[Paper Review] Equilibrium Thermochemistry and Crystallographic Morphology of Manganese Sulfide Nanocrystals

Junchi Chen, Tamilarasan Subramani+9 more|arXiv (Cornell University)|Mar 5, 2026

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TL;DR

The paper develops a DFT-based framework (r2SCAN+U) to predict equilibrium morphologies of MnS nanocrystals across RS, ZB, and WZ polymorphs as a function of sulfur chemical potential, and validates predictions with RS-MnS nanocubes and calorimetry.

ABSTRACT

Manganese sulfide (MnS) is a p-type magnetic semiconductor whose physicochemical properties are sensitive to nanocrystal (NC) morphology, yet the thermodynamic driving forces governing morphology across MnS polymorphs remain poorly understood. Here, we use density functional theory (DFT) to predict the equilibrium morphologies of rock salt (RS), zinc blende (ZB), and wurtzite (WZ) MnS NCs as a function of the relative chemical potential of sulfur, $Δμ_{S}$. Benchmarking against Heyd$\unicode{x2013}$Scuseria$\unicode{x2013}$Ernzerhof (HSE06) hybrid functional calculations reveals that the r$^2$SCAN meta-generalized gradient approximation reproduces experimental lattice constants and thermochemical reaction energies but underestimates S-terminated polar surface energies by up to a factor of five; applying a Hubbard $U$ correction (r$^2$SCAN+$U$, $U = 2.7$ eV) to the Mn 3d states brings the results into close agreement with HSE06. Using the validated r$^2$SCAN+$U$ framework with the Gibbs$\unicode{x2013}$Wulff theorem, we predict that RS-MnS NCs favor nanocubes across nearly the entire stability window, ZB-MnS NCs transform from rhombic dodecahedra (Mn-rich) to polyhedra with 16 triangular faces (S-rich), and WZ-MnS NCs adopt rod-like morphologies with $Δμ_{S}$-sensitive base truncation. Synthesized RS-MnS NCs confirm the predicted cubic morphology, and high-temperature oxidative solution calorimetry yields an apparent surface energy of 1.15 $\pm$ 0.38 J$\cdot$m$^{-2}$, higher than the theoretical equilibrium value (0.42$\unicode{x2013}$0.43 J$\cdot$m$^{-2}$) due to high-index facet exposure, surface area uncertainty, and non-ideal surface configurations in real samples. This work establishes a framework for predicting the equilibrium morphologies of metal chalcogenide NCs.

Motivation & Objective

• Reveal thermodynamic driving forces governing MnS nanocrystal morphologies across polymorphs (RS, ZB, WZ).
• Benchmark DFT functionals for lattice constants and thermochemical energies against experiments and hybrids.
• Develop a complete framework to obtain individual polar surface energies via wedge/relative-energy methods.
• Predict equilibrium morphologies as a function of sulfur chemical potential ∆µS using Gibbs–Wulff theory.
• Experimentally validate RS-MnS morphology and calibrate apparent surface energy against theory.

Proposed method

• Benchmark lattice constants and reaction energies for MnS polymorphs using six XC functionals and HSE06 benchmarks.
• Use wedge models to decouple polar surface energies for ZB-MnS and relative-surface-energy methods for WZ-MnS.
• Apply r2SCAN+U (U = 2.7 eV) to Mn 3d states to correct S-terminated polar energies.
• Construct Wulff shapes from computed surface energies as a function of ∆µS.
• Validate RS-MnS surface energies with high-temperature oxidative solution calorimetry and TEM-derived NC sizes.

Experimental results

Research questions

• RQ1 What are the stable MnS nanocrystal morphologies for RS, ZB, and WZ as a function of ∆µS within the bulk MnS stability window?
• RQ2 How well do r2SCAN and r2SCAN+U reproduce lattice constants and surface energies for MnS polymorphs compared to HSE06?
• RQ3 Can Gibbs–Wulff constructions using corrected surface energies predict experimentally observed MnS NC shapes?
• RQ4 How does sulfur chemical potential influence polar surface terminations and facet exposure in each MnS polymorph?
• RQ5 What experimental measurements corroborate the computational morphology predictions for RS-MnS?

Key findings

• RS-MnS nanocrystals are predicted to be cubic across nearly the entire ∆µS stability window, consistent with synthesized cubes.
• ZB-MnS morphologies transition from rhombic dodecahedra to 16-faced polyhedra as ∆µS increases toward S-rich conditions.
• WZ-MnS nanocrystals adopt rod-like morphologies with ∆µS-sensitive base truncation, maintaining a ∼ invariant rod top.
• r2SCAN underestimates S-terminated polar surface energies; applying U = 2.7 eV to Mn 3d states brings r2SCAN+U into close agreement with HSE06 for all facets.
• Experimental RS-MnS nanoscale cubes and calorimetry yield an apparent surface energy of 1.15 ± 0.38 J·m−2, higher than the theoretical 0.42–0.43 J·m−2 due to real-sample effects.