The Current Understanding of Mechanistic Pathways in Zeolite Crystallization.

Zeolite catalysts and adsorbents have been an integral part of many commercial processes and are projected to play a significant role in emerging technologies to address the changing energy and environmental landscapes. The ability to rationally design zeolites with tailored properties relies on a fundamental understanding of crystallization pathways to strategically manipulate processes of nucleation and growth. The complexity of zeolite growth media engenders a diversity of crystallization mechanisms that can manifest at different synthesis stages. In this review, we discuss the current understanding of classical and nonclassical pathways associated with the formation of (alumino)silicate zeolites. We begin with a brief overview of zeolite history and seminal advancements, followed by a comprehensive discussion of different classes of zeolite precursors with respect to their methods of assembly and physicochemical properties. The following two sections provide detailed discussions of nucleation and growth pathways wherein we emphasize general trends and highlight specific observations for select zeolite framework types. We then close with conclusions and future outlook to summarize key hypotheses, current knowledge gaps, and potential opportunities to guide zeolite synthesis toward a more exact science.

Antagonistic cooperativity between crystal growth modifiers.

Ubiquitous processes in nature and the industry exploit crystallization from multicomponent environments1-5; however, laboratory efforts have focused on the crystallization of pure solutes6,7 and the effects of single growth modifiers8,9. Here we examine the molecular mechanisms employed by pairs of inhibitors in blocking the crystallization of haematin, which is a model organic compound with relevance to the physiology of malaria parasites10,11. We use a combination of scanning probe microscopy and molecular modelling to demonstrate that inhibitor pairs, whose constituents adopt distinct mechanisms of haematin growth inhibition, kink blocking and step pinning12,13, exhibit both synergistic and antagonistic cooperativity depending on the inhibitor combination and applied concentrations. Synergism between two crystal growth modifiers is expected, but the antagonistic cooperativity of haematin inhibitors is not reflected in current crystal growth models. We demonstrate that kink blockers reduce the line tension of step edges, which facilitates both the nucleation of crystal layers and step propagation through the gates created by step pinners. The molecular viewpoint on cooperativity between crystallization modifiers provides guidance on the pairing of modifiers in the synthesis of crystalline materials. The proposed mechanisms indicate strategies to understand and control crystallization in both natural and engineered systems, which occurs in complex multicomponent media1-3,8,9. In a broader context, our results highlight the complexity of crystal-modifier interactions mediated by the structure and dynamics of the crystal interface.

High-Index NiO Particle Synthesis in Alkali Chloride Salts: Nonclassical Crystallization Pathways and Thermally-Induced Surface Restructuring.

The formation mechanism(s) of high-index facets in metal oxides is not widely understood but remains a topic of interest owing to the challenges of stabilizing high-energy surfaces. These metal oxide crystal surfaces are expected to provide unique physicochemical characteristics; therefore, understanding crystallization pathways may enable the rational design of materials with controlled properties. Here the crystallization of NiO via thermal decomposition of a nickel source in excess of alkali chlorides is examined, focusing on KCl, which produces trapezohedral NiO (311) particles that are difficult to achieve through alternative methods. Trapezohedral NiO crystals are confirmed to grow via a molten eutectic where NiO nucleation is followed by nonclassical crystallization through processes resembling colloidal assembly. Aggregates comprised of NiO nanocrystals form mesostructures that ripen with heating time and exhibit fewer grain boundaries as they transition into single-crystalline particles. At temperatures higher than those of NiO crystallization, there is a restructuring of (311) facets into microfacets exposing (111) and (100) surfaces. These findings illustrate the complex crystallization processes taking place during molten salt synthesis. The ability to generate metal oxide particles with high-index facets has the potential to be a more generalized approach to unlock the physicochemical properties of materials for diverse applications.

In Situ Imaging of Faujasite Surface Growth Reveals Unique Pathways of Zeolite Crystallization.

