Li-ion conduction in novel Scandium and Gallium doped Li 1.3 Al 0.29 Ga 0.005 Sc 0.005 Ti 1.7 (PO 4 ) 3 NASICON compound

doi:10.21203/rs.3.rs-2824061/v1

Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP) has a high Li⁺ conductivity of ~ 10^− 3 S/cm which can be employed as an inorganic solid electrolyte for solid state batteries. Here we report the electrical properties of gallium and scandium doped forms of LATP viz. Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP), Li_1.3Al_0.29Ga_0.01Ti_1.7(PO₄)₃ (LAGTP) and Li_1.3Al_0.29Sc_0.01Ti_1.7(PO₄)₃ (LASTP) and Li_1.3Al_0.29Ga_0.005 Sc_0.005Ti_1.7(PO₄)₃ (LAGSTP). All the samples were prepared by solid state reaction method. Structural characterization was carried out using X-ray diffraction (XRD) and Fourier Transform Infrared (FTIR) techniques whilst electrical properties were studied using Electrochemical Impedance Spectroscopy (EIS). It was found that the larger cations Ga³⁺ and Sc³⁺ at octahedral sites change the Ti–O–P bond angle in LTP lattice. This distortion of lattice on ion-ion correlation and subsequently on Li⁺ ion conduction in the novel LAGSTP material was found to decrease the Li⁺ ion conductivity to ~ 10^− 5 S/cm.

Li-conducting NASICON

Gallium

Scandium doping

XRD

FTIR

Impedance spectroscopy

Collective correlation factor

Primary and secondary type of Lithium Ion batteries (LIBs) are a commonplace in mobile phones, laptops as well as in wearable and medical diagnostic devices need to be compact, light-weight and safe power sources. The LIB market can be broadly segmented (based on energy output) as that comprising of less than 3000 mAh, between 3000 and 10000 mAh, between 10000 mAh and 60000 mAh and more than 60000 mAh. While wearable devices and sensors use LIBs upto a few hundred mAh capacity, devices like laptops and mobile phones use LIBs below 10000 mAh. There is a high demand of secondary (rechargeable) LIBs in this segment. These batteries use ionic liquids (IL) as electrolytes which have a high ionic conductivity and provide good contact with electrodes. But they are leakage prone and unsafe due to formation of dendrites (which are formed due to parasitic chemical reactions between liquid electrolyte and the lithium metal anode). Over a period of time, the dendrites grow and cause short circuit which results in fire or explosion in the battery [1, 2, 3]. Therefore, solid (instead of liquid) electrolytes which deliver high power density and retain high capacity over longer time periods in LIBs are suggested [4, 5]. Ceramic Li-ion conducting Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP) as powder which has a Li⁺ conductivity ~ 10^− 3–10^− 4 S/cm at room temperature [6, 7] is one such widely studied material which belongs to Li-conducting NASICON (Na Super Ionic Conductor) class of compounds. Its structural base is LiTi₂(PO₄)₃ (LTP) which consists of mutually facing TiO₆ octahedra joined by PO₄ tetrahedra by their corner sharing oxygen atoms [8, 9, 10]. Long parallel chains of mutually facing TiO₆ octahedra are connected by PO₄ tetrahedra (Fig. 1). Vacancies between mutually facing octahedral units at 6b Wyckoff position are called M1 sites which have 6-fold oxygen coordination, while the vacancies at 18e Wyckoff position between octahedral and tetrahedral units between two parallel chains are called M3 sites, which have a 10-fold oxygen coordination. Li⁺ diffuse in the 3D pathways (called conduction bottlenecks/channels) wherein from one to the next vacancy. The arrangement of vacancy sites resembles M1-M3-M1-M3-M1... in these channels. The Li⁺ at M1 site (6b Wyckoff position) is surrounded by six oxygen atoms which makes a LiO₆ trigonal antiprism formed by corner sharing oxygen from surrounding PO₄ tetrahedra. The three oxygen atoms each form the lateral face of LiO₆ polyhedron. (Please refer the red lines marking the sides of a LiO₆ polyhedron in Fig. 1).

