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Showing papers on "Grain size published in 1997"


Journal ArticleDOI
TL;DR: In this paper, the grain size of soil and sediment samples is determined by the sieve method for the coarse fractions and by the pipette method, based on the Stokes sedimentation rates, for the fine fractions.
Abstract: Classically, the grain size of soil and sediment samples is determined by the sieve method for the coarse fractions and by the pipette method, based on the ‘Stokes’ sedimentation rates, for the fine fractions. Results from the two methods are compared with results from laser diffraction size analysis, which is based on the forward scattering of monochromatic coherent light. From a point of view of laboratory efficiency, the laser sizing technique is far superior. Accuracy and reproducibility are shown by measurements on certified materials. It appears that laser grain size measurements of certified materials correspond very well with the certificated measurements. Tests were also done on a set of randomly selected sediments of fluvial, aeolian and lacustrine origin. Except for the (<2 μm) clay fraction, there is a coarsening of the mean diameter of one to two size classes (0.25 ɛ), caused by the non-sphericity of the particles. The platy form of the clay particles induces considerable differences (eight size classes) between pipette and laser measurements: the <2 μm grain size, defined by the pipette method corresponds with a grain size of 8 μm defined by the Laser Particle Sizer for the studied sediments. Using a higher grain size level for the clay fraction, when laser analysis is applied, enables workers in the geological and environmental field to compare classical pipette analysis with a laser sizing technique.

990 citations


Journal ArticleDOI
TL;DR: The elastic and tensile behavior of high-density, high-purity nanocrystalline Cu and Pd was determined in this paper, showing that porosity increases with decreasing porosity, and may be significantly affected by a few large processing flaws.

791 citations


Journal ArticleDOI
TL;DR: In this article, the development of an ultra-fine grain size during equal-channel angular (ECA) pressing of high purity aluminum with an initial grain size of ∼1.0 mm was investigated.

759 citations


Journal ArticleDOI
TL;DR: In this article, the formation of deformation induced high angle boundaries is suggested based on grain subdivision processes which can lead to formation of different texture components within an original grain, and the distribution of their misorientations is estimated based on these mechanisms.

744 citations


Journal ArticleDOI
TL;DR: In this paper, the authors identify the factors responsible for good charge-discharge capacity retention in Li-ion cells, using results of experiments on Li/Sn{sub 2}BPO{sub 6} and Li/snO{ sub 2} cells.
Abstract: Tin oxide composite glasses represent a new class of material for the anode of Li-ion cells. Using results of experiments on Li/Sn{sub 2}BPO{sub 6} and Li/SnO{sub 2} cells, the authors identify those factors which are responsible for good charge-discharge capacity retention. First, the grains (those regions which diffract coherently) which make up the particles of the material should be as small as possible. Then, regions of tin which form are kept small and two-phase coexistence regions between bulk Li-Sn alloys of different composition do not occur. The Sn{sub 2}BPO{sub 6} glass represents the smallest grains possible. Second, the particles themselves should be small so that they can each be well contacted by carbon black during electrode manufacture. Third, the voltage range of cycling must be selected so that the tin atoms do not aggregate into large regions which grow in size. This aggregation is evidenced by the growth of peaks in the differential capacity vs. voltage as a function of cycle number. The peaks represent the coexistence between bulk Li-Sn alloy phases which have substantially different volumes. The coexistence is thought to cause fracturing and loss of contact between the grains. Therefore, materials with small particles, small grains, and smoothmore » sloping voltage profiles which do not change with cycle number (as indicated by a stable differential capacity) give the best cycling performance. The selection of the voltage limits for cycling strongly influences the stability of the voltage profile (as illustrated here), so this must be done with much care.« less

595 citations


Journal ArticleDOI
TL;DR: In this article, the thermodynamics and kinetics of hydride formation in a nanocrystalline alloy are presented, as well as the effect of catalyst particles at the surface of the metal.

408 citations


Journal ArticleDOI
TL;DR: In this paper, the fabrication of several pure metals and alloys with nano-and submicrometer grain sizes by severe plastic deformation techniques, the results of their structural characterization, and data on their mechanical properties at ambient temperature and superplastic conditions.
Abstract: This paper describes the fabrication of several pure metals and alloys with nano-and submicrometer grain sizes by severe plastic deformation techniques, the results of their structural characterization, and provides data on their mechanical properties at ambient temperature and superplastic conditions. Special attention is paid to the relationship between the defect structures of grain boundaries and the mechanical behaviour of produced ultrafine-grained metallic materials.

