The structure of the superconducting high-pressure phase of Sc_3CoC_4
Jan Langmann, Marcel Vöst, Dominik Schmitz, Christof Haas, Georg Eickerling, Anton Jesche, Michael Nicklas, Arianna Lanza, Nicola Casati, Piero Macchi, Wolfgang Scherer
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b The structure of the superconducting high-pressure phase ofSc CoC Jan Langmann, Marcel V¨ost, Dominik Schmitz, Christof Haas, Georg Eickerling, ∗ Anton Jesche, Michael Nicklas, AriannaLanza, Nicola Casati, Piero Macchi, and Wolfgang Scherer † CPM, Institut f¨ur Physik, Universit¨at Augsburg, D-86159 Augsburg, Germany Experimentalphysik VI, Zentrum f¨ur Elektronische Korrelation und Magnetismus,Institut f¨ur Physik, Universit¨at Augsburg, D-86159 Augsburg, Germany Max Planck Institute for Chemical Physics of Solids,N¨othnitzer Straße 40, D-01087 Dresden, Germany Center for Nanotechnology Innovation@NEST,Istituto Italiano di Tecnologia, I-56127 Pisa, Italy Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland Dipartimento di Chimica, Materiali ed Ingegneria Chimica “G. Natta”,Politecnico di Milano, I-20133 Milano, Italy (Dated: February 3, 2021)
Abstract
We investigate pressure-induced structural changes to the Peierls-type distorted low-temperaturephase of the low-dimensional Sc CoC as a possible origin of its pressure-enhanced superconduc-tivity. By means of cryogenic high-pressure x-ray diffraction experiments we could reveal subtle,but significant structural differences between the low-temperature phase at ambient and elevatedpressures. We could thus establish the structure of the superconducting phase of the title compoundwhich interestingly still shows the main features of the Peierls-type distorted low-temperaturephase. This indicates that in contrast to other low-dimensional materials a suppression of periodicstructural distortions is no prerequisite for superconducitivity in the transition metal carbide. . INTRODUCTION Structurally low-dimensional materials and dimensionality-driven physical effects aremaking their way into technical applications. Quantum dots (0D) are actively deployedin display technology or under intensive research for future uses in quantum computing. Nano-wires (1D) enable great improvements in photo- and chemo-electric detectors and ther-moelectric devices. Transistors fabricated of atomically thin graphene layers (2D) mightbecome an integral part of post-silicon microprocessors.
Futhermore, 3D superstructuresof thin metal layers – arranged in the right way to break inversion symmetry – might providepromising candidates for diodes in superconducting electronics. FIG. 1. (a) Infinite [Co(C ) ] ∞ ribbon as basic quasi-1D building unit of the Sc CoC structure;(b) composition of a quasi-2D layer by stacking [Co(C ) ] ∞ ribbons and Sc1 atoms along the a axis of the orthorhombic high-temperature phase; (c) decoupling of the quasi-2D layers along the c axis by interleaved Sc2 and Sc3 atoms. Salient inter-atomic distances are specified (structuraldata from Ref. 8).
2s indicated by the last example, the combination of structural low dimensionality withsuperconductivity can stimulate intriguing effects, even though W. A. Little’s prediction ofroom-temperature superconductivity in quasi-one-dimensional materials still remains anunobserved phenomenon at ambient pressure. Instead, a rich playing field of different order-ing phenomena interacting with superconductivity has unfolded, e.g. structural transitions,charge- and spin-density waves, and antiferromagnetism.
Superconducting compoundswith intrinsically low-dimensional character have a special appeal to solid-state sciences,although the synthesis of large and defect-free single crystals is often challenging. This, forexample, becomes evident from the large number of publications devoted to the well-knownquasi-one-dimensional NbSe or quasi-two-dimensional graphite/graphene andtransition-metal dichalcogenides.
The transition-metal carbide Sc CoC crystallizes in a structure type combining quasi-1Dand quasi-2D features. Quasi-1D [Co(C ) ] ∞ ribbons extending along the crystallographic b axis of the orthorhombic unit cell (Fig. 1a) are formed by covalent bonds between thecobalt atoms and C moieties. Alternating stacking of the [Co(C ) ] ∞ ribbons and scan-dium atoms (Sc1) along the a axis leads to quasi-2D layers (Fig. 1b). Therein, neighboring[Co(C ) ] ∞ ribbons with a separation of 3.39483(3) ˚A are held together by subtle Sc-C interactions. Additional scandium atom layers (Sc2 and Sc3; Fig. 1c) are interleaved alongthe c axis resulting in a large interlayer distance of 5.99855(5) ˚A between adjacent Sc1-Co-Clayers. Superconductivity in Sc CoC emerges below T c ≈ and is anticipatedby a Peierls-type structural transition below 72 K. Therein, the orthorhombic high-temperature (HT) phase structure (space group
Immm ) is transformed into the monocliniclow-temperature (LT) phase structure (space group C /m ) by a doubling of the transla-tional period along the [Co(C ) ] ∞ ribbons. The exact degree and mode of interactionbetween this structural HT → LT phase transition and the onset of superconductivity at evenlower temperatures is, however, not fully established yet. Furthermore, high-pressure studiesof the electrical resistivity and magnetization in polycrystalline samples by Wang et al. re-vealed a drastic increase of the superconducting volume at virtually constant T c values. Theauthors rationalized this behavior by a pressure- and temperature-controlled coexistence ofthe HT and LT phase in the compound, whereby only the HT phase was supposed to becomesuperconducting. But no structural information to verify this hypothesis has been pro-3ided up to now. Therefore, we performed high-pressure and low-temperature single-crystalx-ray diffraction studies in combination with physical property measurements to explore thepressure- and temperature-dependent structure-property relationship in Sc CoC . II. METHODS
Single- and polycrystalline samples of Sc CoC were synthesized by arc-melting accord-ing to the method described in the literature and in addition from a lithium metalflux. Needle-like samples were obtained from arc-melting and platelet-like samples fromcrystallization in a lithium flux (full details of the synthesis and characterization methodsemployed can be found in the Supplemental Material ).Magnetization measurements on a single-crystalline Sc CoC sample were performed atvarious pressures up to 1.48 GPa using a miniature Ceramic Anvil Cell (mCAC) assem-bled with a Cu:Be gasket. The respective pressures were determined at low temperaturesby reference to the pressure dependence of T c for an additional lead piece inside the pres-sure chamber. Both, single-crystal and lead pressure gauge, were surrounded by Daphne7373 serving as a pressure transmitting medium. Supplemental ambient-pressure mea-surements before and after the high-pressure study were performed by gluing the sampleto a glass rod with GE Varnish. For all magnetization measurements a QUANTUM DE-SIGN MPMS3 SQUID magnetometer was employed. The superconducting properties of theSc CoC sample were investigated by cooling the pressure cell or glass rod to 1.8 K underzero-field-cooling conditions and recording the temperature-dependent magnetization whileheating from 1.8 K to 9 K in a magnetic field of 5 Oe.High-pressure electrical resistivity measurements up to 1.26 GPa were performed em-ploying a piston-cylinder-type pressure cell and silicon oil as pressure-transmitting medium.The single-crystalline Sc CoC whisker was contacted by a four-point configuration usingsilver conductive paint and gold filaments. The pressure inside the pressure chamber wasdetermined at low temperatures by measuring the shift of the superconducting transitiontemperature of a piece of lead. For details of the setup see Ref. 53. The temperature-dependent resistivity measurements were carried out for various applied pressures uponcooling and heating cycles between 1.8 K and 300 K in a QUANTUM DESIGN PPMSusing a LINEAR RESEARCH LR700 resistance bridge. Additional ambient-pressure mea-4urements of single-crystalline Sc CoC whiskers four-point contacted with silver-epoxy resinwere taken without surrounding pressure cell and using the standard DC-resistivity optionof a QUANTUM DESIGN PPMS. Uniaxial strain was created by gluing both ends of awhisker to a sapphire substrate using large droplets of silver-epoxy resin.Pressure-dependent lattice parameters at room temperature were obtained from Le Bailfits of synchrotron powder x-ray diffraction data with the software JANA2006. The re-spective diffraction experiments were carried out at the X04SA Materials Science (MS) beam-line at the Swiss Light Source (SLS) using a PSI Mythen II one-dimensional detector and a membrane-driven diamond anvil cell (DAC). The pressure chamber was filled withfinely ground and sieved Sc CoC powder (nominal sieve opening 32 µ m), and a 4:1 vol-ume mixture of methanol and ethanol was used as pressure-transmitting medium. α -quartzpowder was added for pressure calibration by reference to its well-known equation of state. The single-crystal x-ray diffraction data in this work was collected on a HUBER four-circleEulerian cradle goniometer equipped with a DECTRIS Pilatus CdTe 300K pixel detectorand an INCOATEC AgK α microfocus sealed-tube x-ray source ( λ = 0.56087 ˚A).High-pressure low-temperature x-ray diffraction studies of Sc CoC single crystals up to apressure of 5.5 GPa were carried out using a Diacell Tozer-type DAC and Daphne 7575as pressure-transmitting medium. Ruby spheres inside the pressure chamber allowed apressure determination at room temperature via the ruby fluorescence method.
Samplecooling to temperatures above 20 K was achieved utilizing an ARS closed-cycle helium cry-ocooler with exchangeable vacuum and radiation shields surrounding the Tozer-type DAC.The temperature-dependence of selected reflection intensities at various applied pressureswas tracked with a stainless steel vacuum chamber featuring kapton windows. To collectx-ray diffraction data for structure determinations at pressures of 0 GPa and 4 GPa andtemperatures of approx. 40 K and 110 K the stainless steel vacuum chamber was replacedby a beryllium vacuum dome providing a larger accessible reciprocal space fraction.A similar experimental setup featuring the closed-cycle helium cryocooler and an outerand inner beryllium vacuum and radiation shield was used to obtain single-crystal x-raydiffraction data at ambient pressure and sample temperatures of 11 K, 70 K and 100 K.For high-pressure x-ray diffraction measurements on a Sc CoC single-crystal up to10.1 GPa at room temperature a Boehler-plate-type DAC was employed. The fillingprocedure and pressure determination method were analogous to the experiments with the5ozer-type DAC described above, but with a 4:1 volume mixture of methanol and ethanol as pressure-transmitting medium.Obtained x-ray diffraction intensities were evaluated using the EVAL14 suite of programs and subjected to scaling and absorption correction using the programs SADABS/TWINABS. More information on the handling of parasitic scattering and shadowing of the x-ray beamby high-pressure or low-temperature equipment is available in the Supplemental Material. Structural refinements were performed with the program JANA2006. Density Functional Theory (DFT) calculations on the HT phase of Sc CoC were per-formed employing the VASP code. The PBE density functional, an energy cutofffor the plane wave basis set of 500 eV and a Brillouin grid sampling of 4 × × a , b and c lattice parameters of the relaxed HT ambient pressure structure by ± .
02 ˚A and ± .
