Thermophysical properties of lithium thiogallate that are important for optical applications

Abstract

Lithium thiogallate LiGaS₂ is one of the most common nonlinear crystals for mid-IR due to its extreme beam strength and wide transparency range; however, its thermophysical properties have not yet been practically studied. Large crystals of high optical quality are grown. DTA revealed features at 1224 K below melting point (1304 K) that are associated with the oxygen containing compounds of the LiGaO_2−xS_x type. The thermal conductivity of LiGaS₂ (about 10.05 W (m⁻¹ K⁻¹)) and band gap value (3.93 eV at 300 K) are found to be the highest in the LiBC₂ family. Isotropic points in the dispersion characteristics for the refractive index are found and LiGaS₂-based narrow-band optical filters, smoothly tunable with temperature changes, are demonstrated. Intense blue photoluminescence of anionic vacancies V_S is observed at room temperature after annealing LiGaS₂ in vacuum, whereas orange low-temperature emission is related to self-trapped excitons. When LiGaS₂ crystals are heated, spontaneous luminescence (pyroluminescence) takes place, or thermoluminescence after preliminary UV excitation; the parameters of traps of charge carriers are estimated. The obtained data confirm the high optical stability of this material and open up prospects for the creation of new optical devices based on LiGaS₂.

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1. Introduction

Modern science and technology urgently require mid-infrared (mid-IR) lasers for applications in, e.g., IR remote communications, environment monitoring and sensing, and organic tissue imaging.¹ The simplest way to obtain tunable coherent radiation in the middle infrared (mid-IR) is the nonlinear converting of the radiation of an all-solid-state laser emitting in the near IR (for example, at 1.06 μm) with optical parametric oscillation (OPO) or differential frequency generation (DFG) processes.¹ The main requirements for a nonlinear optical crystal are: transparency in a wide wavelength range (I), high second-order nonlinear susceptibility (II), high optical damage threshold (LDT, III), sufficiently high birefringence Δn ∼ (0.03–0.10) (IV), and the possibility of obtaining large crystals (V).^2,3 Note that the simultaneous satisfaction of all above conditions is an enormous challenge because some of them are contradictory. For a long time, only a few crystals met most of these requirements to some extent and were commercially available: silver thiogallate and selenogallate (AgGaS₂ and AgGaSe₂), as well as ZnGeP₂. In the last decade, much attention has also been paid to lithium-containing ternary chalcogenides of the LiBC₂ family, where B = In, Ga, and C=S, Se, Te.^2,4,5 It is established that the main advantage of these crystals is high LDT value. This is a consequence of the higher phonon energy due to the presence of a light lithium ion in the structure and the increased thermal conductivity, as well as the lower two-photon absorption of pump radiation due to the larger band gap. In this group, the highest LDT (>240 MW cm⁻²) is shown for orthorhombic LiGaS₂ (LGS). This crystal is widely used for high average power frequency down conversion from the 1 μm spectral range,⁶ although its nonlinear susceptibility (d₃₁ = 5.8 pm V⁻¹)⁵ is significantly inferior to the parameters AgGaS₂, AgGaSe₂ and ZnGeP₂ (d₃₆ = 18, 32.4 × 18 pm V⁻¹, respectively⁷).

The main part of the work on LiGaS₂ is devoted to the development of methods for growing LiGaS₂ crystals, and the study of the effect of post-growth annealing in a controlled atmosphere on optical properties, using optical spectroscopy methods and first-principles calculations of main output parameters.⁸ The structure of some point defects responsible for the characteristic features in the absorption spectra was determined, the nonlinear susceptibility was estimated and phase matching conditions were calculated. As a result, the OPO and DPG modes were implemented.^5,6,9

At the same time, it should be noted that there is no information about the temperature dependence of the LiGaS₂ lattice parameters and optical characteristics, as well as the thermal conductivity. Thus, for the thermal conductivity of LiGaS₂, only preliminary estimates based on results of the vibrational spectroscopy are known to date: 6.2 to 8.0 W (m⁻¹ K⁻¹) depending on crystallographic direction.¹⁰ The values of the heat capacity of LiGaS₂ in the range of 180 to 460 K are given in ref. 11.

This paper presents the results concerning temperature effects in XRD diffractograms for LiGaS₂, thermogravimetric analysis, differential scanning calorimetry and thermal conductivity, as well as temperature dependence of the band gap, birefringence, PL, thermo- and pyroluminescence. Such studies are important for the identification of phase transitions in LiGaS₂, calculations in the study of temperature fields during crystal growth and for explaining the reasons for high LDT values, as well as for determining the parameters of point defects and evaluating the prospects for creating new optical devices based on LiGaS₂.

2. Results and discussion

2.1. Crystals and their structure

The grown LiGaS₂ single crystals were up to 20 mm in diameter and up to 50 mm long (Fig. 1a). The color of the grown boule varies from colorless to light yellow, depending on the set of defects. The transmission spectrum for a 2 mm thick LiGaS₂ plate measured at room temperature is shown in Fig. 2. The transparency range is 0.326–12.7 μm at room temperature.

Fig. 1 The image of the LiGaS₂ boule (a) and the LiGaS₂ cylinders (b) with axes along different crystallographic directions for measuring the thermal conductivity and the isotropic point.

Fig. 2 Room-temperature transmission spectrum for a 2 mm thick plate cut from as grown LiGaS₂.

For laser applications, colorless crystals with maximum transparency and minimal light scattering are selected. For measuring the thermal conductivity and experiments with an isotropic point, polished cylinders made of LiGaS₂ (Fig. 1b). LiGaS₂ crystals are resistant to temperature changes and can withstand temperature variations in the studied range (77–1000 K), and are suitable for use in various devices.

