Guinier Radius Research Articles

Small-Angle Neutron Scattering Study of Phase Decomposition in Fe–Cu Binary Alloy

Small-angle neutron scattering (SANS) measurements were carried out in order to investigate the structure change during early stage of phase decomposition in an Fe-1. 17 at% Cu alloy. The integrated intensity first increased and then saturated beyond 2.10 4 s aging at 773 K, while the Guinier radius increased with the time exponent of 1/3, emphasizing the coarsening process of precipitates. The peak hardness was observed, when the Guinier radius reached 2.8 nm. The intensity ratio of magnetic scattering component to nuclear one has been analyzed in terms of chemical composition and internal structure of precipitates

Phase separation in a ti—al—mo alloy studied by anomalous small-angle x-ray scattering a synchrotron radiation experiment

Abstract The mode of decomposition of the ordered β2 phase (B2) at 450°C of the alloy Ti-21·6Al-3·4Mo has been studied by transmission electron microscopy (TEM) and anomalous small-angle X-ray scattering performed at the K Ti absorption edge. TEM observations have shown that the precipitation occurs according to a two-phase system, and the α2 spherical precipitates are embedded in a B2 matrix. In order to calculate the composition of both phases some parameters such as the Guinier radius R G, the spherical excluded volume (or diameter D), the number of scattering precipitates per unit volume Nv have been determined by fitting the theoretical scattered intensity curves derived from a two phase model of precipitation to the experimental data. The composition of α2 and β2 phases is fairly constant with the ageing times considered. The plot of the ternary diagram shows that the α2 precipitates are slightly depleted in aluminium with ageing time as compared with the B2 matrix.

Preparation and Characterization of Microporous Sol-Gel Derived Ceramic Membranes for GAS Separation Applications

ABSTRACTMesoporous alumina membranes were modified with microporous silica. The polymeric silica sols consist of very weakly branched polymeric molecules with a fractal dimension of 1.3 and Guinier radius of ≈ 2.0 nm. The resulting top layer material is microporous with a porosity of 40% and a layer thickness of 60 nm. Gas transport is activated with an activation energy of 11 kJ/mol for hydrogen and molecular sieve like separation factors have been obtained. From the mechanism of gas transport the conclusion can be drawn that the pores are of molecular dimensions (0.7 – 1 nm diameter).

Ion aggregation in magnesium‐neutralized polyester resins — Small angle X‐ray scattering study

AbstractEvidence for ion aggregation was found in SAXS studies of models of unsaturated polyester resins: magnesium icosanoate, magnesium α,ω‐dicarboxylatopoly(ethylene adipate), ‐poly(1‐hexylethylene adipate), ‐poly(propylene succinate), and ‐poly(propylene maleate‐co‐fumarate), swollen by various solvents or in the dry state. The results were compared with those obtained for commercial unsaturated polyester resins after neutralization with MgO, leading to the conclusion that the formation of aggregates is the key phenomenon of the so‐called thickening reaction of polyester resins. The existence of high amounts of branched units in the polyester chain does not appear to hinder ion aggregation. The aggregates are small (Guinier radius RG = 4 to 9 Å) and their average distance increases with chain length and swelling.

Effect of Hydrolysis Conditions on the Polycondensation of Al-O-Si Alkoxide

A hydrolysis-condensation reaction of Al-O-Si alkoxide complex was analyzed by in both the mass fractal dimension and the Guinier radius in small angle X-ray scattering curves. The Al-O-Si alkoxide which was synthesized by reacting Al(OC4H9)3 with hydrolyzed Si(OC2H5)4 consisted of chain-like polymers. When metal alkoxide was hydrolyzed with 0.0082mol of HCl or NH4OH per 1mol metal alkoxide, both the mass fractal dimension and the Guinier radius increased in proportion to an increase in the water content, and reached 2.5 and 80A, respectively, at 4mol water per 1mol metal alkoxide. Under the HCl catalyst, both the mass fractal dimension and the Guinier radius decreased up to 1.8 and 20A, respectively, with increasing HCl concentration, indicating that the three-dimensional branched polymers disaggregated into the chain-like polymers. On the other hand, under the NH4OH catalyst, both the mass fractal dimension and the Guinier radius showed the fixed values of 2.5 and 80A, respectively, irrespective of NH4OH concentration.

