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Edited by Catherine J. Murphy, University of Illinois at Urbana–Champaign, Urbana, IL, and approved July 9, 2018 (received for review March 1, 2018)
Significance
Nucleation is the limiting step for thermodynamic phase transitions. While classical models predict that nucleation should be extremely rare, nucleation is surprisingly rapid in the gas-phase synthesis of diamond, silicon, and other industrial materials. We developed an approach for measuring nucleation landscapes using atomically defined precursors and find that diamond critical nuclei contain no bulk atoms, which leads to a nucleation barrier that is four orders of magnitude lower than prior bulk estimations. Our findings suggest that metastable molecular precursors play a key role in lowering nucleation barriers during materials synthesis and provide quantitative support for recent theoretical proposals of multistep nucleation pathways with much lower barriers than the predictions of classical nucleation theory.
Abstract
Nucleation is a core scientific concept that describes the formation of new phases and materials. While classical nucleation theory is applied across wide-ranging fields, nucleation energy landscapes have never been directly measured at the atomic level, and experiments suggest that nucleation rates often greatly exceed the predictions of classical nucleation theory. Multistep nucleation via metastable states could explain unexpectedly rapid nucleation in many contexts, yet experimental energy landscapes supporting such mechanisms are scarce, particularly at nanoscale dimensions. In this work, we measured the nucleation energy landscape of diamond during chemical vapor deposition, using a series of diamondoid molecules as atomically defined protonuclei. We find that 26-carbon atom clusters, which do not contain a single bulk atom, are postcritical nuclei and measure the nucleation barrier to be more than four orders of magnitude smaller than prior bulk estimations. These data support both classical and nonclassical concepts for multistep nucleation and growth during the gas-phase synthesis of diamond and other semiconductors. More broadly, these measurements provide experimental evidence that agrees with recent conceptual proposals of multistep nucleation pathways with metastable molecular precursors in diverse processes, ranging from cloud formation to protein crystallization, and nanoparticle synthesis.
Classical nucleation theory (1⇓⇓–4) proposes that nucleation is a thermally activated process, where atomic clusters, called nuclei, stochastically evolve from metastable solution to form thermodynamically stable phases and materials. In classical models, nuclei are often assumed to be microscopic clusters of the final bulk phase, and nucleation barriers originate in a competition between unfavorable surface energies and favorable bulk free energies, which exhibit differing scaling with particle size. Below a certain size, called the critical size, the unfavorable surface energy is dominant, biasing protonuclei toward dissolution. Random energy and concentration fluctuations allow the protonuclei to grow or shrink diffusively within the nucleation energy landscape, occasionally overcoming the critical nucleation barrier, leading to rapid particle growth (Fig. 1A).
Fig. 1.
Diamond nucleation landscape and diamondoid protonuclei. (A) Approach for measuring nanoscale thermodynamic energy landscapes during nucleation. Molecular nuclei of atomically defined sizes and shapes, diamondoids (28), were used to map out the nucleation energy landscape during diamond PECVD by starting at precise locations on the thermodynamic nucleation energy landscape and measuring relative nucleation probabilities. (B) Diamondoid order, N, versus the number of carbon atoms in each diamondoid (Left) and diamondoid van der Waals surface areas (Right). N is defined as 1 for adamantane, and each subsequent addition of a four-carbon isobutyl substituent increases N by an integer value. (C) Molecular structures of the diamondoid protonuclei, ranging from 10 to 26 carbon atoms in size, are shown below the plot. The diamondoid order, N, is shown above each chemical name. Diamondoids were functionalized with POCl2 self-assembly groups (29) for covalent attachment to PECVD substrates.
The difference in scaling between surface and volumetric energies leads to two key hallmarks of classical nucleation theory: (i) an exponential relationship between subcritical nuclei surface areas and the probability of crossing the nucleation barrier, and (ii) a critical size where relative nucleation probabilities abruptly increase, indicating a boundary between the subcritical regime, where nuclei are thermodynamically biased to dissolve, and the postcritical regime, where nuclei are biased to grow.
