Controlled spherulitic crystal growth from salt mixtures

Abstract

Spherulites are spherical crystals that are polycrystalline assemblies of radially organized crystallites. Despite their wide prevalence and relevance to fields ranging from geology to medicine, the dynamics of spherulitic crystallization and the conditions required for such growth remain ill-understood. Here, we reveal the conditions for controlled spherulitic growth of sodium sulfate crystals from evaporating aqueous solutions mixtures of sulfate salts at room temperature. We reveal that divalent metal ions in the salt solutions induce spherulitic growth of sodium sulfate through non-classical nucleation and self-assembly of (nearly)-oriented nanocrystals. A key result is the very high viscosity (~ 111 Pa ⋅ s) of the highly supersaturated solutions at the onset of spherulite precipitation. This allows for slow dynamics that facilitates the formation of a large number of mesoscopic prenucleation clusters, that subsequently show diffusion-limited growth and assemble into the spherulitic shapes. The spherulites are found to be metastable structures that form in out-of-equilibrium conditions. As the supersaturation decreases during growth, Na₂SO₄ spherulites can also evolve into other shapes depending on the evaporation rate. These findings shed light on the conditions that govern spherulite formation and provide practical strategies for tuning their morphology.

Introduction

Crystallization involves the transition of ions, atoms or molecules from a disordered state (liquid or gas) to an ordered state (solid), where they arrange themselves into a regular pattern. Although classical crystallization theories predict predictable morphologies based on the underlying crystal lattice and nature, complex chemical systems often produce intricate, unexpected structures that challenge our understanding¹. Spherulites—radially symmetric polycrystalline aggregates formed by non-crystallographic branching^2,3—epitomize this complexity, emerging in diverse systems from geological formations to biological materials^4,5,6,7,8,9. Figure 1 shows a remarkable gypsum precipitate formed naturally from a complex mixture of minerals under unknown growth conditions. It consists of distinct morphological layers: small brown crystals near the precipitate’s core, organized into a ball (macro-spherulite), and larger bladed crystals that likely grew on the surface of this ball. Mineralogists study meter-sized spherulites in rhyolitic lava⁴, while in medicine, microscopic spherulites are associated with kidney stone formation and amyloid disorders such as Parkinson’s and Alzheimer’s diseases^5,6,7. Despite this prevalence, existing theories do not adequately capture the dynamic interplay between chemical composition, environmental conditions, and crystal growth kinetics that drives these well-organized out-of-equilibrium morphologies^10,11.

Fig. 1: Calcium sulfate spherulite found in Winnipeg, Manitoba, Canada.

Despite its complex appearance, it is composed solely of gypsum (calcium sulfate, CaSO₄ ⋅ 2H₂O). Large amber-colored bladed gypsum crystals can be seen on top of the polycrystalline gypsum macro spherulite. The bladed crystals grew during a secondary stage of crystallization. Collection of the Gallery of Mineralogy and Geology in Paris, France.

Here, we reveal that by mixing divalent sulfate salts with a monovalent (sodium) sulfate salt solution, controlled spherulitic growth of sodium sulfate with different structural behaviors emerges from evaporative droplets of mixed salt solutions. The process is verified in various mixed sulfate salt solutions, and the range of mixing ratios that lead to the precipitation of spherulitic structures has been determined. To our knowledge, the ability of sodium sulfate to grow as spherulites has not been reported in the literature. Our results show that sodium sulfate spherulites emerge from a non-classical nucleation process at high supersaturation, followed by diffusion-limited growth kinetics as a result of the formation of a highly viscous salt solution upon evaporation. The supersaturation and local viscosity change at the onset of spherulitic growth are determined. The impact of the evaporation rate on the evolution of the spherulitic structures after nucleation and on the final morphology of sodium sulfate polycrystalline self-assembly is also discussed. Our findings not only provide valuable insights into the controlled growth of perfectly developed spherulites at room temperature but also open new avenues for industrial crystallization processes.

Results and discussion

Divalent ion-induced self-assembly of sodium sulfate at the nanoscale

Mixed sulfate salt solutions were prepared in Millipore water (ρ ≈ 18.2 MΩ cm) by mixing sodium sulfate Na₂SO₄ (Sigma Aldrich, purity >99%), with iron sulfate heptahydrate FeSO₄ ⋅ 7H₂O (Sigma Aldrich) or magnesium sulfate MgSO₄ ⋅ 7H₂O (Sigma Aldrich) salts. For simplicity, the resulting solutions are referred to as Fe and Mg solutions.

Sodium sulfate is known to have two stable crystal phases: an anhydrous phase (Na₂SO₄, thenardite, phase V) and a decahydrated phase (Na₂SO₄ ⋅ 10 H₂O, mirabilite)¹². In addition to these mineral forms a metastable anhydrous dendritic/needle-like phase III (Na₂SO₄) is known. Some laboratory experiments have reported another metastable phase that is hydrated by 7 water molecules (Na₂SO₄ ⋅ 7H₂O). The solubility phase diagram of sodium sulfate in water, reported by Steiger et al.¹³, is provided in Fig. S1.

