Synthesis, Electrical Properties and Na+ Migration Pathways of Na₂CuP_1.5As_0.5O₇

Abstract

A new member of sodium metal diphosphate-diarsenate, Na₂CuP_1.5As_0.5O₇, was synthesized as polycrystalline powder by a solid-state route. X-ray diffraction followed by Rietveld refinement show that the studied material, isostructural with β-Na₂CuP₂O₇, crystallizes in the monoclinic system of the C2/c space group with the unit cell parameters a = 14.798(2) Å; b = 5.729(3) Å; c = 8.075(2) Å; β = 115.00(3)°. The structure of the studied material is formed by Cu₂P₄O₁₅ groups connected via oxygen atoms that results in infinite chains, wavy saw-toothed along the [001] direction, with Na⁺ ions located in the inter-chain space. Thermal study using DSC analysis shows that the studied material is stable up to the melting point at 688 °C. The electrical investigation, using impedance spectroscopy in the 260–380 °C temperature range, shows that the Na₂CuP_1.5As_0.5O₇ compound is a fast-ion conductor with σ₃₅₀ °C = 2.28 10⁻⁵ Scm⁻¹ and Ea = 0.6 eV. Na⁺ ions pathways simulation using bond-valence site energy (BVSE) supports the fast three-dimensional mobility of the sodium cations in the inter-chain space.

1. Introduction

The research exploration of new inorganic materials with open framework constructed of polyhedra sharing faces, edges and/or corners forming 1D channels, 2D inter-layer spaces or 3D networks where cations are located, is currently an area of intense activity including several disciplines, in particular solid-state chemistry. In particular, alkali metal phosphates were found to have various applications because of their electric, piezoelectric, ferroelectric, magnetic, and catalytic properties [1,2,3,4]. Among those, the families of materials with the melilite structure [5], the olivine structure [6] and the natrium super ionic conductor (NaSICON) structure [7], attracted attention for their ionic conduction and exchange of ions [6,7].

More recently, in a series of studies arsenate analogs have been synthesized [8,9,10]. But, until today phosphate compounds are more studied as cathodes [11,12] compared to arsenate and this is perhaps due to the toxicity of arsenic III (As₂O₃). However, the oxide of arsenic V (As₂O₅) is less toxic. In addition, the introduction of arsenic into a structure changes its physical and chemical properties and even toxicity. On the other hand, the comparison of the electrochemical properties of LiCoPO₄ and LiCoAsO₄ both with olivine structure and close unit cell parameters, shows reversible (de)intercalation from/into material at average voltages of 4.8 and 4.6 V, respectively for LiCoAsO₄ [10] and a voltage average of 2.5–5 V for LiCoPO₄ [11].

The Na₂MP₂O₇ systems (M = transition metal) [13,14] have a layered structure with the layers [MP₂O₇]_n²ⁿ⁻ and the sodium cations localized in the interlayer space, which favors high ionic conductivity. We recently investigated the effect of the substitution of P by As with a larger ionic radius for ionic conductivity and showed the improvement of ionic conductivity for Na₂CoP_1.5As_0.5O₇ [15], which has an electrical conductivity value of σ_{240 °C} = 7.91×10⁻⁵ Scm⁻¹ and an activation energy Ea = 0.56 eV compared to Na₂CoP₂O₇ (σ_{300 °C} = 2 × 10⁻⁵ Scm⁻¹; Ea = 0.63 eV) [13].

In our search for new polyanion oxides of sodium and transition metals, the exploration of the Na₂O-CuO-P₂O₅-As₂O₅ crystallographic systems allowed us to isolate a new member of di-phosphate arsenates, Na₂CuP_1.5As_0.5O₇, in the polycrystalline powder form. In this paper, characterizations and physicochemical studies of the new member of sodium copper diphosphate-diarsenate material, Na₂CuP_1.5As_0.5O_7, and a comparison with other previous works encountered in the literature will be presented.