The substitution of Ti⁴⁺ by trivalent cation Al³⁺ creates \({Al}_{Ti}^{{\prime }}\) charge vacancy defect in Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP). This charge deficit is compensated when a diffusing Li⁺ ion arrives at this site. They are the interstitial Li⁺ ion (denoted by \({Li}_{i}^{.}\)). LATP owes it super ionic conductivity due to them. \({Li}_{i}^{.}\) are found on either side of Al at the octahedral position [\({{A}{l}}_{{O}}\)] [11, 12, 13, 14] in 36f Wyckoff position. (These sites are denoted as \({\mathbf{M}3}^{{{\prime }}}\) in Fig. 1). Thus, the vacancies have M1–\({\mathbf{M}3}^{{{\prime }}}\)–M3–M1–\({\mathbf{M}3}^{{{\prime }}}\)–M3 arrangement at \({{L}{i}}_{6b}\)–\({{L}{i}}_{36f}\)–\({{L}{i}}_{18e}\)– \({{L}{i}}_{6b}\)–\({{L}{i}}_{36f}\)–\({{L}{i}}_{18e}\) Wyckoff positions (refer Fig. 1). It has been shown that the interstitial \({Li}_{i}^{.}\) at \({\mathbf{M}3}^{{{\prime }}}\) position have low activation barrier of ~ 0.25 eV [15, 16] compared to ~ 0.45 eV barrier at M1 site. The multi-ion correlation between Li⁺ (which can be interstitial \({Li}_{i}^{.}\) as well) support the superior Li⁺ conductivity in LATP [13, 17].

In the present study, the trivalent cations Al³⁺, Ga³⁺ and Sc³⁺ with increasing ionic radii are doped to substitute Ti⁴⁺ and thereby create charge vacancy defects like \({Al}_{Ti}^{{\prime }}\), \({Ga}_{Ti}^{{\prime }}\) and \({Sc}_{Ti}^{{\prime }}\) respectively. As shown in Table-1 nominal sample LATP and gallium and scandium doped LATP samples are created. As a result of decrease in the proportion of aluminum the number of \({Al}_{Ti}^{{\prime }}\) vacancy sites would decrease but the number of interstitial \({Li}_{i}^{.}\) would remain same. The substitution leads to an increase of LTP lattice volume but also distorts the Ti–O–P bond. Several factors including the type and amount of dopant(s), the preparation routes and conditions therein, the sintering temperature and conditions of measurement influence the Li⁺ conductivity in the novel triply doped mixed phase LAGSTP compound. In the following, we discuss the structural changes and how they impact the multi-ion correlation function and thereby the Li⁺ conductivity in the compounds.

Table 1

Nomenclature, chemical formula and wt% of dopant.
Sample Name	Stoichiometric composition of the compound	Al	Ga	Sc
LATP	Li_1.3Al_0.3Ti_1.7(PO₄)₃	2.11%
LAGTP	Li_1.3Al_0.29Ga_0.01Ti_1.7(PO₄)₃	2.04%	0.18%
LASTP	Li_1.3Al_0.29Sc_0.01Ti_1.7(PO₄)₃	2.04%		0.12%
LAGSTP	Li_1.3Al_0.29Ga_0.005Sc_0.005Ti_1.7(PO₄)₃	2.04%	0.09%	0.06%

2.1 Sample preparation

The solid ceramic samples were prepared by mixing 99.9% pure laboratory grade powders of lithium carbonate (Li₂CO₃), ammonium dihydrogen phosphate (NH₄H₂(PO₄)), scandium oxide (Sc₂O₃), gallium oxide (Ga₂O₃), titanium oxide (TiO₂), alumina (Al₂O₃) (Loba Chemie, Mumbai, India) were taken according to the weight percentages of each sample. The powders were mixed thoroughly and ground in a mortar for 30 minutes. Ethanol was added during grinding to ensure proper mixing of the constituents. The resulting fine powder was heated to 200°C for 30 minutes in an open ceramic ampoule. The mix was allowed to cool slowly. The mixture was again ground and heated to 800°C for 5 hours and left in furnace to cool slowly. The mixture was ground to a fine powder and uniaxial cold pressed at 70 Mpa in a pelletizing machine. The resulting cylindrical pellets of 3 mm thickness and 10 mm diameter were heated to 900°C for 8 hours and then allowed to cool slowly. Solid, hard, white ceramic pellets were then subjected to characterization studies as mentioned below.

