AC conductivity study of mechanochemically synthesized solid electrolytes of Li_6−aM_a/nⁿPS₅Cl (M = Ca, Mg, Ba, Zn, Al, Y)

Abstract

Argyrodite-type solid electrolytes of Li₆PS₅Cl doped with multivalent cations (Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺) were prepared via a mechanochemical synthesis method. The lattice constant (a₀), interplanar spacing (d₂₂₀, d₃₁₁, d₂₂₂), and micro-strain (ε) showed that the doping elements were incorporated into the crystal structure of Li₆PS₅Cl. The lattice constant and interplanar spacing of the doped samples were smaller than those of Li₆PS₅Cl. The prepared samples exhibited a positive lattice strain, and the substituted samples exhibited higher strains than Li₆PS₅Cl. The doped samples exhibited higher ionic conductivity than Li₆PS₅Cl at 25 °C. Li_5.94Al_0.02PS₅Cl exhibited the highest σ_DC of approximately 2.36 × 10⁻³ S cm⁻¹ at 25 °C. The charge carrier movement at the grain boundary changing from long-range diffusion in Li₆PS₅Cl to short-range diffusion in Li_5.94Al_0.02PS₅Cl enhanced the conductivity.

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1. Introduction

All-solid-state Li ion batteries using sulfide-based solid electrolytes (SEs) are candidates for technological applications because of their high energy density, thermal stability, and ease of cell design.¹ SEs with high ionic conductivity at 25 °C are important components of all-solid-state Li ion batteries. Li₇P₃S₁₁, Li₁₀GeP₂S₁₂, Li₁₀P₃S₁₂I, and argyrodite-type Li₆PS₅Cl SEs have attracted considerable attention from researchers because of their tunable composition and attractive ionic conductivity at 25 °C.^2–5 Argyrodite-type SEs have been intensively studied because they have a wide electrochemical window and exhibit high ionic conductivity.⁶

The ionic conductivity of Li₆PS₅X (X = Cl, Br, and I) at room temperature ranges from 10⁻⁶ to approximately 1–2 × 10⁻³ S cm⁻¹ and could be improved by the aliovalent substitution of S²⁻, P⁵⁺, and Li⁺. Li_5.5PS_4.5Cl_1.5 exhibited a high conductivity of 9.4 × 10⁻³ S cm⁻¹ at 25 °C,⁷ whereas Li_5.3PS_4.3Cl_1.0Br_0.7 exhibited an ionic conductivity of 16.6 × 10⁻³ S cm⁻¹ at 30 °C.⁸ High-entropy multicationic substituted Li_6.5[P_0.25Si_0.25Ge_0.25Sb_0.25]S₅I exhibited a high ionic conductivity of approximately 13 × 10⁻³ S cm⁻¹ at room temperature,⁹ and Li_6.2Si_0.2P_0.8S₅Cl_0.5Br_0.5 exhibited a high ionic conductivity of 5.12 × 10⁻³ S cm⁻¹ at room temperature.¹⁰ The aliovalent substitution of Li⁺ by a multivalent cation improved the ionic conductivity of Li₆PS₅Cl. The ionic conductivity of Li_5.7Ca_0.15PS₅Cl at 25 °C was approximately 5.2 × 10⁻³ S cm⁻¹, which exceeded that of Li₆PS₅Cl (3.1 × 10⁻³ S cm⁻¹).¹¹ Li_5.4Al_0.2PS₅Br exhibited a room temperature ionic conductivity of 2.4 × 10⁻³ S cm⁻¹, which exceeded that of Li₆PS₅Br (1.0 × 10⁻³ S cm⁻¹).¹² These SEs were prepared through solid-state reactions at a high temperature. Therefore, maintaining low oxygen and humidity concentrations will be a barrier to the mass production of these substances because sulfide-based SEs react with oxygen in a dry atmosphere at approximately 270 °C.¹³ Thus, mechanochemical synthesis, which occurs at room temperature, is a good option, in addition to solid-state reactions at high temperatures. The ionic conductivity of mechanochemically synthesized Li₆PS₅Cl at room temperature was slightly enhanced because of a multivalent cation at the grain boundary.¹⁴

