Sodium Molybdate Liquid Alloys in MoS2 Growth

• Sodium molybdate liquid alloys are Na–Mo–O catalytic liquids engineered to create Mo-rich/S-poor conditions that favor the formation of Mo-polar 5|7 grain boundaries in monolayer MoS2.
• They function as both a precursor reservoir and a kinetic catalyst, lowering activation barriers and promoting defect reordering and smoother boundary migration during vapor–liquid–solid growth.
• Utilizing these alloys improves optical and electronic properties by suppressing deleterious S 5|7 defects, resulting in enhanced photoluminescence and controlled trion formation.

Sodium molybdate liquid alloys, as reported for monolayer MoS$_2$ growth, are Na–Mo–O catalytic liquids deliberately engineered to control grain-boundary (GB) defect topology during vapor–liquid–solid (VLS) synthesis. In this setting, the alloy is not merely a precursor reservoir: its composition, liquid-phase stability, and Na activity impose a Mo-rich / S-poor thermodynamic environment, promote defect reordering, and suppress optically detrimental Na-decorated S-polar boundary defects. The resulting effect is deterministic selection of Mo-polar 5|7 GB cores with a yield exceeding 95%, together with markedly stronger photoluminescence (PL) than in vapor–solid–solid (VSS) growth that produces abundant S 5|7 defects (Choi et al., 30 Jul 2025).

1. Composition, phase state, and thermodynamic role

In the reported system, the relevant catalytic phase is a Na–Mo–O ternary liquid alloy, often described as a sodium molybdate liquid alloy. Its effective composition is a Mo-rich eutectic composition of order $\sim 20$ mol% Mo, and it is liquid above the Na–Mo–O eutectic temperature, $T_m \approx 500^\circ\text{C}$ (Choi et al., 30 Jul 2025). The VLS growth temperature is $600^\circ\text{C}$, so the Na–Mo–O molten alloy forms under those conditions, whereas solid MoO$_x$ on Na-poor glass remains solid up to $T_m \sim 800^\circ\text{C}$.

The alloy forms on soda-lime glass, which contains Na and softens around $T_g \approx 570^\circ\text{C}$. At $600^\circ\text{C}$, Na diffuses out and reacts with Mo–O species to form Na–Mo–O liquid droplets or alloys. By contrast, on alkali-aluminosilicate glass, with higher $T_g \approx 630^\circ\text{C}$, Na is not mobilized and only solid MoO$_x$ forms, leading to VSS growth. The gaseous precursors are Mo(CO)$\sim 20$0 for Mo and (C$\sim 20$1H$\sim 20$2)$\sim 20$3S for S.

A central function of the liquid alloy is to define the chemical-potential boundary condition at the growth front. The quantities $\sim 20$4 and $\sim 20$5 control defect thermodynamics, and the Na–Mo–O liquid is described as Mo-rich / S-poor relative to the vapor environment. Because the liquid is a large reservoir compared to the monolayer film, temporal gas-phase fluctuations only weakly perturb the $\sim 20$6 and $\sim 20$7 experienced by the growing edge and GB. In the paper’s density functional theory (DFT) treatment, the GB formation energy per core is written as

$\sim 20$8

with $\sim 20$9. Within this framework, the alloy enforces low $T_m \approx 500^\circ\text{C}$0, i.e. Mo-rich conditions, under which Mo-polar 5|7 GB defects are thermodynamically favored over S-polar 5|7 defects (Choi et al., 30 Jul 2025).

2. Function in vapor–liquid–solid growth of monolayer MoS$T_m \approx 500^\circ\text{C}$1

The presence or absence of the Na–Mo–O liquid defines the growth mode. On soda-lime glass at $T_m \approx 500^\circ\text{C}$2, Na–Mo–O liquid droplets form on the surface, the vapor precursors decompose and dissolve into the liquid alloy, and MoS$T_m \approx 500^\circ\text{C}$3 nucleates and grows at the liquid–substrate or liquid–MoS$T_m \approx 500^\circ\text{C}$4 triple line. This is described as a classic VLS picture implemented in a strictly 2D film (Choi et al., 30 Jul 2025). On alkali-aluminosilicate glass at the same temperature, only solid MoO$T_m \approx 500^\circ\text{C}$5 is present, so growth proceeds by vapor–solid–solid mechanisms with no liquid alloy.