2. Materials and Methods

A mixture of Cu(NO₃)₂.2.5H₂O, NH₄H₂PO₄ and Na₂HAsO₄.7H₂O in the molar ratio Na:Cu:P:As equal to 2:1:1.5:0.5 was placed in a porcelain crucible and heated to 350 °C for 24 h to eliminate the volatile products H₂O, NO₂, and NH₃. The obtained powder was ground manually using agate mortar and shaped as cylindrical pellets by a uniaxial press. The obtained pellets were heated to 600 °C. After 72 h, the sample was cooled slowly at a rate of 10 °C/h down to room temperature. After grinding finely, a blue polycrystalline powder was obtained.

X-ray powder diffraction (XRD) was used to control and ensure the purity of the obtained powder. The analysis was carried out using XRD-6000 (Shimadzu, Japan) with graphite monochromator (Cukα, λ = 0.154178 nm) and a scan range of 2θ = 10°–70° with step of about 0.02°. The structure was refined using the Rietveld method by the means of the GSAS computer program [16] (EXPGUI, Gaithersburg, Maryland, USA). The crystallographic data of Na₂CuP₂O₇ [17] was used as a starting set. The obtained structural model was confirmed by the Charge Distribution CHARDI model of validation. The CHARDI calculation was done by using the CHARDI2015 computer program (Nespolo, IUCR) [18].

FTIR spectrometer (Agilent Technologies Cary 630 model) was used to allow a direct indexation of the peaks on a spectral range in wave numbers ranging from (1300–400 cm⁻¹).

Differential scanning calorimetry (DSC), with the SDT Q600 model, was used to study the thermal behavior of the obtained and prepared sample. In fact, the device contains two crucibles, one as a reference and the other contains the sample to be analyzed. These two crucibles are heated to 750 °C at a rate of 10 °C/min. The thermal analysis was carried out under a nitrogen atmosphere to avoid the reaction of the sample with the oxygen in the air.

Energy-dispersive X-ray spectroscopy (EDX) and scanning electron microscopy (SEM, Thermo Fisher Scientific model), were used to identify the present elements and the microstructure of the studied material, respectively.

The electrical measurements were preceded by pretreatment of the sample in order to densify the measured sample by reducing the mean particle size of the synthesized powder. Mechanical grinding for 100 min was carried out using the FRISCH planetary micromill pulverisette 7. The polycrystalline sample was shaped as a cylindrical pellet using a uniaxial press. The pellet was sintered in air at an optimal temperature of 610 °C for 2 h with 5 °C/min heating and cooling rates. The geometric factor of the dense ceramic is g = e/S = 0.793 cm⁻¹ where e and S are the thickness and face area of pellet, respectively. Gold metal electrodes ~36 nm thick were deposited using a SC7620 mini sputter coater. The sample was then placed between two platinum electrodes that were connected by platinum cables to the frequency response analyzer (HP 4192A) which was controlled by a microcomputer.

Impedance spectroscopic measurements were performed via the Hewlett-Packard 4192-A automatic bridge supervised by HP workstation. Impedance spectra were recorded with 0.5 V AC-signal in the 5 Hz–13 MHz frequency range.

The bond-valence site energy (BVSE) model [19,20] was used to simulate the alkali migration in the 3D anionic framework. The BVSE model is the latest extension of the bond-valence sum (BVS) model developed by Pauling [21] to describe the formation of inorganic materials. The BVS model was improved by Brown & Altermatt [22] followed by Adams [23], resulting in the expression:

$${\mathrm{s}}_{\mathrm{A}-\mathrm{X}}=\exp \left(\frac{{\mathrm{R}}_0-{\mathrm{R}}_{\mathrm{A}-\mathrm{X}}}{\mathrm{b}}\right)$$

(1)

where s_A-X is individual bond-valence, R_A-X is the distance between counter-ions A and X, R₀ and b are fitted empirical constants, and R₀ is the length of a bond of unit valence.

