Stoichiometric evolutions of PH₃ under high pressure: implication for high-T_c superconducting hydrides

Abstract

The superconductivity of hydrides under high pressure has attracted a great deal of attention since the recent observation of the superconducting transition at 203 K in strongly compressed H₂S. It has been realized that the stoichiometry of hydrides might change under high pressure, which is crucial in understanding the superconducting mechanism. In this study, PH₃ was studied to understand its superconducting transition and stoichiometry under high pressure using Raman, IR and X-ray diffraction measurements, as well as theoretical calculations. PH₃ is stable below 11.7 GPa and then it starts to dehydrogenate through two dimerization processes at room temperature and pressures up to 25 GPa. Two resulting phosphorus hydrides, P₂H₄ and P₄H₆, were verified experimentally and can be recovered to ambient pressure. Under further compression above 35 GPa, the P₄H₆ directly decomposed into elemental phosphorus. Low temperature can greatly hinder polymerization/decomposition under high pressure and retains P₄H₆ up to at least 205 GPa. The superconductivity transition temperature of P₄H₆ is predicted to be 67 K at 200 GPa, which agrees with the reported result, suggesting that it might be responsible for superconductivity at higher pressures. Our results clearly show that P₂H₄ and P₄H₆ are the only stable P–H compounds between PH₃ and elemental phosphorus, which is helpful for shedding light on the superconducting mechanism.

high pressure, hydrides, superconductivity, stoichiometric evolution

INTRODUCTION

Since superconducting mercury was first reported [1,2], scientists have continued to search for new high critical temperature (T_c) materials. In 2004, Ashcroft studied hydrogen-dominant hydrides [3], in which condensed H₂ may contribute to a high T_c. Motivated by this work, extensive theoretical investigations on this system have been reported, such as SiH₄ [4], GeH₄ [5], GaH₃ [6], SiH₄(H₂)₂ [7], CaH₆ [8] and YH₆ [9], etc. A few remarkable high-T_c materials have also been observed in subsequent experimental studies. Recently, Drozdov et al. reported the superconductive transition of H₂S at 203 K and 155 GPa [10], which broke the highest T_c record [11]. Many theoretical [12,13] and experimental [14] studies have explored its stoichiometry and structure, which play an important role in understanding the underlying mechanism of superconductivity.

Very recently, PH₃, a typical hydrogen-rich hydride, has attracted a great deal of research interest because of its superconducting transition discovered by Drozdov and his co-workers [15–20]. Their experimental work revealed that PH₃ might be a high-temperature superconducting candidate. From the resistance measurements, a superconducting transition signature was observed at T_c of 30 K. This increased to 103 K with pressures up to 207 GPa. However, structural information was not provided, and the origin of the superconducting transition remains puzzling. Subsequent theoretical studies [16–19] showed that the P–H compound should also be a complex system, and all the predicted structures were metastable with respect to the elemental phase.

Flores-Livas et al. [16] studied the phase diagram of phosphorus hydrides with different stoichiometries and found that they tended to decompose into phosphorus and hydrogen at high pressure. Liu et al. [17] predicted a PH₃ phase with a monoclinic structure (C2/m) and a T_c of 83 K at 200 GPa, which is closer to the observed superconducting transition temperature. Shamp et al. [18] predicted that PH₃ is thermodynamically unstable during decomposition into the elemental phases, as well as PH₂ and H₂. Two PH₂ phases with C2/m and I4/mmm symmetry were computed as metastable at 200 GPa. The corresponding superconducting critical temperatures were 76 and 70 K, respectively. Bi et al. [19] found that a dynamically stable PH₂ phase was the best according to the observed superconducting transition at 80 GPa. The PH₃ phase to PH₂ phase reaction was exothermic at that pressure, which proves the spontaneity of the reaction.

Until now, the PH₃ phase under compression has remained unknown and no relevant experimental studies have been reported. The high-pressure stoichiometry and structural behavior of PH₃ are critical to understanding the superconducting transition in the P–H system, which needs to be experimentally determined. For this purpose, we studied the structural behavior of PH₃ under high pressure. We identified the pressure-induced step-by-step polymerization of PH₃ and a route to elemental phosphorus that unveiled the unknown transition process and provides experimental evidence for understanding the underlying mechanism of the superconductivity of P–H compounds.