We define the chemical composition of the resulting sulfate salt solutions system by the molar fraction x of the newly introduced divalent ion X (Fe²⁺, Mg²⁺) as follows:

$${x}_{{{{\rm{X}}}}}=\frac{{n}_{{{XSO}}_{4}}}{{n}_{{{XSO}}_{4}}+{n}_{{{Na}}_{2}{{SO}}_{4}}},$$

(1)

where ${n}_{{{{\mathrm{XSO}}}}_{4}}$ is the molar amount of the divalent ion that is dissolved in the aqueous solution. x ranges from 0 (pure Na₂SO₄ solution) to 1 (pure FeSO₄ or MgSO₄ solution). Droplets (volume V₀ = 1 μL) of these mixed salt solutions with various x values were left to dry on cleaned glass slides at T = 21 ± 1 °C and RH = 45  ± 5%. Crystallization in the evaporating droplets with different values of x_Mg or x_Fe can be divided in three main categories, as shown in Fig. 2: (i) precipitation of regular polyhedral-like crystals (black triangles), (ii) precipitation of premature and/or full spherulites (black dots), and (iii) precipitation of a gel-like (amorphous) state (open circles). In Na₂SO₄-MgSO₄–H₂O mixtures, spherulites form when 0.04 < x_Mg < 0.38. Low molar fractions (x_Mg = 0.05–0.12) produce premature large spherulites with a well-defined needle-shaped crystal assembly with bladed crystals growing later in time from the assembly; this behavior is surprisingly similar to that of large bladed crystals grown on top of the gypsum sulfate spherulite in Fig. 1. Higher molar fractions (x_Mg > 0.12) produce fully developed spherulites that are smaller in size, with different shapes from rough (raspberry shape) to very smooth (dense spherical shapes). Above a certain molar fraction (x_Mg > 0.45), spherulitic growth is fully suppressed and a bulk amorphous (gel-like) phase is formed. Experiments done with the Na₂SO₄–FeSO₄–H₂O mixed salt solution show similar morphological transitions in similar x ratios. For Na₂SO₄–FeSO₄–H₂O, spherulites form when 0.03 < x_Fe < 0.29. Exploratory experiments involving the substitution of Fe²⁺ and Mg²⁺ with other divalent salts such as Cu²⁺ and Zn²⁺ also led to similar sodium sulfate spherulite precipitation (Fig. S2), suggesting that the mechanism of spherulitic growth is not system-specific and can occur in different mixtures of divalent sulfate salts. The importance of divalence in triggering spherulitic growth is confirmed by the fact that the mixing of two monovalent sulfate salts (Na₂SO₄ and K₂SO₄) does not lead to the precipitation of sodium sulfate spherulites.

Fig. 2: Microscopic images of precipitated sodium sulfate crystals at different molar fractions of Mg.

Evaporation of unsaturated mixed salt solutions droplets with varying Mg molar fractions x_Mg at T = 21 ± 1 ^∘C resulting in three types of precipitation: (i) polyhedral sodium sulfate crystals (labeled with triangles), (ii) premature to full spherulitic morphologies (labeled with black dots), (iii) evaporating droplets transforming into a gel-like state (amorphous state) (labeled with open circles).

Non-classical crystallization pathway of spherulites

The origin of spherulitic growth has been a subject of debate between classical and non-classical nucleation mechanisms^10,14. Non-classical nucleation occurs when crystal formation proceeds via an/or several intermediate, metastable phases before the final stable crystal form is reached. This typically happens when a metastable dense liquid, amorphous precursor phase or nanocrystals, forms first, lowering the nucleation barrier and enabling faster nucleation inside this intermediate phase¹⁵. Common conditions favoring multi-step nucleation are (a) Presence of a metastable phase with thermodynamic stability between the initial solution and the final crystal phase. (B) Systems with high supersaturation or concentration fluctuations, allowing dense clusters or liquid droplets to form. In Fig. 3a, our investigation under optical microscopy reveals the appearance of dense liquid (micron-sized) pre-nucleation clusters near the contact line. The clusters remain stable for several minutes while the mixed salt solutions continue to evaporate. Spherulites starts to grow from these dense clusters as shown with the red arrow in the time-lapse sequence at the bottom in Fig. 3a. The simultaneous emergence of numerous spherulites from these preclusters indicates a deviation from classical nucleation theory (CNT), which posits that crystals form directly from the supersaturated solution without intermediate phases. In CNT, nucleation proceeds through the formation of a single, thermodynamically stable nucleus that grows into a bulk phase by monomer addition. Similar observations in other systems support a non-classical nucleation mechanism of spherulites^11,16,17. Although mesoscale dense liquid precursors are less commonly observed, they have been reported in the literature in different systems^18,19,20,21. Scanning electron microscopy (SEM) images in Fig. 3b–d show the morphology of spherulites in a fully dried droplet of Fe solution (x_Fe = 0.12). In Fig. 3b, the internal structure of a precipitated spherulite at the edge of the droplet can be seen: edge-grown spherulites are flattened because of the geometrical constraints imposed by the contact line of the evaporating droplet. The box below zooms in on the surface of the spherulite, showing directionally aligned nanocrystals within the spherulites, which subsequently fuse/coalesce toward a more stable crystalline phase of the same material as growth proceeds (a fused area is marked by the white arrow). These images provides direct evidence of crystallization via particle attachment mechanism (CPA). The CPA mechanism, described comprehensively by De Yoreo et al.¹⁵, explains such non-classical crystallization patterns, where dynamics such as monomer and particle diffusion and internal relaxation govern the pathway followed. Chemical characterization by Raman confocal microspectroscopy reveals that the precipitated spherulites consist of an assembly of phase III (Na₂SO₄) nanocrystals. The overlapping Raman peaks (458, 616, 638, 996, 1076–1079, 1131, and 1197–1200 cm⁻¹) between the average spectra of 5 spherulites and the reference spectrum from phase III confirm this composition (Fig. S3).

