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Abstract
We report measurements of the thermo-mechanical properties of two recently developed non-chalcopyrite, trigonal, mid-IR nonlinear optical crystals, BaGa2GeS6 and BaGa2GeSe6. These include orientation dependent hardness and Young’s modulus, thermal expansion in the 200–430 K temperature range, and thermal conductivity in the 184–473 K temperature range. Covering similar wavelength ranges, these new quaternary compounds appear to be very promising alternatives to the classical ternary chalcopyrites AgGaS2 and AgGaSe2 due to the advantageous properties evinced by the thermo-mechanical data.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The quaternary trigonal chalcogenides BaGa2GeS6 (BGGS) and BaGa2GeSe6 (BGGSe) have been recently studied as viable alternatives to the well-established chalcopyrite type (point group $\bar{4}2m$) nonlinear optical crystals AgGaS2 (AGS) and AgGaSe2 (AGSe) which have been known for over 50 years and are commercially available for the mid-IR spectral range. The motivation for this effort has been to overcome some of the main limitations of AGS and AGSe, such as the need for post-growth annealing, the chemical instability of the polished surface, the anisotropic thermal expansion, and the low thermal conductivity and damage resistivity [1]. Such non-oxide nonlinear crystals are applied in parametric frequency down-conversion processes: the sulfides AGS and BGGS are preferable for 1-µm pumping (Nd- or Yb-lasers) due to their larger bandgaps while the selenides AGSe and BGGSe (possessing higher nonlinearity and mid-IR transmission to wavelengths as long as ∼18 µm) are preferable when pumping by Er- and Tm-/Ho- laser systems near 1.6 and 2 µm, respectively [2] or for the generation of the harmonics of CO2 gas lasers.
The successful growth of BGGS and BGGSe by the Bridgman technique, and in particular the large sizes and high optical quality available, have enabled the accurate characterization of their major linear and nonlinear optical properties as well as the realization of some three-wave parametric processes [3]. Most of the optical and thermo-optical properties are now well documented, including the transparency, dispersion, birefringence, thermo-optic coefficients, and nonlinear tensor components of BGGS and BGGSe [1,4]. In this work we study the thermo-mechanical properties of BGGS and BGGSe including hardness and Young’s modulus, thermal expansion and thermal conductivity. Preliminary results on the hardness and Young’s modulus obtained with randomly oriented samples were reported in [5] and preliminary results on the thermal conductivity using unoriented and oriented samples were reported in [6,7]. The wide application and commercialization of these new promising nonlinear crystals require knowledge of their hardness and elastic modulus as a measure for their tensile or compressive stiffness upon application of a force lengthwise. This is related to cutting and polishing procedures, as well as the subsequent cleaning and anti-reflection coating of the optical surfaces or estimation of thermal stress effects. The thermal expansion properties and in particular the anisotropy are essential both in the process of crystal growth by the Bridgman method and for the deposition of dielectric coatings as well as for the design of efficient heat removal by metal crystal holders. The thermo-optic coefficients (already reported for BGGS and BGGSe in [4] and [1], respectively) and the thermal conductivity set a limit to the average power that can be handled by a given nonlinear crystal depending on its residual absorption losses. These properties grow in importance with the trend to use higher repetition rate diode-pumped laser systems for increasing the average power of parametric frequency converters. Low thermal conductivity will lead to inefficient heat removal and thermal gradients, and consequently spatially depending dephasing effects in three-wave parametric interactions, thermal stress and lensing, and ultimately, to indirect optical damage.
2. Hardness and Young’s modulus
BGGS and BGGSe are trigonal (i.e. uniaxial) crystals with point group 3. The samples prepared were polished a-cut and c-cut plates with a thickness in the 1.65–1.74 mm range. The surface had a roughness better than λ/300, a flatness better than λ/6 (λ = 632.8 nm, He-Ne laser), and a quality of 30-20 (Scratch-Dig), as typically specified for optical devices.
The nanoindentation method employed in the present work has some advantages compared to the well-established microhardness tests [8–11]. Nanoindentation helps to avoid crack formation, pile-up/sink-in effects, and strain-induced phase transitions, which often occur in microhardness measurements employing higher loads [8,9]. Consequently, nanoindentation is advantageous when a high level of control over the load is required, e.g. for brittle materials, such as GaAs [10]. Moreover, the values obtained from nanoindentation are more accurate, since the area needed is derived from the indentation depth, rather than from microscopic images [8]. Nanoindentation can be used for thin and small samples [8] and has proven to be very useful for semiconductor single crystals such as Si, GaP, GaAs, and ZnSe [11].