Two roles are explicitly assigned to the sodium molybdate liquid alloy. First, it acts as a source or reservoir that stores Mo and S in a dense phase and provides a steady supply to the growth front. Second, it acts as a catalyst: Na in the liquid lowers kinetic barriers for bond rearrangement and facilitates defect reordering at GBs.

The reported VLS sequence consists of alloy formation, dissolution of gaseous precursors into the droplet, nucleation of monolayer MoS$T_m \approx 500^\circ\text{C}$6 at the liquid–surface interface, and lateral growth sustained by transport through the liquid. During grain coalescence, GBs form while the adjacent MoS$T_m \approx 500^\circ\text{C}$7 remains in dynamic contact with the alloy. The key process is a dissolution–recrystallization cycle in which MoS$T_m \approx 500^\circ\text{C}$8 near the GB can dissolve back into the liquid alloy and reprecipitate. This enables restructuring toward the lowest-$T_m \approx 500^\circ\text{C}$9 configuration and migration that shortens total GB length. In effect, the liquid keeps the boundary in a thermodynamically annealable state during growth rather than allowing it to freeze immediately into a kinetically selected configuration (Choi et al., 30 Jul 2025).

3. Selection of grain-boundary topology and polarity

In monolayer MoS$600^\circ\text{C}$0, a tilt GB between misoriented grains is accommodated by a periodic array of dislocation cores with smallest Burgers vector $600^\circ\text{C}$1. The relevant low-energy cores are 5|7 defects of two polarities. Mo 5|7 defects contain a homoelemental Mo–Mo bond and have $600^\circ\text{C}$2, whereas S 5|7 defects contain a homoelemental S–S bond and have $600^\circ\text{C}$3. The defect orientation relative to the GB is quantified by the inclination angle $600^\circ\text{C}$4: $600^\circ\text{C}$5 corresponds to Mo 5|7 defects with defect direction vector $600^\circ\text{C}$6 parallel to the symmetric GB vector $600^\circ\text{C}$7, and $600^\circ\text{C}$8 corresponds to S 5|7 defects (Choi et al., 30 Jul 2025).

For a given tilt angle $600^\circ\text{C}$9, the defect density $_x$0 along the boundary follows the expected AC-GB model in both VSS and VLS. The principal difference is not the geometrically required density of dislocation sites, but which 5|7 core occupies those sites. DFT shows that the relative formation energy of Mo-polar and S-polar 5|7 defects depends strongly on $_x$1. In Mo-rich / S-poor conditions, Mo 5|7 defects have lower $_x$2 than S 5|7; in Mo-poor / S-rich conditions, S 5|7 becomes more stable. The paper expresses this as the sign change of

$_x$3

with $_x$4 in the Mo-rich regime and $_x$5 in the S-rich regime (Choi et al., 30 Jul 2025).

Experimentally, high-angle annular dark-field scanning transmission electron microscopy and orientation analysis show that VLS-grown GBs are dominated by $_x$6 defects and are overwhelmingly composed of Mo 5|7 cores, with minor Mo 6|8 derivatives. The reported yield of Mo 5|7 exceeds 95% along GBs from a count of 150 defects. By contrast, VSS-grown GBs show a mixed $_x$7 distribution containing both $_x$8 and $_x$9 populations, together with derivative cores including Mo 6|8, Mo 5|7S, S 4|6, and S$T_m \sim 800^\circ\text{C}$0 5|7. This is attributed to temporal and spatial variation of $T_m \sim 800^\circ\text{C}$1 and to kinetic freezing. A concise interpretation is that the sodium molybdate liquid alloy converts GB polarity from a mixed outcome into a single-polarity configuration dominated by thermodynamically favored Mo-polar 5|7 defects (Choi et al., 30 Jul 2025).