Influence of the increasing content of Mo on the precipitation phenomena occurring during tempering in the maraging alloy Fe-12Mn-9Co-5Mo

The influence of the increasing content of Mo from 5 to 8 wt% on the precipitation phenomena occurring in the temperature range 400–500°C in the maraging type alloy with Mn having the following composition: 74Fe-12Mn-9Co-5Mo has been studied by microhardness tests, Mössbauer spectrometry, transmission electron microscopy (TEM) and classical (SAXS) and anomalous (ASAXS) small angle scattering of X rays. We have shown that the precipitation process is entirely modified in the stage II when the Mo content reaches 8 wt%. Indeed, instead of observing the successive or simultaneous precipitation of intermetallic compound Fe 2Mo as well as the ordered isothermal ω phase (alloy with 5 wt% Mo), we have only noted the precipitation of a new compound as referred to X, the crystalline structure of which is hexagonal ( c a = 3.255 ) and which contains iron. The growth kinetics of the quasi-spherical precipitates of the compound X obeys power laws of the type: R G (Guinier's radius) ∝ t α with 0.23 ⩽ α ⩽ 0.27.

Gelation study of alumino-silicates by small-angle neutron scattering

We present results concerning the structure of clusters and the kinetics of aggregation obtained by SANS for different compositions in the H2O, HOiPr, (BuO)2Al-O-Si(OEt)3 system.Information about the growth kinetics has been obtained from the time dependence of the Guinier radius, of the maximum intensity on the scattering curve and of the integral of the intensity over the reciprocal space. We observe, in agreement with 29Si NMR data, that the hydrolysis of the Si-OR groups is the rate-determining process for the polymerization.Information about the internal structure of the structure of the clusters has been obtained from the Porod slope, and about the particle interactions by calculation of the structure factor S(Q). Before the gel point, we observe mass-fractal particles characterized by a fractal dimension of 1.9, in agreement with the existence of a cluster-cluster aggregation mechanism during the gelation.The scattering curves which exhibit a maximum intensity have been fitted using a hard sphere model and a preliminary coarse description for the fractal particles which seems to show that the correlations are due to purely excluded-volume effects.

Hydrolysis-Condensation of Zr-O-Si Alkoxides

A Zr-O-Si alkoxide complex was synthesized and its hydrolysis-condensation reaction was studied using small angle X-ray scattering. Transparent and homogeneous Zr-O-Si alkoxide solutions were formed by reacting Zr(OC3H7)4 with Si(OC2H5)4 hydrolyzed with one mole of water per one mole of Si(OC2H5)4 and HCl catalyst, whereas the solutions hydrolyzed with NH4OH catalyst or without any catalyst resulted in precipitation of ZrO2 crystals. Homogeneous Zr-O-Si alkoxide solutions were hydrolyzed with 0 to 8 moles of water to metal alkoxide, whose X-ray scattering curves were analyzed in both power law and Guinier law. The synthesized Zr-O-Si alkoxide consisted of chain like polymers, which were aggregated into three dimensional branched polymers with water content up to 4 moles per 1 mole metal alkoxide and their size increased up to 65A in the Guinier radius. However, no further changes in size and shape of aggregated polymers were observed with more than 4 moles of water.

Early stage of phase decomposition in an Al-6.7 at% Zn alloy

Abstract The early stage of phase decomposition in Al-Zn alloy has been studied by means of in-situ small-angle scattering using synchrotron radiation. From the analysis of structure factors, the decomposition process of this alloy could be divided into three stages. It was made clear that stage I is the growth process of clusters due to the regime proposed by Binder and Stauffer. Stage II is the process of Ostwald ripening and stage III is one of slowing-down processes of phase decomposition. At stage I, the normalized intensity decreased with increasing volume fraction of clusters. At stage II, where the volume fraction became constant, the structure factor was scaled by using a single parameter of either the Guinier radius or interparticle distance, but it also depended on the volume fraction.

Estimation of the dimensions of micropores in active carbons using the Dubinin-Radushkevich equation

Decreases in the characteristic energy of the Dubinin-Radushkevich equation, E 0, are correlated with increases in micropore sizes determined by molecular probes, W m , using the empirical equation W m = 4.691 exp(−0.0666 E 0); a similar equation can also be used to correlate the more limited data relating E 0 to the Guinier radius of gyration, R g . A new, semiempirical method is proposed which relates E 0 to micropore sizes calculated from adsorption potentials in slit-shaped, model micropores. The two methods for estimating micropore size are applied to adsorption of Ar at 77 K on a steam-activated series of polymer carbons. Both methods show that micropore sizes increase progressively with activation, but for each carbon, the micropore size estimated from molecular probes is greater than that obtained using potentials in model micropores. The differences are attributed to different weightings of the pore size estimates in the micropore size distributions. Estimates based upon molecular probes are weighted towards the tail of the distribution, while those based on model pore potentials are weighted towards the smallest micropores. A method for estimating the size range of micropores is proposed where the lower limit is defined by the adsorption potential maximum in model pores and the upper limit is defined by the correlation between W m and E 0.

