Time of Formation of the First Supercritical Nucleus, Time‐lag, and the Steady‐State Nucleation Rate

Schmelzer, Jürn W. P.; Abyzov, Alexander S.; Байдаков, В. Г.

doi:10.1111/ijag.12243

Cited by 32 publications

(42 citation statements)

References 44 publications

(140 reference statements)

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“…In a similar analysis, instead of

, Angell et al [ 130 ] identified the characteristic time of crystallization with the time-lag in nucleation,

. As already demonstrated in [ 64 , 129 ], this estimate is, in the range of temperatures Kauzmann was interested in, a much better approximation for the average time of formation of the first supercritical nucleus as compared to

. The time-lag can be determined via Equation ( 16 ) [ 24 , 64 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 72%

“…As already demonstrated in [ 64 , 129 ], this estimate is, in the range of temperatures Kauzmann was interested in, a much better approximation for the average time of formation of the first supercritical nucleus as compared to

. The time-lag can be determined via Equation ( 16 ) [ 24 , 64 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 72%

“…As also can be traced from the quotation given above, Kauzmann connected the rate of crystallization with the average time of formation of the first supercritical nucleus at steady-state conditions with a steady-state nucleation rate,

. Only in this case is the average time,

, of formation of the first supercritical crystallite correlated with the work of critical cluster formation (the energy barrier to crystal nucleation),

, via [ 127 , 128 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 99%

See 2 more Smart Citations

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Schmelzer¹,

Тропин

2018

Entropy

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A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play-beyond the topics widely discussed and reviewed here-a major role.

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“…In a similar analysis, instead of

, Angell et al [ 130 ] identified the characteristic time of crystallization with the time-lag in nucleation,

. The time-lag can be determined via Equation ( 16 ) [ 24 , 64 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 72%

. The time-lag can be determined via Equation ( 16 ) [ 24 , 64 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 72%

. Only in this case is the average time,

, of formation of the first supercritical crystallite correlated with the work of critical cluster formation (the energy barrier to crystal nucleation),

, via [ 127 , 128 , 129 ]:

…”

Section: Is the Kauzmann Paradox Really In Conflict With Basic Lawmentioning

confidence: 99%

See 1 more Smart Citation

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Schmelzer¹,

Тропин

2018

Entropy

View full text Add to dashboard Cite

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“…The transition from no bubbles to bubbles occurs at

W_{normaln}^{*} \approx 2.3 \times 1 0^{- 18}

J. In the absence of established experimental constraints on the nucleation time lag or the induction time (Schmelzer et al, ) we neglect both. Under this assumption bubbles nucleate in an experimental sample when ( J max V ) −1 is less than the time over which the sample was held at its final pressure.…”

Section: Resultsmentioning

confidence: 99%

Predicting Homogeneous Bubble Nucleation in Rhyolite

et al. 2019

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Bubble nucleation is the critical first step during magma degassing. The resultant number density of bubbles provides a record of nucleation kinetics and underlying eruptive conditions. The rate of bubble nucleation is strongly dependent on the surface free energy associated with nucleus formation, making the use of bubble number density for the interpretation of eruptive conditions contingent upon a sound understanding of surface tension. Based on a suite of nucleation experiments with up to >1016 bubbles per unit volume of melt, and using numerical simulations of bubble nucleation and growth during each experiment, we provide a new formulation for surface tension during homogeneous nucleation of H2O bubbles in rhyolitic melt. It is based on the Tolman correction with a Tolman length of δ = 0.32 nm, which implies an increase in surface tension of bubbles with decreasing nucleus size. Our model results indicate that experiments encompass two distinct nucleation regimes, distinguishable by the ratio of the characteristic diffusion time of water, τdiff, to the decompression time, td. Experiments with >1013 m−3 bubbles are characterized by τdiff/td≪ 1, wherein the nucleation rate predominantly depends on the interplay between decompression and diffusion rates. Nucleation occurs over a short time interval with nucleation rate peaks at high values. For experiments with comparatively low bubble number density the average distance between adjacent bubbles and the diffusion timescale is large. Consequently, τdiff/td≫ 1 and nucleation is nearly unaffected by diffusion and independent of decompression rate, with bubbles nucleating at an approximately constant rate until the sample is quenched.

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“…The quantity defines the time interval over which the first bubbles nucleate. This is also referred to as the "mean-lifetime of the metastable fluid" [41,42], the "average time of formation of the first supercritical nucleus" [43] or the "experiment/observation time" at the steady state [44]. The attainable length of this quantity is known to decrease as metastability increases, making the measurement of thermodynamic properties deep in the metastable region difficult or even practically impossible [28,36].…”

Section: Nucleation Ratesmentioning

confidence: 99%

The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

Andrade

Haqshenas

Pahk

et al. 2019

Ultrasonics Sonochemistry

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A phenomenological implementation of Classical Nucleation Theory (CNT) is employed to investigate the connection between high intensity focused ultrasound (HIFU) pressure and temperature fields with the energetic requirements of bubble nucleation. As a case study, boiling histotripsy in tissue-mimicking phantoms is modelled. The physics of key components in the implementation of CNT in HIFU conditions such as the derivation of nucleation pressure thresholds and approximations regarding the surface tension of the liquid are reviewed and discussed. Simulations show that the acoustic pressure is the ultimate trigger for millisecond bubble nucleation in boiling histotripsy, however, HIFU heat deposition facilitates nucleation by lowering nucleation pressure thresholds. Nucleation thus occurs preferentially at the regions of highest heat deposition within the HIFU field. This implies that bubble nucleation subsequent to millisecond HIFU heat deposition can take place at temperatures below 100 °C as long as the focal HIFU peak negative pressure exceeds the temperature-dependent nucleation threshold. It is also found that the magnitude of nucleation pressure thresholds decreases with decreasing frequencies. Overall, results indicate that it is not possible to separate thermal and mechanical effects of HIFU in the nucleation of bubbles for timescales of a few milliseconds. This

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Time of Formation of the First Supercritical Nucleus, Time‐lag, and the Steady‐State Nucleation Rate

Cited by 32 publications

References 44 publications

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Predicting Homogeneous Bubble Nucleation in Rhyolite

The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

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