Polytypism and Superconductivity in the NbS_2 System
Catherine Witteveen, Karolina Gornicka, Johan Chang, Martin Månsson, Tomasz Klimczuk, Fabian O. von Rohr
PPolytypism and Superconductivity in the NbS System
Catherine Witteveen, a , b Karolina Gornicka, c , d Johan Chang, b Martin Månsson, e TomaszKlimczuk, c , d Fabian O. von Rohr, a , b ∗ We report on the phase formation and the superconducting properties in the NbS system. Specif-ically, we have performed a series of standardized solid-state syntheses in this system, which allowus to establish a comprehensive synthesis map for the formation of the two polytypes 2H-NbS and3R-NbS , respectively. We show that the identification of two polytypes by means of X-ray diffrac-tion is not always unambiguous. Our physical property measurements on a phase-pure sample of3R-NbS , on a phase-pure sample of 2H-NbS , and a mixed phase sample confirm earlier reportsthat 2H-NbS is a bulk superconductor and that 3R-NbS is not a superconductor above T = Layered transition-metal dichalcogenides (TMDs) with the gen-eral formula MX (with M = group IV transition metal, groupV transition metal, or Re and X = S, Se, or Te) have been ofgreat interest due to their rich electronic properties, in combina-tion with the opportunity to exfoliate them down to the mono-layer. Recently, TMD superconductors have been identified asideal model systems for investigating superconductivity in thetwo-dimensional limit.
Especially noteworthy is the realizationof an intrinsic monolayer superconductor - i.e. the occurrence ofsuperconductivity without the need of a specialized substrate -in monolayers of NbSe . This, together with the observationof unconventional superconducting properties in TMD bulk su-perconductors - e.g. the linear scaling of the superfluid densityin NbSe , or the observation of time-reversal symmetry breakingin superconducting 4H b -TaS - hint towards new opportunitiesto potentially discover unconventional or even topological super-conductivity using van der Waals materials or heterostructuresthereof. Generally, TMDs are subjected to structural polymorphism andpolytypism, meaning there are several different phases with dif- a Department of Chemistry, University of Zürich, Winterthurerstr. 190, 8057 Zürich,Switzerland b Department of Physics, University of Zürich, Winterthurerstr. 190, 8057 Zürich,Switzerland c Department of Solid State Physics, Gdansk University of Technology,80-233 Gdansk,Poland d Advanced Materials Centre, Gdansk University of Technology, ul. Narutowicza 11/12,80-233 Gdansk, Poland e Department of Applied Physics, KTH Royal Institute of Technology, Roslagstullsbacken21, SE-106 91 Stockholm, Sweden ∗ To whom correspondence may be addressed. ferent crystal structures for the same chemical composition. InTMDs different polymorphs occur by the changing coordinationof the chalcogen to the metal atom, and the different polytypesby changing stacking sequences of the MX monolayers. Polytyp-ism is occurring in layered materials, namely when the geometryof a repeating structural layer is maintained but the layer-stackingsequence of the overall crystal structure can be varied. Natu-rally, the crystal structure of a material defines its physical proper-ties, hence these can vary drastically among different TMD poly-morphs. For example, while the 1T’-MoTe polymorph is a Weylsemimetal and superconductor, the 2H-MoTe polymorph is asemiconductor with an indirect bandgap of E gap = However, physical properties of different polytypes are usuallysimilar, since the changes in layer stacking impact the propertiesof the whole material in a less pronounced fashion. For exam-ple, the 2H-NbSe and 4H-NbSe polytypes of NbSe are both su-perconductors with similar critical temperatures of T c = T CDW =
35K and 42 K, respectively.
Among the metallic TMDs, the niobium disulfide system standsout, as none of its polymorphs have been reported to displaycharge-density-wave ordering.