Zeolite crystallization occurs by complex processes involving a variety of possible mechanisms. The sol gel media used to prepare zeolites leads to heterogeneous mixtures of solution and solid states with diverse solute species. At later stages of zeolite synthesis when growth occurs predominantly from solution, classical two-dimensional nucleation and spreading of layers on crystal surfaces via the addition of soluble species is the dominant pathway. At earlier stages, these processes occur in parallel with nonclassical pathways involving crystallization by particle attachment (CPA). The relative roles of solution- and solid-state species in zeolite crystallization have been a subject of debate. Here, we investigate the growth mechanism of a commercially relevant zeolite, faujasite (FAU). In situ atomic force microscopy (AFM) measurements reveal that supernatant solutions extracted from a conventional FAU synthesis at various times do not result in growth, indicating that FAU growth predominantly occurs from the solid state through a disorder-to-order transition of amorphous precursors. Elemental analysis shows that supernatant solutions are significantly more siliceous than both the original growth mixture and the FAU zeolite product; however, in situ AFM studies using a dilute clear solution with a lower Si/Al ratio revealed three-dimensional growth of surfaces that is distinct from layer-by-layer and CPA pathways. This unique mechanism of growth differs from those observed in studies of other zeolites. Given that relatively few zeolite frameworks have been the subject of mechanistic investigation by in situ techniques, these observations of FAU crystallization raise the question whether its growth pathway is characteristic of other zeolite structures.

In situ imaging of two-dimensional surface growth reveals the prevalence and role of defects in zeolite crystallization.

Zeolite crystallization predominantly occurs by nonclassical pathways involving the attachment of complex (alumino)silicate precursors to crystal surfaces, yet recurrent images of fully crystalline materials with layered surfaces are evidence of classical growth by molecule attachment. Here we use in situ atomic force microscopy to monitor three distinct mechanisms of two-dimensional (2D) growth of zeolite A where we show that layer nucleation from surface defects is the most common pathway. Direct observation of defects was made possible by the identification of conditions promoting layered growth, which correlates to the use of sodium as an inorganic structure-directing agent, whereas its replacement with an organic results in a nonclassical mode of growth that obscures 2D layers and markedly slows the rate of crystallization. In situ measurements of layered growth reveal that undissolved silica nanoparticles in the synthesis medium can incorporate into advancing steps on crystal surfaces to generate defects (i.e., amorphous silica occlusions) that largely go undetected in literature. Nanoparticle occlusion in natural and synthetic crystals is a topic of wide-ranging interest owing to its relevance in fields spanning from biomineralization to the rational design of functional nanocomposites. In this study, we provide unprecedented insight into zeolite surface growth by molecule addition through time-resolved microscopy that directly captures the occlusion of silica nanoparticles and highlights the prevalent role of defects in zeolite crystallization.

A second mechanism employed by artemisinins to suppress Plasmodium falciparum hinges on inhibition of hematin crystallization.

Malaria is a pervasive disease that affects millions of lives each year in equatorial regions of the world. During the erythrocytic phase of the parasite life cycle, Plasmodium falciparum invades red blood cells, where it catabolizes hemoglobin and sequesters the released toxic heme as innocuous hemozoin crystals. Artemisinin (ART)-class drugs are activated in vivo by newly released heme, which creates a carbon-centered radical that markedly reduces parasite density. Radical damage to parasite lipids and proteins is perceived to be ARTs' dominant mechanism of action. By contrast, quinoline-class antimalarials inhibit the formation of hemozoin and in this way suppress heme detoxification. Here, we combine malaria parasite assays and scanning probe microscopy of growing ß-hematin crystals to elucidate an unexpected mechanism employed by two widely administered antimalarials, ART, and artesunate to subdue the erythrocytic phase of the parasite life cycle. We demonstrate that heme-drug adducts, produced after the radical activation of ARTs and largely believed to be benign bystanders, potently kills P. falciparum at low exogenous concentrations. We show that these adducts inhibit ß-hematin crystallization and heme detoxification, a pathway which complements the deleterious effect of radicals generated via parent drug activation. Our findings reveal an irreversible mechanism of heme-ART adduct inhibition of heme crystallization, unique among antimalarials and common crystal growth inhibitors, that opens new avenues for evaluating drug dosing regimens and understanding growing resistance of P. falciparum to ART.

Spatiotemporal Coke Coupling Enhances para-Xylene Selectivity in Highly Stable MCM-22 Catalysts.

