Flux-grown Piezoelectric Materials: Application to Α-quartz Analogues

Using the slow-cooling method in selected MoO 3-based fluxes, single-crystals of GeO 2 and GaPO 4 materials with an α-quartz-like structure were grown at high temperatures (T ≥ 950 ° C). These piezoelectric materials were obtained in millimeter-size as well-faceted, visually colorless and transparent crystals. Compared to crystals grown by hydrothermal methods, infrared and Raman measurements revealed flux-grown samples without significant hydroxyl group contamination and thermal analyses demonstrated a total reversibility of the α-quartz ↔ β-cristobalite phase transition for GaPO 4 and an absence of phase transition before melting for α-GeO 2. The elastic constants C IJ (with I, J indices from 1 to 6) of these flux-grown piezoelectric crystals were experimentally determined at room and high temperatures. The ambient results for as-grown α-GaPO 4 were in good agreement with those obtained from hydrothermally-grown samples and the two longitudinal elastic constants measured versus temperature up to 850 ° C showed a monotonous evolution. The extraction of the ambient piezoelectric stress contribution e 11 from the C D 11 to C E 11 difference gave for the piezoelectric strain coefficient d 11 of flux-grown α-GeO 2 crystal a value of 5.7(2) pC/N, which is more than twice that of α-quartz. As the α-quartz structure of GeO 2 remained stable up to melting, a piezoelectric activity was observed up to 1000 ° C.


Introduction
Piezoelectric materials that can operate under very high temperature without degradation are sought for the control of structure materials and control system in turbines, engines, nuclear reactors, etc. [1,2]. However, the use of a piezoelectric material at elevated temperature presents many challenges such as possible phase transition, chemical degradation or structural defect propagation which can cancel or lead to instability of the piezoelectric properties.
Under ambient conditions, GeO 2 exhibits two persistent forms of differing anion coordination around the central cation: the α-quartz-type modification (trigonal) with 4:2 coordination [16] and the rutile-type modification (tetragonal P4 2 /mnm, Z = 2) with 6:3 coordination [4,11,[30][31][32][33][34]. Naturally occurring, GeO 2 is known to be more stable in the rutile structure than in the α-quartz structure. The transformation from the rutile-like form to the α-quartz-type form has been reported to occur under normal atmospheric pressure in the 1024-1045 °C temperature range [11,35]. The kinetics of the allotropic transformation from a trigonal to a tetragonal structure is extremely low, and non-appreciable without the presence of any catalyst such as traces of GeO 2 rutile-like form, chlorides or water [11,[36][37][38][39].
For GeO 2 , the temperature region of existence of the stable trigonal phase goes from 1033 °C up to the melting point of 1116 °C [25,30,76]. When epitaxially-grown in the temperature region where it is metastable, the hydrothermally-grown alpha-quartz form of GeO 2 contains high OH impurities which rather easily catalyze its return to the thermodynamically stable rutile-like structure when heated as low as 180 °C [77][78][79][80][81].
In this context, it appeared that another suitable growth technique for oxides could be applied for the crystallization of α-GaPO 4 and α-GeO 2 materials to get single crystals with a high degree of structural and chemical perfection; the high temperature solution growth technique also known as the fluxed melt growth [82][83][84][85]. Using molten inorganic salts, or flux, playing the role of solvent, crystals of a compound can be obtained below its melting or transformation point. The principle of flux growth is based on the spontaneous nucleation that occurs when a supersaturation is obtained either upon cooling of a high temperature solution or by boiling away a volatile solvent at a fixed temperature [86]. The fluxed melt method presents some advantages compared to hydrothermal-based growth methods: the material can be crystallized at atmospheric pressure and the inorganic solvents used are water-free at high temperature.
This paper presents an overview of the main results obtained from several structural and physical characterizations undertaken on flux-grown α-GaPO 4 and α-GeO 2 piezoelectric crystals. When possible, the results are compared and discussed in the view of hydrothermally-grown α-quartz-like SiO 2 , GeO 2 and GaPO 4 .