In this system, there are threepolymorphs known. The stable 3R-NbS and 2H-NbS polytypeshave been reported as polycrystalline and single crystalline ma-terials, while the metastable 1T-NbS polymorph has been stabi-lized in thin film form. In the NbS system only the 2H-NbS polytype is known to be superconducting with a critical tempera-ture of T c ≈ As we shall show later inthis work, these observations of superconductivity in samples ofthe 3R-NbS polytype may likely be caused the presence of traces a r X i v : . [ c ond - m a t . s up r- c on ] F e b f 2H-NbS , which are challenging to identify by means of X-raydiffraction. The challenge to prepare phase pure samples of 2H-NbS and 3R-NbS has earlier been recognized by Fisher et al. . There it was highlighted that the sulfur pressure during synthesisis crucial for the phase formation of the product.Here, we investigate the reaction conditions for synthesizingthe 2H-NbS and 3R-NbS polytypes under standardized, system-atically altered parameters by means of solid-state synthesis. Ourfindings result in a detailed synthesis map for the whole NbS system. This synthesis map allows for identification of targetedsynthesis conditions for the preparation of phase-pure samples inthis system. Our analysis of the physical and superconductingproperties reveals that specific-heat measurements are crucial forthe identification of superconducting materials. This is especiallytrue in this systems, since we can show that samples with mixedphases may easily be mistaken as bulk superconductors. All samples were prepared by means of high-temperature solid-state synthesis from the pure elements niobium (powder, Alfa Ae-sar, 99.99%) and sulfur (pieces, Alfa Aesar, 99.999%). The nio-bium and sulfur were mixed in their respective ratios, and thor-oughly ground to a fine mixture and pressed into pellets. Eachpellet was sealed in a quartz glass ampoule under 1/3 atm argon.The samples were then heated (with 180 ◦ C/h) to temperaturesranging from T = 600 ◦ C to 950 ◦ C for 3 days.Powder X-ray diffraction (PXRD) patterns were collected onan STOE STADI P diffractometer in transmission mode equippedwith a Ge-monochromator using Cu K α radiation and on aRigaku SmartLab in reflection mode using Cu K α radiation. Scan-ning electron microscopy (SEM) was performed on a Zeiss Supra50 VP.The temperature-dependent magnetization was measured ina Quantum Design magnetic properties measurement system(MPMS) equipped with a 7 Tesla (T) magnet and with a recip-rocating sample option (RSO). The samples were measured in agelatin capsule, where the layered materials naturally arrangedperpendicular to the external magnetic field. The measurementswere performed upon warming the sample in zero-field mode.The specific-heat capacity measurements were performed in aQuantum Design EverCool physical property measurement sys-tem (PPMS) equipped with a 9 T magnet. These measurementswere performed with the Quantum Design heat-capacity optionusing a relaxation technique.SEM images were taken with a JEOL JSM 6060 scanning elec-tron microscope and the elemental composition analysed usingenergy dispersive X-ray (EDX) (Bruker axes) attached to the JEOLJSM 6060. Crystallographic parameters of the 3R-NbS and 2H-NbS poly-types are given in table 1.Figure 1(a) shows their geometry and crystal structure. Thefundamental trigonal prismatic building block [NbS ] is shown, Table 1
Summary of the crystallographic parameters for NbS . Space group R3 m (No. 160) P / mmc (No. 194)Z 3 2 of layers per unit cell 3 2stacking sequence ABC AB which leads to the hexagonal (H) and rhombohedral (R) poly-types, when arranged in layers and stacked accordingly. Specifi-cally, the views along the [001] and [100] direction of the crystalstructure of the two stable 3R-NbS and 2H-NbS polytypes areshown with the highlighted unit cell in black. Whereas the cova-lent bonding within a layer is of trigonal primatic geometry forboth materials, their stacking sequence differs, resulting in thedifferent respective polytypes. The simulated PXRD patterns ofthe two compounds are shown in Figure 1(b). These isotropicPXRD patterns have reflection positions that are very similar be-cause of their common sublattice. Furthermore, the reflectionsthat can be clearly distinct from each other are challenging to ob-serve for real preferentially oriented, anisotropic samples, as wewill discuss in detail below. I n t e n s it y ( a . u . )
2θ (deg.)
