Pressure-Induced Destabilization and Anomalous Lattice Distortion in

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Pressure-Induced Destabilization and Anomalous Lattice Distortion in TcO2 Baisheng Sa,*,† Honglei Yang,† Naihua Miao,‡ Kangming Hu,† Jian Zhou,‡ Bo Wu,† and Zhimei Sun*,‡ †

Multiscale Computational Materials Facility, and Key Laboratory of Eco-materials Advanced Technology, College of Materials Science and Engineering, Fuzhou University, Fuzhou 350108, People’s Republic of China ‡ School of Materials Science and Engineering, and Center for Integrated Computational Materials Science, International Research Institute for Multidisciplinary Science, Beihang University, 100191 Beijing, People’s Republic of China S Supporting Information *

ABSTRACT: Tc-based oxides are of interest because of their complex crystalline structures. In this work, the phonon dispersions, lattice distortions, and elastic constants of TcO2 at external pressures up to 120 GPa were comprehensively studied using first-principles calculations. It is found that the lattice dynamic stability of TcO2 can be assessed by fitting the Γ−Z acoustical phonon branch. The applied external pressure can be divided into three ranges: the low-pressure stable range, the middle-pressure buckling range, and the high-pressure unstable range. Interestingly, the variation tendency of the low-pressure stable range is very close to that of the high-pressure unstable range. On the other hand, the TcO2 lattice responds intensely to external pressure in the middle-pressure buckling range, which can be sustained under about 71 GPa pressure. More importantly, we have unraveled the pressure-induced lattice distortion in TcO2, which leads to anomalous behaviors for the lattice constants, Tc−O bond lengths, and elastic constants at 10 and 20 GPa external pressures. transitions.22,23 However, a comprehensive understanding of the structure evolution of TcO2 at positive external pressure is still lacking. In this work, we went a step further and focused on the lattice dynamic properties and structure evolutions of TcO2 under positive external pressures up to 120 GPa on the basis of density functional theory calculations. We further unraveled the origin of the anomalous lattice distortion in TcO2, which will shed light on the understanding and application of TcO2 and Tc-based complex compounds under pressure.

1. INTRODUCTION Technetium (Tc) is the first artificially made element (Z = 43); it is centrally located in the periodic table and is the lightest radioelement with a long half-life.1−3 Its isotopes include masses from 85Tc to 120Tc, where most of the technetium is isotopically present as 99Tc from the fission of 235U. Man-made 99 Tc is a pure β emitter and has been widely used as the radioactive tracer in diagnostic imaging procedures in nuclear medicine.4 The 4d55s2 electron configuration of Tc makes it possible to form complex compounds5−8 and alloys.9−12 Up to nine valence states ranging from −1 to +7 of Tc have been observed from the redox chemistry.5 There are two identified technetium oxides, the black TcO213 and the yellow Tc2O7.14,15 It is worth noting that distinguished magnetism with anomalously high Neél temperatures in the Tc-based ternary perovskites CaTcO316 and SrTcO317,18 has been found due to the cooperative rotation of the TcO6 octahedra19 and the itinerant to localized transition.20 TcO2 is made up of distorted TcO6 octahedra,13 which plays a key role in the ternary perovskites CaTcO3 and SrTcO3. A systematic understanding of the TcO6 octahedra in TcO2 is of great interest and importance as well. Recently, the negative pressure induced TcO6 octahedron to TcO5 hexahedron polyhedral transformation and corresponding phase transition have been found by means of ab initio random structure searching.21 The phenomenon indicates that the TcO6 octahedra in TcO2 are very sensitive to external pressure. In fact, external pressure is a powerful tool to adjust the physical and chemical properties of materials, especially to induce structure or property © 2017 American Chemical Society

