Table of contents

The second in a series of Euroconferences on the use of neutrons for studies of condensed matter was arranged 9th to 13th of June 1994 at the Wijk conference center in the Stockholm archipelago. The Euroconference was sponsored by the Commission of the European Communities, Nobel Committees for Physics and Chemistry of the Royal Swedish Academy of Sciences, the Goran Gustafsson Foundation and the Royal Institute of Technology. The subject of the Euroconference was this year "Neutrons in Disordered Matter".

A large number of applications for financial assistance from young scientists of many countries in Europe were received. However, because of the limited funding only 17 of them could be accepted on scientific grounds resulting in full or partial support. Three young scientists were entirely supported from local funds. In order to facilitate the discussions and to have an intimate atmosphere the organizers decided it to be essential to limit the number of participants and to have a suitable proportion between young and senior scientists. Thus, in total about 60 participants were attending in the conference. Furthermore each selected young scientist not submitting any contribution has nevertheless been asked to present a poster summarizing his or her research work. Within the frame of a separate CEC contract the participation of five scientists from central and eastern European countries could also be financed.

The Euroconference '94 was divided in a school and a conference part. The specific topics covered during the school part were chosen according to the result of an enquiry sent out together with the first conference announcement. Eight invited lecturers were thus presenting two-hour reviews at the school. During the two-day conference a large number of contributions were presented, both orally and as posters and the proceedings contain about 75% of them including the lecture notes from one of the invited lecturers, P. Lamparter. Also included is the contribution of G. Caglioti whose lecture has been given as an "aperitif talk" before the conference dinner. All contributions have been refereed and revised if necessary.

Finally, we would like to sincerely thank everyone without whom the Euroconference '94 would not have been so successful:

• all the participants for their constant kindness, for their interest and for their very good contributions, as can be judged upon in this proceedings

• Maria Tungström and the staff of Wijk conference center for their professionalism and their permanent availability

• Bo Hortlund and the staff of the travel agency at the Royal Institute of Technology for their enthusiasm in making the travel arrangements.

Symmetry, symmetry breaking and broken symmetries play a central role in science and art, as well as in our daily life.

Symmetry - a no-change as the outcome of a change - is synonym of invariance or indiscernibility. As a permanent reference of a structure it is associated with the meaning of the structures and it is fundamental in order to describe them. But symmetry implies the impossibility to discern, that is to measure and to perceive. In order to measure and to perceive, that is to create information and knowledge, symmetry has to be broken.

The game of life - a life made of selfreproducing information - develops on the watershed of broken symmetries: an ambiguous and indented ridge of symmetries that break and recover themselves in a continuous series of choices. But even the masterpieces of art of all time run on the same ridge. The musical language, for instance, is a universal language - it can be enjoyed without being translated - just because the two contradictory attitudes of the human soul - the symmetric or dreaming attitude and the "informed" or conscious one - compose themselves in it. Similarly, the most successful trademarks exhibit a measured combination of symmetric and therefore reassuring elements, and elements that break symmetry and, in this way, evoke dynamically the rising of new perspectives.

During the conference many examples will be proposed, as well as some suggestive similarities between visual arts, music and science.

Despite its apparent simplicity, a comprehensive interpretation of all the features of the motion of a tagged particle in a liquid is a challenging task. The basic reason for this difficulty lies in the wealth of physical events spanning vastly different length- and time-scales (such as streaming, collisions, cage effects, diffusion) which must be accounted for. In this respect, the accurate data presently available from both incoherent neutron scattering and computer simulation also pose a rather severe benchmark for the theory. In this contribution we shall attempt to encompass all the aspects of the problem by a unified theoretical framework in which phenomenology is kept to a minimum. To consider a specific case, the results are compared with the data in liquid sodium near the melting point, obtained by inelastic neutron scattering experiments, as well as by new, extensive simulations performed on purpose for such an investigation.

The static structure functions of liquid gallium obtained from high resolution time-of-flight measurements in the temperature range 17-70°C are reported. A well-separated double structure in the static structure factor is observed first time. It is concluded that S(Q) is a superposition of two structure functions in the investigated temperature range. The presence of the β phase structure in the liquid-state could explain the strange crystallization of gallium.

