Growth and Thermal Conductivity Study of CuCr₂Se₄-CuCrSe₂ Hetero-Composite Crystals

Abstract

The CuCrSe₂ shows attractive physical properties, such as thermoelectric and multiferroic properties, but pure-phase CuCrSe₂ crystal is still quite challenging to obtain because CuCr₂Se₄ can be easily precipitated from a CuCrSe₂ matrix. Here, taking the advantage of this precipitation reaction, we grew a series of CuCrSe₂-CuCr₂Se₄ hetero-composites by adjusting growth parameters and explored their thermal conductivity property. Determined by electron-diffraction, the orientation relationship between these two compounds is [001] (100) CuCrSe₂‖[111] (220) CuCr₂Se₄. The out-of-plane thermal conductivity κ of these hetero-composites was measured by a time-domain thermo-reflectance method. Fitting experimental κ by the Boltzmann-Callaway model, we verify that interface scattering plays significant role to κ in CuCrSe₂-CuCr₂Se₄ hetero-composites, while in a CuCrSe₂-dominated hetero-composite, both interface scattering and anharmonic three-phonon interaction lead to the lowest κ therein. Our results reveal the thermal conductivity evolution in CuCr₂Se₄-CuCrSe₂ hetero-composites.

1. Introduction

Ternary chromium chalcogenides ACrX₂ (A = Cu, Ag; X = S, Se, Te) are attracting enormous attention in recent years because of their rich physical properties, such as ferroelectric [1,2], multiferroic [3,4,5], and large magnetic-field-induced strain [6]. For example, CuCrSe₂ has good overall thermoelectric performances of the low thermal conductivity, good electronic transport (carrier concentration can reach 1.7 × 10²⁰ cm⁻³), and high Seebeck coefficient (100 μV·K⁻¹) at room temperature [7,8,9]. Remarkably, the low thermal conductivity of CuCrSe₂ is attributed to a novel mechanism: superionic liquid-like diffusivity of Cu ions between two non-equivalent tetrahedral sites at high temperature (≥365 K) [10,11,12,13].

However, in the ACrX₂ system, the pure-phase CuCrSe₂ crystal is quite difficult to obtain because of its complex phases, which can be seen from the Cu-Cr-Se ternary solid-state phase diagram [14]. Currently, in a Cu-Cr-Se system, it is easy to obtain the single phase CuCr₂Se₄, but CuCrSe₂ crystals always coexist with the CuCr₂Se₄ spinel phase, which seems to be responsible for the controversially reported electrical-transport/magnetic results [15,16]. In addition, there are triangle lattice and honeycomb lattice at the (001)-plane of CuCrSe₂ and (111)-plane of CuCr₂Se₄, respectively, which may host the rich magnetic properties in these compounds or their composites [17]. To reveal the intrinsic properties of CuCrSe₂, R. Yano et al. [18] had successfully grown pure-phase CuCrX₂ crystals (X = Se, Te) through a modified chemical-vapor-transport technique (CVT) by using appropriate heat treatment. Yan et al. had successfully obtained a single-phase CuCrSe₂ ingot by vacuum annealing [7], but the growing conditions reported in their papers are extremely harsh. In short, impurity phases are hard to eliminate and it is difficult to control their quantities.

Generally speaking, hetero-composites/heterostructures are an effective way to give rise to the novel functionalities unavailable in single-phase crystals [19,20]. For example, SnSe-SnSe₂ heterostructures decrease the thermal conductivity of SnSe dramatically [19]. Therefore, we want to explore the thermal conductivity of CuCrSe₂-CuCr₂Se₄ composites.

Here, several hetero-composite CuCrSe₂-CuCr₂Se₄ crystals were grown by a CVT using the CrCl₃ transport agent. The weight ratio of coexistence of CuCrSe₂ and CuCr₂Se₄ (hetero-composite) phases can be roughly controlled by growth conditions. The orientation relationship between CuCrSe₂ and CuCr₂Se₄ was determined by electron diffraction. The thermal conductivity of these crystals was measured and analyzed through the Boltzmann-Callaway model to determine the sources of the phonon scattering.