Fig. 3: Self-organized structure of sodium sulfate spherulites nucleate from dense clusters.

a Optical microscopy image showing dense liquid clusters near the contact line of 1 μL solution droplet with molar fraction x_Mg = 0.12. The white box marks the region shown in the time-lapse sequence below (0–10 s), illustrating how clusters evolve into a spherulite. Yellow arrows highlight clusters; the red arrow marks a cluster that develops into a spherulite. b–d Scanning Electron Microscopy images of spherulites grown in an evaporating droplet with iron molar fraction x_Fe = 0.12. b Cross-section of a spherulite (top) showing a self-organized structure of nanocrystals aligned by near-oriented particle attachment. The boxed region is magnified below; the white arrow marks a zone where adjacent nanocrystals have fused together into a more stable structure. c A premature spherulite at early stage of growth. d a fully developed spherulite.

Determination of thermodynamic equilibria and supersaturation

Thermodynamic equilibrium phase diagrams of the ternary systems predict which phases precipitate as water evaporates and ion concentrations increases. Therefore, the thermodynamic solubility phase diagrams for Na₂SO₄–FeSO₄–H₂O and Na₂SO₄–MgSO₄–H₂O are established at T = 21 °C using the experimentally validated molality-based model proposed by Steiger et al.^22,23 (other model parameters are listed in the method section). The model uses Pitzer equations²⁴ to calculate activity and osmotic coefficients, determining thermodynamic solubility products of solid phases. These equations compute excess Gibbs energy in electrolyte solutions, from which activity and osmotic coefficients are derived as functions of composition and temperature. The resulting ternary phase diagrams are presented in Fig. 4a, b. Black lines represent calculated solubilities by the molality-based model. At x = 0, initial solubilities ${m}_{x}^{* }$ of mirabilite (labeled ${m}_{0}^{* }(1)$ in the figure), thenardite (${m}_{0}^{* }(2)$), and phase III (${m}_{0}^{* }(3)$) at T = 21 °C correspond to the intersections with the y-axis (see Supplementary Table I). By introducing divalent ions (Fe²⁺ or Mg²⁺) these solubilities change with increasing x in the Na₂SO₄–FeSO₄–H₂O and Na₂SO₄–MgSO₄–H₂O systems, respectively. Notably, the solubilities of thenardite phase V (labeled (2) in Fig. 4) and phase III (3) decrease in the presence of divalent ions, while the solubility of mirabilite (decahydrate form) (1) slightly increases. The solubility line for the formation of double salt bloedite–Fe (Na₂Fe(SO₄)₂ ⋅ 4H₂O) (labeled (5) in the figure) and bloedite–Mg (Na₂Mg(SO₄)₂ ⋅ 4H₂O (7) becomes relevant in these salt mixtures. In the equilibrium phase diagram, it can also be noted that in pure solutions of FeSO₄–H₂O or MgSO₄–H₂O (i.e., x = 1), melanterite (FeSO₄ ⋅ 7H₂O) (4) and epsomite (MgSO₄ ⋅ 7H₂O) (6) are stable at T = 21 °C with initial solubilities ${m}_{1}^{* }(4)$ and ${m}_{1}^{* }(6)$ (indicated on the x-axis). The initial molal concentrations from evaporative droplet experiments are shown as dots, triangles, and circles in the ternary phase diagrams and correspond to Fig. 2. In addition, experimentally determined regions corresponding to sodium sulfate spherulite precipitation (shaded yellow in Fig. 4) are added by deriving the slope in the phase diagrams of molar fraction x from equation (1):

$${m}_{{{Na}}_{2}{{SO}}_{4}}=\frac{1-{x}_{{{X}}}}{{x}_{{{X}}}}{m}_{{{XSO}}_{4}}$$

(2)

where x denotes the molar fraction of the divalent ion (Fe²⁺ or Mg²⁺).

