B. S. Roshchin

Model approach to solving the inverse problem of X-ray reflectometry and its application to the study of the internal structure of hafnium oxide films

The key features of the inverse problem of X-ray reflectometry (i.e., the reconstruction of the depth profile of the dielectric constant using an experimental angular dependence of reflectivity) are discussed and essential factors leading to the ambiguity of its solution are analyzed. A simple approach to studying the internal structure of HfO2 films, which is based on the application of a physically reasonable model, is considered. The principles for constructing a film model and the criteria for choosing a minimal number of fitting parameters are discussed. It is shown that the ambiguity of the solution to the inverse problem is retained even for the simplest single-film models. Approaches allowing one to pick out the most realistic solution from several variants are discussed.

Condensation of silica nanoparticles on a phospholipid membrane

The structure of the transient layer at the interface between air and the aqueous solution of silica nanoparticles with the size distribution of particles that has been determined from small-angle scattering has been studied by the X-ray reflectometry method. The reconstructed depth profile of the polarizability of the substance indicates the presence of a structure consisting of several layers of nanoparticles with the thickness that is more than twice as large as the thickness of the previously described structure. The adsorption of 1,2-distearoyl-sn-glycero-3-phosphocholine molecules at the hydrosol/air interface is accompanied by the condensation of anion silica nanoparticles at the interface. This phenomenon can be qualitatively explained by the formation of the positive surface potential due to the penetration and accumulation of Na+ cations in the phospholipid membrane.

Kinetics of the formation of a phospholipid multilayer on a silica sol surface

The ordering of a multilayer consisting of DSPC bilayers on a silica sol substrate is studied within the model-independent approach to the reconstruction of profiles of the electron density from X-ray reflectometry data. It is found that the electroporation of bilayers in the field of anion silica nanoparticles significantly accelerates the process of their saturation with Na and H2O, which explains both a relatively small time of formation of the structure of the multilayer of (1 − 7) × 10 s and 13% excess of the electron density in it. A bilayer of phospholipid molecules is considered as the simplest model of a cell membrane [1-5]. We previously observed the crystallization of a multilayer of phospholipid bilayers whose thickness is given by the Debye screening length ΛD in the bulk of a hydrosol substrate on the surface of the aqueous solution of amorphous silicon dioxide nanoparticles [6, 7] (Fig. 1). In this work, the ordering of the multilayer is studied within the model-independent approach to the reconstruction of profiles of the electron density from X-ray reflectometry data without any a priori assumptions on the structure of the multilayer [8-12]. According to our data, the characteristic time of formation of the structure of the surface is (1 − 7) × 10 s; after that, the lipid film can be considered as a two-dimensional organic crystal with a quite high degree of perfection tikhonov@kapitza.ras.ruThe ordering of a multilayer consisting of DSPC bilayers on a silica sol substrate is studied within the modelindependent approach to the reconstruction of profiles of the electron density from X-ray reflectometry data. It is found that the electroporation of bilayers in the field of anion silica nanoparticles significantly accelerates the process of their saturation with Na+ and H2O, which explains both a relatively small time of formation of the structure of the multilayer of 1–7×105 s and ~13% excess of the electron density in it.

Model-Independent X-Ray Scattering Study of a Silica Sol Surface

The structure of the adsorbed layer of alkali ions on the surface of colloidal silica solutions with a particle size of 27 nm has been studied by reflectometry and diffuse scattering of synchrotron radiation with a photon energy of about 71 keV. Electron density profiles in the direction perpendicular to the surface have been reconstructed from experimental data and spectra of the correlation function of heights in the surface plane have been obtained. The revealed deviation of the integral and frequency characteristics of the roughness spectra of the silica sol surface from predictions of the capillary-wave theory is of a fundamental character. This deviation is due to the contribution from roughnesses with low spatial frequencies ν < 10−4 nm–1 and to the interference of diffuse scattering from different layer interfaces of the surface structure.