Identifying zeolite catalysts that can simultaneously optimize p-xylene selectivity and feed utilization is critical to toluene alkylation with methanol (TAM). Here, we show that zeolite MCM-22 (MWW) has an exceptional catalyst lifetime in the TAM reaction at high operating pressure, conversion, and selectivity. We systematically probe the catalytic behavior of active sites in distinct topological features of MCM-22, revealing that high p-xylene yield and catalyst stability are predominantly attributed to sinusoidal channels and supercages, respectively. Using a combination of catalyst design and testing, density functional theory, and molecular dynamics simulations, we propose a spatiotemporal coke coupling phenomenon to explain a multistage p-xylene selectivity profile wherein the formation of light coke in supercages initiates the deactivation of unselective external surface sites. Our findings indicate that the specific nature of coke is critical to catalyst performance. Moreover, they provide unprecedented insight into the synchronous roles of distinct topological features giving rise to the exceptional stability and selectivity of MCM-22 in the TAM reaction.

Manipulation of amorphous precursors to enhance zeolite nucleation.

Crystallization in media comprised of amorphous precursors is becoming a more common phenomenon for numerous synthetic, biological, and natural materials that grow by a combination of classical and nonclassical pathways. Amorphous phases can exhibit a wide range of physicochemical properties that may evolve during the course of nucleation and crystal growth. This creates challenges for establishing causal relationships between amorphous precursor properties and their effect(s) on the selection of mechanistic pathways of crystallization and ultimately the properties of the crystalline product. In this study, we examine ways to manipulate the composition and colloidal stability of amorphous (alumino)silicate precursors that are prevalent in nanoporous zeolite syntheses. Changes in the amorphous precursor properties are evaluated on the basis of their ability to enhance rates of crystal formation. Here, we use fumed silica as the primary silicon source and examine the effects of infusing the source or growth medium with additional alkali metal, which serves as an inorganic structure-directing agent to facilitate the formation of porous crystal structures. We also assess the impact of adding a polymer additive, which reduces the colloidal stability of precursors, wherein we posit that the confined pockets of solution within the interstitial spaces of the precursor aggregates play an important role in regulating the rate of zeolite crystallization. Three commercially relevant zeolites (mordenite, SSZ-13, and ZSM-5) were selected for this study based on their diverse frameworks and methods of preparation. Our findings reveal that alkali infusion significantly reduces the crystallization times for mordenite and SSZ-13, but has little impact on ZSM-5 synthesis. Conversely, we find that polymer addition markedly enhanced the rates of crystallization among all three zeolites, suggesting that this method may be a general approach to reduce zeolite synthesis times. Given the relatively high costs associated with commercial zeolite production, identifying new methods to improve the efficiency of hydrothermal syntheses can have significant practical implications beyond the fundamental benefits of developing new routes to tailor nonclassical crystallization.

Molecular modifiers reveal a mechanism of pathological crystal growth inhibition.

Crystalline materials are crucial to the function of living organisms, in the shells of molluscs, the matrix of bone, the teeth of sea urchins, and the exoskeletons of coccoliths. However, pathological biomineralization can be an undesirable crystallization process associated with human diseases. The crystal growth of biogenic, natural and synthetic materials may be regulated by the action of modifiers, most commonly inhibitors, which range from small ions and molecules to large macromolecules. Inhibitors adsorb on crystal surfaces and impede the addition of solute, thereby reducing the rate of growth. Complex inhibitor-crystal interactions in biomineralization are often not well elucidated. Here we show that two molecular inhibitors of calcium oxalate monohydrate crystallization--citrate and hydroxycitrate--exhibit a mechanism that differs from classical theory in that inhibitor adsorption on crystal surfaces induces dissolution of the crystal under specific conditions rather than a reduced rate of crystal growth. This phenomenon occurs even in supersaturated solutions where inhibitor concentration is three orders of magnitude less than that of the solute. The results of bulk crystallization, in situ atomic force microscopy, and density functional theory studies are qualitatively consistent with a hypothesis that inhibitor-crystal interactions impart localized strain to the crystal lattice and that oxalate and calcium ions are released into solution to alleviate this strain. Calcium oxalate monohydrate is the principal component of human kidney stones and citrate is an often-used therapy, but hydroxycitrate is not. For hydroxycitrate to function as a kidney stone treatment, it must be excreted in urine. We report that hydroxycitrate ingested by non-stone-forming humans at an often-recommended dose leads to substantial urinary excretion. In vitro assays using human urine reveal that the molecular modifier hydroxycitrate is as effective an inhibitor of nucleation of calcium oxalate monohydrate nucleation as is citrate. Our findings support exploration of the clinical potential of hydroxycitrate as an alternative treatment to citrate for kidney stones.