This study enhanced the ionic conductivity of mechanochemically synthesized Li₆PS₅Cl by the aliovalent substitution of Li⁺ with multivalent cations (Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺). Data obtained from alternating current (AC) impedance spectroscopy was analyzed using conductivity isotherms and the dielectric constant and dielectric loss. The ionic conductivity of Li_5.94Al_0.02PS₅Cl was approximately 2.36 × 10⁻³ S cm⁻¹ at 25 °C, which was approximately twice that of Li₆PS₅Cl. Furthermore, this value exceeded the reported ionic conductivity of argyrodite SEs prepared without heat treatment. The activation energy of direct current and Li ion migration suggested that ion movement at the grain boundary was a critical process in the prepared samples.

2. Experimental process

The samples were prepared via a mechanical milling synthesis method. Li₂S, P₂S₅, LiCl, CaCl₂, BaCl₂, MgCl₂, YCl₃, AlCl₃, and ZnCl₂ were obtained from Macklin at 99.9% purity and used without further purification. A typical batch (2.000 g) was prepared by mixing an appropriate amount of each starting material using agar and a mortar for approximately 15 min. The mixture was transferred into a zirconia pot (45 mL) with zirconia balls (approximately 30 g; diameter = 5 mm). The ball-to-powder ratio was approximately 15. The pot was rotated at 550 rpm for 20 h using a Pulverisette 7 (Fritsch Co., Ltd). The samples were recovered and characterized without further heat treatment. All the synthesis experiments were performed in a dry Ar atmosphere.

The structure of the samples was characterized by X-ray diffraction (XRD; X8, Bruker), SEM (S4800, Hitachi) and EDS (ULTIM MAX, Oxford Instrument). The samples were prepared in an Ar-filled glove box and loaded into an air-tight sample holder for characterization.

The samples for resistivity measurements were prepared by uniaxially cold pressing the powder under a pressure of 330 MPa to form a pellet (thickness = 1.2–1.4 mm; diameter = 10 mm), as reported.¹⁵ AC impedance spectroscopy was conducted using a potentiostat (PGSTAT302N, Autolab, Herisau, Switzerland) from 9 MHz to 10 Hz. The samples for the impedance measurements were prepared by uniaxially pressing the sample (approximately 160 mg) into pellets (approximately 10.0 mm in diameter) under a pressure of 330 MPa at room temperature. The pellet was placed in a holder made of polycarbonate with two stainless steel rods as blocking electrodes. Thereafter, the cell was placed in an N₂ flow in a glass tube for temperature dependence measurements. The temperature was gradually increased from room temperature to 110 °C and held at each temperature for 1 h prior to the impedance measurements. The AC applied voltage was 100 mV.

3. Results and discussion

Fig. 1a and b show the XRD patterns of the SEs of Li_6−2xCa_xPS₅Cl and Li_5.94M_0.06/nⁿPS₅Cl (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺), respectively. No impurity was detected, and all the peaks were assignable to the argyrodite phase (JCPDS 34-0688). The lattice constant, interplanar spacing, and micro-strain were calculated using the XRD data to investigate the effect of the multivalent cation substitution on the crystal structure of Li₆PS₅Cl. The crystal structure of the samples was indexed to cubic Li₇PS₆ in the F4̄3m space group (JCPDS 34-0688). The peaks were assigned to the [111], [200], [220], [311], [222], [420], [422], [511], [440], [600], and [620] planes. The lattice parameters were obtained at each diffraction angle (θ) using the Bragg equation.

nλ = 2d sin θ. (1)

Fig. 1 Structural characterization of the prepared samples. (a) XRD patterns of Li_6−2xCa_xPS₅Cl solid electrolytes; (b) XRD patterns of Li_5.94M_0.06/nⁿPS₅Cl solid electrolytes (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺); (c) SEM-EDS results of Li_5.8Ca_0.1PS₅Cl.

The Nelson–Riley equation was employed to determine the lattice constant (a₀).

