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Article

Effect of Carbon and Nitrogen Concentrations on the Superconducting Properties of (NbMoTaW)1CxNy Carbonitride Films

by
Gabriel Pristáš
1,
Slavomír Gabáni
1,
Petra Hviščová
2,
Jozef Dobrovodský
3,
Dmitry Albov
2,
Maksym Lisnichuk
2,
Oleksandr Onufriienko
1,
Janina Zorych
1,4,
František Lofaj
2 and
Karol Flachbart
1,*
1
Institute of Experimental Physics of the Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
2
Institute of Materials Research of the Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
3
Advanced Technologies Research Institute, Slovak University of Technology in Bratislava, 917 24 Trnava, Slovakia
4
Faculty of Electrical Engineering and Informatics, Technical University, 042 00 Košice, Slovakia
*
Author to whom correspondence should be addressed.
Materials 2025, 18(16), 3732; https://doi.org/10.3390/ma18163732
Submission received: 26 June 2025 / Revised: 31 July 2025 / Accepted: 7 August 2025 / Published: 8 August 2025
(This article belongs to the Special Issue High-Entropy Alloys: Synthesis, Characterization, and Applications)
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Versions Notes

Abstract

We report about the effect of nitrogen and carbon concentration on the superconducting transition temperature TC of (NbMoTaW)1CxNy carbonitride films deposited using reactive DC magnetron sputtering. By measuring the temperature dependence of electrical resistance and magnetization of these carbonitrides, with 0.20 ≤ x ≤ 1.17 and 0 ≤ y ≤ 0.73, we observe a TC enhancement that occurs especially at high (x ≥ 0.76) carbon concentrations, with the largest TC = 9.6 K observed in the over-doped fcc crystal structure with x = 1.17 and y = 0.41. The reason why the largest TC appears at high C concentrations is probably related to the lower atomic mass of carbon compared to nitrogen and to the increase in the electron–phonon interaction due to different bonding of carbon (compared to nitrogen) to the Nb-Mo-Ta-W metallic sublattice. However, for concentrations where y > 0.71 and x + y > 1.58, two structural phases begin to form. Additionally, the proximity to structural instability may play a role in the observed BC2 enhancement. Further measurements in a magnetic field show that the upper critical fields BC2 of (NbMoTaW)1CxNy carbonitrides provide BC2/BC2 < 2 T/K, which falls within the weak-coupling pair breaking limit.

