Anomalous Charge State Evolution and Its Control of Superconductivity in M3Al2C (M = Mo, W).

The charge states of elements dictate the behavior of electrons and phonons in a lattice, either directly or indirectly. Here, we report the discovery of an anomalous charge state evolution in the superconducting M3Al2C (M = Mo, W) system, where electron doping can be achieved through "oxidation." Specifically, with the continuous removal of electron donor (Al) from the structure, we found an electron doping effect in the negatively charged transition metals. Over a certain threshold, the charge state of transition metals goes through a sudden reversion from negative to positive, which leads to a subsequent structure collapse. Concomitantly, the previous robust superconducting transition temperatures (Tcs) can be flexibly modulated. Detailed analysis reveals the origin of the superconductivity and the intimate relationship between the charge state and the electron-phonon coupling constant. The peculiar charge state in M3Al2C plays an important role in both its structure and superconductivity.

Introduction

The charge state of atomic constituents in a solid is controlled by the chemical bonding strength and the surrounding structural environment (Pauling, 1960, Repp et al., 2004). It is taken for granted that continuously increasing or removing carrier donors from a system will monotonically shift the charge state of the remaining atoms, if keeping the anions intact. Take LiCoO2 and LiFePO4, for example, the oxidation reaction at the anode (extraction of Li) elevates the charge state of the transition metals to a higher value. Such a behavior has been widely accepted with seldom violations. Deliberate modulation of the charge state through physical or chemical routes could bring about rich phenomena, like structural transition and superconductivity.

Mo3Al2C attracts considerable attention owing to the relatively high superconducting transition temperature (T) and its noncentrosymmetric structure, which holds the promise of spin-triplet pairing superconductivity (Bauer et al., 2010, Koyama et al., 2011, Koyama et al., 2013, Kuo et al., 2012, Karki et al., 2010, Bonalde et al., 2011, Bauer et al., 2014). Meanwhile, there is accumulated evidence for a conventional s-wave pairing; it remains indecisive which phonon mode is responsible for the formation of Cooper pairs (Karki et al., 2010, Bonalde et al., 2011). Furthermore, only one T (= 9 K) is observed, despite the variation of nominal composition and synthesis conditions (Bauer et al., 2010, Bauer et al., 2014). This robustness is rooted in its structure. As shown in Figure 1A, the well-established structure of Mo3Al2C (P4132) can be viewed as four Mo6C octahedra interconnected with each other by corner sharing to form a framework while leaving Al atoms to fill the interstices. Theoretical calculation shows only carbon vacancies could exist, and the Mo and Al sites tend to be fully occupied (Reith et al., 2012). The C content is suggested to be controlled by the synthesis temperature and will influence the superconductivity (Reith et al., 2012). However, samples prepared at different temperatures show quite similar Ts, indicating the high stability of the C confined inside of the Mo cage. On the other hand, the substitution of Nb with poor 4d electrons (hole doping) or Ru with rich 4d electrons (electron doping) at the Mo site slightly lowers the T, but dramatically reduces the superconducting volume fraction (Ramachandran et al., 2016). This deterioration of superconductivity cannot be simply ascribed to a carrier doping effect, but is more suitable to a phase separation phenomenon.

Figure 1

Chemical Etching Process and Valence Evolution

(A) Crystal structure of M3Al2C (M = Mo, W) and the zoom-in of the M6C octahedron to illustrate the chemical etching process.

(B) The collapsed structures of WC and Mo2C formed by further etching. The blue and red arrows at the bottom indicate the valence evolution of the transition metals with the continuous extraction of Al.

Very recently, we reported the discovery of an isostructural phase of W3Al2C with T = 7.6 K (Ying et al., 2019). The replacement of Mo 4d to W 5d orbitals gives rise to a larger specific-heat jump and superconducting gap energy. Different from its Mo-counterpart, W3Al2C shows a significant deficiency at the Al site according to the composition analysis (Ying et al., 2019). This observation gives us a clue to understand the rigid T and the origin of the superconductivity in both Mo3Al2C and W3Al2C. From a structural point of view, the interconnected W6C and Mo6C subunits may be viewed as nanoporous structures, whereas Al ions are weakly connected to the surrounding metals. Considering the amphoteric properties of aluminum toward both acids and bases, it may provide an ideal tuning knob to control the properties of this family. Similar strategies have been applied to the preparation of several MXene materials (Naguib et al., 2011, Li et al., 2018, Alhabeb et al., 2017, Xuan et al., 2016).