We have studied the structure and dynamics of liquid lithium (pure ⁷Li) in a computer experiment: the states (470, 526 and 573K) correspond exactly to those investigated recently in neutron scattering experiments by Verkerk and co-workers. Instead of a potential based on a simple local pseudopotential which is usually sufficient for the alkali metals we have used a potential which is based on a non-local OPW-pseudopotential. Both single-particle and collective correlation functions have been calculated. For all temperatures we achieve very good agreement for the total dynamic structure factor. Also the diffusion constant, the specific heat at constant volume and the adiabatic velocity of sound extracted from our data are in good agreement with the experimentally determined values.

With the improvements introduced in the last decade in the data analysis and in the construction of neutron diffractometers with related detection systems, the static structure factor S(k) of a simple one-component fluid can be presently determined with an accuracy of a few parts per thousand. This improvement in the performance of the experimental techniques makes the neutron S(k) measurements a powerful tool in the analysis of microscopic properties like the interparticle interaction law and in the test of new refined theoretical approaches to the description of the phase transitions. We review here the results of an extended set of diffraction measurements on fluid Kr in the liquid phase along three different isotherms and in the gas phase in proximity of the liquid-gas transition. The structure factors and the corresponding density derivatives are discussed and compared to theoretical results. From the data in the critical region an estimate of the correlation length and its critical behaviour has been derived, even though a more reliable determination of these quantities requires a closer approach to the critical conditions.

Three molten ternary Ge-Sn-Te alloys lying on the quasibinary line Ge-SnTe, and the binary equiatomic alloys SnTe and GeTe have been investigated by neutron "time-of-flight" experiments. Published thermodynamic results are interpreted in terms of the coexistence of SnTe and Ge microgroupings in the melt. Using the experimental obtained data of the binary liquid alloy Sn₅₀Te₅₀ and of liquid Ge the structure factors of the ternary melts are calculated on the base of a microheterogeneous model.

From recent structural analysis of the LiNbO₃ melt, carried out by means of Small Angle x-ray Scattering [SAXS] and High Temperature Diffraction [HTD], it has been possible to describe a local order reduced to the first neighbours. The first three mean interatomic distances, r_{1 Nb-O}, r_{1 Li-O} and r_{1 O-O} were extracted with the high accuracy Δr/r = 0.5%. From the first three coordination numbers n_{1 Nb-O}, n_{1 Li-O} and n_{1 O-O}, it was verified that octahedrally coordinated niobium atoms exist in the melt and the liquid local order shows only some weak deviations with the solid states. A comparison is made with the crystalline phases and particularly with the recent results obtained around the phase transition at T_c similar 1430K. The first interatomic distances in the paraelectric high temperature phase are higher than the values determined in the melt. This fact is explained by a possible rotation of the Nb-O₆ octahedra which are more regular in the liquid. The small changes, observed in the Nb-O, Li-O and O-O bonds, are described in the model of the smallest aggregat constituted by only two Nb-O₆ octahedra. Assuming expansion and tilt of the O-triangles and some broken O-O bonds, the decrease of the first three mean interatomic distances r_ij, the broadening of their i-j distributions Δr_ij and the coordination numbers n_ij can be explained.

The application of neutron diffraction for the investigation of the structure of amorphous materials is shown. The experimental methods and the data-reduction procedures are illustrated by means of representative examples from the group of amorphous metallic alloys, the so-called metallic glasses. However, they apply to amorphous and liquid alloys in general.

The topics associated with diffraction studies are: theoretical formalisms for the description of the atomic structure of non-crystalline systems, contrast variation techniques for the determination of partial correlation functions, neutrons and x-rays as complementary probes, evaluation of the correlation functions from measured intensities, and small angle scattering experiments with inhomogeneous alloys.

Results of structural investigations are presented for metallic glasses from the two groups: metal-metal glasses, such as Ni-Nb and Ni-Dy, and metal-metalloid glasses, such as Ni-P, Ni-B and Ti-Si. Common features as well as differences are discussed.

The construction of three-dimensional structural models is described as a possibility to overcome the limitations inherent in one-dimensional correlation functions from diffraction.

The distribution of hydrogen in amorphous alloys presents a special topic.

Selfconsistent band structure methods based on the LMTO method are developed and applied for calculations of free energy properties of structurally disordered materials. We study temperature variations of phonon related properties in some 3d, 4d and 5d metals of different structure, by the average scattering method, within the quasi-harmonic approximation. As shown earlier for 4d metals [4], the effect of vibrations on the electronic structure is well described by the average scattering around one single atom. Results for phonon moments and some temperature dependent properties like phase stability are presented for several metals showing polymorphism with temperature and at ordinary pressure. The role of electronic free energies for stabilizing the high temperature bcc phase in Ti and Zr metals and related alloys is analysed.