1. Introduction

Superconductivity in compounds consisting of transition metal (TM) elements and non-metals such as carbon and nitrogen has been known since 1930 [1]. Later on, extensive research related to superconductivity in carbides and nitrides has been performed, and it was shown that superconductivity can be observed in several TM carbides or nitrides (see [2,3,4,5,6]), TM-alloy carbides or nitrides (see [7,8]), and carbonitrides containing both carbon and nitrogen (see [9]). Among TM carbides and nitrides, the highest transition temperatures have been observed in molybdenum carbide, MoC, with a superconducting transition temperature, TC, of ~14.3 K [4] and niobium nitride, NbN, with a TC of ~17.3 K [3], which are much higher compared to pure Mo and Nb with 0.92 K and 9.2 K, respectively. For niobium carbonitrides the highest TC ≈ 16.9 K was observed for the NbC0.3N0.7 composition [9]. It is necessary to add that all TM carbides and nitrides mentioned above are considered to be conventional weak-coupling s-wave phonon-mediated Bardeen–Cooper–Schrieffer (BCS) superconductors. In the simplest case, their TC dependence may be described using the relation kBTC = 1.13 ħωD exp(−1/N(EF)V) (see [10]), where ωD denotes the phonon Debye frequency, N(EF) the electronic density of states (DOS) at the Fermi energy EF, V the electron–phonon interaction potential, and kB and ħ the Boltzmann and Planck constants, respectively.
Very recently, multicomponent materials as high entropy alloys (HEAs), containing five or more metallic elements in near-equiatomic proportions, and high entropy ceramics (HECs), which in addition to metallic ones also contain non-metallic atoms such as carbon and nitrogen, have started to be investigated [11,12,13,14]. The reason for this is that in HEAs and HECs, due to the cocktail effect coming from synergy phenomenon of constituent atoms (having a different number of valence electrons, different atomic radii, and a high mixing/configurational entropy that represents a measure of the number of ways in which a particular configuration of metal atoms can be achieved), new and unexpected results can be expected. Overviews of unique properties of HEAs and HECs can be found, e.g., in [15,16,17], as well as reviews and new information about their superconducting properties, e.g., in [18,19,20,21]. It has to be added that RE123 high-Tc superconductors with a HEA-type of the rare earth (RE) site (as e.g., Y0.28Nd0.16Sm0.18Eu0.18Gd0.20Ba2Cu3O7-δ and Y0.18La0.24Nd0.14Sm0.14Eu0.15Gd0.15Ba2Cu3O7-δ, see [22]) exhibiting transition temperatures exceeding 90 K have also been investigated. It is also necessary to note that carbonitride materials and their synthesis processes are quite well understood and actually guided by using theoretical ab initio methods such as density functional theory (DFT), see [23,24], which can be matched to experimental findings of atomistic aspects and even used as a guidance for such.
Regarding superconductivity of high entropy carbides, e.g., in [12], a TC of 2.35 K and topological properties in (Ti0.2Zr0.2Nb0.2Hf0.2Ta0.2)C HEC are reported. Related DFT calculations show that six type-II Dirac points exist in this material, and due to the stability of the structure, robust superconductivity under pressure in this HEC superconductor is also observed. Similarly, in [13] the authors designed and produced a sequence of original bulk (Ti0.2Nb0.2Ta0.2Mo0.2W0.2)C1−xNx (0 ≤ x ≤ 0.45) superconductors, and observed that these high-entropy carbonitrides possess type-II Dirac points in the electronic band structure which imply that they have a potential as candidates to bridge superconductivity with topology. These discoveries indicate that the physical properties and potential applications establish HE carbonitrides as a promising platform for exploring unconventional physics. On the other hand, in [14] it was shown that with the rise of nitrogen concentration x in (TiNbMoTaW)1.0Nx nitride films, a large increase in TC is observed, from 0.62 K for x = 0 up to 5.02 K for x = 0.74. The observed high TC enhancement and the dome-like TC vs. x dependence have been attributed to the phonon frequency increase due to the incorporation of light N atoms and the simultaneous strengthening of the electron–phonon interaction that is probably caused by the high configuration entropy in this HEM. This high configuration entropy offers lots of options for N atoms to find the thermodynamically most appropriate positions in the lattice, and thus to create a suitable phonon mode distribution and strengthen the electron–phonon interaction.
As the introduction of carbon and nitrogen greatly affects the properties of medium and high entropy materials, the aim of the current work is to investigate the impact of C and N incorporation on the superconducting properties of NbMoTaW, mainly their impact on the transition temperature TC. The choice of this medium entropy alloy was based on the fact that practically all possible constituents of this MEA are superconducting, the TM elements (Nb: TC ≈ 9.2 K, Mo: TC ≈ 0.92 K, Ta: TC ≈ 4.4 K, W: TC ≈ 0.01 K), the corresponding carbides (NbC: TC ≈ 11 K, MoC: TC ≈ 14.3 K, TaC: TC ≈ 10 K, WC: TC ≈ 10 K), as well as the corresponding nitrides (NbN: TC ≈ 17.3 K, MoN: TC ≈ 5.8 K, TaN: TC ≈ 6 K). In tungsten nitride WN, a TC of about 4.85 K was observed in films close to the phase boundary between β-W and W2N [25]. On the other hand, based on first-principles calculations [26] it was shown that superconductivity in WN can be found and its TC enhanced significantly to about 31 K through electron doping.
In this contribution, we analyze and discuss in detail the investigations of the superconducting properties of sputtered (NbMoTaW)1CxNy films within a wide range of carbon (x) and nitrogen concentration (y) values. The obtained results show a threefold TC enhancement through C and N incorporation; nevertheless, it appears that carbon concentration plays the dominant role in this enhancement. This is probably related to the lower atomic mass of C compared to N and to the parallel increase in the electron–phonon interaction due to the different bonding of carbon atoms (compared to nitrogen) to the metallic NbMoTaW sub-lattice. However, as the highest TC values are observed at the boundary between one-phase and two-phase crystal structures, it may indicate that the TC enhancement is additionally related to the proximity of structural instability. It should be added that some results on these carbonitride films have already been published [27], this mainly concerns their composition, characterization, and mechanical properties.

