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Single-crystal X-ray diffraction atextreme conditions: a reviewTiziana Boffa Ballarana, Alexander Kurnosova & Dmytro Trotsa

a Bayerisches Geoinstitut, Universitaet Bayreuth, 95440 Bayreuth,GermanyPublished online: 13 Sep 2013.

To cite this article: Tiziana Boffa Ballaran, Alexander Kurnosov & Dmytro Trots (2013) Single-crystalX-ray diffraction at extreme conditions: a review, High Pressure Research: An International Journal,33:3, 453-465, DOI: 10.1080/08957959.2013.834052

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High Pressure Research, 2013Vol. 33, No. 3, 453–465, http://dx.doi.org/10.1080/08957959.2013.834052

Single-crystal X-ray diffraction at extreme conditions: a review

Tiziana Boffa Ballaran∗, Alexander Kurnosov and Dmytro Trots

Bayerisches Geoinstitut, Universitaet Bayreuth, 95440 Bayreuth, Germany

(Received 22 July 2013; final version received 7 August 2013)

The latest developments in single-crystal X-ray diffraction at high pressure and high temperature aredescribed.Advances in diamond anvil cell designs and X-ray sources allow collecting single-crystal diffrac-tion data at pressures up and above 100 GPa and at temperatures above 1000◦C. The technical details ofsingle-crystal X-ray diffraction at high pressure such as the choice of pressure-transmitting media or thedifferent methods for measuring pressures and temperatures have been reviewed. Examples of structuralsolution of complex structures and new materials, structural refinements of high pressure polymorphs aswell as accurate compressibility data are described in order to outline the several advantages of using singlecrystals instead of powdered samples in high pressure diffraction experiments.

Keywords: high pressure single-crystal X-ray diffraction; diamond anvil cell; electrical heating; laserheating

Introduction

Among the general public, the words “high pressure” will most likely bring to mind the thoughtof nice weather; for high pressure scientists of any discipline, however, high pressure representsa unique tool for bringing atoms closer together, consequently probing interatomic potentials aswell as modifying the material properties through transformations to denser phases.

High pressure research is now widespread among several topical areas: in basic physics, forexample, the properties and structures of simple elements at very high pressure have been deter-mined, revealing transformations to complex, often modulated, phases.[1–3] High pressure hasbeen used to synthesise and characterise novel materials, such as, for example, superhard phasesand possible hydrogen storage materials. In the pharmaceutical industry, polymorphism of drugsplays a major role in determining their usefulness or harmfulness and several pharmaceutical havebeen studied by now at high pressure to characterise and synthesise different phases (see, e.g. [4,5]).

High pressure also is one of the favourite tools in geoscience, since processes occurring in theEarth’s interior play a major role in determining the geological activity that can be observed at thesurface. Moreover, the extreme conditions in pressures and temperatures present in the Earth’sand planets interior (up to hundreds of GPas and thousands of degrees) result in complex rockassemblages with physical and chemical properties which are not directly observable from directsampling.

Advances in diamond anvil cell (DAC) design and experimental set-ups as well as in X-raysources and detectors have increased considerably the quality of experimental data which can be

∗Corresponding author. Email: tiziana.boffa-ballaran@uni-bayreuth.de

© 2013 Taylor & Francis

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obtained and give now the opportunity of using single crystal instead of powdered samples fordiffraction experiments at megabar pressures.

The use of single crystals in X-ray diffraction has several recognised advantages with respect topowdered samples, mainly due to the three-dimensional data that can be measured. Because thereare no peak overlaps or preferred orientation problems and usually the signal-to-noise ratio ishigher, single-crystal diffraction data allow to obtain unambiguous solution of structures also foracentric and incommensurate crystals as well as the determination of small structural distortions,cation distribution and reliable displacement parameters. Even at high pressure where the coverageof the reciprocal space is limited by the DAC design, single-crystal diffraction data provide moreinformation than the one-dimensional diffraction patterns collected from powdered samples.

