You are correct Kay, that you need to use the model to detwin the data in the case of perfect twinning - with model bias resulting. In the case of partial twinning you don’t need to use the model. However, at higher twin fractions the uncertainty in the intensity (sigma) becomes very large. Either way, as you approach perfect twinning things get worse and worse. Caution is required.
> On Mar 22, 2016, at 4:22 PM, Edward Snell <[log in to unmask]> wrote:
>
> Hi Teresa,
>
> Am 22.03.16 um 19:19 schrieb Teresa Swanson:
>> JPK- My boundaries were relatively arbitrary. 5% or 10% might be
>> personal preference. But I agree, why not use it with low twin fraction.
>>
>> I see my mistake here on the perfect twinning. - one cannot detwin
>> perfect data reliably, but that does not mean one cannot use the twin
>> law, thanks Kay for pointing that out. My understanding of the twin law
>> use seems to be incorrect- I was assuming that they detwinned the data,
>> but this is not the case. I appreciate the clarification.
>>
>> So, it seems that using the twin law during refinement is acceptable for
>> all ranges of twinning, and the maps are your ultimate guide.
>
> From what I've seen, twin refinement even of untwinned data may give a
> twin fraction larger than zero, and if it reduces the R-factors, people
> will believe this.
>
>>
>> Is it technically/theoretically incorrect to /not/ use a twin law for a
>> heavily twinned structure? Is there any reason to think those maps may
>
> it is technically incorrect
>
>> produce different results as refining with a twin law? Or is either
>> refinement option theoretically acceptable?
>
> the maps should look different.
>
> What I realized only after my previous posting is that (besides the
> reduction of the number of observations) there is another source of
> model bias in maps of twinned structures. My understanding is: when a
> refinement program writes out the map coefficients, it detwins the data
> by using the I_calc from the model. This works even for perfect
> twinning. Example: let's assume perfect twinning, and the current model
> gives I_calc(hkl)=100 and I_calc(h'k'l')=10 for two twin-related
> reflections hkl and h'k'l'. Now if I_obs(hkl)=I_obs(h'k'l')=50 then it
> will calculate the de-twinned I_obs_detwin(hkl)=50*100/(100+10)=45 and
> I_obs_detwin(h'k'l')=50*10/(100+10)=4.5, and use those (after conversion
> to amplitudes) for the map coefficients. Clearly, this introduces model
> bias.
> However, omit maps should not be affected by this.
> Caveat: what I just wrote reflects my current understanding; I did not
> inspect source codes or found this documented in papers.
>
> best,
>
> Kay
>
>>
>> Thanks all!
>>
>> Teresa
>>
>> On Tue, Mar 22, 2016 at 12:10 AM, Kay Diederichs
>> <[log in to unmask] <mailto:[log in to unmask]>>
>> wrote:
>>
>> On Mon, 21 Mar 2016 15:51:20 -0700, Teresa Swanson
>> <[log in to unmask] <mailto:[log in to unmask]>> wrote:
>>
>>> Hello all,
>>>
>>> Our lab has had many discussions on the twinned refinement but we've come
>>> to a bit of a stalemate, as none of us have an intimate knowledge of
>>> twinning theory. I wanted to get some clarification on what the current
>>> consensus is on processing twinned data based on the twin fraction. I have
>>> a few questions here, so I'll try to be as clear as possible. For all of
>>> this, I'm assuming MR for phases, which finds at least one viable solution.
>>> We're also assuming that space group assignment as been done correctly, as
>>> well as twin law assignment.
>>>
>>> It is my understanding that the way we refine twinned data heavily depends
>>> on the estimated twin fraction, and it (roughly) breaks down as such:
>>>
>>> - *1-10%: *You can probably refine this data *without* taking
>> the twin
>>> law in to account and it should be just fine. As long as the R factors are
>>> good and your maps look reasonable, no twin law necessary.
>>
>> I agree (maybe except with the "As long as the R factors are good"
>> half-sentence: what exactly does that mean??)
>>
>>> - *11-45%: *Twin law *should* be used during refinement. If you
>> do not
>>> use the twin law, your R factors will probably stall and your maps may not
>>> be reliable. Be aware of increased model bias and artificially lowered R
>>> factors due to the twin law.
>>
>> I agree.
>> 'increased model bias': the somewhat subtle reason why this applies
>> is that in the limit of alpha going towards 0.5, this reduces the
>> number of independent observations by a factor of 2. This
>> corresponds to the same observations-to-parameters ratio at a
>> resolution of untwinned data which is cubic-root-of-2=1.26 worse
>> than that of the perfectly twinned data (e.g. 2A twinned is like
>> 2.5A untwinned in this respect).
>>
>>> - *45-50%: *This is a grey area. I assume most people just throw
>> these
>>> data sets out. However, if you were to process this, you
>> *cannot* use a
>>> twin law, since the data is (likely) perfectly twinned, and the twin law
>>> cannot discriminate between each lattice.
>>
>> there is no reason to have a separate category here. If you wanted
>> to de-twin the data, yes this would not be possible with alpha>0.4
>> or so. But the refinement programs do _not_ de-twin the data;
>> rather, they "twin the I_calc to match the I_obs".
>>
>> So no reason to throw the data away if you can solve and refine the
>> structure, and properly document it.
>>
>>>
>>> In the cases of perfect twinning, how do you correctly refine your data
>>> set? With or without the twin law? How would you determine if you can trust
>>
>> with twin law
>>
>>> your maps?
>>
>> omit maps
>>
>>>
>>> Whether or not you deploy the twin law during the refinement of a twinned
>>> crystal, are reasonable R factors, reasonable physiological interpretation,
>>> and reasonably placed anomalous signal enough to claim a solved structure?
>>
>> yes, if everything is consistent and the model is good
>>
>>>
>>> I appreciate all insight on these questions, thanks!
>>>
>>
>> HTH,
>>
>> Kay
>>
>>
>>> Teresa Swanson
>>>
>>
>>
>
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