Relationship between Kinematic Viscosity and Cluster Size in Multicomponent Metal Melts

2021 ◽  
Vol 410 ◽  
pp. 102-107
Author(s):  
Vladimir S. Tsepelev ◽  
Yuri N. Starodubtsev ◽  
Yekaterina A. Kochetkova
Keyword(s):  
Viscous Flow ◽  
Kinematic Viscosity ◽  
Transition State Theory ◽  
Cluster Structure ◽  
State Theory ◽  
Logarithmic Scale ◽  
Heating And Cooling ◽  
Metal Melts ◽  
Initial Stage ◽  
Temperature Dependences

We analyzed the temperature dependences of the kinematic viscosity and density of Fe73.5Cu1M3Si13.5B9 melts, where M = Nb, Mo, V, and Cr, in the temperature range from 1450 to 1950 K using the transition state theory. It is shown that the activation energy of viscous flow is proportional to the particle size on a natural logarithmic scale. The lowest viscosity and the highest free volume has the Nb melt. In melts with Mo, V, and Cr, the structural units of viscous flow upon heating and cooling are clusters about 0.6 nm in size. In a melt with Nb, at the initial stage of heating, the vibrations of individual atoms prevail, the movement of which creates viscosity. After heating the Nb melt above the critical temperature of 1770 K, the viscous flow is associated with clusters about 1 nm in size. At the cooling stage, the cluster structure of the Nb melt is retained up to a temperature of 1450 K.

scholarly journals Kinematic Viscosity ofMulticomponent FeCuNbSiB-BasedMelts

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 1042
Author(s):  
Yuri N. Starodubtsev ◽  
Vladimir S. Tsepelev ◽  
Nadezhda P. Tsepeleva
Keyword(s):  
Activation Energy ◽  
Temperature Dependence ◽  
Viscous Flow ◽  
Cluster Size ◽  
Kinematic Viscosity ◽  
Cluster Structure ◽  
Liquid Structure ◽  
Logarithmic Scale ◽  
Structure Transition ◽  
Exponential Factor

The work investigated the temperature dependences of the kinematic viscosity for multicomponent melts of nanocrystalline soft magnetic alloys. It is shown that there is a linear relationship between the reduced activation energy of viscous flow Ea·(RT)−1 and the pre-exponential factor ν0. This ratio is universal for all quantities, the temperature dependence of which is expressed by the Arrhenius equation. It is shown that the activation energy of a viscous flow is linearly related to the cluster size on a natural logarithmic scale, and the melt viscosity increases with decreasing cluster size. The change in the Arrhenius plot in the anomalous zone on the temperature dependence of viscosity can be interpreted as a liquid–liquid structure transition, which begins with the disintegration of clusters and ends with the formation of a new cluster structure.

Anomalous Temperature Dependences of Kinematic Viscosity in a Multicomponent Metal Melts

2021 ◽  
Vol 902 ◽  
pp. 3-8
Author(s):  
Vladimir Tsepelev ◽  
Yuri N. Starodubtsev ◽  
Yekaterina A. Kochetkova
Keyword(s):  
Activation Energy ◽  
Cluster Size ◽  
Kinematic Viscosity ◽  
Heating Temperature ◽  
State Theory ◽  
Melt Structure ◽  
Subsequent Formation ◽  
Natural Logarithm ◽  
Temperature Dependences ◽  
Maximum Heating Temperature

The temperature dependence of the kinematic viscosity was determined in the Fe84.5Cu0.6Nb0.5Si1.5B8.6P4C0.3 melt, which has an anomaly in the temperature range 1700–1900 K. The cluster sizes participating in the viscous flow were calculated using the transition state theory. It is shown that the activation energy Ea is directly proportional to the natural logarithm of the cluster size d, and the melt viscosity decreases with increasing cluster size. In the anomalous region at heating, the activation energy first decreases and then increases. This behavior was associated with the cluster dissolution and the subsequent formation of new clusters with a different size and chemical composition. Upon cooling, the viscosity corresponds to the melt structure formed at the maximum heating temperature.