2.2 Sample Characterization

2.2.1 X-ray Diffraction (XRD)

X-ray diffraction (XRD) was performed using Rigaku MiniFlex CuKα line (λ = 1.5405 Å) in the range of 10° to 70° to determine the primary and secondary phases in the material. Structural refinement was performed on the XRD data using the Match! ver 3.10.1.169 program. After appropriate background correction the peaks corresponding to the main LiTi₂(PO₄)₃ (LTP) phase were identified on basis of their positions. Smoothening procedure was also applied on the peaks. Peaks corresponding to secondary phases were also identified (please refer Supporting Information for details of secondary phases).

2.2.2 Fourier Transform Infrared (FTIR) Spectroscopy

Finely ground 5 mg sample powder was mixed with approximately 5 g potassium bromide (KBr) and ground to prepare ~ 0.5 mm thickness pellets. FTIR (JASCO model FT/IR-4100 type A) was performed in transmittance mode, in the energy range of 350 cm^− 1 to 1600 cm^− 1 with a step size of 3.85 cm^− 1. The FTIR spectrometer was operated by an interfacing computer via Spectrum Manager program. Shift in the peaks corresponding to different modes was determined from the resulting data.

2.2.3 Electrochemical Impedance Spectroscopy (EIS)

Flat surfaces of the cylindrical sample pellets were polished and a thin layer of silver paint was applied on both surfaces. A sample holder with copper collecting plates of the same diameter as that of pellets was used. The assembly was mounted in a cylindrical furnace in which the temperature was controlled by an automatic thermostat controller. The arrangement was interfaced to a Precision LCR meter (model Agilent E4980A) which measured the impedance in a frequency range of 2 MHz to 1Hz and in temperature range of 20°C to 100°C for each sample. The amplitude of the ac signal was fixed at 500 mV and 0.5 V dc biasing voltage was applied during the measurements for all samples.

3.1 X-ray Diffraction

Figure 2 shows XRD plots of all samples. All major peaks of LTP are marked by o symbol in the Fig. 1. LTP corresponds to space group R\(\stackrel{-}{3}\)c. Lattice parameters deduced from XRD data is presented in Table-1. Values of lattice parameters a and c increase in doped samples. This is attributed to the substitution of Ti⁴⁺ cation by larger sized dopant cations Ga³⁺ and Sc³⁺. Additional phases deduced from XRD can be noted from Figs. S1 and S2 in the Supporting Information (SI). It has been noted in a number of studies that tiny amounts of oxide or phosphate phases are formed during synthesis which increase the density of material [18, 19, 20].

Table 2

Lattice parameters deduced from XRD data for all samples.
Sample Name	a (Å)	c (Å)	Lattice Volume (V)
LATP	8.4962	20.1980	1683.55
LAGTP	8.4783	20.9970	1742.78
LASTP	8.4876	20.9400	1741.87
LAGSTP	8.4824	20.9988	1744.62

The substitution in the lattice is governed by the difference in ionic radii of host (\({{r}}_{2}\)) and dopant cations (\({{r}}_{1}\)) denoted by 𝜟r = \({r}_{1}\)–\({r}_{2}\). If the ratio (𝜟r/\({r}_{2}\)) has a smaller value, the dopant cation replaces the host in the lattice [18] without significantly disturbing the crystal structure. However, if the difference value is large, the dopant cation experiences an elastic strain energy as it tries to fit into the lattice site. If the strain energy is large enough, it can lead to segregation of dopant at grain boundary which can have important implications for the properties of the material, such as its electrical conductivity and mechanical strength [18, 21]. As shown in Table-3 below, the ionic size difference between Ga³⁺ and Ti⁴⁺ cations is minimum while that between Sc³⁺ and Ti⁴⁺ is relatively large.

