High-pressure response of vibrational properties of b-As x P 1 – x : in situ Raman studies

The structural evolution of black arsenic-phosphorous ( b-As x P 1 – x ) alloys with varying arsenic concentrations was investigated under hydrostatic pressure using in situ Raman spectroscopy. High-pressure experiments were conducted using a diamond anvil cell, which revealed pressure-induced shifts in vibrational modes associated with P – P bonds ( A 1 g , A 2 g , B g 2 ) , As – As bonds ( A 1 g , A 2 g , B g 2 ) , and As – P bonds in b-As x P 1 – x alloys. Two distinct pressure regimes were observed. In the ﬁ rst regime ( region I ) , all vibrational modes exhibited a monotonic upshift, indicating phonon hardening due to hydrostatic pressure. In the second regime ( region II ) , As 0.4 P 0.6 and As 0.6 P 0.4 alloys displayed a linear blueshift ( or negligible change in some modes ) at a reduced rate, suggesting local structural reorganization with less compression on the bonds. Notably, the alloy with the highest As concentration, As 0.8 P 0.2 , exhibited anomalous behavior in the second pressure regime, with a downward shift observed in all As – As and As – P Raman modes ( and some P – P modes ) . Interestingly, the emergence of new peaks corresponding to the E g mode and A 1 g mode of the gray-As phase was observed in this pressure range, indicating compressive strain-induced structural changes. The anomalous change in region II con ﬁ rms the formation of a new local structure, characterized by elongation of the P – P, As – As, and As – P bonds along the zigzag direction within the b-As x P 1 – x phase, possibly near the grain boundary. Additionally, a gray-As phase undergoes compressive structural changes. This study underscores the signi ﬁ cance of pressure in inducing structural transformations and exploring novel phases in two-dimensional materials, including b-As x P 1 – x alloys. Supplementary material for this article is available online


Introduction
Among two-dimensional (2D) materials, black phosphorous (BP) has drawn immense attention in many fields due to its relevance and potential in a wide range of applications. Its unique properties, such as a tunable direct bandgap (0.3 eV and 2 eV for bulk [1] and monolayer [2] BP, respectively), high carrier mobility [3][4][5], and strong in-plane anisotropy [6], render it suitable for use in photonic, thermoelectric, sensing, and optoelectronic applications. The metastable form of arsenic; black arsenic (b-As), exhibits similar electronic and optical properties [7,8] to BP, including its orthorhombic puckered honeycomb crystal structure. Consequently, further modifications to BP have been made by alloying it with the congener material arsenic, resulting in b-As x P 1-x alloys. These alloys possess a unique crystal structure, high anisotropy, electrical [9], optical [10], and thermal [11,12] properties, similar to BP, but with modifications. Various applications based on b-As x P 1-x alloys have been reported to date, including Er-doped fiber ultrashort laser generators [13], thermoelectrics [12], photonic microheaters [14], and Li-ion batteries [15]. The bandgap of b-As x P 1-x alloys can be tuned down to approximately 0.15 eV, indicating their potential as promising candidates for mid-infrared photodetectors [16][17][18][19]. Experimental reports confirm that b-As x P 1-x alloy-based photodetectors exhibit high detectivity beyond 4.9 × 10 9 Jones in the mid-infrared range of 3-5 μm [16]. As b-As x P 1-x alloys have a similar orthorhombic honeycomb puckered structure as BP (with slight changes), they possess strong inplane anisotropic optical absorption and Raman scattering [18]. Furthermore, a monolayer of b-As x P 1-x can be a highly efficient donor in solar cells due to its high electronic mobility and direct band gap of 1.54 eV, according to theoretical reports [20]. Overall, b-As x P 1-x alloys exhibit outstanding thermal, optical, electrical, and photoelectric properties, including a very narrow bandgap, anisotropic infrared absorption, and bipolar transfer characteristics, making them promising for infrared photodetectors and high-performance field effect transistors [21].