The experience in production of composite refraction lenses from beryllium

The choice of beryllium-based material for the use in X-ray optics has been substantiated based on electron microscopy and X-ray diffraction data. The first results of applying refraction lenses made of this material are reported.

Supersmooth and modified surface of sapphire crystals: Formation, characterization, and applications in nanotechnologies

The results of studying the state of the surface of sapphire crystals by a complex of methods in different stages of crystal treatment are considered by an example of preparing sapphire substrates with a supersmooth surface. The possibility of purposefully forming regular micro- and nanoreliefs and thin transition layers using thermal and thermochemical impacts are considered. The advantages of sapphire substrates with a modified surface for forming heteroepitaxial CdTe and ZnO semiconductor films and ordered ensembles of gold nanoparticles are described. The results of the experiments on the application of crystalline sapphire as a material for X-ray optical elements are reported. These elements include total external reflection mirrors and substrates for multilayer mirrors, output windows for synchrotron radiation, and monochromators working in the reflection geometry in X-ray spectrometers. In the latter case, the problems of the defect structure of bulk crystals sapphire and the choice of a method for growing sapphire crystals of the highest structural quality are considered.

Grazing-incidence small-angle X-ray scattering in a twofold rough-interface medium: a new theoretical approach using the q-eigenwave formalism.

Based on the rigorous Green function formalism to describe the grazing-incidence small-angle X-ray scattering (GISAXS) problem, a system of two linked integral equations is derived with respect to amplitudes of the reflected and transmitted plane q-eigenwaves (eigenstate functions) propagating through two homogeneous media separated from each other by a rough surface interface. To build up the coupled solutions of these basic equations beyond the perturbation theory constraint 2kσθ0 < 1, a simple iteration procedure is proposed as opposed to the self-consistent wave approach [Chukhovskii (2011). Acta Cryst. A67, 200-209; Chukhovski (2012). Acta Cryst. A68, 505-512]. Using the first-order iteration, analytical expressions for the averaged specular and non-specular scattering intensity distributions have been obtained. These expressions are further analysed in terms of the GISAXS parameters {k, θ, θ0} and surface finish ones {σ, l, h}, where θ and θ0 are the scattering and incidence angles of the X-rays, respectively, σ is the root-mean-square roughness, l is the correlation length, h is the fractal surface model index, k = 2π/λ, and λ is the X-ray wavelength. A direct way to determine the surface finish parameters from the experimental specular and diffuse scattering indicatrix scan data is discussed for an example of GISAXS measurements from rough surfaces of α-quartz and CdTe samples.

