Unstable Stacking Fault Free Energies in Silicon through Empirical Modeling

1998 ◽  
Vol 539 ◽  
Author(s):  
M. De Koning ◽  
A. Antonelli ◽  
Martin Z. Bazant ◽  
Efthimios Kaxiras ◽  
J.F. Justo
Keyword(s):  
Finite Temperature ◽  
Transition State Theory ◽  
Harmonic Approximation ◽  
State Theory ◽  
Dislocation Nucleation ◽  
Stacking Fault ◽  
Empirical Modeling ◽  
Zero Temperature ◽  
Free Energies ◽  
Brittle Ductile Transition

AbstractThe temperature dependence of unstable stacking fault free energies on glide and shuffle {111} planes in silicon is investigated using a finite temperature molecular dynamics approach which includes a full treatment of anharmonic vibrational effects. The results are compared to earlier zero temperature ab initio calculations in which finite temperature effects were estimated using a harmonic approximation to transition state theory (TST). The unstable stacking free energies are interpreted within the framework of Rice‘s dislocation nucleation criterium to characterize a possible change from shuffle to glide plane dominance in the context of dislocation nucleation processes at a sharp crack tip. Such a change may be related to the abrupt brittle-ductile transition observed in silicon.

scholarly journals Finite-temperature molecular-dynamics study of unstable stacking fault free energies in silicon

1998 ◽  
Vol 58 (19) ◽  
pp. 12555-12558 ◽  
Author(s):  
M. de Koning ◽  
A. Antonelli ◽  
Martin Z. Bazant ◽  
Efthimios Kaxiras ◽  
J. F. Justo
Keyword(s):  
Molecular Dynamics ◽  
Finite Temperature ◽  
Stacking Fault ◽  
Free Energies

Crystallization kinetics and phase transformation characteristics in seeded monophasic cordierite gel

1991 ◽  
Vol 6 (11) ◽  
pp. 2427-2433 ◽  
Author(s):  
Byung C. Lim ◽  
Hyun M. Jang
Keyword(s):  
Activation Energy ◽  
Phase Transformation ◽  
Crystallization Kinetics ◽  
Transition State Theory ◽  
State Theory ◽  
Nucleation Theory ◽  
Free Energies ◽  
Growth Step ◽  
Activation Free Energy ◽  
3 Dimensional

Crystallization kinetics and phase transformation characteristics of μ- or α-cordierite seeded gels were compared with those of unseeded monophasic gels. The α-cordierite seeding modified the sequence of phase transformation and lowered the temperature of α-cordierite formation from amorphous gel by ∽150 °C. The μ-seeded transformation was characterized by 3-dimensional isotropic growth with essentially zero activation energy for the nucleation step. Combining the nucleation theory with the transition state theory, we have separately estimated the activation free energy of nucleation and that of growth step in the crystallization of amorphous cordierite gel. The estimated activation free energies showed that the crystallization of unseeded cordierite gel is mainly growth controlled.

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.

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