The a₀ was determined from the linear fit equation, which was derived from a plot with a as the y-axis and as the x-axis.

The Williamson–Hall (WH) analysis is a simple method for estimating the lattice strain (ε) by analyzing the X-ray data and considering the peak width as a function of 2θ.

where β_hkl is the full width at half maximum of the diffraction peak, and θ is the Bragg angle. The value of ε was derived from the slope of the regression line, which was obtained by plotting β_hkl cos θ against sin θ.

Table 1 lists the values of the lattice constant (a₀), interplanar spacing (d₂₂₀, d₃₁₁, d₂₂₂), and micro-strain (ε). The a₀ of Li₆PS₅Cl was 9.8401 Å and was consistent with the reported 9.8397(4) Å of Li₆PS₅Cl prepared via the mechanochemical method.¹⁶ The a₀ of Li_5.99Ca_0.005PS₅Cl was practically similar to that of Li₆PS₅Cl, indicating that the doping amount was too small to influence the measurement result. The a₀ of Li_5.94Ca_0.03PS₅Cl was 9.8346 Å, which was smaller than that of Li₆PS₅Cl. The a₀ values of Li_5.94M_0.06/nⁿPS₅Cl (Mⁿ = Mg²⁺, Ca²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺) were close to each other. Thus, the multivalent cation doping reduced the a₀ of Li₆PS₅Cl; this observation was consistent with reported results.^11,12 The values of the interplanar spacing (d₂₂₀, d₃₁₁, d₂₂₂) of the substituted samples were smaller than those of Li₆PS₅Cl. In crystals, cations are surrounded by anions and vice versa such that the electrostatic interaction among oppositely charged ions strengthens the crystal structure. The substitution of Li ions with multivalent cations resulted in the formation of vacancies. A multivalent cation has a higher positive charge density than a Li ion; therefore, the electrostatic attraction with negative ions will be stronger. Thus, the lattice constant and interplanar spacing will be reduced. The lattice strain (ε) represents the displacement of unit cells about their normal positions. All the prepared samples exhibited a positive lattice strain, and the substituted samples exhibited higher strains than Li₆PS₅Cl. SEM-EDS results of Li_5.8Ca_0.1PS₅Cl is shown in Fig. 1c. The SEs are in the form of particles with a size of several hundred nanometer. EDS results indicated that Ca was well dispersed in the prepared powder sample. The results suggest that the multivalent cations were successfully incorporated into the crystal structure of Li₆PS₅Cl.

Table 1 Structural parameters of the prepared samples

	Lattice constant a0 (Å)	d220 (Å)	d311 (Å)	d222 (Å)	Microstrain ε
Li6PS5Cl	9.8401	3.4790	2.9669	2.8406	0.00330
Li5.99Ca0.005PS5Cl	9.8400	3.4790	2.9669	2.8406	0.00418
Li5.94Ca0.03PS5Cl	9.8346	3.4781	2.9661	2.8399	0.00433
Li5.8Ca0.1PS5Cl	9.8341	3.4779	2.9660	2.8397	0.00390
Li5.94Ba0.03PS5Cl	9.8347	3.4771	2.9653	2.8390	0.00460
Li5.94Zn0.03PS5Cl	9.8348	3.4771	2.9653	2.8391	0.00458
Li5.94Mg0.03PS5Cl	9.8356	3.4774	2.9655	2.8393	0.00488
Li5.94Al0.02PS5Cl	9.8354	3.4778	2.9667	2.8404	0.00418
Li5.94Y0.02PS5Cl	9.8349	3.4772	2.9653	2.8391	0.00445

