Anisotropic Crystallization Kinetics and Interfacial Dynamics of Phase-Change Material Sb$_2$S$_3$ from Machine Learning Force Field Simulations

This study utilizes a machine learning force field to reveal that Sb$_2$S$_3$ exhibits anisotropic crystallization driven by its quasi-1D ribbon structure, with interface-controlled growth kinetics characterized by a significantly lower activation energy than diffusion, offering key insights for optimizing its performance in data storage and photonics applications.

The Gist

Imagine you have a magical material called Antimony Sulfide (Sb₂S₃). This material is like a chameleon for computers and light-based technology: it can instantly switch between being a solid, ordered crystal (like a neatly stacked library) and a messy, disordered liquid (like a pile of scattered books). This ability to switch back and forth is what makes it useful for storing data and controlling light.

However, scientists have a hard time seeing exactly how this switching happens at the level of individual atoms. It's too fast and too small for standard microscopes. To solve this, the researchers in this paper built a super-smart computer brain (called a Machine Learning Force Field) that acts like a high-speed, ultra-accurate simulation engine. This "brain" learned the rules of how these atoms interact from complex physics calculations, allowing the team to run a massive movie of the atoms moving for 40 nanoseconds—a huge amount of time in the atomic world.

Here is what they discovered, explained through simple analogies:

1. The "Ribbon" Structure

Think of the solid crystal form of this material not as a block of ice, but as a bundle of long, strong ribbons.

• The Fast Lane: The atoms are glued together very tightly along the length of these ribbons (like strong covalent bonds).
• The Slow Lane: Between the ribbons, the connection is much weaker, like a gentle hug (van der Waals forces).

Because of this, the material grows fastest in the direction of the ribbons. The researchers found that the crystal grows about 4 times faster along the [100] direction (the ribbon direction) than in other directions. It's like a zipper closing: it snaps shut quickly along the teeth, but it's much harder to pull the fabric apart sideways.

2. The "Speed Limit" of the Switch

The team measured how much energy is needed for two different things to happen:

• Moving the atoms (Diffusion): Imagine atoms trying to swim through a crowded pool. This is hard work. The energy needed for this is high (about 1.16 to 1.56 eV).
• Locking into place (Crystal Growth): Imagine the atoms arriving at the edge of the crystal and snapping into their final spot. This is surprisingly easy. The energy needed is much lower (about 0.55 to 0.57 eV).

The Big Discovery: In many other similar materials, the "swimming" (moving atoms) is the slow, difficult part that limits the speed. But for Sb₂S₃, the "swimming" isn't the bottleneck. The bottleneck is actually how fast the atoms can attach to the crystal edge. The material is "interface-controlled." It's like a factory where the workers (atoms) can run to the assembly line very fast, but the machine (the crystal edge) can only snap them into place so quickly.

3. The "Goldilocks" Temperature

The researchers found that the material doesn't grow fastest when it's super hot or super cold.

• If it's too hot, the atoms are too jittery to stick together.
• If it's too cold, the atoms are too sluggish to move.
• There is a "sweet spot" (around 100 degrees below the melting point) where the growth is most efficient. Interestingly, this sweet spot is much closer to the melting point for Sb₂S₃ than for other common materials, meaning it can switch states very quickly with less temperature change.

4. The "Liquid" Memory

Even when the material is melted into a liquid, it doesn't become a completely random soup. The atoms still hold onto a faint memory of their ribbon-like structure. They keep some of their local "dance moves" (bond angles) similar to the solid form. This is why the switch back to solid is so fast and reliable—the atoms don't have to learn a new dance; they just need to remember the steps they were already doing.

Summary

In short, the paper used a powerful computer simulation to watch how Sb₂S₃ turns from liquid to solid. They found that:

1. It grows fastest along its "ribbon" direction.
2. The speed of the switch is limited by how fast atoms can snap into place at the edge, not by how fast they can move through the liquid.
3. This makes it a very efficient material for fast-switching technologies, as it doesn't need to wait for atoms to travel long distances to form a crystal.

This study provides a clear, atom-by-atom map of how this material works, helping engineers understand why it is so good at switching states quickly and reliably.

Technical Summary

Technical Summary: Anisotropic Crystallization Kinetics and Interfacial Dynamics of Phase-Change Material Sb2S3 from Machine Learning Force Field Simulations

Problem Statement
Antimony sulfide (Sb2S3) is a promising phase-change material (PCM) for data storage and photonic applications due to its Earth-abundance, robust phase stability, and superior optical properties (high refractive index contrast with low extinction coefficients) compared to conventional PCMs like Ge2Sb2Te5 (GST). However, experimental techniques face intrinsic limitations in resolving the atomic-scale mechanisms, transient intermediate phases, and local nucleation events that govern crystallization kinetics across broad temperature ranges. A comprehensive understanding of the structural evolution during the crystal-to-liquid transition, specifically regarding facet-dependent growth rates and interfacial dynamics, has been lacking in the literature.