04 ˚A.All phonon dispersion calculations employing the finite displacement approach in a2 × × and VASP as force calculatorusing the same parameters as specified above. III. RESULTS AND DISCUSSION
Starting point of our study are the results published earlier by Wang et al. Theseauthors found a significant increase in the superconducting volume fraction of polycrys-talline Sc CoC samples under the application of modest hydrostatic pressures. In thepresent study, we performed physical property measurements and x-ray diffraction experi-ments on single-crystalline samples. This allows us to explore potential structure-propertyrelationships in Sc CoC and gain deeper insight into the origins of pressure-enhanced su-perconductivity in the low-dimensional material. Also for single-crystalline samples a clearsuperconducting signature is only observed in the electrical resistivity ρ ( T ) (see Fig. 2a) andthe magnetization M ( T ) (Fig. 2b and Fig. 2c) after application of pressure. It is notewor-thy that the enhanced superconducting signal persists for several hours after decreasing the6ressure from 1.48 GPa to 0.19 GPa. It remains remanently present even after removing thesample from the pressure cell (see Fig. 2c). This hints to a potential hysteretical behaviorof the inherent structural changes induced by the application of pressure. Degradation ofthe sample quality as a possible origin of this behavior could be excluded by means of x-raydiffraction before and after performing a high-pressure experiment at 4.5 GPa and 27 K (seeSupplemental Material ). a) M [ e m u / g ] T [K]b) c) Increasing pressure
Decreasing pressure T [K] (cid:1) [ mW(cid:215) c m ] T [K] Increasing pressure
FIG. 2. Temperature- and pressure-dependent development of (a) the electrical resistivity ρ ( T )and (b, c) the magnetization M ( T ) after zero-field-cooling in a magnetic field of 5 Oe for thesuperconducting transition of Sc CoC . Data points in (a) and (b) were recorded while increasingthe pressure and data points in (c) while decreasing the pressure. Note that the ambient-pressuremeasurements of ρ ( T ) (a) and M ( T ) (b, c) were performed without a pressure cell. For bettercomparability, data points were brought to overlap at 4.5 K by applying shifts along the ρ -/ M -axis. In other low-dimensional compounds like the transition-metal dichalcogenides 1 T -TiSe ,2 H -TaSe and 2 H -NbSe the pressure-induced emergence of superconductivity is intimatelylinked to the suppression of a periodic structural distortion at low temperatures, i.e. acommensurate or incommensurate charge-density wave. We therefore tried to clarify,whether the Peierls-type distortion leading to the low-temperature (LT) phase might besuppressed upon application of pressure to enhance the superconductivity in Sc CoC . The structural properties of the ambient-pressure low-temperature phase have been studiedearlier and provide the starting point of this pressure- and temperature-dependent study.Atom displacements and bond lengths mentioned hereafter were determined in an ambient-pressure x-ray diffraction experiment on a high-quality single-crystalline needle of Sc CoC at 11 K (see experimental section and Supporting Material for further details). All bond7engths and displacements in this work are given with their threefold standard deviation,while crystallographic directions are always specified with respect to the axes of the or-thorhombic HT phase (space group Immm ).The LT phase of Sc CoC (space group C /m ) is characterized by modulated displace-ments of Co, Sc1 and C atoms from their HT phase positions in the quasi-2D layers of theSc CoC structure (see Fig. 3a). Precisely, the cobalt atoms along a [Co(C ) ] ∞ ribbon ex-perience shifts of ± d site in the HT phase(information on the calculation of the atom displacements is provided in the Supplemen-tal Material ). Hence, Co–Co distances within chains of cobalt atoms along the a axisdisplay alternating larger (3.5985(9) ˚A) and smaller (3.1569(6) ˚A) values compared to theconstant separation of 3.3948(12) ˚A in the HT phase. This modulation of the Co atomicpositions is complemented by a modulation of the Sc1 atomic positions. Their displacementsof ± b HT positions point along the b axis and alternate alongthe a axis, i.e. their displacement direction is perpendicular to the modulation of the Coatomic positions. As can be seen in Fig. 3a, the modulation of the Co and Sc1 atoms is cor-related in such a way that the Sc1 atoms are shifted towards long Co–Co contacts and evadeshort Co–Co contacts. In analogy to the arrangement of the cobalt atoms, this displacementpattern turns chains of equispaced scandium atoms along the b axis (4.3748(12) ˚A) aboveand below the [Co(C ) ] ∞ ribbons into chains with alternating longer (4.5015(12) ˚A) andshorter (4.2718(12) ˚A) Sc1–Sc1 distances.As a consequence of the HT → LT transition the [Co(C ) ] ∞ ribbons are no longer planar,which is also reflected by rotations of the C units about rotation axes parallel to c . Due tothe lack of a crystallographic m plane perpendicular to a rotations of adjacent C units aboutthe b axis in the same direction (conrotatory) or opposite directions (disrotatory) are bothallowed by symmetry. The potential importance of the carbon atoms for superconductivityin Sc CoC can be derived from isotopic substitution experiments: replacement of C by C leads to a systematic suppression of the superconducting onset temperature T onset c withan isotope coefficient α of 0.58. This observation is in line with the predictions of a DensityFunctional Theory (DFT) study by Zhang et al. The authors proposed that rotations ofthe C units and cobalt and scandium atom displacements are integral parts of key phononmodes coupling conduction electrons into superconducting Cooper pairs.Yet, rotations of the C units are experimentally more difficult to assess by x-ray diffrac-8 .1125(18) Å1(1)° 1(1)°0.064(2) Å4 GPa, 37 K0 GPa, 11 Ka) a b b) FIG. 3. Overlays of the refined atomic positions within a layered building unit of Sc CoC atroom temperature (gray, semi-transparent; atomic positions from Ref. 8) and after cooling to lowtemperatures (a) without or (b) with applied pressure (colored, non-transparent). All atom dis-placements are exaggerated seven-fold, Sc2 and Sc3 atoms have been omitted for clarity. Specifiedvalues of atom displacements and rotation angles are given with their threefold standard deviation. tion than shifts of the heavy atoms cobalt and scandium. The latter displacements invariablylead to the appearance of prominent superstructure reflections with k = (+ , + ,
0) and alsowith k ′ = (cid:0) + , − , (cid:1) due to systematic pseudo-merohedric twinning (see Fig. 6f). Bycontrast, carbon atom displacements may only contribute to the superstructure reflections inthe case of disrotatory displacements of neighboring C units (a more detailed discussion canbe found in the Supplemental Material ). Conrotatory displacements make no contributionto the intensities of the superstructure reflections, and only a minor contribution to the in-tensities of the main reflections, i.e. even a hypothetical rotation by 15 ◦ changes the averagemain reflection intensity by less than 1 %. To obtain precise intensity information for mainand superstructure reflections we therefore employed long exposure times, a high-brilliancemicrofocus x-ray source and a noise-reduced pixel detector with high dynamic range for thesingle-crystal x-ray diffraction experiments discussed in the following (see the experimentalsection and the Supporting Material for more details).Our structural model at 11 K and ambient pressure is characterized by rotations of thetwo symmetry-independent C units in the same direction with rotation angles of 5.6(2) ◦ and 5.7(2) ◦ (highlighted in Fig. 3a). Similar carbon atom shifts resulting in somewhat9maller but still conrotatory rotation angles of 2.8(4) ◦ and 3.0(4) ◦ have been found earlierat 9 K. Notably, the observed conrotatory displacements of subsequent C units along the[Co(C ) ] ∞ ribbons result in the formation of shorter (2.098(4) ˚A) and longer (2.113(3) ˚A)Co-C distances in contrast to an alternative scenario with disrotatory displacements whichwould minimize all Co–C distances. This rules out that strengthening of Co–C bonds pro-vides the only driving force of the carbon atom shifts in the LT phase structure.In the next steps of our analysis we will aim at establishing possible pressure-dependentstructure-property relationships to gain further insight into the potential origins of the char-acteristic superconducting behavior of Sc CoC . Measurements of the electrial resistivity ρ ( T ) already hint towards potential pressure-induced modifications of our reference LT phasestructure: As outlined earlier, the extended phonon softening process leading to a staticPeierls-type structural distortion of Sc CoC at ambient pressure is delimited by two pro-nounced anomalies in ρ ( T ) at 152 K and 83 K (Fig. 4a). Our high-pressure experiments onsingle-crystalline samples in accordance with Wang et al. show that only a single broadanomaly at 156 K can be observed in ρ ( T ) after application of 0.03 GPa (see blue curve inFig. 4b). This anomaly further shifts towards higher temperatures with increasing pressure(dark yellow curve in Fig. 4b). A similar result, i.e. a suppression of the first anomaly atlower temperature in ρ ( T ) and an upward shift of the second one by approx. 10 K, can beobtained by fixing a single-crystalline Sc CoC needle at two points along its long axis ( i.e. parallel to the crystallographic a axis) on top of a sapphire chip (see Fig. 4c).In order to investigate the origin of these pressure-dependent changes in ρ ( T ) we per-formed x-ray diffraction experiments at variable pressure and temperature. Inspection ofBragg intensities as well as atomic positions from structural refinements should reveal,whether (i) only the distortion pattern during the HT → LT phase transition changes underpressure, (ii) the structurally distorted LT phase is suppressed in favor of the undistorted HTphase, or (iii) a designated and structurally distinct high-pressure LT phase of Sc CoC is formed.In support of hypothesis (i) , our measurements indicate that the low-temperature super-structure Bragg reflections with k = (+ , + ,
0) can be observed up to pressures of 5.5 GPa.No indication for a pressure-induced structural phase transition connected with a change ofthe space group can be found. Instead, the collected diffraction data can still be described bya monoclinic lattice and complies with space group C /m . Differences between pressurized10 IG. 4. Temperature-dependent electrical resistivity ρ ( T ) of Sc CoC single-crystals (a) at ambientpressure and without fixation to a substrate, (b) at hydrostatic pressures of 0.03 GPa and 0.82 GPaand (c) glued at both ends on top of a sapphire chip. Insets: Photographic images of the respectivesamples after their preparation for measurements (a) to (c). and unpressurized samples, however, may be recognized by comparing reconstructions of the( h, . , l ) reciprocal space plane at 22 K for pressures between 0 GPa and 5.5 GPa (Fig. 5).Note that at ambient pressure Sc CoC crystals in the LT phase are systematically twinnedwith each of the two differently oriented twin domains contributing half of the superstruc-ture reflections to the ( h, . , l ) plane (green and orange circles in Fig. 5). Cooling crystalsbelow the HT → LT phase transition temperature at elevated pressures reveals that one halfof the superstructure reflections shows increasing intensities, whereas the other half showsdecreasing intensities ( p ≤ p > Taking into account the otherwise unchanged characteristics of the LT phase in recipro-cal space we may connect the strongly modified behavior of the anomalies in ρ ( T ) underpressure (compare Fig. 4a and Fig. 4b) to changes along the pathway from the HT to the LTphase. Therefore, we determined the temperature- and pressure-dependence of the scatteredintensity I XRD ( T, p ) at the positions of representative superstructure reflections (see Fig. 6).11 omain 1domain 2 c* a* pressure (-1.5 0.5 -2)(-1.5 0.5 -3)