2. COMPUTATIONAL DETAILS Our density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package24 (VASP) in conjunction with the projector augmented wave (PAW) generalized gradient approximations25 (GGA) of Perdew−Burke−Ernzerhof26 (PBE) pseudopotentials. The valence electron configurations for the Tc and O were 4s24p65s24d5 and 2s22p4. The automatically generated k-point set of 8 × 8 × 8 with Γ symmetry was used. The relaxation convergences for ions and electrons were 1 × 10−5 and 1 × 10−6 eV, respectively, which were achieved with a cutoff energy of 600 eV. The crystal structures and polyhedra were visualized using the VESTA27 package. The YPHON code28 was applied to obtain the phonon frequencies within the density functional perturbation theory (DFPT) methods.29 We used a 2 × 2 × 2 supercell and 3 × 3 × 3 K-points for the phonon DFPT calculations. Received: June 13, 2017 Published: August 9, 2017 9973

DOI: 10.1021/acs.inorgchem.7b01481 Inorg. Chem. 2017, 56, 9973−9978

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Figure 1. Calculated phonon dispersion curves of TcO2 at given pressures. It is worth noting that good descriptions for the electronic structure and elastic and magnetic properties of CaTcO3 were found by using the GGA + U method.30 However, according to Taylor’s previous results31 and our previous work,21 GGA-PBE described the crystal structure of TcO2 better than the GGA + U method. Moreover, the spin-polarized calculations show that the calculated electronic spinpolarized magnetization parameters for all of the atoms and electrons are equal to 0. Hence, all of the results of present work were without the Hubbard U approach and spin polarization.

influence the structural stability of TcO2. In short, we can judge the lattice dynamic stability of TcO2 by simply analyzing the Γ−Z acoustic phonon branch. To get a quantitative description of the lattice dynamic stability for TcO2 under pressure, we further studied the minimum Γ−Z sound velocities by fitting the slopes of the lowest frequency acoustic dispersion curve along the Γ−Z direction. The fitting details can be found in the Supporting Information. The positive sound velocity protects the good lattice stability, and the negative value indicates the instability of the TcO2 lattice along the c direction. Figure 2 shows the

3. RESULTS AND DISCUSSION We first evaluated the lattice dynamic stability of TcO2 under external pressure by calculating the phonon dispersions. Figure 1 illustrates the calculated phonon dispersion curves of TcO2 at selective pressures. As can be seen in Figures 1a−d, no imaginary phonon mode has been found for TcO2 under external pressure up to 70.4 GPa, suggesting that TcO2 shows good lattice dynamic stability in the pressure range from ambient conditions to 70.4 GPa. However, as shown in Figures 1e,f, with a further increase in the external pressure, there exists a small negative acoustic phonon branch along the Γ−Z (0 0 0.5) direction at 80.7 and 120.3 GPa, indicating that the TcO2 lattice is unstable along the c direction at certain pressures.32 Apart from the negative acoustic phonon branch along the Γ−Z direction, we found no further imaginary phonon dispersion for TcO2. It is also worth noting that increasing the pressure enhances the frequencies of the all the acoustic and optical degenerations, because the external pressure limits the vibration range of the atoms and increases the lattice vibration frequencies to consume the internal energy.33 According to the phonon dispersion curve of TcO2 under ambient conditions in Figure 1a, we can divide the optical branches into three parts by two frequency gaps: the low-frequency part around 6−13 THz, the mid-frequency part around 14−17 THz, and the highfrequency part around 23−24 THz. It can be seen that the gap between the low-frequency and mid-frequency optical branches vanishes at 70.4 GPa pressure. In addition, the gap between the mid-frequency and high-frequency optical branches is decreased with an increase in the pressure. On the other hand, another new gap appears inside the mid-frequency optical branches and further divides the mid-frequency optical branches into two parts. Nevertheless, this behavior does not

Figure 2. Calculated speed of sound along the Γ−Z direction as a function of external pressure.