Two interesting features of the experimentally obtained structure factor are discussed, using the S(Q) of a (model) amorphous silicon sample. In the first part a method is suggested for deciding if the measured data can correspond to a real three dimensional particle arrangement. In the second part it is shown that the Reverse Monte Carlo method is able to provide the correct pair correlation function even if the structure factor is available over only very limited momentum transfer range. The Q range can be as short as 0.4-6 Å⁻¹.

The structure of the metallic glasses Ni₈₀P₂₀ and Ni₈₁B₁₉ was simulated by means of the Reverse Monte Carlo method. The starting configurations for the RMC runs were created by a static version of a Molecular Dynamics algorithm. As basis for the fitting procedure the partial pair correlation functions, as established by neutron diffraction - isotopic substitution experiments, were used, and almost perfect agreement was achieved. From the three-dimensional RMC clusters of 1500 atoms structural properties were deduced, which are not accessible from experimental pair correlation functions. A detailed analysis for the occurrence of distorted trigonal prisms was performed. The degree of trigonal prismatic ordering in the metallic glasses does not exceed substantially that in statistical reference clusters, where the Ni atoms are distributed randomly around the P or B atoms.

Elastic neutron diffraction experiments on amorphous iron, cobalt and their amorphous binary metallic alloys are presented. The measurements allow, for the first time, to describe the atomic distribution in samples obtained in the form of fine (<30 nm) amorphous elemental particles by sonochemical synthesis. In the case of a-Fe, the structural information from the shape of the radial distribution function is consistent with the Random Packing model (RPD) calculations previously made for films of amorphous iron. Finally the atomic magnetic moment of iron and cobalt in the amorphous bulk phase is also evaluated.

Dynamics of the icosahedral phase AlPdMn has been investigated with a centimetre size single grain and using inelastic neutron scattering measurements. Well defined acoustic modes have been observed close to strong Bragg reflections. Phonons broaden significantly as wavevectors exceed 0.35 Å⁻¹. Broad (1 THz) dispersionles excitations also show up with energies close to 1.8, 3.4 and 5.8 THz, some of them being associated to crossing with quasi-Brillouin zone boundaries.

The effects of short-range order for bcc-based Fe-V, Fe-Cr and Fe-Co alloys have been investigated by supercell calculations and approximate self-consistent Linear Muffin Tin Orbital for substitutional disorder. This has allowed us to study the stability and electronic energy properties of ordered superlattices and of random solutions. We analyse the influence of local environment effects on the equilibrium and magnetic properties of the respective alloys. Total energy results show that short range order is important for Fe-Cr and Fe-V so that certain configurations are prefered, while in the Fe-Co system the total energies of several configurations are very close. It also implies that the density-of-states of the FeCo system can be described by the method for substitutional alloys. On the other hand differences in the short range order of FeV or FeCr, have large effects on density-of-states and magnetic order.

Neutron diffraction studies have been made on the newly discovered amorphous transition metal sulfides, MoS_4.65, and WS₅, and the amorphous selenide, CrSe₃. Structure factor data have been transformed to yield the total correlation function T(r). The first four peaks in the T(r) data for the sulfides, MoS_4.65 and WS₅, at around 2.0 Å, 2.4 Å, 2.9 Å and 3.4 Å, are ascribed to the S-S bond length in disulfide (S₂^2-1) groups, the metal-sulfur bond, a metal-metal bond and the first non-bonded S-S distance, respectively. Over a similar range of T(r), the chromium selenide, CrSe₃, shows only two peaks at 2.46 Å and 3.64 Å. In this case, the first peak is made up of a contribution from both the Se-Se distance in diselenide (Se₂^2-) groups and the metal to selenium bond distance. The second peak corresponds to the first non-bonded Se-Se distances. We conclude that the basic structural unit in all these compounds is the octahedral MX₆ group (X = S or Se), and that all the sulfur is found is found in S₂^2- groups. CrSe₃ is more complicated containing both Se^2- and Se₂^2- groups.

The x-ray scattering was measured using a Philips diffractometer, the step-scanning method, molybdenum and copper radiation and a graphite monochromator.