The BVSE model was extensively used in the cation motion simulation in the anionic framework by following the valence unit as a function of migration distance [24]. The valence unit was also recently related to potential energy scale and electrostatic interactions [19,20]. The BVSE method was used with success to simulate the transport pathways of monovalent cations (Na⁺; K⁺ and Ag⁺) in numerous materials including Na₂CoP_1.5As_0.5O₇ [15], Na_1.14K_0.86CoP₂O₇ [25] and Ag_3.68Co₂(P₂O₇)₂ [26]. The BVSE calculations were performed using the SoftBV [27] code and the visualization of isosurfaces was carried out using VESTA3 software (version 3, Koichi Momma and Fujio Izumi, 2018).

3. Results and Discussion

3.1. X-ray Powder Diffraction

The crystallographic study was started by a simple comparison between the XRD pattern of the prepared materials in the Na₂O-CuO-P₂O₅-As₂O₅ system and those of the previous studies of diphosphate Na₂MP₂O₇ [5,7,14,28,29] and Na₂CoP_1.5As_0.5O₇ [15]. In this case, only the Na₂CuP_1.5As_0.5O₇ diffractogram showed a similarity with that of the β-Na₂CuP₂O₇ diphosphate [17]. It crystallizes in the monoclinic system of the C2/c space group. This result prompted us to make a precise refinement using the Rietveld method which was implemented into the GSAS computer software [16]. The final agreement factors are Rp = 5.4% and Rwp = 6.9%. No additional peaks were detected. The final Rietveld plot is presented in Figure 1. The unit cell parameters obtained from the Rietveld refinement are a = 14.798(2) Å; b = 5.729(3) Å; c = 8.075(2) Å; β = 115.00(3)° (

Table 1. Unit cell parameters of the β-Na₂CuP₂O₇ and Na₂CuP_1.5As_0.5O₇ materials.

Parameter	Na2CuP1.5As0.5O7 (Current Work)	β-Na2CuP2O7 [30]
a (Å)	14.798(2)	14.728(3)
b (Å)	5.729(3)	5.698(1)
c (Å)	8.075(2)	8.067(1)
β (º)	115.00(3)	115.15(1)
V (Å3)	620.43(3)	612.80(2)

). The details of the crystallographic data, data collection and final agreement factors are given in

Table 2. Structure refinement results of the Na₂CuP_1.5As_0.5O₇ compound.

Crystallographic Data
Empirical Formula	Na2CuP1.5As0.5O7
Formula Weight; ρcal	305.44 g mol−1; 3.220 g cm−1
Crystalline System; Space Group	Monoclinic, C2/c
Unit Cell Dimensions	a = 14.8688 (8), b = 5.7591 (3), c = 13.5957 (7) β = 147.2406 (12)
Volume; Z	V = 629.97 (6) Å3; 4
Data Collection
Diffractometer	Bruker D8 ADVANCE
Wavelength	λCu Kα = 1.54056 Å
Temperature	298 (2) K
Angle Range	4.91°–69.91°
Step Scan Increment (°2θ)	0.02°
Counting Time	2 s
Refinement
Angle Range	4.91°–69.91°
Rp	0.054
Rwp	0.069
Rexp	0.043
R(F2)	0.05117
Goodness of Fit χ2	2.592
No. of Data Points	3251
No. of Restraints	18
Profile Function	Pseudo-Voigt
Background	Chebyshev function with 20 terms

. The atomic coordinates and isotropic displacement parameters are listed in

Table 3. Fractional atomic coordinates and equivalent isotropic displacement parameters (Ų).

	x	y	z	Uiso	Occ. (<1)
Cu1	¼	¼	½	0.0123 (12)
P1/As1	0.5112 (2)	0.5884 (5)	0.6563 (3)	0.0065 (14)	0.75/0.25
Na1	0.3211 (5)	0.8919 (9)	0.2991 (5)	0.004 (2)
O1	0.6590 (6)	0.4179 (9)	0.7999 (6)	0.006 (2)
O2	0.5389 (4)	0.7622 (10)	0.6011 (6)	0.006 (2)
O3	0.8432 (6)	0.0371 (12)	0.9916 (5)	0.041 (5)
O4	½	0.7267 (9)	¾	0.018 (5)

. The main bond distances are given in

Table 4. Main bond distances (Å) in the coordination polyhedra for Na₂CuP_1.5As_0.5O₇.