RESULTS AND DISCUSSION

Stoichiometric evolutions of PH₃ at room temperature

After the PH₃ gas was loaded into the sample chamber of the diamond anvil cell (DAC) and returned to room temperature, a colorless and transparent sample (Supplementary Fig. 1, available as Supplementary Data at NSR online) was observed. The characteristic Raman peaks (Supplementary Fig. 1, available as Supplementary Data at NSR online) at 978 (υ₂, symmetric bending mode), 1104 (υ₄, asymmetric bending mode), 2317 (υ₁, stretching mode) and 2331 (υ₃, stretching mode; shoulder) cm⁻¹ agreed well with previous reports [21], indicating the existence of PH₃ in the chamber.

The X-rays can damage the sample (Supplementary Fig. 2, available as Supplementary Data at NSR online), so Raman and infrared absorption spectroscopy (IR) were mainly used for our in situ studies of PH₃ at high pressure. Figure 1a and c shows the Raman spectra of the sample during compression. Under high pressure, these characteristic modes blue shifted and broadened (Fig. 1b and d) and eventually vanished at 20.5 GPa. Several new peaks (marked by black asterisks and arrows inFig. 1a) were observed at around 11.7 GPa, which suggested a phase transition. For the P–H stretching modes, we also noticed a dramatic expansion of the characteristic bonds. Figure 1d shows the peak positions of the υ₁ and υ₃ modes as a function of pressure. The peak shift of υ₁ dramatically decreased and started to red shift at 11.7 GPa. We attributed these changes to a transition in the sample near 11.7 GPa.

Figure 1.

(a, c) Raman spectra of PH₃ at various pressures at room temperature. The peak positions of υ₂, υ₄ (b) and υ₁, υ₃ (d) as functions of pressure.

These new peaks in the Raman spectra (Fig. 1a) were consistent with previous studies about P₂H₄ at ambient pressure. The two new peaks at low frequencies correspond to the PH₂ rocking mode and P–P stretching mode in the P₂H₄ molecule, which were observed at around 217 and 436 cm⁻¹, respectively [22,23]. The emergency P–P bond at 11.7 GPa proved the dimerization of PH₃ molecules. The other new peaks at 1007 and 1093 cm⁻¹ were from the PH₂ scissoring modes in the P₂H₄ molecule, which also agrees with previous reports. These factors suggest that the pressure-induced transition is due to the dimerization of PH₃ at high pressure.

To verify the dimerization, we also studied the decompressed sample. A liquid sample was obtained after quenching to ambient conditions, as shown in the microphotograph of the decompressed sample (inset optical images in Fig. 2a). It is well known that P₂H₄ is a liquid at ambient pressure [22,24], which confirms that pressure drives the dimerization of PH₃ to form P₂H₄ via this reaction:

\begin{equation} {\rm{2PH}_3} \to {{\rm{P}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}.} \end{equation}

(1)

We further employed Raman to measure the recovered liquid sample. However, after laser irradiation, the liquid sample decomposed and generated Hittorf's phosphorus [25,26] (Fig. 2a) according to the photodecomposition properties of P₂H₄ [24]. This offers more evidence of our findings.

Figure 2.

(a) The Raman spectrum of the Hittorf's phosphorus transformed from the liquid sample after laser irradiation. The inset images show the photo-induced transition of the liquid residue before and after laser irradiation. (b) The Raman spectrum of the sample decompressed from 25 GPa. The inset picture shows the optical micrograph of the decompressed sample. (c) The frequency trend of the P–H stretching in P_nH_n+2 (n = 1, 2, 3 and 4). (d) The Raman spectrum of the sample quenched from 35 GPa. The inset shows the XRD pattern of the sample at 35 GPa and the optical micrograph of the decompressed sample.

We also employed IR to trace the in situ information of the new product at high pressure. Supplementary Fig. 3a, available as Supplementary Data at NSR online, shows the IR peak near 1095 cm⁻¹ broadened and shifted slightly to a lower frequency with increasing pressure, but an obvious new shoulder was observed at around 1058 cm⁻¹ after decompressing the sample to 11.8 GPa (Supplementary Fig. 3c and d, available as Supplementary Data at NSR online). This new shoulder matched the P₂H₄ scissors mode well, which was observed at around 1052 cm⁻¹ in a solid state at ambient pressure [27]. This characteristic mode confirms the existence of P₂H₄. In addition to the P–H stretching modes in the IR spectra (Supplementary Fig. 3b, available as Supplementary Data at NSR online), a new shoulder at around 2329 cm⁻¹ was observed, and it became stronger and stronger with increasing pressure. After it had quenched to 11.8 GPa, the new shoulder peak was more obvious compared to the IR spectrum measured at 12 GPa during compression. This proves dimerization.