2. Experimental

2.1. Material Synthesis

The single CuCrSe₂ and CuCr₂Se₄ crystals were grown by the chemical vapor transport method using CrCl₃ as a transport agent in an evacuated quartz tube. Before growing single crystals, polycrystalline CuCrSe₂ powders were synthesized by the direct solid-state reaction. Mixtures of high purity Cu (Alfa Aesar 99.999%, Ward Hill, MA, USA), Cr (Alfa Aesar 99.999%, USA), and Se (Alfa Aesar 99.999%, USA) elements with a 1:1:2 atomic ratio were sealed in the evacuated quartz tube. The powder was then heated at 950 °C for 7 days. Then, the tube was quenched in cold water to obtain the mainly CuCrSe₂ polycrystalline powder with a minor CuCr₂Se₄ impurity (XRD data can be seen in Figure S1). The generation mechanism of CuCr₂Se₄ comes from the decomposition of CuCrSe₂, which works in both poloycrystalline powder and crystal growth. Then polycrystalline CuCrSe₂ powders and 5 mg/mL CrCl₃ powders (Alfa Aesar 99.999%, USA) as the transport agents were loaded into the sealed evacuated quartz tube, and then put into a two-zone furnace to grow the crystals. The high-temperature side was kept at the 960 °C, while the temperature of the low-temperature side of the quartz tube was set as a different temperature (870 °C, 900 °C, and 930 °C) to obtain different gradients. The growth was achieved by establishing a temperature gradient, and then finally a rapid quenching to room temperature from the different growth temperatures. The schematic of the CVT growth equipment is shown in Figure 1. Finally, the millimeter-sized crystals with metallic luster were obtained successfully for 2 weeks growth.

2.2. Material Characterization

The crystalline structures were determined by X-ray diffraction (XRD) (Ultima III Rigaku X-ray diffractometer, Cu-K_α radiation, Tokyo, Japan) with 2θ scanned from 10° to 85°. The elemental composition of the as-grown crystals was determined by an energy-dispersive-spectroscopy (EDS) spectrometer equipped in a scanning-electron-microscope (FEI-Quanta, Hillsboro, OR, USA). The microstructure and crystal structure of the crystals were characterized by a Tecnai F20 transmission electronic microscope (TEM, FEI Inc., Hillsboro, OR, USA). The TEM specimens were prepared by a conventional method including grinding and transferring to a copper grid with carbon coating. The back-reflection Laue detector (MWL120, Multiwire Laboratories, Ltd., Ithaca, NY, USA) was used to determine the crystal structure. The temperature dependences of the thermal conductivities along the c-axis were measured by the Time-Domain ThermoReflectance (TDTR) method, which was widely used in the studies of nanoscale thermal transport. Before the TDTR measurement, each sample was polished or cleaved to get a fresh and smooth surface. Each irregular-shaped sample was adhered to the silicon wafer by silver glue for better heat dissipation. Then, a thin layer of aluminum (Al) film with thickness of ~86 nm was deposited on each sample by magnetron sputtering. During the measurements, a train of femtosecond laser pulses (pump beam) arrive on the Al film to heat the surface and serve as the heat source. The surface temperature rises rapidly within several picoseconds, and then declines slowly because of the thermal transport of samples. Meanwhile, a time-delayed femtosecond laser (probe beam) monitors the temperature variation by detecting the temperature-sensitive optical reflectivity. Both the pump and probe laser beams were generated from a mode-locked Ti: sapphire laser (Chameleon, Coherent), and their time delay was precisely controlled by a 600 mm mechanical delay line. The spot diameter of the laser beam was ~20 um and the thermal penetration depth was ~100 nm, which guaranteed a quasi-one-dimensional heat transport in samples to minimalize systematic error caused by the in-plane thermal conductivity [21]. Specifically, the reflected probe signal was received by a silicon-based photodetector, and the in-phase and out-of-phase voltage, i.e., V_in and V_out, were demodulated by a lock-in amplifier. The thermal conductivities of single crystals were analyzed by fitting the ratio of −V_in/V_out at different delay times using a multilayer thermal transport model [22]. More details of our TDTR technique can be found in our previous works [19,23].

