Effect of carbon doping on the structure and superconductivity in AlB₂-type (Mo_0.96Ti_0.04)_0.8B₂

Transition metal diborides (TMDBs) have attracted a lot of attention over the past few decades due to their diverse properties TMD1 ; TMD2 ; TMD3 , including high hardness and shear strength hardness1 ; hardness2 ; hardness3 ; hardness4 , excellent corrosion resistance corrosion1 ; corrosion2 , superior catalytic performance catalytic1 ; catalytic2 , notrivial band topology topology1 ; topology2 , high electrical conductivity and even superconductivity SC1 ; SC2 ; SC3 ; SC4 ; SC5 . Among existing TMDBs, molybdenum diboride is unique in that it exists in both hexagonal AlB₂-type and rhombohedral structures MoB2 . The former is built up by planar transition metal and boron layers stacked alternatively along the $c$-axis, and the latter can be derived from the former by puckering half of the boron layers. Although both phases are not superconducting, superconductivity can be induced by either doping at the transition metal site or applying high pressure. In particular, the $T_{\rm c}$ of AlB₂-type MoB₂ reaches 32 K at $\sim$110 GPa MoB2pressureSC , comparable to that of isostructural MgB₂ MgB2 . At ambient pressure, however, MoB₂ crystallizes in the rhombohedral structure. Instead, partial substitution of Mo by Zr or Sc is needed to stabilize the AlB₂-type phase in metal-deficient (Mo_x$X$_1-x)_1-δB₂ ($X$ = Zr and Sc), which exhibits bulk superconductivity up to 8.3 K SC3 ; SC5 . In addition to Zr, preliminary results are also reported for the group IVB dopants Ti and Hf SC3 .

Carbon is known to be the most effective dopant for enhancing the upper critical field of MgB₂ MgB2C1 ; MgB2C2 . Single crystal results indicate that carbon can substitute up to $\sim$15% of boron in MgB₂, which leads to a monotonic decreases in the $a$-axis while has little effect on the $c$-axis MgB2C3 ; MgB2C4 . With increasing carbon content, the $T_{\rm c}$ of Mg(B_1-xC_x)₂ decreases dramatically and is no longer detectable for $x$ $>$ 0.125. Despite the suppression of $T_{\rm c}$, the zero-temperature upper critical field $B_{\rm c2}$(0) is almost doubled with increasing $x$ from 0 to $\sim$0.04 MgB2C1 ; MgB2C2 . To further optimize the high field performance, codoping of Mg(B_1-xC_x)₂ with Ti was also attempted MgB2TiC . It turns out that the carbon still replaces boron in the MgB₂ phase while Ti precipitates out as either TiB or TiB₂ in the intra-granular region. However, neither carbon doping nor its effect on superconductivity in TMDBs has been investigated to date.

In this paper, we study the structure and physical properties of (Mo_0.96Ti_0.04)_0.8(B_1-xC_x)₂. Structural analysis indicates the formation of an AlB₂-type phase for $x$ = 0, 0.12 and 0.16. The carbon dopant is distributed uniformly in the lattice and induces changes in the lattice parameters, microstructure, and boron binding energies. Physical property measurements show that (Mo_0.96Ti_0.04)_0.8B₂ exhibits bulk superconductivity below 7.0 K while the C-doped samples remain normal down to 1.8 K, the reason for which is discussed.

Polycrystalline (Mo_0.96Ti_0.04)_0.8(B_1-xC_x)₂ samples with $x$ = 0, 0.04, 0.08, 0.12 and 0.16 were synthesized by the arc melting method as described previously SC3 ; SC5 . Stoichiometric amounts of high purity Mo (99.99%), Ti (99.99%), B (99.99%) and C (99.99%) powders were weighed, mixed thoroughly and pressed into pellets in an argon-filled glovebox. The pellets were then melted in an arc furnace under high-purity argon atmosphere (99.999%) with a current of 80 A, which roughly corresponds to a temperature of 2400 ^∘C. The melts were flipped and remelted at least four times to ensure homogeneity, followed by rapid cooling on a water-chilled copper plate. The phase purity of resulting samples was checked by powder x-ray diffraction (XRD) measurements in the 2$\theta$ range of 20-80^∘ using a Bruker D8 Advance x-ray diffractometer with Cu-K$\alpha$ radiation. The step size is 0.025^∘ and the dwelling time at each step is 0.1 s. The lattice parameters were determined by a least-squares method. The morphology and chemical composition were investigated in a Zeiss Supratm 55 Schottky field emission scanning electron microscope (SEM) equipped with an energy dispersive x-ray (EDX) spectrometer. The microstructure was examined in an FEI Tecnai G2 F20 S-TWIN transmission electron microscope (TEM) operated under an accelerating voltage of 200 kV. The x-ray photoelectron spectroscopy (XPS) measurements were performed in a ESCALAB Xi+ spectrometer with Al K$\alpha$ x-rays as the excitation source. The resistivity and specific heat measurements down to 1.8 K were done in a Quantum Design Physical Property Measurement System (PPMS-9 Dynacool), The resistivity was measured on bar-shaped samples using the standard four-probe method, and the applied current is 1 mA. The dc magnetization was measured down to 1.8 K in a commercial SQUID magnetometer (MPMS3) with an applied field of 1 mT.