Methodology
To overcome the timescale and system-size limitations of ab initio molecular dynamics (MD), the authors developed a Machine Learning Force Field (MLFF) based on the Moment Tensor Potential (MTP) framework.

• Force Field Development: An active learning (bootstrapping) approach was employed, starting with one crystalline and 20 non-crystalline structures. The training set was iteratively expanded by sampling configurations from MD simulations and labeling them with Density Functional Theory (DFT) calculations (using VASP with PBE-GGA and vdW corrections). The final dataset comprised 2,094 structures, achieving root-mean-squared errors (RMSE) of 7 meV/atom for energy and 0.17 eV/Å for forces.
• Validation: The MTP model was validated against experimental X-ray diffraction (XRD) data and ab initio MD results. It successfully reproduced lattice parameters, radial distribution functions (RDFs), and interatomic distances for both crystalline and liquid phases.
• Simulation Setup: Large-scale MD simulations were conducted using the LAMMPS-MLIP interface on a 7,680-atom Dual Phase Coexistence (DPC) model. This setup allowed for the simulation of crystal growth over 40 ns at temperatures ranging from 600 K to 1200 K. Three specific crystal facets—[100], [010], and [001]—were investigated to analyze anisotropic growth.

Key Contributions and Results

1. Structural Characterization:

   • Crystalline vs. Liquid: The study confirmed that the crystalline phase possesses distinct coordination geometries (trivalent Sb in distorted trigonal pyramids and pentavalent Sb in square pyramids) with specific bond angles. In contrast, the liquid phase exhibits a broad distribution of bond angles (0–180°) centered around 90° and a reduction in average Sb coordination numbers (from 3/5 in crystal to 2–4 in liquid).
   • Local Order: Despite the loss of long-range order, the liquid phase retains local motifs resembling distorted pyramidal or quasi-tetrahedral Sb–S coordination, facilitating rapid and reversible phase transitions.

2. Anisotropic Crystal Growth Kinetics:

   • Facet Dependence: The growth rates ($V_g$) were found to be highly anisotropic. The [100] facet exhibited the fastest growth velocity, followed by [010] and [001]. At 875 K, the [100] growth rate was approximately 1.6 times faster than [010] and 2.8 times faster than [001].
   • Mechanism: The rapid growth along the [100] direction is attributed to the quasi-1D ribbon-like structure of the Sb2S3 crystal, where strong Sb-S covalent bonds form continuously along the ribbon axis, reducing surface energy. Lateral interactions between ribbons are weaker (van der Waals).
   • Thermodynamics: The maximum growth rate occurred at 875 K, corresponding to an optimal undercooling ($\Delta T_{opt}$) of approximately 100 K relative to the simulated melting point (975 K). This $\Delta T_{opt}$ is significantly lower than that of GST (270 K) and GeTe (210 K), suggesting better thermal responsiveness for Sb2S3.

3. Activation Energies and Growth Mechanism:

   • Growth vs. Diffusion: Using the Wilson-Frenkel model, the activation energy for crystal growth ($\Delta E_{a}^{WF}$) was calculated to be 0.55–0.57 eV across the facets. In contrast, the activation energy for atomic diffusion ($\Delta E_a$) in the interfacial liquid layer was significantly higher, ranging from 1.16 to 1.56 eV.
   • Interface Control: The finding that $\Delta E_{a}^{WF} < \Delta E_a$ indicates that Sb2S3 crystallization is interface-controlled rather than diffusion-limited. Atomic attachment at the solid–liquid interface is energetically favored over long-range atomic transport. This contrasts with GST and GeTe, where growth is predominantly diffusion-limited.

Significance
The paper demonstrates that the developed MTP-based MLFF can accurately capture the atomistic origins of structural evolution and crystallization kinetics in Sb2S3 at a scale (7,680 atoms, 40 ns) inaccessible to ab initio methods. The study provides the first detailed mechanistic view of facet-dependent growth in Sb2S3, revealing that its crystallization is driven by local ordering at the interface rather than bulk diffusion. These insights into the anisotropic growth rates, low optimal undercooling, and interface-controlled kinetics offer a foundation for optimizing Sb2S3 functionality, specifically regarding switching speed, reliability, and energy efficiency in next-generation optical and electronic devices.