For the nanoindentation measurements we employed a Nano Indenter G 200 system (Keysight Technologies, USA), equipped with thermal drift compensation (i.e. taking into account the effect of thermal expansion and contraction of both equipment and test material). Optically polished fused silica was used as a calibration standard. The tests were performed in the Continuous Stiffness Mode (CSM), with a small sinusoidal oscillation superimposed on the main load. This is a dynamic technique, in which the elastic modulus is calculated continuously during each local unloading step. NanoSuite 6 Software was used to process the collected data. The total indentation depth was 2000 nm at a constant strain rate target of 0.05 s-1. The frequency amounted to 45 Hz and the oscillations amplitude was 2 nm. The surface approach velocity amounted to 10 nm/s and the surface approach distance was 1 µm. A Berkovich tip, with a nominal tip radius (bluntness) of about 50 nm was employed.
The tests were performed at room temperature (RT, 293 ± 1 K). The relative humidity was ~40%. The samples were attached to a holder with a bond adhesive, in the same way as the fused silica reference sample. Their surface was cleaned with acetone prior to the measurement. In each case, ten consecutive indents were performed, and the spots were lined in two rows with 50-µm spacing between adjacent spots, as shown in the inset of Fig. 1. A slight sink-in effect on the residual impression of the Berkovich diamond indenter can be seen. Nevertheless, the Oliver-Pharr approach [12] for elastic moduli estimation is still valid. The hardness, HIT is then calculated as:
where P is the contact force, and A is the contact area (surface contact area, projected onto a plane normal to the direction of indentation).
Fig. 1. BGGSe (a-cut) loading/unloading curves: The individual tests are plotted in different colors. The inset shows a microphotograph of the surface after the nanoindentation tests. The separation between the individual imprints amounts to 50 µm.
Hence, Young’s modulus, EIT, is calculated from the modulus of elasticity of the indenter, Ei, and the reduced elastic modulus of the sample, Er:
Here S denotes the contact stiffness which is measured at each oscillatory step and β represents a geometrical factor which depends on the indenter (for a Berkovich tip β = 1.034).
The loading curves for the a-cut BGGSe sample are shown in Fig. 1. The curves superimpose well, which is an indication of excellent sample homogeneity and emphasizes the reliability of the results.
The hardness and Young’s modulus dependences on the depth for the a-cut BGGSe sample are displayed in Fig. 2(a) and 2(b), respectively. Some variations can be observed but they are only down to ~390 nm and this can be attributed to the surface roughness.
Fig. 2. Hardness (a) and Young’s modulus (b) versus displacement for the a-cut BGGSe: The different colors designate individual tests.
The averaged results for both materials and orientations are summarized in Table 1. The Vickers numbers (microhardness values) VHN are calculated according to VHN [kg/mm2] = 92.7 HIT [GPa].
Table 1. Hardness and Young’s Modulus of BGGS and BGGSe
Normally, the hardness is correlated with the crystal bandgap and its melting temperature: 3.37 eV (BGGS) and 2.38 eV (BGGSe), and 1256 K (BGGS) and 1150 K (BGGSe) [1]. It is thus higher for the sulfide compound. The bandgaps of AGS and AGSe amount to 2.76 and 1.83 eV, respectively [13]. Their melting temperatures are 1270 and 1124 K, respectively [13]. Vickers microhardness values of 320 and 230 kg/mm2 have been reported in the literature for AGS and AGSe, respectively [14]. Hence, BGGS and BGGSe exhibit superior hardness compared to their chalcopyrite counterparts AGS and AGSe, respectively, which makes them very promising for practical use and future commercialization. Their hardness is closer to the recently characterized ternary Ba compounds: BaGa4S7 (BGS) and BaGa4Se7 (BGSe) [15]. The hardness of BGGS is roughly 24% lower compared to the orthorhombic BGS (bandgap: 3.59 eV; melting temperature: 1378 K) while the hardness of BGGSe is roughly 13% higher compared to the monoclinic BGSe (bandgap: 2.73 eV; melting temperature: 1323 K).