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Fig. 2a–d show the frequency dependence of the real part of conductivity, σ′, of Li₆PS₅Cl, Li_5.94Ca_0.03PS₅Cl, Li_5.94Mg_0.03PS₅Cl, and Li_5.94Al_0.02PS₅Cl obtained from 10 Hz to 9 MHz at different temperatures, respectively, using conductivity isotherms. Fig. S1a–c† show the conductivity isotherms of Li_5.96Ca_0.002PS₅Cl, Li_5.9Ca_0.05PS₅Cl, and Li_5.8Ca_0.1PS₅Cl, respectively. Furthermore, Fig. S2a–c† show the conductivity isotherms of Li_5.94Ba_0.03PS₅Cl, Li_5.94Zn_0.03PS₅Cl, and Li_5.94Y_0.02PS₅Cl, respectively. The isotherms of all the samples comprised three regions: electrode polarization, a plateau-like region, and polarization conductivity at low, intermediate, and high frequencies, respectively. The high-frequency polarization conductivity could be explained by the power law behavior, σ_ω ∝ ωⁿ, where n is a fractional exponent (0 ≤ n ≤ 1) and is associated with the interaction between the ions and environment.¹⁷ The accumulation of ions at blocking electrodes caused electrode polarization.¹⁸ The isotherms were analyzed using the Jonscher power law to understand the ion dynamics of the prepared electrolytes. The conductivity in the intermediate- and high-frequency regions followed the Jonscher power law equation.

σ = σ_DC + Aωⁿ, (5)

→ σ − σ_DC = Aωⁿ → log₁₀(σ − σ_DC) = n log₁₀ ω + log₁₀ A, (6)

where σ_DC is the direct current (DC) conductivity, A is a prefactor, and n is the frequency exponent in the range of 0 < n < 1.¹⁹ A and n are thermally activated quantities. σ_DC, A, and n were obtained at each temperature by fitting the conductivity spectra using eqn (6). Table 1 lists the values of A and n. All the values of A and n exceeded 0, indicating the frequency and temperature dependence of the conductivity. The A values of the doped samples were approximately 10¹ to 10² times that of Li₆PS₅Cl, suggesting that the multivalent cation doping enhanced the frequency dependence conductivity.

Fig. 2 Conductivity isotherms of (a) Li₆PS₅Cl; (b) Li_5.94Ca_0.03PS₅Cl; (c) Li_5.94Mg_0.03PS₅Cl and (d) Li_5.94Al_0.02PS₅Cl measured from 10 Hz to 9 MHz.

Fig. 3a and c show the temperature dependence of the ionic conductivity, σ_DC, of the SEs of Li_6−2xCa_xPS₅Cl and Li_5.94M_0.06/nⁿPS₅Cl (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺), respectively. The log₁₀(σ_DC) satisfied a practically linear dependence on an inverse temperature; therefore, it followed the Arrhenius equation, σ = σ₀ exp(−E_a,DC/(k_BT)). The DC activation energy, E_a,DC, was calculated and is shown in Table 2. The E_a,DC of Li₆PS₅Cl was approximately 16 kJ mol⁻¹. The E_a,DC of the doped samples exceeded that of Li₆PS₅Cl in the range of 28–31 kJ mol⁻¹. Furthermore, the E_a,DC of Li_6−3xAl_xPS₅Br (x = 0.1, 0.15, 0.2, 0.25, 0.3) has been reported to exceed that of Li₆PS₅Br.¹² Thus, the aliovalent substitution of Li ions in argyrodite-type SEs led to an increase in E_a,DC. The ionic conductivity of Li₆PS₅Cl at 25 °C was approximately 1.25 × 10⁻³ S cm⁻¹. Fig. 3b and d show the ionic conductivity (σ_DC) of the SEs of Li_6−2xCa_xPS₅Cl and Li_5.94M_0.06/nⁿPS₅Cl (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺) at 25 °C and 50 °C, respectively. At 25 °C, all the doped samples exhibited ionic conductivities higher than that of Li₆PS₅Cl. Li_5.94Al_0.02PS₅Cl exhibited the highest σ_DC (approximately 2.36 × 10⁻³ S cm⁻¹) at 25 °C. The σ_DC of Li₆PS₅Cl and Li_5.94Al_0.02PS₅Cl were 2.15 × 10⁻³ and 6.00 × 10⁻³ S cm⁻¹ at 50 °C, respectively. The σ_DC and E_a,DC results confirmed that the multivalent cation was successfully incorporated into the crystal structure of Li₆PS₅Cl.