Scope of this paper is to review these latest developments in DAC design, heating techniquesand X-ray sources which are now available for single-crystal diffraction study at high pressure.A detailed analysis of the possible methods for generating and measuring pressure during theseexperiments also is reported. At the end, few examples are described in order to demonstrate notonly the challenges but also the advantages of using single crystals for solving complex structuresof high pressure polymorphs or new materials, as well as to better constrain the compressibilityand the high pressure structural evolution of known compounds.

DAC for single-crystal studies

The advent of the Merrill–Bassett cell [6] marks the beginning of routine high pressure structuralstudies using single crystals. Since then, many modifications of DACs have been presented inthe literature and are now available, their common feature being that of using two gem-qualitydiamonds with opposed configuration, with the sample placed between the polished culets insidethe hole of a metal gasket. In this configuration, very little force is required to create extremelylarge pressures in the sample chamber. The major requirement of such DACs has been outlined byMerrill and Bassett [6]: they have to be small enough to be mounted on a standard goniometer headand fit in a single-crystal diffractometer cradle. Moreover, they should have a large opening angleto ensure sampling of most of the reciprocal space of the material studied, without major absorptionof the X-ray beam by various components of the diamond cell. An accurate description of theprinciples for preparation and operation of DACs for single-crystal diffraction and spectroscopicexperiments is given by Miletich et al.[7]

Choosing the size of the diamond culets is a critical point in single-crystal diffraction studies,since it determines both the maximum pressure that can be achieved during an experiment and thedimension of the pressure chamber, i.e. the thickness of the indentation of the gasket (usually steel,rhenium or tungsten) and of the diameter of the hole drilled at its centre. In turn the dimensions ofthe sample chamber determine the maximum dimensions of the single crystal that can be studiedwithout being bridged by the diamonds. Smaller culets (200–300 μm) will reach pressures largerthan 50 GPa but will require crystals smaller than 20 μm and therefore difficult to measure withan in house diffractometer.

High-quality diffraction data can be collected nowadays, thanks to developments in the designof diamond anvils such as, for example, conical diamond anvils [8] supported by tungsten carbideseats which provide the possibility of reaching high temperatures and at the same time avoidingthe usual halo coming from the diffraction pattern of Be backing plates.

X-ray sources

In house diffractometers equipped with conventional glass tubes required large single crystals tobe loaded into the DAC, due to the absorption of the direct beam by the DAC components and

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consequent final low signal-to-noise ratio of reflections from small samples. This meant that onlya limited pressure range could be studied. For example crystals thicker than 50–70 μm are easilybridged above 10–15 GPa when using a steel gasket. For organic materials, as in the case of phar-maceutical compounds, the above conditions are ideal, since rich polymorphism occurs alreadybelow 10 GPa. However, this is a quite low limit if the behaviour of mineral in the Earth’s interioris the subject of investigation, since the pressures involved are much larger than 10 GPa. Morebrilliant X-ray radiations can be obtained in modern diffractometers by using either microfocussources or rotating anodes. The brilliance increase is such that even Ag radiation can be used in aconventional diffractometer with the advantage of reduced absorption and extinction as well as ofa larger d-spacing range due to its smaller wavelength with respect to Mo. Smaller crystals (witha thickness down to 10–15 μm) and crystals containing elements with very low scattering powercan, now, be easily studied with such in house diffractometers.[9,10] The brilliance of the inci-dent X-ray beam at synchrotron facilities is still the perfect choice for reaching extreme pressureconditions, i.e. above 100 GPa, since in this case single crystals of just few micrometres can bemeasured. There are, of course, many challenges for the preparation of such experiments, suchas loading so small crystals at the centre of the diamond culets or perfectly aligning them on anX-ray beam that is only slightly larger than the crystals. The advantages, however, are enormous,since one can obtain three-dimensional structural data at conditions similar to those of the Earth’sinterior and more and more single-crystal studies have now been performed at several beam linesaround the world.

Another major development which is worth mentioning is that of new X-ray sources whichprovide a broad-bandpass mode with a large energy spread.[11,12] The use of such “pink” beamin an approach which combines both monochromatic single-crystal diffraction and Laue single-crystal (micro) diffraction with stationary crystallites has the advantage of increasing the numberof reflections that can be collected in a single shot and therefore is ideal for those materialssensitive to the X-ray beam.