The hardness of such semiconductor crystalline materials is related to their chemical bond ionicity and crystallographic structure [16]. An increasing metallic character of the compound leads to lower hardness [16], however, such characteristic trends are confined within a given crystal family, e.g., the I-III-VI2 chalcopyrites (to which AGS and AGSe belong) [14].
As can be concluded from Table 1, the anisotropy of the hardness of BGGS and BGGSe is rather weak, about 6.7% and 3.4%, respectively. The anisotropy of Young’s modulus is slightly larger (~9% for BGGS and ~12% for BGGSe). Still, for practical implementation, it seems that measurements with random orientation are also sufficient [5]. This is so because different nonlinear crystal cuts are used in each case of application as defined by the phase-matching condition for a specific three-wave interaction.
3. Thermal expansion
The thermal expansion was determined using powdered samples with a Bruker D8 Discover Davinci X-ray diffractometer with Co Kα radiation at 1.78897 and 1.79285 Å, paired with an Oxford Chimera temperature control system from 200–430 K (±0.2 K). We used FullProf software [17] to analyze the data in terms of a Le Bail fit [18]. The XRD peak profiles were defined using a Thompson-Cox-Hastings formulation of the pseudo-Voigt function with axial divergence asymmetry. The background was adjusted manually and the displacement was refined only for the lowest temperature analyzed and kept fixed as temperature was increased.
Figure 3 shows the lattice parameter temperature dependence for BGGS. The goodness of the fits χ2 was in the 3–4 range. The RT (300 K) values for the a and c constants are 9.59994(12) Å and 8.68259(18) Å, respectively. The values reported in [19] at 293 K are 9.5967(11) Å for a and 8.671(2) Å for c. Another literature source reports a = 9.6020(1) Å and c = 8.6889(2) Å at 93 K [20]. These data are included in Fig. 3 together with our present temperature dependent results. Good agreement is seen only for the a lattice constant value from [19]. Such deviations can be attributed to differences in the growth conditions, since all three measurements are based on different sources (i.e. crystal growers) or to differences in calibration between the different diffractometers. These possibilities will not affect the derived thermal expansion coefficients we present below. Our experimental data are fitted well by a quadratic polynomial A + BT + CT2 with the coefficients given in Table 2. We have plotted in Fig. 3 also the relative thermal expansion coefficient α as a linear fit obtained by differentiating the quadratic polynomials. The values at RT (300 K) are αa = 12.1 ppm/K and αc = 6.93 ppm/K.
Fig. 3. Lattice parameters a (a) and c (b) of BGGS versus temperature (experimental data: symbols, quadratic fit: red lines) and relative linear thermal expansion α =L-1dL/dT where L corresponds to a or c, in linear approximation (blue lines). The error bars for our measurements are within the symbols. Open symbols reproduce lattice constant data from Lin et al. [19] and Yin et al. [20].
Table 2. Quadratic fits A + BT + CT2 of the BGGS and BGGSe lattice constants
The thermal expansion of the chalcopyrite AGS was studied more recently in [21] with a dilatometer. The 300 K values from their fit are αa = 13.7 ppm/K and αc = −9.49 ppm/K. The strongly anisotropic thermal expansion of AGS with opposite signs is a well-known problem which was identified as the cause for crystal and ampoule cracking in initial Bridgman growth attempts of AGS [13,22]. This problem is apparently absent in BGGS.
The thermal expansion coefficients of the ternary orthorhombic BGS compound were just reported in [23] using single crystal XRD. The data indicate almost temperature independent expansion coefficients with small anisotropy (between 8.45 and 11.3 ppm/K for the three crystallographic directions).
Figure 4 shows the lattice parameter temperature dependence for BGGSe. Again, the goodness of the fits χ2 was in the 3–4 range. The RT (300 K) values for the a and c lattice constants are 10.03716(13) Å and 9.10199(17) Å, respectively. They show some difference to the values reported in [19] at 293 K, 10.0438(13) Å for a and 9.114(2) Å for c, but seem to match well another report at 93 K [20], giving a = 10.008(1) Å and c = 9.090(2) Å. These data are included in Fig. 4 together with our present temperature dependent results. Our experimental data are fitted well by a quadratic polynomial A + BT + CT2 with the coefficients given in Table 2. We have plotted in Fig. 4 also the relative thermal expansion coefficient α as a linear fit obtained by differentiating the quadratic polynomials. The values at RT (300 K) are αa = 12.2 ppm/K and αc = 3.84 ppm/K.