All peaks were indexed by orthorhombic cell (Pna2₁) with parameters close to LiGaS₂,¹² refinement was stable and gives low R-factors (Table 1 and Fig. 3). The z coordinate of Ga ion was fixed because of Pna2₁ space group has origin in 2₁ axis and this requires fixing z coordinate of one ion. Coordinates of atoms and main bond lengths are in Tables S1 and S2† respectively. Crystal structure is presented in Fig. 3. To get information on the temperature dependence of the unit cell parameters, 22 X-ray patterns in range 2θ-5–120° were collected from 303 K to 723 K spending 35 minutes on each pattern.

Table 1 Main parameters of processing and refinement of the LiGaS₂ sample

Compound	LiGaS2
Space group	Pna21
a, Å	6.51625(7)
b, Å	7.86428(8)
c, Å	6.22055(6)
V, Å^3	318.776(6)
Z	4
2θ-interval, °	10–140
Rwp, %	6.63
Rp, %	5.21
Rexp, %	2.78
χ^2	2.39
RB, %	2.27

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Fig. 3 Crystal structure of LiGaS₂.

Tables with fractional atomic coordinates and isotropic displacement parameters (Table S1) and main bond lengths of LiGaS₂ (Table S2) are given in the ESI.†

The S-atom lattice is very nearly perfectly hexagonal closest packed. The metal atoms occupy one half of the tetrahedral interstices, namely all tetrahedra which point in the +z direction, but are ordered on these sites so that the Li and the Ga atoms populate alternate puckered (220) sheets.¹² The tetrahedra with Ga are smaller than those containing Li and mean S–S distances are 3.733 and 3.973 Å respectively. The Ga atom is displaced from the center of its tetrahedron towards the base by about 0.08 Å, giving rise to the long Ga…S bond. Similar but somewhat larger displacement takes place for Li.

The LiGaS₂ structure is similar to that of the enargite mineral, which is the orthorhombic form of Cu₃AsS₄, with the Pmn2₁ space group. The latter has closely similar cell dimensions but with interchange of the a and b dimensions. In both structures the tetrahedrally coordinated cations may be regarded as occurring in strings parallel to [010], [210] and [2i0]. In LiGaS₂ each [010] string consists of alternate Li and Ga atoms; the other strings contain pairs of Li atoms alternating with pairs of Ga atoms. The puckered (220) sheets govern the registration between the strings. The present compound is strictly isostructural with LiGaO₂ and with β-NaFeO₂.¹³

2.2. TGA and DSC results

The TGA-DSC results for LiGaS₂ are shown in Fig. 4. When a single-crystal LiGaS₂ sample is heated in a high-purity helium atmosphere (Fig. 4), an endothermic peak (onset 1224 K) is first observed on the DSC curve. At the same time, the mass of the sample is practically unchanged. The melting point of the sample is defined as 1304 ± 7 K, which is quite well consistent with the previously obtained 1298 ± 7 K data.¹¹ After melting, there is a noticeable loss of mass, due to the process of incongruous evaporation of the sample.¹¹ Features in the range of 1200–1300 K can be associated with the phase transition.

Fig. 4 TGA-(black line) and DSC-curves (red) for the LiGaS₂ crystal. The heating rate is 10 K min⁻¹ in a helium atmosphere.

2.3. Temperature dependences in XRD

Fig. 5 shows the temperature dependences in the range of 280–750 K for the lattice parameters a, b, c and the volume of the unit cell V in LiGaS₂ (blocks (a–d), respectively). It can be seen that all the lattice parameters increase monotonically with increasing temperature, as in the case of other crystals of the LiBC₂ family with an orthorhombic structure (LiInS₂, LiInSe₂ LiGaSe₂). The thermal expansion coefficients ΔL/(L × ΔT) for LiGaS₂ are a_X = 8.13 × 10⁻⁶, a_Y = 18.9 × 10⁻⁶, and a_Z = 6.83 × 10⁻⁶. An important advantage of such crystals in comparison with crystals with the chalcopyrite structure is a less pronounced anisotropy in the thermal expansion coefficients along different crystallographic directions. In the AgGaS₂, AgGaSe₂, and ZnGeP₂ crystals with the chalcopyrite structure, the thermal expansion coefficients along and across the optical axis are quite significant in magnitude, but on the other hand they have a different sign. As a result, when the temperature changes a crystal expands in one direction and contracts in the other. For example, for silver thiogallate, α (⊥_c) = 12.5 × 10⁻⁶ and α (‖_c) = −13.2 × 10⁻⁶, and this significantly complicates the growth of large crystals of high optical quality.

Fig. 5 Thermal dependences of cell parameters a (a), b (b) and c (c) of LiGaS₂.

To clarify the situation with a possible phase transition near 1224 K, the XRD studies of the LiGaS₂ sample was performed with gradual heating until the temperature of the assumed phase transition was reached (Fig. 6). It was found that there is no phase transition, and an additional phase appears above 980 K, the amount of which increases to 1180 K and decreases above 1230 K with the restoration of the reflex intensities of the original LiGaS₂ phase. From Fig. 6, it can be seen that the detected compound is stable in the temperature range of 980–1230 K. A comparison of the position of the diffraction peaks (Fig. S2 in ESI†) of the detected additional phase and the LiGaO₂ compound suggests that the new phase is an oxygen-containing compound.¹⁴ A slight shift of the reflexes towards lower values of 2Theta indicates an increase in the lattice parameters, which may be due to partial sulfur substitution with O²⁻ anions and the formation of an isostructured LiGaO_2−xS_x compound of rhombic symmetry (Pna2₁). Thus, the thermal effect detected on the DSC curve indicates the dissolution of LiGaO_2−xS_x in LiGaS₂ in a certain temperature range.

