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Ragone plot

The Ragone plot is a logarithmic graph that depicts the relationship between specific energy (typically in watt-hours per kilogram, Wh/kg) and specific power (in watts per kilogram, W/kg) for energy storage devices, highlighting the inherent trade-off where higher power output generally corresponds to lower energy capacity.^[1] This visualization enables direct comparison of performance across diverse technologies, such as batteries, supercapacitors, and fuel cells, by normalizing metrics to device mass or volume.^[1] Named after David V. Ragone, the plot originated in a 1968 SAE Technical Paper titled "Review of Battery Systems for Electrically Powered Vehicles," where it was first used to evaluate battery chemistries for automotive applications through empirically derived curves.^[2] Initially focused on electrochemical systems, its adoption expanded in the 1990s with the rise of lithium-ion batteries and supercapacitors, evolving into a standard tool for assessing off-design performance in energy storage research and engineering.^[1] Ragone plots are constructed from experimental data obtained via constant-power discharge tests, where devices are cycled at varying power levels until limits like voltage cutoffs are reached, yielding energy as the product of power and discharge time.^[1] They can also derive from theoretical models or manufacturer datasheets, often incorporating efficiency factors to reflect real-world usability.^[1] Beyond batteries, applications now include hybrid storage systems, thermal energy devices, and even non-electrochemical technologies like compressed air energy storage, aiding in optimal selection, sizing, and optimization for applications from electric vehicles to grid-scale renewables.^[1]

Overview

Definition

A Ragone plot is a logarithmic scatter plot that visualizes the relationship between specific energy, defined as energy per unit mass (typically in Wh/kg), and specific power, defined as power per unit mass (typically in W/kg), for various energy storage devices. This graphical tool captures the inherent trade-off where higher specific energy often corresponds to lower specific power, and vice versa.^[3] The plot employs a double-logarithmic scale on both axes to accommodate the wide dynamic range of performance metrics across different technologies, from low-power, high-energy systems like fuel cells to high-power, low-energy devices like capacitors, enabling direct visual comparisons that would be challenging on linear scales.^[3] Specific energy represents the total extractable energy normalized by the device's mass and is fundamentally derived from the device's capacity to store charge under its operating voltage. For electrochemical energy storage devices, it is approximated by the equation

E = \frac{V \cdot Q}{m},

where E is the specific energy (Wh/kg), V is the average cell voltage (V), Q is the total charge capacity (Ah), and m is the total mass of the device (kg). This form arises because the total energy stored, E_{\text{total}} = V \cdot Q (in Wh, assuming constant voltage), is then divided by mass to yield the specific value; in practice, since voltage varies during discharge due to factors like internal resistance and electrochemical kinetics, a more precise calculation integrates voltage over the discharge curve as E_{\text{total}} = \int V \, dq / 3600 (to convert joules to watt-hours), but the average voltage approximation suffices for comparative purposes in Ragone plots. This metric quantifies how much energy a device can deliver relative to its weight, a critical factor for applications prioritizing endurance over rapid discharge.^[3] Specific power, conversely, measures the rate at which this energy can be delivered per unit mass and is derived from the device's ability to sustain current flow under load. It is given by the equation

P = \frac{V \cdot I}{m},

where P is the specific power (W/kg), V is the operating voltage (V), I is the discharge current (A), and m is the mass (kg). Fundamentally, power output stems from the instantaneous product of voltage and current, P_{\text{total}} = V \cdot I, normalized by mass; during constant-power discharge protocols used to generate Ragone data, the current adjusts dynamically as voltage drops to maintain fixed power, reflecting losses from ohmic resistance, activation overpotentials, and diffusion limitations, which limit maximum achievable power. This equation highlights how specific power decreases with increasing load duration, as higher currents accelerate these loss mechanisms.^[3]