4. Kinetic reordering, migration, and high-angle boundary self-organization

The liquid environment affects not only thermodynamics but also kinetics. Under a classical VSS zipping picture, once two tilted grains meet, local geometry constrains which $T_m \sim 800^\circ\text{C}$2 values can appear and the resulting GB structure is kinetically pinned. In the Na–Mo–O-mediated VLS regime, MoS$T_m \sim 800^\circ\text{C}$3 near the boundary can dissolve into the liquid alloy and resolidify, while Na lowers activation barriers for breaking and reshaping Mo–Mo and Mo–S bonds. This allows local defect motifs to reorder into a single thermodynamically optimal Mo 5|7 array and permits curvature-driven GB migration. The observed VLS boundaries are therefore smoother, with fewer kinks, and shorter in total length than VSS boundaries (Choi et al., 30 Jul 2025).

The same thermodynamic bias persists at high tilt angle, where a dense array of identical 5|7 defects would otherwise generate excessive elastic strain. In many systems, such strain can be relieved by alternating Mo 5|7 and S 5|7 cores. Here, because S 5|7 is thermodynamically disfavored under Mo-rich VLS conditions, the reported relaxation pathway is deformation twinning via mirror twin boundaries (MTBs). The paper presents a case with overall misorientation $T_m \sim 800^\circ\text{C}$4 between grains A and B, decomposed into an MTB between A and A$T_m \sim 800^\circ\text{C}$5 with $T_m \sim 800^\circ\text{C}$6 and a low-angle tilt GB between A$T_m \sim 800^\circ\text{C}$7 and B with $T_m \sim 800^\circ\text{C}$8. The associated local shear strain is reported as $T_m \sim 800^\circ\text{C}$9 at the high-angle GB intersection, relaxing to $T_g \approx 570^\circ\text{C}$0 elsewhere (Choi et al., 30 Jul 2025).

The mechanistic sequence described is specific: an initially formed high-angle GB comprises closely packed Mo 5|7 defects; strain accumulates near the weakest Mo–Mo homoelemental bond; rather than introducing thermodynamically disfavored S 5|7 cores, the lattice undergoes lateral slip of S planes, nucleating and propagating an MTB with 4|4 chains. Throughout this process, the liquid alloy acts as a buffer that absorbs and emits dislocations or defects while preserving the Mo-polar preference. This suggests that sodium molybdate liquids function as kinetic mediators of boundary self-organization as much as they function as precursor reservoirs (Choi et al., 30 Jul 2025).

5. Optical and electronic consequences of Na-mediated defect chemistry

The optical contrast between VLS and VSS boundaries is established using samples in which growth mode is switched in situ: growth begins in VLS mode at $T_g \approx 570^\circ\text{C}$1, then the sample is cooled to $T_g \approx 570^\circ\text{C}$2, below $T_g \approx 570^\circ\text{C}$3, so that Na–Mo–O solidifies and growth switches to VSS. This yields a single crystal containing GBs formed by both mechanisms under nearly identical macroscopic conditions. Grain interiors in the two regions show similar PL intensity and spectra, indicating that the growth-mode dependence is localized primarily at GBs (Choi et al., 30 Jul 2025).

For representative boundaries with $T_g \approx 570^\circ\text{C}$4, VLS GBs exhibit PL intensity comparable to or higher than neighboring grain interiors and show no significant peak shift. VSS GBs, by contrast, exhibit PL intensity reduced by up to $T_g \approx 570^\circ\text{C}$5 and a PL peak red shift of $T_g \approx 570^\circ\text{C}$6 meV at a power density of $T_g \approx 570^\circ\text{C}$7 W/cm$T_g \approx 570^\circ\text{C}$8. In continuous polycrystalline films, VLS-grown samples with Mo-5|7 GBs have stronger global PL, whereas VSS-grown samples containing many S 5|7 GBs are weaker. Deconvolution into neutral exciton and negative trion contributions gives $T_g \approx 570^\circ\text{C}$9 for VLS and $600^\circ\text{C}$0 for VSS, indicating higher trion weight in VLS films despite the stronger PL (Choi et al., 30 Jul 2025).