Considering the lattice structures of elements in Group V, they exist in two phases: the α (A17) phase and β (A7) phase. The α phase has an orthorhombic honeycomb puckered crystal structure with the space group Cmca, while the β phase is a rhombohedral buckled layered crystal structure with the space group R3m. Among the elements, phosphorous exists in the α phase as BP, while other pnictogens (such as As, Sb, and Bi) form their most stable allotropes in the β phase known as gray As, gray Sb, and metallic Bi, respectively. For arsenic, the α phase is identified as black arsenic (and known as b-As), which is analogous to BP in terms of its orthorhombic puckered layered crystal structure and other characteristics. Blue phosphorous corresponds to the β phase of phosphorous, forming a rhombohedral buckled structure similar to gray arsenic. Therefore, b-As x P 1-x alloys (α phase) exhibit an orthorhombic structure for As concentrations below 83%.
The lattice structure of a material can be deformed by strain, resulting in changes in its electronic structure and subsequently affecting properties such as bandgaps, electrical properties, magnetic properties, optical properties, thermal conductivities, catalytic properties, phase transition, and interlayer coupling [22]. Alloying, intercalation, and inducing high-pressure are well-known methods used to modify crystal structures.
Strained 2D materials have been extensively studied over the years [23][24][25][26]. Particularly, first-principal calculations predict that lithium-intercalated BP, under high-pressure conditions, could transform into the blue-P structure. However, experimental work by Rajapakse et al have shown that lithium intercalation in BP only leads to bond expansion [27], while high pressure applied to intercalated BP induces structural reorganization in BP [28]. Interestingly, recent work by Gao et al reported a phase transition from b-As to gray arsenic (g-As) [29] under high pressure. It has been observed that the onset of g-As structure occurs at a critical pressure of 3.48 GPa, and both b-As and gray-As coexist between 3.48 and 5.37 GPa before b-As completely converts to g-As above 5.37 GPa. The process has been shown to be reversible up to 3 GPa, with a conversion of back to b-As. However, above 5.37 GPa, the transformed gray-As structure remains even after pressure was released [29]. Our previous studies on Li intercalation to b-As x P 1-x alloys also provided confirmation of a Li-intercalation driven phase segregation in b-As x P 1-x alloys (α phase) resulting in the formation of gray As (β phase) with the emergence of new peaks characteristic of gray arsenic after a critical degree of lithiation. However, the response of b-As x P 1-x alloys under high pressure has not been studied thus far, despite their intriguing properties and potential applications.
This study primarily focuses on understanding the effect of high-pressure on the crystal structure of b-As x P 1-x alloys by investigating their vibrational modes using in situ Raman spectroscopy. Specifically, the study examines the structural variations of b-As x P 1-x alloys with varying As concentrations under hydrostatic pressure generated by a diamond anvil cell (DAC). Tuning properties under strain is important for achieving high-performance devices and exploring new opportunities.

Methodology
Synthesis and characterization b-As x P 1-x alloys with varying As concentrations were synthesized using the chemical vapor transport method. A detailed synthesis process is explained in the supporting information. Three alloys, namely b-As 0.4 P 0.6 , b-As 0.6 P 0.4, and b-As 0.8 P 0.2 , were characterized using transmission electron microscopy, scanning electron microscopy, Raman spectroscopy, x-ray diffraction, and energy-dispersive x-ray spectroscopy techniques, and were subsequently subjected to highpressure experiment. Further details of the characterizations are available in the supporting information (figures S1 and S2).

High-pressure experiment
The high-pressure experiments were conducted using a DAC setup. The DAC (Diacell HeliosDAC Almex EasyLab) consisted of two 800 μm culet diamonds, which held the sample in between, supported by a gasket and pressurized, as shown in figure 1. The pressure was generated by the gas membrane-driven movement of the top culet diamond (attached to the piston). An Inconel gasket of thickness 0.2 mm, which was indented up to 0.05 mm and had a circular hole drilled using a micro electrical discharge machine, served as the sample chamber. The sample was placed in the gasket hole and immersed in Dimethylformamide (DMF) to subject it to quasi-hydrostatic pressure while obtaining in situ Raman spectra. DMF was chosen as the pressure medium due to its transparency, low evaporation rate, and the absence of additional Raman peaks within the spectral range of interest [28].