Table 3

Difference of dopant and host cation radius.
Dopant – Host Cation pair	𝜟r = \|\({{r}}_{1}\) – \({{r}}_{2}\)\|	𝜟r/\({{r}}_{2}\) (in %)
Al³⁺ – Ti⁴⁺	0.07	11.67%
Ga³⁺ – Ti⁴⁺	0.02	3.33%
Sc³⁺ – Ti⁴⁺	0.12	20.00%

1) For Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP) sample, the substitution of Ti⁴⁺ (VI) (0.605 Å) by \({Al}_{O}\)³⁺ (VI) (0.535 Å) creates vacancy defects \({Al}_{Ti}^{{\prime }}\) which are filled by interstitial \({Li}_{i}^{.}\) as stated above.

2) For Li_1.3Al_0.29Ga_0.01Ti_1.7(PO₄)₃ (LAGTP), the ionic size difference (𝜟r) between Ga³⁺ (VI) (0.62 Å) and Ti⁴⁺ (VI) (0.605 Å) is small (Table–2), hence the substitution is easily possible. A charge vacancy defect \({Ga}_{Ti}^{{\prime }}\) is created. A slightly larger sized Ga³⁺ though increases the LTP lattice volume (Table–2) [22].

3) Similarly, for Li_1.3Al_0.29Sc_0.01Ti_1.7(PO₄)₃ (LASTP), the size difference (𝜟r) between Ti⁴⁺ (VI) (0.605 Å) and Sc³⁺ (VI) (0.745 Å) creates charge defect \({Sc}_{Ti}^{{\prime }}\) and increases the LTP lattice volume (Table–2) [23].

4) In Li_1.3Al_0.29Ga_0.005Sc_0.005Ti_1.7(PO₄)₃ (LAGSTP), Al³⁺, Ga³⁺ and Sc³⁺ cations are present which substitute Ti⁴⁺ and create vacancy defects \({Al}_{Ti}^{{\prime }}\), \({Ga}_{Ti}^{{\prime }}\) and \({Sc}_{Ti}^{{\prime }}\) in the LTP lattice of this sample.

The substitution of Ti⁴⁺ by larger Ga³⁺ and Sc³ cations increases the lattice volume as the value of c parameter increases. Therefore, the bond length of M–O in the covalent M–O–P bond (where M = Ti, Ga, Sc) changes. The decrease in charge results in change of the electronic configuration. This can be deduced by calculating the electronegativity on each of the element in M–O–P bond. The average excess positive and negative charges (δ) on the elements of M–O–P bond is calculated using Sanderson’s procedure [24, 25] and summarized in Table–5. It can be seen that there is an increase in negative charge on oxygen when Ti⁴⁺ is substituted by lower oxidation state cations Ga³⁺ and Sc³⁺ in the M–O bond. Due to this the electrons from P are drawn closer to the oxygen in O–P bond, which distorts the M–O–P bond. This position of oxygen in the O–P–O and O–Ti–O changes.

Table 4

Average excess charge on each element in M–O–P bond (where M = Ti, Ga, Sc).
For Ti–O–P bond
δ_Ti	0.3296	δ_O	-0.33051	δ_P	0.19723
For Ga–O–P bond
δ_Ga	0.171264	δ_O	-0.68095	δ_P	0.23855
For Sc–O–P bond
δ_Sc	0.433459	δ_O	-0.43346	δ_P	0.20955

