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Frenkel

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. [Pg.275]

J. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford, 1946. [Pg.343]

If attractive forces are present, then according to an equation by Frenkel (see Ref. 2), the average time of stay t of the molecule on the surface will be... [Pg.602]

The general approach goes back to Frenkel [63] and has been elaborated on by Halsey [64], Hill [65], and McMillan and Teller [66]. A form of Eq. XVII-78, with a = 0,... [Pg.628]

This may be based on Eq. XVI-2 [232] or on related equations with film thickness given by some version of the Frenkel-Halsey-Hill equation (Eq. XVII-79) [233,234],... [Pg.672]

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189]. Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].
Frenkel D and Smit B 1996 Understanding Molecular Simulation From Algorithms to Applications (San Diego Academic)... [Pg.2281]

Eppenga R and Frenkel D 1984 Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets Mol. Phys. 52 1303-34... [Pg.2282]

Frenkel D, Mulder B M and McTague J P 1984 Phase-diagram of a system of hard ellipsoids Phys. Rev.L 52 287-90... [Pg.2284]

Meijer E J, Frenkel D, LeSar R A and Ladd A J C 1990 Location of melting point at 300 K of nitrogen by Monte Carlo simulation J. Chem. Phys. 92 7570-5... [Pg.2284]

Siepmann J I and Frenkel D 1992 Configurational bias Monte Carlo—a new sampling scheme for flexible chains Moi. Phys. 75 59-70... [Pg.2285]

Frenkel D, Mooij GAM and Smit B 1992 Novel scheme to study structural and thermal properties of continuously deformable molecules J. Phys. Oondens. Matter4 3053-76... [Pg.2285]

Frenkel D 1986 Free-energy computation and first-order phase transitions Moiecuiar Dynamics Simuiation of Statisticai Mechanicai Systems ed G Ciccotti and W G Hoover (Amsterdam North-Holland) pp 151-88... [Pg.2285]

Frenkel D 1995 Numerical techniques to study complex liquids Observation, Prediction and Simuiation of Phase Transitions in Oompiex Fiuids vol 460 NATO ASi Series C ed M Baus, L F Rull and J-P Ryckaert (Dordrecht Kluwer) pp 357-419... [Pg.2285]

Siepmann J I, McDonald I R and Frenkel D 1992 Finite-size corrections to the chemical potential J. Phys. Oondens. Matter 4 679-91... [Pg.2285]

Lynden-Bell R M, van Duijneveldt J S and Frenkel D 1993 Free-energy changes on freezing and melting ductile metals Mol. Phys. 80 801-14... [Pg.2286]

Ruiz-Montero M J, Frenkel D and Brey J J 1997 Efficient schemes to compute diffusive barrier crossing rates Mol. Phys. 90 925-41... [Pg.2288]

Consta S, Wilding N B, Frenkel D and Alexandrowicz Z 1999 Recoil growth an efficient simulation method for multi-... [Pg.2384]

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... [Pg.2557]

Frenkel D and Mulder B 1985 The hard ellipsoid-of-revolution fluid. 1. Monte-Carlo simulations Mol. Phys. 55 1171-92... [Pg.2569]

Frenkel D 1992 Computer simulations of phase transitions in liquid crystals Phase Transitions in Liquid Crystals ed S Martellucci and A N Chester (New York Plenum)... [Pg.2569]

Stroobants A, Lekkerkerker FI N W and Frenkel D 1986 Evidence for smectic order in a fluid of hard parallel spherocylinders Phys.Rev.Lett 57 1452-5 Erratum 57 2331... [Pg.2569]

Frenkel D 1988 Thermodynamic stability of a smectic phase in a system of hard rods Nature 332 822-3... [Pg.2569]

Eldridge M D, Madden P A and Frenkel D 1993 Entropy-driven formation of a superlattioe in a hard-sphere binary mixture Mol. Phys. 79 105-20... [Pg.2695]

D. Frenkel and B. Smit. Understandinq Molecular Simulation. Academic Press, 1996. [Pg.315]

Rosenbluth algorithm can also be used as the basis for a more efficient way to perform ite Carlo sampling for fully flexible chain molecules [Siepmann and Frenkel 1992], ch, as we have seen, is difficult to do as bond rotations often give rise to high energy rlaps with the rest of the system. [Pg.462]