Cu1O4		(P1/As1)O4
Cu1—O1iii	1.9938 (3)	(P1/As1)—O1	1.5457 (3)
Cu1—O1x	1.9938 (3)	(P1/As1)—O2	1.5015 (3)
Cu1—O3iii	1.9247 (3)	(P1/As1)—O3x	1.5387 (3)
Cu1—O3x	1.9247 (3)	(P1/As1)—O4	1.6248 (3)
Na1O6
Na1—O1i	2.3985 (4)	Na1—O2iv	2.3220 (4)
Na1—O1vi	2.6566 (4)	Na1—O2vi	2.5780 (4)
Na1—O2	2.3541 (4)	Na1—O3i	2.3485 (4)

Symmetry codes: (i) −x + 1, −y + 1, −z + 1; (ii) x−1/2, −y + 1/2, z + 1/2; (iii) −x + 1, y, −z + 3/2; (iv) −x + 1, −y + 2, −z + 1; (v) x−1/2, −y−1/2, z + 1/2; (vi) x−3/2, −y + 1/2, z−1/2; (vii) −x + 1/2, y−1/2, −z + 1/2; (viii) −x + 1/2, y + 1/2, −z + 1/2; (ix) x, −y + 1, z−1/2; (x) x−3/2, −y−1/2, z−1.

. The charge distribution analysis and the bond-valence computation are summarized in

Table 5. Charge distribution analysis of cation polyhedra in Na₂CuP_1.5As_0.5O₇.

Cation	q(i).sof(i)	Q(i)	CN(i)	ECoN(i)	dar(i)	dmed(i)
Cu1	2.000	1.96	4	3.96	1.955	1.959
M1	5.000	5.03	4	3.88	1.544	1.552
Na1	1.000	0.98	6	5.47	2.400	2.443

q(i), formal oxidation number; Q(i), computed charge; sof(i), site occupation factor; d_ar(i), arithmetic average distance; d_med(i), weighted average distance; CN, coordination number; ECoN(i), effective coordination number. M1 = (0.75P + 0.25As=).

.

By comparing the unit cell parameters of the studied material with those of β-Na₂CuP₂O₇, the P/As substitution effect increases the volume of the unit cell (Table 1), which is explained by the distance of As―O bonds being greater than that of P―O.

3.2. Infrared Spectroscopy

The IR absorption spectrum of the studied Na₂CuP_1.5As_0.5O₇ material is shown in Figure 2. The spectrum shows the presence of the series of distinct bands attributed to asymmetric and symmetrical valence vibrations of the P-O-P and As-O-As bridges. These bands are characteristic of the pyrophosphate (P₂O₇)⁴⁻ and diarsenate (As₂O₇)⁴⁻ groups (

Table 6. Proposed assignment of the vibration bands of Na₂CuP_1.5As_0.5O_7.

Attribution	Wave Number (cm−1)
νas (PO3)	1188
	1164
νas (AsO3)	1100
νs (PO3)	1064
	1025
νs (AsO3)	994
νas (POP) Stretching Vibrations	901
νas (AsOAs) Stretching Vibrations	841
νs (POP) Stretching Vibrations	814
	772
	721
νs (AsOAs) Stretching Vibrations	694
	653
δas (PO3) Deformation Modes	629
	595
δs (PO3) Deformation Modes	544

) [30] and similar to those of the Li₂CuP₂O₇ spectrum [31].

3.3. DSC Thermal Analysis

In order to determine the thermal stability of the studied compound, the DSC analysis was used in the range from room temperature to 750 °C. The analysis result is illustrated in Figure 3. An endothermic peak was observed at 688 °C. This peak corresponds to the melting point of our compound. While, an exothermal peak is shown at 743 °C, after the fusion, probably corresponds to the oxidation of fractions of Cu²⁺ to Cu³⁺ in the obtained liquid phase. Overall, the thermal analysis via DSC shows that Na₂CuP_1.5As_0.5O₇ material is stable up to a temperature of 674 °C. The sharpness of the endothermic peak in the DSC analysis suggests good crystallinity of our synthesized powder.