Recent theoretical advances (5⇓–7) have extended classical nucleation theory, for example, by including both size and density as order parameters to describe nucleation pathways (6) or including size-dependent interfacial free energies (7). Multistep pathways, additional thermodynamic barriers, and the existence of distinct subcritical and postcritical regimes with differing scaling in nucleation rates and probabilities are key elements of these updated theories.
However, there is still a large discrepancy between the theoretical models and experimental measurements, which show that nucleation occurs much more rapidly than predicted by classical nucleation theory (8⇓⇓–11). Resolving the origin of such rapid nucleation rates remains an area of active investigation, often explained by metastable states that lower nucleation barriers (9⇓⇓⇓⇓⇓–15) or multistep pathways. One of the central challenges has been that these essential regimes have remained inaccessible experimentally. This is particularly true for industrially important gas-phase reactions, such as plasma-enhanced chemical vapor deposition (PECVD) of diamond and silicon (16⇓⇓–19). For example, diamond is used as a functional coating in many applications (16) and is an emerging material for quantum information technologies (20) and advanced biolabeling (21). While there is a rich history of studying diamond growth, the extreme conditions of diamond synthesis have prevented the measurement of diamond nucleation energetics (17, 18).
Nucleation energy landscapes have never been measured at the atomic level due to the extreme challenges associated with observing the dynamic, few-atom clusters thought to participate in nucleation processes. Recently, researchers have made strides toward visualizing nucleation in liquid–liquid and colloidal systems, where optical imaging was used to study colloids (22, 23) and proteins (12, 24), since large particle sizes permit direct observation. Emerging techniques, like liquid-state transmission electron microscopy (25⇓–27), enabled striking advances in visualizing nanoscale growth. However, the putative dynamic nuclei, in the order of tens-of-atoms size, remain inaccessible, and questions surrounding the influence of the probe beam remain.
Rather than attempt to directly image few-atom clusters, we developed a way to measure nucleation energy landscapes by creating atomically defined putative protonuclei and quantifying the relative densities of diamond nanoparticles, ρ (in particles per square meter), formed from monolayers of each protonuclei. Different-sized subcritical nuclei have different free energies with respect to the critical nucleus (Fig. 1A) and grow or contract stochastically over time. If a nucleus reaches the critical size, r* (Fig. 1A), the particle is taken to then grow deterministically. Hence, if seed protonuclei are larger than r*, then there should be an abrupt increase in the observed particle density.
The probability, P, that a protonuclei crosses this nucleation barrier can then be calculated as a mean first-passage time (5), which scales exponentially with the energy difference between a nucleus of size i and the critical nucleus of size r*, as shown in Eq. 1:
By starting with monodisperse monolayers of diamondoid protonuclei, we initialize the system at specific points on the hypothetical nucleation energy landscape in Fig. 1A. Assuming that all of the diamondoids are located along the same nucleation pathway, the measured density of fully formed diamond nanoparticles, ρ, should scale as the nucleation barrier passage probability, P. As a result, by measuring the relative number of particles that nucleate from subcritical diamondoids, we can ascertain the relative nucleation energetics.
Interestingly, if one of the diamondoids is larger than r*, then we should also observe an abrupt, superexponential increase in density, ρ, as nucleation and growth probabilities enter a different regime for protonuclei that exceed the critical size, since there is no thermodynamic barrier to growth above the critical size. The atomically defined series of nuclei we studied were formed using diamondoids (28), which are molecular fragments of diamond, ranging from 10 to 26 carbon atoms (Fig. 1C).
Results
Nucleation Densities from Diamondoid Monolayers.