FIG. 5. Pressure-induced detwinning of a Sc CoC sample at T = 22 K, as observed by x-raydiffraction in case of characteristic Bragg reflections from two twin domains (twin law [[-1 0 0],[0 1 0], [0 0 1]], i.e. an m plane perpendicular to the a axis of the orthorhombic HT unit cell). Thedisplayed sections of the ( h, . , l ) plane contain only superstructure reflections and were recordedafter applying pressures up to 5.5 GPa and cooling to 22 K. The decreased scattering intensity at5.5 GPa is due to a beginning deterioration of the sample crystallinity. Consistent with ρ ( T ), the increase of I XRD ( T, p ) with decreasing temperature, which occursin two steps at ambient pressure (Fig. 6a), renders into a continuous increase under pressure(Fig. 6b to Fig. 6e). We note, however, that a quantitative comparison of applied pressurevalues in ρ ( T ) and M ( T ) studies with those of the x-ray diffraction experiments is ham-pered by the differing sample environments and pressure determination methods employed(see experimental section and Supplemental Material ).From our data we may conclude that the LT phase is stabilized substantially, as is in-dicated by a shift of the onset temperature of the superstructure reflection intensities from142 K at 0 GPa (Fig. 6a) to 231 K at 4 GPa (Fig. 6d). A pressure of 5.5 GPa preservesthe superstructure reflections up to room temperature (Fig. 6e, see also the SupplementalMaterial ), although at the cost of a degradation of the sample crystallinity. Interestingly,the isoelectronic and isostructural transition metal carbides Sc IrC and Sc RhC also showa periodically distorted structure in analogy to the LT phase of Sc CoC at room tem-perature but without prior cooling or pressure application. There are, however, neitherhints to superconductivity nor to the existence of an undistorted high-temperature phasecomparable to Sc CoC for these highly related compounds. In particular, systematic twin-ning as indicator of a potential t HT → LT transition has not been observed in the iridium12 b* a* domain 2domain 1 (-1 1 0)
FIG. 6. Temperature-dependence of the scattered intensity I XRD ( T, p ) at the positions of repre-sentative superstructure reflections for pressures between 0 GPa (a) and 5.5 GPa (e). A section ofthe ( hk
0) plane (f) illustrates the location of the superstructure reflections for twin domains 1 and2 with respect to the main reflections. and rhodium congeners of Sc CoC . This discrepancy may be due to the fact that the 3 d metal cobalt is characterized by a significantly smaller covalent radius and weaker transitionmetal-carbon bonds in comparison with the 4 d and 5 d group members rhodium and iridium.The resulting higher structural flexibility of Sc CoC could thus be a prerequisite to allowthe existence of both, a HT and a LT phase structure.The occurrence of a subtle competition between the HT and LT phase in Sc CoC isreflected in the extended phonon softening regime preceding the HT → LT transition atambient-pressure. Also its signatures in the temperature dependencies of ρ ( T ) (Fig. 4a)and I XRD ( T, p ) (Fig. 6a) react sensitively and in a highly related way already to small changesin pressure. Application of a pressure below 0.6 GPa is sufficient to induce a cross-over ofboth physical properties from a course with two anomalies limiting the phonon softening13
IG. 7. Response of the phonon dispersion of HT Sc CoC (DFT study) to (a) hydrostatic pressure,and (b) to a reduction of the lattice parameter a . (cid:0)✁✂✂✄☎✁✆✁✝✄✞✟✁✠✡☛☞✌✍ ✎✏✑✒✎✏✑✓✔✎✏✑✓✎✏✑✏✔✏✏✑✏✔ ✕ ✖✗✘✙✚✏ ✓ ✒ ✛ ✜ ✔ ✢ ✣ ✤ ✥ ✓✏✦✧★✩ ✪ ✫✬✦✭✩✮ ✯✮ ✰✮ ✱✙✲ ✎✏✑✏✒✎✏✑✏✓✏✏✑✏✓✏✑✏✒ ✳ ✖✴✚✏ ✔✏ ✓✏✏ ✓✔✏ ✒✏✏ ✒✔✏ ✛✏✏✵✲ FIG. 8. Changes of the experimental (empty symbols) and theoretical (filled symbols) latticeparameters of Sc CoC (a) with varying pressure at constant temperature and (b) with varyingtemperature at ambient pressure (data from Ref. 8). regime towards low and high temperatures to a course with a single anomaly (see Fig. 4band Fig. 6b to Fig. 6e). Unfortunately, x-ray scattering and absorption by the employedpressure cell did not permit the investigation of the very weak and diffuse x-ray scatteringfeatures in analogy to Ref. 38. Pressure-dependent ab initio phonon dispersion calculationsfor the HT phase structure, however, can provide more insight into the underlying causesfor the modification of ρ ( T ) and I XRD ( T, p ) under pressure. Fig. 7a illustrates the pres-ence of a soft branch between the high-symmetry points W and T of the phonon dispersion14lready at ambient-pressure conditions. The phonon mode along the branch is character-ized by displacements of the cobalt and scandium atoms (Sc1) in the ab plane anticipatingtheir displacements in the LT phase of Sc CoC (see Fig. 3a). On progressing along thepath from T to W the LT-phase-like pattern of atomic displacements at T is modified bymodulations of decreasing wave length along the c axis. Yet, carbon atom contributionsto the mode in analogy to the displacements shown in Fig. 3a are absent. These can befound in a separate medium-frequency phonon mode at Γ with still unclear behavior uponcooling below the HT → LT phase transition temperature. So far, there is only evidence fora profound temperature-dependence of the W–T phonon branch. Approaching the HT → LTtransition temperature from above results in a reduction of the phonon frequency at T tozero. The same W–T phonon branch also displays an extraordinary sensitivity to hydro-static pressure (see Fig. 7a and the Supplemental Material ). Its frequency is subjectedto a strong and steady red shift with increasing pressure, while the frequencies of all otherphonon branches show the expected blue shift. These trends indicate a gradual destabi-lization of the HT phase structure with increasing pressure in line with the experimentallyobserved pressure-induced enhancement of the transition temperature from the HT to theLT phase. Despite the red frequency shift of the W–T phonon branch in our calculations (Fig. 7a)and the preservation of the low-temperature superstructure reflections upon heating to roomtemperature at 5.5 GPa in our diffraction experiments (Fig. 6e), application of pressure alonedoes not suffice to induce a transition of Sc CoC from the HT to the LT phase structure.No superstructure reflections could be observed in single-crystal XRD experiments up tothe destruction of the sample at 10.1 GPa, when the pressure cell was kept constantly atroom temperature (see the Supplemental Material ). An overlay of structural models at0.2 GPa and 4.2 GPa in the Supplemental Material illustrates that the pressure-inducedshifts of the atomic positions remain negligible under these conditions. Likewise, no phasetransition could be inferred from the pressure-dependence of the lattice parameters obtainedfrom room-temperature powder XRD experiments (Fig. 8a). The experimentally observedlinear decrease of the lattice parameters upon application of up to 10.1 GPa with a strongerabsolute compression of c (∆ c = 0.20 ˚A) compared to a and b (∆ a = 0.07 ˚A, ∆ b = 0.06 ˚A)is very well reproduced by DFT studies of the compressibility behavior of the HT phase(Fig. 8a). 15his behavior might be related to the strongly differing development of the lattice pa-rameters of Sc CoC either upon cooling or upon increasing hydrostatic pressure. Previousvariable-temperature neutron diffraction studies between 277 K and 1.8 K showed that areduction of temperature is accompanied by increases of the b and c parameters by approx.0.01 ˚A, and a decrease in the a parameter by approx. 0.02 ˚A (Fig. 8b). An increase ofhydrostatic pressure, by contrast, results in the compression of all lattice parameters. Thus,a strongly anisotropic pressure response of Sc CoC may be suspected in accordance withthe low-dimensional structure of the compound. The validity of this hypothesis is underlinedby the fact that the application of uniaxial stress along the long axis of single-crystallineSc CoC needles leads to pronounced changes in the temperature-dependent electrical resis-tivity (see Fig. 4c). We therefore performed a DFT study probing the response of the phonondispersion to a uniaxial compression along each of the three unit cell axes by varying theHT phase lattice parameters independently (refer to the Supplemental Material for furtherdetails). The strongest frequency reduction along the W–T phonon branch is obtained bya reduction of the a parameter correlating with the distance between adjacent [Co(C ) ] ∞ ribbons (see red and blue curves in Fig. 7b). Negative frequencies along the path indicatethe instability of the HT phase structure after a compression of the a lattice parameter bymore than approx. 0.02 ˚A. A similar dispersion behavior is only achieved by the applicationof hydrostatic pressure in the range of 20 GPa.After pointing out the destabilization of the HT phase under pressure we will now focus onthe pressure-induced structural changes to the LT phase. Although the space group C /m applies to the LT phase structure under ambient-pressure and high-pressure conditions, somedegrees of freedom for the atom arrangement remain. We find for example that the distancebetween adjacent [Co(C ) ] ∞ ribbons is reduced from 3.378(7) ˚A at 0 GPa to 3.34(2) ˚Aat 4 GPa. An even smaller compression from 6.0105(3) ˚A to 5.9849(8) ˚A is found for theinterlayer distance between adjacent quasi-2D Sc1-Co-C layers. Further free parametersin the HT → LT phase transition involve the magnitude of the cobalt and scandium atomshifts, and the extent and relative orientation of the C unit rotations. Fig. 3a and Fig. 3bvisualize the effect on the atom positions, when Sc CoC is cooled to T <