Fig. 4: Morphodroms of spherulitic structures from mixed salt solutions.

Solubility isotherms at T = 21 ^∘C for two ternary systems: a Na₂SO₄--FeSO₄--H₂O and b Na₂SO₄--MgSO₄--H₂O. In both panels, black lines represent calculated solubilities by the molality-based model, accompanied by initial molal concentrations from evaporative droplet experiments shown as dots, triangles, and circles that correspond to Fig. 2. The phases are labeled as follows: (1) Na₂SO₄ ⋅ 10H₂O (mirabilite); (2) Na₂SO₄ (thenardite, phase V); (3) Na₂SO₄ (phase III); (4) FeSO₄ ⋅ 7H₂O (melanterite); (5) Na₂Fe(SO₄)₂ ⋅ 4H₂O (double salt bloedite-Fe); (6) MgSO₄ ⋅ 7H₂O (epsomite); (7) Na₂Mg(SO₄)₂ ⋅ 4H₂O (double salt bloedite-Mg). The intersections at the y-axis (labeled as ${m}_{0}^{* }$(1), ${m}_{0}^{* }$(2), and ${m}_{0}^{* }$(3)) indicate the solubilities of the sodium sulfate phases without the introduction of divalent ions. The ranges of x-values where sodium sulfate spherulites precipitation is detected are highlighted in yellow: for Na₂SO₄--FeSO₄--H₂O, 0.03 < x_Fe < 0.29 in (a) and for Na₂SO₄--MgSO₄--H₂O, 0.07 < x_Mg < 0.38 in (b). The dashed arrow indicates the trajectory of a drying mixed salt solution (x = 0.12) upon evaporation crossing the solubility of phase III (red dot).

In Fig. 4, the trajectory of evaporating solutions with a molar fraction x = 0.12 are indicated by the dashed arrows. At the point of precipitation the supersaturation can be determined; The supersaturation β is defined as the ratio of the molality of total sulfate in the supersaturated solution (m_S) at the onset of precipitation, respectively, i.e. $\beta ={m}_{{{{\rm{S}}}}}/{m}_{{{{\rm{S}}}}}^{* }$ (see method section). The intersection with the solubility line of phase III (red dot) gives the saturation concentration (${m}_{0.12}^{* }(3)$ =4.6 mol ⋅ kg⁻¹). However, the concentrations at the onset of spherulitic nucleation reach in the experiments far beyond the field of view in Fig. 4 (6.2 mol ⋅ kg⁻¹). We find β_Mg = 1.4 ± 0.3 for the Na₂SO₄–MgSO₄ mixture and even higher supersaturation for the Na₂SO₄–FeSO₄ system (β_Fe > 3.3). At high concentrations, phase III needles can be expected and may transform into a thermodynamically more stable polymorph once the driving force relaxes and mass transport catches up. Indeed, here the precipitation of phase III is confirmed by Raman but in a peculiar form of spherulites. Whether kinetic forms dominate over thermodynamic (stable) forms depends on factors that influence the driving force and ions transport controlling diffusion and surface integration rates. In the following experiments on viscosity and relative humidity (RH), RH sets the evaporation rate and thus the supersaturation profile, while viscosity controls diffusion/surface-integration kinetics.

Growth mechanism driven by viscosity changes

To study the growth mechanism we follow the growth as a function of time of spherulites in a x_Mg = 0.12 solution at different locations in the droplets (Fig. 5a) at constant relative humidity (RH = 50%). Interestingly, the spherulites grow in a diffusion-limited fashion, i.e. proportional to the square root of time; the growth rates vary between spherulites located in the droplet periphery (lower growth rates) and spherulites closer to the droplet center (higher growth rates). Fe-containing solutions show growth characteristics that are remarkably similar to Mg-containing solutions, with comparable morphology and growth rates (Fig. S4). Key factors influencing growth include hydrophilic surface effects and droplets contact angle (~30°); the lower the contact angle, the more confined the solution at the droplet edges. Consequently, there will be a gradient in ion concentration and viscosity from the center to the periphery of the droplet²⁰. We therefore investigate the evolution of the viscosity of the mixed salt solution as it evaporates.

