Decoupling Silicon-Alloy Phase Transitions from Metallic Lithium Re-Intercalation Peaks in Differential Voltage Relaxation Spectra

Pulse

Immediately following fast charging, an open-circuit relaxation curve captures overlapping electrochemical signals from both electrodes. In cells with silicon-alloy composite anodes, voltage relaxation after current interruption departs from simple exponential decay driven purely by concentration gradients. Instead, the anode potential reflects two relaxation mechanisms acting over similar timeframes: phase transitions in lithiated silicon create structural shifts and stress relaxation, while any surface-plated metallic lithium spontaneously re-intercalates into the neighboring graphite or silicon host.

Differential voltage relaxation analysis converts raw voltage-time data into logarithmic differential spectra ~ the derivative of cell voltage with respect to logarithmic time, written as dV/d(log t). This transformation sharpens gradual inflection points into clear peaks. Near full capacity, the formation of amorphous and crystalline lithium-silicon phases shifts the negative electrode’s equilibrium potential.

If charging rates exceed local lithium insertion capabilities, metallic lithium plates onto particle surfaces. During rest, this metallic layer functions as a parasitic internal micro-galvanic cell, driving lithium ions into empty interstitial sites and producing a distinct voltage plateau in the relaxation profile.

A cell charged at 1.5C and 15 degrees Celsius displays a primary relaxation peak at 420 seconds with an amplitude of 18 millivolts per logarithmic time decade.

Separating these mechanisms is essential for reliable health diagnostics and safety validation. Mistaking a metallic lithium re-intercalation peak for a harmless silicon phase transition leads to underestimating plating severity and missing early warnings of dendrite growth and internal shorts. On the other hand, mistaking silicon stress relaxation for active plating triggers false safety alarms that can retire healthy packs prematurely.

Disentangling the two signals requires tight control over pulse amplitude, rest duration, ambient temperature, and state of charge.

Silicon expands significantly during lithiation, creating mechanical stress across the composite electrode that alters the chemical potential of lithium in the alloy host. As this stress dissipates during open-circuit rest, the electrode potential shifts upward, closely mimicking the voltage rise caused by metallic lithium re-intercalation. Uncoupling these overlapping effects requires mapping how each responds to temperature, recent current history, and local charge distribution across the electrode stack.

Plateau

Thermodynamics dictates how lithiated materials behave at rest. Silicon-alloy anodes pass through sequential phase transformations as lithium enters the host structure, moving from pristine crystalline silicon to highly lithiated amorphous states, and eventually forming crystalline Li15Si4 at high states of charge and low anode potentials. Each transition appears as a two-phase equilibrium or a continuous solid solution, setting specific open-circuit potential plateaus.

Once current stops, electrode potential relaxes toward the thermodynamic equilibrium dictated by the local surface state of charge.

Thermodynamic Indicators of Plated Metal

Surface-deposited metallic lithium follows its own thermodynamic regime. Because pure lithium rests at zero volts against a lithium reference potential, surface plating clamps local anode potential near zero volts. During post-charge rest, this plated layer dissolves spontaneously as electrons enter the host matrix and lithium ions move into nearby un-lithiated graphite or silicon sites.

This chemical re-intercalation holds the anode potential low and flat until the metallic lithium reservoir is consumed, after which the voltage shifts rapidly.

Dissolution of the metallic layer leaves a sharp edge in the relaxation differential spectrum. As soon as the film disappears, the anode potential rises steeply toward the host’s intrinsic equilibrium potential. In the dV/d(log t) domain, this sudden drop creates a narrow, symmetric peak whose area correlates directly with the amount of reversibly plated lithium.

During rapid insertion, local anode potential can temporarily drop below zero volts.

Structural Stress and Phase Boundary Dynamics

During rapid lithium insertion, silicon alloy particles build up severe internal mechanical stress due to steep concentration gradients between shell and core. These gradients generate local pressure fields that shift electrochemical potential according to stress-potential coupling relations. As the cell rests, lithium diffuses inward to equalize concentration while stress relaxes through elastic recovery and plastic deformation.

This combined diffusion and stress relaxation alters cell voltage over longer timescales, producing a broad derivative peak that overlaps the metallic lithium re-intercalation window.

Standard IEC 62660-1 specifies that capacity qualification tests must exclude relaxation features occurring within thirty seconds of current interruption to eliminate pure ohmic drop errors.

Because plated lithium corrodes electrolyte rapidly, distinguishing chemical dissolution from mechanical stress relaxation relies on peak symmetry and activation energy. Silicon phase transitions carry a lower activation energy than the charge-transfer-controlled re-intercalation of metallic lithium. By measuring relaxation across multiple temperatures, activation energies can be extracted from Arrhenius plots of peak time constants to separate physical phase transitions from metallic dissolution.