Pressure calibration inside DAC was done using the Photoluminescence spectra of the Ruby-R2 line shift. Subsequently, the sample was loaded into the DAC, and in situ Raman spectra were collected while applying and releasing pressure. The peak parameters of the Raman spectra were analyzed using Fityk software. A deconvoluted Raman spectrum is included in figure S3 of the supporting information.

Computational scheme
The structural analysis for b-As x P 1-x alloys under pressure was conducted using density functional theory (DFT) [30,31] implemented in the Vienna ab initio simulation package [32], employing a plane wave basis set code. The electron-ion interaction was described using the projector augmented wave algorithm [33], and the Perdew-Burke-Ernzerhof [34] generalized gradient approximation approach [35] was utilized for the exchange-correlation functional. The van der Waals interaction was taken into account using the zero damping DFT-D3 method proposed by Grimme et al [36].
To construct b-As x P 1-x alloys, A 2 × 2 × 2 rectangular unit cell of BP containing 64 P atoms was initially considered. The distribution of As atoms in the alloys was optimized by randomly substituting P atoms with As atoms within the unit cell. Among the total of 64 P atoms per unit cell, there are n n 64 64 -! ! ( ) ! possible configurations to substitute n P atoms with n As atoms, but many configurations can be reduced through symmetry analysis. A full structural relaxation process was then performed, without any restriction on the unit cell volume, unit cell shape, or atomic positions. To investigate  In situ Raman spectra obtained at different pressure values for three b-As x P 1-x samples, As 0.4 P 0.6, As 0.6 P 0.4, and As 0.8 P 0.2 . The spectrum after the pressure was released is also shown for each sample. The spectra indicated in pink and violet correspond to pressure regions I and II, respectively. the effect of the pressure on the structural evolution of b-As x P 1-x alloys, a hydrostatic pressure ranging from 0 to 10.81 GPa was applied. Figure 2 presents the Raman spectra of all three b-As x P 1-x samples under varying pressure. The spectra exhibit three main regions of peaks. In the high-frequency region (≈340-470 cm −1 ), Raman modes associated with P-P bonds are observed and labeled as A , g 1 B g 2 , and A , g 2 corresponding to outof-plane, in-plane along the zigzag direction, and in-plane along the armchair directions, respectively. Furthermore, in the low-frequency region of (≈200-270 cm −1 ), Raman modes associated with As-As bonds are observed and labeled as A ,  The mid-region (≈300-360 cm −1 ) exhibits two vibrational modes associated with As-P bonds.

Results and discussion
It has been reported that with increasing As concentration, the peak positions related to As-As modes and P-P modes systematically redshift at zero pressure [12]. As the arsenic concentration in the alloy increases, a decrease in peak intensities for P-P vibrational modes is observed, while peak intensities corresponding to As-As vibrations increase.
Under hydrostatic pressure, As 0.4 P 0.6 and As 0.6 P 0.4 samples show shifting and broadening of all peaks as the pressure increases up to 9.79 GPa. Subsequently, the spectra of each sample return to their original state when the pressure is released.
All the spectra were fitted with three peaks associated with As-As modes, three peaks associated with P-P modes, and two peaks associated with P-As modes using Lorentzian line shape analysis. As the pressure increases, the Raman spectra exhibit significant changes, such as shifting and broadening of all peaks. In general, changes in peak intensities provide evidence for a change in atomic orientations, while changes in peak positions and peak broadening provide evidence for structural compression due to pressure. Figure 3 illustrates the Raman peak positions of the three P-P vibrational modes as a function of pressure for all three b-As x P 1-x samples. In the case of the As 0.4 P 0.6 sample ( figure  3(a)), all three peaks exhibit an overall blueshift with increasing pressure up to 9.79 GPa. The analysis of the peak shift with pressure reveals different behavior in two different pressure regions as discussed below. The obtained dω/dP values are indicated in table S1 of the supporting information.
