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 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 Comparison of the observed size-dependent melting point of CdSe nanocrystals to theoretical predictions

2018 ◽  
Vol 9 (1) ◽  
pp. 39-43
Author(s):  
Albert Demaine Dukes III ◽  
Christopher Dylan Pitts ◽  
Anyway Brenda Kapingidza ◽  
David Eric Gardner ◽  
Ralph Charles Layland
Keyword(s):  
Melting Point ◽  
Surface Area ◽  
Melting Temperature ◽  
Volume Ratio ◽  
Melting Point Depression ◽  
Cdse Nanocrystals ◽  
Size Dependent ◽  
Theoretical Predictions

Cadmium selenide nanocrystals were observed to have a size-dependent melting point which was depressed relative to the bulk melting temperature. The observed size-dependent melting point ranged from 500-1478 K, while a model based on the surface area to volume ratio predicted that is should range between 774-1250 K. The nanocrystals were heated in situ in the electron microscope, and the melting point was almost immediately followed by the vaporization of the CdSe nanocrystals, allowing for straightforward determination of the melting temperature. The differences between the observed melting point of CdSe nanocrystals and the values predicted by the surface area to volume ratio model indicates that additional factors are involved in the melting point depression of nanocrystals.

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.

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 Valence and Conduction Band-Edge Energies of Semiconductor Nanocrystals

ACS Nano ◽  
2011 ◽  
Vol 5 (7) ◽  
pp. 5888-5902 ◽  
Author(s):  
Jacek Jasieniak ◽  
Marco Califano ◽  
Scott E. Watkins
Keyword(s):  
Conduction Band ◽  
Semiconductor Nanocrystals ◽  
Band Edge ◽  
Conduction Band Edge ◽  
Size Dependent

scholarly journals MODELLING THE MELTING TEMPERATURE OF A LIPID‐BASED CRITICAL TEMPERATURE INDICATOR: A COMPARISION BETWEEN SIMPLEX-LATTICE AND SIMPLEX-CENTROID DESIGNS

2018 ◽  
Vol 35 (2) ◽  
Author(s):  
KARINE CRISTINE KAUFMANN ◽  
ODINEI HESS GONÇALVES ◽  
EVANDRO BONA ◽  
FERNANDA VITÓRIA LEIMANN
Keyword(s):  
Critical Temperature ◽  
Melting Point ◽  
Melting Temperature ◽  
Predictive Ability ◽  
Ternary Mixtures ◽  
Lipid Mixture ◽  
Color Changes ◽  
Lattice Design ◽  
Simplex Lattice ◽  
Improved Model

Critical temperature indicators (CTI) find applications in food industry in cases when defrost may not occur or a specific temperature may not be reached, , indicating changes through visual changes, such as melting, color changes, etc. Lipid mixtures are promising candidates to formulate CTI since the final melting point of the mixture may be manipulated by the proportion of each lipid. In this work a lipid mixture consisting of stearic acid, lard and peanut oil was used to develop a CTI mixture. Simplex-lattice and Simplex-centroid experimental designs were compared to modelling the melting temperature of the lipid mixture. Addition of axial points to the experimental design improved predictive ability of the models while the inclusion of inverse terms was necessary to improve models accuracy. Simplex-lattice design presented an improved ability to predict the melting point of binary mixtures, while the simplex-centroid design resulted in an improved model for predicting melting point of the ternary mixtures

scholarly journals How Atoms of Polycrystalline Nb 20.6 Mo 21.7 Ta 15.6 W 21.1 V 21.0 refractory High-Entropy Alloys Rearrange during the Melting Process

2021 ◽  
Author(s):  
Shin-Pon Ju ◽  
Chen-Chun Li
Keyword(s):  
Molecular Dynamics ◽  
Melting Point ◽  
Single Crystal ◽  
Melting Temperature ◽  
Md Simulation ◽  
Melting Process ◽  
Structural Rearrangement ◽  
High Entropy Alloys ◽  
High Entropy ◽  
Melting Mechanism