Late relaxation inflections are sometimes attributed to non-hazardous structural rearrangements within the silicon matrix rather than active lithium plating. However, acceptance testing shows that genuine lithium re-intercalation peaks vanish completely when charging rates remain below the thermodynamic plating threshold at elevated temperatures, whereas silicon mechanical stress relaxation peaks persist across all charging rates whenever total state of charge is high.

Kinetics

Time-domain differentiation resolves overlapping electrochemical processes by separating their time constants. Converting raw open-circuit voltage recorded across a three-thousand-second rest period into differential voltage relaxation space ~ by taking the derivative of voltage with respect to the natural logarithm of time ~ yields distinct peaks at specific time coordinates that mark the governing relaxation mechanisms.

Worked Example of Peak Separation Analysis

Consider a 4.8 Ah 21700 cylindrical cell with a silicon-graphite composite anode containing a 12 percent silicon mass fraction. The cell is fast-charged at 2.0C to 100 percent state of charge under two thermal regimes: a 25 degrees Celsius baseline charge and a 5 degrees Celsius cold fast charge. Following current interruption at a 4.20 V cutoff, open-circuit voltage is sampled at 100 Hz for the first 10 seconds, then at 1 Hz for the remaining 3,600 seconds of rest.

At 25 degrees Celsius, the dV/d(log t) relaxation spectrum shows a single broad peak centered at t = 180 seconds with an amplitude of 12.4 mV/decade. This peak reflects lithium redistribution within the silicon-graphite matrix alongside mechanical stress release across the alloy particles. The feature spans 1.8 logarithmic decades, with a long tail extending past 1,000 seconds.

At 5 degrees Celsius, slower charge-transfer kinetics promote metallic lithium plating on the anode surface, producing two separate peaks in the relaxation spectrum. A sharp, high-amplitude peak appears at t = 85 seconds, reaching 34.6 mV/decade with a narrow full-width at half-maximum of 0.45 logarithmic decades. A second, smaller peak emerges later at t = 2,100 seconds, reflecting thermally delayed silicon stress relaxation.

Peak locations pinpoint the kinetic mechanisms involved. Here, the sharp peak at 85 seconds marks the exact time needed for the surface-plated lithium layer to re-intercalate into the graphite host. Integrating the area under this peak gives the total voltage displacement from metallic plating, offering a direct, non-destructive metric for plated lithium mass.

Where Does Metallic Lithium Re-Intercalation Obscure Phase Transition Kinetics?

Overlaps occur during charging at intermediate low temperatures, such as 10 degrees Celsius, where the time constant for metallic lithium re-intercalation shifts into the 300 to 800 second window ~ directly atop the primary silicon phase boundary signal. In this window, the two peaks blend into a single convoluted feature, masking individual peak centers and risking misdiagnosis of cell health.

Because uncompensated resistance distorts relaxation profiles, uncoupling merged features requires taking the second derivative of full-cell voltage with respect to logarithmic time, d2V/d(log t)2. Zero-crossing points in this second-derivative spectrum pinpoint the inflection times of the underlying components.

1. Data acquisition capturing open-circuit voltage at sampling frequencies non-linearly spaced from 100 Hz down to 0.1 Hz over a minimum relaxation time of 3,600 seconds.
2. Smoothing filter application using a non-causal Savitzky-Golay polynomial filter with a moving window scaled logarithmically to prevent signal attenuation at long times.
3. Logarithmic derivative computation calculating first and second derivatives of filtered voltage with respect to natural logarithm of time.
4. Baseline subtraction fitting a third-order polynomial to the tail region between 2,000 and 3,600 seconds to remove background solid-state diffusion drift.
5. Multi-peak deconvolution applying asymmetric Gaussian-Lorentzian cross-functions to solve individual peak amplitudes, widths, and time constants.

Because temperature shifts relaxation time constants, skipping multi-temperature peak tracking causes quantitative errors in lithium plating estimation that exceed 40 percent. Ignoring the thermal sensitivity of metallic re-intercalation leads to misinterpreting severe plating as routine silicon phase shifts, allowing damaged cells to remain in high-rate operation until dendrites cause failure.

Resolution

High-resolution analysis removes spectral ambiguity caused by cell aging, rising electrode impedance, and thermal fluctuations. Standard relaxation tracking breaks down when cell internal resistance grows, because ohmic IR recovery hides fast relaxation dynamics during the first sixty seconds of rest. Combining pulsed relaxation techniques with differential capacity correlation improves feature separation.

Correlating differential relaxation spectra with incremental capacity dQ/dV curves from low-rate discharge pinpoints the exact open-circuit potential regions where silicon phase changes occur. These silicon phase shifts happen at predictable equilibrium potentials regardless of cell age, whereas metallic lithium re-intercalation occurs strictly below zero volts anode potential during charge, generating a sharp relaxation signature scaled to the charge-step overpotential.