In region I (highlighted with pink), all three modes experience a linear blueshift (upshift) with increasing pressure up to a maximum applied pressure, P c = 4.64 GPa. Subsequently, in region II (highlighted with blue in figure  3(a)), the modes exhibit a blueshift at varying rates within the pressure range of 4.64-9.79 GPa. The application of hydrostatic pressure compresses the sample from all directions, resulting in shortened bond lengths and increased vibrational energy, which is reflected as an upshift of the phonon modes in the Raman spectra. This phenomenon is referred to as 'pressure-induced hardening of phonon modes'.
Again, in Region II, an upshift is observed for all modes with increasing pressure, albeit at a different rate compared to Region I. It is believed that some pressure-induced structural reorganization occurs during this phase. These reorganizations cause subtle changes in the structure leading to compression or expansion of bond lengths thereby driving the system to a new local structure. Under these pressure conditions, the material transitions toward a new partially equilibrium state.
For the As 0.6 P 0.4 sample ( figure 3(b)), all three peaks display an overall blueshift with increasing pressure up to 9.79 GPa. Similar to the previous sample, the Raman modes exhibit distinct behaviors in two pressure regions. In region I, all three modes undergo a linear upshift with increasing pressure up to a maximum applied pressure, P c = 6.64 GPa. This is followed by a linear blueshift at a different rate in Region II, as observed in figure 3(b), within the pressure range of 6.64-9.79 GPa.
However, the As 0.8 P 0.2 sample (figure 3(c)) exhibits somewhat different characteristics within the accessible pressure range. A linear upshift is observed for the A 1 g and A 2 g modes, while the B 2g mode shows a downward shift with increasing pressure up to a maximum applied pressure, P c = 7.84 GPa (region I). Subsequently, for pressures greater than 7.84 GPa, the modes show an upshift (or weak dependence) at a different rate compared to Region I. The x dependence of P c on x is shown in figure S4 of the supplementary document.  Figure 4 illustrates the Raman peak positions of the three As-As vibrational modes as a function of pressure for the three b-As x P 1-x samples. All three peaks for the As 0.4 P 0.6 and As 0.6 P 0.4 samples exhibit an overall blueshift with increasing pressure but at different rates within the two regions. In the case of the As 0.6 P 0.4 sample, new peaks identified as the E g mode and A 1g mode of gray-As emerge in region II and undergo an upshift with increasing pressure. Interestingly, for the As 0.8 P 0.2 sample, the A 2 g and B 2g modes exhibit a downshift whereas the A 1 g mode shows a slower upshift in the second region. The E g and A 1g modes appear to emerge in the second pressure region of this sample and undergo a blueshift as the pressure continues to increase.
It is believed that a small amount of rhombohedral gray-As segregates from orthorhombic b-As x P 1-x in the As 0.6 P 0.4 and As 0.8 P 0.2 samples after surpassing a threshold pressure value in each sample. The downward shifting of the Raman modes in region II can be interpreted as the elongation of the As-As bonds of the b-As x P 1-x phase at or near the grain boundary with the gray-As phase, which undergoes compressive structural changes.
The Raman spectra were found to recover upon the release of the pressure for all three samples.