2. Materials and Methods

Three series of films (I, Ib, and II, see Table 1), with different C and N concentrations, were deposited in the Cryofox 500 system (Polyteknik, Oestervraa, Denmark) using a NbMoTaW target with equimolar composition (99.9% purity) and a C target (99.9% purity) with a diameter of 76.2 mm and 4 mm thickness (Testbourne Ltd., Basingstoke, UK). However, Time-of-Flight Elastic Recoil Detection Analysis (ToF ERDA) investigations of the target revealed its contamination by about 15 at% of carbon. The substrates were (0001) sapphire wafers with a diameter of 50.8 mm and a thickness of 430 μm. The pre-deposition process involved substrate plasma cleaning, chamber evacuation below 5 × 10−3 Pa, and substrate heating to 500 °C. This was followed by the establishment of working pressure at Ar flow of 25 sccm (standard cubic centimeter per minute) and target pre-sputtering in a 25 sccm Ar + Z sccm N2 sccm atmosphere, where Z denotes the N flow. This was performed to remove the possible target contamination from previous depositions and to prepare the sputtering conditions. The film deposition parameters were optimized for the NbMoTaW film, and included 300 W power on the target at temperature of 500 °C. The nitrogen flow Z added into the argon sputtering atmosphere varied from 0 sccm up to 7 sccm. In series II, a DC power of 600 W was applied on the carbon target. In series I and 1b, the only variable was the N flow added to the Ar sputtering atmosphere; in series II, a power of 600 W was used to sputter carbon from the C target. The thickness of the produced films ranged from 350 nm to 850 nm.
The structure of the sputtered films was investigated by scanning electron microscopy (SEM) using devices FESEM/FIB Auriga Compact and EVO MA 15, Zeiss, Oberkochen, Germany. In parallel, X-ray measurements were made on Rigaku Ultima IV, Rigaku Corporation, Tokyo, Japan with parallel beam CoKα radiation and a fixed incident beam angle of 5º scan modes, to eliminate diffractions from sapphire substrate. The crystalline phases were determined by the Crystal-Impact Match! Software, (version 3) and unit cell parameters were refined by the Full-Prof program package (version April2021). The film texture was established by comparing the experimental diffractograms with calculated texture-free diffractograms.
The chemical composition of the investigated films was determined using ToF-ERDA (High Voltage Engineering Europa B.V., Amersfoort, The Netherlands) measurements at the 6 MV tandem ion accelerator and the analyzing beam with an energy of 45 MeV (for details see [28]). Recoiled ions from films were detected by the TOF-ERDA spectrometer equipped by a Gas Ionizing Chamber (High Voltage Engineering Europa B.V., Amersfoort, The Netherlands) with sensitivity of 0.02 at. %. An example of a ToF ERDA spectrum is shown in the Supplementary Materials. More details about the preparation of films and their characterization; X-ray diffraction patterns, transmission electron microscopy figures, and Raman spectra that enabled their chemical and phase composition to be determined can be found in Ref. [27].
The electrical resistance of the carbonitride films has been measured using a probe alternating current method in a 4He-cryostat with variable temperature insert in the temperature range between 1.8 K and 300 K. Four spring contacts were used to make reliable electrical contacts. When performing resistance measurements in different magnetic fields, the field was oriented perpendicularly to the plane of the film. Additional magnetization measurements between 2 K and 300 K in a magnetic field B of 1 mT were carried out in a commercial magnetic measurement system (MPMS, Quantum Design, Quantum Design, San Diego, CA, USA).

3. Additional Comments on the Choice of the Target Composition

An important parameter that has to be considered when designing a suitable initial HEA for subsequent HEA carbonization or/and nitridation is the ability of HEA metals to form thermodynamically stable carbon or nitride compounds, which varies along the periodic table (see [29,30]). This ability points to strong carbide formers for all metals (Nb, Mo, Ta, and W) of our HEA, and strong nitride formers in group 5 of the periodic table, such as Nb and Ta. On the other hand, metals in group 6, such as Mo and W, are considered as weak nitride formers. Highly stable transition metal nitrides, based on strong nitride formers, are typically so-called interstitial compounds, where N atoms at low concentrations can occupy voids in the metal structure. At higher N concentrations, these interstitial compounds usually transform into a NaCl-type (fcc) crystal structure. Whereas by contrast, the nitride bond strength decreases to the right of the periodic table, the formation enthalpy of fcc-type nitrides also decreases, and more complex structures with other stoichiometries become more common. The reason for this trend is the filling of anti- and non-bonding electronic states as the valence electron count increases [31]. Examples of complex nitride structures can also be found, for example, among tungsten nitrides which include hexagonal WN, W2N, W5N4, W5N8, rhombohedral W2N3, W7N6 or cubic W3N4 structures [32]. Nevertheless, due to the limited atom mobility during film deposition methods, such complex structure formation is not expected.
Another important parameter which has to be considered is related to the atomic size differences in HEA constituents, namely, HEAs with increasing atomic size difference prefer to form the bcc structure instead of the fcc one (see [33,34]). This preference comes from the ability of the bcc structure to accommodate larger atomic size differences with lower strain energy. If the average deviation from the composition-weighted average atomic radius of the included metals δ = (Σci (1−ri/ra)2)1/2, where ra = Σci ri is the composition-weighted average atomic radius, and ci and ri the atomic percentage and atomic radius of the i-th element, exceeds a threshold value of δ ≈ 6.4%, the bcc → fcc transition during nitridation or carbonization of HEAs may not happen [30,33,34]. When calculating this deviation for the case of Nb25Mo25Ta25W25 with atomic radius data taken from [35] (with Nb: ri = 143 pm, Mo: ri = 136 pm, Ta: ri = 143 pm, W: ri = 137 pm), a deviation of δ ≈ 4.7% can be obtained, which lies below the 6.4% threshold. Thus, from this point of view, there should be no obstacles to the formation of the fcc phase in corresponding carbides or nitrides.