40 K with andwithout an applied pressure of 4 GPa, respectively. In Fig. 3a the atomic positions at11 K and ambient pressure are marked by green non-transparent spheres, while Fig. 3bshows the atomic positions after applying a pressure of 4 GPa and cooling to 37 K (orange16on-transparent spheres).It becomes evident that the general displacement pattern of the cobalt and scandiumatoms in the LT phase remains rather invariant upon pressure application: At both 0 GPaand 4 GPa, the cobalt atoms along the [Co(C ) ] ∞ ribbons are shifted in positive and nega-tive a direction by similar extents of 0.11038(18) ˚A and 0.1125(18) ˚A, respectively. Also theshifts of the Sc1 atoms along the b axis are remarkably similar with values of 0.0574(3) ˚Aat 0 GPa and 0.064(2) ˚A at 4 GPa and 37 K. By contrast, the rotation angles of the C units obtained from the structural refinements display a distinct pressure dependency (high-lighted in Fig. 3a and Fig. 3b): At 0 GPa and 11 K, the C units are subjected to significantrotations out of their HT phase positions with rotation angles between 5.6(2) ◦ and 5.7(2) ◦ .Nearly vanishing rotation angles of 1(1) ◦ are, however, observed at 4 GPa and 37 K (seethe Supplemental Material for further details). This observation might be linked to thepressure-induced detwinning of Sc CoC samples: The two possible twin domains in theambient-pressure LT phase mainly differ by a different rotation sense of the C units inan otherwise nearly unchanged arrangement of cobalt and scandium atoms. A vanishingC rotation angle makes these twin domains nearly identical leaving only marginal differ-ences in the cobalt and scandium atom positions (further information in the SupplementalMaterial ). As a result, the realization of a single-domain state extending over the entiresample volume might be favored. The absence of further anomalies in the electrical resistiv-ity between 37 K and the superconducting transition temperature at 4.5 K (Fig. 4b) impliesthat this detwinned high-pressure low-temperature phase is the one hosting superconduc-tivity in Sc CoC .In a last step we proceed to link the observed temperature- and pressure-dependentchanges in the superstructure reflection intensity I XRD ( T, p ) (see Fig. 6) to changes observedin the atomic positions. To do so we performed x-ray diffraction experiments at 0 GPaand 4 GPa for selected temperatures above and below the step-like increase of I XRD ( T, p )observed at approx. 80 K and 0 GPa. Fig. 9 gives an overview of the observed temperature-dependence of the Co (blue circles) and Sc1 atom displacements (magenta rectangles) andthe C -unit rotations (black triangles) at 0 GPa (a) and 4 GPa (b). Data points from x-raydiffraction experiments with and without usage of a DAC are indicated by filled and opensymbols, respectively.It turns out that the structural models obtained at ambient pressure and above 75 K17 ✁✂✄☎✆✝✞✟✞✠✡☛☞✌ ✍✍✎✍✏✍✎✍✑✍✎✍✒✍✎✍✓✍✎✔✍✎✔✏✍✎✔✑ ✕✖✗✘✗✙✖✚✛✜✢✍✣✔✍✔✣✤✥✦✧ ★ ✤✥✦✧✩✪✦ ✫✬✭✮ ✯✰ ✱✲✳✴✵✎✮ ✶✷✔ ✱✲✳✴✵✎✮ ✯✸ ✹✔✺ ✻✰✼✎✮ ✯✸ ✹✏✺ ✻✰✼✎✽✣ ✾ ✔✑✏ ✾(cid:0)✁✂✄☎✆✝✞✟✞✠✡☛☞✌ ✍✍✎✍✏✍✎✍✑✍✎✍✒✍✎✍✓✍✎✔✍✎✔✏ ✿❀✡✆✡✁❀✠☛❁✌✍✣✔✍✔✣❂ ❃❄❅✍ ✣✍ ✔✍✍ ✔✣✍ ✏✍✍ ✏✣✍ ❆✍✍❇ ❈❉❊❋ ❈❉❊●❍■❍ ✏❆✔ ✾ FIG. 9. Temperature-dependence of the displacements of the Co (blue circles) and Sc1 atoms(magenta squares) and the rotation angles of the two symmetry-inequivalent C -units (C (1) andC (2), black triangles) for (a) 0 GPa and (b) 4 GPa. Note that error bars refer to the threefoldstandard deviation and that the carbon atom displacements corresponding to each C rotationangle (right ordinate) are specified on the left ordinate. Critical temperatures which mark theonset of the formation of superstructure reflections were taken from Fig. 6a and Fig. 6d. In caseof the 0 GPa study also the jump-like increase of the superstructure reflection intensity connectedto the completion of the Peierls-type transition at 75 K was marked by an additional dotted line.Solid lines serve as guides to the eye. represent intermediate steps in the progression of Sc CoC towards its final state below75 K (see Fig. 9a). Consistent with the non-zero value of the superstructure reflectionintensity in the same temperature- and pressure-regime (Fig. 6a) shifts of the atoms fromtheir positions in the HT phase structure are already present at this stage (Fig. 9a). Thereby,larger values of I XRD ( T, p ) correspond to larger shifts of the atomic positions. It should beemphasized, however, that the phonon softening process during the HT → LT transition isnot yet completed for temperatures above 75 K, so that all atom displacements are likely18o be of a correlated, but still dynamical nature. When the atom displacements becomerather static on cooling below 75 K, a step-like increase and a subsequent saturation of thesuperstructure reflection intensity is observed.As already stated above, direction and maximal displacements of the Co and Sc1 atomsare not altered significantly by appyling a pressure of 4 GPa. Yet, the absence of a step in I XRD ( T, p ) and the higher onset temperature of 231 K (0 GPa: 142 K) correlate with theattainment of these maximum displacements at temperatures significantly above 75 K (seeFig. 9b). The main structural difference between 0 and 4 GPa can thus be attributed to thedifferent extent of the out-of-plane rotation of the C units at all investigated temperatures.Hence, the application of pressure effectively prevents the displacement of the carbon atomsfrom their HT phase positions, but does not suppress the formation of a periodic structuraldistortion. IV. CONCLUSION
To conlude, we suggest a connection between the occurence of volume superconductivityand subtle structural modifications to the known Peierls-type distorted low-temperature(LT) phase of Sc CoC under pressure. We demonstrated that the differences betweenthe ambient- and elevated-pressure LT phase structure are limited to a reduction of the C rotations out of the [Co(C ) ] ∞ ribbon plane from 5.6 ◦ - 5.7 ◦ to nearly zero. This bringsthe C moieties back to their high-temperature (HT) phase positions in an otherwise stilldistorted arrangement of cobalt and scandium atoms.On an atomistic level the changed equilibrium position of the C units may affect phononicand electronic properties of the electron-phonon coupling driven superconductor Sc CoC .The importance of carbon atom vibrations for the emergence of superconductivity is high-lighted by C/ C isotope substitution experiments indicating a clearly non-zero isotope co-efficient of 0.58. A key role of C librational modes in the coupling of conduction electronsinto Cooper pairs is also pointed out by DFT studies employing the Eliashberg formalism. Thus, establishing structure-property relationships in favor of pressure-induced volume su-perconductivity presents an interesting, but challenging task for future theoretical studies.But the subtle changes in the C rotation also affect the properties of Sc CoC on amacroscopic level: They render the two possible twin domains in LT-Sc CoC nearly indis-19inguishable and set the stage to the realization of detwinned, single-domain crystals above1.9 GPa. Thus, a continuous superconducting sample volume may only be realized after thedisappearance of twin domain walls from pressurized Sc CoC . Such a barrier function oftwin domain walls for superconducting currents has been investigated recently by Song etal. for FeSe.We finally note that our results point to the simultaneous existence of volume super-conductivity and a Peierls-type distorted phase at elevated pressures. There seems to beno pressure-adjustable competition between periodic structural distortion and superconduc-tivity like in many other structurally low-dimensional materials. Subtle pressure-induced modifications of the atom arrangement in the distorted phase might already sufficeto reconcile both phenomena in Sc CoC . ACKNOWLEDGMENTS
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I. Synthesis of samples 3II. Investigated samples 4III. High-pressure magnetization measurements 6IV. High-pressure electrical resistivity measurements 9V. High-pressure powder x-ray diffraction studies 11VI. Single-crystal x-ray diffraction experiments 16A. Data collection and reduction 16B. Overview of experiments 19C. Ambient-pressure low-temperature measurements without pressure cell 21D. High-pressure low-temperature measurements 24E. Superstructure reflections at room temperature 26F. Test for sample degradation in high-pressure/low-temperature studies 29G. High-pressure measurements at room temperature 32VII. Phonon dispersion relations under uniaxial strain 35VIII. Analysis of experimental data 36A. Calculation of atom displacements 36B. Sensitivity of superstructure reflection intensities to atom displacements 39C. Reliability of the refined atom displacements 41D. Differences between twin domains 49References 502 . SYNTHESIS OF SAMPLES
All Sc CoC single crystals in this work were grown from polycrystalline samples. Thesewere obtained by arc-melting pieces of the constituent elements scandium (Smart Elements,5N), cobalt (Cerametek Materials, 5N5) and carbon (Alfa Aesar, 5N5) in a purified argonatmosphere (500 mbar). Homogeneity was ensured by re-melting the sample several times(see also Refs. 1 and 2).Single-crystalline needles of Sc CoC (see Fig. S2) develop spontaneously at the surfaceof polycrystalline samples after rapid quenching from high temperatures in the arc-meltingfurnace. Thereby, a large temperature gradient from sample top to bottom is achieved usinga water-cooled copper crucible (see also Refs. 3 and 4).Larger plate-like single crystals (see Fig. S1, Fig. S3 and Fig. S4) were grown by crystal-lization from a lithium flux. For this purpose, powder from a ground polycrystalline sampleof Sc CoC and small lithium pieces (Alfa Aesar, 3N) were filled into a tantalum ampoulein a stoichiometric ratio of 1:20. The tantalum ampoule was closed by welding under argonatmosphere (500 mbar), sealed into an evacuated quartz ampoule and placed in a mufflefurnace. After heating to 600 ◦ C with a heating rate of 20 ◦ C/h the temperature was heldconstant for 24 hours and then reduced to 500 ◦ C with a cooling rate of 100 ◦ C/h. Theheat treatment was terminated after two to four weeks by quenching the samples in a waterbath. Single crystals were obtained by opening and turning the tantalum ampoule underinert conditions. Remaining flux medium was dissolved in ethanol (see also Ref. 4).3
I. INVESTIGATED SAMPLES a b c FIG. S1. Photographic image of the single-crystalline Sc CoC sample used in the high-pressuremagnetization measurements. Crystal axes a , b and c referring to the orthorhombic high-tempera-ture phase unit cell are indicated by colored lines. (cid:4)(cid:5)(cid:6) (cid:7)(cid:8) a c b FIG. S2. Photographic image of the Sc CoC single crystal used in the ambient-pressure low-temperature x-ray diffraction experiments without pressure cell. Crystal axes a , b and c referringto the orthorhombic high-temperature phase unit cell are indicated by colored lines. IG. S3. Photographic images of the Sc CoC single crystals used in the high-pressure low-temperature x-ray diffraction experiments for (a) tracking of superstructure reflection intensities,(b) structure determinations, and (c) tests for sample degradation under the high-pressure/low-temperature conditions. Crystal axes a , b and c referring to the orthorhombic high-temperaturephase unit cell are indicated by colored lines. (cid:9)(cid:10)(cid:11) (cid:12)(cid:13) (cid:181)(cid:14) FIG. S4. Photographic images of the Sc CoC single crystals used in the high-pressure x-raydiffraction experiments at room temperature for (a) structure determination, and (b) reciprocalspace mapping. Crystal axes a , b and c referring to the orthorhombic high-temperature phase unitcell are indicated by colored lines. II. HIGH-PRESSURE MAGNETIZATION MEASUREMENTS
For performing high-pressure magnetization measurements a miniature Ceramic AnvilCell (mCAC) was used. The ceramic anvils had a culet diameter of 1.8 mm and theprefabricated Cu:Be gasket had a pressure chamber diameter of 900 µ m and a thickness of900 µ m. Placing a piece of lead inside the pressure chamber allowed to infer the internalpressure from its superconducting transition temperature T c . As pressure transmittingmedium served Daphne 7373 with a quasi-hydrostatic limit of 2.2 GPa - 2.3 GPa.