Fig. 6 A series of X-ray diffractograms of the LiGaS₂ sample obtained in a high vacuum (∼5 × 10⁻⁴ mBar) at temperatures in the range of 780–1230 K. The dotted line shows the most intense reflexes related to the oxygen-containing phase. On the diffractogram obtained at T = 1080 K, all reflexes related to this phase, supposedly LiGaO_2−xS_x, are marked with asterisks.

2.4. Thermal diffusivity and thermal conductivity in LiGaS₂

To measure the thermal conductivity, one of the non-stationary methods was used, in which the thermal diffusivity is directly measured, and then calculated taking into account the known values of the heat capacity and density. The thermal diffusivity δ is a physical quantity that characterizes the rate of change (equalization) of the temperature of a substance in nonequilibrium thermal processes. Numerically, the thermal conductivity is equal to the ratio of the thermal conductivity to the specific heat capacity at constant pressure c_p. The thermal conductivity of the crystal χ can be calculated using the following formula:¹⁵

χ = δ × c_p × ρ, (1)

where ρ is density.

Measurements at a given temperature T were carried out in a series of two “flashes” of the laser after the sample was thermostated. The interval between the “flashes” was 3 minutes. Since LiGaS₂ is transparent at the wavelength of the laser light source generation, the samples were previously coated with a layer of graphite on both ends to increase the absorption capacity of the surfaces. The measurement error of α for solid samples on the LFA-427 unit is 2–5%, depending on the temperature. The obtained values of thermal diffusivity for LiGaS₂ and the values of thermal conductivity calculated from them according to the formula (1) for various crystallographic directions (X, Y, Z), as well as the temperature dependence in the range of 20–300 °C for χ_Z, are presented in Table 2 and Fig. 7. The calculations used the values of the specific heat capacity c_p at 300 and 460 K for LiGaS₂: 90.08 and 98.6 J mol⁻¹ K⁻¹, respectively, as well as molecular mass M = 140.78 g mol⁻¹ (ref. 17) and density (specific gravity) 2.94 g cm⁻³.¹ The thermal expansion of the samples was not taken into account. Previously, based on the data of vibrational spectroscopy, the values of thermal conductivity at 300 K for LiGaS₂ were estimated in the range of 6 ÷ 8 W (m⁻¹ K⁻¹).¹⁶ The values of the thermal conductivity χ, measured by us experimentally, were even about 25% higher: 8.440, 9.108 and 10.058 W mK⁻¹ along X, Y, Z, respectively. The maximum values of χ are obtained for room temperature along Z direction. In Fig. 7a one can see that with an increase in temperature to 580 K, the thermal conductivity decreases by more than 2 times. Also for this sample, the thermal conductivity during cooling in the region of 473 K was measured and a good agreement with the data obtained during heating was established. Such behavior of thermal conductivity as a function of temperature is characteristic of the dominant lattice (phonon) contribution to the total thermal conductivity.

Table 2 Coefficients of thermal diffusivity δ and thermal conductivity χ for LiGaS₂, LiInS₂ and AgGaS₂

Crystallographic direction, mode	T, K	δ for LiGaS2, mm^2 s^−1	χ for LiGaS2 W (m^−1 K^−1)	χ for LiInS2, W (m^−1 K^−1)	χ, for AgGaS2, W (m^−1 K^−1)
X	296.5	4.662	8.440	6.2 (ref. 16)	1.5 (ref. 16)
Y, heating	296.7	5.031	9.108	6.0 (ref. 16)	1.5 (ref. 16)
	371.7	3.725	7.141
	470.7	2.635	5.222
	571.9	2.061	4.267
Y, cooling	573.6	2.035	4.213
	473.3	2.659	5.345
Z	296.6	5.556	10.058	7.6 (ref. 16)	1.4 (ref. 16)

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Fig. 7 Thermal conductivity for chalcogenides: (a) LiGaS₂ along X, Y and Z directions at room temperature and temperature deendence for χ_Z in the 300 to 557 K range. Arrows indicate heating or cooling regime. (b) Comparison of values for commercial AgGaS₂, AgGaSe₂ and for crystals of the LiBC₂ family with B = In, Ga and C=S, Se.

Fig. 7b compares the thermal conductivity values for commercial AgGaS₂ and AgGaSe₂, and the values for members of the LiBC₂ family, for which the thermal conductivity has so far been measured experimentally. As you know, the thermal conductivity of materials or energy transfer is determined by elastic vibrations (phonons), and above all by their energy. In turn, the latter is determined by the mass of the participating ions and the energy of the phonons increases with decreasing ion mass. As a consequence, the thermal conductivity is relatively low in silver thiogallate and, as our experiments show, it is almost 7 times higher in lithium thiogallate. Thus, LiGaS₂ effectively implements energy dissipation under local heating in the laser scheme and the crystal has a high optical damage threshold. The literature provides LDT values of 34, 40, and more than 240 MW cm⁻² at pumping with 1.064 nm, 15 ns pulses for AgGaS₂, LiInS₂, and LiGaS₂, respectively.¹⁶

2.5. Thermooptic effects in LiGaS₂

2.5.1. Birefringence. Studies were carried out to determine the nature of the anomaly in DSC at T ∼ 1223 K. The reason for this anomaly may be a phase transition with a decrease in symmetry, for example, from rhombic polar symmetry to rhombic centrosymmetric: mm2 ↔ mmm. In this case, at room temperature, there would have to be twins with a multidirectional polarization of ±P, which can be detected by etching (001) LiGaS₂ plates. Specially conducted experiments on etching in dilute bechromate at room temperature showed only etching of scratches, while domains or twins were not detected.