4. Results and Discussion

4.1. Composition and Structure

The crystal structure of investigated (NbMoTaW)1CxNy films, which is described in more detail in [27], as well as the chemical composition, are given in Table 1. It can be seen that the transition from the bcc structure of the initial (NbMoTaW)1C0.2N0 HEA metal (polluted by carbon) to the NaCl-like fcc structure of (NbMoTaW)1CxNy films is observed in the concentration range 0 < x + y < ~0.5. At higher x + y concentrations, the films exhibit a fcc crystal structure; however, for high C concentration (x > 1.17), this structure also contains C clusters, and for high N concentration (y > 0.71), an additional hexagonal close-packed structure (hcp) begins to emerge. A schematic visualization of the fcc structure of (NbMoTaW)1CxNy carbonitrides is shown in Figure 1. Illustrated is the case with (x + y)/M < 1, i.e., when the ratio between the concentration of carbon and nitrogen atoms (x + y) and the concentration of metal atoms (M = Nb + Mo + Ta + W = 1) is sub-stoichiometric and contains vacancies.

4.2. Resistance and Magnetization Results

The temperature dependencies of electrical resistance R(T) of the investigated films, normalized to their resistance values R0 just above the superconducting transition temperature onset, are shown in Figure 2. Abrupt changes (drops) of R(T)/R0 to zero in this figure represent typical superconducting transitions. The corresponding TC values have been defined as the temperatures at which R(T) reaches the 50% value of its normal state resistance R0. These, by electrical resistance determined TC values, have been confirmed for some films by diamagnetic drops parallel magnetization measurements (see Figure 3). However, it is interesting that on (Nb0.35Mo0.17Ta0.23W0.25)C0.80N0 and (Nb0.32Mo0.18Ta0.24W0.26)-C1.17N0.41) films in series II, which contain high C concentrations, two TC onsets were observed on resistance R(T)/R0 dependencies. On (Nb0.35Mo0.17Ta0.23W0.25)C0.80N0, a higher one at 9.2 K and a lower one at 8.28 K, and on (Nb0.32Mo0.18Ta0.24W0.26)C1.17N0.41), a higher one 10.1 K and a lower one at 9.6 K. Nevertheless, the magnetization measurements (see Figure 3) point to the fact that at TC values of 8.28 K and 9.6 K, respectively, the entire films go into the superconducting state. It should be noted that the inaccuracy of transition temperature determination, usually given by the ratio Δ(TC)/TC, where Δ(TC) represents the temperature range between R(T)/R0 = 0.9 and R(T)/R0 = 0.1, was for the C–rich samples Δ(TC)/TC ≈ 3%, and for other films Δ(TC)/TC ≈ 0.5%.
All obtained TC values are shown in Figure 4 as a dependence of N concentration y (a) and C concentration x. These dependencies show that high C concentration plays a dominant role in the about threefold TC enhancement. Moreover, one can see that the highest TC values of 6.3 K for the nitrogen-rich series (with y ≈ 0.7, see Series Ib) and of 9.6 K for the carbon-rich series (with x = 1.17 and y = 0.41, see Series II), are observed in samples at the verge of fcc structure instability. Namely, at higher concentrations, two-phase structures begin to form: a fcc + hcp structure for y > 0.71 (see Series 1b) and a fcc + C clusters structure for x + y > 1.58 (see Series II). This indicates that in investigated carbonitrides the TC enhancement is also related to the proximity of structural instability, as predicted in [36].
On the other hand, in the case of samples with a considerably over-stoichiometric sum of N and C concentrations (when x + y > 2), no superconducting transition was observed. Reasons for this are discussed in the next part.
As it can also be seen from Figure 4a, the TC dependence on N concentration y in the nitrogen-rich series (Series I) is not monotonic. With increasing y, TC first decreased from an initial value of 3.25 K to 2.49 K at y = 0.23, then gradually increased to a maximum value of TC = 5.61 K at y = 0.71. The initial decline of TC is apparently associated with the transition of the bcc structure of the initial HEA lattice to the fcc structure of HEA nitrides. The N concentration range in which the bcc → fcc structural change takes place is apparently a region with a high degree of disorder (also containing a mixture of bcc and fcc clusters). This high degree of disorder can lead to suppression of superconductivity (see [37,38]). Furthermore, it was shown in [38] that nonmagnetic impurities destroy superconductivity when the residual resistivity exceeds about 1 μΩ cm, i.e., when the carrier mean free path l falls below the superconducting coherence length ξ. To make an estimate, according to [39] the Ginzburg–Landau coherence length ξGL(0) can be used, calculated as ξGL(0) = (Φ0/2πBc2(0))1/2, where Φ0 denotes the magnetic flux quantum and Bc2 the upper critical magnetic field, reaching a value of ~15 nm in, for example, (NbTa)0.67(MoHfW)0.33 HEA superconductor. Simultaneously, the theoretical analysis of the electronic structure of another HEA superconductor (ScZrNb)1−x(RhPd)x, with 0.35 < x < 0.45 [40], leads to an electron mean free path between 3.2 Å and 9.2 Å, i.e., to an l < 1 nm. Thus, the high degree of disorder that is apparently present in the bcc → fcc structural transition area is likely the main cause for the observed TC suppression.
The second series of nitrogen-rich films (Series Ib), in which a higher N concentration was achieved, exhibits the highest TC value of 6.3 K in the fcc phase, with x = 0.68 (see Figure 4, red points). But, at higher N concentration (x = 0.73), a two-phase (fcc + hcp) crystal structure forms and TC starts to decrease. This points to the fact that the highest TC is observed in the fcc phase, but near the border between fcc and (fcc + hcp) phases.
Results on C-rich films, on the other hand, show that C incorporation leads to higher TC values than in the case of N incorporation. According to the conventional Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity, the stronger influence of carbon incorporation compared to nitrogen incorporation may come from its lower atomic mass, which leads to a phonon frequency increase. But the enhancement of the electron–phonon interaction may also play an important role due to a different valence electron count (VEC) of C atoms (having a VEC(C) = 4, see the periodic table of elements) compared to N atoms (in this case VEC(N) = 5), which can lead to different bonding between carbon and metal (compared to nitrogen and metal) atoms. Therefore, even if the C incorporation and N incorporation similarly influence the TC at their higher concentrations, the more pronounced TC enhancement by carbon seems to be a result of its lower atomic mass, and different configuration of valence electrons that leads to a stronger electron–phonon interaction. Also in this case, the highest TC value of 9.6 K is obtained in the fcc phase, but at the border between two phases, the fcc phase and the (fcc + C clusters) phase, for concentrations where x + y > 1.58 (see Table 1, Series II). A view of the chemical bonding (not the electron–phonon interaction) in TM carbides, nitrides, and carbonitrides can be found, e.g., in [31,41].
In addition, with increasing nitrogen and carbon concentrations, a tendency to a semiconducting-like temperature dependence of resistance R(T) can be observed, i.e., with values R0 > R300, (see the R300/R0 ratios in Table 1). This is caused by the gradual localization of conduction electrons in metallic NbMoTaW film through their bonding to incorporated N and C atoms.