Alamo et al [26, 27] have suggested that in NASICON systems like NaZr₂P₃O₁₂ (NZP) the shift in position of oxygen results in change of rotation between angles formed by plane formed by O–P–O and O–Ti–O bonds in structural model(s) which ultimately leads to anisotropic variation in lattice parameters (decrease in a and increase in c parameter). This is observed in Table-3 for our samples. Padmakumar et al [28, 29] have demonstrated the network flexibility of the \({M}_{2}^{IV}\)(PO₄)₃ (M = cation at octahedral site like Ti) in LTP compound is due the ‘coupled rotation of tetrahedra’ which is noted in Table–1 as anisotropic change in the lattice parameters a and c. From other computational studies it has been suggested (using bond angle variance (BAV) approach) that the distortion of Ti–O–P bond changes the activation energy experienced by Li⁺ inside the conduction bottleneck [14]. The variation in M–O–P bond angle ultimately affects the P–O bond since the TiO₆ octahedra is joined to PO₄ tetrahedra via corner sharing oxygen in the LTP lattice (refer Fig–1). In the below, we discuss the impact on O–P bond from FTIR study.

3.2 Fourier Transform Infrared Spectroscopy

The stretching and bending vibratory modes of P–O–P bond (in (PO₄)³⁻ group) in the wave number (energy) range of 350–1600 cm^− 1 are discussed. Fig, 3(a) shows modes of P–O–P bond in the range 350–700 cm^− 1 and Fig. 3(b) shows in 700–1600 cm^− 1 range. The band at 412 cm^− 1 (Fig. 3(a)) represents symmetric bending modes of O–P–O bond in (PO₄)⁻³ units [30] for nominal composition LATP which shifts to 431 cm^− 1 for doped samples. The asymmetric bending mode bands of O–P–O bond at 509 cm^− 1 energy for LATP shifts to 512 cm^− 1 for LAGSTP sample [30, 31]. The band at 632 cm^− 1 in LATP, LAGTP and LAGSTP represents the asymmetric stretching mode [30, 32] shifts to 628 cm^− 1 for LASTP sample.

In the following we describe change in the P–O–P bond between two PO₄ tetrahedra joined via a corner sharing oxygen. The band at 744 cm^–1 for LATP, LAGTP and LASTP samples for asymmetric bending modes of P–O–P bond [31] shifts to 748 cm^− 1 for LAGSTP sample. The rattling vibrations of a mobile Li⁺ ion at the M1 vacancy sites in the LTP lattice [31] disturbs the electronegative charge configuration of oxygen thereby affecting the asymmetric bending modes of the P–O–P bond. It is further affected by the electro-repulsive influence of other of Li⁺ in nearby vacancy sites (discussed further in text). In case of doped samples, this configuration is further affected by substitution of Ti⁴⁺ by Ga³⁺ or Sc³⁺ which is seen as a shift to 748 cm^− 1 for LAGSTP sample.

A small shift from 833 cm-1 (for LATP and LAGTP) to 829 cm-1 (LAGSTP) and 836 cm-1 (LASTP) for symmetric stretching mode are observed. Anisotropic shift in asymmetric stretching mode [32] of the P–O–P bond at ~ 971 cm^− 1 (for LATP is noted in Table–5. Some workers [30] have reported the band at ~ 833 cm^− 1 to correspond to P–O–P symmetric stretching of (PO₃)²⁻ unit in LiTi₂(PO₄)₃ [33]. The shift in the bands observed in all of the above observation is due to change in restoring force of the covalent bond which is modified due to entry of dopant cations in the LTP lattice. The restoring strength of a covalent bond is given by force constant (k) as follows:

\(\stackrel{-}{{\nu }}\) = \(\frac{1}{2\pi c}\) [\(\sqrt{\frac{k}{\mu }}\) ] where reduced mass µ = \(\frac{1}{{m}_{1}}\) + \(\frac{1}{{m}_{2}}\)….. (1)

where \({{m}}_{1}\) and \({{m}}_{2}\) are atomic masses of P and O in this case. \(\stackrel{-}{{\nu }}\) is the wave number corresponding to a given band. It can be noted from Table–5 that the wave number and hence the force constant (k) differs for doped samples compared to nominal composition LATP.

