Uncovering the Phase Transition of Berlinite (α-AlPO4) under High Pressure: Insights from First-principles Calculations

LI Neng, HU Hai, GUO Fei, TAO Haizheng

(1.State Key Laboratory of Optical Fiber and Cable Manufacture Technology (Yangtze Optical Fiber and Cable Joint Stock Limited Company), Wuhan 430073, China; 2. State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Wuhan 430070,China)

Abstract: We investigated the mechanism of crystalline-to-amorphous phase transition (CAPT) for amorphous berlinite (a-AlPO4) under high pressure using ab initio constant-pressure techniques. Our results show that the pressure to the change in phase transition takes place at around 20 GPa, which is inconsistent with the previous results of around 15 GPa. To confirm the feasibility of our model, the calculated X-ray powder diffraction for crystal berlinite is concordant with the standard PDF card. By assessing a full spectrum of properties including atomic structure, bonding characteristics, electron density of states and real-space pair distribution function at each pressure, we reveal the details of phase transition. Importantly, all the information from our present results elucidates that Al-O bonds play an irreplaceable role during the process of phase transition to uncover the structural and electronic properties of berlinite. Overall, our work substantiates that it is essential to utilize a wide range of changes in order to provide a comprehensive understanding on the nature of the CAPT in other inorganic oxides.

Key words: aluminophosphate; atomic and electronic structures; phase transition; ab initio calculation

1 Introduction

The phase transformation of crystalline to amorphous for a-quartzberlinite (a-AlPO4) was firstly reported in 1990 via experiment[1-5]. The researchers apply a pressure of around 20 GPa to a crystalline berlinite sample in a diamond anvil cell at 300 K. Several methods were used to characterize the phase transformation, including X-ray diffraction and infrared spectroscopy. The atomic research centre in India reported that AlPO4became amorphous at 12 GPa and observed the peak of the (102) lattice plane vanishing at 14 GPa in the X-ray diffraction pattern[6]. In another study, Kruger and Jeanloz also observed that the distinctive powder diffraction pattern of the sample vanished when the pressure increased above 15±3 GPa[7]. They found that the Al-O antisymmetric tetrahedral stretching mode of 800 cm-1was missing in the infrared absorption spectra of berlinite sample at 16.9 GPa[7].

However, Garg and Sharma reported a different result using the molecular dynamics calculations[8].They discovered that this disordered phase could only be stable when the applied pressure was beyond 20 GPa. Structural parameters were calculated in attempt to illustrate the structural change, such as radial distribution functiong(r), diffraction patterns and the number of tetrahedrons[1,9,10]. Nevertheless, owing to the paucity of information on the electronic density of state at each pressure and the change of bond length and angle distribution, the details regarding the process of phase transformation have not been fully understood at the atomic level.

During the next twenty years, no further discovery on phase transformation of crystal to amorphous under high pressure was reported because of the insufficient testing methods in the atomic level in experiment and the update of more accurate pair potential in theoretical calculation[4,5,11]. As such, the present computational work will be a cornerstone and act as a paradigm for the exploration of practical possibilities in demystifying how the phase transition process of berlinite occurs under high pressure.

Herein, we optimize the berlinite model using the projector augmented wave (PAW) potentials with generalized gradient approximation (GGA)[12,13], which have been proved accurate in calculations. We calculate the electronic structure using new orthogonalized linear combinations of atomic orbitals (OLCAO)[14], which is expedient and efficient for the calculation of electronic structure and optical properties. In this work, bond lengths and angle distributions are systematically calculated to illustrate the details of phase transformation.The changes of electronic density of state with pressure are also calculated. It is interesting to note that the intermediate band appears near Fermi energy level when the applied pressure increases to around 20 GPa, which has not been reported previously.

