A comparison of simulation tools for Muon-Induced X-ray Emission (MIXE) in thin films: a study case with lithium batteries

This paper presents a comparative study of SRIM, GEANT4, and PHITS simulation tools for modeling muon transport and X-ray emission in lithium battery thin films, finding that while all three accurately predict muon depth profiles, PHITS offers the added capability of generating X-ray spectra with high accuracy in relative intensities despite a systematic energy offset in K-line transitions.

The Gist

Imagine you have a very special, invisible flashlight. But instead of shining light, this flashlight shoots tiny, heavy particles called muons (think of them as "super-heavy electrons"). When these muons hit an object, they don't just bounce off; they get stuck inside the atoms, causing the atoms to glow with a very specific, high-energy light (X-rays). This is called Muon-Induced X-ray Emission (MIXE).

Scientists use this "muon flashlight" to look inside things without breaking them open—like peering into a sealed lithium-ion battery to see how the chemicals are moving, or looking at an ancient artifact to see what it's made of.

However, before they can use this tool in the real world, they need to know exactly how deep the muons will go and what kind of light they will produce. To figure this out, they use computer programs (simulations) to predict the outcome.

This paper is a "taste test" comparing three different computer programs to see which one does the best job predicting what happens inside a battery.

The Three Contenders

The authors tested three famous simulation tools:

1. SRIM: Think of this as the old-school, lightweight calculator. It's fast and great for simple, solid objects. However, it wasn't originally built for muons, so the scientists had to trick it by pretending muons were just heavy protons. It's like using a bicycle map to navigate a highway; it works for short trips, but gets confused if there are long stretches of empty road (like air) before the destination.
2. GEANT4: This is the gold-standard, Swiss Army knife. It's the most complex and accurate tool, used by physicists worldwide. It's like a high-end GPS that knows every pothole and detour. It's very reliable but can be heavy and slow to run.
3. PHITS: This is the new challenger with a special trick. It's very similar to GEANT4 in how it tracks the particles, but it has a built-in feature to predict the "glow" (the X-ray spectrum) that the others don't do as easily. However, it has a quirk: it sometimes guesses the color of the light slightly wrong (like calling a red light "orange"), even though it gets the brightness right.

The Test Drive: A Lithium Battery

The scientists used a lithium-ion battery as their test subject. Imagine the battery is a multi-layered sandwich:

• The Bread: Plastic and aluminum foil (the pouch).
• The Filling: Layers of chemicals (NMC, graphite) and separators (like paper or thin plastic).
• The Air: There is a gap of air between the muon beam and the battery.

They fired muons at the battery at different speeds and asked the three computer programs: "Where do the muons stop, and what X-rays do they make?"

The Results: Who Won?

1. Tracking the Muons (Where do they stop?)

• GEANT4 and PHITS were almost identical twins. They both predicted exactly where the muons would get stuck in the battery layers, even when the muons had to travel through a long stretch of air first. They are both excellent for this job.
• SRIM got confused by the air. Because it's a simpler program, it struggled to calculate the path through the empty space before hitting the battery. It's like a runner who gets tired just running on the track before the race even starts. However, once the muons were inside the solid battery layers, SRIM was actually quite good and fast.

2. Predicting the Glow (The X-ray Spectrum)

• PHITS was the only one that could generate the full "spectrum" (the list of colors/energies of the X-rays). This is crucial because different elements (like Nickel or Copper) glow at specific frequencies.
• The Glitch: PHITS had a systematic error. For heavier elements, it predicted the X-ray energy to be slightly too high (like a radio station playing a song at the wrong speed). It was off by a noticeable amount.
• The Good News: Even though the "pitch" was wrong, the volume was right. PHITS correctly predicted how bright the light would be for each element. This means scientists can still identify which elements are present (e.g., "That's Nickel!") and how much of them there are, they just need to fix the "pitch" calibration.

The Takeaway

This paper is essentially a user manual for scientists who want to use muons to study batteries or other complex objects.

• If you just need to know how deep the muons go: You can use SRIM for a quick, rough estimate, or GEANT4/PHITS for high precision.
• If you need to predict the X-ray colors: PHITS is the best tool available, provided you apply a "correction factor" to fix its energy bias.
• The Future: The authors suggest that in the future, they can combine the best of both worlds: use PHITS to track the particles and predict the brightness, but swap in a more accurate database for the exact energy colors.

In short: The scientists found that while no single computer program is perfect, PHITS is a powerful new tool that, once tuned up, will allow researchers to "see" inside batteries and other objects with incredible clarity, helping us build better energy storage and preserve history.

Technical Summary

1. Problem Statement

Muon-Induced X-ray Emission (MIXE) is a non-destructive analytical technique used to probe atomic-scale properties and perform depth-resolved elemental analysis in complex, layered systems (e.g., lithium-ion batteries, cultural heritage artifacts). While the experimental capabilities at the Paul Scherrer Institute (PSI) are well-established, there is a critical need for robust simulation tools to:

• Predict muon stopping depth profiles in multilayer geometries with varying densities.
• Simulate the resulting muonic X-ray spectra for experimental design and data interpretation.
• Address the lack of standardized benchmarks for Monte Carlo codes in this specific energy regime and geometry.

The authors aim to evaluate the reliability and practicality of three major simulation frameworks—SRIM, GEANT4, and PHITS—for modeling muon transport, stopping, and atomic cascades in a benchmark lithium-ion battery cell.