Cooperative Surface Passivation and Hierarchical Structuring of Zeolite Beta Catalysts.

We report a method to prepare core-shell zeolite beta (*BEA) with an aluminous core and an epitaxial Si-rich shell. This method capitalizes on the inherent defects in *BEA crystals to simultaneously passivate acid sites on external surfaces and increase intracrystalline mesoporosity through facile post-hydrothermal synthesis modification in alkaline media. This process creates more hydrophobic materials by reducing silanol defects and enriching the shell in silica via a combination of dealumination and the relocation of silica from the core to the shell during intracrystalline mesopore formation. The catalytic consequences of *BEA core-shells relative to conventional analogues were tested using the biomass conversion of levulinic acid and n-butanol to n-butyl levulinate as a benchmark reaction. Our findings reveal that siliceous shells and intracrystalline mesopores synergistically enhance the performance of *BEA catalysts.

Enhanced Selectivity and Stability of Finned Ferrierite Catalysts in Butene Isomerization.

Designing zeolite catalysts with improved mass transport properties is crucial for restrictive networks of either one- or two-dimensional pore topologies. Here, we demonstrate the synthesis of finned ferrierite (FER), a commercial zeolite with two-dimensional pores, where protrusions on crystal surfaces behave as pseudo nanoparticles. Catalytic tests of 1-butene isomerization reveal a 3-fold enhancement of catalyst lifetime and an increase of 12 % selectivity to isobutene for finned samples compared to corresponding seeds. Electron tomography was used to confirm the identical crystallographic registry of fins and seeds. Time-resolved titration of Brønsted acid sites confirmed the improved mass transport properties of finned ferrierite compared to conventional analogues. These findings highlight the advantages of introducing fins through facile and tunable post-synthesis modification to impart material properties that are otherwise unattainable by conventional synthesis methods.

Accelerating the Crystallization of Zeolite SSZ-13 with Polyamines.

Tailoring processes of nucleation and growth to achieve desired material properties is a pervasive challenge in synthetic crystallization. In systems where crystals form via nonclassical pathways, engineering materials often requires the controlled assembly and structural evolution of colloidal precursors. In this study, we examine zeolite SSZ-13 crystallization and show that several polyquaternary amines function as efficient accelerants of nucleation, and, in selected cases, tune crystal size by orders of magnitude. Among the additives tested, polydiallyldimethylammonium (PDDA) was found to have the most pronounced impact on the kinetics of SSZ-13 formation, leading to a 4-fold reduction in crystallization time. Our findings also reveal that enhanced nucleation occurs at an optimal PDDA concentration where a combination of light-scattering techniques demonstrate these conditions lead to polymer-induced aggregation of amorphous precursors and the promotion of (alumino)silicate precipitation from the growth solution. Here, we show that relatively low concentrations of polymer additives can be used in unique ways to dramatically enhance SSZ-13 crystallization rates, thereby improving the overall efficiency of zeolite synthesis.

Controlling Nucleation Pathways in Zeolite Crystallization: Seeding Conceptual Methodologies for Advanced Materials Design.

A core objective of synthesizing zeolites for widespread applications is to produce materials with properties and corresponding performances that exceed conventional counterparts. This places an impetus on elucidating and controlling processes of crystallization where one of the most critical design criteria is the ability to prepare zeolite crystals with ultrasmall dimensions to mitigate the deleterious effects of mass transport limitations. At the most fundamental level, this requires a comprehensive understanding of nucleation to address this ubiquitous materials gap. This Perspective highlights recent methodologies to alter zeolite nucleation by using seed-assisted protocols and the exploitation of interzeolite transformations to design advanced materials. Introduction of crystalline seeds in complex growth media used to synthesize zeolites can have wide-ranging effects on the physicochemical properties of the final product. Here we discuss the diverse pathways of zeolite nucleation, recent breakthroughs in seed-assisted syntheses of nanosized and hierarchical materials, and shortcomings for developing generalized guidelines to predict synthesis outcomes. We offer a critical analysis of state-of-the-art approaches to tailor zeolite crystallization wherein we conceptualize whether parallels between network theory and zeolite synthesis can be instrumental for translating key findings of individual discoveries across a broader set of zeolite crystal structures and/or synthesis conditions.