SulfurNiobium b bca
Simulated pattern of 3R–NbS in Cu K α1 a=b=3.33 Å c=17.92 Å Coll. code ICSD 42099Coll. code ICSD 436967
Simulated pattern of 2H–NbS in Cu K α1 a=b=3.31 Å c=11.86 Å Side viewTop viewCoordination sphere ba Trigonal Prismatic (H, R)
NbS Fig. 1 (a) Polytypes of NbS . Left side: illustration of the trigonalprismatic coordination sphere, later resulting to the 3R-NbS and 2H-NbS . Middle: top view, and right: side view showing the number ofvan-der-Waals layers per unit cells. In green the metal Nb, in yellow thechalcogenide S. (b) Simulated PXRD patterns of 3R-NbS in red and2H-NbS in blue with Cu K α radiation, including the respective Millerindices of the reflexions. olycrystalline samples of NbS were prepared under standard-ized conditions by means of conventional solid state synthesis.Each synthesis was performed (i) with a total mass of m = 400 mgof the reactants, (ii) in quartz glass ampoules (standing upright inthe muffle furnace) of precise length of l =
75 mm, a diameter of d wall = d thickness = ◦ C/h, for a total heating duration of precisely 72 h, (iv) allsamples were eventually quenched into water after the reaction.Subsequent quenching of the samples in water proved to be im-portant in order to remove excess of residual sulfur. Especiallythe samples synthesized with a sulfur excess had residual yellowunreacted sulfur at the top of the quartz tubes, well separatedfrom the dark grey NbS products.A total of 56 samples were prepared and analysed by meansof powder X-ray diffraction, resulting from different synthesis at-tempts of varying nominal stoichiometries in NbS x with x rangingfrom 1.7 to 2.3 in 0.1 steps and synthesis temperatures rangingbetween 600 ◦ C to 950 ◦ C in 50 ◦ C steps. Three samples oxidizedin the process, which is rendered by three missing points in figure3. No impurities of side-products or the starting materials wereobserved in any of these samples. All resulting products were darkgrey. The highly crystalline samples had all a metallic luster, dis-tinguishing them from their amorphous counterpart. An analysisof the morphology of the samples synthesized at 2.3 eq for varioustemperatures was done by means of SEM (see SI). At low synthe-sis temperatures, no distinct shape of crystals is formed, whereaswe obtain platy crystals at higher synthesis temperatures.Stoichiometries and/or synthesis temperatures outside of thesespecific conditions lead to the formation of considerable amountsof impurities. PXRD patterns for all samples are shown in theSupplemental Information. In order to illustrate the resulting dif-ferences between them, three representative patterns are shownin Figure 2. These three pattern correspond to a phase-pure sam-ple of 3R-NbS (red line), a phase pure sample of 2H-NbS (blueline), and a mixed sample, containing both polytypes (grey line).These three samples were also the ones that later were used forphysical properties measurements (see below). It should be notedthat the PXRD pattern look, at first glance, remarkably similar,hence a detailed analysis is required to accentuate the differences.In PXRD, preferred orientation creates a systematic error inthe observed intensities of diffraction peaks. The platy shape ofthe two NbS polytypes poses a challenge for obtaining an unbi-ased method to distinguish them by means of X-ray diffraction.In the Bragg-Brentano geometry, i.e. reflection mode, the inten-sity of the 00l reflections will be heavily increased, because the(001) planes are