Thermal Vibrations of Atoms in Cubic Crystals II: The Amplitude of Atomic Vibrations

Cartz, L.

doi:10.1088/0370-1301/68/11/321

Cited by 41 publications

(19 citation statements)

References 21 publications

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“…The two-dimensional criterion is thusL2 2 0.35. I t is of interest to compare this figure with the corresponding one for the inelting of single-crystal solids: In the latter case the value , -0.1 has been found to be appropriate (19); however, it is important to realize that the case considered here is actually quite different from that of solids insofar as first order phase transitions are not treated and the forces are the long range repulsions of the similarly charged adions and their images rather than the crystalbinding fields of an ionic crystal or the short range forces found in metals and covalent crystals. We should accordingly not expect the analogous values to carry over from one situation to the other.…”

Section: Thermal Averaging Calculationmentioning

confidence: 91%

Thermal Stability of an Adsorbed Array of Charges in the Einstein Approximation

Macdonald¹,

Barlow²

1965

Can. J. Chem.

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For an infinite hexagonal array of ions adsorbed on a conducting plane of infinite extent, the thermal fluctuation from strict lattice ordering in the neighborhood of a given adion is considered. The ions are imaged in the uniform, conducting adsorbent and are assumed to move freely in the plane; they thus arrange themselves in a perfect hexagonal array a t absolute zero temperature. By use of the accurate planar potential seen by one adion moving in the field arising from a n infinite number of fixed hexagonally arrayed surrounding ions, the root-meansquare (r.m.s.) amplitude of planar vibration of the ion relative to its neighbors is approximately determined for several values of nearest neighbor distances between ions, rl. On the basis of these results, we find, for example, that for a distance, P, between the center of charge of a n ion and the imaging plane of 3 A, an ionic valence z, of unity, and a n effective dielectric constant of e, a hexagonal array with rl = 15 A is stable up t o a temperature, To, of approximately 1760/e OK while one with rl = 21 A is stable up to about 760/e OK. Results apply t o adsorption from either a gas or liquid phase and, as well, to a n array of real dipoles adsorbed on a nonconducting surface. The appropriate values for e are of the order of 2 and 6, respectively, for adsorption from gas or from aqueous electrolytes. For various rl's, explicit expressions for T o are obtained which depend on e, 8, and z, . -

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Section: Thermal Averaging Calculationmentioning

confidence: 91%

Thermal Stability of an Adsorbed Array of Charges in the Einstein Approximation

Macdonald¹,

Barlow²

1965

Can. J. Chem.

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“…Utilizing larger amplitudes may have adverse effects and cause instabilities in the system. 27,28 After generating randomly positioned trajectories throughout phase space, we use velocity rescaling to equilibrate the individual trajectories at the temperature at which properties need to be calculated (i.e., the target temperature). The illustration of scheme 1 can be seen in Fig.…”

Section: Trajectory Generation Schemesmentioning

confidence: 99%

Ensemble averaging vs. time averaging in molecular dynamics simulations of thermal conductivity

Gordiz

Singh

Henry

2015

Journal of Applied Physics

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In this report, we compare time averaging and ensemble averaging as two different methods for phase space sampling in molecular dynamics (MD) calculations of thermal conductivity. For the comparison, we calculate thermal conductivities of solid argon and silicon structures, using equilibrium MD. We introduce two different schemes for the ensemble averaging approach and show that both can reduce the total simulation time as compared to time averaging. It is also found that velocity rescaling is an efficient mechanism for phase space exploration. Although our methodology is tested using classical MD, the approaches used for generating independent trajectories may find their greatest utility in computationally expensive simulations such as first principles MD. For such simulations, where each time step is costly, time averaging can require long simulation times because each time step must be evaluated sequentially and therefore phase space averaging is achieved through sequential operations. On the other hand, with ensemble averaging, phase space sampling can be achieved through parallel operations, since each trajectory is independent. For this reason, particularly when using massively parallel architectures, ensemble averaging can result in much shorter simulation times (∼100–200X), but exhibits similar overall computational effort.

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“…shows that the GLMC is a ''law of corresponding states,'' 22 In this paper, we report the first measurements of ␦ Critical and the corresponding critical boron concentration associated with the onset of amorphization of Ni-B solid solution during implantation of Ni with 50-keV B ϩ ions. Energy-filtered selected-area electron diffraction ͑EFSAED͒ ͑Ref.…”

Section: The Lindemann Model For Solid-state Amorphizationmentioning

confidence: 95%

Boron-implantation-induced crystalline-to-amorphous transition in nickel: An experimental assessment of the generalized Lindemann melting criterion

et al. 1999

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The generalized Lindemann melting hypothesis has recently been used to develop a unified thermodynamic criterion for melting applicable to both heat-induced melting and disorder-induced crystalline-to-amorphous ͑c-a͒ transformation. The hypothesis stipulates that the sum ͗ 2 ͘ Total of the static and dynamic root-meansquare ͑rms͒ atomic displacements is a constant fraction of the nearest-neighbor distance along the melting curve of a solid. To test this hypothesis, energy-filtered selected area electron-diffraction intensity measurements were used to determine the generalized Lindemann parameter ␦ϭͱ͗ 2 ͘ Total /d nn , in which d nn represents the nearest-neighbor distance, as a function of boron concentration during implantation of 50-keV B ϩ into polycrystalline Ni at 77 K. The onset of amorphization was found to occur close to 10 at. % boron, which is in good agreement with the value predicted by T o curve calculated using the generalized Lindemann hypothesis. Moreover, the critical value of the generalized Lindemann parameter for amorphization, ␦ Critical

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Thermal Vibrations of Atoms in Cubic Crystals II: The Amplitude of Atomic Vibrations

Cited by 41 publications

References 21 publications

Thermal Stability of an Adsorbed Array of Charges in the Einstein Approximation

Thermal Stability of an Adsorbed Array of Charges in the Einstein Approximation

Ensemble averaging vs. time averaging in molecular dynamics simulations of thermal conductivity

Boron-implantation-induced crystalline-to-amorphous transition in nickel: An experimental assessment of the generalized Lindemann melting criterion

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