X-Ray Reflectometry of DMPS Monolayers on a Water Substrate

The molecular structure of dimyristoyl phosphatidylserine (DMPS) monolayers on a water substrate in different phase states has been investigated under normal conditions by X-ray reflectometry with a photon energy of ∼ 8 keV. According to the experimental data, the transition from a two-dimensional expanded liquid state to a solid gel state (liquid crystal) accompanied by the ordering of the hydrocarbon tails -C14H27 of the DMPS molecule occurs in the monolayer as the surface pressure rises. The monolayer thickness is (20±3) Å and (28±2) Å in the liquid and solid phases, respectively, with the deflection angle of the molecular tail axis from the normal to the surface in the gel phase being 26±8. At least a twofold decrease in the degree of hydration of the polar lipid groups also occurs under two-dimensional monolayer compression. The reflectometry data have been analyzed using two approaches: under the assumption about the presence of two layers with different electron densities in the monolayer and without any assumptions about the transverse surface structure. Both approaches demonstrate satisfactory agreement between themselves in describing the experimental results. Phospholipids on a water surface form an insoluble monomolecular layer, a film that is a two-dimensional thermodynamic system with parameters (Π, T ). Under certain conditions, the structure of the layer is described by a symmetry axis perpendicular to the waterair interface [1, 2]. In particular, the Langmuir monolayer formed by dimyristoyl phosphatidylserine (DMPS) molecules is such a system (Fig. 1). Under normal conditions, the phase transition from a twodimensional liquid to a gel structure (liquid crystal) occurs in this film as the surface pressure Π rises at constant temperature T [3, 4]. However, simulations of such systems even using molecular dynamics methods leave the question about the molecular nature of electrostatic effects in monolayers open. Considerable help in solving this question may be expected from the use of direct methods of recording the structural changes in a monolayer. In particular, X-ray scattering was successfully used previously in [2, 5] to study the behavior of zwitterionic lipid monolayers. In this paper we propose to use such a technique to study the monolayer structures of anionic DMPS lipids with a pronounced phase transition. Indeed, under DMPS monolayer compression there are two distinctly different regions of change in electric potential (potential drop in the lipid monolayer): a comparatively tikhonov@kapitza.ras.ru Figure 1. Molecular structure of dimyristoyl phosphatidylserine (DMPS). small and smooth change in potential in the liquid state of the monolayer gives way to its sharp increase (∼ 200mV) when the lipid passes into a solid gel phase. Various hypotheses [4], for example, a change in the hydration state of the polar phospholipid groups [5, 6], are proposed to explain this fact. We think that Xray reflectometry data can be useful for testing these hypotheses. In this paper, based on our measurements of the X-ray reflectivity with a photon energy of ∼ 8 keV, we have reconstructed the electron density profile across the surface of a DMPS monolayer in its different phase states. Two approaches to analyzing the experimental data were used to extract the structural information: with a priori information (model approach) and without any assumptions about the transverse surface structure (modelless approach). The samples of DMPS phospholipid monolayers were prepared and studied in an airtight cell with X-ray-transparent windows in accordance with the technique described in [7, 8]. Some volume of a phospholipid solution with a concentration of 0.5mg/ml in a 5 : 1 chloroformmethanol mixture was spread with a syringe over the surface of a liquid substrate (a KCl solution in deionized water with a concentration of 10mmol/L and pH=7) placed in a fluoroplastic dish with a diameter D = 100mm. The solution volume required for our experiments was calculated for three values of the finite area A per molecule chosen for different lipid phase states in the monolayer. The dependence of the surface pressure, Π(A) = γ0 − γ(A), measured on DMPS layers in [3, 4] is uniquely specified by A (see Fig. 2). Here, the surface tension of pure water under normal conditions is γ0 = 72.5mN/m, while γ(A) is the surface tension in the presence of a lipid film. According to this dependence, at A ≈ 100 Å the monolayer is in an expanded liquid state I, while at A ≈ 50 Åthe monolayer is a two-dimensional inhomogeneous structure II and contains an equilibrium mixture of liquid and solid phase domains. Finally, at A ≈ 34 Å the DMPS monolayer is in a condensed state IIIThe molecular structure of dimyristoyl phosphatidylserine (DMPS) monolayers on a water substrate in different phase states has been investigated by X-ray reflectometry with a photon energy of ~8 keV. According to the experimental data, the transition from a two-dimensional expanded liquid state to a solid gel state (liquid crystal) accompanied by the ordering of the hydrocarbon tails C14H27 of the DMPS molecule occurs in the monolayer as the surface pressure rises. The monolayer thickness is 20 ± 3 and 28 ± 2 Å in the liquid and solid phases, respectively, with the deflection angle of the molecular tail axis from the normal to the surface in the gel phase being 26° ± 8°. At least a twofold decrease in the degree of hydration of the polar lipid groups also occurs under two-dimensional monolayer compression. The reflectometry data have been analyzed using two approaches: under the assumption about the presence of two layers with different electron densities in the monolayer and without any assumptions about the transverse surface structure. Both approaches demonstrate satisfactory agreement between themselves in describing the experimental results.