oriented in such a way to be in reflection con-dition with the diffractometer. In the Debye-Scherrer geometry,i.e. transmission mode, the X-rays pass through the platelets andthus the intensities of the hk0 reflections will be heavily increased,since the (hk0) planes are perpendicular to the (001) planes. Acomparison of the obtained PXRD patterns for the same sampleon the two different instrument modes for the 2H-NbS polytypeis given in the Supplemental Information.Both polytypes are crystallizing in a hexagonal setting. Equa- tion 1 helps to calculate the d hkl . d hkl = ( h + k + hka ) + l c (1)It is true that their c axes follow the relation c = c whileshowing similar a parameter. Therefore, the position of the 00lreflections originating from the crystal planes parallel to the lay-ers will remain invariant: d ( H ) = d ( R ) with n being aninteger. The rhombohedral centering of the 3R polytype in hexag-onal setting will show only every third reflection on the [001] axis(003, 006, 009) and the 2H polytype, because of its 6 ( ) screw ro-tation, every second reflection on this axis (002, 004, 006), bothat identical 2 θ positions.The hk0 reflections originating of the crystal planes perpendicularto the layers of both NbS polytypes will also remain invariant,because of the same length of a. Thus both polytypes can thusbe only distinguished from one another by the position and in-tensities of h0l, 0kl and hkl reflections, which is particularly diffi-cult since the intensities of these reflections are least pronounced.They are still observable in transmission mode, hence, here allsamples were analysed by means of PXRD of the Debye-Scherrergeometry.In Figure 2(b), we show a zoom-in for the a 2 θ range of 30-35 ◦ , where these reflections are most pronounced. The 100 and012 reflections of 3R-NbS , and the 100 and 101 of 2H-NbS al-low for the differentiation of the two polytypes. Especially in thesample containing a mixture of both the presence of all four ofthese reflections - arising from both of the two polytypes - be-comes most apparent in direct comparison. We can state thatthere is a substantial amount of the 3R-NbS polytype presentin this sample, however a quantitative analysis of the amountsof the different phases is not possible with a PXRD analysis, dueto the preferred orientation. Simply comparing the 100 of the2H polytype with the 101 reflections of the 3R-NbS polytype at31 ◦ and 31.5 ◦ might give the wrong impression that the 2H-NbS is the minority phase, while it actually is the majority (approxi-mately 75 %) phase, as we will argue below. It should be notedthat the 102 reflection of 2H-NbS in any of the obtained sam-ples is comparably broad, which may likely be originating fromstacking faults or turbostratic disorder arising from the randomorientation of successive layers about the stacking direction. System
The performed systematic syntheses and their respective analysesby means of PXRD in the NbS system, allow for the compilationof a comprehensive synthesis map, which is shown in Figure 3.The careful analysis of the obtained PXRD pattern allowed us todistinguish between 4 different regions: (i) amorphous, (ii) phasepure 2H-NbS , (iii) phase pure 3R-NbS , and (iv) mixed phase re-gions of both the 2H and the 3R polytypes. The amorphous region * was here defined for samples with the FWHM being larger than * Here, "amorphous" is used as a collective term describing the non-crystalline andlow-crystalline region of the synthesis map.