Here, by applying a chemical etching method, we successfully extract Al from M3Al2C (M = Mo, W). Most prominently, the combination of theoretical calculations, heat capacity, and X-ray photoelectron spectroscopy (XPS) measurements reveals an anomalous electron doping effect by extracting electron donors (Al), which is in sharp contrast to the preconceived knowledge. Further extraction leads to a sudden reversion of the charge state in the transition metals and concomitantly collapses the crystal structure from corner sharing to edge and face sharing. As a consequence, the previous rigid T can be continuously shifted while keeping a full superconducting volume fraction. Based on the Debye-Einstein analysis of the high temperature heat capacity and phonon calculations of the samples with different Al contents, we suggest the superconductivity in the M3Al2C system originates from the charge state of M, which leads to the hardening of the M-M and M-C vibrations.

Results and Discussion

Intrinsic Aluminum Vacancy

We first investigate the influence of Al vacancy toward the dynamical stability of the structure. According to Figure 2, the phonon dispersions of fully occupied W3Al2C show imaginary optical modes all over the first Brillouin zone. In Mo3Al2C, part of the reciprocal space (e.g., the R point) is free from imaginary frequencies (Reith et al., 2012) and its absolute values are also smaller than that of W3Al2C, indicating vacancies should appear in W3Al2C to stabilize the P4132 cubic structure. Generally, the inclusion of vacancies at all three sites (Al: Figure 2B, W and C: Figure S1) can eliminate the imaginary modes. A scrutiny of the relaxed structures reveals an opposite effect of Al and C vacancies toward the W6C subunit. The inclusion of one C vacancy increased the average W-C bond length by 1.0% and the corresponding W6C octahedral volume by 2.0%, agreeing well with that of Mo3Al2C (1.4% and 3.6%) (Reith et al., 2012). However, Al vacancy shrank the W-C bond length and octahedral size by −0.3% and −2.6%, respectively. This contradiction implies the existence of charge redistribution and will be discussed later.

Figure 2

Intrinsic Aluminum Vacancy

(A and B) Phonon dispersions up to 5 THz of fully occupied W3Al2C and of W3Al1.75C. Imaginary frequencies are shown as negative values.

(C) Vacancy formation energy for one W, Al, or C atom in the W3Al2C unit cell from 0 to 2,100 K. The vacancy formation energy of Al in Mo3Al2C is superimposed for comparison. The thermal electronic contribution Felectron is considered (see Section 2).

Previous calculation showed that only C vacancies are allowed in the Mo3Al2C (Reith et al., 2012). It is thus interesting to observe appreciable Al deficiencies in W3Al2C judging from its chemical composition (Ying et al., 2019). We tackle this issue by analyzing the vacancy formation energies in W3Al2C. As we know, standard DFT calculations are only valid at T = 0 K, and the formation energy is defined as . X denotes the extracted element and there are four chemical formula W3Al2C in a unit cell. To describe the synthesis condition, we included the temperature-dependent vibrational free energy Fphonon and thermal electronic contribution Felectron in the calculations, and thus, the formation energy can be written as . Details of the calculation can be found in the Methods section and the definition of and are similar to that of . As shown in Figure 2C, the vacancy formation energy of W, Al, and C are all negative above certain temperatures, which means the spontaneous vacancy formation are favored at the synthesis temperature. This is in sharp contrast to that of Mo3Al2C, where only the formation of C vacancies are possible (Reith et al., 2012). We note that the previous calculation did not consider the Felectron. Thus, the vacancy formation energy of Al in Mo3Al2C including Felectron was superimposed in Figure 2C for comparison. We will not consider the W vacancies as its formation energy is relatively large compared with that of Al and C vacancies. Prominently, the vacancy formation energy of Al of W3Al2C is even smaller than that of C over the whole temperature range. Considering structural rigidity of M and C as mentioned in the introduction, we investigated the role of Al vacancies in M3Al2C.

Because of the amphoteric property of Al and its weak connection with the surrounding transition metals, it is possible to tune the content of Al through a soft chemical method. Here, NaOH was used as an etching agent. The XRD refinements of the raw and etched W3Al2−C0.8 are shown in Figure S2. Composition analyses show that the Al content decreases from 1.75 to 1.4 in W3Al2−C0.8 and 2.0 to 1.52 in Mo3Al2−C0.85. The M6C building blocks are found to be quite rigid, and their lattice parameters only shrank 0.2% and 0.25% for W3Al1.4C0.8 and Mo3Al1.52C0.85, respectively. The shrinkage of the W-C bond (−0.6%) and octahedron volume (−1.6%) after etching is consistent with the calculation results.

