- freely available
Crystals 2014, 4(2), 168-189; doi:10.3390/cryst4020168
Published: 23 June 2014
Abstract: Using the slow-cooling method in selected MoO3-based fluxes, single-crystals of GeO2 and GaPO4 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 GaPO4 and an absence of phase transition before melting for α-GeO2. The elastic constants CIJ (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-GaPO4 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 e11 from the CD11 to CE11 difference gave for the piezoelectric strain coefficient d11 of flux-grown α-GeO2 crystal a value of 5.7(2) pC/N, which is more than twice that of α-quartz. As the α-quartz structure of GeO2 remained stable up to melting, a piezoelectric activity was observed up to 1000 °C.
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.
Non-pyroelectric single crystals with the α-quartz-like structure exhibiting both higher piezoelectric constants and a higher thermal stability as compared to α-quartz would be promising materials to build miniaturized high temperature piezoelectric-operated devices without cooling. In the XO2 (X = Si, Ge) and MPO4 (M = Fe, Al, Ga, B) family, the α-quartz-like structure is composed of either only XO4 corner-shared tetrahedra or of both MO4 and PO4 tetrahedra forming a trigonal system [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. The α-phase (P3121 or P3221, respectively left-handed or right-handed, Z = 3) is derived from the β-phase (P6222 or P6422) by a symmetry loss induced by a tilt of the tetrahedra around the b-axis. Two structural distortion parameters exist to quantify this phenomenon: the average intertetrahedral bridging angle θ (X–O–X or M–O–P) and the tetrahedral tilt angle δ [11,14,17,18,19,20]. Based on experimental characterizations and theoretical studies on α-quartz analogues, it was demonstrated that the higher piezoelectric properties of α-GaPO4 and α-GeO2 materials compared to α-SiO2, α-FePO4 and α-AlPO4 compounds were directly related to their structural distortion with respect to the β-quartz structure type (for β-SiO2 θ = 153.3° and δ = 0° at 575 °C) [11,14,17,21,22,23,24,25,26,27].
In addition, the well-known α-β phase transition, which appears around 573 °C in α-SiO2 (θ = 144.2°) [19,26] does not occur when the tilt angle δ is over 22° (leading to θ under 136°) [9,13,14,22,25]. In other words, the transition from an α phase to a β phase is absent for α-GeO2 and α-GaPO4 crystallized materials (θ = 130.04° and θ = 134.60°, respectively) [13,14,17,22,28,29].
Under ambient conditions, GeO2 exhibits two persistent forms of differing anion coordination around the central cation: the α-quartz-type modification (trigonal) with 4:2 coordination  and the rutile-type modification (tetragonal P42/mnm, Z = 2) with 6:3 coordination [4,11,30,31,32,33,34]. Naturally occurring, GeO2 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 GeO2 rutile-like form, chlorides or water [11,36,37,38,39].
A transition from the thermodynamically stable α-quartz-like GaPO4 phase to the β-cristobalite modification is known to occur above 960 °C [13,40,41,42,43,44,45,46]. This high temperature allotropic transition does not permit the growth of α-GaPO4 crystals by conventional melt techniques. Single crystals of α-GaPO4 were grown using epitaxial hydrothermal-based methods in a retrograde-solubility range at T < 250 °C and in the range of direct temperature dependence of solubility at T > 300 °C from highly corrosive acid solutions [40,43,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62]. However, for gallium orthophosphate material, it seems quite difficult to obtain very high quality crystals with these solution-based growth methods. The presence of twins, dislocations and/or a quite high level of hydroxyl group incorporated via the growth medium tend to deteriorate the piezoelectric properties especially at high temperatures as physical properties are very sensitive to material perfection [43,49,50,57,63,64,65,66,67,68,69,70,71,72,73]. The OH impurities in α-GaPO4 single crystals are responsible for the “milky” appearance of the samples when exposed to high temperature (600 °C). This typical behavior is due to water trace precipitation effects and corresponds to the upper temperature limit of physical property measurements [65,69,74,75].
For GeO2, 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 GeO2 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-GaPO4 and α-GeO2 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 . 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-GaPO4 and α-GeO2 piezoelectric crystals. When possible, the results are compared and discussed in the view of hydrothermally-grown α-quartz-like SiO2, GeO2 and GaPO4.
2. Flux-Growth and Morphology
2.1. Flux-Grown α-GaPO4
In high temperature solution growths, GaPO4 presents direct solubility. Non-toxic sodium chloride with its melting point at 800 °C, is a suitable solvent to grow α-GaPO4 single crystals under the temperature of the allotropic α-quartz to β-cristobalite phase transition . A graphite crucible, filled with an appropriate mixture of GaPO4 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-GaPO4 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-GaPO4 crystals containing flux inclusions were grown up to 5 × 5 × 2 mm3 in size with a rough surface.
From spontaneous crystallization with the slow cooling method (1.2–5 °C·h−1) between 950 and 600 °C, colorless, transparent and flux inclusion-free as-grown α-GaPO4 crystals of millimeter-size have been obtained in MoO3-based solvents X2O:3MoO3 (X = Li, K) [44,87,88,89]. The melting point of these molybdenum-based solvents are between 500 and 600 °C which allows α-GaPO4 growth under the allotropic phase transition temperature [44,89]. The unseeded growth experiments were done under atmospheric conditions in Pt crucibles covered (but not sealed) with a lid containing a starting mixture of α-GaPO4 and X2O:3MoO3 (X = Li, K) powder in different weight ratios. Plate-like single crystals with very smooth surface roughness were grown in K2O:3MoO3 having a volume up to 6 × 4 × 1 mm3. With Li2O:3MoO3 flux, the as-grown α-GaPO4 crystals presented unshaped bulk morphology with a quite rough surface and volume up to 5 × 2.5 × 2 mm3 [44,87,89].
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 Li2O:3MoO3 flux, a visually high quality crystal of 8 mm long to 3 mm large and 2.5 mm thick (V = 60 mm3) presenting two smooth major faces was grown [89,90].
All these X2O:3MoO3 flux-grown α-GaPO4 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-GaPO4 material [7,9].
