What is "detwinning" as a 2D crystallography technique?

The Phys.org article [Iron selenide revealed as 'garden-variety iron-based superconductor'](https://phys.org/news/2019-05-iron-selenide-revealed-garden-variety-iron-based.html) is quoted below. Normally I would hesitate to quote so much but in this case it all seems germane.


**Question:** What is "detwinning" as a crystallography technique? It seems a bit complicated for 2D crystals, with phrases like "... reasoning that the pressure needed to align the larger sample would also cause the layers of iron selenide to snap into alignment." it sounds like manual re-arrangement at almost the atomic scale.


The article links to [Anisotropic spin fluctuations in detwinned FeSe](https://www.nature.com/articles/s41563-019-0369-5) in Nature Materials. (also in [arXiv](https://arxiv.org/abs/1905.08399) and [Researchgate](https://www.researchgate.net/publication/333260261_Anisotropic_spin_fluctuations_in_detwinned_FeSe))




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[![enter image description here](https://i.stack.imgur.com/C8o4e.jpg)](https://i.stack.imgur.com/C8o4e.jpg)



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> Tong Chen, a Rice PhD student "detwinned" iron selenide crystals by gluing them atop much larger crystals of barium iron arsenide. Using a 2014 method developed at Rice, the larger crystals are placed under pressure and detwinned, causing the smaller iron selenide crystals to also snap into alignment. Credit: Jeff Fitlow/Rice University
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> Physicists refer to this directionally dependent behavior as anisotropy or nematicity, and while structural nematicity is known to occur in iron selenide, Dai said it has been impossible to measure the exact electronic and magnetic order of the material because of a property known as twinning. Twinning occurs when layers of randomly oriented 2-D crystals are stacked. Imagine 100 baseball diamonds stacked one atop the other, with the line between home plate and second base varying randomly for each.
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> "Even if there is directionally dependent electronic order in a twinned sample, you cannot measure it because those differences average out and you wind up measuring a net effect of zero," Dai said. "We had to detwin samples of iron selenide to see if there was nematic electronic order."
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> Study lead author Tong Chen, a third-year Ph.D. student in Dai's research group, solved the twinning problem by cleverly piggybacking on a 2014 study in which Dai and colleagues applied pressure to detwin crystals of barium iron arsenide. It was impossible to apply the same method to iron selenide because the crystals were 100 times smaller, so Chen glued the smaller crystals atop the larger ones, reasoning that the pressure needed to align the larger sample would also cause the layers of iron selenide to snap into alignment.
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> Chen spent weeks creating several samples to test in neutron scattering beams. About 20 to 30 1-millimeter squares of iron selenide had to be aligned and placed atop each crystal of barium iron arsenide. And applying each of the tiny squares was painstaking work that involved a microscope, tweezers and special, hydrogen-free glue that cost almost $1,000 per ounce.
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> The work paid off when Chen tested the samples and found the iron selenide was detwinned. Those tests with neutron scattering beams at Oak Ridge National Laboratory, the National Institute of Standards and Technology, the Technical University of Munich and U.K.'s Rutherford-Appleton Laboratory also showed iron selenide's electronic behavior is very similar to that of other iron superconductors.
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TL,DR: Detwinning splits twins.


A crystal may consist of multiple domains, i.e. areas (2D crystal) or
volumes (3D crystal) sharing the same chemical composition (what atoms and
molecules occur), and crystal phase (think polymorphism as e.g. introduced
for anatase vs rutil). Per sé, each of these domains can be seen as a small
crystal, i.e. with isotropic and anisotropic properties. The spatial alignment
of these sub-units can be described relative to the coordinate system of
the large crystal, as well among each other.


In the model of *mosaic crystals*, the crystal consists of small grains;
their orientation (in respect to the coordinate system of the large
crystal) typically varies only a little, and the variation is *random*.
This contrasts to *twins*; here the orientation of the domains *relative
to each other* can be described by symmetry operations like a mirror
plane (leading to *mirror twins*), an axis of rotation (*rotation
twins*), a centre of inversion (*inversion twins*). That is, you can
describe domains relative to each other and their atomic positions by
a transformation matrix, a *twin law*. (An important tool solving and
refining a crystallographic models by X-ray diffraction.) The mere
description of a crystal *as twinned*, however, does not describe (yet)
the number of of individual twin domains in the crystal, nor the ratio
of the volumes concerned:


[![enter image description here](https://i.stack.imgur.com/C7UwB.png)](https://i.stack.imgur.com/C7UwB.png)


(source: [Britannica](https://www.britannica.com/science/feldspar/Crystal-structure#ref618147))