A pressure-induced phase transition from black As (α phase) to gray As (β phase) has been previously reported by Chaofeng et al [1]. During this process, the intermediate state is characterized by the coexistence of b-As and g-As, occurring within the pressure range between 3.48 and 5.37 GPa. In our study of b-As x P 1-x alloys (α phase), under the application of pressure, a distinct peak associated with the E g mode of g-As (β phase) becomes explicitly observable. Additionally, there is a noticeable increase in the peak area of the As-As peak cluster (excluding the E g peak), providing convincing evidence for the emergence of gray As, specifically the A 1g peak. It is important to note that the emergence of gray As is observed at higher pressures for b-As x P 1-x alloys compared to the findings reported by Chaofeng et al [1] for b-As. Specifically, for As 0.6 P 0.4 and As 0.8 P 0.2 which have higher As concentrations, the appearance of g-As occurs at around 8 GPa, and for As 0.4 P 0.6 alloy which has a lower As concentration, the emergence of g-As is not observed within the range of applied pressures, up around 11 GPa. The reversibility of the process and the transition back to the initial b-As x P 1-x alloy phase upon pressure release further confirms the coexistence of both phases within the intermediate, composition-dependent, pressure range, which aligns with the study reported by Chaofeng et al [1]. Figure 5 shows the Raman peak positions of the two As-P vibrational modes as a function of pressure for the three b-As x P 1-x samples. All three peaks for the As 0.4 P 0.6 and As 0.6 P 0.4 samples show an overall blueshift with increasing pressure at different rates within the two regions. However, in Figure 4. As-As peak positions versus pressure profiles of all three b-As x P 1-x samples, As 0.4 P 0.6 (a), As 0.6 P 0.4 (b), and As 0.8 P 0.2 (c), respectively. Dotted lines are linear fits in two distinct pressure regions. The peak positions of the new modes (identified as segregated gray As) emerged in samples with higher As concentrations (As 0.6 P 0.4 and As 0.8 P 0.2 ) are shown in orange and dark blue. the As 0.8 P 0.2 sample, both peaks show a red shift in the second region. Again, this is consistent with the elongation of the As-P bonds of the b-As x P 1-x phase at or near the grain boundary with the gray-As phase which undergoes compressive structural changes.
To understand the different Raman characteristics in two different pressure regimes (regions I and II), we analyzed the lattice constants, volume, and bond lengths (including armchair and zigzag bonds) under pressure using our DFT results. According to our DFT calculations, bond lengths along the armchair direction monotonically decrease with pressure by approximately 0.03-0.05 Å, as shown in the top panel of figure 6. This indicates a hardening of phonon modes, which is consistent with the experimental observation of an upshift in Raman A g 2 modes.
However, by comparing the structural parameters (refer to figure S5), we found that the dominant changes in bond lengths and the lattice constants under pressure mainly occur along the zigzag direction. As depicted in the bottom panel of figure 6, the bond lengths along the zigzag direction initially remain unchanged or slowly decrease with pressure in the first regime, and then abruptly extend to larger values by approximately 0.2-0.4 Å in the second regime. The transition point is observed to depend on the As concentration. These changes in bond lengths along the zigzag direction suggest a local structural change under pressure.
The increase in bond lengths along the zigzag in the second regime leads to a softening of vibration modes, which is consistent with the redshift of As-As and As-P modes of the sample with the highest As concentration (As 0.8 P 0.2 ). It is possible that the presence of the gray-As phase, which undergoes compressive structural changes, in close proximity to the b-As x P 1-x phase may also influence the As bonds.

Conclusions
The structural evolution of black arsenic-phosphorous (b-As x P 1-x ) alloys with varying arsenic concentrations was studied under hydrostatic pressure using in situ Raman spectroscopy. Significant pressure-induced shifts were observed in all vibrational modes corresponding to P-P bonds (A 1 g , A 2 g , B g 2 ), As-As bonds (A 1 g , A 2 g , B g 2 ), and As-P bonds for different As concentrations.
For alloys with lower As concentrations, a regime (Region I) characterized by a monotonic upshift of all modes was observed, indicating phonon hardening due to hydrostatic pressure. In a second regime (Region II), a linear blueshift (or negligible change in some modes) at a reduced rate with pressure was observed, suggesting local structural reorganization in the samples and less compression of bond lengths.
The alloy with a higher As concentration also exhibited two distinct regimes within the accessible pressure limit. In Region I, there was a blueshift of all modes, while in Region II, a downward shift of As-As, and As-P Raman modes (and some P-P modes) was observed. Interestingly, the emergence of new peaks identified as the E g mode and A 1g modes of the gray-As phase was observed in this pressure range, indicating compressive strain. These anomalous changes in region II Figure 6. P-P, As-P, and As-As bond lengths of b-As x P 1-x alloys under pressure. Top panel (a)-(c) indicates P-P, As-P, and As-As bonds along the armchair direction, and bottom panel (d)-(f) along the zigzag direction, respectively. confirmed the formation of a new local structure, interpreted as the elongation of the P-P, As-As, and As-P bonds along the zigzag direction in the b-As x P 1-x phase at or near the grain boundary with the emergence of the gray-As phase undergoing compressive structural changes.