Table 5

Asymmetric and Symmetric bending and stretching modes of O–P–O and P–O–P bonds in (PO₄)^3- tetrahedral units and calculated values of force constant k.
Sample Name	Asymmetric Bending of O–P–O bond		Symmetric Bending of O–P–O bond		Asymmetric Stretching of O–P–O bond		Symmetric Stretching of O–P–O bond
Sample Name	Wave Number (cm^− 1)	Force Constant (k)	Wave Number (cm^− 1)	Force Constant (k)	Wave Number (cm^− 1)	Force Constant (k)	Wave Number (cm^− 1)	Force Constant (k)
LATP	509	0.09701	412.69	0.06377	632.53	0.14982	578	0.1251
LAGTP	509	0.09701	412.69	0.06377	632.53	0.14982	578	0.1251
LASTP	509	0.09701	416.54	0.06497	628.68	0.14800	578	0.1251
LAGSTP	512	0.09816	431.97	0.06987	632.53	0.14982	578	0.1251

Sample name	Asymmetric Bending of P–O–P bond		Asymmetric Stretching of P–O–P bond		Symmetric Stretching of P–O–P bond
Sample name	Wave Number (cm^− 1)	Force Constant (k)	Wave Number (cm^− 1)	Force Constant (k)	Wave Number (cm^− 1)	Force Constant (k)
LATP	744.38	0.20749	971.94	0.35374	833	0.25983
LAGTP	744.38	0.20749	975.8	0.35655	833	0.25983
LASTP	744.38	0.20749	968.09	0.35094	836	0.26171
LAGSTP	748.24	0.20964	971.94	0.35374	829	0.25734

The increase in the value of force constant for doped samples suggests a rigidity induced by distortion and an increase in the electronegativity on oxygen atom in the O–P and P–O bonds as stated earlier.

In the following we discuss the results of electrical (Li⁺) conductivity. The distortion of LTP lattice and its effect on collective correlation factor which affects the Li⁺ conductivity are considered.

3.3 Electrical Conductivity

Figure 4 shows conductivity plots as a function of frequency for all samples. The nominal composition sample LATP has highest whilst LASTP has the lowest value of conductivity.

From the variation in the length of mid frequency plateau region and the power law behavior in high frequency region it can be suggested that the mode of conductivity relaxation is different for all the four samples. Figure 5 shows conductivity isotherm for LATP and LAGSTP samples. The Li⁺ conductivity of LATP is atleast an order higher than LAGSTP. The conductivity increases with temperature for both the samples. The conductivity data is fitted (shown as solid lines) using power law stated as equation–2 [34]:

\({\sigma }^{{\prime }}\left(\omega \right)\) = \({\sigma }_{d}\) + \({A\omega }^{n}\) …... (2)

Here \({\sigma }^{{\prime }}\left(\omega \right)\) is the frequency dependent conductivity, \({\sigma }_{d}\) is the dc conductivity which can be noticed as a plateau in the low/mid frequencies, A is the conductivity pre-factor term while n is the frequency exponent.

The plateau in mid frequency range indicates frequency independent (dc conductivity) translational diffusional motion of Li⁺ whereas the power law behavior shows a strong frequency dependence in high frequency region. The cross-over from diffusional dc conductivity to hopping ac conductivity occurs at cross over frequency (ν*) is marked. From Fig. 5 it can be inferred that for both the samples and temperature, the condition \({\sigma }^{{\prime }}\left({\nu }^{*}\right)\) = 2\({\sigma }_{d}\) holds true. It can also be noted that the length of the plateau (from onset to the crossover) is more for LATP. The distortion of covalent M–O–P bond and the associated rigidity (given by force constant k) in the modified lattice of doped sample LAGSTP change the ion relaxation behavior. So far we have discussed the changes in lattice structure in which Li⁺ ions diffuse. In the below we discuss the dynamics of Li⁺ in the lattice. The ionic conductivity (σ) according to the Nernst-Einstein equation is given as follows:

\({{\sigma }}_{{i}{o}{n}{i}{c}}\) = \(\frac{{{F}}^{2}}{{R}{T}{{H}}_{{R}}}\) . \(\sum _{i}{c}_{i}{D}_{i}^{*}\) ….. (3)