Fig. 3 (a) Temperature dependence of ionic conductivity of Li_6−2xCa_xPS₅Cl solid electrolytes; (b) the ionic conductivity at 25 and 50 °C of Li_6−2xCa_xPS₅Cl solid electrolytes; (c) temperature dependence of ionic conductivity of Li_5.94M_0.06/nⁿPS₅Cl solid electrolytes (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺); (d) the ionic conductivity at 25 and 50 °C of Li_5.94M_0.06/nⁿPS₅Cl solid electrolytes (Mⁿ = Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺).

Table 2 DC activation energy E_a,DC, activation energy E_a,m of ion migration at grain boundary, and characteristic time τ_0,m of ion migration at grain boundary

	Li6PS5Cl	Li5.96Ca0.002PS5Cl	Li5.94Ca0.03PS5Cl	Li5.9Ca0.05PS5Cl	Li5.8Ca0.1PS5Cl
Ea,DC/kJ mol^−1	16	26	29	28	31
Ea,DC/eV	0.16	0.26	0.29	0.28	0.31
Ea,m/kJ mol^−1	19	24	28	31	34
Ea,m/eV	0.19	0.24	0.28	0.31	0.34
τ0,m/s	5.47 × 10^−7	2.56 × 10^−9	6.31 × 10^−9	1.57 × 10^−9	6.79 × 10^−9

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	Li5.94Ba0.03PS5Cl	Li5.94Zn0.03PS5Cl	Li5.94Mg0.03PS5Cl	Li5.94Al0.02PS5Cl	Li5.94Y0.02PS5Cl
Ea,DC/kJ mol^−1	27	28	29	29	29
Ea,DC/eV	0.27	0.28	0.29	0.29	0.29
Ea,m/kJ mol^−1	31	31	31	33	30
Ea,m/eV	0.31	0.31	0.31	0.33	0.30
τ0,m/s	8.66 × 10^−9	1.39 × 10^−9	4.42 × 10^−9	2.26 × 10^−9	1.64 × 10^−9

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Fig. 4a–d show the frequency dependence of the real part of permittivity, ε′, of Li₆PS₅Cl, Li_5.94Ca_0.03PS₅Cl, Li_5.94Mg_0.03PS₅Cl, and Li_5.94Al_0.02PS₅Cl obtained from 10 Hz to 9 MHz at different temperatures, respectively. Fig. S3a–c† show the frequency dependence of the ε′ of Li_5.96Ca_0.002PS₅Cl, Li_5.9Ca_0.05PS₅Cl, and Li_5.8Ca_0.1PS₅Cl, respectively. Furthermore, Fig. S4a–c† show the frequency dependence of the ε′ of Li_5.94Ba_0.03PS₅Cl, Li_5.94Zn_0.03PS₅Cl, and Li_5.94Y_0.02PS₅Cl, respectively. The increase in the plots in the low-frequency region was attributable to the electrode–electrolyte interface polarization due to the accumulation of ions near the electrode. This led to the formation of a space-charged layer that blocked the electric field and enhanced the electrical polarization. The ε′ of all the samples increased with an increase in temperature, indicating that charge carrier movement was thermally activated. The ε′ reflects the amount of energy stored in the form of polarization when an electric field is applied.²⁰ In most ion-conducting materials, ε′ decreases with an increase in frequency.²¹ The plot of Li_5.94Mg_0.03PS₅Cl at room temperature continuously decreased in the intermediate- and high-frequency regions; however, the plots of the other samples obtained at room temperature exhibited maxima at 10⁵–10⁶ Hz. Maxima were observed in all the plots at 50 °C or above. The change in the shape of the plots of Li_5.94Mg_0.03PS₅Cl suggests that a change occurred in the microstructure, and this process was temperature-dependent.

Fig. 4 Frequency dependent of the real part of permittivity, ε′, of (a) Li₆PS₅Cl; (b) Li_5.94Ca_0.03PS₅Cl; (c) Li_5.94Mg_0.03PS₅Cl and (d) Li_5.94Al_0.02PS₅Cl measured from 10 Hz to 9 MHz.