Fig. 8 shows the temperature dependence of the birefringence measured in a wide range from 373 K to 1173 K. Features at temperatures above 870 K are associated with the degradation of the polished surface of the crystals: at a higher temperature, the surface becomes matte. The crystal is vaporized, as a result of which the upper surface is covered with plaque flakes, while the lower surface remains unchanged. It can be seen that the birefringence measured at 400 nm increases monotonically and approximately linearly with an increase in temperature from 100 to 950 K. Curves 1–3 are smooth and no special features are detected: thus, there are no phase transitions in this range.

Fig. 8 Temperature dependences of the birefringence of LiGaS₂ at a wavelength of about 400 nm: (1) Δn_b, (2) Δn_c, (3) Δn_a.

Fig. 9 shows the birefringence dependence of Δn_b, Δn_c and Δn_a. for a biaxial LiGaS₂ crystal from the wavelength in the range of its transparency. It can be seen that the birefringence values Δn_a and Δn_c are quite close to each other (∼0.04), but they are both quite far from Δn_b. In this case, the dependence Δn_b = f(T) passes through zero twice, i.e. there are two so-called isotropic points. Fig. 10 shows the transmission spectra for a LiGaS₂ plate located between two polaroids when they are crossed (curve (1)) and when the polaroids are parallel (2). In this case, the spectra show characteristic anomalies in the visible region of the spectrum in the form of a narrow dip (1) and in the form of a narrow passband (2) at the same wavelength. A similar feature was previously observed in some anisotropic crystals in the presence of natural or induced gyrotropy at the wavelength of the isotropic point. Examples of such crystals are double single crystals of CdS, CdSe, ZnO, AgJ, MnF₂, Al₂O₃, ZnTe, and mixed compounds based on these crystals.¹⁸ Of the triple chalcogenides used in nonlinear optics, such narrow-band filtration was previously observed in AgGaS₂ and AgGaSe₂ crystals with a chalcopyrite structure (symmetry-42m).¹⁹

Fig. 9 Dependence of the birefringence Δn on the wavelength for LiGaS₂. The arrows show two isotropic points, where Δn = 0.

Fig. 10 Transmission spectra for (100) LiGaS₂ plate with a thickness of 5 mm placed between crossed (1) and parallel (2) film polarizers.

At room temperature, for the (100) LiGaS₂ plate, both features are located at 451.5 nm, and they correspond to one of the isotropic points. Another similar feature is expected in the mid-IR, at about 7 μm. It is established that the position of the described line significantly depends on the temperature. Fig. 11 shows a set of transmission lines for the case of crossed polarizers, when the temperature of the LiGaS₂ crystal varied in the range from 77 to 550 K (points 1–14). At the same time, the position of the line is shifted from 430 to 490 nm, respectively.

Fig. 11 Transmission spectra for a (100) LiGaS₂ plate 5 mm thick placed between the crossed polarizers. Spectra were measured at fourteen different temperatures in the temperature range of 77 K (curve (1)) to 550 K (14).

Fig. 12 shows the dependence of the position of the isotropic point in the visible region of the spectrum as a function of temperature. This dependence is well approximated by the dependence , where the parameter values are A = 429.75, B₁ = 0.02, and B₂ = 1.7 × 10⁻⁴. The value of the line width at half-height gradually changes from 2.4 at 77 K to 5.4 nm at 550 K with a spectral resolution of about 0.5 nm. Thus, the LiGaS₂ plate in combination with two polarizers can be used as a narrow-band optical filter, smoothly tunable by changing the temperature of the crystal (Fig. 13).

Fig. 12 The position of the isotropic point as a function of temperature. The dependence is approximated by the polynomial , where the parameter values are A = 429.75, B₁ = 0.02, and B₂ = 1.7 × 10⁻⁴.

Fig. 13 Absorption spectra for LiGaS₂ in the region of the fundamental absorption edge, measured at 12 different temperatures in the range from 77 to 300 K and presented in coordinates (αhν)² = f(hν) (Tauc plot). The insert shows the temperature dependence for the band gap in LiGaS₂. The points are obtained experimentally, while the line shows the result of the approximation in accordance with the Varshni equation.²¹

2.5.2. Temperature dependence of the band gap. The fundamental absorption edge for LiGaS₂ is at about 326 nm in the UV region. The Tauc analysis of the shape edge shows the straightening in the coordinates (k × hν)² = f(hν), where k is the absorption coefficient, and hν is the photon energy.²⁰ This indicates that for LiGaS₂, direct allowed electronic transitions are responsible for band-to-band electronic transitions. LiGaS₂ crystals have a band gap E_g of 3.88 eV at room temperature, which is the maximum value among ternary chalcogenides. For AgGaS₂ and LiInS₂, the E_g values are 2.7 and 3.57 eV, for selenides these values are even lower.¹⁶ As a result, LiGaS₂ crystals are almost colorless compared to the substantially colored crystals of other ternary chalcogenides. As a result, at 800 nm excitation LiGaS₂ is characterized by a two-photon absorption coefficient (TPA) of about 0.01 cm GW⁻¹, which is significantly lower than the values for AgGaS₂ (3.5 cm GW⁻¹) and LiInS₂ (0.04 cm GW⁻¹).¹⁶ This reduces the energy absorbed during pumping and reduces the danger of crystal optical damage when using it in OPO.