Viscosity of Liquid Nanocrystalline Alloys

2021 ◽  
Vol 880 ◽  
pp. 35-41
Author(s):  
V.S. Tsepelev ◽  
Yuri N. Starodubtsev ◽  
Nadezhda P. Tsepeleva
Keyword(s):  
Activation Energy ◽  
Electrical Resistivity ◽  
Viscous Flow ◽  
Critical Point ◽  
Free Volume ◽  
Electrical Resistance ◽  
Kinematic Viscosity ◽  
Chemical Compositions ◽  
Cooling Stage ◽  
Temperature Dependences

Temperature dependences of the kinematic viscosity, density, and electrical resistivity of Fe72.5Cu1Nb2Mo1.5Si14B9 and Fe84.5Cu0.6Nb0.5Si1.5B8.6P4C0.3 multicomponent melts have been studied. We found different behavior of the temperature dependences of viscosity near the critical point Tk = 1760 K during heating, which is associated with different chemical compositions of the clusters in the melt. In the cooling stage, the activation energy of the viscous flow for these two melts is the same and equal to 43 kJ·mol-1. At a temperature of 1720 K, the relative free volume is 5.1 and 7.5 % of the total melt volume for Fe72.5Cu1Nb2Mo1.5Si14B9 and Fe84.5Cu0.6Nb0.5Si1.5B8.6P4C0.3 respectively. In the cooling stage, the electrical resistance of melt is higher than at the heating stage.

Microscopic Interpretation of Arrhenius Parameters

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Activation Energy ◽  
Transition State ◽  
Transition State Theory ◽  
Average Energy ◽  
Zero Point ◽  
State Theory ◽  
Exponential Factor ◽  
Quantum Tunnelling ◽  
Microscopic Interpretation ◽  
The Difference

This chapter reviews the microscopic interpretation of the pre-exponential factor and the activation energy in rate constant expressions of the Arrhenius form. The pre-exponential factor of apparent unimolecular reactions is, roughly, expected to be of the order of a vibrational frequency, whereas the pre-exponential factor of bimolecular reactions, roughly, is related to the number of collisions per unit time and per unit volume. The activation energy of an elementary reaction can be interpreted as the average energy of the molecules that react minus the average energy of the reactants. Specializing to conventional transition-state theory, the activation energy is related to the classical barrier height of the potential energy surface plus the difference in zero-point energies and average internal energies between the activated complex and the reactants. When quantum tunnelling is included in transition-state theory, the activation energy is reduced, compared to the interpretation given in conventional transition-state theory.

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

Quasiclassical Trajectory and Transition State Theory Studies of the N(4S) + H2↔ NH(X3Σ-) + H Reaction

2002 ◽  
Vol 106 (16) ◽  
pp. 4125-4136 ◽  
Author(s):  
Ronald Z. Pascual ◽  
George C. Schatz ◽  
Gÿorgÿ Lendvay ◽  
Diego Troya
Keyword(s):  
Transition State ◽  
Transition State Theory ◽  
State Theory

scholarly journals Helium Isotopes Quantum Sieving through Graphtriyne Membranes

Nanomaterials ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 73
Author(s):  
Marta I. Hernández ◽  
Massimiliano Bartolomei ◽  
José Campos-Martínez
Keyword(s):  
Low Temperatures ◽  
Quantum Tunneling ◽  
Transition State Theory ◽  
Selective Adsorption ◽  
State Theory ◽  
Helium Isotopes ◽  
Quantum Calculations ◽  
Approximate Methods ◽  
Helium Atoms ◽  
Quantum Behavior

We report accurate quantum calculations of the sieving of Helium atoms by two-dimensional (2D) graphtriyne layers with a new interaction potential. Thermal rate constants and permeances in an ample temperature range are computed and compared for both Helium isotopes. With a pore larger than graphdiyne, the most common member of the γ-graphyne family, it could be expected that the appearance of quantum effects were more limited. We find, however, a strong quantum behavior that can be attributed to the presence of selective adsorption resonances, with a pronounced effect in the low temperature regime. This effect leads to the appearance of some selectivity at very low temperatures and the possibility for the heavier isotope to cross the membrane more efficiently than the lighter, contrarily to what happened with graphdiyne membranes, where the sieving at low energy is predominantly ruled by quantum tunneling. The use of more approximate methods could be not advisable in these situations and prototypical transition state theory treatments might lead to large errors.

Sign in / Sign up

Export Citation Format

Share Document