Influence of vacancies on the static and dynamic properties of monoatomic liquids

Stojić, M.; Stojić, B.Babić; Milivojević, D.

doi:10.1016/s0921-4526(03)00077-2

Cited by 9 publications

(8 citation statements)

References 42 publications

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“…From figure 2 it is clear that the optimal value of the solvent hard sphere diameter is approximately σ 1 = 3.032 24 Å. With σ 1 given by step one (22), is a relation for σ 2 .…”

Section: Methods For Mass Diffusion Coefficient Estimationmentioning

confidence: 97%

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Estimation of the solute diffusion coefficient of a dilute liquid alloy: static structure factor and isothermal compressibility estimates obtained using the rational function approximation of the radial distribution

Scott¹,

Smith²

2009

J. Phys.: Condens. Matter

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A simple method for estimating the mass diffusion coefficient of a dilute binary liquid alloy that sequentially uses experimental data for the static structure factor and isothermal susceptibility of the solvent is presented, as well as another using the static structure factor alone and a method using the isothermal susceptibility alone. A fourth method that simultaneously uses the static structure factor and isothermal susceptibility is also noted. Of significance is the fact that these methods do not require information about the interatomic potential. Stability with respect to weights in the optimization process employed has been established and is reported, as well as some indication of the upper limits on the applicable solute concentration. Comparisons are made with results from a high quality capillary experiment for Pb 1 wt% Au liquid alloy performed in microgravity, and with velocity autocorrelation estimates derived from molecular dynamics simulation. The results suggest that the capillary experiments are influenced by reverse diffusion of the solvent, and actually measure an average of the mass diffusion coefficients, D(ij), weighted by the equilibrium concentrations of the solvent, x(1), and solute, x(2), defined by [Formula: see text] The three methods are required to provide upper and lower estimates for the mixed solvent-solute diffusion coefficient, which is not directly accessible from the experimental data, and demonstrate agreement with the experiment via D(tot).

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“…From figure 2 it is clear that the optimal value of the solvent hard sphere diameter is approximately σ 1 = 3.032 24 Å. With σ 1 given by step one (22), is a relation for σ 2 .…”

Section: Methods For Mass Diffusion Coefficient Estimationmentioning

confidence: 97%

“…Values for the isothermal compressibility of liquid lead are found in [22] and [23]. From this the following expression for the isothermal susceptibility as a linear function of the temperature can be derived:…”

Section: Estimation Of Hard Sphere Equivalent Atomic Diametersmentioning

confidence: 99%

Estimation of the solute diffusion coefficient of a dilute liquid alloy: static structure factor and isothermal compressibility estimates obtained using the rational function approximation of the radial distribution

Scott¹,

Smith²

2009

J. Phys.: Condens. Matter

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“…Experimental studies about this last aspect are rather scarce. Stojic et al 28 studied vacancies in molten Ge by measuring the structure factor and its dependence on melt temperature and discussed the equilibrium with the vacancies in the Ge crystal. It might be useful to perform similar studies for Si.…”

Section: Impact Of Stress On [V/ G0] Cr I Tmentioning

confidence: 99%

Silicon Single Crystal Growth from a Melt: On the Impact of Dopants on thev/GCriterion

Vanhellemont

Kamiyama

Sueoka

2013

ECS J. Solid State Sci. Technol.