Flux-Grown α-GaPO 4
In high temperature solution growths, GaPO 4 presents direct solubility. Non-toxic sodium chloride with its melting point at 800 °C, is a suitable solvent to grow α-GaPO 4 single crystals under the temperature of the allotropic α-quartz to β-cristobalite phase transition [75]. A graphite crucible, filled with an appropriate mixture of GaPO 4 and NaCl was sealed in a silica ampoule under Argon. By cooling from 900 to 600 °C and pulling down the ampoule (12 mm· day −1 ) within a temperature gradient (2-5 °C· cm −1 ) or by using the gradient freeze method, α-GaPO 4 crystals having NaCl -foreign‖ phase as shown by X-ray powder diffraction diagrams were obtained. Thus, the accelerated crucible rotation technique was applied and relatively clear and unshaped α-GaPO 4 crystals containing flux inclusions were grown up to 5 × 5 × 2 mm 3 in size with a rough surface.
With a slow cooling rate of 0.1 °C· h −1 from 950 to 750 °C, followed by a cooling rate of 2 °C· h −1 from 750 to 600 °C, in Li 2 O:3MoO 3 flux, a visually high quality crystal of 8 mm long to 3 mm large and 2.5 mm thick (V = 60 mm 3 ) presenting two smooth major faces was grown [89,90].
All these X 2 O:3MoO 3 flux-grown α-GaPO 4 materials crystallized in the trigonal system without any secondary phase detectable and with lattice parameters in perfect agreement with those published on hydrothermally-grown α-GaPO 4 material [7,9].

Flux-Grown α-GeO 2
The first attempt at growing an α-GeO 2 crystal by the unseeded fluxed melt method was undertaken by Finch et al. [91] in the late sixties. Among many compounds explored as potential solvents, Li 2 O:2MoO 3 and Li 2 O:2WO 3 were selected. With the slow cooling growth technique from 1100 to 950 °C at 1 °C· h −1 or less, colorless and well developed α-GeO 2 crystals were grown up to 3 mm on the edge. Crystals from Li 2 O:2MoO 3 contained impurities or defects. X-ray powder diffraction diagrams were consistent with the hexagonal modification of GeO 2 . In the majority, crystals were predominantly bonded by rhombohedral faces with prism faces incompletely developed. In the seventies using the top seeded solution growth (TSSG) method with Li 2 O:WO 3 as flux, a colorless α-GeO 2 single-crystal with a maximum final diameter of 5 mm was obtained [92]. The as-grown crystal, which did not present the hexagonal-like morphology, was not sharply facetted and homogeneously transparent (white inclusions). The experimental procedure was quite unclear and some important parameters were missing. Concerning the chemical and structural quality of this TSSG-crystal, little information was given.
Recently, unseeded slow cooling growth experiments were performed from 970 to 600 °C at a cooling rate of 1 °C · h −1 with a solute to flux ratio of 10/90 by weight in a Pt covered crucible (not sealed) [93,94]. Using K 2 W 2 O 7 flux, the majority of the as-grown α-GeO 2 crystals contained yellow flux inclusions. Thus, other inorganic solvents were investigated in the MoO 3 -based systems since they present low melting temperature and low evaporation at high temperatures (loss of mass <1% after two weeks at T > 700 °C for K 2 Mo 4 O 13 flux) [93,94]. Well-faceted and visually colorless and transparent α-GeO 2 single-crystals were obtained in fluxes such as K 2 Mo 4 O 13 , Rb 2 Mo 4 O 13 and Rb 2 Mo 2 O 7 . The as-grown crystals had no visible flux inclusions, bubbles or cracks and presented very smooth surface roughness [16,93,94]. The α-GeO 2 millimeter-size crystals, up to 3 mm, presented either an unshaped morphology or a pseudo-cubic shape as already found for natural α-quartz [95]. In the case of pseudo-cubic crystals, the positive r rhombohedral faces were prevalent with the restricted presence of the negative z rhombohedral faces while m faces were absent [93,94]. The crystal structure and quality of these flux-grown α-GeO 2 materials were studied by both powder and single-crystal X-ray diffraction at room temperature [16,93,94]. The refinements confirmed the crystallization of the α-quartz-type structure and the lattice parameters and volumes were in good agreement with the literature data [4,10,11,32,80]. The excellent final reliability factors of the refinements indicated that the as-grown α-GeO 2 crystals were of high quality precluding the presence of any considerable amount of twinning [16]. The value of the Flack coefficient which is an indicator of the presence of growth portions containing mirror-image was found close to zero. The uniform coloration of the natural faces under polarized light indicated the lack of optical domains in the flux-grown α-GeO 2 single crystals [16,93].
