Lithium Mobility in Borate and Phosphate Glass Networks

3.1 Conductivity

For the conductivity experiments circular Ag electrodes with 1 mm diameter for Li–borate and 3 mm for Li–phosphates were applied on polished glass surfaces. To produce the electrodes, Ag lacquer (Co. Dr. Ropertz-GmbH) was deposited on the sample surfaces. Samples were placed into the impedance sample holder between two Pt-cones. A spring-tension mechanism was applied to one of PtRh-cones via a ceramic rod to ensure good electrical contact. Afterwards the sample holder was inserted into an earth-grounded gold tube, serving as an insulating shield. Impedance measurements were performed in a tube furnace Nabertherm R50/500/13. During the experiment the temperature was continuously recorded at a distance of 2 mm, using an electrically shielded type-K thermocouple. Heating rate was varied between 0.8 and 0.9 K/min. Maximum temperature for each composition was set to ca. 50° below the T_g, to ensure that the material properties are not altered due to melting or crystallization risk from slow cooling, particularly valid for the Li–borate sample. Sintering of the electrodes took place directly in the sample holder and impedance spectra were collected during sintering and later compared with those collected during the subsequent experiment to ensure that the sample and the sample-electrode interface remained intact.

The electrical conductivity was measured periodically during heating and cooling using a Novocontrol Alpha AKB impedance analyzer equipped with a Novocontrol ZG4 module to allow a four terminal configuration. Before the measurements, the spectrometer was calibrated using a short circuit arrangement and a certified 100 Ω resistance. Additionally, internal high capacity references were used to calibrate the system. Impedance spectra were collected during from 2 MHz to 0.5 Hz at each selected temperature. The heating/cooling program was not interrupted for recording impedance data, and the spectra correspond to a temperature interval of ~8 K at low temperature and 1–3 K at the highest temperature. However, the temperature corresponding to the centre of the conductivity plateau was always determined with a precision better than ±1 K.

3.2 Isotope exchange experiments

To determine the self-diffusion coefficient of lithium for each composition, we planned to perform experiments at three target temperatures with two diffusion couples for each selected temperature. For each temperature an individual couple was prepared, annealed and later analysed. The target temperatures were determined based on the T_g for each composition and set between (T_g – 50 K) and 373 K. The duration of each isotopic exchange run was estimated based on the diffusion coefficients derived from conductivity measurements [13], [20] as the time needed for the development of 1 mm diffusion profile. Isotope exchange experiments were conducted in the in a tube furnace Nabertherm R50/500/13/P330, using the same ceramic sample holder as in our previous diffusion studies.

In order to reduce the contribution of heating to the isotopic exchange profile, the sample holder was inserted in the preheated furnace. The duration of the sample exposure to the target temperature, T_target varied between 10 h and 10 days. The effective time t_eff which each of the diffusion samples spent at T_target was calculated as:

here E_a is the activation energy for diffusion obtained from the conductivity measurements, R is the universal gas constant and T(t) is the average temperature the sample has in the time interval dt.

None of the samples exhibited visible alterations after the diffusion experiments. The samples were fixed in epoxy (Araldite^®) and cut perpendicular to the contact plane of the diffusion couple. The surface was polished for further analyses by femtosecond laser ablation system combined with inductively coupled plasma mass spectrometry, fs LA ICP-MS.

3.3 Measurement of diffusion profiles

The diffusion profiles of lithium isotopes were analyzed using an in-house-built fs LA-ICP-MS. The deep UV fs laser system used in this experimental setting is based on a Newport/Spectra Physics^® Solstice Ti-sapphire regenerative amplifier system, comprising a tunable Ti-sapphire femtosecond seed source pumped by a 5 W continuous wave Nd:YLF laser which is internally frequency-doubled to produce 532 nm, a regenerative amplifier pumped by a 15 W internally doubled Nd:YLF and a pulse stretcher and compressor setup. The output wavelength range is widely tunable and set to a wavelength of 775 nm which generates a beam with a wavelength of 194 nm in the fourth harmonic. The pulse width is estimated to be better than 200 fs in the deep UV since a direct measurement of the pulse width is difficult in the DUV to obtain. The detailed description of the experimental setup has been presented in works of Horn [10], [11].

