Critically assessing sodium-ion technology roadmaps and scenarios for techno-economic competitiveness against lithium-ion batteries

Componential floor-constrained learning curves

The typical Wright’s learning curve follows the form

where the price of a technology Y at a given cumulative experience x is described by the price of the first unit A and a rate of price reduction b. Here the learning rate (or experience rate) is defined as the percentage price reduction after every doubling of cumulative experience, given by

As established above, these curves have been demonstrated to accurately capture the price trends across various sectors in a technology-agnostic manner, but they can also overestimate price reductions when technologies approach their price floors dictated by physical limits. In such scenarios, the equation can be modified to incorporate a floor constraint, shown by

Here \(A_\rmfloor,0\) and \(A_\rmfloor,\rmt\) illustrate that the price floors can evolve dynamically with time. Cumulative experience is also normalized for a more practical implementation of the general form in equation (1) that enables one to use the known price and cumulative ‘incurred’ experience of components in the present and backcast and forecast accordingly. It also enables us to use actual quantities produced (in kT or Mm², for example) in fitting historical data where such production data is available, and switch to using anticipated demand (in GWh) in projecting future price trends. Agreement on present pricing is therefore all that is required to yield continuity between historical and forecasted prices. In this paper, we implement dynamically varying minerals price floors obtained from historical and forecasted price trends to capture the price evolution of individual component costs of a battery. This enables us to capture individual learning rates, market growth rates and price floors between material components, which are unlikely to always be the same.

Physically accurate technology roadmaps

To capture the evolution of materials intensities within cell designs owing to technical advancements in materials performance and cell engineering, we implement a modified Moore’s law to capture improvements as a function of time. We first model physically accurate cell designs via bottoms-up modelling to obtain exact materials intensities for each component (in kg kWh⁻¹ or m² kWh⁻¹) based on the bill-of-materials. Cell designs are then assigned to specific years that represent the requisite technological progress, and we fit a curve with an asymptotic limit defined by theoretical or practical engineering limits. The curve follows the form

where M_min is defined by equations (6)–(11) for each material component. Here the cathode and anode minimum materials intensities are defined by their respective maximum theoretical specific capacities and allowable electrode thicknesses. The minimum electrolyte materials intensity is defined by the total pore volume within the electrodes only. The minimum separator materials intensity (in m² kWh⁻¹) is defined by a maximum cathode thickness and therefore capacity loading. The minimum positive and negative current collector materials intensities are then calculated from the separator materials intensity but converted to a mass basis (kg kWh⁻¹) based on the densities and minimum practical thicknesses of the foils. For the other material components category, the asymptotic limit M_min is omitted as there is no basis for a minimum limit. In a similar fashion, the maximum theoretical cell-level specific energy is calculated by summing up a balanced anode- or cathode-limited unit-cell based on the provided limits, where equation (4) is modified to approach an asymptotic maximum as opposed to a minimum, with the form

The equations defining the calculation of minimum materials intensities is as follows:

For each material component, the A and b parameters in equation (4) are fitted after the M_min parameter is calculated. Occasionally, when one parameter is assumed to not experience marked improvements, such as the specific capacity of graphite (current values ~360 mAh g⁻¹ are already near the theoretical capacity), the fitted parameter b may end up <0, making the exponential term >0 with a very shallow slope. This is an artefact of fitting, and we do not expect actual material performance to decline with time. Therefore, in cases where the fitted b parameter ends up negative, we instead use a flat line with zero slope centred at the average of the fitted values. The engineering limits used in our modelling are summarized in Supplementary Table 4.

Combining the modified Wright’s law with the modified Moore’s law

After having established (a) floor-constrained learning curves and (b) materials intensities for each component scaling as a function of cumulative experience and time, respectively, we can combine them to produce a generalized equation, which captures the overall cell price. This is represented in general form as

The first term of the right-hand side aggregates the individual material component costs of a battery cell, each defined by its own learning rate, \(-b_n\), normalized cumulative experience, \(\left(\fracx_n,tx_n,0\right)\), price floor, \(a_n_\rmfloor,t\), and a material intensity scalar, \(M_n,t\), that captures the kg kWh⁻¹ or m² kWh⁻¹ contribution required for the representative modelled cell design. Here \(n\in\) positive active material, negative active material, electrolyte, separator, positive current collector, negative current collector and others. While in practice, all material components will have hard physical limits of a price floor, some components have negligible minerals costs, including polyolefins and conductive carbons. Therefore, for those materials, \(a_n_\rmfloor,t\) and \(a_n_\rmfloor,0\) are zeroed. The second term of the right-hand side captures the costs associated with manufacturing, including equipment depreciation, labour, scrap, SG&A, other overheads, warranty and profit. Notably, this second term is an unconstrained learning curve as there is no direct physical basis to institute a hard price floor. One may consider implementing manufacturing CapEx as a potential price floor, but as we do not yet have a clear methodology to firmly establish a minimum, we leave it unconstrained in this paper. Note that the learning parameter associated with manufacturing costs inherently captures other technical factors such as processing yield improvements and economies-of-scale, which we do not further resolve in our current work. See Supplementary Fig. 64 for fitting details. The materials intensity scalar is used to capture the improvements to cell design and active materials specific capacities, both of which are key contributors to historic cell price declines. This componential approach captures the nuance that different components of a battery will experience different materials improvements, learn at different rates, experience different market growth scenarios and be constrained by respectively different floors.