4.3. TC vs. VEC—Transition Temperature Dependence on the Valence Electron Count

To take a closer look at how TC develops with the overall VEC of studied high entropy alloy carbonitrides (including the VEC of N atoms with VEC = 5 and C atoms with VEC = 4), Figure 5 shows this dependence for the above-discussed (NbMoTaW)1CxNy films. The upper gray trend line in this figure with a dome-like shape represents the TC vs. VEC dependence for transition metals and their alloys in the crystalline form taken from ref. [42]. This trend line is often referred to as the Matthias TC vs. VEC rule and exhibits a maximum of TCmax ≈ 11 K near VEC ≈ 4.7 el./atom (a second dome-like dependence obtained in [42], not shown in Figure 5, with a maximum of TCmax ≈ 16 K is formed at VEC ≈ 6.5 el./atom, see also [18,20]).
From the displayed TC vs. VEC dependencies one can see that the TC values of all carbonitrides lie inside the dome bordered by the trendline [42] (including the carbonitrides studied in [13]). And, also from here it turns out that the incorporation of N and C into HEAs has a different impact, and that high C concentration leads to a more pronounced TC enhancement. However, as for example, the TC of MoC (with a total VEC = 5) reaches a value of 14.3 K, which exceeds the value of TCmax ≈ 11 K, it is not excluded that also some high entropy carbonitrides or high entropy carbides will not obey the Mattias TC vs. VEC rule [42] and provide a higher TC.
It should also be noted that in the investigated carbonitride films with a high over-stoichiometry (i.e., with a sum of concentrations x + y > 2, see the last line in Table 1) no superconducting TC was detected. This is probably caused by the strong localization of mobile conduction electrons of the metallic NbMoTaW sublattice due to their bonding to the high concentration of C and N atoms. This localization leads to an insulating state, which was documented by the observation of an electrical resistance increase with decreasing temperature. Similar results about the localization of mobile conduction electrons were observed in zirconium nitride ZrNy with a high N concentration [43], where for y > 1.15, an insulating state was detected.

