Surface dust particles were collected from the Tengger Desert, China (37.57° N, 104.93° E) (Fig. 1). The experimental procedure is summarized in Fig. 2. Dust particles were sieved (200 mesh, 74 µm, nylon) and used for suspension preparation. A weighed dust aliquot was mixed with 20 mL ultrapure water (Millipore, resistivity > 18.2 MΩcm) in a glass vial and manually shaken for 1–2 min to ensure thorough mixing. After standing for 5 min to allow coarse particles to settle, the upper 10 mL was collected as the first dust suspension (hereafter referred as S-dust). A second suspension was prepared using the same procedure but subjected to ultrasonic treatment at 40 kHz for 30 min at 25 °C in an ultrasonic bath (KQ2200DA, Kunshan Ultrasonic Instrument Ltd.). This sample is hereafter referred to as ultrasonicated dust (Us-dust). The sonication duration was selected based on Knopf and Alpert (2013) to reduce particle aggregation and promote the dispersion of fine dust particles in the 20 mL suspension. The upper portion (∼ 10 mL) of each 20 mL dust suspension was collected and serially diluted with ultrapure water for immediate used in the ice nucleation experiments. To determine dust mass concentration, 6 mL of each suspension was filtered using 0.2 µm polycarbonate filter membrane (GTTP04700, Isopore™) and the insoluble part was weighed. Ultrasonic treatment increased the dust mass concentration in suspension by about 5 times. The following suspensions were used. For S-dust, the mass concentrations were 2.0 × 10⁻² wt%, 3.0 × 10⁻³ wt%, and 7.0 × 10⁻⁴ wt%. The mass concentrations for Us-dust were 1.0 × 10⁻¹ wt%, 1.87 × 10⁻² wt%, 3.5 × 10⁻³ wt%, 7.0 × 10⁻⁴ wt%, and 1.4 × 10⁻⁴ wt%.

All aging treatments used the Us-dust suspension with dust mass concentration of 1.87 × 10⁻² wt%. We added AS, NaCl, HNO3, and H2SO4 to the Us-dust suspension for 12 h prior to ice nucleation experiments. Final AS concentrations (99.95 %, Sigma) were 5 × 10⁻⁵, 5 × 10⁻⁴, 5 × 10⁻³, 2 × 10⁻³, 1 × 10⁻³, and 5 × 10⁻² M. Final NaCl concentrations (99.995 %, Sigma) were 5 × 10⁻⁴, 5 × 10⁻³, 5 × 10⁻² M. Final H2SO4concentrations (99.7 %, Hushi) were 2.5 × 10⁻⁴, 2.5 × 10⁻³, 2.5 × 10⁻² M. Final HNO3 concentrations (99.7 %, Hushi) were 5 × 10⁻⁴, 5 × 10⁻³, 5 × 10⁻² M. Heat treatment was conducted on the Us-dust suspension at 95 °C for 30 min.

Single particle analysis was conducted by the computer-controlled scanning electron microscopy equipped with an energy dispersive X-ray spectroscopy (CCSEM/EDX, Quanta 650, FEI Inc.; Genesis, EDAX Inc.) to determine particle size and elemental composition. Dust particles were collected from the suspensions following the method from our previous work (Xue et al., 2024; Zhao et al., 2024). Briefly, the upper portion (∼ 10 mL) of each 20 mL dust suspension was nebulized. The generated aerosols were carried by high-purity nitrogen through a diffusion dryer and collected onto TEM copper grids (01814-F, Ted Pella) using an impactor (SKC, Inc.). CCSEM/EDX analysis at the working voltage of 20 kV followed the established method from our previous work (Knopf et al., 2014; Laskin et al., 2002; Wang et al., 2012; Xue et al., 2024; Zhao et al., 2024) and is described briefly here. The elemental composition and the area equivalent dimeter (calculated by the 2-D projected particle area, hereafter referred as particle size) were quantified for about 1040 S-dust and 1180 Us-dust particles. We obtained atomic percentages for C, N, O, Na, Mg, Al, Si, P, S, Cl, K, Ca, and Fe. C, N, and O determined by EDX were semiquantitative and excluded from classification. For each particle, the normalized atomic percentage of element X was calculated as [X]=XNa+Mg+Al+Si+K+Ca+Fe+P+S+Cl. Based on the elemental composition, particles were grouped into five types, namely illite, kaolinite, chlorite, quartz, and feldspar, using a rule-based classification scheme (Fig. 3). This method has been widely used to identify different dust types based on the elemental fingerprints of monomineralic dust (Hu et al., 2022; Kandler et al., 2007; Wang et al., 2022; Zhao et al., 2024). Mean elemental compositions of each dust type were shown in Fig. S1 in the Supplement.