The structural models of graphite- and diamond-type have been tested to describe the type of short-range order in three types of commercial carbon black (CARBEX-330, SAKAP-6, SAPEX-20). The Rietveld refinement was used to fit the experimental diffraction pattern of the carbon black to structural data of those crystalline models. Assuming that the "crystallite" size in the carbon black is comparable with the size of the unit cell of corresponding crystalline model, the line broadening in the Rietveld refinement was modelled. The DBWS-9006PC program was used for calculations of lattice constants and atom positions in unit cell. The best fit was obtained for the graphite-type model.

The radial distribution analysis was made to compare the results with values of atomic distances obtained by the Rietveld method for the graphite-type model. After the background correction (I_b), effects of the polarization (P), the absorption (A), the fluorescence (I_F) and the Compton correction (I_C) we may describe the diffusion x-ray scattering [I^D(k)] as:

I^D(k) = (I_exp − I_b − I_F − I_c)PA

The calculating of radial distribution function (RDF) and pair distribution function P(r) for the carbon black were performed using a computer program on an IBM At computer. The radii of coordinate spheres for the carbon black were determined by the analysis of peak positions of the pair distribution function.

It is shown that diffuse neutron scattering on C₆₀ single crystals is able to provide very detailed information (i) on the short-range order in the high temperature phase and (ii) on the remaining orientational disorder in the low temperature phase. Data analysis based on computer simulation techniques is explained and the results are compared with those of other methods.

We present the results of diffuse neutron scattering experiments on a single crystal of disordered α-VD_0.781 at room temperature. The short range order of the deuterium atoms was described quantitatively in terms of SRO parameters. From these the D-D interaction parameters for a metal hydrogen system were determined for the first time by using the inverse Monte Carlo method.

In the past photon diffraction has been carried out mainly using the characteristic radiation from x-ray tubes in the energy range from about 820keV. Comparison of these experiments with neutron diffraction results is difficult since in this energy range the photoelectric absorption is the predominant process. The photoelectric absorption decreases with λ³, so increasing the energy to about 100keV has a drastic effect on the absorption coefficient. Photons in the high energy range can be obtained conveniently from modern synchrotron sources. High energy photon diffraction has additional further advantages, e.g. the larger accessible Q-range, the diminishing correction terms and the small scattering angles. We report here on a feasibility study on glassy SiO₂ and liquid N-Methylformamide (NMF).

The structures of the two fast ion conducting glass systems (AgI)_x (Ag₂O–2B₂O₃)_1-x and (LiCl)_x (Li₂O–2B₂O₃)_1-x have been examined. The neutron diffraction experiments revealed large similarities in the short range order of the B–O network for the two glass systems. However, remarkable differences are observed for the intermediate range order. This is evident from the low-Q part of the total structure factor; the first sharp diffraction peak (FSDP) at 1.6 Å⁻¹ is almost unaffected by LiCl doping, while in the case of AgI doping a new strong low-Q peak appears at about 0.8 Å⁻¹. To investigate the underlying structural differences Reverse Monte Carlo (RMC) simulations have been performed. The simulations show that the experimental FSDPs are caused mainly by density fluctuations in the B–O network. The anomalous low-Q peak of the AgI doped glasses is thus explained by that AgI locally expands the B–O network and causes longer range correlations between borate groups. The network have larger density fluctuations and voids, which, in turn, are beneficial for the formation of open pathways in which the cations can move.

A combination of results from x-ray and neutron diffraction is used to obtain structural information about the metal-oxygen coordination shell in oxide glasses. Two ways to extract structural parameters of the Me-O coordination are presented. The first variant is a direct combination of both distance correlation functions which are considered simultanously in a least-squares fit procedure. On the other hand a suitable difference of the two structure factors is introduced, which do not contain any O-O correlation. The corresponding distance correlation function directly shows the Me-O peak.

The samples are metaphosphate glasses with Me = Al, Zn, Mg, Ca, Ba and Na and two sodium silicate glasses (76.5 and 67 mol% silicon dioxide). Four oxygens are found in contact to the Mg ion. But two additional, more distant positions are detected. Thus, the sum of all oxygen atoms in the coordination sphere is 6 rather than 4. The Zn cation is located in a real ZnO₄-tetrahedron. The number of oxygens in the environment of the Na ion is of about five both in the metaphosphate glass and in the silicate glasses. But a surprising result is a splitting observed for the Na-O distance peak in case of silicate glasses.