4.4. Upper Critical Magnetic Field Bc2

To obtain further information about the superconducting properties of the (NbMoTaW)1CxNy films, resistance R(T) measurements in different magnetic fields B were carried out. Figure 6a shows the R(T) dependence of these films exposed to magnetic fields between 0 T and 8 T, demonstrating the decrease of TC with increasing B. As a criterion for the TC determination in magnetic fields, we used again the temperature value at which 50% of the normal state resistance R0 just above TC was reached. From these results we constructed the corresponding upper critical magnetic field Bc2 vs. T phase diagrams (see Figure 6d). The observed Bc2 vs. T dependencies were described by the Werthamer–Helfand–Hohenberg (WHH) model [44], which for a nitrogen-rich sample with x = 0.26 and y = 0.71 (TC = 5.61 K) provides a Bc2 value of 9.16 T and for a carbon-rich sample with x = 1.17 and y = 0.41 (TC = 9.6 K) a Bc2 value of ~13.8 T. On the other hand, the nitrogen-free HEA (x = 0) shows a Bc2 value of ~4 T. It should be added that in the WHH model, both spin paramagnetism and spin–orbit scattering are taken into account; however, it can be seen that spin–orbit interaction destroys the spin as a good quantum number and brings the superconducting state closer to that of the normal one (and therefore has a direct implication for TC).
Thus, the determined zero-temperature Bc2(0) values (see Table 1) provide Bc2(0)/TC ratios below 1.86 T/K and point to the fact that the upper critical field in the investigated HEA nitrides does not exceed the weak-coupling Pauli paramagnetic pair breaking limit. Namely, in the weak-coupling BCS theory of superconductivity, the Pauli paramagnetic pair breaking limit is BPauli = Δ(0)/(√2 μB) ≈ 1.86[T/K] TC, with μB being the Bohr magneton and Δ(0) the superconducting gap at T = 0 (see [45,46]). The mentioned Pauli paramagnetic limit may be different for strong-coupled superconductors [47,48].

5. Conclusions

Transport and magnetization investigations of sputtered (NbMoTaW)1CxNy carbonitride films show that the concentration of C plays the dominant role in the observed about threefold enhancement of the superconducting transition temperature TC. This is probably related to the lower atomic mass of C compared to N, which can lead to a phonon frequency increase and to the parallel increase in the electron–phonon interaction due to different bonding of C atoms (compared to N atoms) to the metallic sub-lattice. However, as the highest TC values are observed at the verge of the fcc structure stability (for concentrations where y > 0.71 and x + y > 1.58 two-phase structures begin to form), it indicates that the TC enhancement is additionally related to the proximity of structural instability.
Further investigations will be needed, especially on high-entropy carbonitrides in the form of bulk samples, from which it would be possible to determine exactly how the electronic density of states, the phonon modes, and the electron–phonon interaction change with C and N incorporation, especially at their higher concentrations.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/ma18163732/s1, Figure S1: Time-of-flight Elastic Recoil Detection Analysis (ToF ERDA) measurement to determine the chemical composition of the Series Ib (NbMoTaW)1CxNy film marked in Table 1 as “new, with N-flow 7N”: (a)—live record with the identification of elements related to each curve; (b)—concentration depth profiles calculated from the curves of individual elements.

Author Contributions

Conceptualization, K.F. and F.L.; Methodology, F.L., P.H., J.D., D.A., and M.L.; Formal analysis, G.P., S.G., and K.F.; Investigation, G.P., S.G., O.O., and J.Z.; Resources, G.P. and F.L.; Data curation, G.P. and S.G.; Writing—original draft preparation, K.F.; Writing—review and editing, G.P., F.L., S.G., and K.F.; Visualization, G.P., S.G., J.Z., and K.F.; Supervision, K.F. and F.L.; Project administration, G.P. and F.L.; Funding acquisition, G.P. and F.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Slovak Research and Development Agency under the contracts no. APVV-23-0624 and APVV-21-0042, by the Slovak Scientific Grant Agency under Contract No. VEGA 2/0091/24 and by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under project No. 09I03-03-V04-00281. Liquid nitrogen for experiments was sponsored by U. S. Steel Košice, s.r.o.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in the study are included in the article; further inquiries can be directed to the corresponding author.