Aftera background measurement of the closed mCAC with a piece of lead (dimensions: 105 µ m × µ m × µ m) and Daphne 7373 inside its pressure chamber (orange triangles in Fig. S5and Fig. S6) the actual sample measurement with an additional Sc CoC single crystal (di-mensions: 225 µ m × µ m × µ m; mass: 69.2 µ g; photographic image in Fig. S1)at pressures of 0.11 GPa, 1.18 GPa, 1.45 GPa, 1.48 GPa and 0.19 GPa (pressure releasemeasurement) took place (see Fig. S5 and Fig. S6 for an overview of the raw data collectedupon increasing and decreasing the applied pressure, respectively). Reciprocal space planesreconstructed from x-ray diffraction data collected before and after the high-pressure studycan be found in Fig. S7. As comparative measurements serve magnetization measurements,where the same Sc CoC single crystal was fixed on a glass rod with GE Varnish before(cyan diamonds in Fig. S5) and after the high-pressure study (violet triangles in Fig. S6).All magnetization measurements were performed under zero-field-cooling conditions em-ploying a MPMS3 superconducting quantum interference device (SQUID) magnetometer(QUANTUM DESIGN). The measured temperature range was between 1.8 K and 9 K witha heating rate of 0.2 K/min at 5 Oe. For analyzing the data, the background measurementwas in each case subtracted. 6 M [ - e m u ] T [K] Increasing pressure M [ - e m u ] T [K] FIG. S5. Unprocessed magnetization data M ( T ) collected with increasing pressure. Data pointsof a reference measurement with only a lead piece and pressure-transmitting medium inside thepressure chamber are plotted with orange triangles. M [ - e m u ] T [K] Decreasing pressure M [ - e m u ] T [K] FIG. S6. Unprocessed magnetization data M ( T ) collected with decreasing pressure. Data pointsof a reference measurement with only a lead piece and pressure-transmitting medium inside thepressure chamber are plotted with orange triangles. ) b) c(cid:15) d(cid:16)b(cid:17)(cid:18)(cid:19)(cid:20)e (cid:21)(cid:22) (cid:23)(cid:24)(cid:25)(cid:26)(cid:27)a(cid:28)t(cid:29)(cid:30) (cid:31) !" ( hk
0) ( h l )( hk
0) ( h l ) FIG. S7. Reconstructions of reciprocal-space planes ( hk
0) and ( h l ) from room-temperature x-ray diffraction data collected for a Sc CoC single crystal before (a, b) and after performing ahigh-pressure magnetization study on it (c, d). V. HIGH-PRESSURE ELECTRICAL RESISTIVITY MEASUREMENTS
For high-pressure electrical resistivity measurements a nonmagnetic piston-cylinder-typepressure cell was used. By using silver conductive paint a crystalline Sc CoC whisker(dimensions: 15 µ m × µ m × µ m) was four-point contacted via gold filaments whichwere attached to copper wires. Beforehand and in order to stabilize this setup, the whiskerwas at one side slightly fixed to a mica plate employing GE-7031 varnish. On the backsideof this mica plate a lead platelet was attached, which itself was connected via the four-pointmethod and served as pressure manometer. A silicon oil was utilized as pressure-transmittingmedium inside the Teflon cap of the high-pressure cell. For determining the resistivity aLINEAR RESEARCH LR700 resistance bridge was used. In order to cool the high-pressurecell setup from 300 K to 1.8 K the cryostat function of a physical property measurementsystem (PPMS; QUANTUM DESIGN) was employed. Monitoring the temperature of thehigh-pressure cell was possible by a thermometer (LAKE SHORE) fixed inside the shell of thepressure cell. For each pressure point the resistivity was measured during the cooling processto 1.8 K. After that the pressure was determined by fine-sliced resistivity measurements ina temperature range of 0.3 K around the superconducting transition temperature of Pb. Lastly followed the resistivity measurement while heating the setup from 1.8 K to 300 K. The unprocessed resistivity data for pressures of 0.03 GPa and 0.82 GPa is given in Fig. S8.9
50 100 150 200 250 3000102030405060708090 p [GPa] (cid:1) [ mW(cid:215) c m ] T [K] FIG. S8. Unprocessed electrical resistivity data ρ ( T ) for the measurements under hydrostaticpressures of 0.03 GPa (blue) and 0.82 GPa (dark yellow). For comparison, ρ ( T ) is also given formeasurements under ambient pressure (orange) and uniaxial stress (magenta) that were performedon different samples. . HIGH-PRESSURE POWDER X-RAY DIFFRACTION STUDIES High-pressure powder x-ray diffraction experiments were performed at the X04SA Ma-terials Science (MS) beamline at Swiss Light Source (SLS) employing a primary beamenergy of 25 keV and a PSI Mythen II one-dimensional detector. A radiation wave lengthof 0.49573 ˚A was determined from the LaB cell parameters refined for an initial calibrationmeasurement on a NIST SRM 660a powder standard.Pressures up to 10.29(4) GPa were generated by a diamond anvil cell (DAC) equippedwith 0.5 mm wide culets and stainless steel gaskets providing a pressure chamber with 200 µ mdiameter and 45 µ m - 60 µ m thickness. The pressure cell was loaded with finely groundand sieved Sc CoC powder (nominal sieve opening 32 µ m) and a 4:1 MeOH:EtOH volumemixture serving as a pressure-transmitting medium. Powdered α -quartz was added as aninternal pressure gauge exploiting the well-established compression behavior of its latticeparameters. With the exception of the DAC filling process all sample preparation stepswere performed under an inert argon atmosphere to prevent a potential sample degradation.During data collection the pressure cell was oscillated continuously by ± ◦ around the ω axis, i.e. perpendicular to the primary beam, to bring a large number of differentlyoriented crystallites into diffracting position. Remote operation of the DAC by a helium-gas-driven membrane system allowed to change the pressure while maintaining a consistentsample orientation.Exemplary powder x-ray diffraction patterns obtained at pressures of 0 GPa, 9.15(4) GPa,and 10.29(4) GPa (see Fig. S9, Fig. S10, and Fig. S11) illustrate the absence of additionalreflections within the investigated pressure range between 0 GPa and 10.29(4) GPa. Onlya simultaneous broadening of the reflection profiles for Sc CoC and α -quartz is observedfor pressures above 9.15(4) GPa (Fig. S11) pointing to an incipient non-hydrostaticity ofthe employed pressure medium (quasi-hydrostatic limit ≈
10 GPa ). Thus, all observedreflections can be attributed to Sc CoC in its high-temperature phase (space group Immm ),the pressure calibrant α -quartz or parasitic scattering from the surroundings of the pressurechamber, i.e. from the DAC body including the gasket and the diamonds. In Le Bail fits of the diffraction data with the program JANA2006 the latter reflections were added to thebackground description (specified by 100 points), whereas Sc CoC and α -quartz reflectionsin the 2 θ range between 3 ◦ and 30 ◦ were modelled by purely Lorentzian profiles (fit lines11nd difference plots at selected pressure can be found in Fig. S9 to Fig. S11, an overview ofprofile Rp factors and lattice parameters is available in Tab. I). Standard deviations of therefined lattice parameters are specified with applied Berar’s correction as implemented inJANA2006. (cid:1) -Fe (cid:1) -Fe(110) (111) (220) ¤ (211)(200) (cid:1) -Fe ** experiment Le Bail fit * gasket ( (cid:1) -Fe) ¤ diamond HT-Sc CoC (cid:1) -quartz difference i n t en s i t y [ a r b . u .] p = 0.0 GPa * ¤ a) (cid:1) [°] (cid:1) - quartz(100) Sc CoC (011) b) FIG. S9. (a) Room-temperature powder x-ray diffraction pattern (black crosses), Le Bail fit (orangeline) and according difference plot (red line) for a Sc CoC sample at a pressure of 0.0 GPa( λ = 0.49573 ˚A). Expected reflection positions for Sc CoC in its high-temperature phase and α -quartz are indicated by green and blue bars, respectively. Asterisks and diamonds mark thepositions of parasitic reflections from the gasket and the pressure-cell diamonds, while regionsexcluded from the Le Bail fit are shaded in gray. (b) Enlarged view of the (011) reflection forSc CoC and the (100) reflection for α -quartz. (cid:1) -Fe (110) (111) (211) (cid:1) -Fe * experiment Le Bail fit * gasket ( (cid:1) -Fe) ¤ diamond HT-Sc CoC (cid:1) -quartz difference i n t en s i t y [ a r b . u .] p = 9.15(4) GPa * ¤ a) (cid:1) [°] (cid:1) - quartz(100)Sc CoC (011) b) FIG. S10. (a) Room-temperature powder x-ray diffraction pattern (black crosses), Le Bail fit (or-ange line) and according difference plot (red line) for a Sc CoC sample at a pressure of 9.15(4) GPa( λ = 0.49573 ˚A). Expected reflection positions for Sc CoC in its high-temperature phase and α -quartz are indicated by green and blue bars, respectively. Asterisks and diamonds mark the posi-tions of parasitic reflections from the gasket and the pressure-cell diamonds, while regions excludedfrom the Le Bail fit are shaded in gray. (b) Enlarged view of the (011) reflection for Sc CoC andthe (100) reflection for α -quartz. (110) (111) (cid:1) -Fe experiment Le Bail fit * gasket ( (cid:1) -Fe) ¤ diamond HT-Sc CoC (cid:1) -quartz difference i n t en s i t y [ a r b . u .] p = 10.29(4) GPa * ¤ a) (cid:1) [°] (cid:1) - quartz(100)Sc CoC (011) b) FIG. S11. (a) Room-temperature powder x-ray diffraction pattern (black crosses), Le Bail fit(orange line) and according difference plot (red line) for a Sc CoC sample at a pressure of10.29(4) GPa ( λ = 0.49573 ˚A). Expected reflection positions for Sc CoC in its high-temperaturephase and α -quartz are indicated by green and blue bars, respectively. Asterisks and diamondsmark the positions of parasitic reflections from the gasket and the pressure-cell diamonds, whileregions excluded from the Le Bail fit are shaded in gray. (b) Enlarged view of the (011) reflectionfor Sc CoC and the (100) reflection for α -quartz. [GPa] GoF Rp wRp a [˚A] b [˚A] c [˚A] V [˚A ] Rp factors and refined lattice parameters forthe Le Bail fits of all high-pressure powder x-ray diffraction patterns. I. SINGLE-CRYSTAL X-RAY DIFFRACTION EXPERIMENTSA. Data collection and reduction
All single-crystal x-ray diffraction studies were performed using a four-circle Eulerian cra-dle goniometer (HUBER) and a sample-to-detector distance of 7 cm. Reflection intensitieswere collected by a Pilatus 300K pixel detector with a CdTe detection layer (DECTRIS).A micro-focus AgK α tube ( λ = 0.56087 ˚A) with a montel multilayer optic (INCOATEC)served as x-ray source.Sample cooling to a minimum temperature of 11 K was done with a closed-cycle heliumcryocooler (ARS). Two alternative types of heat and radiation shields (outer and optionalinner shield) were used: Stainless steel shields equipped with Kapton windows that add onlya weak and continuous background to the collected x-ray diffraction images but stronglyrestrict the accessible portion of reciprocal space, and beryllium shields (domes) that allowthe measurement of a larger number of reflection intensities but create stronger parasiticscattering in the form of speckled rings (see Fig. S12b). The type of heat and radiationshields employed in each experiment is specified in Tab. II and Tab. III.High pressure was generated by commercially available diamond anvil cells (DACs; seeTab. II and Tab. III) of Diacell Tozer-type (ALMAX EASYLAB) and of Boehler-plate-type (ALMAX EASYLAB) equipped with conical Boehler-Almax anvils (culet diameter600 µ m). Due to its smaller size the first DAC type was mounted inside the sample cham-ber of the closed-cycle cryostat, whereas the latter DAC type was only operated at room tem-perature (employed pressure-transmitting media are listed in Tab. II and Tab. III). Specifiedpressure values were always determined ahead of the x-ray diffraction experiment at roomtemperature using the fluorescence signal of ruby spheres inside the pressure chamber.
