Crystal structure

Lithium-containing NASICON-type crystals are described by the general formula LiM
₂(PO
₄)
₃, in which M stands for a metal or a metalloid (Ti, Zr, Hf, Sn, Ge),^[5] and display a complex three-dimensional network of corner-sharing MO
₆ octahedra and phosphate tetrahedra.^[7] Lithium ions are hosted in voids in between, which can be subdivided into three kinds of sites:^[2][6]

• Li(1) 6-fold coordinated sites at Wyckoff 6b position;
• Li(2) sites at Wyckoff 18e position;
• Li(3) sites at Wyckoff 36f position.

LGP crystal structure (top view).^[6]

In order to promote lithium conductivity at sufficiently high rates, Li(1) sites should be fully occupied and Li(2) sites should be fully empty.^[5] Li(3) sites are located between Li(1) and Li(2) sites and are occupied only when large tetravalent cations are present in the structure, such as Zr, Hf, and Sn.^[8] If some Ge⁴⁺ cations in the LiGe
₂(PO
₄)
₃ (LGP) structure are partially replaced by Al³⁺ cations, the LAGP material is obtained with the general formula Li
_1+xAl
_xGe
_2-x(PO
₄)
₃.^[7] The single-phase NASICON structure is stable with x between 0.1 and 0.6;^[5] when this limit is exceeded, a solid solution is no more possible and secondary phases tend to be formed.^[2] Although Ge⁴⁺ and Al³⁺ cations have very similar ionic radii (0.53 Å for Ge⁴⁺ vs. 0.535 Å for Al^3+[5]), cationic substitution leads to compositional disorder and promotes the incorporation of a larger amount of lithium ions to achieve electrical neutrality.^[2] Additional lithium ions can be incorporated in either Li(2) or Li(3) empty sites.^[8]

In the available scientific literature, there is not a unique description of the sites available for lithium ions and of their atomic coordination, as well as of the sites directly involved during the conduction mechanism. For example, only two available sites, namely Li(1) and Li(2), are mentioned in some cases, while the Li(3) site is neither occupied nor involved in the conduction process.^[5][7] This results in the lack of unambiguous description of LAGP local crystal structure, especially concerning the arrangement of lithium ions and site occupancy when germanium is partially replaced by aluminium.^{[2][5][7][6][9]}

LAGP displays a rhombohedral unit cell with a space group R3c.^[7]

Vibrational properties

Transport properties

LAGP is a solid ionic conductor and features the two fundamental properties to be used as a solid-state electrolyte in lithium-ion batteries, namely a sufficiently high ionic conductivity and a negligible electronic conductivity. Indeed, during battery operations, LAGP should guarantee the easy and fast motion of lithium ions between cathode and anode, while preventing the transfer of electrons.^[3]

As stated in the description of the crystal structure, three kinds of sites are available for hosting lithium ions in the LAGP NASICON structure, i.e. the Li(1) sites, the Li(2) sites and the Li(3) sites. Ionic conduction occurs because of hopping of lithium ions from Li(1) to Li(2) sites or across two Li(3) sites. The bottleneck to ionic motion is represented by a triangular window delimited by three oxygen atoms between Li(1) and Li(2) sites.^[7][6]

The ionic conductivity ${\displaystyle \sigma }$ in LAGP follows the usual dependency on temperature expressed by an Arrhenius-type equation, which is typical of most of solid-state ionic conductors:^[5]

${\displaystyle \sigma ={\frac {\sigma _{0}}{T}}e^{-{\frac {E_{a}}{k_{B}T}}}}$

where

σ₀ is the pre-exponential factor,

T is the absolute temperature,

E_a is the activation energy for ionic transport,

k_B is the Boltzmann constant.

