The organization of chromatin in the nuclei of rat lymphocyte was studied by time-of-flight spin-echo small-angle neutron scattering (ToF-SESANS). The procedures of the measurements in ToF and monochromatic SESANS modes were compared. It is shown that the sensitivity of the ToF method is significantly higher than that of the monochromatic mode. As a result, the SESANS correlation function can always be extracted from the ToF measurement of polarization, while this is not always the case with the monochromatic mode. The applicability of SESANS to fractal objects at the micrometre scale is demonstrated. The SESANS correlation function is well fitted by the exponential decay G(z) = exp(−z/ξ) with the correlation length ξ = 3.7 ± 0.1 µm. The exponential decay of the SESANS correlation function can be connected to the logarithmic correlation function γ(r) = ln(r/ξ) and the cubic law of the scattering intensity I(Q) = Q−3, which is in agreement with the concept of scattering from fractal objects. This finding is interpreted as evidence of a very specific logarithmic fractal structure of the large-scale organization of chromatin. The model of the logarithmic fractal is visualized as a hierarchical object obeying the volume-conservation principle at different scales.@en

Spin-echo small-angle scattering (SESANS) technique is a method to measure the structure of materials from nano- to micrmeter length scales. This method could be important for studying the packaging of DNA in the eukaryotic cell. We measured the SESANS function from chicken erythrocyte nuclei which is well fitted by the exponential function G(z) = exp(-z/ξ), where ξ is the correlation length of a nucleus (in experimental data ξ = 3, 3 μm). The exponential decay of G(z) corresponds to the logarithmic pair correlation function γ(r) = ln(ξ/r). As the sensitivity of the SESANS signal depends on the neutron wavelength, we propose the SESANS setup with the changeable wavelength in the range from 2 to 12 Å. Such option allows one to study in great detail the internal structure of the biological cell in the length scale from 10^-2 μm to 10 μm.

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The closed porous structure in ceramic materials is investigated by spin-echo small-angle neutron scattering. A series of ceramic samples of oxygen–ion conductors based on bismuth molybdate with the general formula Bi_12.8X_0.2Mo₅O_{34 ± δ} (X = Mg, Ba, Ca, Sr) is obtained by powder sintering for 6−45 h at a temperature close to the melting point. The samples are characterized by scanning electron microscopy and X-ray fluorescence analysis. It is found that they had a stoichiometric chemical composition, are singlephase, and contain clean pores between crystal grains. The pore size is determined by spin-echo small-angle neutron scattering and ranges from 2.2 to 3.5 μm. It is demonstrated that longer sintering times correspond to larger pores (the increase in their average diameter is as large as 30%). It is found that the studied materials lack a fractal pore structure.

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Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q−3 in the range of momentum transfer Q∈10−3–10−2nm−1. Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3×102)–(3×104) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ(r)=ln(ξ/r) for r<ξ, where ξ=(3.69±0.07)×103 nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal γ(r/a)=γ(r)+ln(a), i.e., the scaling down by a gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.@en