We report on a study of (AgI)_x(AgPO₃)_1–x glasses in which, for the first time neutron diffraction, x-ray diffraction and EXAFS experimental data have been combined quantitatively within a structural model of a disordered material. The Reverse Monte Carlo method has been applied to create seven structural models which have been used to explain the origin of the "first sharp diffraction peak" in this material, about which there has been considerable speculation. The "modified random network" and "diffusion pathway" models are found to be good qualitative descriptions of the structure. Applying a simple free volume model, a percolation transition in the ionic conductivity is observed between x = 0.2 and x = 0.3. A second transition is predicted for x > 0.5 when Ag⁺ ions bridging the phosphate chains cease to form a connected network; the glass-forming limit.

Neutron diffraction studies of AgI doped AgPO₃ glasses show the growth of a sharp diffraction peak at Q ≈ 0.7 Å ⁻¹ with increasing salt content, indicative of a change in intermediate range order. We show that this peak is due to local density fluctuations in the network of PO₄ tetrahedra caused by the requirement to maintain connectivity while decreasing the average density. The phosphate backbone shows an inhomogeneous density distribution over regions of diameter ≈ 16 Å within which the number of atoms in a sphere of radius R increases at a rate lower than R³. It is proposed that this local inhomogeneity is related to the observation of a "phonon-fracton crossover" in the dynamics of similar glasses.

The results of a Reverse Monte Carlo (RMC) modelling of amorphous hydrogenated carbon (a-C:H) are presented. The RMC method has been implemented with the introduction of maximum co-ordination number and "triplet" constraints, whilst fitting both neutron and x-ray diffraction data. The positions of 5000 "atoms" in a box, with full periodicity, are altered until the associated model structure factor, S(Q), and pair distribution function, G(r), agree with the analogous experimental data within the errors. Once the data has been fitted, it is possible to generate model partial pair distribution functions (i.e. those associated with C–C, C–H and H–H), bond angle distributions, co-ordination number distributions, etc. X-ray data is used to provide information on the carbon-carbon network, whilst neutrons are also sensitive to the cross-terms involving hydrogen. The fitting of both types of data simultaneously therefore provides sufficient information to generate a viable "physical" model for the structure of these materials. The effects of increasing the number density inside the box have also been investigated.

The results of complementary inelastic neutron scattering and infrared spectroscopy studies on the structure of amorphous hydrogenated carbon (a-C: H) as a function of temperature are presented, up to a maximum temperature of 1000 °C. These complementary data show that changes in the network structure occur on heating to only 200 °C, with the amorphous network becoming progressively aromatic even before significant hydrogen loss occurs at temperatures above 400 °C. Reference is also made to earlier, diffraction-based studies of the effects of heating a-C: H).

We present a novel application of the use of small-angle neutron scattering to investigate the structure of surface adsorbed polymer surfactant layers on colloidal particles in dispersion. The approach which we use enables separation of surface scattering from background scattering overcoming most of the limitations of previous approaches, and hence should prove to be a wide-spread applicability. This technique is applied to surface-adsorbed dispersing agents on titanium dioxide/toluene dispersions.

Determination of the local structure of a polymer glass by scattering methods is complex due to the number of spatial and orientational correlations, both from within the polymer chain (intrachain) and between neighbouring chains (interchain), from which the scattering arises. Recently considerable advances have been made in the structural analysis of relatively simple polymers such as poly(ethylene) through the use of broad Q neutron scattering data tightly coupled to atomistic modelling procedures. This paper presents the results of an investigation into the use of these procedures for the analysis of the local structure of a-PMMA which is chemically more complex with a much greater number of intrachain structural parameters. We have utilised high quality neutron scattering data obtained using SANDALS at ISIS coupled with computer models representing both the single chain and bulk polymer system. Several different modelling approaches have been explored which encompass such techniques as Reverse Monte Carlo refinement and energy minimisation and their relative merits and successes are discussed. These different approaches highlight structural parameters which any realistic model of glassy atactic PMMA must replicate.