Fig. 4. Lattice parameters a (a) and c (b) of BGGSe versus temperature (experimental data: symbols, quadratic fit: red lines) and relative linear thermal expansion α =L-1dL/dT where L corresponds to a or c, in linear approximation (blue lines). The error bars for our measurements are within the symbols. Open symbols reproduce lattice constant data from Lin et al. [19] and Yin et al. [20].
The thermal expansion of the chalcopyrite AGSe was studied more recently in [24] by interferometric dilatometry. The 300 K values from their fit are αa = 14.1 ppm/K and αc = −11.2 ppm/K. Similarly, this anomalous thermal expansion behavior of AGSe resulted in crystal and ampoule cracking problems in initial Bridgman growth experiments [13,22]. In the case of BGGSe the expansion along both axes is positive and the anisotropy is less pronounced.
The thermal expansion coefficients of the ternary monoclinic BGSe compound, determined by dilatometry, were found to be roughly constant in the 293–573 K temperature range, with values between 9.24 and 11.7 ppm/K along the three crystallographic axes, i.e. almost isotropic [25]. In any case the anisotropy of the thermal expansion of BGSe is weaker compared to BGGSe.
Figure 5 shows the anisotropy of the thermal expansion defined as αa – αc and the volumetric relative thermal expansion coefficient defined as βv = 2αa + αc, for BGGS and BGGSe. The linear dependences were calculated by taking the derivatives of the fits in Table 2, as shown by the blue lines in Figs. 3 and 4. In the major part of the temperature range the thermal expansion is stronger in BGGS, although this is the compound with higher melting temperature, i.e. higher bond energy. The difference in the volumetric thermal expansion at RT is, however, small, less than 10%, similar to the difference in the hardness. The volumetric thermal expansion coefficient shows the variation of the crystal density ρ with temperature dρ/dT = –βvρ. As can be seen the overall effect of temperature on the crystal density is rather small. That both linear expansion coefficients in BGGS and BGGSe tend to decrease with temperature is a feature different from the chalcopyrites AGS and AGSe [21,24]. From the present data it is unclear whether they can become negative at yet higher temperatures approaching the melting points. It can be seen from Fig. 5(a) that the anisotropy of the thermal expansion is roughly 2–3 times smaller compared to AGS and AGSe.
Fig. 5. Anisotropy of the relative thermal expansion αa – αc (a) and volumetric relative thermal expansion coefficient βv = 2αa + αc (b) for BGGS (blue lines) and BGGSe (red lines) versus temperature.
4. Thermal conductivity
The a- and c-cut BGGS and BGGSe plates used for the thermal conductivity measurements had polished face aperture of roughly 6 × 6 mm2 and thickness between 1.63 and 1.72 mm.
The thermal diffusivity (κ) and specific heat capacity (cp) of the BGGS and BGGSe samples were measured in a contactless way for heat propagating along the a- and c-axes over a temperature range of 184 to 473 K by the flash analysis technique [26,27]. The thermal conductivity (k) is calculated using the formula
The RT density ρ values for BGGS and BGGSe are 3.89 and 5.20 g/cm3, respectively [3]. For their temperature dependence we used the results from the previous section.
The instrument used for the measurement was a NETZSCH Flash Analyzer LFA 467 HyperFlash E 1461. Its measurement method is in accordance with the international ASTM E1461-01 Standard [28]. The instrument is designed as a vertical system with a plane parallel sample placed in the center. An embedded Xenon lamp placed at the bottom is used as a flash source to generate a short (20 to 1200 µs) duration pulse which is absorbed at the bottom face of the sample. The temperature rise on the opposite side is monitored without contact with the sample as a function of time by a high speed infrared HgCdTe detector placed at the top of the system. The detector allows measurements of the time of the heat transfer from one side to another at temperatures ranging from 173 to 773 K. Both faces of the samples were coated with a thin (100–150 nm) Au film by thermal evaporation. To avoid reflection from the bottom (entrance) face and enhance the heat emission from the top (exit) face, these Au films were overcoated three times by graphite (Graphit-33, CRC), each time rotating the sample 90° and covering the entire surface. For the ideal case of instantaneous laser pulse, no heat losses and a uniform material,
where L is the sample thickness and t1/2 denotes the time to reach half of the maximum temperature rise onto the exit surface [26]. The “transparent” correction model [29] was chosen from the menu of the flash analyzer. The effect of the thermal expansion on the sample thickness was taken into account using the data from the previous section.In addition to thermal diffusivity, the instrument also provides a measurement of the sample’s specific heat capacity cp through comparison with a reference sample. For these measurements, the reference sample chosen was a ceramic (Pyroceram), with dimensions similar to those of the samples under test: aperture of 6 × 6 mm2, and thickness of 1.996 mm.