50 °CNbS
950 °CNbS
900 °CNbS
2θ (deg.) I n t e n s it y ( a . u . )
950 °CNbS
950 °CNbS
900 °CNbS I n t e n s it y ( a . u . )
2θ (deg.) ( )( )( )( )( )( ) ( ) ( )( ) ( ) ab Cu K α1 Cu K α1 NbS – mix Fig. 2
Powder x-ray diffraction patterns for different synthesis temper-atures and compositions resulting in the different polytypes. (a) PXRDpatterns obtained in the transmission mode using Cu K α radiation overa 2 θ range of 10 ◦ to 60 ◦ . Clearly observable is the strong intensity ofthe hk0 reflections, due to the preferred orientation of the samples. (b)Zoom in the 2 θ = 30 - 35 ◦ , showing the h0l and 0kl reflections, allowingthe distinction of the polytypes. θ =0.21 ◦ for the reflection at 2 θ ≈ ◦ , which corresponds toeither the 002 reflection of 2H-NbS , or the 003 reflection of 3R-NbS polytype. For samples with larger values of FWHM the 2H-NbS and 3R-NbS polytypes could not be distinguished in anunbiased fashion. The gradual change from amorphous to crys-talline samples can be especially well observed in the PXRD pat-terns of the samples at a fixed sulfur content (see SupplementalInformation). An analysis of the morphology of the samples syn-thesized at 2.3 eq for various temperatures was done by meansof SEM (see SI). The points in the synthesis map correspond toeach synthesized sample and indicate the exact temperature ofsynthesis and sulfur content used. The formation of phase-pure2H-NbS was only observed in a very narrow temperature andstoichiometry interval. Overall, we find that the 3R-NbS poly-type preferentially forms in a stoichiometric or sulfur deficiencyenvironment, whereas excess of it is needed for the formation ofthe 2H-NbS polytype. This observation is also in agreement withearlier findings by Fisher et al , where substantial sulfur pressures were found to be crucial for stabilization of the 2H-NbS poly-type. It might be speculated that the 3R polytype preferentiallyforms with a sulfur deficiency, because its ABC stacking reducesthe likelihood of having two sulfur vacancies directly above or be-low each other. However, our systematic EDX analysis, for boththe 2H-NbS and 3R-NbS polytypes, reveals samples very sim-ilar sulfur contents of 1.89 and 1.92, respectively (see SI). Ourfindings do not only affect the formation of polycrystalline sam-ples, but they also have implications for the preparation of singlecrystals of the different NbS polytypes, as it is very likely thatthe two different phases can be intergrowth of each other, whichis also called allotwins. Temperature-dependent magnetization and temperature-dependent specific-heat measurements were performed (seeFigure 4) to determine the superconducting properties of theobtained samples. Specifically, phase pure 2H-NbS , phase-pure3R-NbS , and a sample with both polytypes were investigated(same sample as discussed in Figure 2). The superconductingcritical temperatures are found to be T c = polytype, and 5.7 K in the magnetization and the specific heatfor the mixed phase sample. In neither measurement, we findany superconducting transition in the phase-pure 3R polytypesample above a temperature of T > were likely originatingfrom 2H-NbS impurities, as we will show in the following. In Figure 4(a), we show the magnetization measurements asthe unitless magnetic susceptibility χ = M / H for all three sam-ples. The measurements were performed in a temperature rangebetween T = µ H = 2 mT in zero-field cooled (ZFC) mode. A bulk super-conductor is an ideal diamagnet in the Meissner state, hence, amagnetic susceptibility in the ZFC mode of χ = -1, correspondingto a 100 % shielding fraction, is expected. At temperatures below T = 2 K, the diamagnetic signal of 2H-NbS saturates at a valueof nearly 200 % of the shielding fraction. This value exceeds thetheoretical value for an ideal diamagnet by a factor of approxi-mately 2. This large shielding fraction is due to demagnetizationeffects. Thereby, the effective magnetic field is reduced due to ademagnetizing magnetic field H D , which in turn is generated bythe magnetization M within the superconductor according to H in = H ext − H D = H ext − n M = (cid:18) − n (cid:19) H ext (2)with n being the so-called demagnetizing factor. For geomet-rically, well-defined cases such as e.g. ellipsoids or plates H D islinearly related to the magnetization M by a constant. The de-magnetization fields are commonly more challenging to calculate,especially for arbitrarily shaped real objects. For the extreme caseof an ideal diamagnet in the shape of a plate, which is placed per-pendicular to an external magnetic field H ext the demagnetizingfactor approaches unity. Here, for the measurements of polycrys-talline samples of layered TMDs, the plate-like samples naturally R–NbS mixamorphous N bS . N bS . eq. sulfur R eac ti on t e m p e r a t u r e ( ° C ) S y n t h e s i s M a p Fig. 3