calculated sound velocities along the Γ−Z direction, νΓ−Z, as a function of the external pressure. Under ambient conditions, our calculated speed of sound is νΓ−Z = 3.47 km/s. In the whole pressure range, the sound velocity decreases with an increase in the pressure. Interestingly, we found that the sound velocity plot can be divided into three ranges by linear fitting to the applied external pressure: the low-pressure stable range, the middle-pressure buckling range, and the high-pressure unstable range. Since the sound velocity is in units of km/s and the pressure is in units of GPa, the units of the fitting slope of sound velocity are 10−3 N m3 s−1. The fitting slope of the lowpressure stable range (−0.0305 × 10−3 N m3 s−1 = 30.5 N m3 s−1) is very close to that of the high-pressure unstable range (−0.0325 × 10−3 N m3 s−1 = 32.5 N m3 s−1). Meanwhile, the 9974

DOI: 10.1021/acs.inorgchem.7b01481 Inorg. Chem. 2017, 56, 9973−9978

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Inorganic Chemistry fitting slope of the middle-pressure buckling range has a value more than 3 times (−0.1416 × 10−3 N m3 s−1 = 141.6 N m3 s−1), indicating the fact that the TcO2 lattice responses strongly to the external pressure in this pressure range. According to the fitting results, we found that the lattice dynamic stability can sustain up to about 71 GPa external pressure. Hence, in the following, we mainly focused on the properties of TcO2 below 71 GPa. Figure 3a illustrates the crystal structure for TcO2 under ambient conditions, where the blue spaces show the distorted

octahedron chain along the [100] direction as well as the corner-sharing connected chains can be seen in that figure.21 Our calculated volume variation of TcO2 at various pressure in Figure 3b shows that TcO2 can remain stable up to about 20% volume compression. We plotted the lattice parameters of TcO2 as a function of the external pressure in Figure 3c to further analysis the structure evolution. Our theoretical predicted lattice parameters for TcO2 are a = 5.663 Å, b = 4.793 Å, c = 5.560 Å, and β = 121.27°. It can be found that our calculated lattice parameters agree well with the experimental results under ambient conditions.13 The discrepancies between our theoretical results and the experimental data are less than 1% for all of the lattice parameters. The angle β shows an Stype growth curve with an increase in the external pressure, where the acceleration phase appears at about 10 GPa and the stabilized phase arises at the buckling range of around 71 GPa. There is a gradual decrease in the lattice constant a by an increase in the applied pressure. Although the lattice constant c generally decreases with an increase in pressure, we found a sharp decreasing inflection point at about 10 GPa for the lattice constant c. At the very low pressure range (≤10 GPa), the lattice constant c follows the tendency of the lattice constant a. At pressures higher than ≥10 GPa, the lattice constant c decreases more quickly than the lattice constant a. Under ambient conditions, the TcO2 lattice can be considered as a slightly distorted hexagonal lattice.31 With an increase in the angle β and the difference between lattice constants a and c, we cannot approximate the TcO2 lattice as distorted hexagonal at pressures higher than 10 GPa. On the other hand, the variation of the lattice constant b is more gentle. The 71 GPa external pressure leads to no more than 0.1 Å compression of the lattice constant b. The decrement ratios of lattice constants a and c are 10.5% and 15.3% from 0 to 120.3 GPa, respectively. However, for the lattice constant b, the decrement is only 1.9%. It is worth noting that there exist two kink points in the variation curve for lattice constant b. The first kink point is at about 10 GPa as well. In the pressure range of less than 10 GPa, the lattice constant b follows the tendency of the lattice constants a and c. The second kink point is at about 20 GPa, where the lattice constant b is very close to that under ambient conditions. It is interesting that the variation of the lattice constant b starts to slightly increase between these two kink points. Such a phenomenon looks very similar to the twisted distortion induced lattice expansion in Tc2O7.34 As the TcO6 octahedra have strong ionic binding with each other, the pressure induced twisted distortion mechanism in Tc2O7 cannot explain the anomalous increase in lattice constant b in TcO2. Nevertheless, we found that that the lattice distortion in TcO2 shows anomalous behaviors at 10 and 20 GPa external pressures. To understand the anomalous lattice increase in TcO2 under pressure, we analyzed the variation of Tc−O bonds. In Figure 4a, the six inequivalent Tc−O bonds in the distorted TcO6 octahedra are presented with different colors, where the bond orders are numbered from the longest to shortest. As is shown in Figure 4a, there exists four types of topological orientations of the distorted TcO6 octahedra in the TcO2 lattice. Generally, it can be seen that the Tc−O bond lengths decrease with an increase in external pressure. However, different Tc−O bonds show very different decreasing rates. For instance, under ambient conditions, the Tc−O2 and Tc−O3 bond lengths are very close, whereas the decrease in the Tc−O3 bond length is much faster than that of Tc−O2 from ambient conditions to 20 GPa. Interestingly, the bond lengths of Tc−O3, Tc−O4, and