The results are summarized in Fig. 6. The accuracy in the diffusivity values is estimated to be better than ±2% in the entire temperature range. To calculate the conductivity we used the average values of the measured specific heat for the two orientations, also shown in Fig. 6, which serves to estimate a maximum error of ±5% in the entire temperature range both for the specific heat and the thermal conductivity. The RT thermal conductivity values for BGGS and BGGSe determined from the diffusivity and specific heat measurements exceed those reported in [30] without further details by about an order of magnitude. The thermal conductivity values presented in [7] were obviously overestimated and plagued by errors in the determined specific heat.
Fig. 6. Measured thermal diffusivity κ (a, d) and specific heat capacity cp (b, e) of BGGS (a, b, circles) and BGGSe (d, e, squares), for heat propagating along the a-axis (red) and the c-axis (blue), and the corresponding calculated thermal conductivity k (c,f). The open symbols in (b, e) denote average values from the two measurements on samples with different orientation.
At RT (298 K) we obtain cp(BGGS) = 0.40 ± 0.01 Jg-1K-1 and cp(BGGSe) = 0.27 ± 0.008 Jg-1K-1 based on multiple measurements. These results are confirmed by differential scanning calorimetry (DSC) using the Evercool 1 Physical Property Measurement System (Quantum Design, Inc., USA) with a heat capacity option, which gives only slightly higher (by 2% and 4%, respectively) values for both compounds.
For the thermal conductivity at RT (298 K) we obtain k = 0.91 ± 0.03 Wm-1K-1 along the a-axis and k = 1.10 ± 0.03 Wm-1K-1 along the c-axis for BGGS, and k = 0.63 ± 0.02 Wm-1K-1 along the a-axis and k = 0.76 ± 0.02 Wm-1K-1 along the c-axis for BGGSe. Thus, for both crystals the anisotropy of the thermal conductivity is rather low (< 20%). Comparing with RT values known from the literature on AGS (1.143–1.162 Wm-1K-1 at 298 K [21] and 1.4–1.5 Wm-1K-1 [31]) and on AGSe (0.95–1.03 Wm-1K-1 at 298 K [24] and 1.0–1.1 Wm-1K-1 [31]), we see that BGGS and BGGSe show roughly 30% lower thermal conductivity compared to AGS and AGSe, respectively. Whereas the thermal conductivity of BGGS is also lower compared to its ternary orthorhombic counterpart BGS (1.45–1.68 Wm-1K-1 at 323 K in [32]), the thermal conductivity of BGGSe is somewhat higher compared to its ternary monoclinic counterpart BGSe (0.56–0.74 Wm-1K-1 at 298 K in [25]).
5. Conclusion
In the present work we presented measurements of the hardness and Young’s modulus, and the temperature dependent thermal expansion and thermal conductivity on oriented samples of the newly discovered nonlinear crystals for the mid-IR BGGS and BGGSe. These were basically the only three important properties of these materials, necessary for practical implementation, that were missing in their characterization. Except for the thermal conductivity, these new materials seem to be superior to the classical AGS and AGSe crystals that they are supposed to substitute in the future. In addition, BGGS and BGGSe show weaker anisotropy and no anomalous behavior of the thermal expansion, in contrast to AGS and AGSe.
Funding
Air Force Office of Scientific Research (LRIR No. 19RDCOR022, LRIR No. 23RXCOR003); Asian Office of Aerospace Research and Development (MOST No. F4GGA21207H002); Deutsche Forschungsgemeinschaft (No. PE 607/14–1).
Acknowledgment
This paper is dedicated to the memory of Valeriy V. Badikov who passed away on Dec 21, 2022. Dr. Badikov devoted more than six decades of his life to the development of novel chalcogenide crystals and pioneered the growth of about a dozen of new compounds in sizes suitable for real applications, among them the two title nonlinear materials. His passion and enthusiasm till his last days will be inspirational for all who knew him.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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