Synthesis map of the NbS system for NbS x with x ranging from 1.7 to 2.3 in 0.1 steps and a synthesis temperature range between 600 ◦ C to950 ◦ C in 50 ◦ C steps. Each data point represents a synthesis according to the respective synthesis protocol described in the text. Phase pure samplesof 3R-NbS in blue, phase-pure samples of 2H-NbS in dark green, the mixed-phase region is light green, and the amorphous region is marked in grey.The 2H-NbS polytype appears only in a in a very narrow synthesis window. arranged perpendicular to the external magnetic field, which en-hances the observed diamagnetic shielding fraction heavily. Thiseffect also enhances the shielding fraction of the sample contain-ing a mixture of both polytypes 2H-NbS and 3R-NbS , leadingto a measured shielding fraction of nearly 140 % at T = 1.75 K.This sample might be easily mistaken for a bulk superconductingsample, due to this large volume fraction, the well-defined, sharpsuperconducting transition, and the critical temperature of T c =5.7 K, which is in the range of values reported in the literature forsuperconductors in the NbS system.Therefore, these superconductors with a layered crystal struc-ture resulting in a platy crystal shape are a particularly charac-teristic example of how magnetic susceptibility measurements,and in extension also resistivity measurements – which are show-ing a state of zero-resistance, even at very low concentrationsof superconducting grains – are insufficient for the characteri-zation and confirmation of bulk superconductors. Rather truebulk measurements are needed, especially the measurement ofthe temperature-dependent specific heat C ( T ). At T = T c the spe-cific heat of the paired electrons is larger than the specific heat ofthe electrons in the normal state C super ( T c ) > C el ( T c ) . (3)This leads to a characteristic discontinuity at the criticaltemperature, which according to the Bardeen-Cooper-Schrieffer(BCS) theory is (cid:18) C super − C el γ T c (cid:19) T c = . . (4)Values close or larger than these 1.43 for the discontinuity in the specific heat are a strong indicator, and believed to be prooffor bulk superconductivity. This difference means that less elec-trons are forming Cooper-pairs, then generally would be expectedfrom the density of electronic states at the Fermi level D ( E Fermi ).In Figure 4(b), we show the temperature-dependent specificheat C ( T )/ T in a temperature range between T = 2 and 10 K forphase pure 2H-NbS , phase pure 3R-NbS , and the sample con-sisting of both polytypes. A well-pronounced, sharp discontinuityat the transition to the superconducting state is observed for the2H-NbS polytype, as well as for the mixed sample.In Figure 4(c), we show the analysis of the normal state of thethree samples. The normal state specific heat contributions havebeen fitted to the data according to the general expression C ( T ) T = γ + β T (5)with the Sommerfeld constant γ and β = 12 π nR/5 Θ D , wheren is the number of atoms per formula unit, R is the gas constant,and Θ D is the Debye temperature.We find for the phase pure sample of 2H-NbS an approxi-mately 3 times larger Sommerfeld constant of γ = − K − than the one of 3R-NbS with γ = − K − . This may likely explain, why the 2H-NbS polytype is asuperconductor, while the 3R-NbS polytype is not. This largedifference corresponds to a much higher density of states at theFermi level D ( E Fermi ) for the 2H-NbS polytype. According to theBCS theory the critical temperature is proportional to density ofstates at the Fermi level D ( E Fermi ) ∝ T c , which in turn explains theabsence of superconductivity in 3R-NbS above T = Θ D of and 3R-NbS polytypes,respectively. This is surprising, as the basic building block, i.e. themonolayer of NbS is for both polytypes the same, hence the elec-tronic and phononic differences must be caused by the differentstackings of