Figure 3. (a) Crystal structure scheme of TcO2, where the large gray balls are the Tc atoms, the small red balls represent the O atoms, and the blue spaces show the distorted TcO6 octahedra. (b) Volume variation of the TcO2 unit cell. (c) Lattice parameters of the TcO2 crystal as a function of external pressure. The vertical dashed line presents the lattice stability limitation of TcO2.

TcO6 octahedra. The monoclinic TcO2 crystal belongs to the space group P21/c (No. 14) and can be described as a distorted rutile structure with the experimental measured lattice parameters a = 5.690 Å, b = 4.755 Å, c = 5.520 Å, and β = 121.45° at room temperature.13 The edge-sharing concatenated 9975

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function of external pressure in Figure 4c according to the following definition of the bond length deviation σP: 6

σP 2 =

∑i (li , P − lP) (1)

6

where lP is the average Tc−O bond length at a certain pressure. We found that σP follows the inverted S-type decreasing curve, where the accelerated phase appears at about 10 GPa and the stabilized phase arises at the buckling range. At the buckling range, σP is about halfway down in comparison to that under ambient conditions. With a further increase in the pressure to the unstable range, σP shows a slight increase. Figure 4d presents the volume of the Tc−O6 octahedron in TcO2 as a function of pressure; we found that the volume of the Tc−O6 octahedron gradually decreases with an increase in the external pressure, which follows the general compression trend. To further analyze the anomalous distortion phenomenon of TcO2 at a given pressure, we calculated the elastic constants as a function of external pressure for TcO2 using modified stress− strain methods.35,36 There are 13 independent elastic constants cij for monoclinic TcO2 with the following form:37 ⎛ c11 ⎜ ⎜ c12 ⎜ ⎜ c13 ⎜0 ⎜ ⎜ c15 ⎜⎜ ⎝0

c12 c13

0

c15

c 22 c 23 0 c 25 c 23 c33 0 c35 c44

0

c 25 c35 0

c55

c46

0

0 0

0 0

0⎞ ⎟ 0⎟ ⎟ 0⎟ c46 ⎟ ⎟ 0⎟ ⎟⎟ c66 ⎠

(2)

where the elastic constants c11, c22, and c33 describe the response stiffness of the TcO2 crystal when uniaxial tensile strain is applied along the x, y, and z directions, respectively. c12, c13, and c23 imply the ability of the material to resist xy, xz, and yz biaxial tensile strain, respectively. c44, c55, and c66 express the deformation resistance of the in-plane shear strain parallel to the xy, yz, and zx planes, respectively. c15, c25, c35, and c46 are monoclinic asymmetry perturbation terms. Figure 5 illustrates

Figure 4. (a) Tc−O bond label schematic. Tc−O (b) bond length, (c) bond length deviation, and (d) volume of the TcO6 octahedron for TcO2 as a function of external pressure. The vertical dashed line presents the lattice stability limitation of TcO2. Figure 5. Elastic constants cij for TcO2 as a function of external pressure. The vertical dashed line presents the lattice stability limitation of TcO2.

