A15 Nb₃Si: a 'high' T_c superconductor synthesized at a pressure of one megabar and metastable at ambient conditions

Two samples were used in the current study. The first was Nb₃Si (from the original work [1] at Los Alamos National Laboratory) prepared by arc-melting and annealed at approximately 1780 °C for four hours. As evident from the binary phase diagram [13] for Nb-Si, the desired tetragonal phase of Nb₃Si is stable between 1673 and 1977 °C. According to x-ray diffraction, the annealed sample used in the present work was >80% tetragonal Nb₃Si, with bcc Nb and Nb₅Si₃ as minority second phases. In order to better quantitatively compare the amount of second phase Nb in this starting material with the explosively compressed Recovery 20 sample discussed below, specific heat at low temperatures was performed.

The second sample used in this study was a piece of the original Recovery 20, explosively compressed Nb₃Si from the work [6] by Olinger and Newkirk which had been stored at room temperature for 39 years. The resistivity at pressures up to 88 GPa and specific heat at zero applied pressure of this original, approximately 50%–70% A15, sample were measured for the present work. Then the sample was annealed at increasing temperatures, 1 day at each temperature, starting at 220 °C, with the decreasing amount of A15 material being estimated by dc susceptibility. Upon annealing at one day at 600 °C, the rate of decrease of A15 content was judged to have become large enough to switch to increasing the annealing time (for a total of 5 days) and keeping the annealing temperature fixed at 600 °C. The specific heat of the annealed sample was then measured (section 3.4).

In addition to performing x-ray diffraction on the starting tetragonal and explosively compressed, A15 majority phase, samples, the following measurements were done. Both these samples were measured resistively in a diamond anvil cell apparatus described below, the tetragonal sample up to 120 GPa to search for possible conversion to the A15 phase and the Recovery 20 sample up to 88 GPa to determine the T_c vs pressure behavior of A15 Nb₃Si. The specific heat was measured of (1) the tetragonal Nb₃Si sample, of (2) the explosively compressed Recovery 20 A15 Nb₃Si sample, and of (3) the annealed (for a total of 5 days at 600 °C, in addition to 1 day at 220, 320, 405 and 500 °C) Recovery 20 sample to determine the amount of the A15 phase remaining after annealing.

The low temperature measurement of specific heat utilized the time constant method, and followed the techniques described in reference [14].

For the high-pressure resistivity measurements, a micron-sized Nb₃Si (either tetragonal or majority A15) polycrystal sample (∼30 × 40 × 10 μm [3]) was cut from a larger piece of bulk sample and placed in a gas-membrane-driven diamond anvil cell (OmniDAC from Almax-EasyLab) along with a ruby (∼10 μm in diameter) for pressure calibration [15]. Two opposing diamond anvils (∼0.14 carat, type Ia) were used, which have 0.35 mm diameter culets beveled at 8° to 0.18 mm central flats. A Re metal gasket (∼3 × 4 × 0.25 mm³) was pre-indented to ∼25 μm in thickness and electrospark-drilled to have a hole (∼170 μm in diameter) at the center. The hole was then filled with 4:1 cBN-epoxy mixture to insulate the gasket and mechanically drilled to have a hole (∼80 μm in diameter) at the center, which was filled with soapstone (steatite) for electrically insulating the sample from the gasket and also serving as the pressure-transmitting medium. The thin Nb₃Si sample was then placed on top of four thin (4 μm) Pt leads embedded in the insulation layer for a four-point dc electrical resistivity measurement. Further details of the nonhydrostatic high-pressure resistivity technique are given in a paper by Shimizu et al [16].

The diamond cell was placed inside a customized continuous-flow cryostat (Oxford Instruments). A homebuilt optical system attached to the bottom of the cryostat was used for the visual observation of the sample and for the measurement of the ruby manometer. Pressure was applied (or unloaded) at room temperature (∼297 K) to the desired pressure which then increased upon cooling, e.g. from 92 GPa at room temperature to 120 GPa at 5 K. Then the sample was cooled down to ∼3 K and warmed up again to room temperature at a rate of ∼0.5 K min⁻¹ at each pressure for the temperature-dependent resistivity measurement. Pressures used in the T_c vs pressure phase diagram (figure 2 below) were measured at around 5 to 20 K, in which range pressure is constant to within 1 GPa, and the estimated accuracy is ±5%. To estimate the electrical resistivity from the resistance, we used the van der Pauw method, (assuming an isotropic sample in the measurement plane), ρ = πtR/ln 2, where t is the sample thickness (∼10 μm) with a current of 1 mA. The accuracy of the estimated resistivity is roughly a factor of two considering uncertainties in the initial thickness of the sample. No attempt was made to take into account the changes in the sample thickness under high pressures.