Fig. 5a–d show the frequency dependence of the loss factor, tan δ, of Li₆PS₅Cl, Li_5.94Ca_0.03PS₅Cl, Li_5.94Mg_0.03PS₅Cl, and Li_5.94Al_0.02PS₅Cl obtained from 10 Hz to 9 MHz at different temperatures, respectively. Fig. S5a–c† show the frequency dependence of the tan δ of Li_5.96Ca_0.002PS₅Cl, Li_5.9Ca_0.05PS₅Cl, and Li_5.8Ca_0.1PS₅Cl, respectively. Fig. S6a–c† show the frequency dependence of the tan δ of Li_5.94Ba_0.03PS₅Cl, Li_5.94Zn_0.03PS₅Cl, and Li_5.94Y_0.02PS₅Cl, respectively. Two peaks assignable to ion migration at the grain boundary and bulk were observed in all the plots in the low- and high-frequency regions. The peak in the low-frequency region shifted toward high-frequency with an increase in temperature. Generally, the grain boundary migration resistivity was expected to decrease with an increase in temperature because Li⁺ diffused from the bulk to the grain boundary. Thus, the intensity of the peak corresponding to the grain boundary resistivity in the loss factor decreased with an increase in temperature. The peak in the high-frequency region was not fully observed at 50 °C or above. The maximum value of the peak in the high-frequency region increased with an increase in the temperature, indicating that the number of charge carriers increased because of thermal activation. The migration energy (E_a,m) and migration characteristic time (τ_0,m) of the Li⁺ moving at the grain boundary could be derived from the temperature dependence of the peak position at low-frequency in the tan δ using the Arrhenius equation, τ_m = τ_0,m exp(−E_a,m/(k_BT)). Table 2 lists the obtained E_a,m and τ_0,m values. The E_a,m of the samples was similar to the E_a,DC, implying that the ion migration at the grain boundary was a critical process. The τ_0,m of Li₆PS₅Cl was approximately 5.47 × 10⁻⁷ s. The τ_0,m of the doped samples was approximately 10⁻⁹ s, which was almost 10² times faster than that of Li₆PS₅Cl. Thus, the Li ion moving at the grain boundary changed from long-range diffusion in Li₆PS₅Cl to short-range diffusion in the doped samples. The results suggested that the substitution of the Li ion with multivalent cations resulted in vacancy formation, which was the new hopping position for the Li ion. The addition of multivalent ions to Li₆PS₅Cl enhanced the Li ion mobility with a gradual decrease in the migration time; however, the migration energy increased as reflected in the E_a,m. Multivalent cations have a higher positive charge than Li⁺; thus, Li ions are repelled from their vicinity. From there, an Li ion can be trapped near the multivalent ion site, leading to a high migration barrier. It has been reported that the short inter-cage jump is a critical process in Li_5.4Al_0.2PS₅Br, and this process was associated with an increase in activation energy.¹² In addition, the change from short- to long-range diffusion was associated with a decrease and increase in activation energy and migration time, respectively.²² Thus, the results in this section were consistent with the reported results and ionic conductivity of the samples.

Fig. 5 Frequency dependent of the loss factor, tan δ, of (a) Li₆PS₅Cl; (b) Li_5.94Ca_0.03PS₅Cl; (c) Li_5.94Mg_0.03PS₅Cl and (d) Li_5.94Al_0.02PS₅Cl measured from 10 Hz to 9 MHz.

4. Conclusion

Here, the Li ion in the SE of Li₆PS₅Cl was partially substituted with various multivalent cations (Mg²⁺, Ba²⁺, Zn²⁺, Al³⁺, Y³⁺). The a₀; d₂₂₀, d₃₁₁, d₂₂₂; ε; and σ_DC values confirmed that the multivalent cations were successfully incorporated into the crystal structure of Li₆PS₅Cl. In addition, the charge carrier movement at the grain boundary changed from long-range diffusion in Li₆PS₅Cl to short-range diffusion in the doped samples.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study. The authors thank Philip K. (Enago; https://www.enago.com/vnuhcm/) for the English language review.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ra02621g

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