Shape, size and temperature dependency of thermal expansion, lattice parameter and bulk modulus in nanomaterials

Goyal, Monika; Gupta, B. R. K.

doi:10.1007/s12043-018-1563-8

Cited by 11 publications

(4 citation statements)

References 26 publications

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“…Other more advanced approaches to achieving such predictive tools exist for nanoscale elements, e.g., by deriving a size-dependent thermodynamic equation of state. Such formulations have been successfully used for, e.g., Ag, Al, Cu, Pb, Ni, Si, Zn, and Se [ 76 , 77 ]. However, they have been applied predominately for nano-objects with well-defined crystallographic free surfaces.…”

Section: Discussionmentioning

confidence: 99%

Grain Size-Dependent Thermal Expansion of Nanocrystalline Metals

Olsson,

Awala,

Holmberg-Kasa

et al. 2023

Materials

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In the present work, we have used classical molecular dynamics and quantum mechanical density functional theory modeling to investigate the grain size-dependent thermal expansion coefficient (CTE) of nanocrystalline Cu. We find that the CTE increases by up to 20% with a gradually decreasing grain size. This behavior emerges as a result of the increased population of occupied anti-bonding states and bond order variation in the grain boundary regions, which contribute to the reduced resistance against thermally-induced bond stretching and dictate the thermal expansion behavior in the small grain size limit. As a part of the present work, we have established a procedure to produce ab initio thermal expansion maps that can be used for the prediction of the grain size-dependent CTE. This can serve as a modeling tool, e.g., to explore the impact of grain boundary impurity segregation on the CTE.

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Section: Discussionmentioning

confidence: 99%

Grain Size-Dependent Thermal Expansion of Nanocrystalline Metals

Olsson,

Awala,

Holmberg-Kasa

et al. 2023

Materials

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“…where, Vatom is the volume of an atom and Vcell is the volume of the unit cell. Now, the surface area of nanoparticle is πD 2 and area of each surface atom that contributes to the surface area of nanoparticle is πd 2 /4. Thus, the total surface atoms N is given by [14]…”

Section: Volume Thermal Expansion Coefficient Of Nanoparticlementioning

confidence: 99%

“…The volume of a nanowire of diameter L and height h, is πL 2 h/4, thus in reference of Eq. (6), total number of atoms n becomes The total surface area of the nanowire will be (πL 2…”

Section: Volume Thermal Expansion Coefficient Of Nanowirementioning

confidence: 99%

“…In this study, our aim is to examine the effect of size on volume thermal expansion and effect of temperature on Young's modulus of nanomaterials. Different group of researchers did the both experimental and theoretical works on these properties [1][2][3][4][5][6][7][8][9]. Out of the different theoretical models, the most effective model for thermal expansivity was given by R. Kumar and M. Kumar [10] based upon the most basic concept of cohesive energy of the materials.…”

Section: Introductionmentioning

confidence: 99%

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Thermo-physical Behavior of Nanomaterials with the Change in Size and Shape

Jaiswal¹,

Pandey

Mishra

et al. 2021

International Journal of Thermodynamics

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Thermo elastic properties of nanomaterials has been very interesting among the researchers during the last decade, still it is a great challenge to predict the exact thermoelastic behaviour of nanomaterials. In the present work we have studied the volume thermal expansion coefficient of low dimensional solid and the variation of Young's modulus with change in temperature for different shapes of nanomaterials by considering the effect of packing factor. We have computed the volume thermal expansion coefficient of Silver (Ag), Aluminum (Al), Copper (Cu), and Lead (Pb) with their varying size. The effect of temperature on Young's modulus of Silver (Ag), Gold (Au), Nickel (Ni), Copper (Cu) and Silicon (Si) has also been studied. The computed results are compared with available experimental data which confirms that the volume thermal expansion coefficient increases with reduction in size of the nanomaterials. It has been also observed that the Young's modulus has linear decrement with increase in temperature which indicates that Young's modulus of nanomaterials has negative temperature coefficient.

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Size and shape dependence of optical properties of nanostructures

Goyal

Singh

2020

Appl. Phys. A

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Shape, size and temperature dependency of thermal expansion, lattice parameter and bulk modulus in nanomaterials

Cited by 11 publications

References 26 publications

Grain Size-Dependent Thermal Expansion of Nanocrystalline Metals

Grain Size-Dependent Thermal Expansion of Nanocrystalline Metals

Thermo-physical Behavior of Nanomaterials with the Change in Size and Shape

Size and shape dependence of optical properties of nanostructures

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