As the pressure increased, the P₂H₄ showed piezochromism. It became yellow, then red and darkened, and eventually became opaque at pressures higher than 25 GPa, consistently with the observations of Drozdov et al. at low temperatures (180 K). As the sample became totally opaque, the vibrational signal vanished and hindered the in situ high-pressure vibrational spectra measurement. Therefore, we had to quench the sample to ambient conditions from different pressures (25 and 35 GPa) and employed Raman spectroscopy to investigate the different quenched residues. Interestingly, once the sample became completely opaque above 25 GPa, it maintained its opaque solid state even when decompressed to room pressure. This irreversible process suggests that a new transition occurred at higher pressures.

Figure 2b shows that the Raman spectrum of the residue quenched from 25 GPa after the opaque transition. A weak peak near 873 cm⁻¹ belonging to PH₂ twisting and a strong peak at 2248.5 cm⁻¹ belonging to P–H stretching exist in the spectrum. This new P–H stretching peak is located at a much lower wave number than in PH₃, P₂H₄ (∼2292 cm⁻¹) and P₃H₅ (∼2267 cm⁻¹) [24], suggesting that the residue contained a new kind of phosphorus hydride. Figure 2c shows the P–H stretching mode of P_nH_n+2 shifts to lower frequency as n becomes larger. Following this trend, we deduced that the new phosphorus hydride was P₄H₆, which suggests that the P₂H₄ molecules continued to dimerize and form P₄H₆ at higher pressure.

To confirm the second dimerization, we calculated the Raman modes of P₄H₆ using the Gaussian 09 program at the B3LYP/6–311(d, p) level [28]. Supplementary Table 1, available as Supplementary Data at NSR online, shows the calculated Raman modes of two typical P₄H₆ conformers, in which the four phosphorus atoms are linear and U-type (Supplementary Fig. 4a and b, available as Supplementary Data at NSR online). The calculated Raman spectra show that they both have four characteristic bands corresponding to the stretching vibration (350–450 cm⁻¹) of the P–P bond, twisting vibration (700-900 cm⁻¹) of the PH₂ group, scissoring vibration (∼1070 cm⁻¹) of the PH₂ group and stretching vibration of the P–H bond, respectively. Moreover, the P–H stretching mode can further shift to a lower frequency (2278 cm⁻¹). From Supplementary Table 1, available as Supplementary Data at NSR online, we can see that the P–P stretching bonds and the twisting vibration of the PH₂ group from linear P₄H₆ are closer to our observed peak, suggesting that the linear type P₄H₆ is the more possible conformer in the residue.

Besides the peaks from P₄H₆, several other obvious characteristic modes (123.8, 184.8, 218.9, 285, 357.2, 386.5, 407.7, 443.2 and 505.8 cm⁻¹) were observed below 550 cm⁻¹. These peaks are similar to fibrous red phosphorus characteristic modes [25,26], which indicated that parts of P₄H₆ were thoroughly dissociated when exposed to laser or decompression. At ambient pressure, phosphorus hydrides often undergo disproportionation into phosphorus-rich phosphanes upon exposure to light and heat [24]. However, we did not observe the Raman peaks from other phosphanes from the residue, which proves that P₂H₄ dimerized directly into P₄H₆ at high pressure, corresponding to this equation:

\begin{equation} {\rm{2}}{{\rm{P}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}} \to {{\rm{P}}_{\rm{4}}}{{\rm{H}}_{\rm{6}}} + {{\rm{H}}_{\rm{2}}}. \end{equation}

(2)

From the recovered sample, it is confirmed that P₂H₄ dimerizes at high pressure. However, as both Raman and IR signal disappeared at above 20 GPa, we could not get in situ high-pressure vibrational modes. Therefore, it might be possible that other compounds generated at high pressure, such as P₄H₆·H₂, which may easily decompose back to P₄H₆ and H₂ upon decompression.