3. Results and Discussion

We show the schematic of the CVT growth equipment, as well as the growth parameters to synthesize the different CuCr₂Se₄-CuCrSe₂ hetero-composite crystals in Figure 1 (EDS was used to determine the chemical compositions of these samples, see the following Figure 2a). Different CuCrSe₂-CuCr₂Se₄ hetero-composites can be obtained by rapid quenching from different temperatures. As shown in Figure 1, by quenching at high temperature (~930 °C) we can obtain nearly pure CuCrSe₂ crystals; with a lower quenching temperature (≤900 °C), more CuCr₂Se₄ impurity phase can be generated from the matrix of CuCrSe₂. Using this growth strategy, we grew the different CuCrSe₂-CuCr₂Se₄ hetero-composites.

Figure 2a displays the EDS spectra of these crystals and we calculated the atomic ratios between CuCrSe₂ and CuCr₂Se₄ phase-in as grown crystals according to quantitative EDS results. The results indicate that the ratios of CuCrSe₂ and CuCr₂Se₄ crystal of three samples are 0.6, 0.8, and 0.94, respectively. Here, as-grown crystals are nominated as (CuCr₂Se₄)_1−x(CuCrSe₂)_x (x = 0.94, 0.8, 0.6). The optical micrograph of CuCr₂Se₄-CuCrSe₂ hetero-composite crystals with different composition ratios are shown in the insets of Figure 2a. These crystals show the metallic luster. Figure 2b shows the XRD patterns of as-grown crystal. Evidently, all the reflections of the exposed surface of these samples can be indexed as (00L)-CuCrSe₂ and (LLL)-CuCr₂Se₄, which suggests the exposed surface of CuCr₂Se₄ crystals being the (111)-plane, while that of CuCrSe₂ crystal is the (001)-plane.

We also used the TEM to characterize the micro-structure of the (CuCr₂Se₄)_0.4(CuCrSe₂)_0.6 sample. Figure 3 is a typical bright-field TEM image of this sample. Evidently, there are tile structures and Morie fringes in Figure 3a. Normally, Moire fringes come from the overlap of two layers with either different structures, or misorientation. The selected-area-electron-diffraction pattern of this area is depicted in Figure 3b. Electron diffraction determination substantiates that there are two sets of diffraction patterns, one is the [001]-CuCrSe₂, and the other is [111]-CuCr₂Se₄. The in-plane orientation relationship of these two phase is (2-20)(20-2)─CuCr₂Se₄‖(100)(110)─CuCrSe₂. To double check the orientation relationship between CuCrSe₂ and CuCr₂Se₄, we did the Laue diffraction pattern (see Figure S2) and found the major feature of the Laue pattern is quite similar to the electron diffraction one.

The experimentally observed orientation-relationship between CuCrSe₂ and CuCr₂Se₄ can be easily understood by the atomic models of these two phases. Figure 4a,b are the atomic structures of CuCr₂Se₄ projected along [111]-direction and CuCrSe₂ along [001]-one, respectively. To highlight the similarity between these two compounds, only Cr and Se atoms are drawn in this figure. One can see that Cr-Cr atoms in CuCrSe₂ form the triangle lattice, while those in CuCr₂Se₄ form a honeycomb-like one. The nearest Cr-Cr atomic distance in CuCrSe₂ is around 3.669 Å, which is quite close to that in CuCr₂Se₄ (3.655 Å), which suggests the semi-coherent interface between CuCr₂Se₄ and CuCrSe₂. Therefore, we can observe the orientation relationship between CuCrSe₂ and CuCr₂Se₄ by TEM.