Typical values for the activation energies of bulk LAGP materials are in the range of 0.35 - 0.41 eV.^[12] Similarly, the room-temperature ionic conductivity is closely related to the synthesis conditions and to the actual material microstructure, therefore the conductivity values reported in scientific literature span from 10^–5 S/cm up to 10 mS/cm, the highest value close to room temperature reported up to now.^[2][8][13] Compared to LGP, the room-temperature ionic conductivity of LAGP is increased by 3-4 orders of magnitude upon partial substitution of Ge⁴⁺ by Al³⁺.^[7] Aluminium ions have a lower charge compared to Ge⁴⁺ ions and additional lithium is incorporated in the NASICON structure to maintain charge balance, resulting in an enlarged number of charge carriers. The beneficial effect of aluminium is maximized for x around 0.4 - 0.5;^[2] for larger Al content, the single-phase NASICON structure is not stable and secondary phases appear, mainly AlPO₄, Li
₄P
₂O
₇, and GeO₂.^[14] Secondary phases are typically nonconductive; however, small and controlled amounts of AlPO₄ exert a densification effect which affects in a positive way the overall ionic conductivity of the material.^[2]

The prefactor σ₀ in the Arrhenius equation can in turn be written as a function of fundamental constants and conduction parameters:^[15]

${\displaystyle \sigma _{0}={\frac {1}{3}}{\frac {(Ze)^{2}}{k_{B}T}}nv_{0}l_{0}}$

where

Z is ion valence,

e is the elementary charge,

T is the absolute temperature,

k_B is the Boltzmann constant,

n is the concentration of charge carriers,

v₀ is the average velocity of the ions,

l₀ is the mean free path.

The prefactor is directly proportional to the concentration of mobile lithium-ion carriers, which increases with the aluminium content in the material. As a result, since the dependency of the activation energy on aluminium content is negligible, the ionic conductivity is expected to increase with increasing Ge⁴⁺ substitution by Al³⁺, until secondary phases are formed.^[15] The introduction of aluminium also reduces the grain boundary resistivity of the material,^[2] positively impacting on the total (bulk crystal + grain boundary) ionic conductivity of the LAGP material.

As expected for solid ionic conductors, the ionic conductivity of LAGP increases with increasing temperature.^[15]

Regarding the electronic conductivity of LAGP, it should be as low as possible to prevent electrical short circuit between anode and cathode. As for ionic conductivity, the exact stoichiometry and microstructure, strongly connected to the synthesis method, have an influence on the electronic conductivity, even if the reported values are very low and close to (or lower than) 10^–9 S/cm.^[16][17]

Thermal properties

The specific heat capacity of LAGP materials with general formula Li
_1+xAl
_xGe
_2-x(PO
₄)
₃ fits into the Maier-Kelley polynomial law in the temperature range from room temperature to 700 °C:^[15]

${\displaystyle C_{p}(T)=A+B\cdot T+C\cdot T^{-2}}$

where

T is the absolute temperature,

A, B, C are fitting constants.

Typical values are in the range of 0.75 - 1.5 J⋅g⁻¹⋅K⁻¹ in the temperature interval 25 - 100 °C. The A, B constants increase with the x value, i.e. with both the aluminium and the lithium content, while the constant C does not follow a precise trend.^[15] As a result, the specific heat capacity of LAGP is expected to increase as the Al content grows and the Ge content decreases, which is consistent with data about the relative specific heats of aluminium and germanium compounds.^[15]

In addition, the thermal diffusivity ${\displaystyle \alpha }$ of LAGP follows a decreasing trend with increasing temperature, irrespective of the aluminium content:^[15]

${\displaystyle \alpha \propto T^{-p}}$

The aluminium level affects the exponent ${\displaystyle p}$, which varies from 0.08 (high Al content) to 0.11 (low Al content).^[15] Such small values suggest the presence of a large number of point defects in the material, which is highly beneficial for solid ionic conductors. Finally, the expression for the thermal conductivity can be written:^[15]

${\displaystyle \kappa ={\frac {1}{3}}\cdot C_{v}\cdot v_{ph}\cdot l_{ph}=\alpha \cdot C_{p}\cdot \rho }$

where

C_v is the heat capacity per unit volume,

v_ph is the average phonon group velocity,

l_ph is the phonon mean free path,

${\displaystyle \rho }$ is the density of the material.