The profiles were measured perpendicular to the contact plane of both glass plates in continuous mode by moving the sample with a typical scan speed of 2 μm/s under the laser beam using an integration time of 1 s and a laser repetition rate of 2 Hz. The spatial resolution was ca. 4 μm for Li–borate and Li–Mg–phosphate.

In the case of Li–phosphate couples, the diffusion profiles were too short to measure a line scan (<20 μm). In order to determine the change in the lithium isotopy as a function of distance from the interface, each of the Li–phosphate diffusion couples was opened and cleaned from the LiClO₃ residue by cleaning with a cotton swab. Instead of measuring the ablated profile, an in-depth profile was collected by ablating a circular area in a step-like manner, where after each ablation step the diameter was reduced by 2 μm. The depth of each resulting crater was determined by microscopy, and the change in ⁶Li/(⁶Li+⁷Li) was measured in function of the depth on each half. The two halves of each couple resulted in one full profile. Successful analyses could be performed in this way only for three out of six diffusion couples. One of the Li–phosphate couples was irreparably damaged during opening and the remaining failed profile recreations were unsuccessful due to the lateral shift of measurement positions between the two halves.

4.1 Conductivity experiments

The results of impedance spectroscopy experiments were used to calculate the electrical conductivity, σ by dividing the measured admittance with the cell constant (electrode area/sample thickness), for Li–borate of ca. 2 mm, of ca. 12 mm for Li–phosphate and ca. 14 mm for Li–Mg–phosphate. The electrical conductivities as a function of reciprocal temperature for Li–borate, Li–Mg–phosphate and Li–phosphate glass are plotted in Figure 2 and compared to the Li–trisilicate glass from Bauer et al. [20]. Conductivities recorded during the heating and the cooling cycles agree within the 0.10 log units. The direct current (DC) conductivity, σ_DC, has been read out from the centre of the low frequency DC-conductivity plateau in the plot of the logarithm of the real part of σ vs. logarithm of frequency for each temperature. For each composition the data show a linear dependence of log(σ_DCT) on reciprocal temperature in the whole temperature range, i.e. following an Arrhenius relation

Fig. 2:

Electrical conductivity for the Li–borate and –phosphates are compared to the values for Li–trisilicate.

where σ_DC0T is the pre-exponential factor, and E_a is the activation energy for ionic conduction. A decrease in conductivity from Li–phosphate glass, over Li–borate to Li–Mg–phosphate is evident. This trend is not directly proportional to the lithium content, as the Li–Mg–phosphate glass has the highest concentration of Li-atoms, (see Table 1). The activation energy is the lowest for Li–phosphate sample, 74.7±0.7 kJ/mol, 85.2±1.1 kJ/mol for Li–borate while for Li–Mg–phosphate it is much higher at 90.4±0.9 kJ/mol (see Table 1).

4.2 Results of the isotope exchange experiments

Provided that the diffusion coefficient does not depend on concentration and that the profiles do not extend to the outer faces, the solution of Fick’s second law for one-dimensional diffusion between two semi-infinite media at the given boundary conditions is given as [21]:

where c is the concentration at distance x, c₀ and c₁ represent the initial concentrations in both halves of the diffusion couple, a corresponds to the position of the profile’s inflection point and t stands for the duration [22], [23]. Large scatter was observed in plots of the measured count rate of ⁶Li or ⁷Li as a function of distance, due to temporary variations of the analytical yield, a phenomenon typical in mass spectrometry. The scatter is significantly reduced when the isotopic ratio ⁶Li/(⁶Li+⁷Li) is used as the concentration variable because the analytical conditions affect both isotopes in the same way. A basic assumption in using this variable for determination of the diffusion coefficient is that the Li concentration is constant in the whole sample.

All diffusion profiles obtained for Li–borate and Li–Mg–phosphate are symmetric with an inflection point at the former contact of both halves of the diffusion couple (Figure 3). The profiles combined from depth-ablation measurements of Li–phosphate samples were symmetrical only in less than half of collected data sets. Only symmetrical diffusion profiles, as the one shown in Figure 3c, were used for fitting. Values for diffusion coefficients were determined by fitting the normalized Li-isotopic profiles by Eq. (3). These values should be considered as average self-diffusion coefficients of lithium in this isotopic range. The zero-point of the x-axis was arbitrary chosen, so the inflection point of the profile became an adjustable fitting parameter. The experimental data are well reproduced by the fit curve (Figure 3). Self-diffusion coefficients of lithium in the studied glass compositions are listed in Table 1 and compared at 426 K as the representative temperature point in common for all samples. The experimental values are presented in Figure 4. In the observed individual temperature ranges the experimental diffusion data can be described by an Arrhenius relationship through which E_a for self-diffusion from isotope exchange experiments of individual compositions can be calculated. Thus derived activation energy E_a is 72.2±2.5 kJ/mol for Li–borate, Li–phosphate 72.9±3.0 kJ/mol and 76.9±3.7 kJ/mol for Li–Mg–phosphate, as given in Table 1.

