Logarithmic Size-Dependent Melting Temperature of Nanoparticles

2015 ◽  
Vol 119 (21) ◽  
pp. 11929-11933 ◽  
Author(s):  
Zhiyuan Liu ◽  
Xiaohong Sui ◽  
Kai Kang ◽  
Shaojing Qin
Keyword(s):  
Melting Temperature ◽  
Size Dependent

Size-dependent melting temperature of individual nanometer-sized metallic clusters

1990 ◽  
Vol 42 (13) ◽  
pp. 8548-8556 ◽  
Author(s):  
T. Castro ◽  
R. Reifenberger ◽  
E. Choi ◽  
R. P. Andres
Keyword(s):  
Melting Temperature ◽  
Metallic Clusters ◽  
Size Dependent

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.

An experimental and computational study of size-dependent contact-angle of dewetted metal nanodroplets below its melting temperature

2016 ◽  
Vol 109 (21) ◽  
pp. 213101 ◽  
Author(s):  
Bruno P. Azeredo ◽  
Saikumar R. Yeratapally ◽  
Josh Kacher ◽  
Placid M. Ferreira ◽  
Michael D. Sangid
Keyword(s):  
Contact Angle ◽  
Melting Temperature ◽  
Computational Study ◽  
Size Dependent

Size Effect on Thermal Properties in Low-Dimensional Materials

2010 ◽  
Vol 444 ◽  
pp. 189-218 ◽  
Author(s):  
Ming Zhao ◽  
Qing Jiang
Keyword(s):  
Phase Diagrams ◽  
Melting Temperature ◽  
Binary Solution ◽  
Size Dependent ◽  
Melting Temperatures ◽  
Transition Functions ◽  
Low Dimensional ◽  
Classical Thermodynamics ◽  
S Model ◽  
Melting Entropy

An extension of the classical thermodynamics to nanometer scale has been conducted to elucidate information regarding size dependence of phase transition functions and binary phase diagrams. The theoretical basis of the extension is Lindemanns criterion for solid melting, Motts expression for vibrational melting entropy, and Shis model for size dependent melting temperature. These models are combined into a unified one without adjustable parameters for melting temperatures of nanocrystals. It is shown that the melting temperature of nanocrystals may drop or rise depending on interface conditions and dimensions. The model has been extended and applied to size dependences of melting enthalpy, melting entropy, atomic cohesive energy. Moreover, the above modeling has been utilized to determine the size-dependent continuous binary solution phase diagrams. These thermodynamic approachs have extended the capability of the classical thermodynamics to the thermodynamic phenomena in the nanometer regime.

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

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.

Size-Dependent Melting Temperature of Polymers

2003 ◽  
Vol 12 (1) ◽  
pp. 57-60 ◽  
Author(s):  
Qing Jiang ◽  
Chun Cheng Yang ◽  
Jian Chen Li
Keyword(s):  
Melting Temperature ◽  
Size Dependent

SIZE-DEPENDENT MELTING TEMPERATURE AND THERMAL CONDUCTIVITY OF NANOSCALE SEMICONDUCTORS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4026-4029 ◽  
Author(s):  
L. H. LIANG ◽  
BAOWEN LI
Keyword(s):  
Thermal Conductivity ◽  
Size Effect ◽  
Free Path ◽  
Melting Temperature ◽  
Mean Free Path ◽  
Debye Model ◽  
Size Dependent ◽  
Si Nanoparticles ◽  
Nanoscale Semiconductors ◽  
Phonon Velocity

A model describing size-dependent melting temperature and thermal conductivity of nanosemiconductors is proposed based on Lindermann's melting criterion and Debye model. By the atomic thermal vibration consideration and by introducing intrinsic size effect of phonon velocity and mean free path combined with surface scattering effect, the model predicts that the melting temperature and thermal conductivity of nanosemiconductors decrease as the size reduces. The size effect depends on such material parameters as the vibration entropy, mean free path, the characteristic crystal size and surface roughness. The predictions are in agreement with experimental results of Si nanoparticles, nanowires and thin films.

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