***Detwinning*** then is *a procedure to split the domains apart from
each other*. This can be attempted numerically at an analytical level
(at various stages analyzing diffraction patterns, for example), or
mechanically. Depending on the case, this can be simple, difficult, or
impossible. Diffraction intensities of different domains can overlap, or be separate of each other (merohedral / nonmerohedral twinning)\*\*. The
mechanical approach can fail for (a non-exhaustive list):


* sample crystal *overall* is too small to be manipulated
* domains are too small to be easily recognized, e.g. by polarization
microscopy monitoring manipulation, or/and manipulated
* twin domains can contact each others (easier case), or intersect and
mutually penetrate each other
* Cutting crystals introduces mechanical stress. A split along the
cleavage planes is an approach more gentle and hence less harmful for the
sample quality. Yet the application of mechanical stress can introduce
additional domains, increase mosaicity, or render the fragments too small
for the X-ray *single crystal* diffraction equipment at disposition.
(However, diffraction analysis is not constrained to X-rays, (cf. vide
supra). Crystals suitable for electron diffraction (not *imaging*\*)
can be *considerably* smaller than the ones for in-house X-ray diffraction
analysis [down to µm scale].)


Finally the discern of 2D/3D crystallography. Apparently, there is no
generally accepted definition how many µm along $(x,y,z)$ represent the
critical threshold between a film/a surface 2D crystal, and a volumetric
3D one. Probably better defined with the number of translations of the
unit cell along vectors $(a,b,c)$, I guess.


\* Gruene, T.; Holstein, J. J.; Clever, G. H.; Keppler, G. Establishing
electron diffraction in chemical crystallography. *Nat Rev Chem* **2021**, *5*,
660–668. <https://doi.org/10.1038/s41570-021-00302-4>


\*\* Herbst-Irmer, R. Twinning in chemical crystallography – a practical guide. *Zeitschrift für Krist. Cryst. Mater.* **2016**, *231*, 573-581. <https://doi.org/10.1515/zkri-2016-1947>


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The work is about the magnetic structure of the material, probed with neutron diffraction. Thus, the twinning disorder is not only in the positions of the atoms but also in the orientation of the nuclear spins.


Wikipedia states in an article on magnetic structure:



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> Such ordering can be studied by observing the magnetic susceptibility as a function of temperature and/or the size of the applied magnetic field, but a truly three-dimensional picture of the arrangement of the spins is best obtained by means of neutron diffraction. Neutrons are primarily scattered by the nuclei of the atoms in the structure. At a temperature above the ordering point of the magnetic moments, where the material behaves as a paramagnetic one, neutron diffraction will therefore give a picture of the crystallographic structure only. Below the ordering point, e.g. the Néel temperature of an antiferromagnet or the Curie-point of a ferromagnet the neutrons will also experience scattering from the magnetic moments because they themselves possess spin. The intensities of the Bragg reflections will therefore change. In fact in some cases entirely new Bragg-reflections will occur if the unit cell of the ordering is larger than that of the crystallographic structure. This is a form of superstructure formation. Thus the symmetry of the total structure may well differ from the crystallographic substructure. It needs to be described by one of the 1651 magnetic (Shubnikov) groups rather than one of the non-magnetic space groups.
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Here is a conceptual sketch of the expected diffraction image (reciprocal space or Q-space) from a [paper](https://DOI:%2010.1103/PhysRevB.102.054430) on a different material, NaFeAs (with the same senior author):


[![enter image description here](https://i.stack.imgur.com/sl9LI.png)](https://i.stack.imgur.com/sl9LI.png)


The green dots are the signals they are interested in. The red dots are from parts of the crystal where the spins have a different pattern. The uniaxial strain (squeezing in one direction rather than placing in a pressure chamber exerting pressure in all directions) suppresses the signals shown with the red dots, but in this case not completely.


For a general introduction about twinning (merohedral and non-merohedral), see e.g. [this paper](https://journals.iucr.org/d/issues/2003/11/00/ba5036/ba5036.pdf). What the Phys.org article is trying to say is that the 2D order is perfect, but in order to get 3D order, they applied pressure along one crystal axis. You can see this nicely in a perfect crystal of a barium-iron-arsenide crystal that undergoes a twinning transition at low temperature. Here is the description from a [video](https://youtu.be/AHVvVnSMwVk) showing the transition, with a screenshot below:



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> Structural "twin" domains forming in a barium-iron-arsenide crystal as it is cooled down to 5 K (- 451 °F). This video, using polarized optical microscopy, shows the formation of these domains, which are caused by a slight change of the positions of the atoms within the crystal.
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[![enter image description here](https://i.stack.imgur.com/7V5Y4m.png)](https://i.stack.imgur.com/7V5Y4m.png)


As you can see from the titles of the journals where this work is published, this would probably get a better answer from a physicist familiar with solid state methods, magnetic properties and superconductivity.


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