An analysis is presented for the absorption corrections necessary for the x-ray analysis of diffraction data from a liquid sample confined within a cylindrical sample cell. The evaluation of necessary absorption integrals has been formulated in a numerical calculus procedure appropriate for a digital computer. The procedure has been verified against previous graphical computations.

Measurements have been made at the critical mixing composition of the system 2,6-lutidine-water for a (Tc-T) range of 0.001°–7.5°C for the intensity and Rayleigh linewidth and of 0.007°–27.4°C for the shear viscosity. We find that Ic−1(0) ∝ (ε)(1.26± 0.02),ξs=(2.0± 0.2)(ε)−(0.61± 0.08) Å,D=(0.290± 0.020)(ε)(0.554± 0.015)× 10−5cm2/sec,ξΓ=(2.92± 0.19)(ε)−(0.567± 0.015) Å,where ε =(Tc-T)/Tc,  Ic(0) is the intensity extrapolated to zero angle, ξΓ the correlation length from intensity measurements, D the mutual diffusion coefficient, and ξΓ the correlation length obtained from fitting the Kawasaki equation to linewidth measurements with the above value of D. We find that the Ornstein-Zernike-Debye theory is valid for (Tc-T) >0.03°C and the Kawasaki mode-mode coupling theory gives a good over-all description of the behavior of the linewidth of the Rayleigh line. The Kadonoff-Swift-Kawasaki result γ - psi = ν seems to be valid with ν=νs=νΓ. We also find that the excess shear viscosity does not exhibit a simple power law dependence on (Tc-T) as the critical temperature is approached.

Results are derived which show that in the analysis of x-ray or neutron-scattering data from mixtures of amorphous solids or liquids, a meaningful scattering function, i(s), can always be computed without recourse to simplifying assumptions regarding the atomic scattering functions. Fourier inversion of i(s) yields a distribution function, H(r) = ΣΣxixjHij(r), where xi is the atomic fraction of species i, and Hij(r) is the convolution of the true net radial-distribution function, hij(r), with a particular function of the atomic scattering factors. The much-used assumption that all atomic-scattering factors are proportional to the same function yields an H(r) that is a weighted sum of the hij(r), but does not offer any means of ascertaining the individual hij(r) terms if only one scattering experiment is performed.

X-ray diffraction measurements were made on argon at 13 states in the general critical region on a density—temperature grid covering the range 0.280 g/cc⩽ρ̄⩽0.982 g/cc and −130°C≤T≤−110°C. Features of the intensity patterns vary rather simply with density and only weakly with temperature. Computed values of the radial distribution functions show similar dependence on T and ρ̄. The first three maxima in the distribution functions are at average locations of 3.90, 7.51, and 10.9 Å.

A cluster expansion is written for the partition function of a polymer chain. An exact expression relating “nodal” and “elementary” graphs is presented. An analog of the Percus–Yevick approximation is made which leads to an integro-difference equation. This equation is solved exactly using a hard-core potential for the special case of the hard-core diameter equal to the polymer segment length (the “pearl-necklace” model). Results of numerical calculations are given for other values of this diameter ranging from zero to the segment length. This leads to values of γ ranging correspondingly from 1.0 to 2.0, where 〈ρ1N2〉Mγ with 〈ρ1N2〉 the mean-square end-to-end distance and M the molecular weight. The numerical results for 〈ρ1N2〉 as a function of chain length are in good agreement with the second-order perturbation theory of Fixman for small hard-core diameters.