A comparative study of high-pressure behaviors of the two polymorphs of Ho2Ge2O7

Two polymorphs of polycrystalline Ho2Ge2O7, one with tetragonal structure and the other with cubic structure, were synthesized by using different methods. The structural stabilities of these two polymorphs under high pressure were investigated by angle-dispersive X-ray diffraction (ADXRD). Pressure-induced amorphization was found in the tetragonal Ho2Ge2O7, which is suggested to be associated with the breaking-up of long chains of the edge-shared polyhedron group Ho4O20. By contrast, cubic Ho2Ge2O7 is stable at high pressures up to 33.3 GPa.


Introduction
Spin ice has proven to be one of the most fruitful marriages of theoretical and experimental condensed matter physics. [1][2][3][4] It is a remarkable magnetic ground state that can arise in geometrically frustrated pyrochlores, A 2 B 2 O 7 , when magnetic rare-earth ions are situated on the vertices of a lattice of corner-sharing tetrahedra. Competing nearest-neighbor and long-range dipolar interactions result in a short-range ordered ground state for each tetrahedron in which two spins point in and two spins point out. 5 The spin-ice state was rst observed in Ho 2 Ti 2 O 7 by Harris et al. in 1997;6 since that time, spin ices have been a subject of active experimentation, allowing theorists to come a long way towards understanding this remarkable ground state. Despite signicant interest in this class of compounds, only a handful of spin-ice materials have been discovered to date, including the titanates A 2 Ti 2 O 7 , 6-8 the stannates A 2 Sn 2 O 7 9,10 and, more recently, the germanates A 2 Ge 2 O 7 . 11,12 Recently, the observation of emergent monopole excitations which have captured the attention of the broader scientic community have made spin-ice materials more intriguing. [13][14][15][16][17][18] Ho 2 Ge 2 O 7 , a member of the rare-earth pyrogermanate series A 2 Ge 2 O 7 , has been attracting extensive interest because it was found to be a new highly correlated spinice material with the highest density of monopoles in the Ho series at low temperatures, and the best natural candidate for monopole studies. 19 From a structural point of view, rare-earth pyrogermanates A 2 Ge 2 O 7 possess a variety of crystal structures under ambient conditions, such as triclinic phase for Ln ¼ La, Pr, Nd-Gd, tetragonal phase for Ln ¼ Gd-Lu, and monoclinic phase for In 2 Ge 2 O 7 and Sc 2 Ge 2 O 7 . Moreover, depending on the synthesis method, different structural modications of Ln 2 Ge 2 O 7 can be obtained. By conventional solid state synthesis, Ho 2 Ge 2 O 7 has the tetragonal structure. However, the cubic phase of Ho 2 Ge 2 O 7 can be synthesized by the high-pressure and high-temperature (HPHT) method. Therefore, pressure is an important weapon in a researcher's arsenal for exploring phase space. Pressure is also used to drive materials into new electronic states. Under high pressure, some materials become superconductors, others undergo magnetic phase transitions, and others undergo metal-insulator phase transitions. 20,21 In magnetic pyrochlore oxides, pressure has been shown to freeze the spin-liquid ground state of Tb 2 Ti 2 O 7 . 22 So, studies on the stability of Ho 2 Ge 2 O 7 under high pressure are particularly important to understand its exotic magnetic phenomenon.
In this work, we successfully synthesized the two types of Ho 2 Ge 2 O 7 using different methods. The structural stabilities of these two polymorphs of Ho 2 Ge 2 O 7 were investigated by angledispersive synchrotron X-ray powder diffraction (ADXRD) at high pressures. Pressure-induced amorphization was found in the tetragonal Ho 2 Ge 2 O 7 . Meanwhile, the cubic Ho 2 Ge 2 O 7 was stable up to the highest pressure tested.