Figure 2d shows that the Raman spectra of the residue quenched from 35 GPa. After decompression to 1 atm, typical black phosphorus modes were observed [29,30]. Therefore, P₄H₆ eventually decomposed into elemental phosphorus at 35 GPa. Hence, the corresponding reaction is as follows:

\begin{equation} {{\rm{P}}_{\rm{4}}}{{\rm{H}}_{\rm{6}}} \to 4{\rm{P + 3}}{{\rm{H}}_{\rm{2}}}. \end{equation}

(3)

From the in situ high-pressure XRD (Fig. 2d), the typical diffraction rings of cubic phosphorus further confirmed the thorough decomposition of P₄H₆ at high pressure.

Stoichiometric evolutions of PH₃ at low temperature

The superconductivity of elemental phosphorus has already been studied both experimentally and theoretically [31–33]. The maximum T_c is about 9.5 K at 32 GPa before it decreases with pressure. Near 100 GPa, the T_c is about 4.3 K at 160 GPa, and no superconducting transition was detected in the temperature range from 4 to 40 K. The much lower T_c of phosphorus compared to 100 K indicates that PH₃ or other phosphorus hydrides should be responsible for the superconductivity observed at 200 GPa in Drozdov's work. Since Drozdov et al. increased the pressure at low temperature (T <200 K) [15], we speculate that this discrepancy is due to the different experimental protocols used in these two works. Low temperature could hinder the polymerization/decomposition of phosphorus hydrides and secure phosphorus hydrides to much higher pressure.

To find out whether low temperature can hinder the reactions and further indentify the superconducting candidate, we studied the high-pressure behavior of PH₃ at low temperature (<200 K). First, we compressed PH₃ up to 31 GPa, when P₂H₄ dimerized into P₄H₆ at room temperature. However, after we decompressed the sample to ambient pressure at low temperature, the sample became transparent again (the inset image in Fig. 3a). As shown in Fig. 3a, the sample decomposed after laser irradiation and the resulting opaque solid (the inset image in Fig. 3a was identified as Hittorf's phosphorus) and two characteristic Raman modes from P₂H₄ (2307 and 2317 cm⁻¹) were also found. The transparency of the residue and strong peaks from P₂H₄ suggest P₂H₄ was dominant in the sample decompressed from 31 GPa at low temperature. However, it can only survive below 25 GPa at room temperature, proving that low temperature can greatly hinder the polymerization of phosphorus hydrides. We further compressed the sample up to 60 GPa, and studied the Raman spectrum of the quenched residue. Similar photodecomposition and typical Hittorf's P Raman modes (Supplementary Fig. 5, available as Supplementary Data at NSR online) were observed, which further suggested that P₂H₄ could remain up to 60 GPa at low temperature.

Figure 3.

(a) The Raman spectrum of the sample quenched from 31 GPa. The inset image shows the photo-induced transition after laser irradiation. (b) The Raman spectra of the sample collected during decompression from 102 GPa. (c) The Raman spectra of the residue quenched from 205 (blue line) and 102 (red line) GPa, respectively. (d) The phase diagrams of PH₃ at room temperature and low temperature.

As the superconductivity was observed at pressures >80 GPa, we compressed PH₃ at low temperature up to 102 and 205 GPa, respectively, to investigate the responsible superconducting candidate. As shown in Fig. 3b and c, we did not observe any peaks from the Raman spectra at 102 and 205 GPa, due to its metallic state as identified by Drozdov et al. After decompressing to 31 GPa, a strong peak at around 2212 cm⁻¹ was observed, and it shifted to around 2250 cm⁻¹ after the sample was quenched to ambient conditions. We also observed several other peaks at around 383, 418, 798 and 880 cm⁻¹, which agreed well with our simulated P₄H₆ (Supplementary Table 1, available as Supplementary Data at NSR online) Raman, confirming the residue recovered from 102 GPa and 133 K was P₄H₆. As shown in Fig. 3c, the Raman spectrum of the sample decompressed from 205 GPa is almost the same as that from 102 GPa, suggesting P₄H₆ could be stable up to 205 GPa at low temperature. As P₄H₆ was observed after decompression from 102 and 205 GPa, we propose that the corresponding superconducting candidate in Drozdov's work could be P₄H₆. By combining the PH₃ structure evolutions at both room and low temperatures, we could obtain the phase diagram of PH₃ under high pressure (Fig. 3d). As shown in Fig. 3d, at room temperature, two-step dimerization occurred at around 12 and 25 GPa, and P₄H₆ finally decomposed into elemental phosphorus at 35 GPa. However, at low temperature, P₂H₄ could exist up to 60 GPa. P₄H₆ was maintained from 102 to 205 GPa.