To test this concept for diamond, a silicon substrate was functionalized with a monolayer of phosphonyl dichloride (POCl2)-modified diamondoid protonuclei, which were covalently attached to the surface via P–O–Si bonds (29). PECVD diamond growth was then performed using standard conditions, resulting in different densities of large diamond particles depending on the size of the diamondoid seed (Fig. 2). The number of diamond particles per square millimeter was measured with scanning electron microscopy (SEM), representing the probability that the protonuclei crossed the nucleation barrier before being etched away by the plasma.
Fig. 2.
Diamondoid-seeded PECVD growth densities. (A) Photograph of PECVD growth using 10 × 6-mm silicon wafers in a 1% CH4, 99% H2 plasma. Scanning electron microscopy (SEM) images of representative diamond particles. (White scale bars: 500 nm.) (B) Representative SEM images comparing nanoparticle growth densities on a wafer seeded with the largest precritical diamondoid [1(2)3]tetramantane (Top) to a wafer seeded with the postcritical diamondoid [1(2,3)4]pentamantane. The small white dots are faceted diamond nanoparticles, as shown in A. (C) Particle growth densities following vertical substrate growth at 750 °C with a feed gas concentration of 99% H2 and 1% CH4. Each data point corresponds to at least eight independent experiments for the diamondoid pictured, with the diamondoid attachment orientation as shown. The error bars indicate the standard error of the mean. The 750 °C conditions occurred at a distance of 2 mm from the top edge of the seeded wafer, and other temperature conditions during the vertical growth are shown in SI Appendix, Fig. S1. Diamond growth densities were largely independent of temperature for the 100 °C range tested in the vertical configuration. The purple shading illustrates nucleation densities on unseeded vertical orientation substrates that were immersed in pure toluene before growth.
Fig. 2C shows the measured diamond nanoparticle densities grown from six different diamondoid monolayers, grown at 750 °C in a 99% H2, 1% CH4 PECVD plasma at 23.5 torr and 350 W. A vertical wafer configuration (30) enabled testing multiple conditions in parallel, as the temperature of the wafer varies from 950 °C at the top to 250 °C at the bottom. Each point corresponds to the average particle density from at least eight different independent experiments for each diamondoid. The diamond particles exhibited a faceted, “quasispherical” shape (Fig. 2A) with a large diamond–silicon contact angle, so the substrate surface energy has minimal impact on the measured diamond nucleation energy barrier.
To ensure that the measured growth densities map the underlying thermodynamic nucleation energy landscape, the experiments reported in Fig. 2 and SI Appendix, Fig. S1 were carried out under very low carbon supersaturation, where nucleation is quasi-reversible and governed by the underlying thermodynamic energy landscape (4⇓–6). Diamond nanoparticles grown under the 1% CH4, 99% H2 conditions shown in Fig. 2 have narrow size distributions and preferentially exhibit the lowest surface energy (111) facet of the diamond lattice. Further decreasing the CH4 content in the PECVD feed gas to less than 0.25% results in full etching of the diamondoid monolayers. These observations are consistent with nucleation and growth in a largely thermodynamically controlled regime.
As shown in SI Appendix, Fig. S2, raising the supersaturation of carbon in the plasma phase by increasing the CH4 content of the feed gas or replacing H2 with Ar, which is inert, readily drives nucleation and growth into a kinetic regime. For example, under feed gas conditions of 1% CH4 in 99% Ar, selected to mimic the conditions of ultrananocrystalline diamond (UNCD) synthesis (31), diamond growth densities are much higher, but particle size distributions are heterogeneous and diamond particles form rod-like shapes due to preferential growth of the higher surface energy (100) facet for kinetic reasons (SI Appendix, Fig. S2). Increasing the concentration of CH4 in the feed gas above 10% resulted in the exclusive growth of graphitic carbon, even in the presence of H2.
To assess the generality of our conclusions, diamond growth densities were determined at different heights on the substrate, representing a range of plasma conditions in the low supersaturation regime. Experiments were also repeated with a different PECVD chamber with a remote plasma source. As shown in Table 1 and SI Appendix, Fig. S1, the nucleation barrier, critical nucleus size, and diamond–plasma interfacial energy were in agreement across varying conditions, despite vastly different temperatures and nucleation rates, showing the results are general and not particular to one chamber or growth geometry.