Here \({{c}}_{{i}}\) denotes the concentration of ion, R is the gas constant, T is the temperature and \({{H}}_{{R}}\) is the Haven’s ratio while \({{D}}_{{i}}^{{*}}\) indicates the self-diffusion coefficient of the ion. The term \({{D}}_{{i}}^{{*}}\) includes self-correlation of an ion due to forward and backward hopping of the ion. That is, the ion can jump back to the same vacancy site from where it performed forward hop. When the nearby ions are perturbed by electro-repulsion due to random back and forward jumps of a single ion in the vacancy site, it is termed as multi-ion correlation and denoted by Haven’s ratio \({{H}}_{{R}}\). We discuss two scenarios for multi-ion correlation in the below.

As shown in Fig. 6(a), a Li⁺ ion (either from M1, M3 or \({\mathbf{M}3}^{\mathbf{{\prime }}}\) sites) performs self-correlation motion as it hops forward to a vacancy and then jumps back to its original site. As shown in Fig. 6(b) this self-correlation motion of Li⁺ ion at site-1 (Li1) jumps forward to a vacancy site-1 (Li1-Vac) can perturb (shown by dashed lines) a nearby Li⁺ at site-2 (Li2) to jump into a nearby vacancy site to its nearest vacancy site (Li2-Vac). Such successful jumps contribute to Li⁺ conductivity. Similarly, as shown in Fig. 6(c), a Li⁺ at site-2 (Li2) perturbs and repels Li⁺ at Li1 site. As a result, the Li⁺ at Li1 jumps to a nearby vacancy site called Li1-Vac site while Li⁺ from Li2 site jumps to just vacated Li1 site. Since the activation energy of interstitial Li⁺ at \({\mathbf{M}3}^{\mathbf{{\prime }}}\) sites is low, such multi-ion correlation the scenarios noted in Fig. 6(b) and Fig. 6(c) are possible in the 3D conduction pathways (channels). According to He et al [17], this type of ‘concerted motion’ due to collective behavior of Li⁺ is responsible for a superior Li⁺ conductivity in LATP.

The equation-3 can be written as:

σ = \(\frac{{{N}({z}{e}}^{2})}{{k}{T}}\). \({{D}}_{{\sigma }}\) ….... (4)

where diffusion coefficient is given as \({{D}}_{{\sigma }}\)=\(\frac{{{D}}^{{*}}}{{{H}}_{{R}}}\) …..… (5)

The inset contains plot for LASTP sample (in blue color).

Experimentally, the Haven’s ratio \({{H}}_{{R}}\) is calculated from tracer diffusion studies. Recently, Roling et al [35] have calculated the collective correlation factor \({{f}}_{{l}}\)(which contains information about multi-ion correlation) from the electrical conductivity data as follows:

\({{f}}_{{l}}\) = \(\frac{6 {{\sigma }}_{{i}{o}{n}}{R}{T}}{{{c}}_{{L}{i}}{{F}}^{2}{{a}}^{2}{{\nu }}^{{*}}}\) …..... (6)

where R, T, F, a and ν* denote the gas constant, temperature, Faraday’s constant, inter-ion jump distance and cross over frequency respectively. The value of a (~ 0.3–0.63 nm) and Li + concentration as ~ 10²⁷/m³. The collective correlation factor (\({{f}}_{{l}}\)) plotted in Fig. 7 as a function of temperature in general shows an increase with temperature. \({{f}}_{{l}}\) is highest for LATP while lowest for LASTP. \({{f}}_{{l}}\) depends on the inter-ionic jump (a) distance between nearest neighbor sites as follows [35]:

\({{f}}_{{l}}\) = <\({r}^{2}{(t}^{*})>/2{a}^{2}\) …….. (7)

where \({r}^{2}{(t}^{*})\) is ion–ion correlation in time \({t}^{*}\). As noted in Table–2, due to the large lattice volume of LAGSTP, the distance between neighboring sites (a) decreases the value of \({{f}}_{{l}}\). Therefore, doping of larger cations Ga³⁺ and Sc³⁺ lowers the ion-ion correlation and hence the Li⁺ conductivity.