A colorless, well facetted, highly-transparent and large-size single crystal, up to 0.5 cm 3 , of the piezoelectric phase of GeO 2 was grown by TSSG from a high temperature solution using K 2 Mo 4 O 13 as solvent [27,93]. The obtained volume made this isometric flux-grown GeO 2 single crystal, Figure 1, with the metastable α-quartz like structure, the largest reported in the literature. The macroscopic hexagonal morphology, similar to the well-known morphology of α-SiO 2 , was in accordance with an α-quartz-like structure and facilitated the identification of the different natural crystallographic faces [96][97][98].
The visual estimation of the OH contamination of the α-GaPO 4 single crystals flux-grown from NaCl solvent was studied by annealing experiments [75]. The -milky‖ clouding was a direct estimation of the OH − concentration; the higher the OH content, the more -milky‖ is the sample. These NaCl flux-grown α-GaPO 4 crystals presented slight clouding and thus significant OH contamination.
In a typical room temperature non-polarized infrared transmission spectrum of an α-GaPO 4 material containing significant OH-groups, a broad and intense band between 2500 and 3600 cm −1 is observed (O-H infrared region) associated with H-bonded molecular water. This broad band is superimposed upon three well-separated peaks at 3167, 3290 and 3400 cm −1 and sometimes upon a sharp absorption band at 3508 cm −1 related to an isolated OH-group stretching band [43,55,65,68]. The amplitude of the peak centered around 3400 cm −1 is attributed in one part to the absorption by the GaPO 4 lattice and in another part to O-H stretching vibrations [65].
For X 2 O:3MoO 3 (X = Li, K) flux-grown α-GaPO 4 materials, the collection of the non-polarized infrared data was done in transmission mode at room temperature on as-grown samples, i.e., not polished samples. Only the three bands at 3167, 3290 and 3400 cm −1 were registered. The OH content was materials [44,46,[88][89][90]101]. Compared to the spectra of hydrothermally-grown GaPO 4 , they did not present the characteristic broad and intense absorption band from 3600 to 2500 cm −1 due to quite strong OH contamination estimated with the extinction coefficient α calculated at 3400 cm −1 from the expression α = 1/d[log(T 3800 /T 3400 )]-α 3400 * where d represents the sample thickness in cm, T represents the % IR transmission at respectively 3800 and 3400 cm −1 , and α 3400 * represents the absorption coefficient due to intrinsic lattice vibrations of α-GaPO 4 at 3400 cm −1 [65]. The α 3400 * was estimated to be 0.078 cm −1 based on hydrothermally-grown material [65,68,102].
The calculated value of the extinction coefficient α at 3400 cm −1 was close to 0.03 cm −1 for X 2 O:3MoO 3 (X = Li, K) flux-grown GaPO 4 and close to 0.15 cm −1 for hydrothermally-grown material [88]. Thus, the infrared spectra correspond to X 2 O:3MoO 3 (X = Li, K) flux-grown α-GaPO 4 samples without significant OH-content in perfect accordance with the absence of -milky‖ clouding of the samples even after several times heating up to 850 °C [103].
Chemical analyses of X 2 O:3MoO 3 (X = Li, K) flux-grown α-GaPO 4 crystals were done using glow discharge mass spectrometry (GDMS) and induced coupled plasma-atomic emission spectroscopy (ICP-AES) [89]. The results demonstrated the presence of foreign chemical elements coming from the solvent with a Mo-content as high as 0.3% for GaPO 4 crystals grown in K 2 O:3MoO 3 flux. Na, Ca, Fe, Al and Si elements were also found with a major contamination from Al element (320 ppm to 0.13%).
Room temperature non-polarized Raman spectra of commercial α-GeO 2 powder or α-GeO 2 stain-etch sample exhibited some features around 760-780 cm −1 which were found to disappear once the sample was annealed in air above 400 °C [39,93,[104][105][106]. These features have been assigned either to oxygen vacancy complexes or to water bound to Ge-O entities or to a Ge-O stretching vibration of a water-distorted GeO 4 entity [39,104,105].