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The so called v/G criterion defines a critical value 0 crit of the ratio of the pulling rate v over the thermal gradient G at the melt-solid/interface. For a ratio larger than this critical value, the crystal is vacancy-rich while for values below the critical value, the crystal is self-interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of so called "perfect silicon". The basic analytical expression for the critical ratio is analyzed and it is shown that thermal stress at the melt-solid interface and doping have an important effect on the 0 crit value. Furthermore, DFT calculations suggest that near the melt-solid interface the formation energy of the intrinsic point defects is lower than in the bulk of the crystal. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials at the free surface and most probably also at the melt-solid interface that are considerably different from those in the bulk. It is illustrated how the v/G criterion can be further refined by taking into account these effects.The so called "Voronkov criterion" which allows predicting if a Si single crystal pulled from a melt will be vacancy-or self-interstitialrich, is the basis for defect-free Si crystal and wafer production. In its most simple form it is written as the critical ratio 0 crit of the pulling speed v over the thermal gradient G0 at the melt-solid interface 1-3with C eq and D the intrinsic point defect thermal equilibrium concentration and diffusivity, respectively, both at the melt temperature T m . E f is the intrinsic point defect formation energy and C the actual concentration of the intrinsic point defects at the melt-solid interface. The criterion was later further generalized by including also the possible effect of vacancy and self-interstitial drift which was shown however to be of minor importance. 3 An important question is which values one should use for the thermodynamic parameters of the intrinsic point defects in Eq. 1 as a very wide range of values have been reported in literature. The values for the self-diffusion coefficient D S D Si have however converged during the last years and in the temperature range between 855 and 1388 • C, D S D Si (in cm 2 s −1 ) is accurately described by 4with f I and f V the diffusion-correlation factors for self-interstitials and vacancies, respectively. Also the uncertainty on the transport capacity C eq D of the vacancy and the self-interstitial has decreased significantly. Assuming f I = 0.73, Bracht et al. 5,6 obtained (in cm −1 s −1 ) C eq V D V = 6.2C Si exp − 4.33 eV k B T [3] C eq I D I = 43C Si exp − 4.56 eV k B T . For the diffusivity of the vacancy Watkins recently proposed best estimates (in cm 2 s −1 ) for the double positively charged vacancy V 2+ and for the uncharged vacancy V 0 diffusivities, given by 7 D V 2+ = 6.5 × 10 −5 exp − 0.32 eV k B T [4] D V 0 = 0.0012 exp − 0.45 eV k B T . * Electrochemical Society Active Member. z E-mail: jan.vanhellemont@ugent.be Combining Eqs. 3 an...

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“…The observed hyperfine splitting value of A iso = 6.8 mT (63.77 × 10 -4 cm -1 ) is characteristic of Mn 2+ ions in a tetrahedral crystal field environment, as found in bulk CdS (A iso ) 65.3 ( 0.4 × 10 -4 cm -1 ), 40 of ∼6.9 mT in CdS:Mn nano system, 22 of ∼6.9 mT in ZnS:Mn nanoparticles, 41 and of 6.5 mT in Mn doped ZnSe nanocrystals. 42 The presence of forbidden lines are due to slight distortion from the ideal tetrahedral structure. However, the PL results with different concentrations of Mn 2+ show PL peaks around 360-370 nm, which suggests that they originate from β-MnS on the surface of the CdS in conformity with the PL work Goede et al 25,30 and not from CdS.…”

Section: Signal Imentioning

confidence: 99%

Davydov Split PL Emission and EPR Correlation in β-MnS Layered CdS Nanorods

Sambandam

Manoharan

2009

J. Phys. Chem. C

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A comparison of manganese activated CdS nanorods with the nonactivated ones prepared by simple chemical methods in micellar medium reveals quantum confinement and blue shift in optical spectroscopy as a function of Mn 2+ . Powder XRD of all samples reveals orientation along the 002 plane, confirmed by HRTEM. Nonactivated CdS gives a blue band edge emission at 455 nm in the PL spectrum getting quenched on Mn 2+ addition. The PL spectra of Mn 2+ added CdS exhibit first an emission at 367.7 nm, which later gets subjected to Davydov splitting with a separation of ∼0.045 eV, the singlet intensity decreasing and the doublet intensity increasing with Mn 2+ input. This PL property is manifested in EPR as due to two different Mn 2+ environments: (i) individual tetrahedrally coordinated uncoupled Mn 2+ ions; (ii) Mn 2+ -Mn 2+ physical dimer moieties. These are interpreted to arise from (i) the formation of a first layer of MnS on a CdS surface and (ii) the latter due to a second layer of MnS on top of the first to form MnS-MnS dimers. Mn 2+ is present as metastable -MnS. The Davydov splitting is accompanied by a small energy shift. The double layer formation is confirmed by a bleaching experiment. Also noted is a low intensity band edge emission of CdS perturbed by Mn 2+ blue-shifted from the quenched 455 nm emission. ICP and EDS confirm the purity of samples.

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Influence of vacancies on the static and dynamic properties of monoatomic liquids

Cited by 9 publications

References 42 publications

Estimation of the solute diffusion coefficient of a dilute liquid alloy: static structure factor and isothermal compressibility estimates obtained using the rational function approximation of the radial distribution

Estimation of the solute diffusion coefficient of a dilute liquid alloy: static structure factor and isothermal compressibility estimates obtained using the rational function approximation of the radial distribution

Silicon Single Crystal Growth from a Melt: On the Impact of Dopants on thev/GCriterion

Davydov Split PL Emission and EPR Correlation in β-MnS Layered CdS Nanorods

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