Determination of the structure of liquids: an asymptotic approach

2013 ◽  
Vol 46 (6) ◽  
pp. 1582-1591 ◽  
Author(s):  
Martin Mayo ◽  
Eyal Yahel ◽  
Yaron Greenberg ◽  
El'ad N. Caspi ◽  
Brigitte Beuneu ◽  
...  

Accurate determination of a liquid structure, especially at high temperatures, remains challenging, as reflected in the scatter between different measurements. The experimental challenge is compounded by the process of the numerical transformation from the structure factor to the radial distribution function. The resulting uncertainty is often greater than that required to resolve issues associated with changes in the short-range order of the liquid, such as the existence of liquid–liquid phase transitions or correlations between thermophysical properties and structure. In the present contribution it is demonstrated for liquid bismuth as a model system that the structure factor can be obtained to high accuracy, by comparing several independent measurements in different setups. A simple method is proposed for improving the accuracy of the radial distribution functions, based on the extension of the finite range of momentum transfer,q, in the measured data by analytical asymptotic expressions. A unified mathematical formalism for the asymptotic dependence of the structure factor is developed and the asymptotic form of the Percus–Yevick hard-sphere solution is obtained as a special limiting case. The multiple expressions in the literature are shown to reflect uncertainty in the nature of the repulsive interatomic interaction at short separation distances. Applying this asymptotic method, it is shown that it enables access to details of the fine structure of the liquid and its temperature dependence.

1988 ◽  
Vol 41 (3) ◽  
pp. 469
Author(s):  
HJ Juretschke ◽  
HK Wagenfeld

Unless special precautions are taken, the experimental determination of two-beam structure factors to better than 1 % may include contributions from neighbouring n-beam interactions. In any particular experimental configuration, corrections for such contributions are easily carried out using the modified two-beam structure factor formalism developed recently (Juretschke 1984), once the full indexing of the pertinent n-beam interactions is known. The method is illustrated for both weak and strong primary reflections and its applicability in special cases, as well as for less than perfect crystals, is discussed.


Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 541
Author(s):  
Georgios Nicolaou ◽  
George Livadiotis

The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.


2001 ◽  
Vol 47 (157) ◽  
pp. 205-212 ◽  
Author(s):  
Martin J. Siegert ◽  
Shuji Fujita

AbstractCauses of ice-sheet layering at ice depths greater than about 900 mina transect between Dome C and the Transantarctic Mountains are examined using 60 MHz radar data, collected in the 1970s by the U.K.–U.S.–Danish collaboration. Normally, a dual-frequency technique is required for accurate determination of internal reflection mechanisms. However, by extracting the depth-related features of 60 MHz radar profiles and comparing them with the dual-frequency data collected by the Japanese Antarctic Research Expedition, we have identified a simple method to estimate internal reflection mechanisms. Two zones can be distinguished: (1) the CA zone, where change in electrical conductivity due to variation in acidity is the major cause of internal reflection, and (2) the PCOF zone, where change in dielectric permittivity due to crystal-orientation fabrics is the major cause of internal reflections. Our analysis shows that the radar data reveal the development of PCOF zones in regions where large amounts of ice shearing are expected. This analysis shows how a similar interpretation of the full radar-data archive may reveal information on internal reflection mechanisms across a large part of the East Antarctic ice sheet.


1982 ◽  
Vol 242 (5) ◽  
pp. C404-C408 ◽  
Author(s):  
D. M. Bers

A simple method for the accurate determination of free [Ca] in ethyleneglycol-bis(beta-aminoethylether)-N,N'-tetraacetic acid (EGTA)-buffered Ca solutions is described. This method is useful for calibration of Ca macro- and microelectrodes to low free [Ca] and should improve the reliability of calculated free [Ca] in more complex solutions. Briefly, free [Ca] in Ca-EGTA solutions is measured with a Ca electrode, bound Ca is calculated, and Scatchard and double-reciprocal plots are resolved for the total [EGTA] and the apparent Ca-EGTA association constant (K'Ca) in the solutions used. The free [Ca] is then recalculated using the determined parameters, giving a more accurate knowledge of the free [Ca] in these solutions and providing an accurate calibration curve for the Ca electrode. These solutions can then be used to calibrate other Ca electrodes (e.g., Ca microelectrodes) or the calibrated Ca electrode can be used to measure free [Ca] in solutions containing multiple metal ligands. This method allows determination of free [Ca], K'Ca, and total [EGTA] in the actual solutions used regardless of pH, temperature, or ionic strength. It does not require accurate knowledge of K'Ca or EGTA purity and circumvents many potential errors due to assumption of binding parameters. K'Ca was found to be 2.45 +/- 0.04 X 10(6) M-1 in 100 mM KCl, 10 mM N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid, and 1 mM EGTA at pH 7.00 and 23 degrees C. Total [EGTA] varied with supplier but was always less than quoted.


Sign in / Sign up

Export Citation Format

Share Document