2 Computational methods

Fig.1 The 4×4×2 supercell of crystal berlinite. Berlinite AlPO4 exists in the α-quartz structure (α-AlPO4) at ambient conditions. Al and P atoms replace Si atoms in adjacent tetrahedrons

Table 1 Atomic positions of berlinite (α-AlPO4) model (Z = 22;space group: 152 P3121; a=4.943 Å, and c=10.95 Å)

We obtained the berlinite model from Findit software, an inorganic crystal structure database.The atomic positions in the model are listed in Table 1. The structural parameters are shown as follows:Z=22, space group No. 152 (P3121),a=4.94292 Å, andc=10.94761 Å. We built a 4×4×2 supercell according to the structural parameters, as shown in Fig.1. Berlinite is isostructural to SiO2, with Al and P atoms replacing Si atoms in adjacent tetrahedrons[15-17]. After constructing the berlinite model, we first calculated the X-ray power diffraction pattern using Crystal Maker and compared it with the experimental data to confirm the feasibility of the model. The structural relaxation of the 4×4×2 berlinite supercell was carried out by using ab initio simulation package (VASP)[12,13], and various physical properties were calculated using the orthogonalized linear combination of atomic orbitals (OLCAO) method[14]. The method has been applied to atomic and electronic mechanism on many other complex materials in the recent years[17-22].

For structural relaxation, the projector augmented wave (PAW) potentials with generalized gradient approximation (GGA) supplied in the VASP package were used for the exchange-correlation potential. We used a cutoff energy of 400 eV, a relatively high accuracy for the ground state electronic convergence limit(10-5eV) and force convergence (-10-2eV/Å). The stress level of the final equilibrium structure is 0.004 GPa. A 3×3×2k-point was used to ensure the accuracy of optimization. In the OLCAO calculation, and a full basis consisting of atomic orbitals of Al (1s, 2s,2p), P (1s, 2s, 2p), and O (1s, 2s, 2p) was used for the self-consistent electronic structure calculation. The real-space pair distribution function (RPDF) for Al-O and P-O pairs was calculated using interactive structure analysis of amorphous and crystalline systems[23].

3 Structures and model construction

In order to confirm the feasibility of the berlinite model, we calculated the X-ray powder diffraction(XRD) pattern of the model using crystal maker and compare it with data from experimental measurements.It can be seen from Fig.2 that the main peak of the computational pattern is similar to that of the experimental data, such as lattice plane [102] and [100].Therefore, the berlinite model is good enough to reflect the structure of the berlinite crystal. However, there are some differences and we speculate that the cause of deviation contributes to the following two reasons: the experimental sample is far from a prefect crystal with impurities and defects, which results in many dislocation and other peaks appearing in experimental data compared with the computational pattern. The approximation algorithm in Bragg equation provides a few errors, which make the diffraction angle of some peaks in computational pattern deviate from that in experimental data.

Fig.2 The XRD powder pattern calculated using crystal maker is compared with the experimental data. The similarity between the two diffraction patterns verifies the feasibility of our model and the differences are attributed to the defects and impurities of the sample

4 Results and discussion

4.1 The structural change of berlinite upon densification

It is interesting to examine the structural and electronic change in berlinite under pressure. To simulate the application of external pressure, we shrunk the lattice parameters in proportion, that is, isostatic pressing and then optimize the model using Vienna Ab-initio simulation package (VASP) with plane wave pseudo potential, as shown in Table 2. The external pressure, density, volume, and free energy of the optimized berlinite models were also summarized in table, and the change of density and energy with respect to pressure is depicted in Fig.3. Apparently, the density and energy of a model increase gradually with the augment of external pressure. Obviously, pressure can be seen as a form of transforming energy to matters the same way as temperature. The atoms in the crystal have to generate some degrees of disorder upon absorbing the energy to destroy the most stabilized crystalline structure. Furthermore, Fig.3 shows that the sudden change of density and energy with pressure occurs at an inflection point A at 19.42 GPa. This can be attributed to the structural change of the berlinite model at about 20 GPa. We can not confirm, however, that the crystalline-to-amorphous phase transition (CAPT) indeed occurs at around 20 GPa. Further calculations on electronic properties such as density of state (DOS), bond lengths (BLs) and bond angles (BAs) will have to be used to explicate this structural changing process.