Considering no peak splitting at both low and high diffraction angles of the Al-extracted sample (Figure S3A) and the continuous peak evolution (Figure S3B), the extraction of aluminum can be viewed as homogeneous without phase separation. As no superstructure peaks can be identified from the XRD diffraction, the remaining Al should be randomly distributed. It is thus not clear why only about one-quarter of Al can be extracted from the porous interstices for both Mo and W cases. Further reaction at a moderate temperature (below 140∘C) did not increase the content of Al vacancies. However, a slight increase of the reaction temperature to above 150∘C completely collapses the structure from M3Al2C to WC or Mo2C with a sudden loss of all the structural aluminum. To understand all these phenomena, it is necessary to trace the evolution of the charge state during the reaction (Figure 1B).

Anomalous Charge State Evolution

Bader analysis of the charge transfer could give us a deeper insight. To our surprise, the charge state of W after the extraction becomes more negative from [W]−0.37 in Figure 1B to [W]−0.43 in Figure 3C. At the same time, the carbon also becomes more negatively charged from [C]−1.42 to [C]−1.47. To balance the charge state, the average electron donation of Al raises from [Al]+1.08 to [Al]+1.37, which is to say, the loss of electrons from one Al vacancy is overcompensated by other Al atoms. The same conclusion is applied for the charge state evolution in Mo3Al2C. Because the valence of Mo and W in the binary carbides must be positive, one could expect the sudden reversion of the charge state in the transition metals from negative to positive at further extraction. This observation well explains the existence of a lower limit of Al in M3Al2−C0.8 and agrees well with the sudden phase transition from the corner-sharing P4132 structure to an edge/face-sharing WC or edge/corner-sharing Mo2C.

Figure 3

Anomalous Charge State Evolution

(A–C) Bader analysis of the charge states for fully occupied W3Al2C, W3Al2C0.75 (one carbon vacancy), and W3Al1.75C0.75 (one Al and one C vacancies).

(D) XPS and peaks of W3Al1.40C0.8, W3Al1.75C0.8, pure W metal, and WO3. The peak position was calibrated by using the absorbed C1s as shown in Figure S4, where the signals of absorbed carbon and the lattice carbon can be clearly distinguished. The positively charged W in WO3 shifted oppositely to a higher binding energy. The extra two peaks of W3Al1.4C0.8 in (D) come from the oxidation state of WO2+.

We substantiate the results of calculation by XPS. As shown in Figure 3D, a systematic shift of the W4f peaks to a lower binding energy can be seen clearly from W metal to W3Al1.75C0.8 and W3Al1.4C0.8, indicating the charge state of W becomes more negative. From Figure S4, we can see that the peak of structural C1s also moves to a lower binding energy (more negatively charged), in line with the Bader analysis. Since both W and C are inert toward NaOH and C ion is embedded inside the W cage, the observed charge state evolution cannot be caused by reducing the number of anions. We also measured the thermal desorption spectroscopy (TDS) spectra of the etched W3Al1.4C0.8 and Mo3Al1.52C0.85. No other species such as H+ or OH− can be detected.

This anomalous charge state evolution, to our knowledge, has not been reported before. The negative valences and the anomalous charge state evolution of Mo3Al2−C0.85 are shown Figure S5. Although proved theoretically and experimentally for M3Al2−C0.8, a clear understanding of this peculiar behavior is still lacking. The choice of elements with proper electron affinity should be crucial, but whether the structure is an important ingredient is unknown. The MXene material can be an independent arbitrator. However, species like -O or -OH are always present after the NaOH treatment to compensate the dangling bonds in MXenes, which complicate further analyses.

Tunable Superconductivity

As shown in Figure 4A, the T of etched W3Al2−C0.8 shifts from 7.5 to 6.4 K. For Mo3Al2−C0.85, a much significant decrease of T from 9.1 to 5 K is achieved. It is possible to finely control the T by varying the reaction time, as illustrated in Figure 4B. A prominent feature of the etched W3Al2−C0.8 and Mo3Al2−C0.85 is that their diamagnetization signal reach χ = −1 at low temperature. Although the etched W3Al1.4C0.8 shows a nearly full diamagnetism, we note that a core-shell structure with a non-superconducting bulk embedded inside a superconducting shell sometimes may give a similar signal. It is thus important to exclude this possibility by using a bulk sensitive method such as heat capacity. A shown in Figure S6, a full gap opening toward 0 K is reached, confirming the bulk superconductivity in the Al-etched sample. Thus the superconducting volume of W3Al2−C0.8 remains almost the same before and after etching. This is quite different from the previous report of Nb- and Ru-doped Mo3Al2C where the change of T is barely observable but the superconductivity is quickly quenched by doping (Ramachandran et al., 2016). A plausible explanation is given in the discussion.

