the diffraction data.