Here we can also compare the thermal stability of Na₂CuP_1.5As_0.5O₇ to that of the recently studied Co analog Na₂CoP_1.5As_0.5O₇. The Cu material is stable from room temperature to the melting temperature, which is around 688 °C. In contrast, the Na₂CoP_1.5As_0.5O₇ material undergoes a phase transition at a temperature of 675 °C before melting at ~700 °C. This shows that the Na₂CuP_1.5As_0.5O₇ material is more stable than the Na₂CoP_1.5As_0.5O₇ material [15].

3.4. SEM Microstructure and EDX Analysis of Na₂CuP_1.5As_0.5O₇

Energy-dispersive X-ray spectroscopy (EDX) and scanning electron microscopy (SEM) analysis were used to confirm the chemical composition and examine polycrystalline morphology, respectively (Figure 4). The EDX analysis of the polycrystalline powder revealed the presence of the expected elements, i.e., sodium, copper, phosphorus, arsenic, and oxygen. The micrograph on SEM of the sample shows agglomeration of uniform parallelepiped crystallites. The mapping elemental analysis of Na₂CuP_1.5As_0.5O₇ confirmed the uniform distribution of the constituent elements (Figure 5).

3.5. Crystal Structure Description

The structural unit of Na₂CuP_1.5As_0.5O₇ is presented in Figure 6. It contains two P₂O₇ units connected by a vertex with two CuO₄ of square planar geometry. The charge neutrality of the structural unit is ensured by four sodium ions (Na⁺).

The Cu₂P₄O₁₅ groups of the structural unit are bound by oxygen peaks to result in infinite chains and are wavy saw-toothed along the [001] direction (Figure 7). The Na⁺ ions are located in the inter-chain space.

Other projections of the structure of Na₂CuP_1.5As_0.5O₇ according to the [100] and [001] directions are shown in Figure 8.

The structure of our material differs from that of the allotropic form α-Na₂CuP₂O₇ [17], which has a two-dimensional anionic framework formed by the connection of vertices of PO₄ tetrahedra, and CuO₅ polyhedra.

Compared to the sodium cobalt diphosphate-diarsenate Na₂CoP_1.5As_0.5O₇ investigated recently by Marzouki et al. [15], we notice that despite a similar composition, Na₂CuP_1.5As_0.5O₇ crystallizes in a different structure type. Indeed, the cobalt material crystallizes in the tetragonal system of the P4₂/mnm space group with the unit cell parameters a = 7.764(3) Å, c = 10.385(3) Å. In contrast, the studied material Na₂CuP_1.5As_0.5O₇, crystallizes in the monoclinic system of the C2/c space group with the unit cell parameters a = 14.798(2) Å; b = 5.729(3) Å; c = 8.075(2) Å; β = 115.00(3)°. The difference is undoubtedly determined by the preference of the Jahn–Teller active d⁹ Cu²⁺ to adopt square coordination (Figure 6).

3.6. Electrical Properties: Effect of P/As Doping

The prepared pellet of the Na₂CuP_1.5As_0.5O₇ compound was sintered at 550 °C for 2 h with a 5 °C/min heating and cooling rate. The relative density of the obtained pellet is D = 88%. The thickness and surface of the pellet are e = 0.36 cm and S = 0.454 cm², respectively. The electrical measurements of the obtained sample were carried out using complex impedance spectroscopy in the temperature range of 260–380 °C. The recorded spectra are shown in Figure 9.

The best fits of impedance spectra were obtained when using a conventional electrical circuit R_g//CPE_g-R_gb//CPE_gb, where CPE are constant phase elements (Figure 9a) and subscripts g and gb indicate bulk grain and grain boundary contribution, respectively:

$$ZCPE=\frac{1}{A\left(jɷ\right){)}^p}$$

(2)

The true capacitance was calculated from the pseudo-capacitance according to the following relationships:

$${ɷ}_0={\left(RA\right)}^{-1/p}={\left(RC\right)}^{-1}$$

(3)

(where ω₀ is the relaxation frequency, A is the pseudo-capacitance obtained from the CPE, and C is the true capacitance.