The above learning curves can be correlated with time by defining individual component market growth rates. Here we use Gompertz sigmoidal functions to describe the annual demand of individual battery components, as they provide better fits to market projections than standard logistic functions¹⁸. The annual production capacity at year t can be defined as

where \(q_n,\rmbase\), \(q_n,\rmsat\) and \(r_n\) represent the starting annual production capacity, the annual production capacity upon market saturation and growth rate of component n, respectively. Notably, not all battery components experience the same market growth conditions. For example, whereas the demand for graphite materials in tonnes per annum scales closely with the cumulative demand of total Li-ion batteries owing to it being the predominant anode chemistry, LFP and NMC materials will each scale at a lower rate owing to their fractional market share. With this, the cumulative capacity can be obtained from

Minerals pricing

Each mineral dataset was converted into aggregate averages with a sample size of n ≥ 3 if including proprietary industry sources, or n = 1 if data was only available from USGS. Owing to the proprietary nature of each of the industry-supplied forecasts, the minerals pricing datasets are averaged at each time step with 95% CI to prevent traceability to any one data source using the formula

While USGS datasets do not provide minerals price forecasts, industry intelligence firms do, and we use their 2023 forecasts as our baseline scenario for the key minerals (lithium, nickel, cobalt and so on) looking forward. As expected, there is good agreement on historical minerals pricing but notably larger variances between forecasts within the next decade. Owing to inherently large uncertainties associated with forecasting prices of volatile minerals, we also perform analysis of self-generated fixed price scenarios (for example, high/mid/low) on the key commodities to evaluate the sensitivity of outcomes (Supplementary Note 4 and Supplementary Figs. 8 and 9).

Historical material component pricing

All prices obtained from industry and literature were inflation-adjusted to USD2023. For any year with multiple data points, averages and CIs were calculated using the same methodology above. For tabulating annual production quantities (in kT or Mm²), gaps in data were interpolated using the requisite compound annual growth rates (CAGRs) established by the bounding years for which data was available, where CAGR is defined by

Cell modelling

To accurately model cells, representative half-cell voltage versus specific capacity (mAh g⁻¹) curves of positive and anode material candidates (for example, LFP, NMC622, NMC811 and graphite) were extracted from literature and were mathematically scaled to meet target electrode coating mass loadings, active mass fractions, areal capacity loadings and calender densities (and therefore porosities). Importantly, first cycle (de)lithiation or (de)sodiation curves were utilized in order to capture differences in first cycle efficiencies between positive and negative electrode pairings, and full cell voltage curves were obtained by subtracting negative from positive. This approach is critical to obtaining accurate predictions of realizable energy densities⁴⁸ (Supplementary Fig. 65). Cell modelling details are discussed at length in Supplementary Note 9, along with validation against experimental data in Supplementary Note 10, Supplementary Table 5 and Supplementary Figs. 66 and 67.

Once the electrode balancing procedure is completed to obtain accurate unit cell designs, the electrode parameters were inputted to the BatPaC (v5.1) spreadsheet model produced by Argonne National Laboratory²² to obtain exact mass and areal quantities per stored energy content (kg kWh⁻¹ or m² kWh⁻¹). In addition, we leverage the detailed manufacturing cost calculations within BatPaC to obtain the present-day manufacturing costs on a per-kWh basis. We take this approach for the following reasons. (1) Despite being highly detailed in modelling manufacturing-related costs, BatPaC has shortcomings in capturing the true voltage, capacity and energy characteristics of cells owing to inherent limitations of a spreadsheet approach. Especially considering occasional mismatched first cycle efficiencies between cathode and anode pairings and uniquely slopey or stepped voltage curves of emerging Na-ion materials, the true energy (Wh)—which is the area underneath the voltage curve between capacity and voltage windows—can often be miscalculated. This may result in errors in calculating true $ kWh⁻¹ (ref. ⁴⁸). (2) We note that BatPaC only models large format (>60 Ah) pouch cells, whereas some of the cells modelled (for example, Tesla 4680 cylindrical cells) do not share the same format. However, we replicate all cell designs using BatPaC to enable systematic comparisons across generations and chemistries, and we also note that materials intensity, energy densities and manufacturing costs at the GWh scale will not deviate substantially between formats. This general approach allows us to systematically evaluate new cell designs and obtain cell manufacturing costs associated with each design while being more nuanced in electrode balancing. See Supplementary Note 11 for details on BatPaC Modifications made in our modelling efforts.

Current Na-ion material price assessment survey

To obtain present-day pricing of materials used in the nascent industry of Na-ion batteries, we take the approach of surveying industry experts and reports with insights on actual current-day pricing^24,25. We survey from n = 11 sources on the key material components used in Na-ion batteries. Not all sources were able to provide estimates for every material component, but most material components had at least n = 3 sources. If a given source provided a range of pricing corresponding to a low and high estimate, both values were used to appropriately weight the samples instead of the mid-range value. Specifically for biomass- and phenolic resin-based HC materials, which can currently be sourced from producers in China and Japan at substantially disparate costs, we also delineate which region the prices are quoting. In our modelling, we only use prices from China given the substantially higher concentration of Na-ion commercialization activity in that region. The results of our pricing survey are shown in Fig. 3b.