Our TEM characterization suggests that CuCrSe₂ layers are mainly stacked with CuCr₂Se₄ along the c-axis of CuCrSe₂ or 111-axis of CuCr₂Se₄. Therefore, we think the modified thermoconductivity mainly happens along the out-of-plane direction. The out-of-plane thermal conductivity (κ) of these CuCr₂Se₄-CuCrSe₂ hetero-composite crystals was measured by TDTR from 60 to 300 K. Figure 5 summarizes the experimental and fitting of TDTR data of (CuCr₂Se₄)_1−x(CuCrSe₂)_x measured at 300 K on how to extract their thermal conductivity. Inset of Figure 5 presents the −V_in/V_out signals of one sample (x = 0.8) measured at room temperature and the associated fittings. Reasonable fitting exhibits the reliability of the measurements. On conducting the same experiment at different temperatures on three samples, the temperature-dependent out-of-plane thermal conductivities of (CuCr₂Se₄)_1−x(CuCrSe₂)_x were obtained and are shown in Figure 5. Although TDTR measures thermal conductivities including both electron- and phonon-thermal conductivity, the electrical thermal conductivity (κ_e) is almost negligible, compared to κ_L. One can see from Figure 5 that at low temperature (from 60 to 180 K), the κ of these samples increases monotonously with temperature T raised, then κ in hetero-composite (CuCr₂Se₄)_1−x (CuCrSe₂)_x (x = 0.8, 0.6) are nearly saturated when T is increased from 180 to 300 K; however, κ in (CuCr₂Se₄)_0.06 (CuCrSe₂)_0.94 has a maximum value at about 200 K and then decreases when T is increased from 200 to 300 K.

To quantitatively understand the above-mentioned different κ-T behaviors, we fitted experimental ${\kappa }_L$ data using the Debye-Callaway model [24,25]:

$${\kappa }_L=\frac{k_B}{2{\pi }^{2}v}{\left(\frac{k_B}{\hslash }\right)}^3{T}^3{{\displaystyle \int }}_0^{{\theta }_D/T}\frac{x^4{e}^x}{{\tau }_c^{-1}\left(e^x-1\right)}dx$$

(1)

where $x=\hslash \mathsf{\omega }/k_{B}T$ is a dimensionless number, ω is the phonon frequency, $k_B$ is the Boltzmann constant, $\hslash$ is the reduced Planck constant, ${\theta }_D$ is the Debye temperature, v is the velocity of sound, and ${\tau }_c^{-1}$ is the phonon scattering relaxation time. The phonon relaxation rate can be written as:

$${\tau }_c^{-1}=\frac{v}{L}+B{\omega }^{2}T{e}^{-{\theta }_D/T}+\mathrm{C}\frac{\left(\frac{{\omega }_0\gamma }{2{\pi }^2}\right){\omega }^2}{{\left({\omega }_0^2-{\omega }^2\right)}^2+{\left(\frac{\gamma }{\pi }\right)}^2{\omega }_0{}^2{\omega }^2}$$

(2)

where L is the average size of lamellae leading to interface scattering, and B is a fitting parameter of three-phonon Umklapp scattering. The first, second, and third terms on the right side of Equation (2) represent interfacial scattering, three-phonon Umklapp scattering (anharmonic effect), and phonon resonance scattering, respectively. In the fitting process, we found that the C value in these compounds is too small, compared with that in previous literature [26,27]. The small C suggests the negligible effect of phonon resonance scattering in CuCrSe₂ at T < 300 K, which is different from the high-temperature case (T > 365 K) where phonon resonance scattering is crucial to κ of CuCrSe₂, as reported previously [12]. Therefore, in what follows, we only report the fitting results based on the first two terms in Equation (2). The fitting results are shown in the solid curves of Figure 6a. The data of (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94 are enlarged at the inset of Figure 6a because of its much smaller κ, compared to other samples. Evidently, experimental κ can be well fitted by Equation (1). The fitting parameters L and B are summarized in

Table 1. The parameters in fitting thermal conductivity of samples by the Debye-Callaway model.