Theoretical calculations

We further performed structural searches on P₄H₆ at 100, 150 and 200 GPa with maximum simulation cells up to 4 formula units (f.u.); two stable structures with space group Cmcm (<182 GPa) and C2/m (>182 GPa) were found. Phonon dispersions calculations of the two structures do not give any imaginary frequencies and therefore this verifies their dynamic stabilities (Fig. 4). The superconducting T_c was estimated using the Allen and Dynes modified McMillan equation [34] with a typical choice of |${\mathop \mu \limits}^* \, = \,0.13.$| The electron–phonon coupling constant λ of the Cmcm structure is only 0.59 (Table 1) at 100 GPa, and a superconducting T_c of 13 K was obtained. A relatively large λ value of 1.39 was found for the C2/m structure at 200 GPa, and the superconducting T_c was estimated to be 67 K. As summarized in Table 1, the estimated T_c agrees with the values measured by Drozdov et al., suggesting that P₄H₆ could be responsible for the superconductivity.

Figure 4.

Phonon dispersions, phonon density of states projected onto atoms (PHDOS), the spectral functions α²F(ω)/ω and electron–phonon coupling integration of λ(ω) for the (a) Cmcm structure at 100 GPa and (b) C2/m structure at 200 GPa, respectively.

Table 1.

The calculated electron–phonon coupling constants (λ), the logarithmic average phonon frequency (ω_log) and the T_c with μ* = 0.13.

Phases	Pressure (GPa)	λ	ωlog	Tc (μ* = 0.13)
Cmcm	100	0.59	889	13 K
C2/m	200	1.39	700	67 K

Similar to H₂S, PH₃ is unstable at high pressure. Instead of becoming more hydrogen-enriching, it dehydrogenates through a series of polymerization/decomposition processes upon compression. This could be one of the critical factors that limit the maximum T_c near 100 K, at the same pressure where the H–S system has a T_c up to 180 K. These phenomena from H₂S and PH₃ highlight that avoiding the pressure-induced dehydrogenation or becoming more hydrogen-enriched is vital for a superconducting hydride with a high T_c.

CONCLUSION

In summary, we determined the stability of PH₃ under high pressure. At room temperature, two steps of polymerization were obtained. P₂H₄ and P₄H₆ were the reaction products of the first and second step dimerization, respectively. Above 35 GPa, the generated P₄H₆ completely decomposed into elemental phosphorus. However, at low temperature, P₄H₆ could remain up to 205 GPa. Vibrational measurements and theoretical simulation confirmed the formation of P₂H₄ and P₄H₆, which enriches the phase diagram of the P–H system under high pressure. Our work proves that the P₄H₆ phase can be generated under high pressure and suggests that it might be responsible for the reported superconducting transition.

METHODS

Solidified PH₃ was prepared via a cryogenic method and sealed into a symmetric DAC at ∼2 GPa for our in situ high-pressure measurements. T301 stainless steel and tungsten gaskets were used for the room-temperature and low-temperature measurements, respectively. The ruby fluorescence and Raman shifts of the diamond were used to calibrate the pressure. A micro-Raman system (Renishaw, UK) with a 532-nm laser excitation was used to obtain the sample's Raman spectra. The high-pressure in situ IR spectra were collected on a Bruker VERTEX 70v FTIR spectrometer and a custom-built IR microscope. High-pressure XRD measurements were carried out at the BL15U1 beamline of the Shanghai Synchrotron Radiation Facility (λ = 0.6199 Å) [35]. Low temperature was generated by cryostat using liquid nitrogen. Detailed information about each cycle is provided in the Supplementary Materials, available as Supplementary Data at NSR online. The ab initio structure predictions for P₄H₆ were performed using the particle swarm optimization technique implemented in the CALYPSO code [36,37]. CALYPSO has been used to investigate many materials at high pressures [38–42]. The ab initio structure relaxations were performed using density functional theory with the Perdew–Burke–Ernzerhof generalized gradient approximation implemented in the Vienna ab initio simulation package (VASP) [43]. Details of the simulations are provided in the Supplementary Materials, available as Supplementary Data at NSR online.

FUNDING

This work was mainly supported by the National Natural Science Foundation of China (11874076), the National Science Associated Funding (NSAF, U1530402) and the Science Challenging Program (TZ2016001).

Author notes

Equally contributed to this work.