The electrical parameter values calculated at different temperatures are shown in Table 4. The values of the capacities C_gk and C_gbk are approximately 10⁻¹¹ and 10⁻¹⁰ Fcm⁻¹ for the bulk and grain boundaries, respectively [15]. In fact, with a relative density of D = 88%, the conductivity of the prepared sample (

Table 7. Electrical parameters values of equivalent circuits of Na₂CuP_1.5As_0.5O₇ determined by impedance spectroscopy at 260–380 °C.

T (°C)	T (K)	Rg (104 Ω)	Ag (10−10 F sp−1)	Cgk (10−11 Fcm−1)	Rgb (104 Ω)	Agb (10−10 F sp−1)	Cgbk (10−10 Fcm−1)	Rt (104 Ω)	ρt (104 Ω cm)	σ (10−5 S cm−1)	σd (10−5 S cm−1)
260	533	5.54	2.1	2.0	17.04	1.7	1.7	22.58	28.58	0.35	1.59
290	563	2.70	3.4	3.3	7.82	1.8	1.70	10.52	13.32	0.75	3.41
320	593	1.43	3.4	3.3	4.18	1.5	1.5	5.61	7.10	1.41	6.41
350	623	1.21	3.4	3.3	2.26	1.4	1.3	3.47	4.39	2.28	10.36
380	653	1.01	8.4	8.0	1.51	1.2	1.2	2.52	3.19	3.13	14.23

) increases from 0.35 10⁻⁵ Scm⁻¹ at 260 °C to 3.13 10⁻⁵ Scm⁻¹ at 380 °C. On the other hand, the 12% porosity of our sample prompted us to estimate the conductivity values of the fully dense sample of Na₂CuP_1.5As_0.5O₇ using the empirical formula proposed by Langlois and Coeuret [32]:

$$\sigma =\frac{\left(1-\mathrm{P}\right)}{4}{\sigma }_{\mathrm{d}}$$

(4)

where σ and σ_d are the electrical conductivity of porous and dense samples, respectively. P is the porosity of the sample.

This correction has been used in previous works such as Na₂CoP_1.5As_0.5O₇ [15]. Taking into account the porosity factor P = 0.12, the conductivity value of dense material will be σ_d = (4σ/0.88). The conductivity values of dense sample calculated at different temperatures are summarized in Table 7. In this case, the experimental conductivity of 3.5 10⁻⁶ Scm⁻¹ corresponds to the corrected value of 1.59 10⁻⁵ Scm⁻¹ at 260 °C.

The curve Ln (σ × T) = f (1000/T) is linear (Figure 10), satisfying the Arrhenius law LnσT = Lnσ₀ − Ea/kT (k = Boltzmann constant). The activation energy calculated from the slope of this curve is Ea = 0.60 eV.

The electrical investigation of the studied material shows that the activation energy, which is unaffected by porosity and thus easier to use for comparison, decreases for Na₂CuP_1.5As_0.5O₇ compared to that of Na₂CuP₂O₇ [33], i.e., 0.60 eV and 0.89 eV, respectively. Consequently, the effect of P/As substitution increases the electrical conductivity of the parent material Na₂CuP₂O₇ at lower temperatures [33]. Overall, a comparison of the conductivity values of the studied material Na₂CuP_1.5As_0.5O₇ (at T = 350 °C, σ_{D = 88%} = 2.28 × 10⁻⁵ Scm⁻¹; σ_d = 2.28 × 10⁻⁴ Scm⁻¹ and Ea = 0.60 eV) with those found in the literature shows that our material can be classified among the fast ionic conductors as shown in

Table 8. Activation energies of ionic conductivity for some sodium-ion materials.

Material	Activation Energy (eV)	Temperature Range (°C)	Ref.
Na2CuP1.5As0.5O7	0.60	260–380	current work
Na2CoP1.5As0.5O7	0.56	240–360	[15]
Na1.14K0.86CoP2O7	1.34	360–480	[24]
Na2.84Ag1.16Co2(P2O7)2	1.36	510–630	[34]
NaCo2As3O10	0.48	160–410	[35]
Na4Co5.63Al0.91(AsO4)6	0.56	400–550	[36]
Na2Co2(MoO4)3	1.20	180–513	[37]

.