The structural refinement profile for the sample with $x$ = 0.12 is displayed in Fig. 1(b). In the unit cell of AlB₂, the Al and B atoms occupy the (0, 0, 0) and (0,3333, 0.6667, 0.5) sites, respectively. For (Mo_0.96Ti_0.04)_0.8(B_1-xC_x)₂, the Mo and Ti atoms are set to share the former site while the B and C atoms are set to share the latter one. As can be seen, all the diffraction peaks can be well fitted based on this structural model, which is corroborated by the small reliability factors ($R_{\rm wp}$ = 6.0% $R_{\rm p}$ = 4.3%). These results confirm the AlB₂-type structure of (Mo_0.96Ti_0.04)_0.8(B_1-xC_x)₂, which is sketched in the inset of Fig. 1(b).

Figure 3(a) shows the high-resolution TEM (HRTEM) image taken along the [0 0 1] zone axis for the (Mo_0.96Ti_0.04)_0.8B₂ sample. One can see sharp lattice fringes with a spacing of 0.263 nm, which matches well with that between the (100) planes. The corresponding selected area electron diffraction (SAED) displayed in Fig. 3(b) exhibits a well-defined spot pattern and the spots near the center can be indexed as the (100), (010) and (110) reflections. The HRTEM image and corresponding SAED taken along the [0 1 0] zone axis for the same sample are displayed in Figs. 3(c) and (d). Along this zone axis, two lattice spacings of 0.263 nm and 0.315 nm can be resolved, in line with those of the (100) and (001) planes, respectively. Also, the spots near the center are indexable to the (100), (101) and (001) reflections. It is worth noting that, similar to (Mo_0.96Zr_0.04)B₂ SC3 , planar defects along the $c$-axis are also detected for (Mo_0.96Ti_0.04)_0.8B₂, as indicated by the arrows in Fig. 3(c). However, the absence of streaking in the SAED pattern [see Fig. 3(d)] implies that the density of such defects is significantly lower in the latter than in the former. This is consistent with the expectation that the defects are suppressed by the presence of metal deficiency SC3 .

The HRTEM images and corresponding SAED patterns taken along the [0 0 1] and [0 1 0] zone axes for the (Mo_0.96Ti_0.04)_0.8(B_0.88C_0.12)₂ are shown in Figs. 4(a-d). The lattice fringes remain well visible and the two resolved lattice spacings of 0.263 nm and 0.315 nm agree well with those of the (100) and (001) planes, respectively. It is thus clear that the crystallinity dose not degrade upon carbon doping. However, contrary to (Mo_0.96Ti_0.04)_0.8B₂, a number of planar defects are detected along the [0 0 1] zone axis of (Mo_0.96Ti_0.04)_0.8(B_0.88C_0.12)₂, as seen in Fig. 4(a). Indeed, the corresponding SAED pattern shown in Fig. 4(b) exhibits streaking along the (00$l$) directions. Given that the streaks are absent along the [0 1 0] zone axis and the transition metal layers remain unchanged, it is most likely that the planar defects come from the C-doped boron layers. In pristine boron layers, the boron atoms form a continuous network of six-membered rings. The substitution of boron by smaller carbon is expected to distort the rings, which promotes the formation of planar defects.

The low-temperature resistivity ($\rho$), magnetic susceptibility ($\chi$) and specific heat ($C_{\rm p}$) data for the (Mo_0.96Ti_0.04)_0.8B₂ sample are displayed in Figs. 6(a-c). As can be seen, $\rho$ starts to drop on cooling below 7.4 K, indicating the onset of a superconducting transition. The $\rho$ drop is sharp down to $\sim$6.8 K, but afterward becomes much slower, and achieves zero only below $\sim$6 K. From the midpoint of the $\rho$ drop, the superconducting transition temperature $T_{\rm c}$ is determined to be 7.0 K. Coinciding with $T_{\rm c}$, a diamagnetic transition in the zero-field cooling (ZFC) $\chi$ and a distinct $C_{\rm p}$ anomaly are detected. In particular, the diamagnetic signal at 1.8 K corresponds to a shielding fraction of $-$4$\pi\chi$ $\approx$ 87.4% , which is more than one order of magnitude larger than that reported previously SC3 . These results indicate the bulk nature of superconductivity in (Mo_0.96Ti_0.04)_0.8B₂.