The non-polarized Raman signal of a MoO 3 -based flux-grown α-quartz GeO 2 single crystal was collected in the 50-4000 cm −1 range and no other modes than the four non-degenerate A1 ones and the eight doubly-degenerate E modes predicted by group theory for α-quartz-type GeO 2 (D 3 point group) were observed [93,[106][107][108]. In agreement with infrared measurements [27,93], neither hydroxyl groups nor water inclusions were detected by Raman spectroscopy. Furthermore, these MoO 3 -based flux-grown α-GeO 2 samples were heated up to 1000 °C several times without presenting the well-known milky hue attributed to the release of water from hydroxyl impurities with increasing temperature [109]. Ambient polarized Raman measurements performed on flux-grown α-quartz GeO 2 single crystals along with state of the art density functional theory (DFT) based calculations were reported [93,106,107]. An excellent agreement was obtained between experimental and theoretical Raman lines for both wavenumbers and relative intensities which permitted to unambiguously assign the symmetry and the nature of α-quartz GeO 2 modes. This Raman study pointed out that high temperature flux-grown GeO 2 single crystals of α-quartz-like structure were of high structural quality (impurities would have resulted in shifts of the Raman lines or in additional bands), and that vibrations in the α-quartz GeO 2 structure were relatively quasi-harmonic as the calculated frequencies at −273 °C were almost the same as the experimental values at 25 °C.
Optical transmittance was measured in the UV-VIS-NIR region for a plate with a surface perpendicular to the c axis prepared from a MoO 3 -based TSSG-grown α-GeO 2 single crystal [27]. The transmission spectrum was taken on an as-grown crystal plate of 330 μm in thickness. The transmission fraction, found to be over 97% in the VIS-NIR region, showed that the TSSG-grown α-GeO 2 crystal was of very good optical quality. The high chemical purity and the homogeneity of the TSSG-GeO 2 crystal were also revealed by the absence of absorption bands. The α-GeO 2 crystal exhibited transparency down to the UV region. Below 300 nm, a strong absorption was visible due to the fundamental absorption within the band gap with a cutoff at 205 nm.
Optical transmission was reported for hydrothermally-grown α-GeO 2 crystal [79]. The spectrum showed a considerable absorption in the 0.20-0.210 μm range associated with the presence of several bands [79].

Flux-Grown α-GaPO 4
Differential scanning calorimetric (DSC) experiments were done on flux-grown α-GaPO 4 single crystals crystallized via spontaneous nucleation in MoO 3 -based fluxes as Li 2 O:3MoO 3 and K 2 O:3MoO 3 [44,46,89,90,101]. On heating runs up to 1200 °C (2-10 °C · min −1 ) of α-GaPO 4 as-grown single crystals or powdered samples, only a sharp endothermic peak appeared in the 950-964 °C temperature range, Figure 3, caused by the structural transition from the α-quartz GaPO 4 phase to the β-cristobalite modification stable above 960-980 °C [40][41][42]. The successive cooling (−5 °C/min) data registered from 1200 °C back to room temperature of a sample containing some as-grown single crystals (different sizes and faces) presented a unique exothermic feature with double maxima at onset temperature of 937 °C for the first thermal cycle, and at onset temperature of 925 °C in the second cycle [101].
When the as-grown α-GaPO 4 crystals were powdered and sieved to a regular grain size (20 μm), the successive cooling (−2 or −10 °C/min) curves, from 1200 to 20 °C, showed only one exothermic peak in the 942-908 °C temperature range depending on the flux composition, Figure 3.
This exothermic feature corresponded to a total transformation of the β-cristobalite GaPO 4 phase into the α-quartz phase as confirmed by the X-ray powder pattern of the end product of the DSC analysis [44,46,89,90]. This was the first time that GaPO 4 had been found, after a DSC cycle, exclusively in the α-quartz modification after cooling from the β-cristobalite phase without annealing periods.
For hydrothermally-grown α-GaPO 4 material grown at 230 °C (indirect solubility), only one strong exothermic peak was visible on the cooling curve close to 578 °C corresponding to a total transformation of the β-cristobalite to α-cristobalite [43]. The crystallization temperature of the α-GaPO 4 phase would be an important parameter to favor the reversible α-quartz/β-cristobalite transition.
The thermal evolution of flux-grown α-GaPO 4 single crystals grown from 950 to 600 °C in MoO 3 -based solvents was also followed by Raman spectroscopy [45]. A direct α-quartz/β-cristobalite transition was observed at a temperature close to 980 °C upon heating. Back transformation to the α-quartz-type form was found to occur readily at 920 °C in perfect agreement with the DSC experiments [44,46,89,90,101].