Figure 4

Tunable Superconductivity

(A and B) The magnetization of W3Al2−C0.8 and Mo3Al2−C0.85 before and after etching. The susceptibilities were calibrated using Pb as a reference. The kink at ∼3 K in (B) comes from the residual Mo2C during arc melting, where the evaporation of Al is inevitable.

(C) Heat capacity of W3Al2−C before and after etching. The measurements were performed under an external field of 9 T to suppress the T to a lower temperature.

(D) Density of states (DOS) for W3Al1.75C0.75 and W3Al1.5C0.75. The electrons at the E remain to be the same before and after etching.

To determine whether the decline of T is related to carrier doping, we measured the low temperature heat capacity of the raw and etched W3Al2−C0.8. The measurement was carried out under a magnetic field of H = 9 T to suppress the T to a lower value, and the relation of versus T2 was plotted. As shown in Figure 4C, the Sommerfeld coefficients of raw and etched samples are almost identical (γ = 7.0∼7.2 mJ⋅mol−1 K−2). Considering the small change of the lattice parameter after extraction (0.2%), the effective mass of the electron and the bands could be viewed as unchanged, and the charge transfer for both samples should be roughly the same. This result is confirmed by the identical density of states (DOS) at the Fermi surface (Figure 4D). Quantitatively, the DOS for both samples is located at around 2.45 states/eV per formula unit. Substituting this value into the formula , where R is the gas constant, we get γ ∼ 5.88 mJ⋅mol−1⋅K−2, which closely agrees with the extracted value from the heat capacity.

Vibration Modes

The tunable T provides us an opportunity to clarify the origin of superconductivity in the M3Al2C system. From Figure 4C, the Debye temperature can be extracted from the slope of the heat capacity, which is 259 and 274 K for raw and etched W3Al2−C0.8, respectively. We temporarily use the McMillan expression (McMillan, 1968) to estimate the electron-phonon coupling constant (λ):where is the Debye vibration frequency. The residual screened Coulomb repulsive interaction μ∗ can be viewed as a constant for a certain system with a typical value ranging from 0.1 to 0.16. Intuitively, the T should be positively correlated with the Debye frequency. The opposite tendency of the T evolution with the Debye temperature implies the decline of λ after Al extraction. By using μ∗ = 0.13 and their respective Debye temperatures, we got the λ = 0.77 for W3Al1.75C0.8 and 0.71 for W3Al1.4C0.8. The decrease of λ drives us to further investigate the phonon vibration modes in the present system.

To clarify the decisive phonon mode for the superconductivity, we investigate the high-temperature heat capacity and phonon DOS. In Figure 5A, the heat capacity of W3Al1.4C0.8 was measured from 7.5 to 200 K and fitted by using the hybrid Debye-Einstein model:where the subscripts D and E denote the Debye and Einstein modes, respectively, and R is the gas constant. means states at an energy . For example, in W3Al1.4C0.8, there are 5.2 atoms per formula unit and 15.6 phonon modes in total. Three acoustic phonons were averaged as one Debye mode, whereas the rest of the optical phonons were described as two Einstein modes (i = 2). The sum of (N + N) equals the number of atoms in the formula unit.

Figure 5

Vibration Modes of W3Al2C

(A) Heat capacity of W3Al1.4C0.8 from 7.5 to 200 K. The components of Debye-Einstein fitting curves are superimposed.

(B and C) Phonon spectra of W3Al1.75C0.75 and W3Al1.5C0.75. Blue arrow indicates the spectra weight of W-Al vibration. Red and dark gray arrows denote the W-C vibration of W and C dominated components, respectively.

The fitting of W3Al1.75C0.8 can be found in Figure S7, and the fitted parameters are summarized in Table 1. Comparing with the low-temperature fitting, the Debye temperatures fitted from high temperature have lower values. This is caused by the inclusion of two Einstein modes to describe the optical vibrations. By inspecting the phonon contribution, the Debye mode and the second Einstein mode are dominant, whereas the first Einstein mode can be neglected. All the three temperatures (, and ) shifted toward higher values, indicating the growing stiffness of the lattice.

