Assessment of thermal expansion coefficient for pure metals

Zhang, Bo; Li, Xiaobo; Li, Dan

doi:10.1016/j.calphad.2013.08.006

Cited by 42 publications

(20 citation statements)

References 10 publications

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“…Thermal expansion of the island rings‐silicon, graphene, gold, where A, and B, 11 C 12,13 [Color figure can be viewed at wileyonlinelibrary.com]…”

Section: Simulation Resultsmentioning

confidence: 99%

“…However, the elongation limits of all materials are the applied conditions. The relation of the volume expansion coefficient as a function of the temperature can be evaluated by Grüneisen' s equation, 11 which can be express as Equations ) 12

bold-italicβ = \frac{1}{V} {(\frac{∂V}{∂T})}_{P}

bold-italicβ = \frac{{bold-italicC}_{bold-italicV}}{Q_{0} {[1 - k (U / {bold-italicQ}_{bold0})]}^{2}}

\frac{∆ bold-italicV}{{bold-italicV}_{bold0}} = bold-italicβ ∆ bold-italicT

where ∆V / V 0 is the fractional change in volume, C V is the capacity of molar heat considered at constant volume, U is the lattice vibrations energy, Q 0 and k are constant quantities.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermo‐electro‐optic energy conversion using plasmonic island embedded silicon microring circuit

Bunruangses

Youplao

Punthawanunt

et al. 2020

Micro & Optical Tech Letters

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We propose the use of the thermo‐electro‐optic energy conversion system for daily sunlight charger. A circuit consists of a modified silicon microring circuit embedded by a plasmonic island at the center. The island materials consist of silicon‐graphene‐gold layers. The thermal expansion of the island materials from the daily sunlight can affect the change in island material lengths and transfer to the plasmon wave path difference, which can perform the energy conversion and a charger. In manipulation, the daily sunlight statistic from South East Asia, the significant daily charging mobility of 4.34 × 10−6 cm2. (V. s)−1/Vs with the input light power of 10 mW can be obtained, which may be useful for one of the selected alternative energy sources.

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“…Thermal expansion of the island rings‐silicon, graphene, gold, where A, and B, 11 C 12,13 [Color figure can be viewed at wileyonlinelibrary.com]…”

Section: Simulation Resultsmentioning

confidence: 99%

bold-italicβ = \frac{1}{V} {(\frac{∂V}{∂T})}_{P}

bold-italicβ = \frac{{bold-italicC}_{bold-italicV}}{Q_{0} {[1 - k (U / {bold-italicQ}_{bold0})]}^{2}}

\frac{∆ bold-italicV}{{bold-italicV}_{bold0}} = bold-italicβ ∆ bold-italicT

where ∆V / V 0 is the fractional change in volume, C V is the capacity of molar heat considered at constant volume, U is the lattice vibrations energy, Q 0 and k are constant quantities.…”

Section: Introductionmentioning

confidence: 99%

Thermo‐electro‐optic energy conversion using plasmonic island embedded silicon microring circuit

Bunruangses

Youplao

Punthawanunt

et al. 2020

Micro & Optical Tech Letters

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“…Alternatively, Hallstedt et al [61] proposed to describe the temperature dependence of the molar volume directly by a polynomial in T. Both models describe the molar volume above the reference temperature which is usually room temperature. Zhang et al [63] derived a Debye-Griineisen equation to describe the thermal expansion between 0 K and the melting temperature and evaluated the thermal expansion for 42 metallic elements.…”

Section: Models and Gibbs Energy Minimizationmentioning

confidence: 99%

The Calphad Method and Its Role in Material and Process Development

Kattner¹

2016

TMM

109

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Successful design of materials and manufacturing processes requires the availability of reliable materials data. Commercial alloys usually contain a large number of elements, and the needed data for the design of new materials and processes are rarely available. The CALPHAD (CALculation of PHAse Diagrams) method enables the development of thermodynamic and property databases, that in conjunction with extrapolation methods of the descriptions of binary and ternary systems to higher-order systems, allow the calculation of data for higher-order systems. The results obtained from CALPHAD calculations have been shown to be invaluable in the design of new materials. This review presents an overview of the CALPHAD method, software tools and databases and gives examples of its application.

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“…Recently, Zhang et al [84] demonstrated yet another approach for modeling the thermal expansion. This approach was used to evaluate 42 pure metallic elements and was based on Debye-Grüneisen model.…”

Section: Molar Volume and Thermal Expansionmentioning

confidence: 99%

The development of phase-based property data using the CALPHAD method and infrastructure needs

Campbell

Kattner

Liu

2014

Integr Mater Manuf Innov

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Initially, the CALPHAD (Calculation of Phase Diagrams) method was established as a tool for treating thermodynamics and phase equilibria of multicomponent systems. Since then the method has been successfully applied to diffusion mobilities in multicomponent systems, creating the foundation for simulation of diffusion processes in these systems. Recently, the CALPHAD method has been expanded to other phase-based properties, including molar volumes and elastic constants, and has the potential to treat electrical and thermal conductivity and even two-phase properties, such as interfacial energies. Advances in the CALPHAD method or new information on specific systems frequently require that already assessed systems be re-assessed. Therefore, the next generation of CALPHAD necessitates data repositories so that when new models are developed or new experimental and computational information becomes available the relevant low-order (unary, binary, and ternary) systems can be re-assessed efficiently to develop the new multicomponent descriptions. The present work outlines data and infrastructure needs for efficient CALPHAD assessments and updates, highlighting the requirement for data repositories with flexible data formats that can be accessed by a variety of tools and that can evolve as data needs change. Within these repositories, the data must be stored with the appropriate metadata to enable the evaluation of the confidence of the stored data.Keywords: CALPHAD; Thermodynamics; Diffusion; Property data; Data and file repositories; Materials data infrastructure ReviewThe first efforts using computational methods to describe Gibbs energy functions to represent the phases and describe phase equilibria were made more than 60 years ago as reviewed in [1]. However, only after computers became available did these efforts become systematic. In 1970, Kaufman and Bernstein [2] presented a collection of analytical thermodynamic descriptions of the Gibbs energy of the phases of binary and ternary systems as functions of temperature and concentration. These descriptions could be used for the calculation of phase equilibria and thermochemical properties in a large number of systems. This collection established the CALPHAD method as a valuable tool for the treatment of multicomponent a phase equilibria and spawned the development of several software packages and databases with collections of thermodynamic descriptions of multicomponent systems [1]. However, it soon became

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Assessment of thermal expansion coefficient for pure metals

Cited by 42 publications

References 10 publications

Thermo‐electro‐optic energy conversion using plasmonic island embedded silicon microring circuit

Thermo‐electro‐optic energy conversion using plasmonic island embedded silicon microring circuit

The Calphad Method and Its Role in Material and Process Development

The development of phase-based property data using the CALPHAD method and infrastructure needs

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