To extract the Sommerfeld coefficient $\gamma$, the normal-state $C_{\rm p}$ data is fitted by the Debye model,

$$C_{\rm p}/T=\gamma+\beta T^{2},$$

(1)

where $\beta$ is the phonon specific heat coefficient. This gives $\gamma$ = 3.61 mJ/molK² and $\beta$ = 0.01052 mJ/molK⁴, and then the entropy-conserving construction yields the normalized specific heat jump $\Delta$$C_{\rm p}$/$\gamma$$T_{\rm c}$ = 0.41. With $\beta$, the Debye temperature $\Theta_{\rm D}$ is calculated to be 802 K using the equation

$$\Theta_{\rm D}=(12\pi^{4}NR/5\beta)^{1/3},$$

(2)

where $N$ = 2.8 is the number of atoms per formula unit and $R$ is the gas constant. Then the electron-phonon coupling constant $\lambda_{\rm ep}$ is estimated to be 0.54 using the inverted McMillan formula Mcmillam

$$\lambda_{\rm ep}=\frac{1.04+\mu^{\ast}\rm ln(\Theta_{\rm D}/1.45\emph{T}_{\rm c})}{(1-0.62\mu^{\ast})\rm ln(\Theta_{\rm D}/1.45\emph{T}_{\rm c})-1.04},$$

(3)

where $\mu^{\ast}$ = 0.13 is the Coulomb repulsion pseudopotential. This, together with $\Delta$$C_{\rm p}$/$\gamma$$T_{\rm c}$, implies that (Mo_0.96Ti_0.04)_0.8B₂ is a weak coupling superconductor.

The upper critical field ($B_{\rm c2}$) of (Mo_0.96Ti_0.04)_0.8B₂ is determined by resistivity measurements under magnetic fields up to 5 T, the result of which is shown in Fig. 6(d). The application of field leads to the shift of resistive transition toward lower temperatures. For each field, $T_{\rm c}$ is determined using the same criterion at zero field, and the resulting temperature dependence of $B_{\rm c2}$ is plotted in Fig. 6(e). Extrapolating the $B_{\rm c2}$($T$) data to 0 K using the Werthamer-Helfand-Hohenberg model WHH gives the zero-temperature upper critical field $B_{\rm c2}$(0) = 5.2 T. This $B_{\rm c2}$(0) is comparable to that of (Mo_1-xSc_x)_1-δB₂ SC5 and much smaller than the Pauli paramagnetic limit $B_{\rm P}$(0) = 1.86$T_{\rm c}$ $\approx$ 13.1 T Paulilimit , indicating that it is limited by the orbital effect. Once $B_{\rm c2}$(0) is known, the Ginzburg-Landau (GL) coherence length $\xi_{\rm GL}$(0) is calculated to be 8.0 nm according to the equation

$$\xi_{\rm GL}(0)=\sqrt{\frac{\Phi_{0}}{2\pi B_{\rm c2}(0)}},$$

(4)

where $\Phi_{0}$ = 2.07 $\times$ 10^-15 Wb is the flux quantum.

In summary, we have investigated the structure and properties of (Mo_0.96Ti_0.04)_0.8(B_1-xC_x)₂ diborides prepared by the arc-melting method. The samples with $x$ = 0, 0.12, and 0.16 have a nearly single AlB₂-type phase with a uniform elemental distribution. The carbon doping leads to a slight increase in the $a$-axis, a significant reduction in the $c$-axis, the formation of planar defects along the (100) planes, and a shift of the B 1$s$ peaks towards higher binding energies. Moreover, the C-free (Mo_0.96Ti_0.04)_0.8B₂ ($x$ = 0) is confirmed to be a bulk superconductor below $T_{\rm c}$ = 7.0 K, while no resistivity drop is observed down to 1.8 K for $x$ = 0.12 and 0.16. This suppression of superconductivity is attributed to weakening of electron-phonon coupling as a consequence of the electron filling of boron $\pi$ bands by carbon doping. Our results not only represent the first study on the effect of carbon doping in transition metal diborides, but also help to better understand the superconductivity in this family of materials.

We thank the foundation of Westlake University for financial support and the Service Center for Physical Sciences at Westlake University for technical assistance in SEM measurements. The work at Zhejiang University is supported by the National Natural Science Foundation of China (12050003).