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In order to better understand the results of our high pressure search for A15 conversion of tetragonal Nb₃Si up to 120 GPa, we discuss our T_c vs pressure results on Recovery 20, A15 Nb₃Si first. As shown in figure 2, starting at 2 GPa T_c of A15 Nb₃Si falls monotonically at a rate of about 0.2 K/GPa, consistent with the earlier work of Lim et al [11]. Above about 40 GPa two things happen in the T_c vs pressure data on A15 Nb₃Si in figure 2. First, the rate of decrease in T_c with increasing pressure starts to level off. Second, the presence of ∼15% second phase of Nb in the explosively compressed material (see specific heat data discussed below) shows up at ⩾55 GPa as a second resistive transition (red squares) above the A15 transition. Since the weak pressure dependence of this upper transition above 40 GPa is consistent with that [12] of pure Nb under pressure, we conclude that the ∼15% Nb volume fraction determines the onset T_c in this pressure range. Within this interpretation, the A15 T_c continues to be suppressed above 40 GPa, appearing as a second, lower T, resistive anomaly as seen in figure 2.

Representative resistance data at low temperature (during the loading condition) from which the T_c values in figure 2 are derived are shown in figure 3. The higher temperature transition for P ⩾ 55 GPa, as discussed, is identified as being that of the Nb impurity phase. This is consistent with several features of the data. (1) It is known that T_c of Nb vs pressure is relatively flat [12], which argues for the upper transition at 55–88 GPa being that of Nb. (2) The drop in resistance at the upper transition for 55–88 GPa is only partial, whereas the resistance at the lower transition goes all the way to zero. This implies that the lower transition is the T_c of the majority, 50%–70%, A15 phase in the Recovery 20 sample, while the upper, partial resistive transition is the superconducting transition of the minority, 15% (see specific heat data below) Nb impurity phase. The fact that the minority second phase Nb exhibits only a partial superconducting transition (ρ does not go to 0) in figure 3 is consistent with its amount being below the 3D percolation limit.

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Now that we have established the behavior of T_c vs pressure for A15 Nb₃Si, let us consider our high pressure resistance measurements of the tetragonal Nb₃Si sample. Is there any evidence of a T_c from a partial conversion to the A15 structure from applying pressure at room temperature to the tetragonal Nb₃Si structure? T_c results as determined from resistance measurements on the tetragonal Nb₃Si sample are shown as blue circles in figure 2. Due to the ∼10% second phase of Nb in this tetragonal sample (as determined by specific heat of the starting material as discussed below), there is the constant presence of a partial superconducting transition from Nb starting at around 8.8 K at 2 GPa and going down to ∼7 K (T_c ^onset) at 120 GPa. Again, this is consistent [12] with measurements on pure Nb with some trace impurities (in our case dissolved Si). In order to settle this question, we present high pressure unloading data on the tetragonal Nb₃Si sample in figure 4, where the inserted arrows correspond to the measured data up to 88 GPa (and extrapolated thereafter) for T_c on the explosively compressed ('Recovery 20') Nb₃Si shown in figure 2. As can be clearly seen, no apparent anomaly corresponding to the A15 Nb₃Si T_c is observed in our results for high pressure applied to tetragonal Nb₃Si at room temperature. This leaves us with the surmise that the temperatures reached [6] in the explosive compression production (∼1000 °C) of A15 Nb₃Si are necessary to overcome thermodynamic sluggishness from the kinetics of the phase transformation between the structures sketched in figure 1.

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We now address this issue by performing enthalpy calculations on various possible Nb₃Si structures. We follow these theoretical calculations with annealing experiments on a piece of Recovery 20 A15 majority phase Nb₃Si, with the assumption that the thermal conversion A15 → non-superconducting tetragonal Nb₃Si gives an approximation of the required thermal energy for the reverse process.

Figure 5 shows our calculation of the enthalpy of Nb₃Si as a function of pressure for the three experimentally known crystal structures-P4₂ n (tetragonal), Pm 3 n $\left(\mathrm{A}15\right)$, and $Pm{\_}3m$ (cubic perovskite) [17] using density functional theory as implemented in VASP [18, 19]. The plane wave cutoff was set to 520 eV and a k-point density of 60 points per Å⁻¹ was used for the density functional theory relaxations at varying pressure. We used the Perdew–Burke–Ernzerhof generalized gradient approximation [20] for the exchange-correlation energy and the projector augmented wave pseudopotentials [21]. As shown in figure 5, the A15 phase becomes stable above 50 GPa, and at 100 GPa displays an approximately 0.07 eV atom⁻¹ lower enthalpy than the tetragonal P4₂ n phase.

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Without any knowledge of annealing effects on explosively compressed A15 Nb₃Si (other than the fact that it had not reconverted to tetragonal Nb₃Si after being stored at room temperature for 39 years), we began this investigation with a rather low annealing temperature (220 °C) for one day. We discovered that the amount of A15 material present in the 11 mg piece of Recovery 20 which we committed to this annealing was fairly robust against annealing. We successively annealed the sample at ever increasing temperatures (320, 405, 500, and 600 °C) for one day at each temperature, followed by a 4 day anneal at 600 °C. We measured the diamagnetic susceptibility using a dc magnetometer after each anneal to approximate the decrease in the quantity of A15 superconductor present. To avoid interference from the diamagnetic susceptibility contribution from the 15% Nb second phase (see specific heat determination below), we focused on the magnitude of the diamagnetic signal at 9.5 K, i.e. above the T_c of the second phase Nb.

