Partial structure functions

The reduced intensity observed in an X-ray diffraction experiment corresponds to the sum over the different partial structure functions, each weighted by the product of the scattering factors for the two atomic species involved. In an aqueous solution of a salt MX, which contains four atomic species M, X, O, and H, the number of different pair interactions is ten and the reduced intensity function can be written ... 

There is an equivalent relationship between the partial structure functions, SapiQ) and the total structure function, S Q). In the Faber-Ziman scheme, the weighting is chosen such that each partial structure factor, Sa iQ), has the same property of the total structure factor that as Q go, So,p(Q)= 1- This means that we can define the Fourier couple between S iQ) and Ga (r) in the same way as for the total structure function, i.e. ... 

Concentration as well as temperature dependences of p in both the amorphous [5.86-89] and the liquid state [5.90-92] are understood in the framework of the diffraction or extended Faber-Ziman model [5.90, 92, 93]. Experimentally determined total as well as model partial-structure functions have been successfully applied. Disregarding inelastic-scattering effects and extensions of... 

The partial structure function H m(q) can be determined by radiation scattering only if the subsets s4 and 38 are sufficiently contrasted with respect to the rest of the sample. Accordingly, we shall see that the concept of contrast length8,9 can be introduced in a very natural manner. 

The possibility of controlling the contrast length b enables the experimentalist to deduce the partial structure functions of a mixture from small-angle scattering experiments. 

Saito M, Waseda Y (2000). Anomalous X-ray scattering for determining the partial structural functions of binary liquids. J Synchrotron Radiat 7 152-159... 

Another important function is the modified partial structure function S jCk) = h j(k) + where 6ij is the Kronecker delta... 

Bathia and Thornton(22) introduced three new partial structure functions which are linear combinations of the above S j(k) s. These new functions are the density-density partial structure... 

Results for 1-1 Molten Salts. The two most important parameters influencing the partial structure functions and the correlation functions of molten salts are the radius-ratio (rr) and the plasma parameter. Abramo, et al.(23) using a numerical solution of the MSA for an MX-type fluid of charged hard spheres of different diamters, have carefully examined these aspects, for molten 1-1 salts, concentrating their attention mainly on the effect of the ion size and the radius-ratio. They also reported, in some cases, comparison with experimental results. The general agreement is fair, in some cases excellent and some generalizations are possible. 

Whenever the radius-ratio is changed, the structure function Sii(k) of the smaller ion is seriously affected both from the quantitative and the qualitative point of view. This is shown in Figure 7 where we present our own calculations of the three partial structure functions for molten NaCl at 1148 K, obtained for two sets of radii in case 1 we used Pauling diameters, in case 2 we used = 2.06 A and a = 2.80 A... 

Results of Mixtures of 1 1 Molten Salts. We are not aware of any MSA calculation for mixtures of molten salts. One of us has recently completed(24) calculations of the partial structure functions S j(k) for various LiBr-KBr mixtures, for which molecular dynamics simulations were available(25). 

Abstract Partial structure functions and mean curvatures of a ternary amphiphilic system consisting of water, n-octane and nonionic amphiphile C12E5 with equal volume fraction of oil and water have been studied by means of small-angle neutron scattering (SANS). Isotopic contrast variation technique was used to obtain suitable scattering contrasts of oil and water. We observed that the cross partial structure functions, that arise from the correlation between water-surfactant or oil-surfactant, change sign when the temperature... 

Key words Amphiphile -microemulsion - lamella - partial structure function - mean curvature... 

In this paper we have determined the partial structure functions and explained the nature of different phases as a function of temperature in terms of Gompper and Schick s spin-lattice model [9, 10]. We measured partial structure functions in order to determine mean curvature from it. The mean curvature was measured as a function of temperatures using the method proposed by Lee and Chen [6]. 

Partial structure functions stem from the eorrelation between the volume fraction fluctuations of any two components, such as, water-water, water-surfactant, etc., of a three-component system. Partial structure functions S (q) are defined by... 

In order to understand the behavior of an amphiphile in terms of partial structure functions in a ternary system, we consider the interaction energy parameter C, characterizing the imbalance of amphiphilicity defined by Gompper and Schick [9, 10], which is the difference between the interaction of amphiphile with water and oil. Hence, one would expect C = 0 at the hydrophile-lipophile balance (HLB) line, amphiphile favors oil to water for C > 0 and the opposite holds for C < 0. C has an interesting role in the phase diagram. For equal volume fractions of water and oil (5(t) = — < > 0) and C = 0, the phase diagram... 

Partial structure functions and mean curvatures in ternary water/H-octane/Ci2E5 system with equal volume fraction of water and oil were determined by means of small-angle... 

Saito M, Park C, Omote K, Sugiyama K, Waseda Y (1997) Partial structural functions of molten CuBr estimated from the anomalous X- ray scattering measurements. J Phys Soc Jpn 66 633-640... 

---