View this table:
Table 1.
Nucleation barriers and calculated diamond–plasma interfacial energies
In this low supersaturation regime, relative growth densities as a function of particle size exhibit the two key elements of classical nucleation theory. First, the growth density depends exponentially on the protonuclei size from adamantane through tetramantane, with the slope remaining strikingly consistent over a large range of conditions. Second, the growth density increases abruptly upon reaching pentamantane, exhibiting a pronounced break from the exponential relationship of the smaller diamondoids.
A nucleation barrier where pentamantane exceeds the critical size is the most plausible explanation for these two observations. The nucleus size appears to be the dominant factor during nucleation, yet symmetry also plays a secondary role, as evidenced by the higher diamond density seeded by the symmetric [1(2,3)4]pentamantane isomer, relative to the lower-symmetry [12(1)3]pentamantane. Since both isomers of pentamantane exceed the critical size, these data suggest a critical nucleus size between 22 and 26 carbon atoms or about 0.8 nm in diameter.
Determination of Nucleation Energy Barrier and Interfacial Energy.
A significant advantage of this approach is that relative nucleation energy barriers and the effective surface energy of the diamondoid protonuclei can be determined without needing to assume that critical nuclei behave as small clusters of the bulk phase. The energy barriers separating each of the diamondoid molecules in the subcritical regime were determined by normalizing the growth densities of each of the subcritical diamondoid nuclei to that of [1(2)3]tetramantane as a reference, using Eqs. 2 and 3:
Fig. 3.
Estimation of plasma–nucleus interfacial energy calculated based on relative nucleation probabilities. The y axis (ΔGx-tetra) is the proportion of the nucleation energy barrier separating the subcritical diamondoids using [1(2)3]tetramantane as a reference at 750 °C. ΔGx-tetra is determined using Eq. 3, and the error bars indicate the standard error of the mean. The x axis (ΔA) is the calculated van der Waals surface area differences between each of the subcritical diamondoids and [1(2)3]tetramantane. The 12 ± 6 mJ⋅m−2 slope is the energy cost per unit surface area created during diamond nucleation, assuming that each diamondoid is at different points along the nucleation pathway.
Fig. 3 shows the measured subcritical energy landscape at 750 °C. The nucleation barrier is in the order of 10−20 J, which is comparable to thermal energy at the PECVD temperatures (kBT), and the slope yields a diamond–plasma interfacial energy of 12 ± 6 mJ⋅m−2 at 750 °C. As shown in Table 1, the nucleation barriers and interfacial energies agree to within a factor of 3 across the conditions tested.
Discussion
Our results show that the probability of diamond nanoparticle growth exponentially depends on the size of the diamondoid seed. Furthermore, we observe an abrupt increase in diamond growth densities at a critical size between 22 and 26 carbon atoms (Fig. 2). The exponential scaling and the presence of a critical size are two key predictions of classical nucleation theory. From our results, the measured energy of the nucleation barrier is on the order of 10−20 J, which is several kBT under growth conditions.
In contrast, capillary models of diamond nucleation (18, 32, 33) using energetics calculated from the bulk diamond lattice and surface energy, γcleave, predict an interfacial energy of 1–3 J⋅m−2, leading to an estimated nucleation barrier of 10−16 J. This exceeds 1,000 kBT under diamond growth conditions and implies a critical nucleus of about 5,000 atoms (Fig. 4A). Within this previous theoretical framework, diamondoids should be incapable of seeding diamond growth.
Fig. 4.