After 4 day annealing at 600 °C, we stopped the annealing procedure and measured the specific heat of the annealed 11 mg of the explosively compressed, 50%–70% A15 sample ('Recovery 20'), and compared these annealed data with the specific heat of the unannealed Recovery 20 sample. These data are shown in figure 6, and indicate that 35% of the A15 portion of the sample remains after annealing. The thermal energy needed to aid the reaction kinetics of the conversion of the tetragonal structure of Nb₃Si into the (3% denser) A15 structure is not the same as for the reverse (A15 → tetragonal). However, at least the rather long time at 600 °C needed to partially reconvert the A15 Nb₃Si into the tetragonal structure is clearly consistent with the result that our attempt to convert the tetragonal Nb₃Si to the A15 structure at pressures up to 92 GPa at room temperature (120 GPa at low temperature) did not achieve the required reaction kinetics.

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The specific heat data around 9 K are expanded in figure 7 to indicate the Nb fraction in the starting, unannealed sample of Recovery 20 (16%) and in the annealed sample (5%). The specific heat (not shown) of the starting sample of tetragonal (⩾80%) Nb₃Si (see figure 2, blue points, and figure 4 for resistivity data thereon) indicates that 10% of that sample is Nb.

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A sample of A15 Nb₃Si produced [6] by explosive compression (approximate peak pressure 90–110 GPa, peak temperature 1000 °C, residual temperature 500 °C) in 1981 at Los Alamos National Laboratory was subjected to pressures up to 88 GPa in order to determine the superconducting transition temperature T_c as a function of pressure, with T_c ^mid falling to 5.2 K at the highest pressure. This sample was then annealed to approximately determine the temperature and time needed to transform A15 Nb₃Si back into the tetragonal structure. Then, in order to determine if tetragonal Nb₃Si can be transformed to the A15 structure at room temperature by applied pressures up to 92 GPa at room temperature (120 GPa at low temperatures), a sample of the original, before implosion LANL starting material (Nb₃Si annealed at 1780 °C for four hours, with ⩾80% tetragonal structure) was measured.

Theoretical calculations of the enthalpies vs pressure of three possible Nb₃Si structures were carried out to help guide the pressure measurements. The result is that the A15 structure becomes the lowest enthalpy lattice arrangement above 50 GPa, with approximately 70 meV atom⁻¹ lower enthalpy than the tetragonal structure at 100 GPa.

Although a second phase of Nb was present in all the samples, it was straightforward to distinguish which resistive transition corresponded to the A15 phase. No evidence of the A15 transition was detected in unloading data on the starting tetragonal material at 120, 105, and 83 GPa. Thus, we conclude that the original explosive compression conversion of tetragonal → A15 Nb₃Si at pressures up to 110 GPa indeed required the high temperatures (∼1000 °C) associated with the rapid compression to assist the reaction kinetics. This is consistent with our annealing data on the A15, where temperatures of 600 °C for 5 days, as well as 4 days of lower temperature annealing, were required to convert 65% of the A15 phase (as determined by bulk specific heat measurements) back to normal tetragonal Nb₃Si material.

Based on these experiments, and the original estimate [6] of the 1 μsec time-at-temperature (∼1000 °C) and pressure (110 GPa) of the explosively compressed A15 Nb₃Si, the present work indicates that combined conditions of high pressure and high temperature are necessary to convert tetragonal Nb₃Si to the A15 structure. The long-lived nature of metastable A15 Nb₃Si (annealing for 39 years at room temperature failed to result in any sizable back transformation) points to the presence of a significant kinetic barrier. In that sense, it is not surprising that high temperatures are necessary to overcome this barrier. The present work highlights that high pressure phases formed with the addition of high temperatures are more likely to survive at ambient conditions than those formed via room temperature compression alone, since for the phase to form at room temperature the kinetic barrier must necessarily be small.

The barrier to atomic rearrangement raised by slow kinetics is the key to metastability at ambient conditions. The present work, where annealing at room temperature for 39 years did not transform the metastable A15 Nb₃Si structure back to the tetragonal (with its 90 meV atom⁻¹ lower enthalpy) serves as a clear example of this. While computational methods now allow reliable prediction of thermodynamically stable phases, the prediction of such barriers and the associated kinetics are out of reach in most cases. Whether high temperature superconducting hydride phases can be retrieved to ambient conditions following ultra-high pressure synthesis thus remains an open question for experiments, though the high mobility of hydrogen may make this particularly challenging.

Given the current interest in the high-T_c hydrides, the present work serves as a prototypical example of a superconducting structure that forms under very high (megabar) pressures but survives to ambient conditions.