Fig.3 Energy and density of the berlinite model under pressure.The energy curve shows a sudden change at point A, 19.42 GPa

4.2 Physical properties of the berlinite model upon densification

In order to obtain more details on the structural change of berlinite under pressure at atomistic level,we analyzed the real-space pair distribution function(RPDF) according to Eq. (1):

where,αandβlabel two different atoms in materials,nαβ(r) is the number ofβatoms at the spherical shell,one a atom as the centre of sphere, andras the radius.

Table 2 The lattice parameters of the models and the relative ambient pressure, density and energy after optimization

Fig.4 The radial pair distribution functions (RPDFs) were calculated using interactive structure analysis of amorphous and crystalline systems

Fig.5 (a) Al-O and (b) P-O bond lengths with respect to external pressure

The calculated total and partial RPDFs for Al-O and P-O pairs are shown in Fig.4. At zero pressure, the RPDFs for Al-O and P-O pairs have only one well-resolved peak at about 1.73 Å and 1.52 Å, respectively,which agrees with previous works. This phenomenon obviously contributes to the speciality of periodicity for crystal. At pressures below 20 GPa, the Al-O and P-O partial RPDFs maintain the same features as they did at zero pressure, indicating that the periodicity of crystal has not changed. On the other hand, the value of RPDFs slightly decreases, which infers that the range of the bond lengths for Al-O and P-O pairs has the tendency to broaden under lower pressure. When the pressure exceeds beyond 20 GPa, there appears a sudden change that the range of BLs suddenly broadens to 1.480-1.602 Å for P-O pairs and 1.677-1.829 Å for Al-O pairs with the value of RPDFs greatly decreasing(see Fig.4(d)). We can also observe the same sudden change from Fig.3 (point B). The energy in our berlinite model increases at a faster rate. Both sudden changes indicate that the structure of berlinite transforms to another phase at the pressure of around 20 GPa. Comparing the three plots in Figs.4(d)-4(f) to the ones in the left (Figs.4(a)-4(c)), it is distinct that the new phase formed by pressure above 20 GPa is less resistance to pressure.

Fig.6 (a) The total density of state (TDOS) and (b-d) partial density of state (PDOS) for berlinite

The most information about the structural change under high pressure can be obtained from the calculated RPDFs. However, they are unable to visually reflect the relaxation of atoms and the change of BLs and BAs in the structure. Therefore, we calculated the BLs and BAs to further investigate the structural change at each pressure. The bond lengths of Al-O and P-O pairs are displayed in Fig.5(a) and Fig.5(b), respectively. Compared with the RPDFs (Fig.4), the trends in BLs with continuous pressure are the same. We know that [AlO4]and [PO4] tetrahedrons in crystalline berlinite are not regular and the BLs of Al-O and P-O pairs are near 1.73 Å and 1.52 Å, respectively. From the figure, it is evident that the BLs for both atomic pairs are slightly shorter under 20 GPa, but their ranges are not visibly broader. Therefore, it is noteworthy that there occur some displacements at each site in the crystal lattices,but the periodicity of crystalline maintain the same under 20 GPa.