3.7. BVSE Simulation: Na⁺ Migration Pathways in Na₂CuP_1.5As_0.5O₇

The BVSE calculation revealed in addition to the equilibrium site Na1, the presence of two interstitials sites (i1 to i2) and ten saddle points (s1 to s10) (

Table 9. Bond-valence sites energies and positions of equilibrium site (Na1), interstitial sites (i1 and i2) and saddle points (s1 to s10).

Site	x	y	z	Energy (eV)
Na1	0.185	0.611	0.701	0.000
i1	0.524	0.875	0.424	0.288
i2	0.262	0.194	0.986	0.715
s1	0.560	0.125	0.632	0.354
s2	0.226	0.083	0.215	0.466
s3	0.006	0.389	0.250	0.550
s4	0.125	0.528	0.069	0.602
s5	0.250	0.250	0.000	0.749
s6	0.173	0.431	0.958	0.870
s7	0.714	0.208	0.583	0.960
s8	0.821	0.708	0.375	1.260
s9	0.190	0.333	0.653	1.289
s10	0.167	0.361	0.833	1.643

). Thus, there are ten local pathways as shown in

Table 10. Local transport pathways in the anionic framework, energetic barrier (eV) and hop distance (Å).

Local Path	Site 1	Saddle	Site 2	Barrier (eV)	Hop Distance (Å)
1	i1	s1	Na1	0.354	1.904
2	Na1	s2	Na1	0.466	3.119
3	i1	s3	i1	0.261	4.145
4	i1	s4	Na1	0.602	2.593
5	i2	s5	i2	0.033	0.955
6	i2	s6	i1	0.582	2.922
7	i2	s7	Na1	0.960	3.282
8	i1	s8	Na1	1.260	3.168
9	Na1	s9	i1	1.289	3.168
10	i2	s10	i1	1.355	3.956

. Figure 11 shows the position of equilibrium sites and interstitial sites in the unit cell.

Figure 11 shows that the migration along the b direction does not involve any interstitial sites, and the diffusion occurs from the equilibrium site Na1 to its symmetry image, with a jump distance of approximately 3.119 Å and with an activation energy of approximately 0.466 eV (Figure 12a).

Along the c direction, Figure 11 shows that the sodium moves from the Na1 position to the interstitial sites i2 then to i1 to reach the equivalent Na1 site (Figure 12b) with an activation energy along this direction of approximately 0.96 eV (Figure 12b).

Along the a direction, the sodium atoms pass through the following sites: Na1-i1-i1-Na1-i2. The activation energy along this direction is approximately 0.96 eV (Figure 12c). Thus, the activation energy of the title compound for 1D and 3D ionic conductivity is approximately 0.466 eV and 0.96 eV, respectively. Figure 13 shows the isosufaces of conduction pathways.

Consequently, based on the BVSE calculations, the fast ionic conductivity observed for the material can be explained by the three-dimensional mobility of Na⁺ ions in the inter-ribbon space, likely with more favorable diffusion along the b-axis.

4. Conclusions

A new quaternary oxide Na₂CuP_1.5As_0.5O₇ was identified in the Na₂O-CuO-P₂O₅-As₂O₅ system. It crystallizes in the monoclinic C2/c space group and is isostructural to β-Na₂CuP₂O₇. The partial substitution of P appears to be beneficial for ionic conductivity as the material exhibits lower activation energy of 0.6 eV vs. 0.89 eV for the parent β-Na₂CuP₂O₇. According to the impedance spectroscopy performed on the 88% dense pellet, the bulk ionic conductivity reaches the value of 2.28 10⁻⁵ Scm⁻¹, which allows Na₂CuP_1.5As_0.5O₇ to classify as a fast ion conductor. The bond-valence site energy calculations suggest that the Na⁺ diffusion is three-dimensional with some preference for transport along the b axis.