2.2. Flux-Grown α-GeO2
The first attempt at growing an α-GeO2 crystal by the unseeded fluxed melt method was undertaken by Finch et al.  in the late sixties. Among many compounds explored as potential solvents, Li2O:2MoO3 and Li2O:2WO3 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-GeO2 crystals were grown up to 3 mm on the edge. Crystals from Li2O:2MoO3 contained impurities or defects. X-ray powder diffraction diagrams were consistent with the hexagonal modification of GeO2. 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 Li2O:WO3 as flux, a colorless α-GeO2 single-crystal with a maximum final diameter of 5 mm was obtained . 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 K2W2O7 flux, the majority of the as-grown α-GeO2 crystals contained yellow flux inclusions. Thus, other inorganic solvents were investigated in the MoO3-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 K2Mo4O13 flux) [93,94]. Well-faceted and visually colorless and transparent α-GeO2 single-crystals were obtained in fluxes such as K2Mo4O13, Rb2Mo4O13 and Rb2Mo2O7. The as-grown crystals had no visible flux inclusions, bubbles or cracks and presented very smooth surface roughness [16,93,94]. The α-GeO2 millimeter-size crystals, up to 3 mm, presented either an unshaped morphology or a pseudo-cubic shape as already found for natural α-quartz . 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-GeO2 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-GeO2 crystals were of high quality precluding the presence of any considerable amount of twinning . 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-GeO2 single crystals [16,93].
A colorless, well facetted, highly-transparent and large-size single crystal, up to 0.5 cm3, of the piezoelectric phase of GeO2 was grown by TSSG from a high temperature solution using K2Mo4O13 as solvent [27,93]. The obtained volume made this isometric flux-grown GeO2 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-SiO2, was in accordance with an α-quartz-like structure and facilitated the identification of the different natural crystallographic faces [96,97,98].
3. Impurities Contamination
3.1. Flux-Grown α-GaPO4
The OH contamination of the crystalline lattice during crystallization via growth medium, which decreases the Q-factor of the resonators, has been largely reported in the literature concerning α-GaPO4 grown by the hydrothermal method [43,52,53,55,57,68,71,99,100].
The visual estimation of the OH contamination of the α-GaPO4 single crystals flux-grown from NaCl solvent was studied by annealing experiments . 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-GaPO4 crystals presented slight clouding and thus significant OH contamination.
In a typical room temperature non-polarized infrared transmission spectrum of an α-GaPO4 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 GaPO4 lattice and in another part to O–H stretching vibrations .
For X2O:3MoO3 (X = Li, K) flux-grown α-GaPO4 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 GaPO4, 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(T3800/T3400)]-α3400* where d represents the sample thickness in cm, T represents the % IR transmission at respectively 3800 and 3400 cm−1, and α3400* represents the absorption coefficient due to intrinsic lattice vibrations of α-GaPO4 at 3400 cm−1 . The α3400* 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 X2O:3MoO3 (X = Li, K) flux-grown GaPO4 and close to 0.15 cm−1 for hydrothermally-grown material . Thus, the infrared spectra correspond to X2O:3MoO3 (X = Li, K) flux-grown α-GaPO4 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 .
Chemical analyses of X2O:3MoO3 (X = Li, K) flux-grown α-GaPO4 crystals were done using glow discharge mass spectrometry (GDMS) and induced coupled plasma-atomic emission spectroscopy (ICP-AES) . The results demonstrated the presence of foreign chemical elements coming from the solvent with a Mo-content as high as 0.3% for GaPO4 crystals grown in K2O:3MoO3 flux. Na, Ca, Fe, Al and Si elements were also found with a major contamination from Al element (320 ppm to 0.13%).
3.2. Flux-Grown α-GeO2
As for hydrothermally-grown α-GaPO4 single crystals, OH contamination of the lattice was reported for hydrothermally-grown α-GeO2 [43,79,80,94]. In a non-polarized infrared spectrum collected in the transmission mode of a hydrothermally-grown α-GeO2 material containing significant OH-groups, Figure 2, a well-pronounced broad band between 2500 and 3800 cm−1 is observed with maxima at about 3455, 3500 and 3562 cm−1 attributed to Ge–OH vibration groups [43,79,81,94]. For both spontaneously nucleated MoO3-based flux-grown α-GeO2 samples and TSSG-grown α-GeO2 oriented plates of simple crystallographic orientations, infrared spectra characterize OH-free flux-grown α-GeO2 crystals [27,93] as evidenced by the absence of both a broad band and sharp peaks in the 2800–3500 cm−1 range, Figure 2.
Room temperature non-polarized Raman spectra of commercial α-GeO2 powder or α-GeO2stain-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 GeO4 entity [39,104,105].
The non-polarized Raman signal of a MoO3-based flux-grown α-quartz GeO2 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 GeO2 (D3 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 MoO3-based flux-grown α-GeO2 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 .
Ambient polarized Raman measurements performed on flux-grown α-quartz GeO2 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 GeO2 modes. This Raman study pointed out that high temperature flux-grown GeO2 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 GeO2 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 MoO3-based TSSG-grown α-GeO2 single crystal . 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-GeO2 crystal was of very good optical quality. The high chemical purity and the homogeneity of the TSSG-GeO2 crystal were also revealed by the absence of absorption bands. The α-GeO2 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-GeO2 crystal . The spectrum showed a considerable absorption in the 0.20–0.210 μm range associated with the presence of several bands .
4. Thermal Characterizations
4.1. Flux-Grown α-GaPO4
Differential scanning calorimetric (DSC) experiments were done on flux-grown α-GaPO4 single crystals crystallized via spontaneous nucleation in MoO3-based fluxes as Li2O:3MoO3 and K2O:3MoO3 [44,46,89,90,101]. On heating runs up to 1200 °C (2–10 °C·min−1) of α-GaPO4 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 GaPO4 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 .
When the as-grown α-GaPO4 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 GaPO4 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 GaPO4 had been found, after a DSC cycle, exclusively in the α-quartz modification after cooling from the β-cristobalite phase without annealing periods.
Effectively, concerning the hydrothermally-grown α-GaPO4 material grown at 300 °C (direct solubility), the successive cooling curve (−10 °C/min) from 1200 °C back to 20 °C, showed two main exothermic peaks [43,90]: one with an onset temperature of 910 °C due to a partial transformation of the β-cristobalite GaPO4 phase in α-quartz phase and a second, close to 578 °C, attributed to the β-cristobalite/α-cristobalite transition [40,41,42].
For hydrothermally-grown α-GaPO4 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 . The crystallization temperature of the α-GaPO4 phase would be an important parameter to favor the reversible α-quartz/β-cristobalite transition.
The thermal evolution of flux-grown α-GaPO4 single crystals grown from 950 to 600 °C in MoO3-based solvents was also followed by Raman spectroscopy . 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-GaPO4 sample grown in a Li2O-3MoO3 flux over the temperature range 950–600 °C was determined from powder X-ray diffraction data collected from 30 to 900 °C . 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 MoO3-based flux-grown α-GaPO4 crystals.