Fig. 3:

Diffusion profiles of Li–borate, –magnesium phosphate and –phosphate. Lithium–borate and Li–Mg–phosphate profiles were obtained using laser ablation ICP-MS linearly across the interface between the two halves of a diffusion couple. Profile for Li–phosphate represents the combination of two individual measurements of the two halves, where the change in isotope concentration was obtained by ablating subsequent circular layers, from interface surface in depth.

Fig. 4:

Comparison of self-diffusivities of Li in different types of glass networks. Lithium mobility in aluminosilicate is the highest even though the Li-content is the lowest of the compared compounds.

5.1 Correlative lithium movements

The ionic conductivity is affected by both mobility and the local concentration of the charge carriers. To get insights to the dynamic of lithium, diffusion coefficients were calculated using the Nernst–Einstein-Equation [6], [19], [24]:

D_σ corresponds to the self-diffusion coefficient of lithium ions. It is calculated from the electrical DC conductivity of the sample (σ_DC), absolute temperature T, the Boltzmann constant k, charge carrier concentration N and the charge of the diffusing ion q. Charge carrier concentrations are calculated from glass density and glass composition, assuming a statistical distribution of lithium ions. The valuable insight into the prevailing migration mechanism and the information about efficiency of individual jumps are classically obtained through the comparison of the tracer diffusion coefficient D_i^* and the ionic diffusivity, D_i,σ :

in which H_R represents the Haven ratio [25], [26] and D_i,σ corresponds to the diffusion coefficient derived from ionic conductivity. Lonergan et al. describes H_R as a correction factor for the deviation from the Nernst–Einstein relation, caused by the correlated charge transport, resulting directly in a decrease of the diffusion coefficient [27]. When H_R=1, an independent charge transport is assumed, unconstrained by structure. However, as the classical tracer methods are not applicable in Li-diffusivity studies, the self-diffusion coefficients based on isotopic exchange experiments are considered as proportional to D_i^*

The correlation factor f can vary between 0 and 1 relative to the diffusion mechanism. In single crystal materials a low f value indicates a vacancy-dominated and significantly correlated movement, whereas f=1 is characterized by an uncorrelated dynamic via interstitials [28]. In the case of glasses where long-range periodicity is absent, interpretation of correlation effects is not as straightforward. To overcome that problem Wegener and Frischat [29] proposed a model in which the glass network is treated as consisting of many randomly oriented crystallites and the full long-range motion is observed as a sequence of numerous small steps. This allows transferring ideas of diffusion mechanism derived for crystals to glasses, although the definition of vacancies and interstitial sites is less clear for glasses. Combining Eqs. 5 and 6 the H_R/f ratio links the self-diffusion with the ionic diffusivity:

The high value of H_R/f ratio (see Table 1) observed for Li–phosphate of 0.98 and for Li₂O·Al₂O_3·4 SiO₂ of 0.93 indicate unconstrained lithium mobility through the potential landscape, which offers open structure with an abundance of low potential barriers. Li–borate and Li–trisilicate exhibit more constrains of network on Li-mobility. In Li–silicate, the constraint is due to the presence of Li-rich regions separated by insulting silica-rich matrix and the H_R/f ratio reflects the abundance of Li-rich regions and characteristics of clustering, such as inter-connectivity, dimensionality and tortuosity [20]. In Li–borate, the spatial distribution of the two types of borate structural species influences distribution of negative potentials, obstructing Li-mobility, as will be assessed in more details further in the text. In contrast, the value of 0.30 for Li–Mg–phosphate is an indication of high constrains for mobility of Li-cations, most probably by the incorporation of Mg-atoms into the glass network in terms of mixed cation effect [30].