Fig. 14 shows such constructions for 12 different temperatures in the range of 77–300 K. It can be seen that the absorption edge shifts towards lower energies as the temperature increases. In this case, the band gap E_g, determined by the intersection of the approximating line with the abcissa axis, increases from 4.03 eV at 77 K to 3.88 eV at 300 K. The insert in Fig. 14 shows the temperature dependence for E_g. We found that it is well described by the semi-empirical Varshni equation:²¹

E_g(T) = E₀ − α₁T²/(T + β₁) (2)

where E₀ is the band gap at T = 0, while the parameters α₁ = 4 × 10⁻³ and β₁ = 1850 K.

Fig. 14 PL spectra recorded at T = 80 K, at 300 nm (1) and 375 nm (2) excitation for LiGaS₂ annealed in vacuum. The insert shows the room temperature PL patterns obtained at UV excitation with 300 nm light (upper image with orange emission) and 375 nm (lower image with blue PL).

2.5.3. Temperature dependence of photoluminescence (PL). The PL spectra for LGS as-grown and after annealing in different atmospheres have been studied in detail in our works.⁸ The following main features have been identified in the PL spectra: (1) two bands of about 416 and 452 nm responsible for sulfur vacancies in crystallographically different positions in the LGS lattice (F-centers), both types of PL being excited in the same band of 375 nm near the edge of fundamental absorption; and (2) a wide band with a maximum in the range of 550–620 nm excited most efficiently during band-to-band electronic transitions and associated with self-trapped excitons (STE) at different point defects.²² The blue PL in the 425 nm band is characteristic of LiGaS₂ crystals with anion deficiency, which occurs, for example, after sample annealing in vacuum.

The temperature dependence for the PL glow in the main bands is shown in Fig. 15. For both PL bands temperature dependence is well described by the Mott model for two recombination channels, one radiative and one non-radiative, from the relaxed excited state.²³ Here the temperature dependence of quantum efficiency η follows the expression:

η(T) ≈ 1/(1 + τ_Rν₀ exp(−ΔE/kT)) (3)

where τ_R is the radiative lifetime at low temperature, ΔE is the energy barrier to the nonradiative decay route, and ν₀ is a jump frequency. The proportional sign is used because other nonradiative decay channels must be available before the system reaches the relaxed excited state.

Fig. 15 The temperature dependence of the integral PL in the bands of about 600 nm (1) and 425 nm (2) in LiGaS₂ at excitation of 300 and 375 nm, respectively. The dots represent the experimental data, while the dotted curves show the results of calculations according to eqn (3) with the parameters ΔE = 0.14 eV, τ_Rν₀ = 4 × 10³ (1) and ΔE = 0.35 eV, τ_Rν₀ = 1.7 × 10⁴ (2).

Fig. 15 shows the experimental points and the results of their approximation for the orange and blue glow (dotted curves). For the blue glow of V_S, the parameters ΔE = 0.35 eV and preexponential factor τ_Rν₀ = 1.7 × 10⁴ are well suited, while for the orange glow of STE, the parameters are ΔE = 0.14 eV and τ_Rν₀ = 4 × 10³. In the case of STE, there is an initial stage of PL rise with an activation energy of ΔE₁ ∼ 0.02 eV, which indicates the need to overcome a small activation barrier for exciton self-localization. Thus, in the case of LiGaS₂, it is possible to directly cause intense blue room-temperature PL by special post-growth annealing crystal in vacuum. At 365 nm excitation, the quantum yield of PL in LGS is estimated relative to Rhodamine 640 with a quantum yield η close to unity. At room temperature, the values of η are about 0.1 for the blue luminescence of F-centers and 0.0095 for the glow of STE. As can be seen from Fig. 15, the intensity of blue PL flares increases about 10 times when the temperature drops to 180 K, whereas with a further decrease in temperature, some weakening of the PL is observed. A completely different behavior is demonstrated by a weaker exciton PL: it is constant in the low-temperature range and quenched above room temperature. Low values of η make it difficult to widely use LGS at room temperature, but at 180 K the quantum yield of the blue PL is close to unity. Nevertheless, the analysis of the PL spectra allows us to obtain valuable information about the conditions for growth or annealing crystals, as well as about the state of point defects. It should be noted that a similar (in the blue region) PL associated with F-centers is also observed in LiInS₂.

To date, this is the only known case of bright photoluminescence at room temperature in the visible region of the spectrum among the crystals of ternary chalcogenides, including the LiBC₂ family. The crystal is considered as promising for use in various optical devices including active media for lasers and light sources.

2.5.4. Thermoluminescence (TL). The analysis of TL curves provides valuable information about the parameters of shallow levels in the band gap.²⁴ The UV illumination of LiGaS₂ crystals at low temperature is accompanied by the accumulation of a significant light sum. The TL curve obtained by further heating the crystal in the dark is shown in Fig. 16. The analysis of the peaks shape shows that they are rather symmetric and the values of full width at half-maximum (FWHM) at rise and at decay are rather close. This indicates a second order of TL kinetics when the probability of recombination of free carriers is negligible compared with the probability of their retrapping.²⁴

Fig. 16 TL curve for LiGaS₂ after 365 nm excitation at 80 K and the results of deconvolution into 8 components (shown in thin lines). The resulting parameters for the corresponding capture centers are shown in the Table 3 below.

The shape of TL peak is described by the following expression:²⁴

where n₀ is the initial concentration of electrons, s is the escape factor, β is the rate of linear heating (K min⁻¹), k is the Boltzmann's constant, E_T is the thermal activation energy (eV) and T₀ is the initial temperature. Position of eight TL maxima as well as the results of calculations (parameters E_T and s) are given in Table 3. There is a good coincidence between the sum of these components and the experimental curve (curve shown in bold black).