4.2. Flux-Grown α-GeO2
In the temperature range from room temperature to 1200 °C, the DSC heating-curve of GeO2 crystals with the α-quartz structure grown by the spontaneous nucleation method in selected fluxes (MoO3-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-GeO2 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 GeO2. 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 SiO2 with the well-known α-quartz/β-quartz transformation close to 573 °C [19,28]) and that no secondary phases such as the GeO2 rutile-like phase or flux-derived phases were detected.
Variable-temperature Raman spectroscopy measurements performed on high temperature flux-grown α-quartz GeO2 single crystals in MoO3-based solvents were reported [93,106]. Vibrations in α-GeO2 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 SiO2 or AlPO4, 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 GeO2 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-GeO2 should not be degraded significantly up to its melting point (1116 °C).
To confirm the thermal stability (aging), an as-grown α-GeO2 single crystal obtained by spontaneous nucleation in MoO3-based flux was annealed in air at high temperature (800–900 °C) over several months . The impact of this thermal cycle on the α-quartz-like structure of GeO2 was followed by Raman measurement. This long annealing process validated the excellent aging behavior under very high thermal stress of the α-quartz GeO2 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-GeO2 single crystals accessible with the flux growth techniques (water-free, chemical inclusion-free and rutile phase-free) as illustrated by the optical transmission curve .
5. Elastic Constants
5.1. 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 CIJ (I, J indices from 1 to 6): C11, C33, C44, C66, C12, C13 and C14 (2C66 = C11 − C12). 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).
5.1.1. Flux-Grown α-GaPO4
By the ultrasonic method, a determination of four out of six independent single-crystal elastic stiffness constants CEIJ at constant electric field was undertaken on millimeter suitable shaped plates obtained from as-grown α-GaPO4 single crystals spontaneously crystallized by slowly cooling a Li2O:3MoO3 flux saturated with GaPO4 [46,89,110]. The average size of the MoO3-based flux-grown GaPO4 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: CE13).
Single-crystal high-resolution Brillouin spectroscopy experiments were carried out to measure five out of six (CE13 is missing) elastic constants CEIJ of flux-grown α-GaPO4 material [90,103]. Optical quality single-crystals of α-GaPO4 with millimeter size were flux-grown from X2O:3MoO3 (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  and on other hand, on an as-grown α-GaPO4 single crystal polished as a cube with 2 mm side length showing X (100), Y (010) and Z (001) faces .
Table 1 gives the resulting single crystal elastic stiffness constants CEIJ obtained on high temperature flux-grown α-GaPO4 materials in MoO3-based solvents. They are compared with a reported experimental set of data concerning the hydrothermally-grown GaPO4 single crystals as well as with reported computed values .
The values of the flux-grown single crystal elastic stiffness constants CEIJcompared 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 CE11 and CE66.
|Table 1. Computed and experimental elastic stiffness constants CEIJ [GPa] of α-GaPO4.|
|Elastic constant||Hydrothermal-Growth||Computed values (−273 °C)||Flux-Growth|
|79.80 ||64.01 [46,110]|
|CE12 [=(CE11 − 2CE66)]||21.81 |
|16.60 ||13.51 [46,110]|
|3.20 ||5.52 [46,110]|
|106.30 ||103.29 |
|39.90 ||39.39 [46,110]|
|31.60 ||21.25 [46,110]|
5.1.2. Flux-Grown α-GeO2
The room temperature experimental values of single-crystal elastic stiffness constants CEIJ at constant electric field of flux-grown α-GeO2 in MoO3-based solvents were determined using Brillouin scattering, Table 2 . 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), (2–10) and (003) (hkl)-crystallographic planes.
These flux-grown α-GeO2CIJ 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]. CDIJ are elastic stiffness constants at constant electric displacement i.e., not corrected from the piezoelectric effect where e11 is the piezoelectric stress constant and ε11 the dielectric tensor at constant strain.
The crystal elastic constants values of the MoO3-based flux-grown α-GeO2 material present close similarities with most of the published CIJ data on hydrothermally-grown α-GeO2 crystals, Table 2. Therefore, the small discrepancy, registered more especially on the C11 and C14 moduli, was attributed to the strong reduction of the OH concentration in the lattice of flux-grown α-GeO2 crystals which was believed to induce a slightly stiffer behavior . 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-GeO2 elastic moduli presented very good agreement with computed values at 0 K of Lignie et al. , Table 2. The largest discrepancy was observed for the C66 (nearly 13% softer for the theoretical value) while very good accordance was found for the C12 and C14 elastic constants.
The numerical value of the piezoelectric term, deduced from the CD11 to CE11 difference, Table 2, is 1.29(2) GPa . The authors deduced for the flux-grown α-GeO2 material a d11 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-GeO2 crystal, Table 3.
|Table 2. Computed and experimental elastic stiffness constants CIJ [GPa] of α-GeO2.|
|Elastic constant||Hydrothermal-Growth||Computed values||Flux-Growth |
|CE11 CD11||64.00 |
|CE13||32.00 ||25.70 |
|| CE14|||2.00 |
|CE66 CD66||21.00 |
|Table 3. Piezoelectric strain coefficient d11 of α-GeO2 and α-SiO2 (given for comparison).|
|Piezoelectric constant||Hydrothermal-Growth||Predicted values||Flux-Growth||Hydrothermal-Growth|
|d11 (10−12 C/N)||4.04 |
|5.7(2) ||2.31 |
The flux-grown α-GeO2 exhibits a d11 piezoelectric strain constant more than twice that of α-quartz SiO2, Table 3, confirming the improvement of the piezoelectric properties with the structural distortion in the α-quartz analogues [17,117].
5.2. High Temperature
5.2.1. Flux-Grown α-GaPO4
High-resolution Brillouin spectroscopy studies concerning the CIJ elastic stiffness constant evolution with temperature of high-temperature flux-grown α-GaPO4single-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-GaPO4 single crystals obtained by slow cooling from 950 to 600 °C in X2O:3MoO3 fluxes (X = Li, K) were used to follow the thermal evolution of CD11 and CE33 elastic constant . CD11 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]. CE33 presented a monotonous decrease with temperature up to 850 °C while CD11 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 .