Al-Zn合金の時効に及ぼす試料厚さの影響

Effect of the specimen thickness on the aging of Al-4 and 10 mass%Zn alloys was studied by measurements of the electrical resistance and the intensity of small-angle X-ray scattering (SAXS). When the quenching temperature (TQ) was high, the value of resistance attained when it substantially stopped to change in the aging process, was not influenced by the specimen thickness. In the case of low TQ, the resistance was higher for the thin specimen, caused by impoverishment of vacancies. The integrated intensity of SAXS depended neither on the thickness nor on TQ when TQ≥673 K, but it decreased with decreasing thickness and with decreasing TQ when TQ≤613 K. Both Guinier radius and Porod radius for the specimen of 0.1 mm thickness were smaller than those for the one of 0.2 mm thickness when TQ was low, but they became independent of thickness when TQ was higher than 673 K. The quenching temperature at which Guinier radius was maximum, was higher for the 0.1 mm thick specimen than that for the 0.2 mm thick one. These results have been discussed from the viewpoint of the diffusion of vacancies to the surface and their annihilation during aging.

Dynamical structure change during reversion in AlZn binary alloy

To give information on the dynamical property of reversion phenomena in Al-Zn alloy, time-resolved small-angle X-ray scatterings have been measured using synchroton radiation. The time-dependent dissolution rate of G.P. zones is well described by the Johnson-Mehl-Avrami equation. The experimental time-exponent and temperature-dependent relaxation time deviate largely from expectations, suggesting that the reversion process is not controlled by the diffusion of solute atoms in the matrix. It has been found that Guinier radius increases slightly during reversion.

The interpretation of structure functions in quenched binary alloys

We study the segregation process in quenched binary alloys by analyzing and comparing the time evolution of the structure function and of the grain distribution obtained from computer simulations on a model system. We find good agreement between cluster sizes and densities determined directly on the computer sample and ones obtained by the Guinier method from the structure function. We then describe a graphical method for determining the scaling behaviour of the structure function S( k, t) which gives good statistics because the whole curve S( k, t) vs k is used. This yields very good agreement between the scaling function (scaled with the Guinier radius) obtained from the computer simulations and from a variety of real experiments. This function shows a universal behaviour independent of the alloy composition, the temperature and even the substance investigated. Our results are also not consistent with the more recent theoretical work (Binder et al., Furukawa et al.) which give alternate derivations and extensions of the Guinier formulas.

Experimental Observation of a Time-Scaling Characteristic in Alloy Decomposition in the AlZnMg System

Neutron-scattering results on the decomposition in two AlZnMg alloys, after three different quenching procedures and for three annealing temperatures, can be represented by an unique curve if reduced variables for Guinier radius, $\ensuremath{\rho}=\frac{{R}_{G}(t)}{{R}_{0}}$, and the volume fraction of clusters, $v=\frac{V(t)}{{V}_{\ensuremath{\infty}}}$, are used. The invariant curve $\ensuremath{\rho}$ vs $v$ reflects predominant nucleation at the beginning---i. e., increase of volume fraction connected with a small variation of ${R}_{G}$---and the coarsening regime when the equilibrium volume fraction is approached.

A neutron scattering investigation of the early stages of guinier-preston zone formation in AlZnMg(Cu)-alloys

A diffuse neutron scattering investigation of the early stages of the Guinier-Preston zone formation in AlZnMg(Cu)-alloys has been made. All samples show at smaller wavevectors (<1 Å −1) elastic diffuse intensity which can be described by two Guinier radii. The smaller radius does not change with annealing time and may indicate the presence of small ‘nuclei’, unaffected by the further decomposition. The larger radius, however, shows a considerable time dependence and characterizes the size of the Guinier-Preston zones. For larger annealing times normal growth was found, but for times just after quench a decrease of the radius was observed. This decrease may be explained in the following way: just after quench greater but dilute Guinier-Preston zones form, which with time become smaller and denser. Only after this initial compactification the normal growth starts.

