Empirical Regularities in the Behaviour of the Critical Constants of Fluid Alkali Metals

Hensel, F.; Hohl, G.; Schaumlöffel, D.; Pilgrim, W.‐C.; Franck, E. U.

doi:10.1524/zpch.2000.214.6.823

Cited by 25 publications

(14 citation statements)

References 6 publications

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“…On the other hand, the experimentally observed coexistence curves for liquid alkali metals, such as K, Rb, Cs, etc., display quite different behavior from that of SF 6 [13,14]. These metals exhibit marked deviations from the Law of the Rectilinear Diameter with a smooth downward curvature extending over quite a wide range of temperature even below T ≃ 0.9 T c ; but they do not show a sharply dropping singularity near criticality as seen for SF 6 : see Fig.…”

Section: Introductionmentioning

confidence: 84%

“…Deviations from the Law of the Rectilinear Diameter have indeed been observed in several careful experiments on various fluids [11,12,13,14,15,16]. Among these, the seminal study of SF 6 by Weiner et al [12] more than 30 years ago reported a surprisingly sharp and abrupt singular downturn of the diameter very close to T c .…”

Section: Introductionmentioning

confidence: 86%

“…Our goal here is to compare quantitatively the calculated diameters of the HCSW fluid and the RPM to the experimental data for SF 6 and the liquid metals [12,13,14]. The comparison is instructive in that one can gauge how well these simple models capture some essential features of real fluids and, at the same time, throw light on various experimental [17] and theoretical [23] proposals.…”

Section: Introductionmentioning

confidence: 99%

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Singular coexistence-curve diameters: Experiments and simulations

Kim

Fisher

2005

Chemical Physics Letters

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Precise calculations of the coexistence-curve diameters of a hard-core square-well (HCSW) fluid and the restricted primitive model (RPM) electrolyte exhibit marked deviations from rectilinear behavior. The HCSW diameter displays a |t| 1−α singularity that sets in sharply for |t| ≡ |T −Tc|/Tc 10 −3 ; this compares favorably with extensive data for SF6, also reflected in C2H6, N2, etc. By contrast, the curvature of the RPM diameter varies slowly over a wide range |t| 0.1; this behavior mirrors observations for liquid alkali metals, specifically Rb and Cs. Amplitudes for the leading singular terms can be estimated numerically but their values cannot be taken literally. * Corresponding Author: xpectnil@ipst.umd.edu Several models for fluids, however, have been advanced that violate the law [2,3,4]. These models suggest that the diameters of real fluids should exhibit an entropy-like singularity varying as |t| 1−α near criticality where t ≡ (T − T c )/T c and α ≃ 0.109 is the critical exponent for the specific heat; the slope of the diameter was thus expected to diverge at criticality in the same fashion as the specific heat. The traditionally accepted scaling theory of the critical region, which incorporates mixing between the temperature T and the chemical potential µ in the scaling fields (but does not include the pressure), also generates this entropylike singularity [5,6]. However, the recent discovery of a Yang-Yang anomaly [7,8] in fluid criticality turns out to entail a further singular term in the diameter proportional to |t| 2β , where β ≃ 0.326 is the critical exponent for the order parameter [7,9]. And such a term also arises in other classes of exactly soluble model [7,10]. In fluid criticality, one normally has 2β ≃ 0.65 < 1− α so that the |t| 2β term dominates the |t| 1−α contribution when t → 0−.

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Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Singular coexistence-curve diameters: Experiments and simulations

Kim

Fisher

2005

Chemical Physics Letters

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“…We then apply the finite temperature aiGEMC method to compute the liquid-vapor equilibrium of sodium for which several experimental data sets are available. [33][34][35] The critical densities and temperatures range from 0.175 to 0.3 g cm À3 in density and from 2485 to 2573 K in temperature. The sodium vapor is mainly an atomic gas without large clusters, 36 which thus greatly simplifies the structural constraints.…”

Section: Introductionmentioning

confidence: 99%

Ab initioGibbs ensemble Monte Carlo simulations of the liquid–vapor equilibrium and the critical point of sodium

Winisdoerffer

Soubiran

et al. 2021

Phys. Chem. Chem. Phys.

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“…The possibilities of experimental research are also limited. Due to the difficulty of conducting experiments at high temperatures, the critical point and binodal parameters were obtained only for a small amount of substances, which include alkali metals and mercury, which have relatively low temperature characteristics [6][7][8][9][10][11]. For other materials, there are only theoretical estimates within the framework of various models, among which phenomenological methods [12][13][14][15][16][17][18][19][20][21][22][23][24] and atomistic modeling methods [25][26][27][28][29][30][31] stand out.…”

Section: Introductionmentioning

confidence: 99%

Atomistic modeling of the critical region of copper using a liquid-vapor coexistence curve

Demin¹,

Koroleva²,

Shapranov³

et al. 2019

MathMon

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A liquidvapor coexistence curve was obtained for copper by the method of molecular dynamics modeling (MDM), and the corresponding critical parameters were determined: temperature, density, and pressure. The interaction potential of particles was of the "embedded atom" type (EAM). The critical temperature T cr was determined from the MDM results using the average cluster size method in the critical region. To clarify the critical density value, the empirical rule of rectilinear diameter was used. The results of modeling of this work were compared with the results of evaluating of the critical parameters of copper by other authors using different approaches.

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Empirical Regularities in the Behaviour of the Critical Constants of Fluid Alkali Metals

Cited by 25 publications

References 6 publications

Singular coexistence-curve diameters: Experiments and simulations

Singular coexistence-curve diameters: Experiments and simulations

Ab initioGibbs ensemble Monte Carlo simulations of the liquid–vapor equilibrium and the critical point of sodium

Atomistic modeling of the critical region of copper using a liquid-vapor coexistence curve

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