For the Brillouin scattering measurements using the backscattering geometry undertaken on a α-GaPO4 crystal shaped as a cube with X-, Y- and Z-faces , the CE11, CE33, CE44 and CE12 constants showed monotonic elastic softening upon heating up to 850 °C while CE66 and CE14 showed continuous stiffening. Most of the CIJ elastic stiffness constant derives by only a few percent upon heating, while CE14 increases by about 50% and CE12 decreases by about 35%. The first-order temperature coefficients T(1)CIJ were negative for CE11, CE33, CE44 and CE12 elastic constants  in perfect agreement with previous reports on hydrothermally-grown α-GaPO4 crystals [67,110,112,118].
5.2.2. Flux-Grown α-GeO2
Different sets of CIJ elastic stiffness constants at constant electric displacement and ambient conditions have been reported on flux- and hydrothermally-grown α-GeO2 [23,24,109,116]. However, only one set of elastic data concerning their thermal evolution is reported in the literature . It concerns a high resolution Brillouin scattering study of MoO3-based flux-grown α-GeO2 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 GeO2 material up to melting (1116 °C) [93,94]. The C11, C33, and C12 elastic constants show monotonic elastic softening upon heating while C44 and C66 show continuous stiffening.
The thermal evolution of the piezoelectric term, deduced from the difference between CD11 and CE11, was found stable up to 1000 °C, Figure 4 [93,109] meaning that MoO3-based flux-grown α-GeO2 crystals exhibit piezoelectric activity even at very high temperature.
In the family of α-quartz isotypes, high quality α-GaPO4 and α-GeO2 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-GeO2.
The main structural and chemical results obtained from infrared studies (OH-content), thermal behavior analysis and Brillouin scattering experiments on MoO3-based flux-grown α-GaPO4 and α-GeO2 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-GaPO4 and α-GeO2 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-GeO2 with minor adaptations. The potential of α-GeO2 single crystal for the realization of piezoelectric devices is also confirmed as its d11 piezoelectric constant at ambient temperature is found to be more than twice that of α-quartz. The piezoelectric property of α-GeO2 is still conserved at high temperature as a significant piezoelectric contribution to C11 still exists at 1000 °C.
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.
Conflicts of Interest
The authors declare no conflict of interest.
- Zhang, S.; Yu, F. Piezoelectric materials for high temperature sensors. J. Am. Ceram. Soc. 2011, 94, 3153–3170, doi:10.1111/j.1551-2916.2011.04792.x.
- Jiang, X.; Kim, K.; Zhang, S.; Johnson, J.; Salazar, F. High temperature piezoelectric sensing. Sensors 2014, 14, 144–169, doi:10.3390/s140100144.
- Smith, G.S.; Alexander, L.E. Refinement of the atomic parameters of α-quartz. Acta Cryst. 1963, 16, 462–471, doi:10.1107/S0365110X63001298.
- Smith, G.S.; Isaacs, P.B. The crystal structure of quartz-like GeO2. Acta Cryst. 1964, 17, 842–846, doi:10.1107/S0365110X64002262.
- Le Page, Y.; Donnay, G. Refinement of the crystal structure of low-quartz. Acta Cryst. 1976, B32, 2456–2459, doi:10.1107/S0567740876007966.
- Le Page, Y.; Calvert, L.D.; Gabe, E.J. Parameter variation in low-quartz between 94 and 298 K. J. Phys. Chem. Solids 1980, 41, 721–725, doi:10.1016/0022-3697(80)90078-5.
- Goiffon, A.; Bayle, G.; Astier, R.; Jumas, J.-C.; Maurin, M.; Philippot, E. Cristallochimie des phases GaPO4, AlAsO4 et GaAsO4. Etude comparée des structures de type quartz-α. Rev. Chim. Minér. 1983, 20, 338–350. (In French).
- Goiffon, A.; Jumas, J.-C.; Philippot, E. Phases de type quartz α: Structure de FePO4 et spectrométrie Mössbauer du fer-57. Rev. Chim. Minér. 1986, 23, 99–109. (In French).
- Goiffon, A.; Jumas, J.-C.; Maurin, M.; Philippot, E. Etude comparée à diverses températures (173, 293 et 373 K) des structures de type quartz α des phases MXO4 (MIII = Al, Ga et XV = P, As). J. Solid State Chem. 1986, 61, 384–396. (In French), doi:10.1016/0022-4596(86)90047-2.
- Glinnemann, J.; King, H.E.; Schulz, H.; Hahn, Th.; la Placa, S.J.; Dacol, F. Crystal structures of the low-temperature quartz-type phases of SiO2 and GeO2 at elevated pressure. Z. Kristall. 1992, 198, 177–212, doi:10.1524/zkri.1992.198.3-4.177.
- Haines, J.; Cambon, O.; Philippot, E.; Chapon, L.; Hull, S. A neutron diffraction study of the thermal stability of the α-quartz-type structure in germanium dioxide. J. Solid State Chem. 2002, 166, 434–441, doi:10.1006/jssc.2002.9625.
- Guillot, R.; Fertey, P.; Hansen, N.K.; Allé, P.; Elkaïm, E.; Lecomte, C. Diffraction study of the piezoelectric properties of low quartz. Eur. Phys. J. B 2004, 42, 373–380, doi:10.1140/epjb/e2004-00393-4.
- Haines, J.; Cambon, O.; Prudhomme, N.; Fraysse, G.; Keen, D.A.; Chapon, L.C.; Tucker, M.G. High-temperature, structural disorder, phase transitions, and piezoelectric properties of GaPO4. Phys. Rev. B 2006, 73, 014103:1–014103:10, doi:10.1103/PhysRevB.73.014103.
- Labéguerie, P.; Harb, M.; Baraille, I.; Rérat, M. Structural electronic, elastic, and piezoelectric properties of α-quartz and MXO4 (M = Al, Ga, Fe; X = P, As) isomorph compounds: A DFT study. Phys. Rev. B 2010, 81, 045107:1–045107:9, doi:10.1103/PhysRevB.81.045107.
- Giangrisostomi, E.; Minicucci, M.; Trapananti, A.; di Cicco, A. Multiple-scattering X-ray absorption analysis of quartz-like, rutile-like, and amorphous germanium dioxide. Phys. Rev. B 2011, 84, 214202:1–214202:8, doi:10.1103/PhysRevB.84.214202.
- Lignie, A.; Granier, D.; Armand, P.; Haines, J.; Papet, P. Modulation of quartz-like GeO2 structure by Si substitution: An X-ray diffraction study of Ge1−xSixO2 (0 ≤ x < 0.2) flux-grown single crystals. J. Appl. Cryst. 2012, 45, 272–278.