5.2 Effects of glass structure

Comparison of the experimental results reveals consistency between conductivity and self-diffusion in the studied material (Figures 2 and 4). Where the Li–phosphate with 20 mol% Li₂O proved to be the most conductive, it also exhibited the highest self-diffusion coefficients. On the other hand, Li–borate has considerably lower self-diffusivity than the other compared glasses. In contrast, Li–aluminosilicate with the lowest available concentration of mobile Li-cations, 16.7 mol%, exhibits the highest conductivity and self-diffusion. It would be expected for conductivity results to show some proportionality to the concentration of available mobile atoms per unit of volume. However, as the observed data do not exhibit this trend, it appears that the principle driving force for Li-transport is more complex and strongly dependent on the glass network chemistry. Glass chemistry and structure shape the potential landscape through which activated mobile atoms progress. In the case of glass compositions used in this study, a borate and a phosphate network are of distinctly different structures. Additionally, in phosphate glasses there is a well-defined difference in Li-mobility depending on the absence or presence of Mg as an additional network modifier.

Potential landscape in the case of Li–borate glass is very complex. It is influenced by the two types of borate building units in glass structure, i.e. (BO₃)⁻ and (BO₄)⁻. (BO₃)⁻ is a planar building unit where one B-atom is surrounded with three oxygen atoms. (BO₄)⁻ on the other hand, comprises one tetrahedrally coordinated B-atom and the overall amount of this building unit is influenced by the alkali content. (BO₄)⁻ units increase the packing density in alkali-borate structure and contribute to the glass network stability, more so than the planar (BO₃)⁻ units, but only to the maximum of 25–30 mol% of total alkali content, depending on the size of the alkali cation [31]. With the addition of alkali oxides, the stability of glass deteriorates with the increase of the B-B distance [6]. In the case of our Li–borate glass sample, the overall alkali content of 25 mol% indicates high amount of polymerized (BO₄)⁻ units in the structure.

Hudon and Baker [32] have pointed out the interaction between the different types of borate building units and the modifying cation of high ionic potential, such as alkalis and alkaline earth. In the vicinity of planar (BO₃)⁻ units, oxygens are strongly polarized towards the B-atom, which has a high ionic potential, thus restricting the interaction with the modifying cations in the vicinity. As a consequence, the potential landscape features localities of substantial coulombic repulsion between charged modifying cations. In tetrahedral (BO₄)⁻ units on the other hand, B³⁺ cations make covalent bonds with the oxygen to alkali oxides, resulting in coordinate covalent bonds weaker than B–O bonds in planar (BO₃)⁻ units. Lithium has high ionic potential, based on its charge per ionic volume [13] and as such can relatively easily polarize nearby oxygen of (BO₄)⁻ units, attracting the negative charge of the surrounding oxygens towards itself. As a result, in the vicinity of (BO₄)⁻ units, the potential landscape is featuring a number of shallow potential wells, which can be considered favorable for Li-mobility. NMR analyses for critical binary Na–borate glass composition, i.e. 25 mol% alkali oxide, revealed that these two building units tend to be randomly distributed, resulting in a variety of negative potentials of different strengths caused by different combinations of (BO₄)⁻ and (BO₃)⁻ units per unit of volume [6], [16], [17]. In contrast to the (BO₄)⁻ units, the effect of randomly distributed (BO₃)⁻ units on the potential landscape forms barriers for long-range transport in the case of diffusion experiments. This effect of the borate potential landscape on Li-mobility is reflected on the H_R/f value of 0.54 which reflects the combined effect of different types of localized potentials, which either obstruct or conduct mobilized Li-cations.

Work of Matsuo et al. [33] on transport properties Li in binary borate glasses with different Li:B ratio has demonstrated that the conductivity increases with the concentration of Li₂O, and thereby also of the (BO₄)⁻ units, although not in a linear fashion. Li–borates exhibit a threshold concentration above which the amount of energy needed for activation of Li-cations reduces. In binary Li–silicates, a comparable threshold of ca. 8 mol% Li₂O can be observed, above which the increase in concentration increases the conductivity. One of the principal differences between the binary silicate and borate Li-compounds is that in silicate glasses, increase in Li-concentration above 15 mol% affects conductivity in almost negligible degree. In borates, the increase in conductivity is evident up to where Li:B ratio equals 1. The driving force behind this, together with the already mentioned combination of potentials around (BO₄)⁻ and (BO₃)⁻ units is a more even spatial distribution of Li-cations in comparison to silicate networks. In Li–silicates, combinations of the tetrahedral (SiO₄) group bonding as different Q-species, result in a variety of local potentials and a large number of deep negative potential wells. Additionally, there is a tendency of local chemical un-mixing causing regions with higher Li concentration and insulating Si-rich matrix surrounding them [20].