352 citations


Journal ArticleDOI
TL;DR: In this paper, the thickness of a traction-carpet stratum is determined by the cumulative amount of sediment settled during the lifespan of a moving traction carpet, and the thickness ratio is further controlled by applied shear stress, sediment fallout rate, and grain size.
Abstract: Traction carpets are highly concentrated bedload layers that are developed beneath and driven by turbulent overlying flows. They have a "convex-up" velocity profile and comprise a lower frictional and an upper collisional region. The frictional region, having a particle concentration more than 80% of the packed bed, is characterized by nearly continuous grain contacts, low strain rate, and hampered grain segregation. On the other hand, the collisional region has a particle concentration between 15% and 80% of the packed bed and is characterized by active grain collisions and higher strain rate. Deposition from the traction carpets occurs via progressive aggradation of the bed, rather than via en masse freezing, while the downward grain flux from the overlying flow maintains them. The thickness of a traction-carpet stratum is therefore determined by the cumulative amount of sediment settled during the lifespan of a traction carpet and can be much larger than the thickness of a moving traction carpet. Inverse grading can be produced in the collisional region by the vertical gradient of dispersive pressure, which is related to nonuniform distribution of particles. When a thick frictional region develops, however, the inverse size distribution in the collisional region is poorly recorded in the deposits. Depositional features of traction-carpet strata are therefore determined by the duration of a traction carpet and the thickness ratio of collisional to frictional regions. The thickness ratio is further controlled by the applied shear stress, sediment fallout rate, and grain size. Generally, a collisional region is better developed beneath a highly competent and coarse-grained (gravelly) flow, whereas a thick frictional region is developed beneath a heavily sediment-laden fine-grained (sandy) flow. This explains the more common occurrence of inverse grading in coarse-grained deposits.

311 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of ppm level H2 on the d.c. resistance of a planar resistor with SnO2 particle size variation (∼ 20 to 50 nm) is reported.

284 citations


Journal ArticleDOI
TL;DR: In this article, the authors demonstrate the existence and domain of partial transport using observations of grain entrainment on time series of bed photographs of flume experiments with a widely sorted sand/gravel mixture.
Abstract: Grains of a single size within a mixed-size bed are entrained over a range of flows. Within this range some grains exposed on the bed surface are active (entrained at least once over the duration of a transport event), while the remaining surface grains are immobile, a condition we define as partial transport. We demonstrate the existence and domain of partial transport using observations of grain entrainment on time series of bed photographs of flume experiments with a widely sorted sand/gravel mixture. The active proportion of the bed surface increases with bed shear stress τ0. At a given τ0, 90% of the active grains are entrained when the cumulative mass transported exceeds approximately 4 times the active mass on the bed. Mobilization of grains in a size fraction increases from 10% to 90% over a range of τ0 of a factor of 2. The bounds of this range increase with grain size Di so that at a given τ0, sizes over a range of a factor of 4 are in a state of partial transport. Fractional transport rates are independent of Di for fully mobilized fractions and decrease rapidly with Di for partially mobile fractions. Partial transport is associated with substantial transport rates of finer, fully mobile sizes, limits both the rate and size distribution of grain exchange with the bed subsurface, and may be the dominant transport condition in many gravel-bed rivers.

278 citations


Journal ArticleDOI
TL;DR: A C-rich sediment sample from the Peru Margin was sorted into nine hydrodynamically-determined grain size fractions to explore the effect of grain size distribution and sediment surface area on organic matter content and composition as discussed by the authors.

Journal ArticleDOI
TL;DR: The low-energy cluster beam deposition technique (LECBD) is applied to produce cluster assembled films with hitherto unknown nanostructured morphologies and properties as discussed by the authors, which can be applied to various fields of applications such as optical and optoelectronic nano-structures, magnetic and magneto-optic nanostructure and quantum devices.
Abstract: The low-energy cluster beam deposition technique (LECBD) is applied to produce cluster assembled films with hitherto unknown nanostructured morphologies and properties. Neutral clusters having the very low energy gained in the supersonic expansion at the exit of the inert gas condensation-type source are deposited without fragmentation upon impact on the substrate. Depending on the deposition conditions (nature, size and flux of incident clusters, nature and temperature of the substrate, vacuum conditions), granular nanostructures resulting from the diffusion and coalescence of supported clusters are obtained with materials of any type (covalent or metallic). A critical size for coalescence limits the supported grain size and, finally, highly porous thick films growing by random stacking of nanoparticles are obtained. A recent model developed by combining several dynamical processes simultaneously occurring on the substrate (deposition - diffusion - aggregation, DDA) is used to simulate the cluster assembled film morphology in good agreement with the experimental observations. Examples of novel materials obtained by LECBD are presented to illustrate the interesting potentialities of the technique. In the case of covalent materials such as carbon and silicon, 'amorphon'-type disordered structures, different from the conventional amorphous structures (a-C and a-Si), are obtained with some unique properties. With transition metal (Fe, Co and Ni) cluster assembled films, a specific magnetic behaviour, resulting from the competition between the intrinsic properties of the grains (magnetocrystalline anisotropy) and the interactions between grains, is observed. Also, films of clusters embedded in various co-deposited matrices are produced in order to control the interactions between grains via the matrix materials (insulating, conducting ...). Interesting optical properties (from metallic clusters in ) or giant magnetoresistance effects (from Co clusters in silver) are reported for such systems, emphasizing the future role of LECBD in various fields of applications such as optical and optoelectronic nanostructures, magnetic and magneto-optic nanostructures and quantum devices.