Frozen fraction (fice(T)) is defined as the ratio of the number of frozen droplets (Nice) at a certain temperature (T) to the total number of droplets (Ntotal), i.e., fice(T)=Nice/Ntotal. Frozen fraction reflects the distribution of ice formation event at different temperatures. Ice nucleation active site density (Ns) is the number of ice active site per unit particle surface area and is calculated using Eq. (2) according to Vali (1971): 2Ns=-ln(1-fice(T))A[m-2] where A is the total particle surface area immersed in a single droplet. A was calculated by the particle mass in the droplet and the average surface area per unit particle mass (Am). Particle mass in each droplet equals the dust mass concentration in suspension times the droplet volume (1 µL). Am was estimated from CCSEM/EDX particle data by 3Am=∑Si∑Vi×ρi where Si is the surface area of the individual particle i (assumed spherical, Si=πdi2); Vi is the volume of the individual particle i, Vi=πdi3/6; di is the diameter of the particle i; ρi is the density of different particle types, specifically, ρquartz = 2.62 gcm-3, ρchlorite = 2.42 gcm-3, ρillite = 2.6 gcm-3, ρkaolinite = 2.6 gcm-3, and ρfeldspar = 2.6 gcm-3 (Menut et al., 2020). Uncertainty in Ns (95 % confidence intervals) was calculated using Poisson nucleation statistics (Koop et al., 1997).

Experimental data were used to derive Jhet, providing a time-dependent description of heterogeneous nucleation. Jhet at temperature Ti for a given temperature interval (ΔT) was calculated based on the method from previous studies (Alpert et al., 2011; Koop et al., 1997; Zobrist et al., 2007): 4Jhet(Ti)=Niceittoti×Ai where Nicei is the total number of ice nucleation events in the ith temperature interval, and ttoti×Ai is product of observation time and dust surface area available for nucleation in that interval. ttoti×Ai is given by 5ttoti×Ai=∑j=1NiceiTsti-Tice,jicrAliq,ji+ΔTcrAliqi where Tsti is the start temperature of ith temperature interval; Tice,ji and Aliq,ji are the freezing temperature and dust surface area of the jth droplet that froze within the interval; Aliqi is the total dust surface area in the droplets remaining liquid at the end of the interval; cr is the cooling rate (10 Kmin-1); ΔT of 0.5 K is used.

The experimentally derived Jhet was parameterized using the water activity based framework which relates the droplet freezing temperature uniquely to droplet water activity (Alpert et al., 2022; Knopf and Alpert, 2013; Xue et al., 2024; Zhao et al., 2024). It has been applied to both homogeneous and heterogeneous ice nucleation (China et al., 2017; Knopf and Alpert, 2013; Koop and Zobrist, 2009). In this framework, Δaw is used to describe the freezing ability of droplets, which represents the deviation of the water activity of droplets at freezing temperature from the water activity at the ice-melting equilibrium state at the same temperature (Koop et al., 2000). Δaw was calculated for each droplet at its freezing temperature. The corresponding Jhet was parameterized by a linear regression of log (Jhet) against Δaw (or temperature). Note that the derived Jhet values reported in this study correspond to a cooling rate of 10 Kmin-1; therefore, comparisons with studies using different cooling rates should be made with caution. The surface area used to calculate Ns and Jhet was estimated from the geometric particle diameters measured by CCSEM/EDX, rather than Brunauer-Emmett-Teller (BET) specific surface area. Because these methods quantify different surface area metrics, comparisons with literature Ns and Jhet values or parameterizations based on BET surface area should be made cautiously. Dynamic light scattering (DLS) measurements were performed to independently assess the particle size distribution in the suspensions and estimate the geometric surface area per 1 µL droplet (Sect. S2 and Fig. S4). The DLS- and CCSEM-derived surface area estimates were within the same order of magnitude, although the latter were approximately 2–3 times higher.