Finned zeolite catalysts.

There is growing evidence for the advantages of synthesizing nanosized zeolites with markedly reduced internal diffusion limitations for enhanced performances in catalysis and adsorption. Producing zeolite crystals with sizes less than 100 nm, however, is non-trivial, often requires the use of complex organics and typically results in a small product yield. Here we present an alternative, facile approach to enhance the mass-transport properties of zeolites by the epitaxial growth of fin-like protrusions on seed crystals. We validate this generalizable methodology on two common zeolites and confirm that fins are in crystallographic registry with the underlying seeds, and that secondary growth does not impede access to the micropores. Molecular modelling and time-resolved titration experiments of finned zeolites probe internal diffusion and reveal substantial improvements in mass transport, consistent with catalytic tests of a model reaction, which show that these structures behave as pseudo-nanocrystals with sizes commensurate to that of the fin. This approach could be extended to the rational synthesis of other zeolite and aluminosilicate materials.

Factors controlling the molecular modification of one-dimensional zeolites.

Interactions between organic molecules and inorganic materials are ubiquitous in many applications and often play significant roles in directing pathways of crystallization. It is frequently debated whether kinetics or thermodynamics plays a more prominent role in the ability of molecular modifiers to impact crystal nucleation and growth processes. In the case of nanoporous zeolites, approaches in rational design often capitalize on the ability of organics, used as either modifiers or structure-directing agents, to markedly impact the physicochemical properties of zeolites. It has been demonstrated for multiple topologies that modifier-zeolite interactions can alter crystal size and morphology, yet few studies have distinguished the roles of thermodynamics and kinetics. We use a combination of calorimetry and molecular modeling to estimate the binding energies of organics on zeolite surfaces and correlate these results with synthetic trends in crystal morphology. Our findings reveal unexpectedly small energies of interaction for a range of modifiers with two zeolite structures, indicating the effect of organics on zeolite crystal surface free energy is minor and kinetic factors most likely govern growth modification.

A Comparative Analysis of In Vitro Toxicity of Synthetic Zeolites on IMR-90 Human Lung Fibroblast Cells.

Broad industrial application of zeolites increases the opportunity of inhalation. However, the potential impact of different types and compositions of zeolite on cytotoxicity is still unknown. Four types of synthetic zeolites have been prepared for assessing the effect on lung fibroblast: two zeolite L (LTL-R and LTL-D), ZSM-5 (MFI-S), and faujasite (FAU-S). The cytotoxicity of zeolites on human lung fibroblast (IMR-90) was assessed using WST1 cell proliferation assay, mitochondrial function, membrane leakage of lactate dehydrogenase, reduced glutathione levels, and mitochondrial membrane potential were assessed under control. Intracellular changes were examined using transmission electron microscopy (TEM). Toxicity-related gene expressions were evaluated by PCR array. The result showed significantly higher toxicity in IMR-90 cells with FAU-S than LTL-R, LTL-D and MFI-S exposure. TEM showed FAU-S, spheroidal zeolite with a low Si/Al ratio, was readily internalized forming numerous phagosomes in IMR-90 cells, while the largest and disc-shaped zeolites showed the lowest toxicity and were located in submembranous phagosomes in IMR-90 cells. Differential expression of TNF related genes was detected using PCR arrays and confirmed using qRT-PCR analysis of selected genes. Collectively, the exposure of different zeolites shows different toxicity on IMR-90 cells.

Local Ordering of Molten Salts at NiO Crystal Interfaces Promotes High-Index Faceting.

Given the strong influence of surface structure on the reactivity of heterogeneous catalysts, understanding the mechanisms that control crystal morphology is an important component of designing catalytic materials with targeted shape and functionality. Herein, we employ density functional theory to examine the impact of growth media on NiO crystal faceting in line with experimental findings, showing that molten-salt synthesis in alkali chlorides (KCl, LiCl, and NaCl) imposes shape selectivity on NiO particles. We find that the production of NiO octahedra is attributed to the dissociative adsorption of H2 O, whereas the formation of trapezohedral particles is associated with the control of the growth kinetics exerted by ordered salt structures on high-index facets. To our knowledge, this is the first observation that growth inhibition of metal-oxide facets occurs by a localized ordering of molten salts at the crystal-solvent interface. These findings provide new molecular-level insight on kinetics and thermodynamics of molten-salt synthesis as a predictive route to shape-engineer metal-oxide crystals.