Purpose

The Ragone plot serves as a fundamental tool for visualizing the inherent trade-off in energy storage devices, where systems optimized for high specific energy typically exhibit lower specific power, and those designed for high specific power deliver reduced specific energy.^[1] This graphical representation enables engineers to select appropriate technologies for diverse applications; for instance, lithium-ion batteries with high energy density are favored for electric vehicles requiring prolonged range, while supercapacitors providing rapid power bursts suit power tools demanding short, intense discharges.^[1] In device design, the plot facilitates performance prediction across varying discharge rates by mapping how energy output diminishes with increasing power demands, allowing designers to anticipate operational limits without exhaustive simulations.^[1] It also supports benchmarking of novel materials or configurations against established benchmarks, such as comparing emerging silicon anodes in lithium-ion batteries to conventional graphite counterparts, to assess potential improvements in the energy-power envelope. For applications needing balanced moderate energy and power, such as portable electronics or hybrid vehicles, the selection process involves: first, quantifying the required specific energy and power thresholds based on duty cycles; second, overlaying these requirements as a target region on the plot; third, identifying technologies whose curves intersect this region; and fourth, prioritizing candidates via additional criteria like cost or cycle life, thereby avoiding the need for full-scale prototype testing early in development.^[1]^[4]

History

Origin with David Ragone

David V. Ragone, an associate professor of metallurgical engineering at the University of Michigan with expertise in thermodynamics and propulsion systems, developed the foundational energy-power plot in 1968 while analyzing battery performance for advanced applications.^[5] The plot originated in a technical presentation focused on electrochemical energy storage systems suitable for high-performance electric propulsion, where understanding the interplay between specific energy and specific power was essential for device selection.^[2] Ragone first presented the diagram in his paper "Review of Battery Systems for Electrically Powered Vehicles," delivered at the Society of Automotive Engineers Mid-Year Meeting in Detroit. In this work, the plot served as a graphical tool to compare the capabilities of various rechargeable batteries, illustrating how energy density decreases with increasing power output—a key trade-off for propulsion efficiency.^[2] The initial scope centered on primary and secondary batteries, with exemplary curves depicting the performance of lead-acid batteries, offering moderate energy and power densities suitable for conventional vehicles, against silver-zinc batteries, which demonstrated higher energy densities ideal for demanding, short-duration applications like aerospace systems.^[2]^[6]

Adoption and Evolution

Following its initial presentation in 1968, the Ragone plot gained traction in battery research during the 1970s and 1980s, particularly as consumer electronics demanded more efficient power sources. Researchers extended the framework to evaluate nickel-cadmium batteries, which were prevalent in portable devices, by plotting their energy and power densities to assess performance trade-offs under varying discharge rates. Publications during this period marked milestones in its adoption, demonstrating how the plot facilitated comparisons across battery chemistries and operating conditions.^[1] By the 1990s, the Ragone plot's utility expanded beyond traditional batteries into supercapacitors and fuel cells, spurred by the rising interest in electric vehicles that required hybrid energy systems balancing high power and energy. In 1996, W.G. Pell and B.E. Conway provided a quantitative model for Ragone plots applicable to both batteries and electrochemical capacitors, highlighting the transition between supercapacitor-like and battery-like behaviors and establishing methodological guidelines for non-faradaic storage devices.^[7] This integration aligned with the electric vehicle boom, where the plot became essential for benchmarking prototype fuel cell systems against batteries and capacitors in terms of specific power and energy.^[1] In the 2000s, the Ragone plot achieved widespread standardization in materials science and electrochemistry, evolving into a ubiquitous tool for systematic device evaluation. Theoretical advancements, such as the 2000 framework by Christen and Carlen, formalized the plot's derivation from device physics, providing guidelines for consistent scaling and interpretation across electrochemical systems, including influences from internal resistance and discharge protocols.^[8] This period saw its incorporation into research and industry publications, including those from IEEE on energy storage testing, ensuring reproducible plotting in research and industry. By enabling precise benchmarking, the plot has profoundly influenced energy storage development, with Ragone's original 1968 work and the broader concept amassing over 10,000 citations by 2025.^[1]