Figure 4 shows the particle classification for the S-dust and Us-dust samples. Particles were mainly in the size range of 0.2–2 µm. S-dust and Us-dust exhibited a peak size of about 0.35 and 0.7 µm, respectively. Size distributions of the same particle type between S-dust and Us-dust were slightly different (Fig. 4b and f). Particle number contribution of Us-dust by kaolinite, quartz, illite, chlorite, and feldspar was 32 %, 29 %, 19 %, 12 %, and 7 %, respectively. Compared with S-dust, chlorite, illite, and feldspar in Us-dust is about 12 %, 11 %, and 2 % higher, respectively, whereas kaolinite decreased by 23 % and quartz remained unchanged (Fig. 4c and g). The contribution to particle surface area of Us-dust by illite, quartz, chlorite, kaolinite, and feldspar was 37 %, 24 %, 23 %, 12 %, and 5 %, respectively. Compared with S-dust, Us-dust showed higher contributions from chlorite (13 %), illite (4 %), and feldspar (2 %), and lower contributions from quartz (3 %) and kaolinite (15 %) (Fig. 4d and h).

Figure 5 summarizes IMF experimental results for ultrapure water droplets and dust-containing droplets. Both S-dust and Us-dust at the investigated concentrations induced IMF at higher temperatures than water droplets (Fig. 5a). T50 changed from 252.4 to 254.6 K for S-dust as concentration increased from 7.0 × 10⁻⁴ wt% to 2.0 × 10⁻² wt%. T50 changed from 253.6 to 258.5 K for Us-dust as concentration rose from 1.4 × 10⁻⁴ wt% to 1.0 × 10⁻¹ wt%. T50 shows that Us-dust nucleated ice more efficiently than S-dust (Fig. 5b). At comparable dust surface area concentration, T50 of Us-dust was about 2 K higher than S-dust. T50 increased by about 1.1 and 1.2 K per decade increase in dust surface area concentration for S-dust and Us-dust, respectively. We defined ΔT50w, as the T50 difference between dust-containing droplets and water droplets. Figure 5c compares the ΔT50w for S-dust, Us-dust, and other monomineralic dust. ΔT50w of monomineralic dust ranks as follows: K-feldspar > Na/Ca-feldspar > quartz > illite > kaolinite > chlorite. T50w for Us-dust was consistent with Na/Ca-feldspar but lower than K-feldspar, while ΔT50w for S-dust was lower than Na/Ca-feldspar, but higher than chlorite and illite. We have shown that the contributions of chlorite, illite, and feldspar in both number and surface area were higher in Us-dust compared to S-dust (Fig. 4). Given that the ΔT50w of chlorite and illite are lower than Us-dust, the improved IMF ability of Us-dust relative to S-dust may be partly attributed to the increased feldspar content.