Schematic of diamond nucleation reaction coordinates. (A) Nucleation of condensed carbon phases from supersaturated carbon vapor, where relative chemical potentials are per carbon atom with two distinct states: μvapor and μsolid. Estimating nucleation barriers from the bulk cleavage energy leads to a barrier exceeding 1,000 kBT under PECVD conditions; this approach inherently assumes that nucleation is a single-step process into the bulk crystalline diamond phase. In contrast, the measured nucleation barrier is in the order of several values in kBT. (B) Two-step diamond growth mechanism as the simplest example of a multistep diamond nucleation and growth pathway, with three distinct states: μvapor, μsurface, and μbulk. The critical nucleus is composed entirely of surface atoms with diamond-like bonding, requiring an additional bulk transformation step to form bulk diamond. The carbon supersaturation in the plasma drives nucleation, and the nucleation barrier is determined by the plasma–nucleus interfacial energy, which is strongly influenced by the diamond surface termination (38).
These capillary calculations are two to four orders of magnitude larger than the 10−20-J barrier and 26-atom critical nucleus measured here. For prior classical, single-step models of diamond nucleation to be consistent with the probabilities we measure, the driving chemical potential in the plasma would need to exceed 4,500 kJ⋅mol−1, which is not physically realistic (32). Therefore, while the nucleation energy landscape retains the size dependence of classical theory, bulk properties cannot be used to quantitatively predict PECVD diamond nucleation energetics.
In addition, the postcritical nucleus, pentamantane, does not contain a single “bulk” atom, calling into question the concept that the driving force for nucleation is formation of the bulk phase. In classical nucleation theory, the nucleation barrier results from differing scaling between a favorable “volumetric” energy that results from the creation of bulk atoms and an unfavorable “surface” energy from the creation of surface atoms. Here, we find that all of the atoms in diamond critical nuclei are surface atoms and that the critical barrier is crossed before forming internal atoms with volumetric scaling. Thus, our results suggest that the presence of a nucleation barrier during diamond synthesis has a different molecular mechanism than in classical nucleation theory.
We propose that the nucleation-driving force for these molecular clusters comes from the formation of favorable surface chemical bonds that scale as the nucleus surface area, which replaces the bulk volumetric driving force of classical nucleation theory. The barrier still originates in an unfavorable entropic contribution, which is captured by the effective molecular surface energy determined in Fig. 3. Since both the creation of favorable surface bonds and the growth of unfavorable interface scale as the nucleus surface area, the abrupt change in nucleation probability shown in Fig. 2 cannot result purely from geometric scaling arguments. To be consistent within this model, at least one of the two surface terms must exhibit an explicit size dependence to give rise to the observed diamond critical nucleation behavior.
A size-dependent interfacial energy is one plausible explanation for the critical barrier. For example, a recent theoretical study of nucleation using model “polycube” clusters shows that size-dependent surface energies may be a key element of nucleation (7). Here, the critical increase in diamond nucleation probability could be explained if the nucleus–plasma interfacial energy abruptly decreases between a cluster size of 22 and 26 carbon atoms. Alternatively, the surface-bonding energy could also have a size dependence. Additionally, a recent extension to classical nucleation theory predicts that cluster distribution functions for nuclei in the subcritical regime may exhibit departures from a diffusive exploration of phase space characterized by the Boltzmann population distribution of classical nucleation theory in certain cases (6). The implications of this finding remain under active investigation, and further theoretical progress along these lines may shed additional insight into the data reported here.
Consequently, our measurements show that two key tenets of classical nucleation theory are observed at molecular scales, but with origins that differ from the capillary assumption-based intuition of competing geometric scaling between nucleus surface areas and volumetric energies. Accordingly, these measurements support recent suggestions (8, 11, 34) to unify both classical and nonclassical concepts into a comprehensive framework.
One model that is consistent with our observations is that diamond growth occurs via a two-step pathway with distinct nucleation and bulk transformation steps, as shown in Fig. 4B. Critical diamond nucleation occurs through the formation of metastable, hydrogen-terminated diamondoid clusters before forming the bulk phase. The nucleation step follows the expected exponential size dependence of classical theory, but with an interfacial energy and nucleation energy barrier that is much lower than ideal classical estimates that rely on bulk properties. The second, bulk transformation step then occurs as diamondoid nuclei atoms react into bulk diamond atoms.