- Philippot, E.; Palmier, D.; Pintard, M.; Goiffon, A. A general survey of quartz and quartz-like materials: Packing distortions, temperature, and pressure effects. J. Solid State Chem. 1996, 123, 1–13, doi:10.1006/jssc.1996.0145.
- Philippot, E.; Armand, P.; Yot, P.; Cambon, O.; Goiffon, A.; McIntyre, G.J.; Bordet, P. Neutron and X-ray structure refinements between 15 and 1073 K of piezoelectric gallium arsenate, GaAsO4: Temperature and pressure behavior compared with other α-quartz materials. J. Solid State Chem. 1999, 146, 114–123, doi:10.1006/jssc.1999.8316.
- Grimm, H.; Dorner, B. On the mechanism of the α-β phase transformation of quartz. J. Phys. Chem. Solids 1975, 36, 407–413, doi:10.1016/0022-3697(75)90066-9.
- Zwijnenburg, M.A.; Huenerbein, R.; Bell, R.G.; Cora, F. A computational study into the (tetrahedral) distortion of TX2 α-quartz materials: The effect of changing the chemical composition away from SiO2. J. Solid State Chem. 2006, 179, 3429–3436.
- Kihara, K. An X-ray study of the temperature dependence of the quartz structure. Eur. J. Mineral. 1990, 2, 63–77.
- Philippot, E.; Goiffon, A.; Ibanez, A.; Pintard, M. Structure deformations and existence of the α-β transition in MXO4 quartz-like materials. J. Solid State Chem. 1994, 110, 356–362, doi:10.1006/jssc.1994.1180.
- Balitsy, D.V.; Silvestrova, O.Y.; Balitsky, V.S.; Pisarevsky, Y.V.; Pushcharovsky, D.Y.; Philippot, E. Elastic, piezoelectric, and dielectric properties of α-GeO2 single crystals. Crystallogr. Rep. 2000, 45, 145–147, doi:10.1134/1.171151.
- Pisarevsky, Y.V.; Silvestrova, O.Y.; Philippot, E.; Balitsky, D.V.; Pisharovsky, D.Y.; Balitsky, V.S. Piezoelectric, Dielectric and Elastic Properties of Germanium Dioxide Single Crystals. In Proceedings of the 2000 IEEE/EIA International Frequency Control Symposium and Exhibition, Kansas City, MO, USA, 7–9 June 2000.
- Cambon, O.; Haines, J. Structure-piezoelectric Property Relationships in α-Quartz Isotypes: Design and Characterization of High Performance Piezoelectric Materials. In Proceedings of the 2003 IEEE International Frequency Control Symposium and and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, Tampa, FL, USA, 4–8 May 2003.
- Cambon, O.; Haines, J.; Fraysse, G.; Détaint, J.; Capelle, B.; van der Lee, A. Piezoelectric characterization and thermal stability of a high-performance α-quartz-type material, gallium arsenate. J. Appl. Phys. 2005, 97, 074110:1–074110:7, doi:10.1063/1.1874293.
- Lignie, A.; Ménaert, B.; Armand, P.; Pena, A.; Debray, J.; Papet, P. Top seeded solution growth and structural characterizations of α-quartz-like structure GeO2 single crystal. Cryst. Growth Des. 2013, 13, 4220–4225, doi:10.1021/cg4000523.
- Engel, G.F.; Krempl, P.W. Stability of α-phases of quartz-isomorphs. Ferroelectrics 1984, 54, 9–12, doi:10.1080/00150198408215803.
- Kolodiev, B.N.; Makhina, I.B. GeO2—A promising new piezoelectric. Sov. Phys. Crystallogr. 1989, 34, 455–456.
- Laubengayer, A.W.; Morton, D.S. The polymorphism of germanium dioxide. J. Am. Chem. Soc. 1932, 54, 2303–2320, doi:10.1021/ja01345a019.
- Baur, W.H.; Khan, A.A. Rutile-type compounds. IV. SiO2, GeO2 and a comparison with other rutile-type structures. Acta Cryst. 1971, B27, 2133–2139.
- Rao, K.V.K.; Naidu, S.V.N.; Iyengar, L. Precision lattice parameters and the coefficients of thermal expansion of hexagonal germanium dioxide. J. Appl. Cryst. 1973, 6, 136–138, doi:10.1107/S0021889873008307.
- Yamanaka, T.; Kurashima, R.; Mimaki, J. X-ray diffraction study of bond character of rutile-type SiO2, GeO2 and SnO2. Z. Kristallogr. 2000, 215, 424–428.
- Micoulaut, M.; Cormier, L.; Henderson, G.S. The structure of amorphous, crystalline and liquid GeO2. J. Phys. Condens. Matter 2006, 18, R753–R784, doi:10.1088/0953-8984/18/45/R01.
- Madon, M.; Gillet, P.; Julien, C.; Price, G.D. A vibrational study of phase transitions among the GeO2 polymorphs. Phys. Chem. Miner. 1991, 18, 7–18, doi:10.1007/BF00199038.
- Kotera, Y.; Yonemura, M. Kinetics of the transformation of germanium oxide. Trans. Faraday Soc. 1963, 59, 147–155, doi:10.1039/tf9635900147.
- Newns, G.R.; Hanks, R. Thermal behavior of germanium dioxide. J. Chem. Soc. A 1966, 954–957, doi:10.1039/j19660000954.
- Sarver, J.F. Polymorphism and subsolidus equilibria in the system GeO2-TiO2. Am. J. Sci. 1961, 259, 709–718, doi:10.2475/ajs.259.9.709.
- Bielz, T.; Soisuwan, S.; Kaindl, R.; Tessadri, R.; Többens, D.M.; Klötzer, B.; Penner, S. A high-resolution diffraction and spectroscopic study of the low-temperature phase transformation of hexagonal to tetragonal GeO2 with and without alkali hydroxide promotion. J. Phys. Chem. C 2011, 115, 9706–9712, doi:10.1021/jp202457b.
- Perloff, A. Temperature inversions of anhydrous gallium orthophosphate. J. Am. Ceram. Soc. 1956, 39, 83–88, doi:10.1111/j.1151-2916.1956.tb15629.x.
- Barz, R.-U.; Schneider, J.; Gille, P. High-temperature phase transitions of gallium orthophosphate (GaPO4). Z. Kristallogr. 1999, 214, 845–849, doi:10.1524/zkri.19220.127.116.115.
- Jacobs, K.; Hofmann, P.; Klimm, D.; Reichow, J.; Schneider, M. Structural phase transformations in crystalline gallium orthophosphate. Solid State Chem. 2000, 149, 180–188, doi:10.1006/jssc.1999.8520.
