Size-dependent melting temperature of nanoparticles based on cohesive energy

2014 ◽  
Vol 28 (19) ◽  
pp. 1450157 ◽  
Author(s):  
Kai-Tuo Huo ◽  
Xiao-Ming Chen
Keyword(s):  
Melting Temperature ◽  
Cohesive Energy ◽  
Metallic Nanoparticles ◽  
Present Model ◽  
Packing Fraction ◽  
Size Dependent ◽  
Crystal Cell ◽  
K Factor ◽  
The Relationship ◽  
Crystalline Plane

Size-dependent melting temperature of metallic nanoparticles is studied theoretically based on cohesive energy. Three factors are introduced in the present model. The k factor, i.e. efficiency of space filling of crystal lattice is defined as the ratio between the volume of the atoms in a crystal cell and that of the crystal cell. The β factor is defined as the ratio between the cohesive energy of surface atom and interior atom of a crystal. The qs factor represents the packing fraction on a surface crystalline plane. Considering the β, qs and k factors, the relationship between melting temperature and nanoparticle size is discussed. The obtained model is compared with the reported experimental data and the other models.

scholarly journals Modelling of size-dependent thermodynamic properties of metallic nanocrystals based on modified Gibbs–Thomson equation

2021 ◽  
Vol 127 (5) ◽  
Author(s):  
Manauwar Ali Ansari
Keyword(s):  
Electrical Conductivity ◽  
Particle Size ◽  
Heat Capacity ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Debye Temperature ◽  
Melting Temperature ◽  
Specific Heat Capacity ◽  
Cohesive Energy ◽  
Size Dependent

AbstractIn this paper, a new theoretical two-phase (solid–liquid) type model of melting temperature has developed based on the modified Gibbs–Thomson equation. Further, it is extended to derive other different size-dependent thermodynamic properties such as cohesive energy, Debye temperature, specific heat capacity, the thermal and electrical conductivity of metallic nanoparticles. Quantitative calculation of the effect of size on thermodynamic properties resulted in, varying linearly with the inverse of characteristic length of nanomaterials. The models are applied to Al, Pb, Ag, Sn, Mo, W, Co, Au and Cu nanoparticles of spherical shape. The melting temperature, Debye temperature, thermal and electrical conductivity are found to decrease with the decrease in particle size, whereas the cohesive energy and specific heat capacity are increased with the decrease in particle size. The present model is also compared with previous models and found consistent. The results obtained with this model validated with experimental and simulation results from several sources that show similar trends between the model and experimental results. Graphic abstract

scholarly journals Analysis of shape, size and structure dependent thermodynamic properties of nanowires

2020 ◽  
Vol 48 (5-6) ◽  
pp. 481-495 ◽  
Author(s):  
M. GOYAL ◽  
B. R. K. GUPTA
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Cohesive Energy ◽  
Present Model ◽  
Packing Fraction ◽  
Energy Band Gap ◽  
Thermodynamic Variables ◽  
Energy Activation ◽  
Size And Structure ◽  
Temperature Surface

A simple model based on thermodynamic variables is used to study the effect of shape, size and structure on the various thermodynamic properties of nanowires. The expression of cohesive energy derived by Qi and Wang [16] is used and ratio of surface atoms to total number of atoms is expressed in terms of shape parameter, radius of nanowire and atomic packing fraction. The variation in cohesive energy, activation energy, melting temperature surface energy, Bulk modulus, Energy band gap Debye temperature and coefficient of volume thermal expansion in nanowires of Zn, β-Sn, TiO 2 (rutile) is studied for cylindrical, triangular, tetragonal, hexagonal and rectangular nanowires using the model. The results obtained are compared with the experimental data available and results from Guisbiers model [11, 12]. The values predicated from the present model are found close to Guisbiers model results and available experimental data.

Modelling for the Prediction of Melting Temperature for Metallic Nanoparticles

2020 ◽  
Vol 12 (1) ◽  
pp. 27-30
Author(s):  
Sachin ◽  
Brijesh K. Pandey ◽  
Ratan Lal Jaiswal
Keyword(s):  
Physical Properties ◽  
Melting Temperature ◽  
Metallic Nanoparticles ◽  
Marked Change ◽  
Simulated Data ◽  
Packing Fraction ◽  
Sharp Change ◽  
Fundamental Relation ◽  
Face Centered Cubic ◽  
Shape And Size

At nano level, materials show very interesting physical properties with the variation of shape and size. The prediction of this behaviour has been a burning issue in the recent years in the scientific community as well. Even the physical properties of these materials are poorly investigated experimentally. To explain the sharp change in the properties of metals, as reported by some investigators, at their nanolevel, different models have been proposed. It is observed that in their theoretical prediction, they have not considered the exact arrangement of atoms in the lattice. In our attempt to understand the behaviour of the nanomaterials, we have studied the melting temperature of some nanosolids having face centered cubic lattice such as Aluminium (Al), Copper (Cu), Paladium (Pd), Platinum (Pt) and Gold (Au), considering different shapes with their sizes ranging from 30 nm to more smaller dimensions. For modelling analysis, we have considered the very basic and fundamental relation of cohesive energy with melting temperature along with modification with two realistic physical quantities-packing fraction and particle shape factor simultaneously to account the arrangements of atoms within the nanoparticle and on the surface as well. Our study shows that there is a very marked change in the melting temperature of the metallic nanosolids below 20 nm. Although in the earlier reported works, it has been claimed that this variation occurs at somewhat higher values. In this variation, the tetrahedral structure exhibits maximum variation of melting temperature while spherical one corresponds to the minimum change. In case of gold, our simulated data has been compared with available experimental values which is found in good agreement with it. This agreement between experimental and computed data validates our proposed model for the prediction of melting temperature of nanoparticles at varying dimensions viz, shape and size. Thus our proposed modification in the existing model is more appropriate in the prediction of melting point of nanoparticles with its varying shape and size.