The reported resolution of this apparent paradox lies in boundary-specific Na defect chemistry. DFT density of states calculations show that bare Mo 5|7, Mo 6|8, S 5|7, and S 4|6 defects all produce deep midgap states. Na binds more strongly at these defect cores than on pristine lattice, and each defect can host at least two Na atoms in energetically favorable configurations. However, the electronic consequence of Na adsorption depends on the core type. For Mo 5|7, Mo 6|8, and S 4|6, the Fermi level remains deep below the conduction-band minimum by $600^\circ\text{C}$1 eV even with two Na atoms; the donated electrons are largely trapped in deep defect states, so these sites do not strongly dope the film $600^\circ\text{C}$2-type. For S 5|7, by contrast, the density of midgap states is relatively low even after Na adsorption, so Na donors shift $600^\circ\text{C}$3 into or near the conduction-band minimum. The surplus electrons enter the conduction band, producing effective $600^\circ\text{C}$4-type doping and trion formation (Choi et al., 30 Jul 2025).

Within the paper’s interpretation, S 5|7 + Na complexes are donor-type defects that cannot fully localize donated electrons and simultaneously act as non-radiative recombination centers for charged excitons, substantially quenching PL. Mo 5|7 + Na and related Mo-type defects behave differently: they act as deeper traps and do not promote the same non-radiative channels. Because VSS growth generates a significant fraction of S 5|7 defects, reported as $600^\circ\text{C}$5 along GBs, VSS films contain many sites that both increase free-carrier density and introduce strong non-radiative recombination. VLS growth with sodium molybdate liquid alloys suppresses S 5|7 formation, thereby suppressing the availability of S 5|7 sites for Na to form donor-type defects (Choi et al., 30 Jul 2025).

The trion–exciton analysis is summarized using a three-level exciton–trion model,

$600^\circ\text{C}$6

assuming $600^\circ\text{C}$7 and a constant factor $600^\circ\text{C}$8. From measured $600^\circ\text{C}$9, the reported electron densities are $T_g \approx 630^\circ\text{C}$0 for VLS films and $T_g \approx 630^\circ\text{C}$1 for VSS films. The stronger PL in VLS despite nonzero trion weight is therefore attributed not to the absence of doping, but to the suppression of the specific Na-decorated S 5|7 non-radiative pathway (Choi et al., 30 Jul 2025).

6. Design principles, limitations, and broader significance

The study identifies three functions of sodium molybdate liquid alloys as catalytic liquids. They act as thermodynamic boundary-condition setters by tuning $T_g \approx 630^\circ\text{C}$2 and $T_g \approx 630^\circ\text{C}$3 into the Mo-rich regime where Mo 5|7 is the global minimum of GB formation energy. They act as kinetic catalysts for defect reordering, GB migration, smoothing, and deformation twinning. They also act as defect-chemistry controllers, because suppression of S-polar GB cores suppresses the formation of Na-decorated S 5|7 donor defects that degrade optical properties (Choi et al., 30 Jul 2025).

A broader implication drawn in the paper is that GB polarity and defect type can be engineered not by relying only on global vapor stoichiometry, which is difficult to keep spatially uniform, but by using a well-defined liquid alloy reservoir at the growth front. The proposed design principles are correspondingly concrete: select an alloy system whose eutectic composition and liquidus support a stable liquid phase in the desired temperature window; tune alloy composition so that the metal and chalcogen chemical potentials place the target defect in the lowest-$T_g \approx 630^\circ\text{C}$4 regime; use reactive or catalytic species that lower bond-rearrangement barriers and promote dissolution–reprecipitation; and consider explicitly how alloy constituents interact with defect cores, since that interaction can be either benign or detrimental depending on defect type (Choi et al., 30 Jul 2025).

The work also states several limitations and open questions. Residual Na contamination is technologically relevant because Na atoms decorate GBs and act as dopants; post-growth control or removal may therefore be required for device applications. Control of liquid-alloy thickness, distribution, and composition over wafer scale remains challenging, and the long-term stability of Na–Mo–O under repeated thermal cycling and ambient exposure requires study. The general concept may extend to other 2D $T_g \approx 630^\circ\text{C}$5 materials such as WS$T_g \approx 630^\circ\text{C}$6, WSe$T_g \approx 630^\circ\text{C}$7, and MoSe$T_g \approx 630^\circ\text{C}$8, but each material system would require its own phase-diagram analysis to identify suitable eutectic compositions and growth windows. This suggests that sodium molybdate liquid alloys are best understood not as a universal recipe, but as a prototype of catalytic liquid media for programming the defect landscape of polycrystalline 2D films at atomic resolution (Choi et al., 30 Jul 2025).