In case of ambient-pressure low-temperature studies without pressure cell parasitic scat-tering from the beryllium heat and radiation shields was determined and subtracted ex-plicitly (procedure illustrated in Fig. S12). For this purpose, the investigated sample wastranslated reproducibly out of and into the x-ray beam using a linear nanopositioner (AT-TOCUBE). In case of high-pressure studies masks were applied to regions of the diffractionimages shadowed by the DAC body or dominated by strong Bragg reflections from the DACdiamonds (Fig. S13). Additionally the two strongest innermost Debye rings of beryllium16ere masked (compare Fig. S13a and Fig. S13b) in case of high-pressure low-temperaturemeasurements.Reflection intensities were evaluated employing the EVAL14 suite of programs andsubjected to scaling and absorption correction employing SADABS/TWINABS. Structuralmodels were refined with the program JANA2006 using the HKLF4 reflection format foruntwinned and the HKLF5 reflection format for systematically twinned samples below theHT → LT phase transition. f@ABCDoEFG background resulta) c)b)
FIG. S12. Background subtraction procedure for ambient-pressure low-temperature measurementswithout pressure cell: For each x-ray diffraction image (a) an individual background (b) is deter-mined by translating the sample out of the beam. Subtraction of the background leads to theresult displayed in (c). Insets show 3D profiles of the regions marked by red rectangles. Note thatthe inset in (b) is plotted with an eight times enlarged z scale. I C shadowdiamond reflectionberylliumscattering unmasked masked a) b)
FIG. S13. X-ray diffraction image from a high-pressure low-temperature experiment (a) before and(b) after application of masks to cover regions shadowed by the DAC body, diamond reflectionsand prominent Debye rings from the beryllium heat and radiation shield. . Overview of experiments1 2 3 sample dim. [ µ m ] 40 × ×
290 55 × ×
141 68 × × a – Tozer DAC Tozer DACculet diam. [ µ m] – 600 600press. chamber – 285 270diam. [ µ m]press. chamber – 90 88height. [ µ m]press. determ. b – – / ruby fluoresc. – / ruby fluoresc.press. transm. – – / Daphne 7575 – / Daphne 7575mediumhydrostat. lim. [GPa] – – / 3.9 - 4 [34] – / 3.9 - 4 [34]at T = RTtemperature [K] 11, 70, 100 22 - 300 36, 106 / 37, 107sample cryostat closed cycle He closed cycle He closed cycle Hevacuum chamber beryllium domes steel cubes beryllium domeparasitic scatt./ subtracted – maskedshadows a sample / ruby spheres were wetted with perfluorinated polyether and placed in the pressure chamber. b performed at T = 294 K. TABLE II. Overview of single-crystal x-ray diffraction experiments. sample dim. [ µ m ] 48 × ×
152 73 × ×
186 70 × × a – / Tozer DAC Boehler DAC Boehler DACculet diam. [ µ m] – / 600 600 600press. chamber – / 270 240 255diam. [ µ m]press. chamber – / 85 94 92height. [ µ m]press. determ. b – / ruby fluoresc. ruby fluoresc. ruby fluoresc.press. transm. – / Daphne 7575 4:1 MeOH:EtOH 4:1 MeOH:EtOHmediumhydrostat. lim. [GPa] – / 3.9 - 4 [34] ≈
10 [20] ≈
10 [20]at T = RTtemperature [K] 13, RT / 27, RT RT RTsample cryostat closed cycle He – –vacuum chamber steel cubes – –parasitic scatt./ – masked maskedshadows a sample / ruby spheres were wetted with perfluorinated polyether and placed in the pressure chamber. b performed at T = 294 K. TABLE III. Overview of single-crystal x-ray diffraction experiments (continued). . Ambient-pressure low-temperature measurements without pressure cell T [K] 11 70 100unit cell dimensions a = 5.53630(10) ˚A a = 5.53600(10) ˚A a = 5.53720(10) ˚A b = 12.0210(2) ˚A b = 12.0167(2) ˚A b = 12.00370(10) ˚A c = 5.53640(10) ˚A c = 5.53590(10) ˚A c = 5.53710(10) ˚A β = 104.8070(10) ◦ β = 104.7720(10) ◦ β = 104.4620(10) ◦ V = 356.222(11) ˚A V = 356.101(11) ˚A V = 356.372(10) ˚A calculated density 4.5095 g · cm − · cm − · cm − crystal size 40 × × µ m wave length 0.56087 ˚Atransm. ratio (max/min) 0.747 / 0.686 0.747 / 0.633 0.747 / 0.646absorption coefficient 5.016 mm − − − F (000) 456 θ range 3 ◦ to 36 ◦ ◦ to 37 ◦ ◦ to 37 ◦ range in hkl ± ± ± R int = 0.0123) 2112 ( R int = 0.0158) 2153 ( R int = 0.0148)reflections with I ≥ σ ( I ) 2007 1986 1947data / parameters 2142 / 43 2112 / 43 2153 / 43goodness-of-fit on F R indices [ I ≥ σ ( I )] R = 0.0220 R = 0.0381 R = 0.0302 wR = 0.0414 wR = 0.0665 wR = 0.0535 R indices (all data) R = 0.0271 R = 0.0446 R = 0.0389 wR = 0.0424 wR = 0.0673 wR = 0.0549extinction coefficient 0.0461(14) 0.043(2) 0.0231(15)largest diff. peak and hole 1.97 / -2.18 e · ˚A − · ˚A − · ˚A − TABLE IV. Crystal data and structure refinements for ambient-pressure single-crystal x-ray diffrac-tion experiments without pressure cell and at temperatures of 11 K, 70 K and 100 K. fractional atomic coordinates U eq atom [K] x y z [˚A ]Co 11 0.26595(2) 0 0.26673(2) 0.00204(3)70 0.26559(3) 0 0.26635(3) 0.00240(5)100 0.25987(2) 0 0.26046(2) 0.00243(5)Sc1 11 0.75582(3) 0 0.24273(3) 0.00207(6)70 0.75570(4) 0 0.24290(4) 0.00241(9)100 0.75383(3) 0 0.24498(3) 0.00239(10)Sc2 11 0 0.187417(10) 0 0.00210(9)70 0 0.187442(16) 0 0.00244(11)100 0 0.187747(13) 0 0.00233(10)Sc3 11 0 0.311540(10) 0.5 0.00210(9)70 0 0.311550(16) 0.5 0.00244(11)100 0 0.311642(13) 0.5 0.00235(10)C1 11 0.4110(3) 0.12557(5) 0.0766(2) 0.0031(2)70 0.4103(4) 0.12568(7) 0.0763(4) 0.0035(3)100 0.4109(3) 0.12514(5) 0.0773(3) 0.0033(3)C2 11 0.0889(3) 0.12487(5) 0.4233(2) 0.0030(2)70 0.0896(4) 0.12490(7) 0.4238(4) 0.0034(3)100 0.0890(3) 0.12471(5) 0.4228(3) 0.0033(3)TABLE V. Refined fractional atomic coordinates and mean-square atomic displacement parametersobtained from ambient-pressure single-crystal x-ray diffraction experiments without pressure celland at temperatures of 11 K, 70 K and 100 K. mean-square atomic displacement parameters [˚A ]atom [K] U U U U U U Co 11 0.00229(6) 0.00176(4) 0.00219(6) ∗ ∗
70 0.00239(9) 0.00275(7) 0.00238(9) ∗ ∗
100 0.00295(10) 0.00192(5) 0.00276(10) ∗ ∗ Sc1 11 0.00223(12) 0.00202(5) 0.00195(12) ∗ ∗
70 0.00228(17) 0.00291(9) 0.00216(16) ∗ ∗
100 0.00280(19) 0.00224(6) 0.00220(19) ∗ ∗ Sc2 11 0.00295(18) 0.00198(5) 0.00144(17) ∗ ∗
70 0.0036(2) 0.00283(9) 0.00114(19) ∗ ∗
100 0.0034(2) 0.00221(7) 0.00152(19) ∗ ∗ Sc3 11 0.00295(18) 0.00196(5) 0.00147(17) ∗ ∗
70 0.0035(2) 0.00281(9) 0.00119(19) ∗ ∗
100 0.0035(2) 0.00218(7) 0.00153(19) ∗ ∗ C1 11 0.0017(4) 0.00353(17) 0.0037(4) 0.0005(3) 0.00026(16) 0.0002(3)70 0.0015(5) 0.0049(3) 0.0041(6) 0.0002(6) 0.0010(3) 0.0001(6)100 0.0027(5) 0.0035(2) 0.0035(5) 0.0002(4) 0.0008(2) -0.0001(4)C2 11 0.0019(4) 0.00337(17) 0.0037(4) -0.0002(3) 0.00039(16) 0.0000(3)70 0.0015(5) 0.0050(3) 0.0038(6) -0.0001(6) 0.0005(3) 0.0002(6)100 0.0025(5) 0.0036(2) 0.0036(5) 0.0000(4) 0.0004(2) 0.0003(4)TABLE VI. Refined mean-square atomic displacement parameters obtained from ambient-pressuresingle-crystal x-ray diffraction experiments without pressure cell and at temperatures of 11 K, 70 Kand 100 K. Parameters marked by an asterisk are forbidden by symmetry. . High-pressure low-temperature measurements T [K] 37 107unit cell dimensions a = 5.5046(3) ˚A a = 5.5082(2) ˚A b = 11.9698(5) ˚A b = 11.9729(6) ˚A c = 5.4723(7) ˚A c = 5.4832(8) ˚A β = 105.038(3) ◦ β = 104.949(4) ◦ V = 348.22(5) ˚A V = 349.37(6) ˚A calculated density 4.6131 g · cm − · cm − crystal size 68 × × µ m wave length 0.56087 ˚Atransm. ratio (max/min) 0.746 / 0.687 0.746 / 0.670absorption coefficient 5.131 mm − − F (000) 456 θ range 3 ◦ to 33 ◦ range in hkl -6/9, -13/19, -5/4 -6/9, -13/20, -5/4total no. reflections 716 713independent reflections 212 ( R int = 0.0048) 209 ( R int = 0.0077)reflections with I ≥ σ ( I ) 190 178data / parameters 190 / 18 178 / 18goodness-of-fit on F R indices [ I ≥ σ ( I )] R = 0.0425 R = 0.0436 wR = 0.1002 wR = 0.1053 R indices (all data) R = 0.0425 R = 0.0436 wR = 0.1002 wR = 0.1053extinction coefficient – –largest diff. peak and hole 0.69 / -0.76 e · ˚A − · ˚A − TABLE VII. Crystal data and structure refinements for single-crystal x-ray diffraction experimentsat a pressure of 4 GPa and temperatures of 37 K and 107 K. fractional atomic coordinates U eq atom [K] x y z [˚A ]Co 37 0.26648(19) 0 0.2672(3) 0.0027(3)107 0.2663(2) 0 0.2666(3) 0.0035(4)Sc1 37 0.7565(2) 0 0.2417(3) 0.0025(4)107 0.7564(3) 0 0.2418(4) 0.0033(4)Sc2 37 0 0.18764(9) 0 0.0025(4)107 0 0.18771(10) 0 0.0032(4)Sc3 37 0 0.31118(9) 0.5 0.0028(4)107 0 0.31122(10) 0.5 0.0037(4)C1 37 0.4147(12) 0.1261(3) 0.0837(17) 0.0042(8)107 0.4137(14) 0.1262(4) 0.0840(19) 0.0057(9)C2 37 0.0854(13) 0.1250(3) 0.4160(17) 0.0042(8)107 0.0867(14) 0.1248(4) 0.4169(19) 0.0057(9)TABLE VIII. Refined fractional atomic coordinates and mean-square atomic displacement pa-rameters obtained from single-crystal x-ray diffraction experiments at a pressure of 4 GPa andtemperatures of 37 K and 107 K. . Superstructure reflections at room temperature Superstructure reflections indicative of the low-temperature phase of Sc CoC could bepreserved up to room temperature at a pressure of 5.5 GPa, i.e. above the hydrostatic limit ofthe employed pressure medium Daphne 7575 (experiment 2 in Tab. II; see reconstruction ofthe ( h . l ) reciprocal-space plane in Fig. S14b). But this was only possible after cooling thesample to 22 K and heating it back to room temperature and at the cost of a deteriorationof the sample crystallinity (see broadened reflections in the reconstructed ( h l ) plane inFig. S14a).We did not succeed in inducing the phase transition between high-temperature and low-temperature phase by pressure application at room temperature alone (experiment 6 inTab. III). As can be recognized from the reconstructed ( h . l ) planes in Fig. S15 and thex-ray diffraction images in Fig. S16, no superstructure reflections could be observed in aroom-temperature high-pressure experiment up to a maximum pressure of 10.1 GPa. a) b)( h l ) ( h l ) FIG. S14. Reconstructions of reciprocal-space planes (a) ( h l ) and (b) ( h . l ) from room-temperature x-ray diffraction data collected after applying a pressure of 5.5 GPa, cooling to 22 Kand heating to room temperature again. ) b) c) d) h l ) ( h l )( h l ) ( h l ) FIG. S15. Reconstructions of reciprocal-space planes ( h l ) and ( h . l ) from x-ray diffraction datacollected at room-temperature and at pressures of 0.1 GPa (a, b) and 6.7 GPa (c, d). Parasiticscattering from gasket and diamonds leads to ring-shaped features and broad intense reflections,respectively. ) 0.1 GPa b) 5.4 GPa c) d) e) FIG. S16. Selected x-ray diffraction images collected at room temperature and up to a maximumpressure of 10.1 GPa with nearly unchanged orientation of the pressure cell. Main reflectionsexpected for the high-temperature phase of Sc CoC are indicated by white circles. The positionsof superstructure reflections indicative of a transition into the low-temperature phase are markedby yellow (twin domain 1) and cyan circles (twin domain 2). . Test for sample degradation in high-pressure/low-temperature studies To exclude irreversible changes or a degradation of the sample quality in our combinedhigh-pressure/low-temperature studies we reenacted a typical experimental procedure andcollected x-ray diffraction data after each step (experiment 4 in Tab. III). Reconstructionsof reciprocal-space planes ( h l ) and ( h . l ) obtained for a Sc CoC single crystal at ambientconditions (see Fig. S17a and Fig. S17b) and at 13 K (Fig. S17c and Fig. S17d) demonstratethe quality of the investigated sample. Notably, a column of superstructure reflections alongthe c ∗ axis with equal contributions from two distinct twin domains can be recognized inFig. S17d.Inserting the single crystal into the pressure chamber of a Tozer-type diamond anvilcell (DAC) and applying a pressure of 4.5 GPa leaves the sample crystallinity unchanged(Fig. S17e and Fig. S17f; ring-shaped features and additional reflections are due to parasiticx-ray scattering from the gasket and the DAC diamonds, respectively). This does notchange by cooling the pressure cell to 27 K (Fig. S18a and Fig. S18b). As pointed out inthe main paper, every second reflection in the columns of superstructure reflections along c ∗ in Fig. S18b is now absent due to a pressure-induced detwinning process.Still, all pressure-induced changes to the sample are fully reversible. This is pointed outby sharp profiles of the Bragg reflections in the ( h l ) plane (Fig. S18c) and the absence ofscattered intensity in the ( h . l ) plane (Fig. S18d) after heating to room temperature andremoving the single crystal from the pressure chamber of the DAC. Furthermore, the effectof cooling to 13 K again without applied pressure is consistent with the measurements beforethe high-pressure study (compare Fig. S18e and Fig. S18f with Fig. S17c and Fig. S17d).Namely, reflections in the ( h l ) plane are preserved and complete columns of superstructurereflections along c ∗ featuring contributions from two twin domains appear.29 ) b) c) d)e) JK LM N