	L (nm)	B (s/K)	θD (K)
(CuCr2Se4)0.4(CuCrSe2)0.6	0.58	1.12 × 10−18	529
(CuCr2Se4)0.2(CuCrSe2)0.8	0.42	1.33 × 10−17	444
(CuCr2Se4)0.06(CuCrSe2)0.94	0.36	3.75 × 10−16	430

. As read from Table 1, with the increasing of the percentage of CuCrSe₂, the L decreases monotonously, which indicates the increase of the interfacial-scattering contribution. As to the minimum L observed in CuCrSe₂ crystal, this is because the Cr and CuSe₂ layers are stacked alternatively along the c-axis. In this case, the small angle misorientation in CuCrSe₂ is quite universally observed (see electron diffraction in Figure 3b). These small-angle misorientated interfaces can lead to phonon scattering. While CuCr₂Se₄ is a cubic crystal, the misorientation is difficult to observe. Therefore, if the concentration of CuCrSe₂ is higher, L is decreased because there is high density of small-angle misorientation grains. As far as three-phonon scattering is concerned, in (CuCr₂Se₄)_0.4(CuCrSe₂)_0.6 and (CuCr₂Se₄)_0.2(CuCrSe₂)_0.8 crystal, the fitting parameter B is changed from about $1\times {10}^{-18}–1\times {10}^{-17}\mathrm{s}/\mathrm{K}$. However, the fitting parameter B in (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94 is $4\times {10}^{-16}$ s/K, which is 25 times larger than that of (CuCr₂Se₄)_0.4(CuCrSe₂)_0.6. This suggests that there is more significant umklapp scattering in (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94 than in the other two samples.

To more quantitatively determine the contribution of interface scattering and Umklapp scattering in CuCr₂Se₄-CuCrSe₂ hetero-composites, we analyzed thermal resistivity ρ (ρ = 1/κ_L), rather than thermal conductivity κ. According to the Matthiesen rule, the ρ is the summation of thermal resistivity coming for the interface and three-phonon Umklapp scattering (according to the above discuss, the resonance scattering is negligible). Mathematically:

$${\rho }_{total}={\rho }_{umk}+{\rho }_{int}$$

(3)

where ${\rho }_{total}=1/{\kappa }_L$, ${\rho }_{int}=1/{\kappa }_{int}$, and the thermal conductivity of interfacial scattering is:

$${\kappa }_{int}=\frac{k_B}{2{\pi }^{2}v}{\left(\frac{k_B}{\hslash }\right)}^3{T}^3{{\displaystyle \int }}_0^{{\theta }_D/T}\frac{x^4{e}^x}{\frac{v}{L}\left(e^x-1\right)}dx$$

(4)

Combining Equations (3) and (4), we can determine the thermal resistivity coming from interface scattering and three-phonon Umklapp scattering (see Figure 6b–d). One can see from Figure 6b–d that in (CuCr₂Se₄)_0.4(CuCrSe₂)_0.6 interface scattering nearly contributes all thermal resistivity, and in (CuCr₂Se₄)_0.2(CuCrSe₂)_0.8 the interface scattering and Umklapp scattering roughly contribute 80% and 20% thermal resistivity, respectively. Different forms of these two samples, Umklapp scattering in (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94 is more significant to thermal resistivity at, for example, 300 K, where the contribution of umklapp scattering is larger than interface scattering. In other words, in (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94, both interface scattering and Umklapp scattering lead to the lowest thermal conductivity therein.

4. Conclusions

In this work, taking advantage of CuCr₂Se₄ being easily precipitated from CuCrSe₂ matrix, we grew a series of hetero-composite CuCrSe₂-CuCr₂Se₄ crystals by adjusting the growth conditions. The orientation relationship between CuCrSe₂ and CuCr₂Se₄ is [001] (100)‖[111] (220) determined by electron diffraction. The out-of-plane thermal conductivity κ of these crystals was measured by using the time-domain thermoreflectance (TDTR) method. Analysis of thermal resistivity of these hetero-composites, by Boltzmann-Callaway models, suggests that interface scattering plays a quite significant role to κ in (CuCr₂Se₄)_0.4(CuCrSe₂)_0.6 and (CuCr₂Se₄)_0.2(CuCrSe₂)_0.8 hetero-composites, but it is both anharmonic three-phonon and interface scattering leading to the lowest thermal conductivity in (CuCr₂Se₄)_0.06(CuCrSe₂)_0.94. Our results reveal the thermal conductivity evolution in CuCr₂Se₄-CuCrSe₂ hetero-composites.