- Pey, F. Synthèse et Caractérisations de Matériaux Homéotypes du Quartz. Ph.D. Thesis, Université Montpellier II, Montpellier, France, October 2004. (In French).
- Beaurain, M.; Armand, P.; Papet, P. Synthesis and characterization of α-GaPO4 single crystals grown by the flux method. J. Cryst. Growth 2006, 294, 396–400, doi:10.1016/j.jcrysgro.2006.05.074.
- Angot, E.; le Parc, R.; Levelut, C.; Beaurain, M.; Armand, P.; Cambon, O.; Haines, J. A high temperature Raman scattering study of the phase transitions in GaPO4 and the AlPO4-GaPO4 system. J. Phys. Condens. Matter 2006, 18, 4315–4327, doi:10.1088/0953-8984/18/17/018. 21690784
- Beaurain, M.; Armand, P.; Balitsky, D.; Papet, P. Physical Characterizations of α-GaPO4 Single Crystals Grown by the Flux Method. In Proceedings of the 2007 Joint Meeting of the European Time and Frequency Forum (EFTF) and the IEEE International Frequency Control Symposium (IEEE-FCS), Geneva, Switzerland,, 29 May–1 June 2007.
- Hirano, S.; Miwa, K.; Naka, S. Hydrothermal synthesis of gallium orthophosphate crystals. J. Cryst. Growth 1986, 79, 215–218, doi:10.1016/0022-0248(86)90439-2.
- Hirano, S.; Kim, P. Hydrothermal synthesis of gallium orthophosphate crystals. Bull. Chem. Soc. Jpn. 1989, 62, 275–278, doi:10.1246/bcsj.62.275.
- Engel, G.; Klapper, H.; Krempl, P.; Mang, H. Growth twinning in quartz-homeotypic gallium orthophosphate crystals. J. Cryst. Growth 1989, 94, 597–606, doi:10.1016/0022-0248(89)90081-X.
- Cochez, M. Cristallogénèse et Caractérisations du Phosphate de Gallium, GaPO4, Matériau Piézoélectrique à Fort Coefficient de Couplage. Ph.D. Thesis, Université Montpellier II, Montpellier, France, September 1994. (In French).
- Hirano, S.; Kim, P.C. Growth of gallium orthophosphate single crystals in acidic hydrothermal solutions. J. Mater. Sci. 1991, 26, 2805–2808, doi:10.1007/BF02387755.
- Philippot, E.; Ibanez, A.; Goiffon, A.; Cochez, M.; Zarka, A.; Capelle, B.; Schwartzel, J.; Détaint, J. A quartz-like material: Gallium phosphate (GaPO4); crystal growth and characterization. J. Cryst. Growth 1993, 130, 195–208, doi:10.1016/0022-0248(93)90852-N.
- Palmier, D.; Goiffon, A.; Capelle, B.; Détaint, J.; Philippot, E. Crystal growth and characterization of quartz-like material: Gallium phosphate (GaPO4). J. Cryst. Growth 1996, 166, 347–353, doi:10.1016/0022-0248(96)00115-7.
- Motchany, A.I.; Chvanski, P.P.; Leonyuk, N.I. Synthesis and solubility of GaPO4 crystals in acid solutions under hydrothermal conditions. J. Cryst. Growth 2000, 211, 506–508, doi:10.1016/S0022-0248(99)00772-1.
- Yot, P.; Cambon, O.; Balitsky, D.; Goiffon, A.; Philippot, E.; Capelle, B.; Détaint, J. Advances in crystal growth and characterizations of gallium phosphate, GaPO4. J. Cryst. Growth 2001, 224, 294–302, doi:10.1016/S0022-0248(01)01013-2.
- Demianets, L.N. Gallium orthophosphate hydrothermal growth at high temperatures (320 °C). Ann. Chim. Sci. Mater. 2001, 26, 67–74.
- Jacobs, K.; Hofmann, P.; Reichow, J. Physico-chemical aspects of the hydrothermal growth of GaPO4. Ann. Chim. Sci. Mater. 2001, 26, 85–90, doi:10.1016/S0151-9107(01)90017-0.
- Barz, R.-U.; Grassl, M.; Gille, P. Study of anisotropic effects in hydrothermal growth of gallium orthophosphate single crystals. Ann. Chim. Sci. Mater. 2001, 26, 95–98, doi:10.1016/S0151-9107(01)90019-4.
- Grassel, M.; Barz, R.-U.; Gille, P. Reducing inversion twinning in single crystal growth of GaPO4. Cryst. Res. Technol. 2002, 37, 531–539, doi:10.1002/1521-4079(200206)37:6<531::AID-CRAT531>3.0.CO;2-5.
- Barz, R.-U.; Grassel, M.; Gille, P. Studies on the solubility of GaPO4 in phosphoric acid. J. Cryst. Growth 2002, 245, 273–277, doi:10.1016/S0022-0248(02)01734-7.
- Balitsky, D.V.; Philippot, E.; Papet, P.; Balitsky, V.S.; Pey, F. Comparative crystal growth of GaPO4 crystals in the retrograde and direct solubility range by hydrothermal methods of temperature gradient. J. Cryst. Growth 2005, 275, e887–e894, doi:10.1016/j.jcrysgro.2004.11.028.
- Byrappa, K.; Yoshimura, M. Hydrothermal Growth of Some Selected Crystals. In Handbook of Hydrothermal Technology, 2nd ed. ed.; 2001.
- Philippot, E.; Goiffon, A.; Maurin, M.; Détaint, J.; Schwartzel, J.; Toudic, B.; Capelle, B.; Zarka, A. Evaluation of high quality berlinite crystals grown in sulphuric acid medium. J. Cryst. Growth 1990, 104, 713–726, doi:10.1016/0022-0248(90)90015-D.
- Zvereva, O.V.; Demianets, L.N. Substrate orientation and hydrothermal growth of GaPO4 single crystals. Crystallogr. Rep. 1995, 40, 990–993.
- Krispel, F.; Krempl, P.W.; Knoll, P.; Wallnöfer, W. OH Impurities in Gallium Phosphate. In Proceedings of the 11th European Frequency and Time Forum, Neuchâtel, Switzerland, 4–6 March 1997.
- Détaint, J.; Zarka, A.; Capelle, B.; Palmier, D.; Philippot, E. Optimisation of the Design of the Resonators Using the New Materials: Application to Gallium Phosphate and Langasite. In Proceedings of the 1997 IEEE International, Orlando, FL, USA, 28–30 May 1997.