• Interfacial film degradation alters lithium ion transfer resistance across the solid electrolyte interphase, broadening metallic re-intercalation peaks and shifting their time centers toward longer rest durations.
• Active silicon particle isolation reduces total anode lithiation capacity, forcing remaining active silicon domains into deeper lithiation states that promote crystalline Li15Si4 formation at lower overall cell states of charge.
• Inhomogeneous current distribution generates localized lithium plating across center electrode folds while outer windings undergo pure silicon phase transitions, yielding multi-peaked relaxation profiles.
• Electrolyte depletion increases concentration polarization during high-current charging pulses, creating artificial long-duration diffusion tails that simulate silicon stress relaxation dynamics.

Quantifying plated metallic lithium mass requires establishing baseline relaxation profiles from fresh cells charged under non-plating conditions at 45 degrees Celsius. Subtracting this baseline silicon stress relaxation curve from post-fast-charge spectra isolates the pure metallic lithium re-intercalation signal.

When current densities at high C-rates exceed local exchange current capabilities, metallic deposits accumulate rapidly and reshape subsequent relaxation derivatives. Filtering algorithms must preserve these sharp, high-frequency inflections while smoothing thermal cycling noise from laboratory test chambers.

How far can logarithmic time resolution be compressed before high-frequency electrochemical noise destroys the mathematical validity of second-derivative zero-crossing determinations?

Diagnostics

Integrating differential relaxation diagnostics into automated screening lines requires explicit test definitions. Offline quality control protocols rely on multi-step, temperature-controlled profiles to confirm batch consistency before pack assembly. Testing hardware must use high-precision voltage sampling cards capable of microvolt resolution without drift across extended rest periods.

Because chemical potentials govern species transport, quality assurance procedures specify exact charging pre-histories to ensure reproducible relaxation spectra. Standardizing the step requires applying a constant current pulse to a set state of charge cutoff, followed immediately by an un-pulsed open-circuit rest lasting precisely 3,600 seconds. Ambient temperature must stay within 0.2 degrees Celsius to prevent thermal voltage shifts from masking phase transition peaks.

• Thermal equilibration period maintaining cell temperature within 0.2 degrees Celsius for two hours prior to applying fast-charge diagnostic current pulses.
• High-precision voltage logging recording cell terminal voltage at 100 Hz for 60 seconds, switching to 1 Hz up to 3,600 seconds with minimum 16-bit analog-to-digital converter resolution.
• Temperature-coefficient tracking repeating relaxation measurements at 15 degrees Celsius and 35 degrees Celsius to compute activation energies for resolved relaxation derivative peaks.
• Differential spectral transformation executing logarithmic time derivative transforms using a fixed-width window to isolate peak time constants.
• Plating mass estimation calculating total plated lithium quantity by integrating peak areas exceeding baseline silicon mechanical stress curves.

The presence of silicon alloys complicates standard aging metrics because stress-driven phase boundaries mean capacity fade alone cannot separate active silicon loss, dead lithium accumulation, and electrolyte consumption. Differential voltage relaxation spectra offer a non-destructive view into these internal degradation pathways without cell tear-downs or costly post-mortem analysis.

A contract clause mandating zero metallic lithium plating under 1.0C charging at 10 degrees Celsius requires verification via multi-temperature differential voltage relaxation spectroscopy.

Cell qualification records require complete documentation of relaxation test parameters. A datasheet showing clean relaxation curves without reporting exact test temperatures, sampling frequencies, and charge cutoff currents provides no real engineering value for fast-charge safety validation.

Margin

Integrating accurate relaxation decoupling algorithms into incoming cell quality checks grounds batch acceptance in physical degradation mechanics rather than gross capacity testing. Misinterpreting lithium plating as benign silicon stress relaxation risks approving cell lots prone to rapid capacity fade, rising impedance, and thermal runaway. Quantifying plated lithium mass at inspection provides the hard data needed to enforce warranty terms against suppliers delivering sub-spec silicon formulations.

When cell qualification specs omit relaxation peak separation metrics, buyers inherit hidden warranty liabilities tied to fast-charge degradation. Silicon-carbon cells showing only minor silicon phase relaxation remain stable across thousands of cycles, whereas those displaying even subtle metallic lithium re-intercalation peaks break down rapidly within two hundred fast-charge cycles.

Financial risk correlates directly with diagnostic capability. Achieving reliable fast-charging in high-energy silicon-alloy cells demands continuous verification of anode interphase kinetics. Implementing differential relaxation decoupling protects capital, sets unambiguous supplier compliance standards, and ensures pack safety across demanding operating temperatures.