T, before HP 0 GPa, RT, before HP( h l ) ( h l )0 GPa, 13 K, before HP 0 GPa, 13 K, before HP( h l ) ( h l )( h l ) ( h l )4.5 GPa, RT 4.5 GPa, RT FIG. S17. Reconstructions of reciprocal-space planes ( h l ) and ( h . l ) from x-ray diffractiondata collected under various conditions, i.e. at room-temperature (a, b) and 13 K (c, d) beforeperforming a high-pressure (HP) experiment, and again at room-temperature but with an appliedpressure of 4.5 GPa (e, f). ) b) c) d)e) f)4.5 GP a, 27 K 4.5 GPa, 27 K( h l ) ( h l )0 GPa, RT, af ter
HP 0 GPa, RT, af ter
HP( h l ) ( h l )( h l ) ( h l )0 GPa, 13 K, af OPQ RS a, 13 K, af ter HP
FIG. S18. Reconstructions of reciprocal-space planes ( h l ) and ( h . l ) from x-ray diffraction datacollected under various conditions, i.e. at 27 K with an applied pressure of 4.5 GPa (a, b), at roomtemperature after removing the crystal from the high-pressure (HP) cell (c, d) and after cooling to13 K again (e, f). . High-pressure measurements at room temperature As pointed out in Sec. VI E, we did not succeed in forcing the transition between thehigh-temperature and low-temperature phase of Sc CoC in high-pressure experiments atroom temperature. Still, the HT phase structure provides some flexibility to react to ap-plied pressure, e.g. the position of the carbon atoms. Therefore, we investigated the ef-fect of pressure on the HT phase structure by performing x-ray diffraction experiments at0.2 GPa and 4.2 GPa (experiment 5 in Tab. III, crystal and refinement details are avail-able in Tab. IX, fractional coordinates and mean-square atomic displacement parameters inTab. X and Tab. XI). TUVWX YZ a b FIG. S19. Overlay of the refined atomic positions within a layered building unit of Sc CoC atroom temperature and applied pressures of 0.2 GPa (gray, semi-transparent) and 4.2 GPa (blue,non-transparent). All atom displacements are exaggerated seven-fold, Sc2 and Sc3 atoms havebeen omitted for clarity. The given coordinate system refers to the orthorhombic unit cell of thehigh-temperature phase. Upon pressure application the distance between adjacent [Co(C ) ] ∞ ribbons along the a axis is reduced from 3.3998(9) ˚A to 3.3701(9) ˚A (all values are given with their threefoldstandard deviation). Analogously, a compression from 6.0061(8) ˚A to 5.9670(5) ˚A is found forthe distance between adjacent quasi-2D Sc1-Co-C layers. Inspection of the overlaid atomicpositions at 0.2 GPa and 4.2 GPa in Fig. S19 reveals no major pressure-induced changes.32nly the C–C bond distance expands insignificantly from 1.452(9) ˚A to 1.455(9) ˚A, whilethe Co–C bond distance is compressed from 2.094(4) ˚A to 2.078(3) ˚A. p [GPa] 0.2 4.2unit cell dimensions a = 3.3998(3) ˚A a = 3.3701(3) ˚A b = 4.3738(2) ˚A b = 4.35220(10) ˚A c = 12.0121(5) ˚A c = 11.9340(3) ˚A V = 178.620(19) ˚A V = 175.040(17) ˚A calculated density 4.4966 g · cm − · cm − crystal size 73 × × µ m wave length 0.56087 ˚Atransm. ratio (max/min) 0.747 / 0.677 0.747 / 0.659absorption coefficient 5.001 mm − − F (000) 228 θ range 3 ◦ to 35 ◦ range in hkl -2/2, -8/5, -14/24total no. reflections 880 871independent reflections 178 ( R int = 0.0086) 172 ( R int = 0.0087)reflections with I ≥ σ ( I ) 169 165data / parameters 178 / 14 172 / 14goodness-of-fit on F R indices [ I ≥ σ ( I )] R = 0.0172 R = 0.0159 wR = 0.0473 wR = 0.0475 R indices (all data) R = 0.0180 R = 0.0165 wR = 0.0474 wR = 0.0476extinction coefficient –largest diff. peak and hole 0.55 / -0.60 e · ˚A − · ˚A − TABLE IX. Crystal data and structure refinements for single-crystal x-ray diffraction experimentsat room temperature and at pressures of 0.2 GPa and 4.2 GPa. fractional atomic coordinates U iso / U eq atom [GPa] x y z [˚A ]Co 0.2 0 0.5 0 0.0039(3)4.2 0 0.5 0 0.0035(3)Sc1 0.2 0.5 0 0 0.0035(4)4.2 0.5 0 0 0.0038(4)Sc2 0.2 0.5 0.5 0.18808(3) 0.0034(3)4.2 0.5 0.5 0.18827(2) 0.0032(4)C1 0.2 0.5 0.6660(3) 0.37515(10) 0.0047(2)4.2 0.5 0.6671(3) 0.37516(9) 0.0039(2)TABLE X. Refined fractional atomic coordinates and mean-square atomic displacement parametersobtained from single-crystal x-ray diffraction experiments at room temperature and at pressuresof 0.2 GPa and 4.2 GPa. Note that the carbon atom was refined isotropically. p mean-square atomic displacement parameters [˚A ]atom [GPa] U U U U U U Co 0.2 0.0051(10) 0.00355(18) 0.00301(13) ∗ ∗ ∗ ∗ ∗ ∗
Sc1 0.2 0.0029(12) 0.0040(2) 0.00372(16) ∗ ∗ ∗ ∗ ∗ ∗
Sc2 0.2 0.0031(10) 0.00355(18) 0.00348(12) ∗ ∗ ∗ ∗ ∗ ∗
TABLE XI. Refined mean-square atomic displacement parameters obtained from single-crystalx-ray diffraction experiments at room temperature and at pressures of 0.2 GPa and 4.2 GPa.Parameters marked by an asterisk are forbidden by symmetry. The carbon atom was refinedisotropically. II. PHONON DISPERSION RELATIONS UNDER UNIAXIAL STRAIN
FIG. S20. Response of the phonon dispersion of HT Sc CoC (DFT study) to a compression orelongation of the lattice parameters a (a, b), b (c, d) and c (e, f). III. ANALYSIS OF EXPERIMENTAL DATAA. Calculation of atom displacements
Displacements ∆ r Co of the cobalt atoms from their positions in the high-temperaturephase of Sc CoC were calculated from the difference between the longer Co–Co distance d and the shorter Co–Co distance d (see Fig. S21a):∆ r Co = 14 ( d − d ) . (1)An analogous procedure was applied for the calculation of the scandium atom (Sc1)displacements ∆ r Sc1 (see Fig. S21b):∆ r Sc1 = 14 ( d ′ − d ′ ) . (2) Co [\]^ b HT a HT a) b) _‘ Sc1C
FIG. S21. Location of short and long distances between (a) cobalt and (b) scandium (Sc1) atomsin the low-temperature (LT) phase structure of Sc CoC . For clarity, only the displacements ofthe Co (a) or Sc1 atoms (b) from their high-temperature (HT) phase positions are depicted. Thegiven coordinate system refers to the orthorhombic unit cell of the HT phase. The rotation angle ∆ α C of the C units is spanned by the vector ~v = A T ( X C b − X C a ) (3)36 o Sc1 b HT a HT C a LT c LT C a C b FIG. S22. Projection of the low-temperature (LT) phase unit cell of Sc CoC into the a LT / c LT plane (coordinate system corresponding to the unit cell of the orthorhombic high-temperature (HT)phase in the lower left corner). For clarity, only the displacements of the carbon atoms from theirHT phase positions are depicted. The location of vectors ~v , ~v p and ~n required for the calculationof the C unit rotation angle ∆ α C (see text) is indicated in the inset. connecting the two constituent carbon atoms C a and C b (red solid arrow in Fig. S22) andits projection ~v p = ~v − ( ~v · ~n ) ~n (4)into the plane of undisplaced carbon atoms (red dashed arrow in Fig. S22). X C a and X C b denote fractional coordinate matrices, while A denotes the basis vector matrix of the low-temperature phase unit cell A T = (cid:16) ~a LT ~b LT ~c LT (cid:17) . (5)Furthermore, the normal vector ~n of the plane of undisplaced carbon atoms (black dashedarrow in Fig. S22) is calculated from the basis vectors of the low-temperature phase unitcell as 37 n = ( ~a LT − ~c LT ) × ~b LT | ( ~a LT − ~c LT ) × ~b LT | . (6)In a final step, the value of ∆ α C can be obtained using the inner product of ~v and ~v p ∆ α C = arccos (cid:18) ~v · ~v p | ~v || ~v p | (cid:19) . (7)38 . Sensitivity of superstructure reflection intensities to atom displacements Information about the displacements of Co, Sc1 and C atoms from their positions inthe high-temperature (HT) phase of Sc CoC is encoded in the intensities of main andsuperstructure reflections. To further elucidate the nature and size of these changes werepeatedly calculated reflection intensities for rigid structural models with different positionsof Co, Sc1 and C atoms using the software JANA2006. As a starting point the Co, Sc1 and C atoms in a structural model of the ambient-pressurelow-temperature (LT) phase at 11 K (see Tab. IV, Tab. V and Tab. VI) were reset to theirhigh-symmetry positions in the HT phase (see Tab. XII). Furthermore, anisotropic atomicdisplacement parameters (ADPs) were replaced by isotropic ones (Tab. XII) and the twinratio was fixed to a value of 0.5. The atoms were then displaced individually and stepwiseinto the direction of their LT phase positions, i.e. the Co and Sc1 atoms were movedlinearly and the C units were rotated in a conrotatory or disrotatory fashion. At each step,only reflection intensities were calculated without refining the model parameters. Ensuingchanges in the averaged intensity of main and superstructure reflections are displayed inFig. S23a and Fig. S23b, while Fig. S23c and Fig. S23d show changes in the intensity of aspecific strongly reacting main and superstructure reflection. fractional atomic coordinates U iso atom x y z [˚A ]Co 0.25 0 0.25 0.002035Sc1 0.75 0 0.25 0.002068Sc2 0 0.18801 0 0.002103Sc3 0 0.31199 0.5 0.002100C1 0.41693 0.12557 0.08307 0.003063C2 0.08307 0.12487 0.41693 0.003034TABLE XII. Fractional atomic coordinates and mean-square atomic displacement parameters usedin the initial structural model for the calculation of reflection intensities. IG. S23. Impact of conrotatory and disrotatory C displacements (solid and dashed black lines),cobalt (blue line) and scandium atom displacements (magenta line) from their HT phase positionson the averaged intensity of (a) main and (b) superstructure reflections. The according effect onthe intensity of an exemplary reflection from each of these categories is illustrated in (c) for themain reflection (3 , , −
3) and (d) for the superstructure reflection (1 . , . , − rotation (lower abscissa) are specified on the upper abscissa. . Reliability of the refined atom displacements We examined the significance of the observed changes in the rotation angles of the C unitsbetween 0 GPa and 4 GPa (experiment 3 in Tab. II) in more detail. The use of a closed-cyclesample cryostat and a diamond anvil cell (DAC) in our low-temperature x-ray diffractionexperiments reduces the achievable data quality in various ways, e.g. by a limitation of theaccessible reciprocal space and by parasitic scattering from the beryllium vacuum shroud(see Sec. VI for more details). To examine the effect of these factors, we collected low-temperature x-ray diffraction data sets ( T <