Tc−O5 overlap around 1.95 Å at about 20 GPa. On the other hand, the changing trend of Tc−O6 with an increase in the pressure is similar to that of lattice constant b; two kink points at about 10 and 20 GPa can be observed. The Tc−O6 bond length remains almost unchanged between these two kink points. At the high-pressure area, the six Tc−O bonds can be divided into three groups (Tc−O1 and Tc−O2, Tc−O4 and Tc−O5, and Tc−O3 and Tc−O6). To further study the structure evolution at different pressures, we analyze the Tc−O bond length variations in the distorted TcO6 octahedra as a

the elastic constants cij for TcO2 as a function of external pressure. Generally, the elastic constants of a material will increase with pressure; this is because the external pressure enhances the interaction between atoms and hence the strength.38 However, anomalous cij behaviors can be found in Figure 5 for TcO2. Herein, according to the response to the external pressure, we can divide cij into three groups: group I, 9976

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denoted by red hollow symbols including c11, c22, c33, c12, c13, and c23, group II shown as blue solid symbols including c44, c55 ,and c66, and group III denoted by black symbols including c15, c25, c35, and c46. For group I, two kink points at 10 and 20 GPa can be observed, similar to the case for the lattice constant b and Tc−O6 bond length. This is because that the group I elastic constants describe the response to the uniaxial and biaxial tensile strains, which are very sensitive to a change in the bond length. The difference is that the group I elastic constants go along with an opposite tendency. In the pressure ranges of less than 10 GPa and more than 20 GPa, the group I elastic constants gradually increase with an increase in the external pressure, as for normal materials. However, the group I elastic constants present anomalous trends of decrease as the external pressure is increased (except for c22). For group II, c44, c55, and c66 first increase and then decrease slightly with an increase in the pressure, while for group III, the variations of c15, c25, c35, and c46 are not predominant. The anomalous behaviors of different group elastic constants come from the various physical origins of the elastic constants. The group I elastic constants describe the response to the uniaxial and biaxial tensile strains, which are very sensitive to a change in the bond length under pressure. In contrast, the group II elastic constants describe the response to the shear strains, which are not very sensitive to a change in the bond length. On the other hand, the group III elastic constants are the monoclinic asymmetry perturbation terms, which have not been significantly influenced due to the fact that the external pressure does not change the symmetry of TcO2. To conclude, the anomalous lattice distortion in TcO2 at 10 and 20 GPa external pressures results in anomalous behaviors to the stiffness responses to uniaxial and biaxial tensile strains as well.

AUTHOR INFORMATION

Corresponding Authors

*E-mail for B.S.: [email protected]. *E-mail for Z.S.: [email protected]. ORCID

Baisheng Sa: 0000-0002-9455-7795 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key Research and Development Program of China (No. 2017YFB0701701), the National Natural Science Foundation of China (Nos. 61504028 and 51501040), the National Natural Science Foundation for Distinguished Young Scientists of China (No. 51225205), the Natural Science Foundation of Fujian Province (No. 2016J01216), and the Science Foundation of the Education Department of Fujian Province Under Grant (No. JA15067).

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REFERENCES

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4. CONCLUSION In summary, we have comprehensively studied the phonon dispersions, crystal structure, and elastic properties of TcO2 under external pressure up to 120.3 GPa on the basis of density functional theory. We not only have found that the TcO2 lattice can remain stable at up to ∼71 GPa external pressure but also can conclude that the lattice dynamic stability of TcO2 can be assessed according to the Γ−Z acoustic phonon branch. By fitting the sound velocity, we can divide the stability of TcO2 under applied external pressure into three ranges: the lowpressure stable range, the middle-pressure buckling range, and the high-pressure unstable range. Interestingly, the fitting slope of the low-pressure stable range is very close to that of the highpressure unstable range. Herein, the angle β shows an S-type growth curve with an increase in the external pressure and the bond length deviation σP follows the inverted S-type decreasing curve, where the accelerated phase appears at about 10 GPa and the stabilized phase arises at the buckling range of around 71 GPa. The pressure-induced lattice distortion in TcO2 shows anomalous behaviors for the lattice constant b, Tc−O6 bond length, and the elastic constants c11, c33, c12, c13, and c23 at 10 and 20 GPa external pressures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01481. Fitting details for the sound velocities (PDF) 9977

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