- Palmier, D. Optimisation de la Cristallogénèse et de la Caractérisation des Propriétés Piézoélectriques du Phosphate de gallium. Ph.D. Thesis, Université Montpellier II, Montpellier, France, November 1996. (In French).
- Marhino, E.; Palmier, D.; Goiffon, A.; Philippot, E. Spatial-OH impurity distribution in gallium phosphate crystals. J. Mater. Sci. 1998, 33, 2825–2830, doi:10.1023/A:1017581718908.
- Wallnöfer, W.; Krempl, P.W.; Krispel, F.; Willfurth, V. Segregation forming and growth defect characterization by heat treatment of hydrothermally grown GaPO4. J. Cryst. Growth 1999, 198–199, 487–491.
- Grassl, M.; Barz, R.-U.; Gille, P. Etch studies on GaPO4 single crystals. J. Cryst. Growth 2000, 220, 522–530, doi:10.1016/S0022-0248(00)00892-7.
- Jacobs, K.; Hofmann, P.; Klimm, D. OH impurities in GaPO4 crystals: Correlation between infrared absorption and mass loss during thermal treatment. J. Cryst. Growth 2002, 237–239, 837–842.
- Prud’homme, N. Cristallisation-dissolution de GaPO4: Phénomènes à l’interface Cristal-Solvant. Etude de la Dissolution Contrôlée de GaPO4 pour la Réalisation de Résonateurs Piézoélectriques à Haute Fréquence. Ph.D. Thesis, Université Montpellier II, Montpellier, France, December 2005. (In French).
- Hofmann, P.; Juda, U.; Jacobs, K. Characterization of etch figures on as-grown surfaces of GaPO4 crystals. J. Cryst. Growth 2005, 275, e1883–e1888, doi:10.1016/j.jcrysgro.2004.11.275.
- Defregger, S.; Engel, G.F.; Krempl, P.W. Linear and nonlinear optical properties of quartz-type GaPO4. Phys. Rev. B 1991, 43, 6733–6738, doi:10.1103/PhysRevB.43.6733.
- Barz, R.U.; Ghemen, S.V. Water-free gallium phosphate single-crystal growth from the flux. J. Cryst. Growth 2005, 275, e921–e926, doi:10.1016/j.jcrysgro.2004.11.079.
- Hill, V.G.; Chang, L.L.Y. Hydrothermal investigation of GeO2. Am. Miner. 1968, 53, 1744–1748.
- Roy, R.; Theokritoff, S. Crystal growth of metastable phases. J. Cryst. Growth 1972, 12, 69–72, doi:10.1016/0022-0248(72)90342-9.
- Demianets, L.N. Hydrothermal synthesis of new compounds. Prog. Cryst. Growth Charact. 1990, 22, 299–355.
- Glushkova, T.M.; Kiselev, D.F.; Makhina, I.B.; Firsova, M.M.; Shtyrkova, A.P. Trigonal germanium dioxide: Its preparation and optical parameters. Moscow Univ. Phys. Bull. 1992, 47, 55–58.
- Balitsky, D.V.; Balitsky, V.S.; Pisarevley, Y.V.; Philippot, E.; Silvestrova, O.Y.; Pushcharovsky, D.Y. Growth of germanium dioxide single crystals with α-quartz structure and investigation of their crystal structure, optical, elastic, piezoelectric, dielectric and mechanical properties. Ann. Chim. Sci. Mater. 2001, 26, 183–192, doi:10.1016/S0151-9107(01)90034-0.
- Balitsky, D.V.; Balitsky, V.S.; Pushcharovsky, D.Y.; Bondarenko, G.V.; Kosenko, A.V. Growth and characterization of GeO2 single crystals with the quartz structure. J. Cryst. Growth 1997, 180, 212–219, doi:10.1016/S0022-0248(97)00224-8.
- Laurent, Y. Obtention de monocristaux au sein d’un flux fondu. Rev. Chim. Miner. 1969, 6, 1145–1186. (In French).
- Elwell, D.; Neate, B.W. Review: Mechanisms of crystal growth from fluxed melts. J. Mater. Sci. 1971, 6, 1499–1519, doi:10.1007/BF02403090.
- Tolksdorf, W. Crystal growth and epitaxy from high-temperature solutions. In Synthesis, Crystal Growth and Characterization; Lal, K., Ed.; North-Holland: Oxford, UK, 1982; pp. 197–211.
- Nielse, J.W. Recent development in crystal growth from high-temperature solutions. In Growth of Crystals; Chernov, A.A., Ed.; Consultant Bureau: New York, NY, USA, 1984; Volume 12, pp. 143–154.
- Roy, R.; White, W.B. High temperature solution (flux) and high pressure solution (hydrothermal) crystal growth. J. Cryst. Growth 1968, 3–4, 33–42.
- Beaurain, M.; Armand, P.; Papet, P. Growth of piezoelectric single crystals by the flux method. J. Cryst. Growth 2005, 2975, e279–e282, doi:10.1016/j.jcrysgro.2004.10.122.
- Shvanskii, E.; Armand, P.; Balitsky, D.; Philippot, E.; Papet, E. Flux growth gallium orthophosphate crystals. Ann. Chim. Sci. Mater. 2006, 31, 97–102, doi:10.3166/acsm.31.97-102.
- Beaurain, M. Monocristaux de α-GaPO4: Croissance par la Technique du Flux et Caractérisations Physiques. Ph.D. Thesis, Université Montpellier II, Montpellier, France, December 2006. (In French).
- Armand, P.; Beaurain, M.; Rufflé, B.; Ménaert, B.; Balitsky, D.; Clément, S.; Papet, P. Characterizations of piezoelectric GaPO4 single crystals grown by the flux method. J. Cryst. Growth 2008, 310, 1455–1459, doi:10.1016/j.jcrysgro.2007.11.049.
- Finch, C.B.; Clark, G.W. Flux growth and characterization of hexagonal germanium dioxide single crystals. Am. Miner. 1968, 53, 1394–1398.
- Goodrum, J.W. Solution top-seeding: Growth of GeO2 polymorphs. J. Cryst. Growth 1972, 13–14, 604–607.
- Lignie, A. Matériaux Piézoélectriques Pour Applications Hautes Températures: Etude de la Croissance de Monocristaux de Ge1−xSixO2 (0 ≤ x ≤ 0,2) et de Leurs Propriétés. Ph.D. Thesis, Université Montpellier II, Montpellier, France, September 2012. (In French).