Synthesis
The tetragonal Ho 2 Ge 2 O 7 was synthesized by standard solid state reaction method. High purity oxides of Ho 2 O 3 (99.99%, powder) and GeO 2 (99.99%, powder) were used as the starting materials. The raw materials with nominal compositions of Ho 2 Ge 2 O 7 were uniformly mixed in an agate mortar. The powder obtained was pressed into small pellets and then calcined at 1373 K in air for 12 h. The cubic Ho 2 Ge 2 O 7 was synthesized by the HPHT method. The as-prepared powders were loaded into a cubic anvil HPHT apparatus (SPD-6 Â 600) at a temperature of 1573 K and a pressure of 5.2 GPa with a holding time of 15 min.

Characterization
Under ambient conditions, the crystal phase structures of the synthesized samples were characterized by X-ray powder diffraction (XRD) using a Rigaku D/max-2500 with Cu Ka radiation (l ¼ 1.54056 A) in the range 2q from 10 to 90 at a scanning rate of 4 min À1 . The high-pressure angle-dispersive XRD patterns for the two types of Ho 2 Ge 2 O 7 were collected at beamline 4W2 of the Beijing Synchrotron Radiation Facility, using a monochromatic wavelength of 0.6199 A. A diamondanvil cell (DAC) was utilized to generate high pressure, using a T301 stainless steel gasket which was pre-indented to 50 mm thickness. One piece of the as-prepared samples, a small piece of ruby as the pressure calibrant 23 and a 16 : 3 : 1 methanol/ ethanol/water mixture as pressure-transmitting medium were loaded into the diamond-anvil cells. The experimental parameters, including the distance between sample and detector, were calibrated using CeO 2 standard reference material. FIT2D soware was employed to convert the image plate records into intensity versus diffraction angle 2q patterns. Rietveld analyses were performed with the soware GSAS. 24 The renement parameters were the lattice constants, the atomic position of oxygen, a Chebyshev polynomial background, pseudo-Voigt prole parameters, a common isotropic thermal parameter for all atom sites and an overall intensity scaling factor.

Crystal structures under ambient conditions
The observed and calculated XRD patterns of the two types of Ho 2 Ge 2 O 7 together with their differences are shown in Fig. 1. The diffraction peaks in Fig. 1a match well with the tetragonal structure Ho 2 Ge 2 O 7 (S.G. P4 1 2 1 2, no. 92) and the obtained cell parameters are: In this kind of crystal structure, each Ho 3+ ion is coordinated to seven oxygen atoms. The Ge 2 O 7 unit consists of two tetrahedra (GeO 4 ) joined by a bridging oxygen atom. The bridging oxygen atoms of the Ge 2 O 7 unit do not coordinate to the Ho 3+ ion. The coordination polyhedron of the Ho 3+ ion is a distorted pentagonal bipyramid with the Ho 3+ ion located nearly in the basal plane. The pentagonal axis is almost parallel to the crystal c-axis. Each HoO 7 polyhedron shares three of its O-O edges with neighboring polyhedra. Schematic illustrations are shown in Fig. 2a and b.
The crystal structure data of the cubic Ho 2 Ge 2 O 7 were rened by Rietveld analysis of the X-ray powder diffraction data. The    Fig. 2c and d. In addition, the rened atomic position coordinates of the two polymorphs of Ho 2 Ge 2 O 7 are given in Table 1.