From our results, we hypothesize that crystalline diamond grows when the chemical potential of carbon in the plasma phase is closely matched to the surface energy of the protonuclei, rather than the ideal classical case where crystalline diamond would only form when the chemical potential of carbon in the plasma is closely matched to that of bulk diamond. This picture agrees with and provides explicit experimental evidence for thermodynamic energy landscapes that support recent proposals of multistep nucleation in diverse contexts, ranging from cloud formation (34) to protein crystallization (35), biomineralization (9), and nanoparticle synthesis (10).
Furthermore, a 26-carbon critical nucleus resolves an outstanding question surrounding growth of diamond versus graphite in PECVD reactors. Prior estimates of carbon critical nuclei being composed of several thousand atoms (33) imply that diamond nuclei should not form thermodynamically relative to graphite (17). However, hydrogen-terminated diamond is more thermodynamically stable than hydrogen-terminated graphite for carbon clusters of less than about 100 carbon atoms in size (36). Our measurement of a 26-carbon critical nucleus resolves this paradox by showing that sp3 diamond-like particles are the favored state at the critical size, consistent with ultra-nanocrystalline diamond growth (31), where sub–5-nm crystalline domain sizes are frequently observed.
These results also have significant implications to other industrial vapor deposition processes. For example, homogeneous nucleation of silicon and other semiconductors impedes the chemical vapor deposition (CVD) production of crystalline films (37), but the cleavage energy of bulk silicon (38) is around 1–2 J⋅m−2, leading to a calculated 10−16-J barrier for homogeneous nucleation. This implies that nucleation should almost never occur, which is in contrast to experimental observations. Since the chemical nature of hydrogenated silicon and diamond surfaces are similar (38), multistep models would predict a nucleation barrier on the order of 10−20 J for silicon. This increases the probability for silicon nucleation during CVD by the tremendous factor of e1,000, at which point the prevalence of silicon nucleation during CVD is readily understood.
Overall, this direct experimental measurement of a nanoscale nucleation energy landscape provides a quantitative test of classical nucleation theory at the molecular level. We find that the diamond nucleation landscape exhibits both the size dependence and abrupt change in growth rate of classical nucleation theory (4). Unexpectedly, we also find that critical nuclei are diamond-like carbon clusters that do not contain a single bulk atom, meaning that a critical size can be characteristic of a system where there is no distinction between surface and bulk effects.
Thus, the nucleation barrier and critical size do not seem to originate from a geometric scaling competition between surface and volumetric energies, but instead appear to arise from either an interfacial energy or surface bonding energy that changes with particle size. These results highlight the importance of revising classical nucleation theory to include complex pathways with metastable molecular precursors that cannot be understood as microscopic clusters with bulk properties (6⇓⇓⇓–10, 34).
Materials and Methods
Diamondoid Purification and Functionalization.
Adamantane, diamantane, triamantane, [121]tetramantane, [1(2)3]tetramantane, [12(1)3]pentamantane (racemic), and [1(2,3)4]pentamantane were isolated and purified from petroleum extracts using previously reported protocols (28). Mass spectrometry, gas chromatography, and NMR spectroscopy were used to ensure diamondoid purity. Diamondoid molecules were then selectively functionalized via multistep synthesis (29) to enable covalent attachment of diamondoid self-assembled monolayers on oxidized silicon surfaces. Adamantane was also functionalized with a 2(trichlorosilyl)ethyl group (SiCl3) at the 1-position to assess the impact of attachment chemistry under the milder remote plasma CVD growth conditions. Diamond growth densities were independent of attachment chemistry for POCl2 and SiCl3 functionalization, further confirming that carbon etching and addition primarily determine diamondoid nucleation energetics.
Formation of Diamondoid Self-Assembled Monolayers.