Construction

Axes and Scaling

The horizontal axis of the Ragone plot represents specific energy, measured in watt-hours per kilogram (Wh/kg), and is plotted on a logarithmic scale typically spanning from 1 to 10,000 Wh/kg. This range accommodates the performance spectrum of energy storage devices, from low-energy systems like capacitors to high-energy options such as fuel cells.^[9]^[3] The vertical axis corresponds to specific power, quantified in watts per kilogram (W/kg), and employs a logarithmic scale ranging from 1 to 1,000,000 W/kg. This setup reflects the diverse discharge rates of devices, enabling clear differentiation between high-power applications and sustained energy delivery.^[9]^[3] The log-log scaling arises from the power-law dependencies in electrochemical processes, where specific power P is approximately proportional to the inverse of specific energy E, expressed as P \propto E^{-1}. This relationship, rooted in the physics of charge storage and delivery, produces diagonal lines with a slope of -1 on the plot, highlighting inherent trade-offs across orders of magnitude in performance metrics.^[3] Although mass-specific units (Wh/kg and W/kg) predominate as the standard for portable and weight-sensitive applications, volumetric variants such as Wh/L for energy and kW/L (or W/L) for power serve as alternatives in scenarios prioritizing space efficiency over mass.^[10]^[3]

Data Plotting Methods

Data for Ragone plots are typically derived from constant power (CP) discharge tests conducted on energy storage devices at varying power levels, where the device is discharged at a fixed power until a limit such as a cutoff voltage is reached.^[1] During these tests, the discharge time is recorded, with specific energy calculated as the product of power and discharge time normalized by the device's mass or volume, and specific power determined directly as the applied power normalized by mass or volume. Constant current (CC) discharges at varying rates serve as a common alternative, where voltage-time profiles are integrated to compute energy, and average power (energy divided by time) is used.^[1] These measurements are repeated across a range of power levels (or C-rates for CC tests) to capture the trade-off between energy and power capabilities. For plotting, individual data points from each discharge test are marked on a log-log scale with specific energy on the x-axis and specific power on the y-axis, often forming a curve that illustrates the device's performance envelope.^[1] To generate a continuous curve for a single device, experimental points can be fitted using empirical relations, such as P = \frac{k}{E}, where P is specific power density, E is specific energy density, and k is a device-specific constant derived from the data via regression techniques.^[1] This hyperbolic form approximates the inverse relationship observed in many systems, particularly at intermediate to high power regimes, and can be solved by linearizing the data (e.g., plotting \log P vs. \log E) to find the slope of -1 and intercept for k. Variability in experimental data is handled by accounting for efficiency losses, such as those described by Peukert's law in batteries, which predicts reduced usable capacity at higher discharge rates due to increased internal resistance and polarization effects.^[4] Consequently, only the usable energy and power—after subtracting losses—are plotted to reflect realistic performance, often incorporating error bars to indicate measurement uncertainties from factors like temperature fluctuations or cell-to-cell variations. Normalization steps ensure comparability, typically converting raw energy to Wh/kg and power to W/kg using the device's active mass, with log-log scaling applied to span orders of magnitude.^[1] Software tools commonly facilitate this process, with MATLAB used for data processing, curve fitting via least-squares methods, and generating log-log plots, as seen in simulations of discharge profiles. Similarly, Python libraries like matplotlib enable log-log plotting and normalization, allowing scripted automation for importing voltage-time data, computing integrals for energy, and fitting empirical curves.^[11] These tools support iterative refinement, such as adjusting for Peukert exponents in battery models before final visualization.^[4]

Interpretation

Power-Energy Trade-offs

The inverse relationship between power and energy density in Ragone plots arises from fundamental differences in the charge storage mechanisms of electrochemical devices. High-energy-density systems, such as batteries, store charge through faradaic redox reactions involving ion intercalation or diffusion into the bulk of electrode materials, which enables substantial energy capacity but is kinetically limited by slow diffusion processes. In contrast, high-power-density devices like supercapacitors rely on non-faradaic electrostatic charge separation at the electrode-electrolyte interface or fast surface-confined redox reactions, allowing rapid charge-discharge cycles but restricting energy storage to surface areas. This trade-off is rooted in the timescales of these processes: diffusion in batteries typically occurs on the order of seconds to hours, while surface processes in supercapacitors happen in milliseconds.^[12] The characteristic slope of approximately -1 on a log-log Ragone plot reflects a near-constant product of power (P) and energy (E), derived from the relation E(P) = P \cdot t(P), where t(P) is the discharge time at power P. This implies that for many devices, the usable energy scales inversely with power because shorter discharge times reduce the extractable energy due to internal resistances and incomplete reactions, leading to P \cdot E \approx constant under ideal conditions. Ragone's original thermodynamic derivation for batteries modeled this as a limit where maximum power is constrained by ohmic losses and reaction kinetics, resulting in diagonal lines of constant discharge time on the plot. This slope interpretation provides a universal framework for understanding efficiency losses across device types.^[8]^[2] Ragone lines represent theoretical upper bounds on performance, determined by material properties and thermodynamic limits such as voltage windows and specific capacities. For lithium-ion batteries, the theoretical gravimetric energy density is approximately 400–500 Wh/kg, constrained by the lithium intercalation capacity in electrode hosts like graphite anodes (372 mAh/g) and high-voltage cathodes.^[13] These lines delineate the envelope beyond which devices cannot operate without violating material or energetic limits, guiding material selection to push toward the boundary.^[14]^[8] The impact of discharge time on Ragone plot positions is evident in how shorter times shift performance toward higher power but lower usable energy, as rapid discharge amplifies voltage drops from internal resistance and polarization, reducing overall efficiency. For instance, at high C-rates (short times), only a fraction of the stored energy is accessible before the voltage falls below operational thresholds, effectively moving the operating point leftward along the plot. This time-dependent behavior underscores the plot's utility in predicting real-world performance under varying load conditions.^[8]