Table 3 Parameters of traps in LiGaS₂ (results of decomposition)

NN	Peak maximum position, K	Thermal activation energy, eV	Preexponential coefficient, s^−1
1	115	0.23	10^8
2	144	0.31	3 × 10^10
3	156	0.45	3 × 10^12
4	190	0.36	10^8
5	217	0.44	3 × 10^8
6	256	0.67	10^12
7	283	0.72	10^11
8	324	0.90	10^12

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It can be seen that the TL glow is localized mainly in the low-temperature region of 140–240 K: exactly where the peak in the temperature dependence of the STE luminescence is observed (Fig. 15). It is possible that the traps are involved in the process of radiative recombination of STE maybe as a result of intermediate localization of charge carriers on traps.

2.5.5. Pyroelectric luminescence (PEL) of LiGaS₂. When LiGaS₂ crystals are heated or cooled in the dark, without any excitation, a spontaneous glow is observed in the form of a sequence of short pulses (flashes) in the temperature range of 80–350 K. In Fig. 17 the emission intensity in LiGaS₂ is shown as a function of the temperature in the cooling (a) and heating (b) modes. Such a glow in the dark, without any special excitation, is characteristic only of pyroelectrics and is the result of a restructuring in the atomic polarization in the crystal at a temperature change.²⁵ This is in good agreement with the results of structural studies in ref.,¹² where the XRD study determined the symmetry of the LiGaS₂ as mm² space group of the monoclinic system (without a center of symmetry). Spontaneous light flashes are a result of the dielectric break-down and they happen on both crystal surface and inside it. We have observed the PEL effect in many typical nonlinear optical crystals such as LiIO₃, β-BaB₂O₄ (BBO), LiB₃O₅ (LBO), Ag₃AsS₃, LiNbO₃, LiGaS₂, KTP, LiGaSe₂, and LiGaGe₂Se₆ (LGGSe).²⁵ On the other hand, the PEL is absent in AgGaS₂ and AgGaSe₂ with a chalcopyrite structure (space group I4̄2d) which are not pyroelectrics. The absence of PEL at temperature greater than 440 K is the result of an increase in electrical conductivity as temperature grows. This increase in conductivity promotes the leak of the pyroelectric charge and the break-down probability becomes smaller. The PEL effect indicates a relatively low LiGaS₂ conductivity and, in turn, a low concentration of electrically active defects. PEL intensity decreases until it completely disappears when the crystals are illuminated or after their preliminary illumination: this is due to an increase in electrical conductivity as a result of such processing and charge runoff. It is assumed that PEL can also occur as a result of local heating of a nonlinear crystal during operation in a laser scheme and be one of the mechanisms of laser damage to crystals.

Fig. 17 Temperature dependence of spontaneous luminescence in LiGaS₂ in the cooling (a) and heating (b) modes.

3. Conclusions

(1) Large LiGaS₂ crystals with a length of up to 50 mm, a diameter of up to 20 mm, of high optical quality were grown.

(2) DSC shows anomalies of about 1224 K, at a temperature below the melting point (1304 K ± 5). In this case, the lattice parameters and birefringence increase smoothly and monotonically with increasing temperature, which indicates the absence of phase transitions in LiGaS₂. Anomalies around 1224 K are associated with the appearance of inclusions of the type LiGaO_2−xS_x.

(3) The thermal conductivity χ was measured for LiGaS₂: the values of 8.44 (X), 9.11 (Y), and 10.05 (Z) W (m⁻¹ K⁻¹) obtained at 300 K are the highest among the crystals of the LiBC₂ family where B = In, Ga, C=S, Se, Te. The thermal conductivity decreases with increasing temperature in the range of 300–600 K in accordance with the model of the dominant lattice mechanism.

(4) The isotropic points in the dispersion characteristics n = f(λ) for LiGaS₂ are revealed. The possibility of using the crystal in narrow-band optical filters smoothly tunable by changing crystal temperature is demonstrated. The position of the transmission line changes from 430 to 490 nm when heated from 77 to 550 K, while the FWHM values increase from 2.4 to 5.4 K. Calibration curves are proposed.

(5) The Tauc analysis shows that band-to-band transitions are determined by direct allowed electronic transitions. The band gap E_g is 4.02 and 3.93 eV at 80 and 300 K, and the dependence E_g = f(T) is described by the semi-empirical Varshni law.

(6) In the PL spectra for LiGaS₂, the most common is the low-temperature glow of self-trapped excitons. Post-growth annealing in vacuum produces anionic V_S vacancies and corresponding intense blue PL at room temperature.

(7) The thermoluminescence curves are analyzed, and the parameters of the charge carrier capture centers with energies in the range of 0.2–0.9 eV are estimated.

(8) LiGaS₂ crystals exhibit pyroluminescene in the range of 80–350 K. This is consistent with the established XRD symmetry of mm². The latter belongs to one of the 10 crystallographic groups with a non-zero vector of spontaneous polarization.

4. Experimental section

4.1. Crystal growth

LiGaS₂ single crystals were grown by the Bridgman–Stockbarger method in a two-zone vertical furnace. The upper and lower parts of the furnace were separated by a diaphragm made of thermal insulation material. The temperature in the melt with an accuracy of ±0.1 °C was maintained at 1423 K, which is ∼100 K higher than the melting point of LiGaS₂. The axial temperature gradient was about ∼2° mm⁻¹. The rate of the ampoule lowering varied in the range of 2–10 mm per day. Ga and S of 99.999% purity and Li of 99.9% purity were used as initial chemical reagents for crystal growth. The charge was poured into an ampoule made of glass graphite, which, in turn, was sealed in a quartz ampoule. This design made it possible to avoid chemical interaction between the Li and the walls of the quartz container.