Journal ArticleDOI
01 Mar 1997-Nature
TL;DR: In this paper, the authors found that the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains had larger angle of repose than the small grains.
Abstract: Granular materials1–5 segregate according to grain size when exposed to periodic perturbations such as vibrations6–12. Moreover, mixtures of grains of different sizes can also spontaneously segregate in the absence of external perturbations: when such a mixture is simply poured onto a pile, the large grains are more likely to be found near the base, while the small grains are more likely to be near the top13–20. Here we report another size-separation effect, which arises when we pour a granular mixture between two vertical plates: the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains have larger angle of repose than the small grains. We find only spontaneous segregation, without stratification, when the large grains have smaller angle of repose than the small grains. The stratification is related to the occurrence of avalanches: during each avalanche, the grains separate into a pair of static layers, with the small grains forming a sublayer underneath the layer of large grains.

Journal ArticleDOI
TL;DR: The magnetic properties of the ball-milled sample are similar to those of ferrimagnetic MgFe2O4 powders having comparable grain size and inversion parameters as mentioned in this paper.
Abstract: Fine powders of ZnFe2O4 with an average particle size of 10 nm and inversion parameter of 0.21 were synthesized by the aerogel procedure. Portions of the powders were calcined in air at 500 and 800 °C and other portions were ball-milled for 10 h. The materials were characterized by x-ray diffractometry, vibrating sample, and SQUID magnetometry, Mossbauer spectrometry, and low temperature calorimetry. Upon calcination the powders underwent significant changes in grain size, inversion parameter, and hence magnetic properties. The magnetic state of the as-produced and calcined samples is best described as disordered and highly dependent on temperature. Upon ball-milling the grain size varied widely and the inversion parameter attained a value of 0.55. The magnetic properties of the ball-milled sample are similar to those of ferrimagnetic MgFe2O4 powders having comparable grain size and inversion parameters.

Journal ArticleDOI
TL;DR: In this paper, the effects of the number of extrusion passes and deformation route for multipass ECAE with billet orientation constant (route A) or rotated 90 deg between all passes (route B) were studied.
Abstract: A technique invented in the former Soviet Union and recently introduced in the United States, called equal channel angular extrusion (ECAE), produces intense and uniform deformation by simple shear and is applied to 25 × 25 × 152-mm billets of Cu 101 and Al 3003. Microcrystalline structures with a grain size of 0.2 to 0.4 µm are created during room-temperature multipass ECAE deformation for true strains lying in the range e=2.31 to 9.24. Evidence shows that intense simple shear deformation promotes dynamic or continuous recrystallization by subgrain rotation. The effects of the number of extrusion passes and deformation route for Cu 101, and the deformation route after four passes for Al 3003, are studied. Increasing the number of ECAE passes in Cu 101 causes strength to reach saturation and grain refinement stabilization after four passes (true strain of 4.68), and subgrain misorientation to increase as the number of passes increases. For multipass ECAE with billet orientation constant (route A) or rotated 90 deg between all passes (route B), two levels of structures are created inside the original grains: shear bands (first level) and very fine subgrains (second level) within the shear bands. For a billet rotation of 180 deg between passes (route C), an unusual event is observed. At each even numbered pass, shear bands nearly disappear and only subgrains are present inside the original grains. Route B gives the highest strength, whereas route C produces a more equiaxed and stable microstructure. Subsequent static recrystallization increases the average grain size to 5 to 10 µm.

Journal ArticleDOI
TL;DR: In this paper, textured textured WS2 and MoS2 films are obtained by the techniques of reactive sputtering and solid state reaction, as long as the substrates used are each coated with a 10-20 nm Ni layer.