Pressure-induced amorphization of the tetragonal Ho 2 Ge 2 O 7
The in situ XRD patterns of the tetragonal Ho 2 Ge 2 O 7 at various pressures up to 22.5 GPa were collected and a few representative patterns are shown in Fig. 3. As can be seen from Fig. 3a, the pressure-dependent X-ray data do not reveal any new diffraction peaks or peak splitting, which indicates that a typical tetragonal structure remains from ambient pressure up to 13.6 GPa. With further increasing pressure, most of the sharp bands have disappeared at 16.9 GPa and no diffraction peaks can be observed, which suggests the formation of an amorphous phase. Aer releasing the pressure, pressure-induced amorphization of Ho 2 Ge 2 O 7 is maintained, which indicates the nonreversible nature of the phase transition. A few small peaks appeared aer quenching and holding the sample under ambient conditions for 10 h. The recorded pattern for 10 h aer release of pressure is almost identical to that of the original phase of tetragonal Ho 2 Ge 2 O 7 , as shown in Fig. 3b.
Pressure-induced amorphization has been the subject of intense study for the past few years because of its importance in materials science and solid state physics. [25][26][27] A pressureinduced amorphization of a-NaVO 3 was observed by Raman spectroscopy, which involved the tetrahedral VO 4 chains breaking up abruptly at the transition pressure. 28 In addition, silicates and metavanadate compounds also have chain structures and are the best examples of amorphous materials. [29][30][31] As can be seen in Fig. 2a (Fig. 4). The bond lengths of Ho-O3(i) and Ho-O3(ii) always remain longer than the other Ho-O bond distance, from ambient pressure to the highest pressure. So the innite Ho 4 O 20 chain is relatively easy to disconnect at this junction. Pressure-induced amorphization of Ho 2 Ge 2 O 7 is suggested to be associated with the breaking-up of long chains of the edge-shared polyhedron group Ho 4 O 20 . The tetragonal Ho 2 Ge 2 O 7 showed long-range order at low magnetic elds, but its behavior was similar to spin-ice freezing in a sufficiently strong magnetic eld. 32 Owing to the appearance of pressure-  induced amorphization, we can speculate that the tetragonal Ho 2 Ge 2 O 7 may become paramagnetic under high pressure.
The pressure dependences of the lattice parameters and volume of tetragonal Ho 2 Ge 2 O 7 up to 22.5 GPa are shown in Fig. 5. It is shown that the lattice parameters and volume of Ho 2 Ge 2 O 7 decrease smoothly with increasing pressure. In order to determine the bulk modulus B 0 , its pressure derivative B 0 0 , and the molar volume under ambient conditions V 0 , the experimental pressure-volume data of the Ho 2 Ge 2 O 7 were tted to a third-order Birch-Murnaghan equation of state (Fig. 5c). 33 The obtained bulk modulus B 0 is 193(4) GPa for the tetragonal phase with xed B Pauling zero-point entropy; magnetization which saturated to half the magnetic moment; a spinfreezing transition in the ac susceptibility; and the characteristic magnetic diffuse scattering of spin ices. 19 The stability of   This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 10540-10545 | 10543 the structure ensures the stability of these excellent properties under high pressure.
The pressure dependence of the unit cell volume of the cubic Ho 2 Ge 2 O 7 is shown in Fig. 7. The data are tted by a third-order Birch-Murnaghan equation of state as is the case for the tetragonal Ho 2 Ge 2 O 7 . The obtained bulk modulus B 0 is 263(4) GPa, quite a bit larger than for other ordered pyrochlore oxide materials. For example, the bulk moduli of A 2 Ti 2 O 7 (A ¼ Ho, Y, Tb, Sm) were 213(2), 204(3), 199(1) and 164.8(1.5) GPa, respectively. 36,37 And also for Gd 2 Zr 2 O 7 , the bulk modulus was 186(12) GPa. 34 By comparison, the hardness of the cubic phase in Ho 2 Ge 2 O 7 is higher than that of the tetragonal phase. The difference in bulk modulus might be due to the differences in structure and cohesive energy among these germanates.

Conclusions
In summary, the structural behaviors of two types of Ho 2 Ge 2 O 7 were studied under high pressure by in situ XRD measurements. Pressure-induced amorphization was found in the tetragonal Ho 2 Ge 2 O 7 , which has a chain structure, and is suggested to be associated with the breaking-up of long chains of the edgeshared polyhedron group Ho 4 O 20 . By contrast, the cubic Ho 2 Ge 2 O 7 structure is stable at high pressures up to 33.3 GPa. The bulk modulus of the tetragonal Ho 2 Ge 2 O 7 was obtained as B 0 ¼ 193(4) GPa, and B 0 ¼ 263(4) GPa was obtained for the cubic phase.

Conflicts of interest
There are no conicts to declare.