4.2. X-ray diffraction studies

Powder X-ray diffraction data were collected on a PANalytical X'Pert PRO diffractometer with a solid state detector PIXcel using Cu Kα radiation over the 2θ range 15–105°. An Anton Paar HTK 1200N camera was used for the high-temperature measurements. The powder diffraction data of LiGaS2 for Rietveld analysis was collected at room temperature with a Bruker D8 ADVANCE powder diffractometer (Cu-Kα radiation) and linear VANTEC detector. The step size of 2θ was 0.016°, and the counting time was 1.5 s per step. The 2θ range of 10–70° was measured with 0.6 mm divergence slit, but 2θ range of 70–140° was measured with 2 mm divergence slit. Rietveld refinement was performed by using TOPAS 4.2 (ref. 26) which accounts esd's of each point by special weight scheme.

Larger slits allow noticeably increase intensity of high-angle peaks without loss of resolution because the high-angle peaks are broad enough to be not affected by bigger divergence beam. The esd's σ(I_i) of all points on patterns were calculated using intensities I_i: σ(I_i) = I_i^1/2. The intensities and obtained esd's were further normalized: I_{i norm} = I_i × 0.6/(slit width), σ_norm(I_i) = σ(I_i) × 0.6/(slit width), taking into account actual value of divergence slit width which was used to measure each particular intensity I_i, and saved in xye-type file. So transformed powder pattern has usual view in whole 2θ range 10–140°, but all high-angle points have small esd's. Difference Rietveld plot of LiGaS₂ is given in Fig. S1 in ESI.†

4.3. Optical properties

Absorption spectra for LiGaS₂ were measured using a UV-2501PC Shimadzu spectrometer in the UV to near IR region and a Fourier transform spectrometer Infralum FT-801, in the mid IR. Transmission spectra at different temperatures and temperature dependences in the heating or cooling mode were measured using a metal vacuum cryostat with fused quartz windows. The transmission spectrum for a 2 mm thick LiGaS₂ plate measured at room temperature is shown in Fig. 3. The transparency range is 0.326–12.7 μm. Transmission spectra were obtained at 14 different temperatures in the range of 80–350 K, and in each case, the shape of the fundamental absorption edge was analyzed following Tauc²⁰ to determine the mechanism of band-to-band electronic transitions. In the study of pyroluminescence (PEL) and thermoluminescence (TL), the rate of change in temperature β in the range of 80–600 K during heating or cooling was maintained at 30° min⁻¹ and was regulated using liquid nitrogen and an ohmic heater controlled from a temperature controller. The isotropic point was detected by characteristic narrow dips/peaks in the transmission spectra when registering the spectral dependence of the transmission of the LiGaS₂ sample located between two parallel-tuned or crossed film polaroids, respectively.

The photoluminescence (PL) spectra were recorded on diffraction luminescence spectrometer SDL1 with excitation from a 1 kW Xe lamp through a diffraction MDR2 monochromator. A cooled FEU83 photomultiplier sensitive up to 1.2 μm (1.03 eV) was used to detect the PL emission. The thermoluminescence (TL) curves were obtained by recording the glow of the crystal during its heating at a constant rate of 30 deg. per min after irradiation at a temperature of 80 K.

The birefringence measurements were carried out in the temperature range of 90–950 K with the use of an Axioskop-40 polarization microscope and Linkam LTS 350 and TS1500 heating stages. Birefringence was measured to an accuracy of ±0.00001 by the Berek compensator method with the use of a Leica instrument.

4.4. Thermophysical measurements

4.4.1. TGA-DSC measurements. The simultaneous thermogravimetric analysis and differential scanning calorimetry (TGA-DSC) measurements wereas carried out with a STA 449 F1 Jupiter thermal analyser (NETZSCH, Germany). The measurements were made in a helium flow (He 99.995%) in the temperature range of 1000–1400 K using the heating rate of 10 K min⁻¹, the gas flow rate of 30 mL min⁻¹ and closed Pt crucibles. The treatment of experiment results was performed using standard Proteus Analysis software.²⁷

4.4.2. Thermal diffusivity and thermal conductivity. The thermal diffusivity δ of the studied samples was determined by the laser flash method on a LFA-427 installation from NETZSCH Co, Germany at room temperature in air and in an atmosphere of high-purity argon (Ar 99.992 vol%) in the temperature range of 300–580 K. The essence of this method is that a flat sample is irradiated from below with a short 1.064 μm laser pulse²⁸ The IR detector registers the temperature change of the upper surface of the sample. The value of δ is determined from the obtained thermogram, taking into account the heat losses according to the model.²⁹ An adjustment is made for the finite duration of the laser pulse and its actual shape.³⁰

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Crystal growth and investigation of physical properties were supported by Russian Science Foundation, Russia (#19-12-00085). Spectroscopic study was performed on a state assignment of the Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Sciences Russia and Ministry of Science and Higher Education, Russia. Measurements of thermal conductivity were funded by RFBR and Novosibirsk region (grant #20-42-543006\20).