Table 1

Physical Parameters of W3Al2−C0.8

	Raw	Etched
T_c(K)	7.5	6.4
Θ_D(K)	204	229
Θ_E1(K)	58	74
Θ_E2(K)	384	423
V_D(%)	37.6	48.7
V_E1(%)	0.6	1.3
V_E2(%)	61	50
Λ	0.77	0.71

The phonon DOS before and after Al extraction are shown in Figures 5B and 5C. In accord with the atomic weight, the phonon contribution of W, Al, and C are roughly located at three different regions of the spectra. Since Al is detached from C, the overlap of the spectra between Al and C is negligible. Although Al is located in the large interstices and weekly attached to the surrounding W, the overlap between Al and W is significant, extending from 2 to 13 THz. This means the filling rate of Al will significantly influence the wobbling frequency of W. As a result, the W-Al spectra shifted to a lower frequency in the etched sample, as indicated by blue arrows. Concomitantly, the W-W and W-C phonon peaks at around 1 THz (red arrow, W component dominated) and W-C peaks above 14 THz (dark gray arrow, C component dominated) shifted to around 2.5 and above 16 THz, respectively. The Einstein mode can be viewed as a combination of both W-Al and W-C optical modes. Considering the enhancement of both and , the increase of W-C frequency should overweigh the decrease of W-Al component. Based on the discussion above, we conclude the W-W and W-C optical modes to be responsible for the superconductivity. This conclusion is reasonable when considering the Al-free WC and Mo2C are also superconductors, but various Al-Mo and Al-W binary compounds do not superconduct (except AlMo3 with a T of 0.58 K). From this point of view, we could also understand the previous reported Nb and Ru substitution at Mo site, which impairs the connection of the Mo-Mo and Mo-C bonding, can effectively quench the volume fraction of the superconductivity (Ramachandran et al., 2016).

Charge State Controlled Structure and Superconductivity

The structure collapse caused by the charge state reversion is easy to understand. We explain the change of the M6C subunit from a charge point of view. We know that the Al vacancies shrink the M-C bond length and the volume of M6C, whereas the inclusion of C vacancies expand them. This contradiction can be qualitatively explained by the competition between Coulomb force and charge redistribution. The extraction of Al decreases the number of W-Al bonds (reduce the attraction force) but moderately increases the valence of W by 16% and Al by 27% (enhance the attraction force). Judging from the results, the reducing effect dominates the shrinkage. However, the removal of one C from the lattice doubled the valence of W, as shown in Figures 3A and 3B. It is the strong Coulomb repulsion of the W-W bonds caused by charge redistribution that expands the subunits.

The relationship between the superconductivity and the charge state is straightforward. As discussed above, the combined effect of M6C shrinkage and the enhancement of the negative charge states in both M and C will enhance the Coulomb repulsion and further the frequency of the M-M and M-C vibrations. The electron-phonon coupling constant is negatively correlated to the phonon frequency according to Migdal, 1958, Eliashberg, 1960:where , , and ω are the imaginary part of phonon self-energy, DOS of the normal metal, and phonon frequency, respectively. This well explains the observed decline of λ and T.

Conclusion

To start with, we found the intrinsic Al vacancy is dynamically favored in W3Al2C but not in Mo3Al2C. A soft chemical etching method was applied, and the content of Al could be feasibly controlled. An interesting discovery is the non-monotonic evolution of the charge state in the transition metals. This observation may provide new insights into the design of functional materials where electron doping can be achieved by the extraction of electron donors. The subsequent collapse of the crystal structure can be well explained by the abrupt reversion of the charge state in the transition metals. This anomaly may be related to the moderate electron negativity of Al and its surrounding chemical environment, which is worth further investigations. Apart from the tunable T, the controllable Al also provides us an ideal opportunity to compare the heat capacity and phonon contribution in different samples, which clarifies the origin of the superconductivity in the M3Al2C system. Detailed analysis shows the negatively charged transition metal and the charge redistribution change the M6C subunits are responsible for the observed phonon hardening. The existence of an intrinsic Al deficiency in the as-prepared W3Al1.75C0.8 implies that a further enhancement of T can be expected through non-equilibrium processes such as electrochemical intercalation at room temperature. According to Figure 2C, the Al sites tend to be fully occupied at low temperature. It is thus also possible to backfill the vacancies thermodynamically through the reaction of the W3Al1.75C0.8 in the bath of certain metals with low melting points. The proposed etching method should be applicable to other superconductors containing Al and Zn.

Resource Availability

Lead Contact

Further information and requests for the samples should be directed to and will be fulfilled by the Lead Contact, Yanpeng Qi (qiyp@shanghaitech.edu.cn).

Materials Availability

All the samples used in this study are available from the Lead Contact without restriction.

Data and Code Availability

All relevant data are available from the corresponding author (qiyp@shanghaitech.edu.cn) upon reasonable request.

Methods

All methods can be found in the accompanying Transparent Methods supplemental file.