High-temperature experiments with single crystal in DACs

Reaching high temperatures in a DAC, while at the same time maintaining the pressure, is avery challenging task; it requires either electrical or laser heating.[13–15] These two methodshave different advantages but also several disadvantages. Electrical heating is very efficient attemperatures below 1000 K. Because the whole pressure chamber (Figure 1) or even, in someset-ups, the whole DAC is heated, the temperature inside the gasket hole is quite homogeneousand it can be maintained for several hours at a practically constant value. However, special carehas to be taken in order to avoid oxidation and graphitisation of the diamonds, as well as oxidationof the gasket, especially if high temperatures need to be reached. Temperature is measured usinga thermocouple which has to be carefully placed close to the sample in order to measure thecorrect temperature inside the DAC. Accurate temperature measurements require, however, acalibration of the thermocouple whose reading clearly depends on how well it is placed. If thethermocouple moves during the experiments even only slightly, major uncertainties (on the orderof tens of degrees and more) can be expected. Moreover, differences in the thermal expansivityof diamonds, seats and DAC materials often lead to a major variation of the pressure inside thesample chamber during heating (see, e.g. [17]).

Laser-heating experiments cover a wide range of pressures and temperatures, with pressuresup to 200–300 GPa, and temperatures between 1300 and 5000 K.[18–21] The sample preparationfor laser-heating experiments is relatively easy and there is practically no risk for the diamonds.However, the temperature measurement is quite complex and requires spectro-radiometric analysisof thermal radiation spectra collected at the centre of the hot spot created by the laser as well

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Figure 1. Electrical heater developed for piston cylinder DACs.[16]

Figure 2. Schematic drawing of the laser-heating set-up at the 13ID-D beam line of the Advance Photon Source atArgonne National Laboratory.

as knowledge of the pressure, temperature and wavelength dependence of emissivity.[22] Thisusually results in large uncertainties in the temperature values, especially at lower temperatures.The temperature variation inside the sample chamber is very large due to the localised laser-heating spot; therefore special care needs to be taken to focus the X-ray beam exactly at the centreof the hot spot. In spite of technological advances which allow quite large and flat laser spots soas to have a relatively large area (up to 30–40 μm2) with almost uniform temperature, the largetemperature gradient in the pressure chamber gives rise to a number of problems such as chemicalinhomogeneities due to migration of chemical species from the hot spot to the colder part ofthe cell.[23,24]

DAC laser-heating facilities are present in many laboratories as well as at specialised beam linesof third-generation synchrotrons.[25–28] However, in the existing laser-heating facilities, the laserbeam hits the DAC at a fixed angle (Figure 2) and therefore it is not suitable for heating a singlecrystal in a DAC since a partial rotation of the DAC, as required in monochromatic single-crystalX-ray diffraction experiments, results in the laser missing its target (i.e. the crystal) and being

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Figure 3. (1) Universal laser-heating head (UniHead) with (2) a π -shaper mounted for single-crystal X-ray diffractionexperiments in DAC at the ID09a beamline at ESRF (Grenoble) modified from Lavina et al.[31]

scattered in arbitrary directions by the diamond anvils. Only recently, a modified portable laser-heating system [29,30] allows the laser head and the DAC to be mounted on a common platform,and therefore to be rotated together (Figure 3). In this way ω-scans of the cell together with thelaser system can be performed, thus maintaining the focusing of the laser onto the crystal. The laserbeam is ∼40 μm in diameter and has a flat top so that small crystals can be homogeneously heatedavoiding temperature gradient in the samples and reducing the risk of chemical inhomogeneity.