References

1. D. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey, Springer Science + Business Media, Inc., N.-Y, 2005.
2. L. Isaenko, A. Yelisseyev, S. Lobanov, A. Titov, V. Petrov, J.-J. Zondy, P. Krinitsin, A. Merkulov, V. Vedenyapin and J. Smirnova, Cryst. Res. Technol., 2003, 38, 379.
3. H.-M. Zhou, L. Xiong, L. Chen and L.-M. Wu, Angew. Chem., Int. Ed., 2019, 58, 9979.
4. L. Isaenko, I. Vasilyeva, A. Merkulov, A. Yelisseyev and S. Lobanov, J. Cryst. Growth, 2005, 275, 217.
5. V. Petrov, A. Yelisseyev, L. Isaenko, S. Lobanov, A. Titov and J.-J. Zondy, Appl. Phys. B, 2004, 78, 543.
6. (a) A. Tyazhev, V. Vedenyapin, G. Marchev, A. Yelisseyev, L. Isaenko, D. Kolker, M. Starikova, S. Lobanov, V. Petrov and J.-J. Zondy, Opt. Mater., 2013, 35, 1612; (b) S. N. Smetanin, M. Jelínek, V. Kubeček, A. F. Kurus and L. I. Isaenko, 2018 Conf. on Lasers and Electro-Optics Pacific Rim, CLEO-PR, 2018–2019.
7. (a) G. Boyd, H. Kasper and J. McFee, IEEE J. Quantum Electron., 1971, 7, 563; (b) H. Kildal and J. C. Mikkelsen, Opt. Commun., 1973, 9, 315; (c) G. D. Boyd, E. Buehler and F. G. Storz, Appl. Phys. Lett., 1971, 18, 301.
8. (a) A. Yelisseyev, Z. S. Lin, M. Starikova, L. Isaenko and S. Lobanov, J. Appl. Phys., 2012, 111, 113507; (b) A. P. Yelisseyev, M. K. Starikova, V. V. Korolev and L. I. Isaenko, J. Opt. Soc. Am. B, 2012, 29, 1003.
9. (a) V. Vedenyapin, A. Boyko, D. Kolker, L. Isaenko, S. Lobanov, N. Kostyukova, A. Yelisseyev and V. Petrov, Laser Phys. Lett., 2016, 13, 115401; (b) S. Qu, H. Liang, K. Liu, X. Zou, W. Li, Q. J. Wang and Y. Zhang, Opt. Lett., 2019, 44, 2422.
10. L. Isaenko, A. Yelisseyev, S. Lobanov, P. Krinitsin, V. Petrov and J.-J. Zondy, J. Non-Cryst. Solids, 2006, 352, 2434.
11. V. Drebushchak, L. Isaenko, S. Lobanov, P. Krinitsin and S. Grazhdannikov, J. Therm. Anal. Calorim., 2017, 129, 103.
12. J. Leal-Gonzalez, S. S. Melibary and A. J. Smith, Acta Crystallogr., Sect. C: Struct. Chem., 1990, 46, 2017.
13. M. Marezio, Acta Crystallogr., 1965, 18, 481.
14. G. M. Kuz’micheva, V. B. Rybakov, A. V. Gaister and E. V. Zharikov, Inorg. Mater., 2001, 37, 281–285.
15. R. Berman, Thermal conduction in solids, Clarendon Press, 1976.
16. (a) L. Isaenko, A. Yelisseyev, S. Lobanov, P. Krinitsin, V. Petrov and J.-J. Zondy, J. Non-Cryst. Solids, 2006, 352, 2434; (b) L. Isaenko and A. Yelisseyev, Semicond. Sci. Technol., 2016, 31, 123001.
17. Q. Li, J. Wei, H. Sun, K. Zhang, Z. Huang and L. Zhang, Sci. Rep., 2017, 7, 13747.
18. (a) G. H. Henry, Phys. Rev., 1966, 143, 627; (b) R. B. Parson, W. Wardzynski and A. D. Yoffe, Proc. R. Soc. London, Ser. A, 1961, 262, 120; (c) J. J. Hopfield and D. C. Thomas, Phys. Rev. Lett., 1965, 15, 22.
19. (a) M. V. Hobden, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1968, 24, 676; (b) M. V. Hobden, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1969, 25, 633.
20. J. Tauc, Mater. Res. Bull., 1967, 3, 37.
21. Y. P. Varshni, Physica, 1967, 34, 149.
22. K. S. Song and R. T. Williams, Self-trapped excitons, Springer, 1993.
23. B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids, Clarendon, 1989.
24. S. W. S. Mc Keever, Thermoluminescence of solids, Cambridge Uni. Press, Cambridge, London, New-York, 1988.
25. (a) A. P. Yelisseyev, L. I. Isaenko and M. K. Starikova, J. Opt. Soc. Am. B, 2012, 29, 1430; (b) A. Yelisseyev, F. Liang, L. Isaenko, S. Lobanov, A. Goloshumova and Z. S. Lin, Opt. Mater., 2017, 72, 795; (c) A. Yelisseyev, L. Isaenko, P. Krinitsin, F. Liang, D. Naumov, A. Goloshumova and Z. S. Lin, Inorg. Chem., 2016, 55, 8672.
26. Bruker AXS TOPAS V4: User's Manual, Bruker AXS, Karlsruhe, Germany, 2008.
27. NETZSCH Proteus Thermal Analysis v.6.1.0 – NETZSCH-Gerätebau GmbH – Selb/Bayern, Germany, 2013.
28. (a) W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, J. Appl. Phys., 1961, 32, 1679; (b) I. V. Savchenko and S. V. Stankus, Thermophys. Aeromechanics, 2008, 15, 729.
29. J. A. Cape and G. W. Lehman, J. Appl. Phys., 1963, 34, 1909.
30. J. Blumm and J. Opfermann, High Temp. – High Pressures, 2002, 34, 515.

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Footnote

† Electronic supplementary information (ESI) available: Difference Rietveld plot of LiGaS₂ (Fig. S1) and tables with fractional atomic coordinates and isotropic displacement parameters (Table S1) and main bond lengths of LiGaS₂ (Table S2) are given in the ESI. Comparison of the X-ray diffractograms for LiGaS₂ obtained at 1080 K (above) and LiGaO₂ is given in Fig. 2S. See DOI: 10.1039/d1ra05698k

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