2. Methodology

The study employed a multi-faceted approach combining experimental data validation with comparative code benchmarking:

• Benchmark Target: A multilayer lithium-ion battery pouch cell was used as the test case. It consists of eight distinct layers (Pouch, Al, NMC, Whatman, Celgard, Graphite, Cu, Pouch) with varying densities (1.05–8.92 g/cm³) and thicknesses (10–260 µm).
• Experimental Setup: Data was sourced from the GIANT spectrometer at PSI's $\pi$E1 beamline. Negative muons ($\mu^-$) were implanted with momenta ranging from 15 to 60 MeV/c. The setup included a plastic scintillator tagger, a titanium window, and a 10 cm air gap before the sample.
• Simulation Frameworks:
  • SRIM (Stopping and Range of Ions in Matter): Used as a lightweight benchmark. Since SRIM does not natively support muons, "pseudo-muons" were modeled as protons with rescaled mass ($m_\mu \approx 0.113$ amu). It lacks native muon capture physics.
  • GEANT4: Used as the reference standard for particle transport (v11.2.1, physics list QGSP_BIC_HP_EMZ).
  • PHITS (Particle and Heavy Ion Transport code System): Used for both transport and muonic cascade simulation (v3.34). It incorporates specific modules for muon capture cross-sections (Suzuki et al.) and the Akylas-Vogel routine for generating muonic X-ray spectra.
• Validation Strategy:
  1. Transport/Stopping: Simulated mean stopping depths (MSD) and range straggling were compared against each other and experimental data across a momentum scan (20–30 MeV/c).
  2. Spectral Modeling: PHITS-generated X-ray spectra were compared against theoretical calculations from MuDirac (a specialized code solving the Dirac equation for muonic atoms) and experimental GIANT data.

3. Key Contributions

• First Comprehensive Benchmark: This is the first study to directly compare SRIM, GEANT4, and PHITS specifically for MIXE applications in micrometer-scale, multilayer systems.
• Identification of SRIM Limitations: The study quantifies the limitations of SRIM in low-density media (e.g., air gaps) preceding thin films, attributing discrepancies to floating-point precision and the lack of muon capture physics.
• Spectral Bias Characterization: The authors identified a systematic energy offset in PHITS-generated spectra for medium-to-high Z elements (K-lines), tracing the root cause to an energy scaling issue in the aama.f cascade routine.
• Validation of Relative Intensities: Despite energy offsets, the study confirms that PHITS accurately predicts relative line intensities and spectral shapes, validating its utility for element identification.

4. Key Results

A. Muon Stopping Depths

• GEANT4 vs. PHITS: The two codes showed excellent agreement (differences < 1–2%) for mean stopping depths across all momenta and layer interfaces, even in the presence of sharp density contrasts (e.g., air to Al).
• SRIM Discrepancies: SRIM showed significant deviations (up to 5–7%) when large low-density volumes (like the 10 cm air gap) preceded the target. This was attributed to numerical precision limits in tracking long trajectories and the averaging procedure used for mean depth.
• Conclusion on Transport: GEANT4 and PHITS are the preferred tools for accurate transport modeling. SRIM remains useful for rapid, preliminary range estimates within compact geometries but is less reliable for complex setups involving air gaps.

B. X-ray Emission Spectra

• Energy Accuracy: PHITS exhibited a systematic overestimation of K-line transition energies for medium and high-Z elements (e.g., Ni, Cu).
  • Example: For $^{58}$Ni K$\alpha_1$, MuDirac predicts ~1432 keV, while PHITS predicts ~1673 keV (a ~16.8% error).
  • The error increases with atomic number ($Z$) due to insufficient relativistic and finite-nuclear-size corrections in the PHITS cascade routine.
• Intensity and Shape: Despite the energy bias, PHITS successfully reproduced the relative intensities and spectral shapes.
  • The ratio of K-line to L-line intensities ($K\alpha/L$) was calculated as 1.54 in PHITS vs. 3.72 in experiment. While the absolute ratio differs (likely due to unmodeled detector efficiency and self-absorption), the code correctly captures the hierarchy of cascade transitions.
• Element Identification: The simulation successfully predicted the momentum-dependent emergence of specific elemental lines (e.g., Cu K-lines appearing only at higher momenta when muons reach the back current collector), confirming the code's ability to model depth-resolved analysis.

5. Significance and Future Outlook

• Practical Utility: The study establishes SRIM and PHITS as practical, user-friendly tools for experimenters. SRIM is suitable for quick range estimation, while PHITS offers a comprehensive solution for both stopping profiles and spectral prediction.
• Path to Correction: The systematic energy bias in PHITS can be remedied by coupling the PHITS transport module with external, high-precision transition energy tables (e.g., from MuDirac) or by integrating the MuDirac routine directly into PHITS. This would allow PHITS to serve as a predictive tool for MIXE spectroscopy.
• Broader Impact: The benchmarking strategy is transferable to other heterogeneous systems, including geological specimens, archaeological artifacts, and solid-state battery architectures.
• Platform Development: These results provide the foundational data for developing a web-based simulation platform to assist future MIXE users in experimental design and data interpretation at PSI and other facilities.

In conclusion, while PHITS requires calibration for absolute energy accuracy in heavy elements, it is validated as a robust tool for predicting muon stopping distributions and relative spectral intensities, making it a cornerstone for the advancement of MIXE applications.