40 K and T ≈
100 K) for a Sc CoC singlecrystal inside a DAC before and after filling the cell with a pressure transmitting mediumand application of 4 GPa. In agreement with our results for a single-crystalline Sc CoC needle without surrounding pressure cell ( T = 11 K and 100 K, experiment 1 in Tab. II)structural refinements on the ambient-pressure DAC data ( T = 36 K and 106 K) pointout conrotatory displacements of neighboring C units along the [Co(C ) ] ∞ ribbons withclearly non-zero rotation angles between 6(2) ◦ and 7(2) ◦ (all angles are specified with theirthreefold standard deviation). Overlays of the structural models of the ambient-pressurelow-temperature phase obtained without and with surrounding DAC are given in Fig. S24a( T <
40 K) and Fig. S24b ( T ≈
100 K). Crystal and refinement details, fractional coordinatesand mean-square atomic displacement parameters are compared in Tab. XIII and Tab. XIV(
T <
40 K), and Tab. XV and Tab. XVI ( T ≈
100 K).Furthermore, we checked the sensitivity of the fit quality indicator wR obs (weighted R value) in structural refinements of the x-ray diffraction data collected with and without DACto changes in the C rotation angles (see Fig. S25 for T <
40 K and Fig. S26 for T ≈
100 K).To this end, the rotation angles of the two symmetry-independent C units in the LT phasestructure of Sc CoC were constrained to follow conrotatory or disrotatory displacementpatterns. After an initial relaxation the structural model was kept rigid and the value of wR obs was recorded while incrementing the C rotation angle in 0.1 ◦ steps between -15 ◦ and15 ◦ .The course of wR obs with varying rotation angle at ambient pressure without DAC isindicated by dashed lines in Fig. S25a and Fig. S26a. Conrotatory displacements of neigh-boring C units lead to a curve with two minima (black lines), whereas disrotatory displace-ments lead to a curve with a single minimum (orange lines). Consistent with the results41 GP gh ijkl mn pqrs uvw xyz Sc1Co C { a b |} FIG. S24. Overlays of the refined atom positions within a layered building unit of Sc CoC atlow temperatures and 0 GPa without (gray, semi-transparent) and with surrounding pressure cell(colored, non-transparent). In (a) the atom positions at below 40 K (without DAC: 11 K, withDAC: 36 K) are compared, and in (b) the atom positions at approx. 100 K (without DAC: 100 K,with DAC: 106 K). Note that all atom displacements are exaggerated seven-fold and that Sc2 andSc3 atoms have been omitted for clarity. The given coordinate system refers to the orthorhombicunit cell of the high-temperature phase. of unconstrained refinements (marked by black open circles) the minima in wR obs for dis-rotatory displacements at 0 ◦ are located at slightly higher wR obs values than the minimaat non-zero angles for conrotatory displacements ( T = 11 K: ∆ wR obs = 0 . T = 100 K:∆ wR obs = 0 . wR obs difference between the minima of the curves for conrotatoryand disrotatory C displacements degrades for the low-temperature DAC measurements at0 GPa ( T = 36 K: ∆ wR obs = − . T = 106 K: ∆ wR obs = 0 . wR obs with varying conro-tatory C displacements directly relates to the large (threefold) standard deviation of theobtained rotation angles in the range of 2 ◦ . Applying a pressure of 4 GPa makes the situa-tion much more clear-cut (see Fig. S25b for T = 37 K and Fig. S26b for T = 107 K): Both,the curves for conrotatory (solid black lines) and disrotatory C unit displacements (solidorange lines) have a substantial curvature and a single minimum close to 0 ◦ in confirmationof the results of unconstrained structural refinements (filled black circles).42 ✁ ✂✄☎✆☎✝✄✞ ✟✠✡☛☞✌ ☛✍ ✌ ✍ ☞✌(cid:0) ✎✝✏✑✒✆✓✔✕✔✞☎ ✟✖✡☛✌✗☞ ☛✌✗✌✍ ✌ ✌✗✌✍ ✌✗☞✘✙ ✚ ✛✜✢ ✣ ✤ ✥✦ ✧★✩✪✫✬ ✌✭✮✯✰☞✌☞✭☞✮☞✯☞✰ (cid:0)✁ ✂✄☎✆☎✝✄✞ ✟✠✡☛☞✌ ☛✍ ✌ ✍ ☞✌(cid:0) ✎✝✏✑✒✆✓✔✕✔✞☎ ✟✖✡☛✌✗☞ ☛✌✗✌✍ ✌ ✌✗✌✍ ✌✗☞✱✲✳✴✲✵✶ ✷ ✸✹✺✴✲✵✶ ✸✹✺✻✼✶✽ ✾✿❀❁ ❂❃❄✽ ✾✿❀❁❅❆❀ ❂❃❄❇✙ ❈ ✛✜✢ FIG. S25. Variation of the weighted R value wR obs with the rotation angle of the C units (lowerabscissa) or the corresponding carbon atom displacement (upper abscissa) in rigid structural modelsfor different low-temperature x-ray diffraction data sets (see text for more detailed explanation). In(a) the behavior of wR obs for ambient-pressure data sets collected without ( T = 11 K, dashed lines)and with ( T = 36 K, solid lines) pressure cell is given, while (b) shows the behavior for a 4 GPa dataset ( T = 37 K, solid lines). In each case, the rotation angles of neighboring symmetry-independentC units were constrained to follow conrotatory (black lines) or disrotatory displacement patterns(orange lines). Rotation angles obtained from unconstrained structural refinements are indicatedby open and filled black circles. ✁✂✄☎ ✆✝✞✟✠✡✆✡✝✡✞✡✟✡✠ ☛☞ ✌✍✎✏✎✑✍✒ ✓✔✕✖✡✆ ✖✗ ✆ ✗ ✡✆☛ ✘✑✙✚✛✏✜✢✣✢✒✎ ✓✤✕✖✆✥✡ ✖✆✥✆✗ ✆ ✆✥✆✗ ✆✥✡✦✧★✩✧✪✫ ✬ ✭✮✯✩✧✪✫ ✭✮✯✰✱✫✲ ✳✴✵✶ ✷✸✹✲ ✳✴✵✶✺✻✵ ✷✸✹✼✽ ✾ ✿❀❁ ☛☞ ✌✍✎✏✎✑✍✒ ✓✔✕✖✡✆ ✖✗ ✆ ✗ ✡✆☛ ✘✑✙✚✛✏✜✢✣✢✒✎ ✓✤✕✖✆✥✡ ✖✆✥✆✗ ✆ ✆✥✆✗ ✆✥✡❂✽ ❃ ✿❀❁ ❄ ❅ ❆❇❇ ❈ FIG. S26. Variation of the weighted R value wR obs with the rotation angle of the C units (lowerabscissa) or the corresponding carbon atom displacement (upper abscissa) in rigid structural modelsfor different low-temperature x-ray diffraction data sets. In (a) the behavior of wR obs for ambient-pressure data sets collected without ( T = 100 K, dashed lines) and with ( T = 106 K, solid lines)pressure cell is given, while (b) shows the behavior for a 4 GPa data set ( T = 107 K, solid lines).In each case, the rotation angles of neighboring symmetry-independent C units were constrainedto follow conrotatory (black lines) or disrotatory displacement patterns (orange lines). Rotationangles obtained from unconstrained structural refinements are indicated by open and filled blackcircles. AC no yesunit cell dimensions a = 5.53630(10) ˚A a = 5.53940(10) ˚A b = 12.0210(2) ˚A b = 12.0309(2) ˚A c = 5.53640(10) ˚A c = 5.53850(10) ˚A β = 104.8070(10) ◦ β = 104.8280(10) ◦ V = 356.222(11) ˚A V = 356.816(11) ˚A calculated density 4.5095 g · cm − · cm − crystal size 40 × × µ m × × µ m wave length 0.56087 ˚Atransm. ratio (max/min) 0.747 / 0.686 0.747 / 0.565absorption coefficient 5.016 mm − − F (000) 456 θ range 3 ◦ to 36 ◦ ◦ to 33 ◦ range in hkl -11/11, -25/25, -11/11 -6/10, -20/21, -6/10total no. reflections 8720 1291independent reflections 2142 ( R int = 0.0123) 390 ( R int = 0.0101)reflections with I ≥ σ ( I ) 2007 318data / parameters 2142 / 43 318 / 19goodness-of-fit on F R indices [ I ≥ σ ( I )] R = 0.0220 R = 0.0342 wR = 0.0414 wR = 0.1064 R indices (all data) R = 0.0271 R = 0.0342 wR = 0.0424 wR = 0.1064extinction coefficient 0.0461(14) –largest diff. peak and hole 1.97 / -2.18 e · ˚A − · ˚A − TABLE XIII. Crystal data and structure refinements for ambient-pressure single-crystal x-raydiffraction experiments without ( T = 11 K) and with surrounding unpressurized Tozer-type dia-mond anvil cell ( T = 36 K). ractional atomic coordinates U iso / U eq atom DAC x y z [˚A ]Co no 0.26595(2) 0 0.26673(2) 0.00204(3)yes 0.26649(12) 0 0.26564(12) 0.0026(2)Sc1 no 0.75582(3) 0 0.24273(3) 0.00207(6)yes 0.75700(14) 0 0.24355(13) 0.0029(3)Sc2 no 0 0.187417(10) 0 0.00210(9)yes 0 0.18746(6) 0 0.0029(3)Sc3 no 0 0.311540(10) 0.5 0.00210(9)yes 0 0.31145(6) 0.5 0.0030(3)C1 no 0.4110(3) 0.12557(5) 0.0766(2) 0.0031(2)yes 0.410(3) 0.1257(2) 0.077(3) 0.0049(5)C2 no 0.0889(3) 0.12487(5) 0.4233(2) 0.0030(2)yes 0.091(3) 0.1251(2) 0.425(3) 0.0049(5)TABLE XIV. Refined fractional atomic coordinates and mean-square atomic displacement parame-ters obtained from low-temperature single-crystal x-ray diffraction experiments without ( T = 11 K)and with surrounding unpressurized Tozer-type diamond anvil cell (DAC; T = 36 K). Note thatthe fractional coordinates refined from DAC data have been transformed in order to correspond tothe same twin individual as the coordinates from non-DAC data. AC no yesunit cell dimensions a = 5.53720(10) ˚A a = 5.5386(2) ˚A b = 12.00370(10) ˚A b = 12.0071(3) ˚A c = 5.53710(10) ˚A c = 5.5365(2) ˚A β = 104.4620(10) ◦ β = 104.386(2) ◦ V = 356.372(10) ˚A V = 356.65(2) ˚A calculated density 4.5076 g · cm − · cm − crystal size 40 × × µ m × × µ m wave length 0.56087 ˚Atransm. ratio (max/min) 0.747 / 0.646 0.746 / 0.583absorption coefficient 5.014 mm − − F (000) 456 θ range 3 ◦ to 37 ◦ ◦ to 32 ◦ range in hkl -11/11, -25/25, -11/11 -6/10, -21/21, -6/10total no. reflections 8509 1234independent reflections 2153 ( R int = 0.0148) 394 ( R int = 0.0143)reflections with I ≥ σ ( I ) 1947 291data / parameters 2153 / 43 291 / 19goodness-of-fit on F R indices [ I ≥ σ ( I )] R = 0.0302 R = 0.0437 wR = 0.0535 wR = 0.1153 R indices (all data) R = 0.0389 R = 0.0437 wR = 0.0549 wR = 0.1153extinction coefficient 0.0231(15) –largest diff. peak and hole 1.94 / -2.20 e · ˚A − · ˚A − TABLE XV. Crystal data and structure refinements for ambient-pressure single-crystal x-raydiffraction experiments without ( T = 100 K) and with surrounding unpressurized Tozer-type dia-mond anvil cell ( T = 106 K). ractional atomic coordinates U iso / U eq atom DAC x y z [˚A ]Co no 0.25987(2) 0 0.26046(2) 0.00243(5)yes 0.25814(11) 0 0.25757(11) 0.0033(3)Sc1 no 0.75383(3) 0 0.24498(3) 0.00239(10)yes 0.75366(14) 0 0.24668(13) 0.0034(3)Sc2 no 0 0.187747(13) 0 0.00233(10)yes 0 0.18785(6) 0 0.0036(3)Sc3 no 0 0.311642(13) 0.5 0.00235(10)yes 0 0.31168(6) 0.5 0.0035(3)C1 no 0.4109(3) 0.12514(5) 0.0773(3) 0.0033(3)yes 0.4103(19) 0.1247(2) 0.076(2) 0.0047(6)C2 no 0.0890(3) 0.12471(5) 0.4228(3) 0.0033(3)yes 0.0893(19) 0.1247(2) 0.425(2) 0.0047(6)TABLE XVI. Refined fractional atomic coordinates and mean-square atomic displacement pa-rameters obtained from low-temperature single-crystal x-ray diffraction experiments without( T = 100 K) and with surrounding unpressurized Tozer-type diamond anvil cell (DAC; T = 106 K).Note that the fractional coordinates refined from DAC data have been transformed in order to cor-respond to the same twin individual as the coordinates from non-DAC data. . Differences between twin domains Single crystals of Sc CoC are subjected to systematic twinning in the phase transitionfrom the high-temperature (HT) to the low-temperature (LT) phase. This twinning processis due to a t i translationengleiche andisomorphic groub-subgroup relationship, respectively) from the orthorhombic space-group Immm of the HT phase structure to the monoclinic space-group C /m of the LT phasestructure. An exemplary twinning operation that transforms the atomic positions in onetwin domain into the atomic positions of the other is a m plane perpendicular to the a axisof the orthorhombic HT unit cell ([[-1 0 0], [0 1 0], [0 0 1]]). Its effect is demonstrated forthe structural models of the LT phase at 0 GPa and 11 K (Fig. S27a) and at 4 GPa and37 K (Fig. S27b). Whereas the twin domains at 0 GPa can be differentiated easily by thesense of rotation of the C units, this is barely possible for the (hypothetical) twin domainswith nearly unrotated C units at 4 GPa. a, 37 K0 GPa, 11 Ka) b a b FIG. S27. Overlay of the atomic positions within the possible twin domains 1 (colored, non-transparent spheres) and 2 (gray, semi-transparent spheres) of Sc CoC (a) in its ambient-pressureand (b) in its high-pressure low-temperature phase. All atom displacements are exaggerated seven-fold. For clarity, only the atoms within a layered building unit are shown, and Sc2 and Sc3 atomshave been omitted. 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