Device Comparison

The Ragone plot serves as a benchmark for comparing energy storage technologies by visualizing their specific energy and specific power densities on a log-log scale, enabling researchers and engineers to identify relative strengths and suitability for applications. Batteries typically occupy a mid-range region, with specific energies around 100–300 Wh/kg and specific powers of 100–1,000 W/kg, reflecting their balanced performance for sustained energy delivery.^[3] In contrast, supercapacitors cluster in the high-power, low-energy domain, exhibiting specific energies near 10 Wh/kg but specific powers exceeding 10,000 W/kg, ideal for rapid charge-discharge cycles.^[3] Fuel cells position in the high-energy, low-power area, often surpassing 1,000 Wh/kg in specific energy while limited to under 100 W/kg in specific power, due to their reliance on continuous fuel supply for prolonged operation.^[15] To quantify comparisons, the area under the Ragone curve for a device provides a metric of overall performance, encapsulating the trade-off envelope between energy and power capabilities.^[3] Intersection points between curves of different devices highlight potential for hybrid systems, where complementary regions (e.g., a battery's energy paired with a supercapacitor's power) optimize combined output.^[16] Figures of merit such as the power-energy product (P × E) further aid evaluation, correlating with the device's characteristic time scale (τ = E/P) and indicating efficiency in balancing metrics.^[14] Normalization is essential for fair benchmarking; data are typically standardized to the same mass basis (Wh/kg and W/kg) or volume basis (Wh/L and W/L) to account for packaging differences across technologies.^[3] To isolate intrinsic performance from degradation effects, comparisons often employ first-cycle data, excluding cycle life variations that could skew long-term assessments.^[17] These protocols ensure reproducible evaluations, focusing on peak capabilities without confounding factors like auxiliary components. Typical Ragone plot layouts feature a logarithmic x-axis for specific energy (spanning 0.1 to 10,000 Wh/kg) and y-axis for specific power (0.1 to 10^6 W/kg), with shaded or labeled regions delineating device classes: a lower-left quadrant for conventional capacitors, a rightward extension for fuel cells, a central band for batteries, and an upper-left for supercapacitors.^[3] Diagonal isocontours of constant discharge time (e.g., seconds to hours) overlay the plot, aiding visual assessment of application-specific fits.^[14]