The temperature dependence of the cell parameters of a α-GaPO 4 sample grown in a Li 2 O-3MoO 3 flux over the temperature range 950-600 °C was determined from powder X-ray diffraction data collected from 30 to 900 °C [103]. The X-ray patterns remained the same from room temperature to 900 °C. Both the lattice parameters and unit cell volumes were found to increase markedly and nonlinearly (third degree polynomial) as a function of temperature. Therefore, no indication of a structural transition was pointed out in the studied temperature range (30-900 °C) in perfect agreement with previous reported results obtained from DSC [44,46,89,90,101] or Raman studies [45,89] concerning MoO 3 -based flux-grown α-GaPO 4 crystals.

Flux-Grown α-GeO 2
In the temperature range from room temperature to 1200 °C, the DSC heating-curve of GeO 2 crystals with the α-quartz structure grown by the spontaneous nucleation method in selected fluxes (MoO 3 -based compounds) showed no other peak than an endothermic feature attributed to the melting of the studied material at maximum of 1116 °C [93,94].
Powder X-ray patterns of flux-grown α-GeO 2 were registered at several temperatures from room temperature up to 1050 °C [93,109]. For each studied temperature, the whole diffraction pattern was assigned to the α-quartz phase of GeO 2 . The very interesting results brought to light by these thermal analyses were that this high temperature flux-grown oxide material did not present a phase transition before melting (unlike SiO 2 with the well-known α-quartz/β-quartz transformation close to 573 °C [19,28]) and that no secondary phases such as the GeO 2 rutile-like phase or flux-derived phases were detected.
Variable-temperature Raman spectroscopy measurements performed on high temperature flux-grown α-quartz GeO 2 single crystals in MoO 3 -based solvents were reported [93,106]. Vibrations in α-GeO 2 were shown to be very slightly anharmonic as evidenced by the very low wavenumber shifts and the weak damping of the modes between room temperature and 1100 °C. In contrast with what has been observed for other α-quartz homeotypes like SiO 2 or AlPO 4 , which undergo an α-quartz to β-quartz phase transition [19,28], neither phase transitions nor a second phase were detected by this Raman study from room temperature to 1100 °C. First-principle calculations with the ABINIT code [93,106,107] revealed the absence of the tetrahedral libration mode in the α-quartz-like structure of GeO 2 which explained the very low degree of thermally-induced dynamic disorder registered in the 30-1100 °C range and further confirmed that the piezoelectric properties of flux-grown α-GeO 2 should not be degraded significantly up to its melting point (1116 °C).
To confirm the thermal stability (aging), an as-grown α-GeO 2 single crystal obtained by spontaneous nucleation in MoO 3 -based flux was annealed in air at high temperature (800-900 °C) over several months [27]. The impact of this thermal cycle on the α-quartz-like structure of GeO 2 was followed by Raman measurement. This long annealing process validated the excellent aging behavior under very high thermal stress of the α-quartz GeO 2 obtained from the flux method since no phase transition and no evolution of the visual transparency were detected. This important result could be directly related to the high crystalline quality of the α-GeO 2 single crystals accessible with the flux growth techniques (water-free, chemical inclusion-free and rutile phase-free) as illustrated by the optical transmission curve [27].

Ambient Conditions
Using Voigt's notation and taking into account the crystal symmetry, the α-quartz structure (point group 32) presents six independent elastic stiffness moduli C IJ (I, J indices from 1 to 6): C 11 , C 33 , C 44 , C 66 , C 12 , C 13 and C 14 (2C 66 = C 11 − C 12 ). To identify the crystalline orientation, α-quartz analogues use a standard Cartesian coordinate system where the Z-axis of α-quartz analogues coincides with the crystallographic c-axis; the X-axis matches the crystallographic a-axis and the Y-axis is normal to the X and Z axes (b-axis being in the XY plane at 120° from a-axis).

