Scaling of Nucleation Rates

Barbara N. Hale

doi:10.1007/BF02647536

Scaling of Nucleation Rates

Barbara N. Hale

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

The homogeneous nucleation rate, J , for T &ll; T c can be cast into a "corresponding states" form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ 0 [ T c - T ], the classical cluster energy of formation /k T = [16π/3]·Ω 3 [ T c / T -1] 3 /(ln S ) 2 &equiv; [x 0 /x] 2 , where Ω &equiv; σ 0 [k ñ 2/3 ] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x 0 /x] 2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x 0 /x] 2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γ c ), where Γ c is the inverse thermal wavelength cubed per second at T = T c . The ln (Γ c ) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n , the discrete integer behavior of n , and a configurational entropy term, τ ln ( n ), is presented.

Original language	American English
Journal	Metallurgical Transactions. A: Physical Metallurgy and Materials Science
Volume	23 A
DOIs	https://doi.org/10.1007/BF02647536
State	Published - Jul 1 1992

Keywords

Cluster Energy
Crystal Growth
Homogeneous Nucleation Rates
Mathematical Models
Phase Transitions
Scaled Nucleation Model
Surface Tension
Thermal Effects
Vapor Pressure

Disciplines

Physics

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https://doi.org/10.1007/BF02647536

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@article{a1f7bdc79c494429ba5aa9827b068342,

title = "Scaling of Nucleation Rates",

abstract = " The homogeneous nucleation rate, J , for T \&ll; T c can be cast into a {"}corresponding states{"} form by exploiting scaled expressions for the vapor pressure and for the surface tension, \σ. In the vapor-to-liquid case with \σ = \σ 0 [ T c - T ], the classical cluster energy of formation /k T = [16\π/3]\·\Ω 3 [ T c / T -1] 3 /(ln S ) 2 \&equiv; [x 0 /x] 2 , where \Ω \&equiv; \σ 0 [k \ñ 2/3 ] and \ñ is liquid number density. The \Ω \≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of \σ and \Ω.) The above [x 0 /x] 2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J \≈ const. - [x 0 /x] 2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (\Γ c ), where \Γ c is the inverse thermal wavelength cubed per second at T = T c . The ln (\Γ c ) is \≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n , the discrete integer behavior of n , and a configurational entropy term, \τ ln ( n ), is presented.",

keywords = "Cluster Energy, Crystal Growth, Homogeneous Nucleation Rates, Mathematical Models, Phase Transitions, Scaled Nucleation Model, Surface Tension, Thermal Effects, Vapor Pressure",

author = "Hale, \{Barbara N.\}",

year = "1992",

month = jul,

day = "1",

doi = "10.1007/BF02647536",

language = "American English",

volume = "23 A",

journal = "Metallurgical Transactions. A: Physical Metallurgy and Materials Science",

}

TY - JOUR

T1 - Scaling of Nucleation Rates

AU - Hale, Barbara N.

PY - 1992/7/1

Y1 - 1992/7/1

N2 - The homogeneous nucleation rate, J , for T &ll; T c can be cast into a "corresponding states" form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ 0 [ T c - T ], the classical cluster energy of formation /k T = [16π/3]·Ω 3 [ T c / T -1] 3 /(ln S ) 2 &equiv; [x 0 /x] 2 , where Ω &equiv; σ 0 [k ñ 2/3 ] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x 0 /x] 2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x 0 /x] 2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γ c ), where Γ c is the inverse thermal wavelength cubed per second at T = T c . The ln (Γ c ) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n , the discrete integer behavior of n , and a configurational entropy term, τ ln ( n ), is presented.

AB - The homogeneous nucleation rate, J , for T &ll; T c can be cast into a "corresponding states" form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ 0 [ T c - T ], the classical cluster energy of formation /k T = [16π/3]·Ω 3 [ T c / T -1] 3 /(ln S ) 2 &equiv; [x 0 /x] 2 , where Ω &equiv; σ 0 [k ñ 2/3 ] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x 0 /x] 2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x 0 /x] 2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γ c ), where Γ c is the inverse thermal wavelength cubed per second at T = T c . The ln (Γ c ) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n , the discrete integer behavior of n , and a configurational entropy term, τ ln ( n ), is presented.

KW - Cluster Energy

KW - Crystal Growth

KW - Homogeneous Nucleation Rates

KW - Mathematical Models

KW - Phase Transitions

KW - Scaled Nucleation Model

KW - Surface Tension

KW - Thermal Effects

KW - Vapor Pressure

UR - https://scholarsmine.mst.edu/phys_facwork/628

UR - https://doi.org/10.1007/BF02647536

U2 - 10.1007/BF02647536

DO - 10.1007/BF02647536

M3 - Article

VL - 23 A

JO - Metallurgical Transactions. A: Physical Metallurgy and Materials Science

JF - Metallurgical Transactions. A: Physical Metallurgy and Materials Science

ER -

Scaling of Nucleation Rates

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