Applications

In Batteries

In Ragone plots for batteries, lead-acid and nickel-metal hydride (NiMH) technologies are typically positioned at the lower end of the performance spectrum, with specific energy densities ranging from 30 to 100 Wh/kg and specific power densities from 100 to 500 W/kg.^[18] These batteries are well-suited for automotive starting applications, where high initial power bursts are required, but their plots reveal a rapid decline in deliverable energy at elevated discharge rates due to internal resistance and polarization effects.^[3] Lithium-ion battery variants, such as nickel-manganese-cobalt (NMC) and lithium iron phosphate (LFP) chemistries, occupy a higher performance regime in Ragone plots, achieving specific energy densities of 150 to 250 Wh/kg and specific power densities spanning 200 to 2,000 W/kg.^[17] Since their commercialization in the 1990s, when energy densities were around 100 Wh/kg, lithium-ion technologies have evolved significantly, reaching over 300 Wh/kg by 2025 through advancements like silicon anodes and solid-state electrolytes.^[19] This progression is evident in updated Ragone plots, which illustrate improved energy retention at moderate to high power demands, enabling broader adoption in electric vehicles and portable electronics.^[3] Emerging sodium-ion batteries, as of 2025, plot at 160–180 Wh/kg specific energy and specific power densities up to 1000 W/kg, positioning them as cost-effective alternatives to lithium-ion for stationary applications like grid storage.^[20]^[21] In April 2025, CATL launched its Naxtra sodium-ion battery with 175 Wh/kg energy density, enabling electric vehicle ranges up to 500 km and mass production by late 2025.^[22] Their Ragone characteristics highlight competitive performance in low-to-medium power regimes, with trends showing potential for parity with LFP in energy density while leveraging abundant, inexpensive materials to reduce overall system costs.^[19] Battery-specific adjustments in Ragone plot construction often incorporate depth-of-discharge (DoD) effects, as partial DoD cycles can shift the energy-power curve by altering effective capacity and efficiency during discharge.^[23] For instance, plotting at 80% DoD rather than full discharge extends the usable power range but reduces the maximum energy metric, providing a more realistic representation for cyclic applications in batteries.^[3]

In Supercapacitors and Fuel Cells

Supercapacitors occupy a distinctive position on the Ragone plot, emphasizing their high-power capabilities at the expense of moderate energy storage, making them ideal for applications requiring rapid charge-discharge cycles such as regenerative braking in vehicles. Electric double-layer capacitors (EDLCs), which store charge electrostatically at the electrode-electrolyte interface, typically achieve specific energy densities of 5–10 Wh/kg and specific power densities exceeding 10,000 W/kg, enabling discharge times under one second.^[14] Pseudocapacitors, incorporating faradaic redox reactions in materials like metal oxides or conducting polymers, extend the energy density to 20–50 Wh/kg while retaining power densities around 10,000–20,000 W/kg, thus shifting their position rightward on the plot compared to EDLCs.^[24] Recent advancements in supercapacitor materials have aimed to expand their Ragone plot footprint, particularly through graphene-based hybrids that mitigate issues like electrode restacking and enhance ion accessibility. For instance, graphene composites with metal oxides or conducting polymers have demonstrated improved specific energies approaching 60 Wh/kg in laboratory settings, while maintaining high power outputs, as reported in 2025 studies on nanohybrid architectures.^[25] These developments position advanced supercapacitors closer to battery-like energy levels without sacrificing their power advantages. Fuel cells, as electrochemical energy converters rather than storage devices, are plotted on Ragone diagrams to evaluate system-level performance, often revealing high theoretical energy densities limited by slow reaction kinetics at the electrodes. Proton exchange membrane fuel cells (PEMFCs) achieve system-level specific energies of over 500 Wh/kg when including fuel mass, but their specific power densities are typically below 500 W/kg due to mass transport and catalytic constraints, resulting in longer operational times on the plot (hours to days).^[26] Unlike closed-system batteries, fuel cell plotting incorporates the mass of consumable fuels like hydrogen in energy calculations, highlighting trade-offs between refueling frequency and sustained power delivery for applications such as stationary power or electric vehicles.^[26] Hybrid systems, such as lithium-ion capacitors combining battery-type anodes with capacitive cathodes, bridge the Ragone plot gap between supercapacitors and batteries by offering intermediate performance metrics. These devices can deliver specific energies around 100 Wh/kg at power densities of 5,000–25,000 W/kg, as exemplified by Sn-C anode configurations with activated carbon cathodes that outperform traditional supercapacitors in energy retention during high-rate discharges.^[27] This positioning enables hybrid supercapacitors to support pulsed power needs while providing extended runtime compared to pure EDLCs.