Fig. 5: Growth kinetics of spherulites in evapora mixed salt solution.

a Spherulite size L as a function of the square root of time t at RH = 50%. Each dataset is for one spherulite as shown in the photographs on the right: spherulites 1 and 2 are close to the contact line while 3, 4 and 5 are closer to the center of the droplet. The linear trend indicates that the growth of the spherulites is controlled by diffusion, with spherulites further away from the edge of the droplet growing faster than those near the center (indicated by slope Δ). The inset plot: the linear relation between local solvent viscosity η and the inverse diffusivity 1/D. A 12-fold viscosity increase is estimated for spherulite 5, and a significantly higher viscosity increase (70-fold) near the droplet’s edge (spherulite 1). b Rheological measurements of viscosity as a function of concentration with different molar Mg factions x. All measurements at T = 21 ± 1 ^∘C. While the viscosity η of the pure sodium sulfate and pure magnesium sulfate solution are in the same order of magnitude as the viscosity of water, the viscosity of the x_Mg = 0.12 solution as a function of the saturation follows an exponential trend. The dashed line indicates $\eta =4\times 1{0}^{-5}\exp (10.6{\beta }_{{{\mathrm{Mg}}}})$ with ${\beta }_{{{\mathrm{Mg}}}}={m}_{{{\mathrm{Mg}}}}/{m}_{{{\mathrm{Mg}}}}^{* }$ (R² = 0.88). The viscosity is measured up to a saturation of β_Mg = 0.73. By then, the viscosity is about 65 times higher than the viscosity of water. The exponential fit predicts that the viscosity is increased to 111 Pa ⋅ s when spherulitic growth is initiated at β_Mg = 1.4 (dotted line).

From the growth measurements in Fig. 5a the increase in solvent viscosity can be estimated using the Stokes-Einstein relation, which states that the diffusion constant D is inversely proportional to the solvent viscosity η, i.e., D ~ 1/η. The slope Δ of the spherulite growth measurements in Fig. 5a, corresponds to $\sqrt{D}$ (in μm/s^1/2), from which we infer that 15.2 μm²/s ≤ D ≤ 92.2 μm²/s. By the following relation, the solvent viscosity is estimated:

$$\frac{\eta }{{\eta }_{i}}=\frac{{D}_{i}}{D}=\frac{kT}{6\pi {\eta }_{i}R}\frac{1}{D},$$

(3)

where D_i is the initial diffusion constant of sulfate in water, reported as 1.07 × 10⁻⁹ m²/s²⁵. The inset plot in Fig. 5a shows the linear relationship between the increased solvent viscosity and the inverse diffusivity. A 12-fold viscosity increase is estimated in the bulk region (spherulite 5), and a 70-fold viscosity increase near the droplet edge (spherulite 1).

Furthermore, we perform rheological measurements on various magnesium sulfate solutions (x_Mg = 0.12) with reduced water fractions up to a saturation of β_Mg = 0.73. This approach simulates the stages of evaporation during which the concentration of ions increases progressively with the evaporation of water in the initial solution of the mixed salt solution (Fig. 5b). The evolution of viscosity during evaporation differs markedly between single-salt (x = 0, x = 1) and mixed-salt (x = 0.12) solutions. Mixed-salt solutions exhibit a pronounced exponential increase in viscosity as evaporation progresses: $\eta =4\times 1{0}^{-5}{e}^{10.6{\beta }_{{{\mathrm{Mg}}}}}$ (R² = 0.88). The viscosity of the solution estimated by extrapolation at the onset of spherulite nucleation (β_Mg = 1.4) is about 111 Pa ⋅ s, indicative of a highly viscous, peanut-butter-like consistency. This is comparable to melt-grown spherulite viscosities²⁶. Such a viscosity increase suggests a sol-gel transition, explaining why diffusion becomes the rate-limiting step for crystal growth in this medium. The combination of divalent ions (Mg²⁺ or Fe²⁺) and Na⁺ appears crucial in achieving this exponential increase in viscosity. This is mainly due to the ability of the cations to form metal aquo complexes such as ${[{{{\rm{M}}}}({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})6]}^{n+}$, with n = 2 or 3, in aqueous solution, and the rate at which they can exchange their coordinated water molecules with the surroundings²⁷. These complexes are predominant for sulfate salts; highly charged metal aquo cations exchange water more slowly than singly charged cations. Consequently, in very concentrated solutions undergoing evaporation, these metal hydroxo complexes can undergo condensation reactions (known as olation) to form polymeric species observed as the amorphous phase, thereby increasing the viscosity. In Fig. 3c, d and Fig. S7 we clearly observe a residu of a gel-like phase covering the spherulites. The yellow area in the morphodroms of Fig. 4 shows a sweet spot in molar fractions where the metal aquo complexes increase the viscosity such that sodium sulfate forms spherulites by diffusion-limited growth, without completely impeding crystallization of the monovalent ion. Within this regime, higher viscosity favors the growth of smaller, denser spherulites (similar to x_Mg = 0.25 in Fig. 2a), whereas lower viscosity enhances ionic mobility, accelerating growth and yielding larger, faceted morphologies.