The calculated total electronic density of states(TDOS) as a function of applied pressure is delineated in Fig.6(a). At zero-pressure, the structure has a band gap of 6.3 eV, which is relatively higher than that of a-SiO2(5.2 eV). Such phenomenon is in line with the previous reports[20,21]. The band gap does not change appreciably as the pressure increases up to 20 GPa,but it is noted that the number of electrons is steadily decreasing at one energy state with the increase of applied pressure. Since the total number of electrons is constant, we can speculate that the applied pressure makes the distribution of electrons broader. This leads to the high-resolution peaks formed by the localization of electrons becoming less sharp. Moreover, the mid-gap from -3.6 to -5.0 eV in the valence band at zero-pressure diminishes gradually as the applied pressure increases and completely disappears at the pressure of around 21 GPa. There is also a drastic change in the shape of the DOS starting from the pressure at about 21 GPa. Intuitively, there is no obvious high-resolution peak for both valence band and conduction band. The band gap also undergoes a drastic change to 4.3 eV with its position moving to lower energy level.The TDOS will not change to any further extent when higher pressure is applied to the model. These phenomena are similar to the densification of quartz glass.Therefore, we conclude that the crystalline berlinite(α-AlPO4) undergoes phase transformation to amorphous state at about 20 GPa. Interestingly, the intermediate band appears near the Fermi energy level when the applied pressure increases to 21 GPa, which has not reported previously. Notably, the intermediate band contributes to the orbitals of Al (3s, 3p, 3d) and O (2p).

4.3 The change in coordination number upon densification

From the aforementioned results and analyses,CAPT occurs at around 20 GPa. Fig.7 compares the model of the initial (low-pressure) berlinite phase with the high-pressure phase. Obviously, the initial model shows distinctive crystalline properties: periodicity and symmetry, but the high-pressure model endows properties of the amorphous state: randomness. As such,when the external pressure is applied to the initial berlinite model, the vibration of atoms in the crystal lattice will aggravate and the energy of the entire system will increase. High pressure propels the atoms to leave their initial positions and generate a little displacement to reduce the system’s energy. In this manner, we can observe the breaking and formation of bonds in the process of phase transition. Besides, the of Al-O and P-O will change with the increasing pressure, as corroborated in Fig.7. The berlinite model retains the 4-fold coordination from zero pressure up to around 20 GPa. With the increasing pressure, the phenomenon of 4 CN and 5 CN coexistence, even 4, 5 and up to 6 CN coexistence appear for Al-O bond. Nonetheless, 6-fold P-O CN is not manifested at the final model (even at high pressure with 23.69 GPa). This again exemplifies that the ability of the Al-O bond to resist external pressure is weaker compared with the P-O bond.

Fig.7 The change of coordination number with increasing pressure for berlinite model. The inset is the atomic structure without and with high pressure

5 Conclusions and prespective

We have calculated the structural parameters(crystal to amorphous) for berlinite under different pressures and compared them with the experimental data. XRD patterns are calculated to confirm the feasibility of our model, and radial pair distribution functions, density of states, bond lengths, and bond angles are calculated to show details of structural change at the atomistic level. In this work, our results elucidate that crystalline berlinite transform to amorphous at around 20 GPa, which is comparatively higher than the previous work (15±3 GPa). This situation can be ascribed to the prefect crystal model for theoretical studies, which has high resistance to pressure. Importantly, the Al-O pair has a smaller resistance to pressure than the P-O pair, which may be the reason that the pressure of structure change for berlinite is lower than quartz (about 25 GPa). In addition, the coordination number of Al-O and P-O bonds increases upon high pressure, which have not been reported in literature. Furthermore, the broadening of the bond length distributions can be clearly linked to the increased population of Al and O atoms or P and O atoms with higher coordination numbers greater than 4 for Al or P. If a crystal consists of a weak bond and it is easily breakable with additional pressure,it can transform to an amorphous state at lower pressure. Overall, our work substantiated that it is essential to utilize a wide range of changes in order to provide a more comprehensive understanding on the nature of the crystal to amorphous phase transformation.

It is fitting to comment on further research than can be anticipated using the computational approach we used here of materials under densification. This approach can also be properly modified to study other inorganic oxides such as B2O3or GeO2or these oxides with properly added impurities such as Ti or alkali metals for targeted study. The techniques used for densification and the ab initio calculations of the bonding and electronic properties under densification can be easily carried over to these similar systems, which can certainly reveal many of the interesting and hither to undiscovered features in the physics of phase transition from crystal to amorphous phases. It is also desirable to extend the simulation to decompressing process and in using smaller pressure increments to further improve accuracy. Some of these works are currently in progress and will be reported in the future.