Abstract The melting mechanism of single crystal and polycrystalline Nb 20.6 Mo 21.7 Ta 15.6 W 21.1 V 21.0 RHEAs was investigated by the molecular dynamics (MD) simulation using the 2NN MEAM potential. For the single crystal RHEA, the density profile displays an abrupt drop from 11.25 to 11.00 g/cm 3 at temperatures from 2910 to 2940 K, indicating all atoms begin significant local structural rearrangement. For polycrystalline RHEAs, a two-stage melting process is found. In the first melting stage, the melting of the grain boundary (GB) regions firstly occurs at the pre-melting temperature, which is relatively lower than the corresponding system-melting point. At the pre-melting temperature, most GB atoms have enough kinetic energies to leave their equilibrium positions, and then gradually induce the rearrangement of grain atoms close to GB. In the second melting stage at the melting point, most grain atoms have enough kinetic energies to rearrange, resulting in the chemical short-ranged order (CSRO) changes of all pairs.

scholarly journals Simple model for the power-law blinking of single semiconductor nanocrystals

2002 ◽  
Vol 66 (23) ◽  
Author(s):  
Rogier Verberk ◽  
Antoine M. van Oijen ◽  
Michel Orrit
Keyword(s):  
Simple Model ◽  
Power Law ◽  
Semiconductor Nanocrystals

scholarly journals Interference Phenomena in Deformed Single Crystals of Ice

1971 ◽  
Vol 10 (59) ◽  
pp. 269-286 ◽  
Author(s):  
G. J. Readings ◽  
J. T. Bartlett
Keyword(s):  
Optical Properties ◽  
Simple Model ◽  
Single Crystals ◽  
Uniaxial Compression ◽  
Basal Plane ◽  
Quantitative Agreement ◽  
Optic Axis ◽  
Interference Fringes ◽  
Alternative Hypotheses ◽  
Active Contribution

AbstractWhen rectangular single crystals of ice were subjected to uniaxial compression parallel to their Long axes and viewed between crossed polarizers, interference fringes were often observed. Some of these interference bands were associated with grain boundaries formed as a result of “kinking”. These can be explained in terms of the known anisotropic optical properties of ice and the change in the orientation of the optic axis across the boundary. This case has been analysed in detail with the aid of Jones’ calculus and good quantitative agreement exists between the theory and the experimental observations.Other interference bands were observed parallel to the trace of the basal plane on the surface of some deformed crystals. Alternative hypotheses for the explanation of this phenomenon have been considered and it seems probable that these bands are a result of slight random misorientations between adjacent slip lamellae. Applying Jones’ calculus to a simple model of such a deformed crystal indicates that the required misorientations are of the order of 1º If this explanation is correct, it implies that dislocations with non-basal Burgers vectors (probablyc[0001]) make an active contribution to the deformation.

The Gallium Melting-Point Standard: A Determination of the Liquid—Solid Equilibrium Temperature of Pure Gallium on the International Practical Temperature Scale of 1968

1977 ◽  
Vol 23 (4) ◽  
pp. 719-724 ◽  
Author(s):  
Donald D Thornton
Keyword(s):  
Melting Point ◽  
Melting Temperature ◽  
Temperature Scale ◽  
Equilibrium Temperature ◽  
Melting Range ◽  
Practical Temperature ◽  
Practical Temperature Scale ◽  
Gallium Melting Point

Abstract The sharpness and reproducibility of the gallium melting point were studied, and the melting temperature of gallium in terms of IPTS-68 was determined. Small melting-point cells designed for use with thermistors are described. Nine gallium cells including three levels of purity were used in 68 separate determinations of the melting point. The melting point of 99.99999% pure gallium in terms of IPTS-68 is found to be 29.7714 ± 0.0014 °C; the melting range is less than 0.0005 °C and is reproducible to ±0.0004 °C.

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