Evaporation rate effects shape evolution

To understand the influence of evaporation rate on spherulitic growth of sodium sulfate we let droplets (x = 0.12) evaporate at relative humidities (RH) between 30 and 80%. Figure 6 illustrates the drying process of 1 μL droplets with x_Mg = 0.12 at low and high RH. In both conditions, the first spherulites generally nucleate near the contact line (where the droplet evaporation is strongest) and propagate inward, toward the droplet center. However, at high evaporation rates (RH ≤ 45%, top panel), larger number of nuclei are generated compared to lower rates, resulting in the growth of smaller spherulites. The large number of nucleation points has been explained earlier by the non-classical crystallization pathway. At high evaporate rate the further growth of individual spherulites is delayed/terminated by the faster increase of solution viscosity and growth of neighboring spherulites, thereby preserving the metastable spherulitic structure. At lower evaporation rates (RH ≥ 60%, bottom panel), nanocrystals within the initially precipitated spherulites have sufficient time to grow to their equilibrium configuration, forming clusters of highly faceted crystals with different morphologies. As spherulitic growth progresses, it depletes the surrounding ion concentration, reducing the supersaturation in the surrounding medium. Thus, smooth faceted crystalline phases (blades) can form on existing spherulites even before they are fully developed. The Raman spectra obtained at each stage of growth provide key insights into the morphological transformation of spherulites (Fig. 7a). Comparison with reference spectra (shown in black) reveals that the initial spherulites consist of phase III (needles), confirming previous results²⁸. The Raman spectra of bladed crystals do not correspond to any known reference spectra in the literature and cannot be identified. These crystals are probably a metastable state, slowly transforming to a more stable state by cracking and recrystallizing (Fig. S6); the Raman spectra after recrystallization correspond to the stable phase V (thenardite), confirming that spherulites evolve toward polycrystalline aggregates with thermodynamically stable crystalline phases. These findings demonstrate that spherulitic precipitation in highly viscous mixed sulfate solutions at very high supersaturation is a metastable intermediate state under non-equilibrium conditions. When the evaporation rate is slow and the growing spherulites have access to ions in the solution around them, they can evolve toward the more stable polycrystalline phase that is characteristic of the given salt—in our case, thenardite. The diverse spherulitic morphologies, ranging from smooth spherical to flower-like and/or needle-like structures, serve as a record of the system’s growth history.

Fig. 6: Impact of evaporation rate on the nucleation and growth of sodium sulfate spherulites.

Typical crystallization stages of a 1 μL droplet with molar fraction x_Mg = 0.12 at a fast evaporation rates (RH ≤ 45%) and b slow evaporation rates (RH ≥ 60%). All scale bars are 50 μm.

Fig. 7: Evolution of spherulites towards more stable phases.

a Raman spectra of late-stage evolution of spherulites in a x_Mg = 0.12 droplet under slow evaporation conditions (RH ≥ 60%). These measurements reveal that the initial spherulites correspond to phase III, bladed crystals formed on the spherulites originate from an unidentified phase, and the final polyaggregates recrystallize into phase V after complete dehydration. The spectra are accompanied by reference spectra of Na₂SO₄ phase III and phase V (shown in black). b Scanning electron microscopy image of a spherulitic polyaggregate after complete dehydration at RH = 63%. The white arrow highlights the growth history of a blade that developed from the spherulite. c Magnification of boxed area in (b); In this later stage spherulite the nanocrystals, as shown in Fig. 3b, coalesced into more stable finger-like structures. The corresponding EDX elemental map (left) confirms that the the fused structures consist of sodium sulfate.

From fundamental understanding to morphological control of spherulitic growth

Models simulating spherulitic growth and the vast majority of experimental case studies suggest that non-crystallographic branching requires impurities in the system^2,3. Some research contradicts this, reporting successful spherulitic growth from pure compounds^26,29,30. Here, we show that divalent (metal) ions in the solution specifically have the ability to induce spherulitic growth of the monovalent salt, by introducing complex competition in ion arrangement as they induce viscosity changes in the highly concentrated medium during evaporation, disrupting classical growth pathways and enabling non-crystallographic branching. The non-classical crystallization pathway of sodium sulfate spherulites is illustrated in Fig. 8a; (1) highly concentrated dense liquid clusters are stabilized in a highly viscous fluid due to the ability of the bivalent ions to form aqua complexes which lowers the surface energy barrier for nucleation compared to direct nucleation from the dilute phase (2) precipitating nanocrystals in the dense cluster self-assembly by (nearly)-oriented attachment in the form of spherulites (3) with further growth these nanocrystals fuse and evolve towards more stable shapes, as described by the mechanism of particle attachment (CPA)¹⁵. More stable phases may develop on top of the spherulite as smooth blade-like structures once the supersaturation in the surrounding environment is decreased.