Nominal composition sample Li_1.3A_0.3Ti_1.7(PO₄)₃ (LATP) along with its gallium and scandium doped counterparts were prepared via solid state reaction method in a single batch. The XRD study revealed LTP as a primary phase in all samples. The changes in structure (Table–2) and electronegativity (Table–4) with respect to ionic size are discussed for the substitution of Ti⁴⁺ by larger cations Ga³⁺ and Sc³⁺. It was found that the substitution increased the LTP lattice volume but also distorted it. By computing the electronegativity charge on each of the elements of M–O–P bond, and from anisotropic behavior of lattice parameters it was inferred that the distortion in LTP lattice in doped samples is due to change in bond length and bond angle of M–O–P and P–O–P bonds. From the FTIR study, the shift in stretching and bending modes was quantified and it was inferred that the dopant induced a rigid character in the covalent bond which affected the characteristic flexibility associated with the LTP lattice. Earlier computational results have attributed the unique high Li⁺ conductivity of the LTP and LATP to the flexible character of the \({M}_{2}^{IV}\)(PO₄)₃ NASICON framework [28]. Thus, loss of flexibility due to presence of large ionic sized dopant impurities contributes to lowering of the Li⁺ conductivity in doubly doped LAGTP and LASTP as well as triply doped LAGSTP samples. Finally, the effect of all the above factors viz. enlargement and distortion in the lattice, the change of force constant of the bond and its effect on conductivity relaxation, was discussed using the recently proposed concept of concerted ionic motion in multi-ion. Scenarios leading to collective correlation function were discussed. A lower value of collective correlation was found to be associated with lower Li⁺ conductivity in doped samples. It was found that a combination of electrostatic repulsive force and a relatively low value of activation barrier in an optimally sized lattice helps Li⁺ perform a concerted/coordinated (forward or backward) hopping to nearest vacancy sites in the 3D conduction pathways. To this end, the size of dopants plays an important role. We believe that the results of this study can be extended to plan future samples to work as catholytes as the novel doubly or triply doped materials are dense (due to oxide phases), chemically safe and exhibit mixed ion-electron conductivity and thereby cut cost in manufacturing and packaging of LIBs.

Acknowledgements

We gratefully acknowledge the support from Physics Department, The M.S University of Baroda, India, for providing the facilities to prepare and characterize the samples for the present study. DHK would like to thank Dr. Holger Putz, (https://www.crystalimpact.de/match) for support and guidance in structural refinement of XRD data. DHK would also like to specially thank Prof Bernhard Roling (University of Marburg, Germany) for guidance and support with ion-ion correlation factor calculations.

Ethical Approval

No experiments about human or animals were conducted.

Competing interests

The authors declare that there are no competing or conflicting interests.

Authors' contributions

Conceptualization and Methodology: Dharmesh Kothari, D. K Kanchan

Material Preparation and Data Collection: Dharmesh Kothari, Ketan Chaudhari

Data analysis and Investigations: Dharmesh Kothari, Deepak Kumar

Original Draft Preparation: Dharmesh Kothari

Review and Editing: Dharmesh Kothari, D. K Kanchan, Deepak Kumar, Ketan Chaudhari

Supervision: D. K Kanchan

All authors read and approved the final manuscript.

Funding

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SupportingInformation.docx

Li-ion conduction in novel Scandium and Gallium doped Li 1.3 Al 0.29 Ga 0.005 Sc 0.005 Ti 1.7 (PO 4 ) 3 NASICON compound

Status:

Version 1

Abstract

Figures

1. Introduction

2. Experimental

2.1 Sample preparation

2.2 Sample Characterization

2.2.1 X-ray Diffraction (XRD)

2.2.2 Fourier Transform Infrared (FTIR) Spectroscopy

2.2.3 Electrochemical Impedance Spectroscopy (EIS)

3. Results And Discussion

3.1 X-ray Diffraction

3.2 Fourier Transform Infrared Spectroscopy

3.3 Electrical Conductivity

4. Conclusion

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1