A detailed study of the relationship between chain stiffness and the local structural arrangements in a series of molten Fluorine containing polymers is presented. Four polymers of the form -(CF₂CFX)_n- are considered with X = F, Cl, Br and D together with poly(ethylene), -(CH₂CH₂)_n-. By comparing the experimental structure factor with those obtained from atomistic models quantitative structural parameters are obtained which describe the intrachain structure. The introduction of differing substituents into these Fluorine containing polymers has a marked impact on the nature of the local chain conformation. Using these models of the intrachain structure as a starting point, we have utilised reverse Monte Carlo techniques to derive information on the spatial and orientational correlations between these chains segments in the melt. Somewhat surprisingly the rather anisotropic chains segments of -(CF₂CF₂)_n- show less orientational correlations between near neighbour segments than the rather flexible -(CH₂CH₂)_n- system.

The potential of QENS (quasi-elastic neutron scattering) to study molecular diffusive motions is well established, but in nematic phases it has not measured up to expectations due to the complexities of such systems. In this work we report the results of a detailed analysis of QENS data obtained for partially deuterated ethoxybenzylidene-bis-butylaniline (d-EBBA) in the aligned nematic and isotropic phases. The spectrometer used was IRIS at R.A.L.; such instrument is unique for this purpose in that it features a reasonably extended q-range together with high resolution. Although some problems still remain, we were able to determine unambiguously rotational (spinning) and translational (perpendicular) diffusion coefficients and their temperature behavior, and analyse some possible rotational diffusion models in the light of the experimentally determined EISF (Elastic Incoherent Structure Factor).

Clear evidences of strong H-bond interactions, that occur in pure molecular Ethylene Glycol (EG), in pure polymeric Poly-Ethylene Glycol (PEG), with mean molecular weight of 200 Da, (PEG200) and in their aqueous solutions, are presented. The experimental result refers to IQENS and compressibility measurements in the liquid phase. All the results can be interpreted if H-bond forces are taken into account. The diffusive motion of protons for the smallest molecules (EG) is well analyzed in the framework of the random jump diffusion model both for pure and aqueous solutions. This motion becomes strongly hindered, giving rise to the spectral features that are typical of translational diffusion in confined region, in the case of aqueous solution of PEG200. Finally a not ideal mixing behaviour is detected by analyzing the compressibility evolution as a function of concentration, when the aqueous solutions are considered.

Neutron single crystal diffuse scattering from D₂O ice Ih has been measured over large regions of reciprocal space on the SXD diffractometer at ISIS. This scattering shows additional features to those predicted solely on the basis of deuteron disorder within the Bernal-Fowler rules. A reverse Monte Carlo modelling technique has been developed for use with single crystal diffuse scattering, and has allowed extensive information to be obtained about the structure of ice Ih.

In small-angle neutron scattering (SANS) experiments, realized on the MURN facility of the pulsed reactor IBR-2 of the Frank Laboratory of Neutron Physics at the Joint Institute for Nuclear Research, Dubna, the hydration processes in samples of ordinary Portland cement (OPC) and single clinker minerals are studied. The measured scattering curve contains information about the fractal behaviour of the interfaces and the size distribution of the scattering particles. Furthermore, a variation of the heavy and light water composition for the hydration water supports the selection of the observable microstructural objects. In dependence on the size distribution of the clinker grains a various time-dependent behaviour of the potential law of the scattering curve is shown. Considering the SANS results of hydrating OPC the exponents of the scattering curve in a given Q-range are varying in dependence on the hydration time and sample thickness. They lie in an interval from about −2 to −4. This is believed to be associated with fractal behaviour. A set of four hydrating C₃S-samples is divided into 2 parts after an under water storage of 53 days. Then 2 samples were stored in an H₂O/D₂O-mixture for reducing the variety of the several hydration products by changing the neutron optical contrast. Considering the time-dependent change of the potential law of the scattering curves of hydrating C₃S-samples some differences in contrast to hydrating OPC powder are visible. Within about 100 days after mixing the dry C₃S powder with water the exponents of the SANS curves in the measured Q-range are higher than −3. If the hydration products of C₃S are forming fractal structures then volume or mass fractals of some nanometers are shown.

A neutron tomography technique with a coordinate resolution of several tens of micrometers has been developed. Our results indicate that the technique resolves details with dimensions less than 100μm and measures a linear attenuation of less than similar 0.1 cm⁻¹. Tomograms can be reconstructed using incomplete data. Limits on the resolution of the restored pattern are analyzed, and ways to improve the sensitivity of the technique are discussed.