Acknowledgments

We are grateful for the help of M. Gabániová with the illustration of the fcc structure of carbonitrides.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Materials 18 03732 g001
Figure 1. Schematic illustration of the fcc structure of (NbMoTaW)1CxNy carbonitrides. Illustrated is the case with (x + y)/M < 1, i.e., when the ratio between the concentration of carbon and nitrogen atoms (x + y) and the concentration of metal atoms (M = Nb + Mo + Ta + W = 1) is sub-stoichiometric and contains vacancies (unoccupied edges of the cube). Metal atoms are shown as large spheres, carbon atoms as gray spheres, and nitrogen atoms as small, green spheres.
Figure 1. Schematic illustration of the fcc structure of (NbMoTaW)1CxNy carbonitrides. Illustrated is the case with (x + y)/M < 1, i.e., when the ratio between the concentration of carbon and nitrogen atoms (x + y) and the concentration of metal atoms (M = Nb + Mo + Ta + W = 1) is sub-stoichiometric and contains vacancies (unoccupied edges of the cube). Metal atoms are shown as large spheres, carbon atoms as gray spheres, and nitrogen atoms as small, green spheres.
Materials 18 03732 g001
Materials 18 03732 g002
Figure 2. R(T)/R0 dependencies of (NbMoTaW)1CxNy films in zero magnetic field, where R(T) denotes the temperature dependence, and R0 is the resistance just above the transition temperature (TC) onset. The samples are labeled based on Table 1.
Figure 2. R(T)/R0 dependencies of (NbMoTaW)1CxNy films in zero magnetic field, where R(T) denotes the temperature dependence, and R0 is the resistance just above the transition temperature (TC) onset. The samples are labeled based on Table 1.
Materials 18 03732 g002
Materials 18 03732 g003
Figure 3. Normalized DC magnetization dependencies M(T)/M(2K) in field of 1 mT for some (NbMoTaW)1CxNy films. Samples are labeled based on Table 1.
Figure 3. Normalized DC magnetization dependencies M(T)/M(2K) in field of 1 mT for some (NbMoTaW)1CxNy films. Samples are labeled based on Table 1.
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Materials 18 03732 g004
Figure 4. Transition temperature (TC) dependencies of the (NbMoTaW)1CxNy films: (a)—on nitrogen concentration y, (b)—on carbon concentration x, and (c)—as a three-dimensional display of TC vs. x = C/M and y = N/M.
Figure 4. Transition temperature (TC) dependencies of the (NbMoTaW)1CxNy films: (a)—on nitrogen concentration y, (b)—on carbon concentration x, and (c)—as a three-dimensional display of TC vs. x = C/M and y = N/M.
Materials 18 03732 g004
Materials 18 03732 g005
Figure 5. TC vs. VEC dependencies for investigated carbonitrides. The upper gray line with a dome-like shape shows the TC vs. VEC dependence (Matthias rule) for transition metals and their alloys in the crystalline form taken from [42]. Gray points represent Series II; green and red points represent the Series I and Series Ib of (NbMoTaW)1CxNy films. Black squares show the approximative course for the bulk (Ti0.2Nb0.2Ta0.2Mo0.2W0.2)C1−xNx (0 ≤ x ≤ 0.45) superconductors [13]. The dotted lines connecting the points are provided as a guide for the eyes.
Figure 5. TC vs. VEC dependencies for investigated carbonitrides. The upper gray line with a dome-like shape shows the TC vs. VEC dependence (Matthias rule) for transition metals and their alloys in the crystalline form taken from [42]. Gray points represent Series II; green and red points represent the Series I and Series Ib of (NbMoTaW)1CxNy films. Black squares show the approximative course for the bulk (Ti0.2Nb0.2Ta0.2Mo0.2W0.2)C1−xNx (0 ≤ x ≤ 0.45) superconductors [13]. The dotted lines connecting the points are provided as a guide for the eyes.
Materials 18 03732 g005
Materials 18 03732 g006
Figure 6. (a) Temperature dependencies of normalized resistance R(T)/R0 for the NbMoTaW)1CxNy film of Series I with x = 0.2 and y = 0.0, (b) Series Ib with x = 0.32, and y = 0.68 and (c) Series II with x = 1.17 and y = 0.41 in increasing magnetic field. (d) Temperature dependencies of the upper critical field Bc2 (symbols) for some of the (NbMoTaW)1CxNy films together with corresponding fits based on the WHH model [44] (lines). The estimated Bc2(0) values are listed in Table 1.
Figure 6. (a) Temperature dependencies of normalized resistance R(T)/R0 for the NbMoTaW)1CxNy film of Series I with x = 0.2 and y = 0.0, (b) Series Ib with x = 0.32, and y = 0.68 and (c) Series II with x = 1.17 and y = 0.41 in increasing magnetic field. (d) Temperature dependencies of the upper critical field Bc2 (symbols) for some of the (NbMoTaW)1CxNy films together with corresponding fits based on the WHH model [44] (lines). The estimated Bc2(0) values are listed in Table 1.
Materials 18 03732 g006
Table 1. Overview of data obtained from performed investigations on (NbMoTaW)1CxNy films. The first column indicates the sample composition determined by ToF ERDA, the name of the corresponding sample from [27] and the measurements performed on the sample. The second column shows the dominating crystal structure of individual films (here bcc stands for body-centered cubic, fcc for face-centered cubic, and hcp for hexagonal close-packed; details can be found in [27]). In the next columns, R300/R0 shows the resistance ratio, where R300 denotes the film resistance at 300 K and R0 the resistance just above the TC onset, TC denotes the superconducting transition temperature (the transition onset value for two samples is given in parentheses), and Bc2 the upper critical field in Tesla. The last column represents the valence electron count (VEC), i.e., the average number of valence electrons per atom in el./atom (including metal, carbon, and nitrogen atoms). n.d. in some table cells stands for not determined.
Table 1. Overview of data obtained from performed investigations on (NbMoTaW)1CxNy films. The first column indicates the sample composition determined by ToF ERDA, the name of the corresponding sample from [27] and the measurements performed on the sample. The second column shows the dominating crystal structure of individual films (here bcc stands for body-centered cubic, fcc for face-centered cubic, and hcp for hexagonal close-packed; details can be found in [27]). In the next columns, R300/R0 shows the resistance ratio, where R300 denotes the film resistance at 300 K and R0 the resistance just above the TC onset, TC denotes the superconducting transition temperature (the transition onset value for two samples is given in parentheses), and Bc2 the upper critical field in Tesla. The last column represents the valence electron count (VEC), i.e., the average number of valence electrons per atom in el./atom (including metal, carbon, and nitrogen atoms). n.d. in some table cells stands for not determined.
Sample Composition
(Sample Label in [25]), Measurements		Crystal
Structure		R300/R0
(RRR)		TC
[K]		Bc2(0)
[T]		VEC
el./at.
Series I
(Nb0.23Mo0.24Ta0.26W0.27)1.0C0.20N0.0
(4ME-C(0)-0N-a), R(T), M(T)		bcc1.0043.254.055.235
(Nb0.24Mo0.25Ta0.25W0.26)1.0C0.24N0.23
(4ME-C(0)-1N), R(T)		bcc with
fcc		0.9892.492.705.180
(Nb0.24Mo0.25Ta0.25W0.26)1.0C0.25N0.43
(4ME-C(0)-2N), R(T)		fcc0.9753.903.945.141
(Nb0.24Mo0.26Ta0.25W0.25)1.0C0.24N0.55
(4ME-C(0)-3N), R(T)		fcc0.9404.836.555.140
(Nb0.24Mo0.26Ta0.24W0.26)1.0C0.24N0.66
(4ME-C(0)-4N), R(T)		fcc0.9055.307.575.140
(Nb0.24Mo0.26Ta0.24W0.26)1.0C0.26N0.71
(4ME-C(0)-5N), R(T), M(T)		fcc0.8475.619.165.126
Series Ib
(Nb0.20Mo0.29Ta0.25W0.26)1C0.29N0.53
(new, with N flow 3N), M(T)		fccn.d.5.2n.d.5.108
(Nb0.20Mo0.29Ta0.25W0.26)1C0.30N0.58
(new, with N flow 4N), M(T)		fccn.d.5.9n.d.5.092
(Nb0.20Mo0.29Ta0.25W0.26)1C0.32N0.68
(new, with N flow 5N), M(T), R(T)		fcc0.8326.39.305.091
(Nb0.22Mo0.28Ta0.24W0.26)1C0.36N0.73
(new, with N flow 7N), M(T)		fcc with hcpn.d.--5.046
Series II
(Nb0.31Mo0.18Ta0.25W0.26)1.0C0.76N0.0
(4ME-C(500)-0N-a), R(T), M(T)		fcc1.0018.789.344.816
(Nb0.31Mo0.18Ta0.25W0.26)1.0C0.77N0.0
(4ME-C(600)-0N-b), R(T)		fcc0.9398.718.704.807
(Nb0.35Mo0.17Ta0.23W0.25)1.0C0.80N0.0
(4ME-C(700)-0N-c), R(T) 		fcc0.9898.28 (~9.2)n.d.4.931
(Nb0.32Mo0.18Ta0.24W0.26)1.0C1.17N0.41
(4ME-C(600)-2N), R(T), M(T)		fcc0.9399.60
(~10.1)		13.834.707
(Nb0.32Mo0.19Ta0.24W0.25)1.0C1.18N1.13
(4ME-C(600)-5N), R(T) 		fcc with
C clusters		0.599--4.771
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Pristáš, G.; Gabáni, S.; Hviščová, P.; Dobrovodský, J.; Albov, D.; Lisnichuk, M.; Onufriienko, O.; Zorych, J.; Lofaj, F.; Flachbart, K. Effect of Carbon and Nitrogen Concentrations on the Superconducting Properties of (NbMoTaW)1CxNy Carbonitride Films. Materials 2025, 18, 3732. https://doi.org/10.3390/ma18163732