Figure 5d shows the Ns for S-dust and Us-dust with parameterizations using the function of log10(Ns)=m1×T+n1. The values of m1 and n1 are shown in Table 1. Overall, Ns for Us-dust was about one order of magnitude higher than S-dust. As shown in Fig. 6a, Ns for Us-dust was comparable to feldspar, falling in between Na/Ca-feldspar and K-feldspar. The Ns of S-dust was similar to Na-feldspar, and was distinctly higher than quartz, illite and chlorite. Previous studies have suggested that K-feldspar may enhance the ice nucleation activity (Boose et al., 2019; Harrison et al., 2016). Notably, both Us-dust and S-dust showed stronger temperature dependences of Ns than previously reported Ns for ATD, natural dust from deserts, and airborne particles during dust storms (Chen et al., 2021; Hader et al., 2014; Niemand et al., 2012; Reicher et al., 2019; Ullrich et al., 2017). Us-dust and S-dust exhibited Ns similar to those airborne particles collected during dust storms below 260 K, but lower Ns above 260 K (Fig. 6b). However, Ns for Tengger desert dust was lower than the Ns parameterizations reported by Niemand et al. (2012) and Ullrich et al. (2017), especially at high temperatures. This observed discrepancy in Ns is likely attributed to the differences in particle size and composition of these surface-collected or airborne dust particles. Additionally, atmospheric aging on dust during long-range transport may also contribute to the discrepancy.

Figure 7 presents the IMF results for Us-dust at 1.87 × 10⁻² wt% after mixing with AS at various concentrations. AS enhanced the IMF ability of Us-dust, leading to higher freezing temperature and Ns as AS concentration increases (Fig. 7a and b). At AS concentration above 5 × 10⁻³ M, Ns was approximately two orders of magnitude larger than untreated Us-dust. We define ΔT50u as the T50 difference between AS treated and untreated Us-dust, using T50 of 256.8 K for the untreated Us-dust at 1.87 × 10⁻² wt%. ΔT50u increased from 0.4 to 4.7 K as AS concentration increased from 5 × 10⁻⁵ to 5 × 10⁻² M (Fig. 7c), following a sigmoidal response reproduced via a Boltzmann function as: 6ΔT50u=0.3997+4.2685/(1+exp((log10[AS]+3.0324)/-0.2845)). Previous studies have suggested that the interaction between dust and ammonium ions (NH4+) can enhance the IMF ability of dust (Anim-Danso et al., 2016; Kumar et al., 2018; Whale et al., 2018; Worthy et al., 2021). The observed sigmoidal response of ΔT50u suggests a concentration dependent activation of ice nucleation sites on dust surface upon AS exposure. At relatively low AS concentration down to 5 × 10⁻⁵ M, the enhancement was modest, with a ΔT50u of 0.4 K, suggesting that only a small fraction of susceptible ice nucleation sites was activated. As the AS concentration increased to 5 × 10⁻³ M, ΔT50u increased markedly to 4.7 K, consistent with a substantial activation of additional ice nucleation sites. At a higher AS concentration of 5 × 10⁻² M, ΔT50u remained nearly constant, suggesting that the enhancement had approached a plateau. One possible explanation is that most of the susceptible ice nucleation sites had already been activated, potentially reflecting saturation of the relevant surface interactions involving NH4+. This interpretation is consistent with the proposed role of ammonium–dust interactions in enhancing ice nucleation, although the underlying molecular mechanism remains to be confirmed. Further discussion is provided in Sect. 3.5.1.

ΔT50u for Us-dust mixed with AS fell within the upper range reported for other minerals (Fig. 7c). At AS concentrations of 10⁻⁴–10⁻³ M, Us-dust exhibited comparable ΔT50u to K-feldspar, but was greater at higher AS concentrations than those reported by Whale et al. (2018) and Worthy et al. (2021). To eliminate biases originating from inconsistent dust concentrations in these studies, AS content was normalized by dust concentration and expressed as the mass ratio of AS to dust (AS/Dust) for intercomparison (Fig. 7d). ΔT50u increased with AS/Dust ratio with a more pronounced sigmoidal shape, which is fitted by a Boltzmann function as: 7ΔT50u=0.3998+4.2682/(1+exp((log10(AS/Dust)+0.1837)/-0.2844)).