the layers, i.e. the electronic and phononic overlapthrough the van-der-Waals gaps. A possible explanation is theenhanced orbital overlap in the 2H-NbS due to its AB stacking,allowing for a higher fraction of atoms to be directly above orbelow other atoms.The entropy-conserving constructions of the superconductingspecific heat discontinuity are shown for the phase pure 2H-NbS sample and the mixed-phase sample in Figure 4(b) resulting invalues for ∆ C / γ T c of 1.30 and 0.98, for the phase-pure 2H-NbS and the mixed sample, respectively. The value ∆ C / γ T c for phase-pure 2H-NbS is in excellent agreement with earlier studies onhigh-quality single crystals of 2H-NbS . Since the specificheat is truly a bulk measure, we can state that the mixed samplewith ∆ C almost being parity to γ T c , contains of maximally 75 %of the 2H-NbS polytype, but it might nevertheless be easily mis-taken for a bulk superconductor. This finding is in agreement withearlier reports for other superconducting systems, where specificheat measurements were also found to be crucial for the identi-fication of bulk superconducting phases . A summary of theobtained superconducting parameters of both samples is given intable 2. Table 2
Summary of the physical and superconducting properties ofNbS . sample γ Θ D T c , heat T c , mag ∆ C / γ T c (mJ mol − K − ) (K) (K) (K)3R–NbS In summary, we have performed a series standardized solid-statesyntheses in the NbS system, which allowed us to establish acomprehensive synthesis map for the formation of the two poly-types 2H-NbS and 3R-NbS . We show that the distinguishingof the two polytypes by PXRD is not trivial, as the differing re-flections are least pronounced due to preferred orientation lead-ing to systematic errors. Furthermore, we find that there is arelatively large stoichiometry and synthesis-temperature region,where mixed samples consisting of both polytypes are formed andthat there are well-defined synthesis conditions that lead to phasepure samples of either polytype.Our physical property measurements on a phase-pure sampleof 3R-NbS , on a phase-pure sample of 2H-NbS , and a mixedphase sample have confirmed earlier reports that 2H-NbS is abulk superconductor. We show that 3R-NbS is not a supercon-ductor above T = C p / T ( m J m o l –1 K –2 ) γ = 6.3(1) Θ D = 361(9)γ = 14.2(2) Θ D = 313(8)γ = 18.4(2) Θ D = 304(7) T ( K ) T ² ( K ² ) μ H = 2 mTμ H = 3 T NbS – mix NbS – mixT c = 6.1 KT c = 5.7 K acb C p / T ( m J m o l –1 K –2 ) Fig. 4
Physical and superconducting properties of a phase pure 2H-NbS (blue), a phase pure 3R-NbS (red), and a sample consisting ofboth polytypes (grey). (a) ZFC temperature-dependent magnetization M ( T ) measured in a field of µ H = C ( T )/ T in the vicinity of the superconducting transition, measured in zero ap-plied field. The solid lines outline the entropy conserving construction.(c) C ( T )/ T in the normal state versus T . The solid lines are fits toEquation 5. H-NbS , we report a value of ∆ C / γ T c = single crystals, is found to be critical, as also singlecrystals might show substantial 3R-NbS inclusions (see, e.g. ref-erences 32,33). These 3R-NbS polytype inclusions may evenoccur in apparently large single crystals of 2H-NbS , due to thesimilar chemistry of the two polytypes. Therefore, inter-growthregions of the two polytypes may be mistaken for stacking faults.We conclude by pointing out that for the investigation of van-der-Waals materials in the NbS system – but also in chemicallyrelated systems – great care has to be taken on choosing the rightsynthesis conditions for obtaining phase pure samples, since theformation of impurity phases is likely, and can even more likely beoverlooked due to structural similarities that cause similar PXRDpatterns. Conflicts of interest
There are no conflicts to declare.
Acknowledgements
The authors thank Manuele Balestra and Mark Blumer for helpduring the synthesis. The authors thank Dr. Robin Lefèvre forhelpful discussions. This work was supported by the Swiss Na-tional Science Foundation under Grant No. PZ00P2_174015.Work at GUT was supported by the National Science Centre(Poland), grant number: UMO-2017/27/B/ST5/03044. This re-search is also funded by the Swedish Research Council (VR)through a neutron project grant Dnr. 2016-06955.
Notes and references
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