AMA Style

Pristáš G, Gabáni S, Hviščová P, Dobrovodský J, Albov D, Lisnichuk M, Onufriienko O, Zorych J, Lofaj F, Flachbart K. Effect of Carbon and Nitrogen Concentrations on the Superconducting Properties of (NbMoTaW)1CxNy Carbonitride Films. Materials. 2025; 18(16):3732. https://doi.org/10.3390/ma18163732

Chicago/Turabian Style

Pristáš, Gabriel, Slavomír Gabáni, Petra Hviščová, Jozef Dobrovodský, Dmitry Albov, Maksym Lisnichuk, Oleksandr Onufriienko, Janina Zorych, František Lofaj, and Karol Flachbart. 2025. "Effect of Carbon and Nitrogen Concentrations on the Superconducting Properties of (NbMoTaW)1CxNy Carbonitride Films" Materials 18, no. 16: 3732. https://doi.org/10.3390/ma18163732

APA Style

Pristáš, G., Gabáni, S., Hviščová, P., Dobrovodský, J., Albov, D., Lisnichuk, M., Onufriienko, O., Zorych, J., Lofaj, F., & Flachbart, K. (2025). Effect of Carbon and Nitrogen Concentrations on the Superconducting Properties of (NbMoTaW)1CxNy Carbonitride Films. Materials, 18(16), 3732. https://doi.org/10.3390/ma18163732

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