When plotted against AS/Dust, ΔT50u for Us-dust generally converges to the range of ΔT50u for K-feldspar (Whale et al., 2018; Worthy et al., 2021). However, ΔT50u for K-feldspar tended to be a linear response against either log values of AS concentration or AS/Dust ratios. ΔT50u for Us-dust was greater than quartz but lower than kaolinite at the investigated AS concentrations. ΔT50u for Us-dust was slightly lower than ATD reported by Worthy et al. (2021), but higher than ATD from Whale et al. (2018). These differences in ΔT50u or its trend was likely controlled by divergent interfacial interactions between AS and various minerals of the investigated dust. In addition, Worthy et al. (2021) suggested that those inconsistencies may be associated with the different contact time between AS and dust.

Figure 8 shows that ΔT50u for Us-dust were close to zero after heat treatment, mixed with NaCl, or acid (H2SO4 or HNO3) treatment. This indicates that these treatments had no impacts on IMF ability of Us-dust when comparing the T50 values. However, these treatments had certain effects on the IMF ability at freezing temperature above 258 K as evidenced by the deviations in Ns (Fig. 8d–f) and frozen fraction (Fig. S5). Specifically, heat and H2SO4 treatments, as well as higher concentrations of NaCl (5 × 10⁻² M) and HNO3 (5 × 10⁻² M) treatments imposed a reduction in Ns, whereas lower concentrations of NaCl (5 × 10⁻⁴ M) and HNO3 (5 × 10⁻⁴ and 5 × 10⁻³ M) treatments led to an increase in Ns. The impact of heat treatment on Us-dust was qualitatively consistent with the results from Zolles et al. (2015), who reported marginal change in the IMF ability of K-feldspar, Na/Ca-feldspar, Kaolinite, and ATD after heating at 523 K for 4–5 h, with the ΔT50u values remaining within their measurement uncertainty.

Previous studies show that NaCl and acids can reduce the IMF ability of K-feldspar, kaolinite, and quartz (Reischel and Vali, 1975; Whale, 2022; Whale et al., 2018; Yun et al., 2021) (Fig. 8a and b). For K-feldspar and kaolinite, higher NaCl concentration led to lower ΔT50u (negative values). Higher HCl and HNO3 concentrations led to a stronger reduction in ΔT50u for K-feldspar (Reischel and Vali, 1975; Whale et al., 2018). However, NaCl and HCl did not affect the IMF ability of ATD (Link et al., 2020; Perkins et al., 2020), which was similar to Us-dust. Although, NaCl, heat, and acid treatments did not substantially change the T50 of Us-dust, they altered Ns leading to the enhancement or reduction in the IMF ability of Us-dust at warmer freezing temperature. A similar phenomenon was also observed for ATD when mixed with inorganic acids (Perkins et al., 2020).

The experimentally derived Jhet and its parameterizations as functions of Δaw and temperature are presented in Figs. 9 and S7, respectively. Us-dust nucleated ice starting from relatively low Δaw (∼ 0.08) and high temperature (i. e., 264 K) at the investigated concentrations. The temperature and Δaw dependence of Jhet for Us-dust is substantially steeper than for S-dust. This is associated with the differences in particle size and composition before and after ultrasonic treatment (Sect. 3.1). AS enhanced the Jhet of Us-dust more progressively with AS concentration. Only minor variations in Jhet for Us-dust (i.e., less than one order of magnitude) were observed above 258 K after heat, acid (H2SO4 and HNO3), and NaCl treatments (Fig. S7). Jhet of Us-dust is a few orders of magnitude higher than kaolinite and illite, but lower than Aluminum oxide and Iron oxide at the investigated Δaw (Fig. 9c). Compared with non-mineral or biological substances, in terms of Jhet (Fig. 9d), Us-dust is less efficient than fungal spores (Iannone et al., 2011), comparable to 1-nonadecanol (Knopf and Forrester, 2011), but more efficient than marine microbes (Thalassiosira Pseudonana and Nannochloris Atomus) (Alpert et al., 2011; Knopf et al., 2011), and humic like substances (leonardite and Pahokee Peat) (Rigg et al., 2013). After mixed with AS, Jhet for Us-dust shifted toward but still lower than aluminum oxide, iron oxide, and fungal spores.