Flux-Grown α-GaPO 4
By the ultrasonic method, a determination of four out of six independent single-crystal elastic stiffness constants C E IJ at constant electric field was undertaken on millimeter suitable shaped plates obtained from as-grown α-GaPO 4 single crystals spontaneously crystallized by slowly cooling a Li 2 O:3MoO 3 flux saturated with GaPO 4 [46,89,110]. The average size of the MoO 3 -based flux-grown GaPO 4 single crystals was too small [44,46,89,90,101] to get all the orientations useful for the measurements of the whole elastic constant set (ex: C E 13 ). Single-crystal high-resolution Brillouin spectroscopy experiments were carried out to measure five out of six (C E 13 is missing) elastic constants C E IJ of flux-grown α-GaPO 4 material [90,103]. Optical quality single-crystals of α-GaPO 4 with millimeter size were flux-grown from X 2 O:3MoO 3 (X = Li, K) solvent in unseeded experiments over the 950-600 °C temperature range. The Brillouin measurements were done, on one hand, on plates of simple X-, Y-and Z-orientation [90] and on other hand, on an as-grown α-GaPO 4 single crystal polished as a cube with 2 mm side length showing X (100), Y (010) and Z (001) faces [103]. Table 1 gives the resulting single crystal elastic stiffness constants C E IJ obtained on high temperature flux-grown α-GaPO 4 materials in MoO 3 -based solvents. They are compared with a reported experimental set of data concerning the hydrothermally-grown GaPO 4 single crystals as well as with reported computed values [111].
The values of the flux-grown single crystal elastic stiffness constants C E IJ compared with those obtained by Brillouin or pulse-echo methods on hydrothermally-grown samples, Table 1, are in good accordance while large discrepancies exist with the computed values concerning C E 11 and C E 66 . The room temperature experimental values of single-crystal elastic stiffness constants C E IJ at constant electric field of flux-grown α-GeO 2 in MoO 3 -based solvents were determined using Brillouin scattering, Table 2 [109]. In this work, three platelets were used, defined in the standard Cartesian coordinate system as X-plate, Y-plate and Z-plate which respectively correspond to the (100), (2)(3)(4)(5)(6)(7)(8)(9)(10) and (003) (hkl)-crystallographic planes.
These flux-grown α-GeO 2 C IJ values are compared in Table 2 with recent computed [109,114,115] and experimental elastic constant data obtained from hydrothermally-grown crystals [23,24,116]. C D IJ are elastic stiffness constants at constant electric displacement i.e., not corrected from the piezoelectric effect where e 11 is the piezoelectric stress constant and ε 11 the dielectric tensor at constant strain. The crystal elastic constants values of the MoO 3 -based flux-grown α-GeO 2 material present close similarities with most of the published C IJ data on hydrothermally-grown α-GeO 2 crystals, Table 2. Therefore, the small discrepancy, registered more especially on the C 11 and C 14 moduli, was attributed to the strong reduction of the OH concentration in the lattice of flux-grown α-GeO 2 crystals which was believed to induce a slightly stiffer behavior [109]. The presence of OH-interactions in the crystal would increase its ionic character and consequently softer its elastic behavior.
When compared with calculated elastic stiffness constants, the flux-grown α-GeO 2 elastic moduli presented very good agreement with computed values at 0 K of Lignie et al. [109], Table 2. The largest discrepancy was observed for the C 66 (nearly 13% softer for the theoretical value) while very good accordance was found for the C 12 and C 14 elastic constants.
The numerical value of the piezoelectric term, deduced from the C D 11 to C E 11 difference, Table 2, is 1.29(2) GPa [109]. The authors deduced for the flux-grown α-GeO 2 material a d 11 piezoelectric strain constant of 5.7(2) × 10 −12 C/N which is in between the calculated and the reported experimental value from a hydrothermally-grown α-GeO 2 crystal, Table 3.   [117] 6.00 [117] 5.7(2) [109] 2.31 [17] The flux-grown α-GeO 2 exhibits a d 11 piezoelectric strain constant more than twice that of α-quartz SiO 2 , Table 3, confirming the improvement of the piezoelectric properties with the structural distortion in the α-quartz analogues [17,117].

Flux-Grown α-GaPO 4
High-resolution Brillouin spectroscopy studies concerning the C IJ elastic stiffness constant evolution with temperature of high-temperature flux-grown α-GaPO 4 single-crystals are reported in the literature [90,103]. Since for Brillouin scattering experiments, the samples have not to be coated with metal layers (electrodes), measurements at high temperatures are not affected by foreign chemical diffusion or bad electrical signal transmission.