Pressure-transmitting media

The choice of the pressure-transmitting medium for a DAC experiment depends on the sampleunder investigation and on the pressure region one wants to cover. The pressure medium shouldbe inert with respect to the sample and it should ensure that the stress applied to the sample ishomogeneous over the entire pressure range of the experiment. To achieve this, the sample mustbe immersed in a medium that displays hydrostatic or quasi-hydrostatic behaviour. Avoiding non-hydrostatic conditions in an experiment is quite important, because non-hydrostatic stresses createinhomogeneous strains in the material under investigation with consequent broadening and shift-ing of the diffraction peaks. This results in a reduction of the signal-to-noise ratio of the measureddiffraction signals and in a different compressibility of the crystalline samples with pressure.[32–35] Furthermore, non-hydrostatic stresses may affect the relative stabilities of polymorphsboth in inorganic [36,37] and organic materials.[38] They may give rise to different paths of phasetransformations [39,40] as well as promote the amorphisation of crystalline samples.[41,42] Thepresence of non-deviatoric stresses is problematic because they cannot be easily characterised inDACs. They arise not only from the fact that no pressure medium can provide completely hydro-static conditions, but also from grain-to-grain interaction in the case of a powdered sample. Themajor advantage of using single crystals instead of powders when dealing with non-hydrostaticstresses resides in the fact that the deviatoric strains of small single crystals can be calculatedusing a cylindrically symmetric stress field, at least as long as non-homogenous strains can beignored [43] and therefore the data can be properly corrected to constrain the “real” hydrostaticbehaviour of the sample under investigation.

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Figure 4. Variation of the FWHM of the 101 reflection of quartz as a function of nominal pressure in Ne (open circles)and He (filled circles). The inset reproduces Figure 2 from Angel et al. [44] in which the width for the 101 reflection hasbeen measured in glycerol (triangles), anhydrous 2-propanol (squares) and 4:1 methanol–ethanol (circles).

The onset of non-hydrostatic stresses within different pressure media including nitrogen, argon,2-propanol, a 4:1 methanol–ethanol mixture, glycerol and various grades of silicone oil has beendetected from the broadening of the rocking curves of X-ray diffraction peaks from a single crystalof quartz.[44] It has been shown that for most pressure media, the hydrostatic limits are below10 GPa if high-temperature annealing is not applied.

To reach pressures larger than 10 GPa and at the same time ensure almost hydrostatic conditions,one has very limited choice, currently – either He [45] or Ne noble gases. The full-width athalf-maximum (FWHM) of diffraction peaks from quartz single crystals loaded in turn withHe and Ne pressure-transmitting media has been measured at the Bayerisches Geoinstitut forthe purpose of this paper using a point detector and a Huber single-crystal diffractometer. Thesame procedure described by Angel et al. [44] has been followed. The resulting FWHM of the(101) reflection is reported in Figure 4 and compared with the similar figure taken from Angelet al. [44] for other pressure media. Solidification of He and Ne at room temperature occurs at∼10 and 5 GPa, respectively. Helium appears to provide close to hydrostatic conditions evenin the solid state, since no broadening of diffraction peaks is observed for a quite soft crystal asquartz (bulk modulus = 37.12 (9) GPa [46]) up to its phase transformation above 20 GPa. A slightbroadening of the (101) reflection is observed above 11 GPa for the crystal in Ne; however, thisseems to result from bridging of the crystal and therefore further experiments need to be performedto better constrain the onset of non-hydrostaticity of Ne. The difficulty in using Ne or He aspressure-transmitting media arises from the fact that an apposite gas loading apparatus is needed.Fortunately, most of the synchrotron facilities offer the possibility of gas loading, although thisrestricts the type of cell one can use, since the gas loading apparatus is often built for specificDAC designs. However, more and more high pressure laboratories have built their own gas loadingdevices and usually these are more versatile (see, e.g. [47]). An important question is, of course,whether such small gas molecules can penetrate into the crystal structure of the sample under

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investigation. For many solids with a compact structure this seems not to be a problem, but thisis not the case for materials with large cages such as zeolites or silica glasses.[48]

Pressure determination methods

The measurement of pressure in a DAC is one of the major contributions to uncertainty in highpressure experiments. A direct calibration of the pressure versus the applied load similar to theprocedure for piston–cylinder or multi-anvil devices is not possible, since an unknown part ofthe load given by every turn of the screws is lost in a non-reproducible way to internal frictionand gasket deformation. In high pressure experiments with DACs, therefore, internal standardmaterials whose changes in physical properties with pressure are known are loaded togetherwith the sample in the pressure chamber. The most widely used method to determine pressurein single-crystal experiments is measuring the fluorescence shift of optical pressure gauges, suchas for example ruby or Sm-doped Y3Al5O12 (Sm:YAG).[49–52] Such materials are secondarystandards since they are calibrated using shock data of a series of metals.[49,53]As a consequence,the uncertainties of the pressure measurement may be quite large, especially when such standardsare used at conditions far from those at which they were calibrated. Large uncertainties on thepressure values are one of the major causes of inaccuracy of equations of state (EoS) and inparticular on pressure derivatives of elastic moduli.