Siepmann J I and D Frenkel 1992. Configurational Bias Monte Carlo A New Sampling Scheme f Flexible Chains. Molecular Physics 75 59-70. [Pg.471]


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AgBr Frenkel defects

Alkali halides Frenkel defect

Anion Frenkel defect

Anti-Frenkel

Anti-Frenkel type defects

Cation Frenkel defect

Charged Frenkel excitons

Current Poole-Frenkel

Defect Frenkel

Defect Frenkel-disorder

Defect anion-Frenkel pair

Defect anti-Frenkel

Defect cation-Frenkel pair

Defect structures Frenkel type

Delocalised (Frenkel) excitons

Diffusion of Frenkel excitons

Dirac-Frenkel time-dependent

Dirac-Frenkel time-dependent variational

Dirac-Frenkel time-dependent variational principle

Dislocations Frenkel

Disorder anti-Frenkel

Disorder, Frenkel type

Disorder, antistructure Frenkel

Enthalpy of Frenkel defects

Equation Frenkel

Equation Frenkel-Halsey-Hill

Equilibrium Concentration of Frenkel Defects Derived from Configurational Entropy

Equilibrium Population of Frenkel Defects in a Crystal

Excitons singlet Frenkel

Excitons, Frenkel theory

Experimental observation of Schottky and Frenkel defects

Fermionic character of Frenkel excitons in one-dimensional molecular crystals

Frenkel Kontorova friction model

Frenkel defect configurational entropy

Frenkel defect definition

Frenkel defect enthalpy

Frenkel defect equilibrium

Frenkel defect equilibrium population

Frenkel defect formation

Frenkel defect interstitial silver ions

Frenkel defects equilibrium number

Frenkel defects experimental observation

Frenkel defects stoichiometry

Frenkel defects, solid electrolytes

Frenkel disorder

Frenkel disorder, intrinsic

Frenkel effect

Frenkel energy balance concept

Frenkel equilibrium

Frenkel excitations

Frenkel exciton

Frenkel exciton Hamiltonian

Frenkel exciton radius

Frenkel exciton spectrum

Frenkel exciton theory

Frenkel excitons

Frenkel excitons surface

Frenkel hopping

Frenkel law

Frenkel mechanism

Frenkel model

Frenkel notion

Frenkel pair defects

Frenkel pairs

Frenkel point defects

Frenkel principle

Frenkel reaction

Frenkel relationships

Frenkel springs

Frenkel value

Frenkel voiding

Frenkel, Coulomb, and mechanical excitons

Frenkel, Halsey and Hill

Frenkel, Halsey and Hill theory

Frenkel, Jacov

Frenkel, Jacov Il’ich

Frenkel-Halsey-Hill isotherm

Frenkel-Halsey-Hill theory

Frenkel-Halsey-Hill theory, fractal

Frenkel-Kontorova model

Frenkel-Ladd method

Frenkel-Poole emission

Frenkel-exciton vibrational

Frenkel-like excitation

Frenkel-pair resistivity

Frenkel-type defects

Frenkel-type process

Frenkel’s model

Lattice defects Frenkel

Mixing of Frenkel and charge-transfer excitons in a finite molecular chain

Mobile Frenkel exciton

Mobility of Frenkel Excitons

On the hybridization of zero-dimensional Frenkel and Wannier-Mott excitons

Poole-Frenkel

Poole-Frenkel effect

Poole-Frenkel excitations

Poole-Frenkel formalism

Poole-Frenkel law

Poole-Frenkel model

Poole-Frenkel process

Schottky and Frenkel Defects

Schottky—Frenkel defects

Silver bromide Frenkel defects

Silver halides, Frenkel defects

Sintering Frenkel model

Small deviation from stoichiometry. II. Imbalanced Frenkel defects

Solid Frenkel defects

The Frenkel, Halsey, Hill (FHH) Isotherm

The Poole-Frenkel Effect

Tightly Bound (Frenkel) Excitons

Variation principle, Frenkel

Viscous sintering Frenkel model

Waste-Recycling Monte Carlo Frenkel

Wilson-Frenkel

Wilson-Frenkel equation

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