In comparison, phosphate glass network is built out of one type of building units, i.e. tetrahedrally coordinated P-atom with five-fold charge, resulting in one of the four oxygens being doubly-bonded. This oxygen does not form bridging bonds with other building units and is referred to as a “terminal” and is not shared between the building units. The addition of Li₂O depolymerizes phosphate glass network by creating non-bridging oxygens and as a result, different types of phosphate tetrahedra, depending on the number of non-bridged oxygens [34]. Therefore, the depolymerized phosphate glass network with low alkali content, can be considered as a system of one dimensional chains, held together by alkalis, e.g. Li in this case [14], [34]. Alkali cations can be observed as rebuilding the phosphate network rather than modifying it in a strict sense of Zachariasen [35]. Based on results of early X-ray photoelectron spectroscopic studies, a partial transfer of charge from the double-bonded terminal oxygen to a non-bridged oxygen is assumed as a mean to balance the difference between the terminal negative potentials [2], [36], [37], [38]. Theoretical modeling by Uchino and Yoko [34] has indicated that Li cations are coordinated by negative potentials of both bridged and non-bridged oxygens. NMR studies by Alam and co-workers [2], [4], [15], [39] has indicated that at low alkali concentrations, Li ions are randomly distributed within the phosphate glass network. Further on, glass composition with 20 mol% of Li₂O represents the glass with the highest degree of depolymerisation of the network, with the largest abundance of the smallest ring unit comprising 3-membered ring made of phosphate tetrahedral around a single Li-cation [4], [40]. With the additional alkali content, the increase in the amount of Li–O bonds stabilizes the structure forming larger rings which connect the individual chain-like phosphate domains. At the Li₂O concentrations ranging between 20 and 25 mol%, Li-cations are in average coordinated by four or five oxygens and this is considered as a critical threshold for a number of structural and physical properties, including such as density and T_g.

With the increase of Li, the coordinating Li–O polyhedra link together and interconnect the depolymerized phosphate chain-structure [41]. The process of redistributing negative charge between the terminal and nearby oxygens in the phosphate building units is advanced further. As a consequence, the Li–O bonds within the polyhedral become less ionic and more covalent. Glass structure as a whole benefits from this change, as the increase in lithium content increases network strength, but the mobility of Li-cations is thus restricted [2]. It can be expected that only a small amount of metastable potentials would be available in the vicinity of Li-cations for short-range jumps. These changes in the structure and local environment of Li-cations, relative to the Li-content, can already assess some of the differences between the binary Li–phosphate glass, 0.2 Li₂O·0.8 P₂O₅ and the Li–Mg–phosphate glass, with 0.3 Li₂O·0.2 MgO·0.8 P₂O₅. With the addition of Mg-atoms, both conductivity and diffusivity decrease. Additionally, the E_a for mobilizing Li-cations is higher when Mg is present in the structure. Mg atoms in low concentrations are coordinated by six oxygens, partly non-bridging and partly terminal [37] and also, they are cations with very high ionic field strength. In the glass structure, Mg cations are characterized by reduced mobility and as such impede the movement of lithium cations by reducing the number of suitable potentials in the vicinity of Li-cations which could be used for successive jumps.

Observed features of lithium mobility in the two types of networks of analysed compounds are clearly different from those observed in Li–silicate and Li–aluminosilicate of comparable lithium content. In lithium-aluminosilicates, the Li:Al ratio plays a significant role in the cation mobility, as considered in the work of Ross et al. [19]. When this ratio is balanced and equals 1, the amount of available potentials is evenly distributed through the network and the oscillations are relatively moderate. In a silicate network, as studied by Bauer et al. [20], the landscape is dominated by the distribution of highly charged negative potentials around the non-bridged oxygens of tetrahedrally coordinated Si, as mentioned earlier. As such, structural and chemical inhomogeneity have a large impact on Li mobility, reducing it in comparison to the Li–aluminosilicate glass.