Fig. 8: Schematic of non-classical crystallization and growth evolution of spherulites (not to scale).

a The spherulites nucleate through a non-classical pathway involving the formation of microsized dense ion clusters, which subsequently crystallize via particle attachment (CPA) by nanocrystals. As growth progresses, the nanocrystals can fuse together, and more stable phases may develop on top of the spherulite as smooth blade-like structures which will crack and transform into the equilibrium phase upon complete dehydration. b The spherulitic morphology evolves from compact forms to highly faceted structures as a function of experimental parameters. High relative humidity (RH) and a large diffusion coefficient (D) allow evolution towards larger, smoother, and more stable morphologies, whereas increased viscosity (η) and higher divalent-ion fractions (x) inhibit crystallization, preserve the out-of-equilibrium metastable spherulitic phase, and promote branching that yields smaller spherulites. This transition highlights the complex interplay between growth kinetics and environmental conditions.

Recent work on ibuprofen crystallization from binary solvents shows, via Raman spectroscopy and SAXS, that a dense liquid intermediate with close packed molecular arrangements acts as a non-classical precursor phase to crystal nucleation²¹. For many systems, CNT estimates the critical nucleus size to be in the few nanometer range (<5–6 nm), whereas in the above-mentioned study, scattering and spectroscopic data indicate that dense-liquid clusters or domains can extend from nanometer-sized aggregates up to hundreds of nanometers, depending on supersaturation and interaction strength. In our system, the dense liquid droplets observed prior to spherulitic growth (~1 μm) should therefore be viewed as assemblies of many sub critical molecular clusters, within which locally ordered regions (crystal-like molecular packing) can grow toward the critical size, rather than as a single monolithic cluster of critical dimensions. This view is consistent with the study of Mani et al., in which Raman spectroscopy and SAXS data show that dense liquid aggregates induced by liquid-liquid phase separation have close-packed molecular arrangements and act as a non-classical precursor phase to nanocrystals nucleation and aggregation via a non-classical pathway²¹.

Figure 8b illustrates the morphological transitions during spherulitic growth, highlighting the key experimental factors that influence the final morphology. Increased viscosity (η) and higher divalent-ion fractions (x) inhibit crystallization, preserve the out-of-equilibrium metastable spherulitic growth, and yield smaller spherulites. High relative humidity (RH) and a large diffusion coefficient (D) allow evolution towards larger and more stable morphologies. The growth of the more stable phase can be initiated at various stages of branching, including sprouting needles, premature (open) spherulites, and fully grown spherulites, leading to a wide range of final morphologies. These insights allow us to successfully grow sodium sulfate spherulites, not only from evaporative microdroplets but also from high-x bulk solutions in Petri dishes, resulting in millimeter-sized spherulites (Fig. S7). These findings shed light on the conditions under which natural peculiar-shaped crystals form, such as the gypsum sulfate spherulite in Fig. 1, or desert roses that form from mineral-rich water in the presence of silica (sands) in arid regions where the evaporation rate is high. It also offers practical strategies for tuning spherulitic morphologies in experimental settings. This capability has significant potential for innovative applications where specific crystal architectures are desired.

Conclusion

In conclusion, we report the ability of Na₂SO₄ to form spherulites composed of anhydrous thenardite crystallites during the evaporation of sulfate salt mixtures due to the presence of divalent ions. Our analysis identifies specific molar fraction ranges conducive to spherulitic growth: 0.03 < x_Fe < 0.29 and 0.04 < x_Mg < 0.38 with supersaturation levels averaging β_Mg = 1.4 ± 0.3 and β_Fe > 3.3. With water loss, these ions—due to their tendency to form aquo complex structures²⁷— in turn induce both a high supersaturation prior to precipitation and a marked increase in viscosity of the solution, reaching a peanut-butter-like consistency (approximately 111 Pa ⋅ s) and leading to the formation of an amorphous phase. Subsequently, spherulitic precipitation proceeds via a non-classical nucleation pathway, originating from mesoscopic dense liquid clusters with locally a higher solute concentration. Their growth in the viscous surrounding medium is shown to be diffusion controlled characterized by ${{{\rm{L}}}} \sim \Delta \sqrt{(t)}$.

Three distinct stages in spherulite formation and growth were identified: (1) the emergence of micron-sized pre-nucleation dense liquid clusters, (2) nucleation and growth from premature to mature spherulites via (nearly)-oriented attachment of nanocrystals, and (3) evolvement into more stable polyhedral forms. These findings offer new insight into multistep crystallization and demonstrate the metastable nature of spherulites. They are produced in non-equilibrium conditions, and if sufficient ions remain in solution to support continued crystallization, spherulites possess the capacity to transform toward thermodynamically more stable morphologies as supersaturation diminishes during growth. This transformation underscores the substantial effect of solution composition on crystallization mechanisms and the intricate interplay between thermodynamics, kinetics, and the resulting morphology.