Size dependent thermal vibrations and melting in nanocrystals

1994 ◽  
Vol 9 (5) ◽  
pp. 1307-1314 ◽  
Author(s):  
Frank G. Shi
Keyword(s):  
Melting Point ◽  
Simple Model ◽  
Melting Temperature ◽  
Present Model ◽  
Semiconductor Nanocrystals ◽  
Quantitative Agreement ◽  
Bulk Crystal ◽  
Size Dependent ◽  
Measurable Parameter ◽  
Thermal Vibrations

A simple model for the size-dependent amplitude of the atomic thermal vibrations of a nanocrystal is presented which leads to the development of a model for the size dependent melting temperature in nanocrystals on the basis of Lindemann's criterion. The two models are in terms of a directly measurable parameter for the corresponding bulk crystal, i.e., the ratio between the amplitude of thermal vibrations for surface atoms and that for interior ones. It is shown that the present model for the melting temperature offers not only a qualitative but even an excellent quantitative agreement with the experimentally observed size-dependent superheating, as well as melting point suppression in both the supported and embedded metallic and semiconductor nanocrystals.

THE EFFECT OF MIE-TYPE POTENTIAL RANGE ON THE COHESIVE ENERGY OF METALLIC NANOPARTICLES

2007 ◽  
Vol 06 (06) ◽  
pp. 461-466 ◽  
Author(s):  
T. BARAKAT ◽  
O. M. Al-DOSSARY ◽  
A. A. ALHARBI
Keyword(s):  
Cohesive Energy ◽  
Metallic Nanoparticles ◽  
Interatomic Potential ◽  
Potential Range ◽  
Size Dependent ◽  
Dependent Potential ◽  
Experimental Values ◽  
The Right ◽  
Potential Parameters ◽  
Type Potential

We investigate the effect of Mie-type potential range on the cohesive energy of metallic nanoparticles using the size-dependent potential parameters method. The predicted cohesive energy for different cubic structures is observed to decrease with decreasing the particle size, and increase with decreasing the range of the interatomic potential, a result which is in the right direction at least to predict the experimental values of Molybdenum and Tungsten nanoparticles.

MODELING THE MELTING TEMPERATURE OF METALLIC NANOWIRES

2010 ◽  
Vol 24 (22) ◽  
pp. 2345-2356 ◽  
Author(s):  
Y. J. LI ◽  
W. H. QI ◽  
B. Y. HUANG ◽  
M. P. WANG ◽  
S. Y. XIONG
Keyword(s):  
Melting Temperature ◽  
Present Model ◽  
Dimensional System ◽  
Cross Sectional ◽  
Size Dependent ◽  
Dynamics Simulations ◽  
Low Dimensional ◽  
Sectional Shape ◽  
Temperature Depression ◽  
Melting Temperature Depression

A model is developed to account for the size-dependent melting temperature of pure metallic and bimetallic nanowires, where the effects of the contributions of all surface atoms to the surface area, lattice and surface packing factors and the cross-sectional shape of the nanowires are considered. As the size decreases, the melting temperature functions of pure metallic and bimetallic nanowires decrease almost with the same size-dependent trend. Due to the inclusion of the above effects, the present model can also be applied to investigate the melting temperature depression rate of different low-dimensional system, accurately. The validity of the model is verified by the data of experiments and molecular dynamics simulations.

A realistic model for transverse shear stiffness prediction of composite corrugated-core sandwich structure with bonding effect

2021 ◽  
pp. 109963622199386
Author(s):  
Tianshu Wang ◽  
Licheng Guo
Keyword(s):  
Present Model ◽  
Shear Stiffness ◽  
Realistic Model ◽  
Torsional Stiffness ◽  
Fem Model ◽  
The Core ◽  
Bonding Effect ◽  
Stiffness Model ◽  
Bonding Area ◽  
The Relationship

In this paper, a shear stiffness model for corrugated-core sandwich structures is proposed. The bonding area is discussed independently. The core is thought to be hinged on the skins with torsional stiffness. The analytical model was verified by FEM solution. Compared with the previous studies, the new model can predict the valley point of the shear stiffness at which the relationship between the shear stiffness and the angle of the core changes from negative correlation to positive correlation. The valley point increases when the core becomes stronger. For the structure with a angle of the core smaller than counterpart for the valley point, the existing analytical formulations may significantly underestimate the shear stiffness of the structure with strong skins. The results obtained by some previous models may be only 10 persent of that of the present model, which is supported by the FEM model.

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