In order to reduce the uncertainties in pressure determination, absolute pressure can be extractedby integration of the isothermal bulk modulus, KT [54,55], according to the relationship:

P = −∫ V

Vo

KT (V)

VdV ,

where V is the unit-cell volume of the sample under investigation. This procedure, however,requires that density (volume) and KT are obtained from independent measurements. Usually,KT is derived from the adiabatic bulk modulus KS , KS = KT (1 + αγ T) (where α is the thermalexpansion and γ is the Gruneisen parameters), determined from elastic constants obtained fromultrasonic measurements, Brillouin spectroscopy, laser-induced phonon spectroscopy, etc.[56]However, for a consistent absolute pressure determination, it is important to determine densityand adiabatic bulk modulus simultaneously on the same sample at the same conditions. Facil-ities at synchrotron radiation beamlines, for example the 13BMD beamline of the GSECARSsector at the Advanced Photon Source, Argonne National Laboratory, give now the possibility ofmeasuring simultaneously the volume compressibility and sound wave velocities using Brillouinspectroscopy with single-crystal samples.[57] Simultaneous measurements of elastic constantsand density at high pressure are, however, time consuming, therefore the use of a fluorescencesensor for determining pressure is much more practical and highly desirable. Several materialshave been now calibrated vs. a primary pressure scale such as boron nitride up to 27 GPa,[58] cubicsilicon carbide up to 75 GPa [59] and Sm-doped Y3Al5O12 (Sm:YAG) up to 58 GPa [60] can beused as more precise pressure gauges in high pressure experiments. For the two first compounds,pressure can be determined through the shift in Raman active bands, whose pressure sensitivityis lower than ruby, whereas the Sm:YAG fluorescence shift with pressure is identical to that ofruby. Sm:YAG also is very suitable for determining pressure at elevated temperatures, since itsfluorescence shift is insensitive to temperature changes.

The coupled use of ruby and Sm:YAG appears, therefore, as a more precise alternative to theuse of thermocouples in electrically heated DACs. By loading two chips of these two materialstogether with the sample in the DAC, one can determine pressure independently from temperatureusing the fluorescence ofYAG and determine temperature using the fluorescence of ruby by fixingthe pressure value obtained from theYAG fluorescence measurement.[61] Note that ruby has been

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calibrated at pressures up to 120 GPa and temperatures up to 700 K by Rekhi et al. [17] and Weiet al.[62]

An alternative way of measuring pressure in single-crystal diffraction experiments is that ofusing the EoS of the pressure-transmitting medium, i.e. of Ne or He. This is possible only whenbrilliant X-ray sources are coupled with two-dimensional detectors so that the diffraction ring ofthe pressure-transmitting medium can be recorded and indexed. The compressibility of Ne hasbeen determined both at room and at high temperatures and therefore it can be used also as ahigh-temperature pressure standard once temperature is known.[63] To our knowledge, no EoShas been reported for He, neither at room nor at elevated temperatures.

Examples

Several studies which make use of single-crystal X-ray diffraction at high pressure will be reportedin this volume. In this section, some examples of studies which can be found in the literature arereported in order to give a broad picture of the variety of applications to which single-crystal X-raydiffraction coupled with synchrotron radiation can be applied nowadays, from structural solutionand characterisation of high pressure polymorphs and new materials, to accurate determinationof compressibility and structural evolution of known compounds. All these examples have beenchosen, because the single-crystal diffraction measurements have been performed well above10 GPa or have been crucial for the success of such studies.