Few-Unit-Cell MFI Zeolite Synthesized using a Simple Di-quaternary Ammonium Structure-Directing Agent.

Synthesis of a pentasil-type zeolite with ultra-small few-unit-cell crystalline domains, which we call FDP (few-unit-cell crystalline domain pentasil), is reported. FDP is made using bis-1,5(tributyl ammonium) pentamethylene cations as structure directing agent (SDA). This di-quaternary ammonium SDA combines butyl ammonium, in place of the one commonly used for MFI synthesis, propyl ammonium, and a five-carbon nitrogen-connecting chain, in place of the six-carbon connecting chain SDAs that are known to fit well within the MFI pores. X-ray diffraction analysis and electron microscopy imaging of FDP indicate ca. 10 nm crystalline domains organized in hierarchical micro-/meso-porous aggregates exhibiting mesoscopic order with an aggregate particle size up to ca. 5 µm. Al and Sn can be incorporated into the FDP zeolite framework to produce active and selective methanol-to-hydrocarbon and glucose isomerization catalysts, respectively.

Enhanced Surface Activity of MWW Zeolite Nanosheets Prepared via a One-Step Synthesis.

The synthesis of two-dimensional (2D) zeolites has garnered attention due to their superior properties for applications that span catalysis to selective separations. Prior studies of 2D zeolite catalysts demonstrated enhanced mass transport for improved catalyst lifetime and selectivity. Moreover, the significantly higher external surface area of 2D materials allows for reactions of bulky molecules too large to access interior pores. There are relatively few protocols for preparing 2D materials, owing to the difficultly of capping growth in one direction to only a few unit cells. To accomplish this, it is often necessary to employ complex, commercially unavailable organic structure-directing agents (OSDAs) prepared via multistep synthesis. However, a small subset of zeolite structures exist as naturally layered materials where postsynthesis steps can be used to exfoliate samples and produce ultrathin 2D nanosheets. In this study, we selected a common layered zeolite, the MWW framework, to explore methods of preparing 2D nanosheets via one-pot synthesis in the absence of complex organic templates. Using a combination of high-resolution microscopy and spectroscopy, we show that 2D MMW-type layers with an average thickness of 3.5 nm (ca. 1.5 unit cells) can be generated using the surfactant cetyltrimethylammonium (CTA), which operates as a dual OSDA and exfoliating agent to affect Al siting and to eliminate the need for postsynthesis exfoliation, respectively. We tested these 2D catalysts using a model reaction that assesses external (surface) Brønsted acid sites and observed a marked increase in the conversion relative to three-dimensional MWW (MCM-22) and 2D layers prepared from postsynthesis exfoliation (ITQ-2). Collectively, our findings identify a facile and effective route to directly synthesize 2D MWW-type materials, which may prove to be more broadly applicable to other layered zeolites.

Time-Resolved Dynamics of Struvite Crystallization: Insights from the Macroscopic to Molecular Scale.

The crystallization of magnesium ammonium phosphate hexahydrate (struvite) often occurs under conditions of fluid flow, yet the dynamics of struvite growth under these relevant environments has not been previously reported. In this study, we use a microfluidic device to evaluate the anisotropic growth of struvite crystals at variable flow rates and solution supersaturation. We show that bulk crystallization under quiescent conditions yields irreproducible data owing to the propensity of struvite to adopt defects in its crystal lattice, as well as fluctuations in pH that markedly impact crystal growth rates. Studies in microfluidic channels allow for time-resolved analysis of seeded growth along all three principle crystallographic directions and under highly controlled environments. After having first identified flow rates that differentiate diffusion and reaction limited growth regimes, we operated solely in the latter regime to extract the kinetic rates of struvite growth along the [100], [010], and [001] directions. In situ atomic force microscopy was used to obtain molecular level details of surface growth mechanisms. Our findings reveal a classical pathway of crystallization by monomer addition with the expected transition from growth by screw dislocations at low supersaturation to that of two-dimensional layer generation and spreading at high supersaturation. Collectively, these studies present a platform for assessing struvite crystallization under flow conditions and demonstrate how this approach is superior to measurements under quiescent conditions.