Small-angle neutron scattering measurements on micellar solutions of sodium alkylbenzenesulfonates having branched alkyl groups

The normal spherical micelles formed by sodium p-(1-pentylheptyl)benzenesulfonate have Guinier radii (R/sub G/), as determined by small-angle neutron scattering (SANS), of 13.7 to 16.6 A in the concentration range 0.0099 to 0.0991 M in D/sub 2/O at 45/sup 0/C. Scattering curves for the more concentrated solutions show an interaction peak which is undoubtedly due to micelle-micelle repulsion. A longer-chain homologue, sodium p-(1-heptylnonyl)benzenesulfonate (also called Texas No. 1), for which there has previously been some question about micelle formation, is also shown to form small, normal micelles (R/sub G/ = 17 A) in aqueous solution.

Al-4 mass%Cu合金の時効初期におけるX線小角散乱

A series of small-angle X-ray scattering photographs with monochromated and point focussed copper Kα1 radiation was taken of a single crystal of an Al-4 mass%Cu alloy at the as-quenched state from 823 K and at successive stages of ageing at 313 K. The crystal was so oriented that the incident direction of the radiation was along [001] axis, and was cooled with liquid nitrogen during the exposure.The pattern of the as-quenched state was homogeneous, but each of the patterns of the aged states consisted of streaks along [100] and [010] directions and a quasi-ring around the trace of the incident beam on the film (even at the shortest ageing time, 16 s). The most intense regions were found in [100], [010], [\bar100] and [0\bar10] directions on the ring. With the progress of the ageing the streaks and the ring became more intense and narrower.The results can be interpreted from points of view of the formation of the G.P. zones parallel to {100} planes ab initio, the effect of the inter-particle interference on scattering of X-rays, and the growth of the G.P. zones with the ageing. Guinier radius of the G.P. zones at each stage can be obtained from intensity change along [110], and the values are reasonably consistent with those obtained from the cross section of the streak. The presence of multilayer zones, besides the one-layer ones, is suggested from the humps found on several intensity curves along [100] at later stages.

Effect of cold working on precipitation behaviour in superconducting Ti-Nb alloys

Abstract The precipitation behaviour in thin foils and wire specimens of Ti-Nb alloys has been investigated mainly by means of small-angle X-ray scattering measurement but also by tramsmission electron microscopy. The small-angle diffuse scattering was observed in the later stage of ageing and it was concluded that α particles formed. The change of relative integrated intensity and Guinier radius was measured during ageing. The integrated intensity in the alloys aged after cold working was rather larger than that in the alloy without cold working, but in contrast the Guinier radius became smaller. The cold working was found to accelerate the precipitation of the α phase. The relative interparticle distance became constant after short term ageing for all specimens with various rates of cold working. A commercial quaternary alloy, Ti-27 at.% Nb-5 at.% Zr-5 at.% Ta, was also examined. Its precipitation behaviour was similar to that of the binary alloys and it produced the largest integrated intensity in smal...

Investigations on the growth kinetics of GP zones and a′R‐precipitates in Al‐Zn alloys

AbstractX‐ray small‐angle scattering (XSAS) and resistivity (R) measurements were particularly done with an Al‐Zn (15 at·,%) alloy in rather wide ranges of both the ageing time ta and ageing temperature Ta, in order to obtain information on the dependence of the growth exponent m of the l = β0tm growth law and the activation energy Eact on ta and Ta.The XSAS‐measurements yielded that within the range of the GUINIER radius rG between 1 nm and 2 nm the growth is essentially retarded (m &lt; 0.1) and for rG &gt; 2 nm m depends on Ta ranging from 0.15 to 0.23 with a maximum at 175°C. Reasons for these effects are discussed. The differences between the m‐values obtained by means of XSAS‐and TEM‐measurements are explained by the distinctions of the two methods applied.The Eact taken from XSAS‐ and R‐measurements show a remarkable increase with ta. At the beginning of the decomposition Eact = (0.49 ± 0.05) eV holds well explainable by the migration of quenched‐in VZn pairs, but at the end Eact = (1.05 ± 0.07) eV was found. This value was also obtained from TEM‐investigations (growth of the length). It fits well the Eact of ZnV pairs in thermal equilibrium at Ta.

Electrical resistivity of η′ precipitates in an Al-Zn-Mg alloy

Abstract The resistivity increment caused by η′ particles has been investigated as a function of their size in an Al-4.8 wt.% Zn-1.26 wt.% Mg alloy. It is found that the resistivity increment due to each particle is a linear function of R G 3, where R G is the Guinier radius of the particle.