Taking everything into account, as the aluminium content in LAGP increases, the ionic conductivity increases as well, while the thermal conductivity decreases, since a larger number of lithium ions enhances the phonon scattering, thus reducing the phonon mean free path and the thermal transport in the material. Therefore, thermal and ionic transports in LAGP ceramics are not correlated: the corresponding conductivities follow opposite trends as a function of the aluminium content and are affected in a different way by temperature variations (e.g., the ionic conductivity increases by one order of magnitude upon an increase from room temperature to 100 °C, while the thermal conductivity increases by only 6%).^[15]

Thermal stability

Detrimental secondary phases can also form because of thermal treatments or during the material production. Excessively high sintering/annealing temperatures or long dwelling times will result in the loss of volatile species (especially Li₂O) and in the decomposition of LAGP main phase into AlPO₄ and GeO₂.^[2] LAGP bulk samples and thin films are typically stable up to 700-750 °C; if this temperature is exceeded, volatile lithium is lost and the impurity phase GeO₂ forms.^[5][12] If the temperature is further increased beyond 950 °C, also AlPO₄ appears.^[5]

Raman spectroscopy and in situ X-ray diffraction (XRD) are useful techniques that can be employed to recognise the phase purity of LAGP samples during and after the heat treatments.^[5]

Chemical and electrochemical stability

LAGP belongs to phosphate-based solid electrolytes and, in spite of showing a moderate ionic conductivity compared to other families of solid ionic conductors, it possesses some intrinsic advantages with respect to sulfides and oxides:

• Extremely high chemical stability in humid air;
• Wide electrochemical stability window;
• Low to negligible electronic conductivity.^[3]

One of the main advantages of LAGP is its chemical stability in the presence of oxygen, water vapour, and carbon dioxide, which simplifies the manufacture process preventing the use of a glovebox or protected environments. Unlike sulfide-based solid electrolytes, which react with water releasing poisonous gaseous hydrogen sulfide, and garnet-type lithium lanthanum zirconium oxide (LLZO), which react with water and CO₂ to form passivating layers of LiOH and Li₂CO₃,^[4] LAGP is practically inert in humid air.^[5]

Another important advantage of LAGP is its wide electrochemical stability window, up to 6 V, which allows the use of such electrolyte in contact with high-voltage cathodes, thus enabling high energy densities.^[18] However, the stability at very low voltages and against lithium metal is controversial:^[19] even if LAGP is more stable than LATP because of the absence of titanium, some literature works report on the reduction of Ge⁴⁺ by lithium as well, with formation of Ge²⁺ and metallic germanium at the electrode-electrolyte interface and dramatic increase of interfacial resistance.^[18]

The possible decomposition mechanism of LAGP in contact with metallic lithium is reported in the equation below:^[9]

${\displaystyle {\ce {2LiGe2(PO4)3 + 4Li -> 3GeO2 + 6LiPO3 + Ge}}}$

Bulk pellets

Thin films

Other techniques

Some other methods to produce LAGP materials have been reported in literature works, including liquid-based techniques,^[6] spark plasma sintering,^[1] and co-precipitation.^[23]

In the following table, some ionic conductivity values are reported for LAGP materials produced with different synthesis routes, in the case of optimized production and annealing conditions.

Lithium-sulfur batteries

LAGP-based membranes have been applied as separators in lithium-sulfur batteries.^[26] LAGP allows the transfer of lithium ions from anode to cathode but, at the same time, prevents the diffusion of polysulfides from the cathode, suppressing the polysulfide shuttle effect and enhancing the overall performance of the battery.^[26] Typically, all-solid-state lithium-sulfur batteries are not fabricated because of high interfacial resistance; therefore, hybrid electrolytes are usually realized, in which LAGP acts as a barrier against polysulfide diffusion but it is combined with liquid or polymer electrolytes to promote fast lithium diffusion and to improve the interfacial contact with electrodes.^[27]