- Lignie, A.; Armand, P.; Papet, P. Growth of piezoelectric water-free GeO2 and SiO2-substituted GeO2 single-crystals. Inorg. Chem. 2011, 50, 9311–9317, doi:10.1021/ic200661q. 21875033
- Tarr, W.A.; Lonsdale, J.T. Pseudo-cubic quartz crystals from Artesia, New Mexico. Am. Miner. 1929, 14, 50–53.
- Hartman, P. Sur la morphologie des cristaux. Bull. Miner. 1978, 101, 195–201. (In French).
- Iwasaki, H.; Iwasaki, F. Morphological variations of quartz crystals as deduced from computer experiments. J. Cryst. Growth 1995, 151, 348–358, doi:10.1016/0022-0248(95)00040-2.
- Philippot, E.; Goiffon, A.; Ibanez, A. Comparative crystal habit study of quartz and MPO4 isomorphous compounds (M = Al, Ga). J. Cryst. Growth 1996, 160, 268–278, doi:10.1016/0022-0248(95)00908-6.
- Philippot, E.; Ibanez, A.; Goiffon, A.; Capelle, B.; Zarka, A.; Schwartzel, J.; Détaint, J. Crystal Growth and Physical Characterizations of GaPO4. In Proceedings of the 6th European Frequency and Time Forum, Noordwijk, NL, USA,, 17–19 March 1992.
- Cochez, M.; Ibanez, A.; Goiffon, A.; Philippot, E. Crystal growth and infrared characterization of GaPO4 in phosphoric-sulphuric media. Eur. J. Solid State Inorg. Chem. 1993, 30, 509–519.
- Beaurain, M.; Armand, P.; Papet, P. Growth of α-GaPO4 and α-GeO2 single crystals by the flux method. J. Phys. IV 2005, 126, 23–26.
- Krempl, P.W.; Krispel, F.; Wallnöfer, W.; Leuprecht, G. GaPO4: A Critical Review of Material Data. In Proceedings of the Ninth European Frequency and Time Forum, Besançon, France, 8–10 March 1995.
- Armand, P.; Beaurain, M.; Rufflé, B.; Ménaert, B.; Papet, P. Temperature dependence of single-crystal elastic constants of flux-grown α-GaPO4. Inorg. Chem. 2009, 48, 4988–4996, doi:10.1021/ic900146y. 19466805
- Sendova-Vassileva, M.; Tzenov, N.; Dimova-Malinovskia, D.; Rosenbauer, M.; Stutzmann, M.; Josepovits, K.V. Structural and luminescence studies of stain-etched and electrochemically etched germanium. Thin Solid Films 1995, 255, 282–285, doi:10.1016/0040-6090(94)05673-2.
- Kaindl, R.; Többens, D.M.; Penner, S.; Bielz, T.; Soisuwan, S.; Klötzer, B. Quantum mechanical calculations of the vibrational spectra of quartz- and rutile-type GeO2. Phys. Chem. Miner. 2012, 39, 47–55, doi:10.1007/s00269-011-0458-8.
- Fraysse, G.; Lignie, A.; Armand, P.; Bourgogne, D.; Haines, J.; Ménaert, B.; Papet, P. Vibrational origin of the thermal stability in the highly distorted α-quartz type material GeO2: An experimental and theoretical study. Inorg. Chem. 2013, 52, 7271–7279, doi:10.1021/ic4009416. 23734712
- Hermet, P.; Fraysse, G.; Lignie, A.; Armand, P.; Papet, Ph. Density functional theory predictions of the nonlinear optical properties in α-quartz-type germanium dioxide. J. Phys. Chem. C 2012, 116, 8692–8698, doi:10.1021/jp300855q.
- Hermet, P.; Lignie, A.; Fraysse, G.; Armand, P.; Papet, P. Thermodynamic properties of the α-quartz-type and rutile-type GeO2 from first-principles calculations. Phys. Chem. Chem. Phys. 2013, 15, 15943–15948, doi:10.1039/c3cp52741g. 23955725
- Lignie, A.; Zhou, W.; Armand, P.; Rufflé, B.; Mayet, R.; Debray, J.; Hermet, P.; Ménaert, B.; Thomas, P.; Papet, P. High-temperature elastic moduli of flux-grown α-GeO2 single crystal. ChemPhysChem 2014, 15, 118–125, doi:10.1002/cphc.201300793. 24302547
- Beaurain, M.; Armand, P.; Detaint, J.; Ménaert, B.; Balitsky, D.; Papet, P. Elastic characterizations of the α-GaPO4 single crystals grown by the flux method. J. Phys. Condens. Matter 2008, 20, 025226:1–025226:7, doi:10.1088/0953-8984/20/02/025226.
- Zhou, Y.; Liu, B. Theoretical investigation of mechanical and thermal properties of MPO4 (M = Al, Ga). J. Eur. Ceram. Soc. 2013, 33, 2817–2821, doi:10.1016/j.jeurceramsoc.2013.04.020.
- Krempl, P.W.; Schleinzer, G.; Wallnöfer, W. Gallium phosphate: A new piezoelectric crystal material for high-temperature sensorics. Sens. Actuator A 1997, 61, 361–363, doi:10.1016/S0924-4247(97)80289-0.
- Krempl, P.W.; Krispel, F.; Wallnöfer, W. Industrial development and prospects of GaPO4. Ann. Chim. Sci. Mater. 1997, 22, 623–626.
- Ghobadi, E.; Capobianco, J.A. Crystal properties of α-quartz type GeO2. Phys. Chem. Chem. Phys. 2000, 2, 5761–5763, doi:10.1039/b006839j.
- Liu, Q.-J.; Liu, Z.-T.; Feng, L.-P.; Tian, H. First-principles study of structural, elastic, electronic and optical properties of rutile GeO2 and α-quartz GeO2. Solid State Sci. 2010, 12, 1748–1755, doi:10.1016/j.solidstatesciences.2010.07.025.
- Grimsditch, M.; Polian, A.; Brazhkin, V.; Balitskii, D. Elastic constants of α-GeO2. J. Appl. Phys. 1998, 83, 3018–3020, doi:10.1063/1.367117.
- Krempl, P.W. Piezoelectricity in quartz analogues. J. Phys. IV 2005, 126, 95–100.
- Wallnöfer, W.; Stadler, J.; Krempl, P. Temperature Dependence of Elastic Constants of GaPO4 and Its Influence on BAW and SAW Devices. In Proceedings of the 7th European Frequency and Time Forum, Neuchâtel, Switzerland, 16–18 March 1993.
© 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).