In the last decade, single-crystal diffraction has been used to resolve the complexity of the highpressure behaviour of simple metals [1,3,64–66] or compounds with low scattering elements asin the case of methane.[67] The major feature of these studies is the fact that single crystals aregrown in situ in the DAC at the pressure of interest and studied mainly at synchrotron beam lines.The three-dimensional diffraction data from single crystals are particularly useful because thelow-symmetry high pressure phases involved very often present modulated structures impossibleto solve from powder data. This is the case, for example, of elemental barium which undergoes aseries of phase transformations to complex phases between 12 and 45 GPa most of which have anincommensurate host–guest crystal structure.[68] One of these (Ba-IVc) structure in particular wasvery difficult to resolve because it lacks translational symmetry along the b direction and thereforeneither a crystallographic unit-cell nor a space group can be assigned. The developed structuralmodel based on a supercell containing 768 Ba atoms can now reproduce the detailed mapping ofthe reciprocal space collected at 19 GPa using a single crystal of Ba-IVc [69] (Figure 5).

Even for commensurate structures, single-crystal data can give a better constraint on the struc-tural behaviour of high pressure polymorphs, especially in the case of low-symmetry compoundsas in the case of dolomite high pressure phases,[70] or give an insight on the structure of newmaterials such as Fe4O5 [71] whose structure has been a mystery for quite a long time.[72]

Study of the evolution of a crystal structure with pressure is of course more straightforwardif single-crystal data are available and can be used to better constrain phase transformations orthe lack of them at high pressure. For example subtle changes in interatomic distances due to avariation of the atomic size associated with a spin transition result in a drastic unit-cell volumedecrease in Ca-ferrite, CaFe2O4, or siderite, FeCO3, [31,73]. In Fe3C, instead, no volume changeis visible at the spin transition above 22 GPa, pressure at which a small jump and a change in slopeis observed for the central shift of Mössbauer spectra. Accurate lattice parameter determinationfrom single-crystal intensity data reveals a change in slope in the normalised stress, F, vs. eulerianstrain, f , plot (Figure 6), which suggests a clear change in the compression behaviour of such amaterial due to the spin transition but no associated structural transition.[74]

Single-crystal data also can be used to better constrain the compressibility behaviour of materi-als, since they do not suffer of non-deviatoric stress due to grain-to-grain interaction of powdered

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Figure 5. Comparison between the experimental diffraction data (top) and the simulated pattern (bottom) for the finalBa-IVc structural model reproduced from Loa et al. [69].

Figure 6. Normalised stress (F) vs. eulerian strain (f ) for a Birch–Murnaghan equation of state calculated for thecompressibility data of Fe3C reported by Prescher et al.[74] A change in compressional behaviour is clearly visible above24 GPa.

samples. Moreover, the onset of non-hydrostatic and non-homogeneous strain in a single crystalcan be more easily recognised due to the immediate broadening of the reflections giving thereforethe possibility of interrupting the experiments or correcting the data with respect to the non-hydrostatic stress.[43] Thanks to such accuracy it has been possible, for example, to investigatethe subtle effect of Fe and Al substitution on the MgSiO3–perovskite structure [75] up to thepressure of the lower mantle and to demonstrate that the coupled substitution of Fe3+ + Al forMg + Si softens the MgSiO3–perovskite structure.

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Figure 7. Crystal structure of the orthorhombic high pressure polymorph of Fe2O3 refined from intensity data collectedat 40.4 GPa and 2300 K.

High pressure studies at high temperature are of course more challenging, since the singlecrystal has to be maintained at the same conditions for a relatively long time to allow collection ofall possible reflections. The stability of electrical heating, however, allows such conditions to beachieved to determine the elastic properties at least for cubic materials like ringwoodite, the highpressure phase of olivine,[57] whereas new developments of a portable laser-heating system allowsstructural refinements from simultaneous high pressure and high-temperature single-crystal data.Thanks to this technique, for example, the orthorhombic structure of the high pressure polymorphof hematite has been assigned to the space group Pbna and has been refined with a model havingthe Rh2O3-type structure (Figure 7).[76] Several improvements of such technique are still needed,especially with respect to increasing the reciprocal space accessible, however we can expect thatmore and more studies will use laser heating coupled with single-crystal diffraction in the future.

Acknowledgements

Support has been provided by ERC advanced Grant no. 227893 “DEEP” funded through the EU 7th FrameworkProgramme.

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