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

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.

Download Full-text

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

Applied Physics Letters ◽

10.1063/1.4968005 ◽

2016 ◽

Vol 109 (21) ◽

pp. 213101 ◽

Cited By ~ 5

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

Download Full-text

Size Dependent Bond Length of Metallic Clusters by Considering Bond Number

Materials Science Forum ◽

10.4028/www.scientific.net/msf.850.314 ◽

2016 ◽

Vol 850 ◽

pp. 314-318

Author(s):

Hui Li ◽

Hao Jie Xiao ◽

Jiang Wang ◽

Hai Xia Zhang ◽

Hai Cheng Xuan ◽

...

Keyword(s):

Bond Length ◽

Bond Number ◽

Single Bond ◽

Metallic Clusters ◽

Structure Relaxation ◽

Atomic Structures ◽

Size Dependent ◽

Model Free ◽

Theoretical Predictions ◽

Ag Clusters

In this study, size-dependent bond length of metallic clusters is established by introducing bond number. This model, free of any adjustable parameters, can be utilized to predict the change rule of bond length with size. If the atomic structure of a cluster is known, the size and shape-dependent bond number are obtained. The cubooctahedral structure is taken for simplicity to describe the shape and geometric characteristics of metallic clusters. It is found that the bond length decreases with the decreased size of metallic clusters, which is due to the structure relaxation and enhanced single bond energy. The theoretical predictions are consistent with the evidences of the simulations for Au and Ag clusters. This confirms the validity of taking cubooctahedron structure, even if the simulated Au and Ag clusters are not cuboctahedron ones. This can be expected to other metallic clusters even with other atomic structures.

Download Full-text

Size Effect on Thermal Properties in Low-Dimensional Materials

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.444.189 ◽

2010 ◽

Vol 444 ◽

pp. 189-218 ◽

Cited By ~ 9

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.

Download Full-text

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

Applied Physics A ◽

10.1007/s00339-021-04535-4 ◽

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

Download Full-text

Prediction of nanoparticles’ size-dependent melting temperature using mean coordination number concept

Journal of Physics and Chemistry of Solids ◽

10.1016/j.jpcs.2008.03.014 ◽

2008 ◽

Vol 69 (8) ◽

pp. 2116-2123 ◽

Cited By ~ 34

Author(s):

Mostafa Mirjalili ◽

Jalil Vahdati-Khaki

Keyword(s):

Coordination Number ◽

Melting Temperature ◽

Number Concept ◽

Size Dependent

Download Full-text

Size dependent thermal vibrations and melting in nanocrystals

Journal of Materials Research ◽

10.1557/jmr.1994.1307 ◽

1994 ◽

Vol 9 (5) ◽

pp. 1307-1314 ◽

Cited By ~ 235

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.

Download Full-text