Diamondoid monolayers were attached to plasma-activated silicon surfaces via the formation of bidentate P–O bonds between POCl2 groups and Si–OH surface groups or tridentate Si–O bonds between SiCl3 groups and Si–OH groups. Control experiments utilizing nonfunctionalized diamondoids were ineffective for seeding diamond growth, highlighting the importance of covalent attachment. Additional control experiments with POCl2 functionalized nondiamondoid carbonaceous monolayers, including linear alkanes and aryl substituents, were ineffective for seeding diamond growth, confirming the importance of diamondoid seeds. Further details of monolayer self-assembly and characterization are provided in SI Appendix, section 1.1.
PECVD Diamond Growth.
High-temperature vertical growths were carried out using a Seki Technotron PECVD system with a 2.45-GHz direct plasma microwave source (see SI Appendix, section 1.2 for full details). Nucleation and growth experiments in the low supersaturation thermodynamic regime were carried out under the following growth conditions: 23.5 torr, 300 standard cubic centimeters per min (sccm) H2, 3 sccm CH4, and 350 W for the first 15 min of nucleation and growth and 23.5 torr, 300 sccm H2, 1.5 sccm CH4, and 350 W for the last 45 min of growth. CH4 concentrations were reduced from 1 to 0.5% after the first 15 min to suppress diamond renucleation while diamond particles were grown to a large enough size to enable rapid determination of diamond growth densities via SEM. Decreasing the feed gas concentration of CH4 to below 0.25% resulted in complete etching of the diamondoid seeds.
Nucleation and growth experiments in the high-supersaturation kinetic regime were carried out under the following growth conditions: 15 torr, 90 sccm Ar, 1 sccm CH4, and 300 W for 1 h. Increasing the feed gas concentration of CH4 to above 10% resulted in the exclusive growth of graphitic carbon.
Control experiments were carried out where silicon wafers were immersed in pure toluene for at least 48 h and then used for vertical growth experiments. Diamond nanoparticles were sporadically observed on unseeded wafers, as shown by the shaded area in Fig. 2C. However, these densities ranged from no observable diamond nanoparticles to a maximum density that was significantly lower than for adamantane seeding. The baseline density of diamond particles observed with no seeding likely results from the stochastic deposition of diamond nanoparticles that homogeneously nucleate in the plasma phase. This implies that homogeneous nucleation provides some of the inherent experimental variability present in the measured nucleation densities.
Determination of Diamond Growth Densities.
The density of diamond particles was measured via SEM and counted following each growth. Diamond nanoparticles were grown to diameters of ∼0.5–1 μm to enable particle densities to be automatically processed and counted via the NIH ImageJ analysis software. Full details can be found in SI Appendix, section 1.3.
Acknowledgments
This work was supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract DE-AC02-76SF00515. M.A.G. acknowledges the funding provided by the Geballe Laboratory for Advanced Materials Postdoctoral Fellowship program at Stanford University. C.F. and M.N. acknowledge support of the Flemish Funds for Scientific Research (FWO), Project G0E7417N (Single-Atom Diamond Quantum Probe: Proof-of-Principle Molecular Engineering Methodology and ERANET Project Nanobit). Part of this work was performed at the Stanford Nano Shared Facilities, supported by the National Science Foundation under Award ECCS-1542152.
Footnotes
- ↵1To whom correspondence should be addressed. Email: nmelosh{at}stanford.edu.
Author contributions: Z.-X.S., M.N., and N.A.M. designed research; M.A.G., H.I., P.J.M., V.P., A.T., and C.F. performed research; J.E.D., R.M.K.C., A.A.F., and P.R.S. contributed new reagents/analytic tools; M.A.G., M.N., and N.A.M. analyzed data; and M.A.G. and N.A.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1803654115/-/DCSupplemental.
Published under the PNAS license.
References
Experimental measurement of the diamond nucleation landscape reveals classical and nonclassical features
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