X-ray study of the structure of phospholipid monolayers on the water surface

The possibility of laboratory X-ray reflectometry study of the structure of dimyristoyl phosphatidylserine (DMPS) phospholipid monolayers on the water surface in various phase states has been demonstrated.The possibility of laboratory X-ray reflectometry study of the structure of dimyristoyl phosphatidylserine (DMPS) phospholipid monolayers on the water surface in various phase states has been demonstrated. Studies of various phospholipid-based systems are of interest because of both fundamental aspects of condensed matter physics and their basis role in biological membranes [1]. However, the preparation of macroscopic samples of phospholipid bilayers or multilayers on solid substrates is limited because the radius of spontaneous curvature of a lipid bilayer in an aqueous medium is less than 50 μm [2]. For this reason, the X-ray and neutron small-angle scattering studies of the structure of the lipid bilayer in an aqueous medium were performed only for three-dimensional aggregates (vesicles) [3-6]. In view of this circumstance, X-ray studies of macroscopically planar monolayer and multilayer lipid structures on an extended horizontal surface of liquid substrates are certainly of interest. X-ray reflectometry studies of the spatial structure of such samples are usually performed on specialized synchrotron stations. The specificity of experiments for liquid samples (in particular, the necessity of the horizontal arrangement of a sample) significantly complicates the design of an optical system and the deflector system of a synchrotron beam. As a result, the number of stations equipped for the study of interfaces between liquids is comparatively small and their work load is high. Furthermore, the intensity of the synchrotron beam is high enough to induce the degradation of lipid films in a time comparable with the duration of a single measurement of the angular dependence of reflected radiation [7]. We created an X-ray diffractometer with the horizontal arrangement of the sample and a mobile emitter detector system [8]. Such a design of the instrument allows X-ray reflectometry studies of liquid samples. The possibility of studying the structure of phospholipid multilayers deposited on a liquid silica sol substrate with this instrument was demonstrated in our works [9, 10]. However, it is noteworthy that the formation of phospholipid monolayers and their structure on the water surface (which possibly better simulates biological membranes) differ from those studied in our previous works. tikhonov@kapitza.ras.ru Figure 1. Molecular structure of dimyristoyl phosphatidylserine (DMPS). Moreover, the contrast in X-ray experiments is to significant extent determined by the ratio between the electron densities of the film and substrate. For example, according to [6], this ratio of the densities of the lipid mesophase and water lies in the range of 0.95−1.05. For such low-contrast systems, a significant change in reflection and scattering curves can be comparable in order of magnitude to the experimental error of a detected signal. Thus, reflectometry study of lipid layers on water imposes additional requirements on the level of parasitic noise of an instrument. It is also worth noting that the solution of the inverse problem of X-ray reflectometry, i.e., the reconstruction of the density of the structure of the sample in the direction perpendicular to its surface, becomes better defined at a wider range of sliding angles in the experiment. In this case, the reflected signal decreases naturally. In similar experiments performed on synchrotron stations, reflected radiation can be detected at a decrease in its intensity by eight to ten orders of magnitude with respect to the primary beam. In this work, we show by example of the study of dimyristoyl phosphatidylserine (DMPS, see Fig. 1) monolayers on water substrates that results comparable in quality can also be obtained in laboratory experiments. Our setup and developed methods for data analysis allow detecting structural effects in thin planar layers on the surface of liquids, in particular, in the presence of surfactants, e.g., phospholipids. The reported results make it possible to estimate geometrical factors reflecting changes in DMPS in phospholipid molecules at a phase transition in the monolayer on the water surface from the expanded liquid state to the gel, liquid-crystal state. DMPS phospholipid monolayer samples were prepared and studied at room temperature T ≈ 298K in an air-tight cell with X-ray transparent windows according to the method described in [10, 11]. A calibrated volume of the phospholipid solution in chloroform-methanol 5 : 1 mixture was deposited by means of

Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.