Limitations and Extensions

Key Assumptions and Limitations

Ragone plots rely on several key assumptions that simplify the representation of energy storage performance. They typically model discharge under ideal constant-current or constant-power conditions, assuming full utilization of stored energy without losses from self-discharge or parasitic reactions.^[1] Additionally, these plots often presume temperature independence, neglecting how variations in operating temperature can alter internal resistance and voltage profiles, leading to inaccurate predictions under non-ideal thermal conditions.^[28] Furthermore, the framework assumes steady-state operation, disregarding cycle-to-cycle degradation such as capacity fade or increased impedance over repeated charge-discharge cycles.^[28] Despite their utility, Ragone plots have notable limitations in capturing real-world complexities. They do not incorporate factors like cost, safety risks (e.g., thermal runaway at high power densities), or operational lifetime, where batteries often exhibit accelerated degradation under high-power regimes due to side reactions and mechanical stress.^[1] The use of logarithmic scales, while enabling broad comparisons, can obscure subtle performance differences in the mid-range of energy and power densities, making it challenging to discern incremental improvements among similar technologies.^[1] Self-discharge effects, if not explicitly modeled, are effectively neglected in standard plots, underestimating long-term energy retention in practical applications. Experimental data informing Ragone plots often introduces biases that overestimate performance. Measurements are predominantly from lab-scale cells, which lack the packaging, cooling, and interconnects of full battery packs, leading to inflated specific energy and power values when scaled up.^[1] Moreover, variations in internal resistance—due to electrode morphology changes or electrolyte degradation—are frequently ignored, resulting in overestimation of achievable power, particularly at high discharge rates where ohmic losses dominate.^[28] A prominent case study illustrating these issues is the early development of lithium-air (Li-air) batteries in the 2010s. Initial Ragone plots projected optimistic specific energies exceeding 600 Wh/kg based on theoretical cathode capacities and low current densities, overlooking practical limits like electrolyte instability and cathode clogging by discharge products. By 2020, revised assessments incorporating these constraints lowered practical projections to around 400–500 Wh/kg for optimized cells, with demonstrated pack-level performance as low as 77 Wh/kg due to unaddressed parasitic masses and poor rate capability.^[29] These revisions highlight how assumptions in classic Ragone plots can propagate over-optimism, necessitating more comprehensive modeling for emerging technologies.

Modern Variations

Modern variations of the Ragone plot address limitations of the traditional two-dimensional format by incorporating additional parameters such as efficiency, cycle life, and cost, often through multi-dimensional or extended representations. One notable extension is the Enhanced-Ragone plot (ERp), which maps usable specific energy and power across varying discharge rates (C-rates) and temperatures, providing a more nuanced view of lithium-ion battery performance under real-world conditions.^[30] This approach allows for statistical validation using multiple cell samples and highlights trade-offs in efficiency, with discharge efficiencies decreasing at higher C-rates for cathodes like NMC and NCA.^[30] Three-dimensional extensions further expand the plot by adding axes for factors like cycle life or cost, enabling comprehensive comparisons of energy storage technologies. For instance, 3D Ragone plots have been developed to visualize performance variations with battery age and temperature, illustrating how degradation impacts power-energy trade-offs over time. Software tools, such as interactive simulators, facilitate the generation and exploration of Ragone plots, aiding in the design and optimization of supercapacitors and hybrid systems by balancing capacity and mass.^[31] Efficiency-inclusive variations integrate round-trip efficiency (η) into the framework, particularly for applications in renewable energy integration, where the product of power (P), energy (E), and efficiency often follows a constant relationship (P × E × η = constant) to assess overall system viability. This adaptation, discussed in theoretical models of Ragone plots, accounts for losses during charge-discharge cycles, helping evaluate storage devices for grid-scale renewables by prioritizing high-efficiency profiles at varying power levels. Artificial intelligence enhancements employ machine learning to predict Ragone curves directly from material properties, accelerating battery design processes. For example, ML models trained on electrochemical data can forecast energy and power densities for novel electrode materials, generating predictive plots that guide optimization in lithium-ion and supercapacitor development. As of 2025, AI-driven tools have been integrated into battery design software, enabling rapid iteration and virtual screening of compositions for improved performance metrics.^[32] Volumetric and areal variants adapt the plot for compact devices like wearables, shifting from mass-specific metrics to volume- or area-normalized ones (e.g., mAh/cm² vs. mW/cm²) to better reflect constraints in thin, flexible formats. These plots reveal superior performance of nanostructured electrodes in micro-supercapacitors, achieving high areal energy densities while addressing the shortcomings of gravimetric measures in space-limited applications. Such representations are essential for comparing fabric-integrated or 3D-printed energy storage in wearables, emphasizing scalability and integration over traditional bulk properties.^[33]

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