Plates of X (100) and Z (001) simple orientations produced from α-GaPO 4 single crystals obtained by slow cooling from 950 to 600 °C in X 2 O:3MoO 3 fluxes (X = Li, K) were used to follow the thermal evolution of C D 11 and C E 33 elastic constant [90]. C D 11 was measured from room temperature up to 1000 °C to follow the α-quartz/β-cristobalite phase transition found close to 970 °C , in good agreement with other thermal studies [30,41,42,44,46,89,101]. C E 33 presented a monotonous decrease with temperature up to 850 °C while C D 11 presented a slight variation over the 20-500 °C temperature range followed by a stronger variation when approaching the phase transition temperature at 970 °C [90].
For the Brillouin scattering measurements using the backscattering geometry undertaken on a α-GaPO 4 crystal shaped as a cube with X-, Y-and Z-faces [103], the C E 11 , C E 33 , C E 44 and C E 12 constants showed monotonic elastic softening upon heating up to 850 °C while C E 66 and C E 14 showed continuous stiffening. Most of the C IJ elastic stiffness constant derives by only a few percent upon heating, while C E 14 increases by about 50% and C E 12 decreases by about 35%. The first-order temperature coefficients T (1) CIJ were negative for C E 11 , C E 33 , C E 44 and C E 12 elastic constants [103] in perfect agreement with previous reports on hydrothermally-grown α-GaPO 4 crystals [67,110,112,118].

Flux-Grown α-GeO 2
Different sets of C IJ elastic stiffness constants at constant electric displacement and ambient conditions have been reported on flux-and hydrothermally-grown α-GeO 2 [23,24,109,116]. However, only one set of elastic data concerning their thermal evolution is reported in the literature [109]. It concerns a high resolution Brillouin scattering study of MoO 3 -based flux-grown α-GeO 2 single crystals from room temperature up to 1000 °C. Any accident as discontinuity or phase transition was registered on the thermal evolution of the elastic constants in agreement with the conservation of the α-quartz-like structure of flux-grown GeO 2 material up to melting (1116 °C) [93,94]. The C 11 , C 33 , and C 12 elastic constants show monotonic elastic softening upon heating while C 44 and C 66 show continuous stiffening.
The thermal evolution of the piezoelectric term, deduced from the difference between C D 11 and C E 11 , was found stable up to 1000 °C, Figure 4 [93,109] meaning that MoO 3 -based flux-grown α-GeO 2 crystals exhibit piezoelectric activity even at very high temperature. . Thermal dependence of pure and piezoelectrically stiffened C 11 elastic constant of flux-grown α-GeO 2 . Errors are smaller than the symbol size.

Conclusions
In the family of α-quartz isotypes, high quality α-GaPO 4 and α-GeO 2 single crystals with a larger thermal stability and higher piezoelectric properties than α-quartz can potentially be used as piezoelectric materials for high temperatures applications. However if these single crystals are grown via hydrothermal-based methods, the presence of significant numbers of hydroxyl groups and structural defects in their network lead to a degradation of their physical properties and even to a phase transformation at relatively low temperature for α-GeO 2 .
The main structural and chemical results obtained from infrared studies (OH-content), thermal behavior analysis and Brillouin scattering experiments on MoO 3 -based flux-grown α-GaPO 4 and α-GeO 2 single-crystals have demonstrated OH-free high quality piezoelectric crystals and an improved thermal stability.
These results confirm on one hand the high potential of flux-grown α-GaPO 4 and α-GeO 2 single crystals as piezoelectric materials for high temperature applications and on the other hand a very powerful method of high temperature flux melted technique to grow high quality α-quartz isotype single crystals.
Moreover, as iso-structural to α-quartz, most of the device designs developed for α-quartz single crystal could be applied for α-GeO 2 with minor adaptations. The potential of α-GeO 2 single crystal for the realization of piezoelectric devices is also confirmed as its d 11 piezoelectric constant at ambient temperature is found to be more than twice that of α-quartz. The piezoelectric property of α-GeO 2 is still conserved at high temperature as a significant piezoelectric contribution to C 11 still exists at 1000 °C .

Author Contributions
Pascale Armand, Adrien Lignie and Marion Beaurain performed crystal growths of flux-grown piezoelectric materials, characterizations and data analysis. All author discussed the results and Pascale Armand wrote the paper.