Finally, the fundamental insights described above enable precise control over the final spherulitic morphology by modulating the molar fraction of divalent ions, evaporation rate, and geometric constraints. Our results reveal the mechanisms of one of nature’s most elegant self-assembly processes from salt mixtures. By unraveling the principles of crystal self-organization, we pave the way for the rational design of complex materials with tailored structural and functional properties. Understanding spherulitic growth mechanisms could revolutionize fields ranging from materials engineering and pharmaceutical formulation to geological modeling and biomineralization.

Materials and methods

Modeling of thermodynamic equilibria

The thermodynamic equilibria in this study are calculated based on the following equations: For a salt Mν_MXν_X ⋅ ν₀H₂O, the equilibrium constant K_MX of the dissolution reaction is:

$${{{\rm{ln}}}} \, {K}_{{MX}} = \, {\nu }_{M}{{{\rm{ln}}}}{m}_{M}+{\nu }_{X}{{{\rm{ln}}}}{m}_{X}+{\nu }_{M}{{{\rm{ln}}}}{\gamma }_{M}\,+ \\ {\nu }_{X}{{{\rm{ln}}}}{\gamma }_{X}+{\nu }_{0}{{{\rm{ln}}}}{a}_{{{{\rm{w}}}}},$$

(4)

where m_M, mx, γ_M, and γ_X are molalities and activity coefficients of cations and anions, respectively. Water activity a_w is defined as:

$${{{\rm{ln}}}} \, {a}_{{{{\rm{w}}}}}=-\phi {M}_{{{{\rm{w}}}}}\sum\limits_{i}{m}_{i},$$

(5)

with ϕ the osmotic coefficient and M_W the molar mass of water (M_W = 1.801528 ×10⁻² kg mol⁻¹). Further details about this model can be found in Steiger et al.²². The Pitzer model parameters for Na₂SO₄(aq), MgSO₄(aq), and Na₂SO₄–MgSO₄–H₂O were reported earlier^22,31. The model parameters for FeSO₄(aq) are based on the model of Kobylin et al.³² with parameters listed in Talreja-Muthreja and Steiger³³. The ternary parameters for the system Na₂SO₄–FeSO₄–H₂O were determined from available solubility data. The parameters for the calculations at 21 °C are θ_Na,Fe = 0 and ${\psi }_{{{\mathrm{Na}}},{{\mathrm{Fe}}},{{{\mathrm{SO}}}}_{{{{\rm{4}}}}}}=0.00234$.

Salt mixture preparation

Na₂SO₄–FeSO₄–H₂O and Na₂SO₄–MgSO₄–H₂O mixtures were prepared by dissolving thenardite (Na₂SO₄) with either FeSO4 ⋅ 7H₂O or MgSO4 ⋅ 7H₂O in Millipore water (Sigma Aldrich, purity >99%). The Na₂SO₄ concentration was set to 0.7 times the mirabilite solubility. Molar fractions x of FeSO₄ or MgSO₄ were calculated using Eq. (1). Salts were weighed with 0.05 g precision and dissolved in water by stirring for 30 minutes.

Evaporation experiments

Droplets (1 ± 0.2 μL) were deposited on hydrophilic glass slides and observed under an inverted Leica DM-IRB microscope at 21 ± 1 °C and 30–80% RH. Crystallization was recorded at 0.5 fps, and spherulite growth rates were measured. Additional experiments in 0.5 × 0.5 mm² microcapillaries determined supersaturation at spherulite precipitation onset.

Supersaturation measurements

To quantify the supersaturation at the onset of sodium sulfate spherulites nucleation in both Fe and Mg solutions, initial volumes of mixed salt solution (x = 0.12) are confined in a microcapillary and allowed to evaporate in a controlled climatic chamber at T = 21  ± 1 °C and RH = 50%³⁴. The change in volume as a function of evaporation time t is subsequently followed by recording the displacement of the two menisci while simultaneously visualizing the onset of spherulite nucleation in the solution with an optical microscope coupled to a CCD camera. This measurement yields the molality at the onset of nucleation (see details in Supplementary D).

Viscosity measurements

Viscosities of solutions with varying water content (x_Mg = 0.12, 0, and 1) were measured using an Anton Paar MCR301 rheometer. Samples were heated to 30 °C for homogeneity, then cooled to 21 °C for measurements. Viscosity was recorded at a shear rate of 900 s⁻¹ until reaching a plateau. The experimental protocol consisted of dissolving salts at elevated temperature (T = 30 °C), followed by cooling to experimental conditions (T = 21 ± 1 °C); subsequently we measured viscosity at different saturation stages, and define the evaporation stages were by the saturation of the Mg solution: ${\beta }_{{{\mathrm{Mg}}}}=\frac{m}{{m}^{* }}$.

Structural and chemical characterization

Raman confocal microspectroscopy (WITec Alpha 300 R, 532 nm laser) provided chemical imaging during evaporation and crystallization. SEM (FEI Verios 460) investigated spherulite structure at nano- to micro-scale, with samples coated in 80 nm gold particles and analyzed at 10 kV and 100 pA.