Journal ArticleDOI
TL;DR: In this article, the defect evolution in nanocrystalline Pd and ZrO2 during energetic particle irradiation is examined with emphasis on the correlation of defect density to the grain size.
Abstract: The microstructural defect evolution in nanocrystalline Pd and ZrO2 during energetic particle irradiation is examined with emphasis on the correlation of defect density to the grain size. Nanocrystalline bulk Pd and ZrO2, synthesized by the inert gas condensation technique with different initial grain sizes, ranging from 10–300 nm were irradiated using 4 MeV Kr ions with fluences from 1 × 1015 to 2 × 1016 Kr/cm2. The defect density was studied by cross-sectional transmission electron microscopy (TEM). A correlation between grain size and defect density was found showing drastic reduction of defect clusters in the small grains below 50 nm. In the smallest ZrO2 (

Journal ArticleDOI
TL;DR: In this article, the possibility of grain size control in indium oxide-sensing layers has been established by using of two preparation methods (electron beam evaporation (EB) and sol-gel technique (SG).
Abstract: In2O3 thin films prepared by sol–gel method make it possible to detect low levels (several hundreds ppb) of nitrogen dioxide in air. The possibility of grain size control in indium oxide-sensing layers has been established by using of two preparation methods—electron beam evaporation (EB) and sol–gel technique (SG). SG-prepared samples show smaller particles sizes (down to 5 nm), higher state of agglomeration, higher sensor resistance in air and higher response to NO2 in comparison to EB samples. Sol–gel technique leads to the preparation of polycrystalline indium oxide with particle sizes of about 5–6 nm after calcination at 400°C and 20 nm after calcination at 700°C. The initial state of particle agglomeration in initial indium hydroxide sol (IHS), stabilized with nitric acid, influences the structure and surface morphology of the resulting indium oxide. While the In2O3 layer prepared by using low agglomerated IHS is smooth and porous, In2O3 layers prepared from highly agglomerated IHS consist of two regions—thin layer and crystallite agglomerates in cubic and rectangular parallelepiped form. The last shows the best results in terms of NO2 sensitivity. Sensor resistance and NO2 sensitivity increase with the decrease of the grain sizes in In2O3.

Journal ArticleDOI
TL;DR: In this paper, an AZ91 alloy with a very small grain size of about 1 μm was processed by ECAE and showed a large elongation of 661% at a low temperature of 473 K, which is 0.5Tm.

Journal ArticleDOI
TL;DR: In this article, it was shown that during cooling of pelitic rocks from amphibolite facies conditions, typical aluminous peak parageneses of garnet-muscovite-kyanite ± biotite may react to form either staurolite, chlorite, or muscovitic (or different combinations thereof) depending on grain size.
Abstract: Diffusive processes are a strong function of temperature. Thus, during cooling of rocks, mineral grains may develop zoning profiles as successively larger parts of the grain “close” to the diffusive exchange with the rock. One of the consequences of this process is that, during cooling, successively larger parts of zoned minerals (depending on grain size) are effectively removed from the reacting part of the rock volume. Thus, the effective bulk composition of metamorphic rocks changes during cooling and the rate of its change will be a function of grain size. Because the sequence of metamorphic reactions seen by a given rock is a strong function of its bulk composition, this process may have the consequence that two rocks of identical overall bulk composition, but of different grain size, may experience a different sequence of reactions. Qualitatively identical peak paragenesis may therefore react to form qualitatively different retrograde reaction textures. The model is applied to examples in the pelitic system. There, garnet is usually the slowest diffusing phase developing zoning profiles during cooling and the effective removal of garnet from the reacting rock volume will cause changes of the effective bulk composition. It is shown that, during cooling of pelitic rocks from amphibolite facies conditions, typical aluminous peak parageneses of garnet-muscovite-kyanite ± biotite may react to form either staurolite, chlorite or muscovite (or different combinations thereof), depending on grain size. During cooling from the granulite facies, aluminous peak parageneses of garnet-cordierite-sillimanite may form biotite, either on the expense of cordierite or garnet, also depending on grain size. The two examples are illustrated with a series of reaction textures reported for amphibolite and granulite terrains in the literature.

Journal ArticleDOI
TL;DR: In this article, the authors used pyroclasts from remelted volcanic rock (olivine-melilitite) to enhance interpretation of fragmentation mechanisms during explosive volcanism.
Abstract: With the aim to enhance interpretation of fragmentation mechanisms during explosive volcanism from size and shape characteristics of pyroclasts experimental studies have been conducted using remelted volcanic rock (olivine-melilitite). The melt was fragmented and ejected from a crucible by the controlled release of pressurized air volumes (method 1) or by controlled generation of phreatomagmatic explosions (Molten Fuel Coolant Interaction (MFCI); method 2). Both methods were adjusted so that the ejection history of the melt was identical in both cases. The experiments demonstrate that exclusively during MFCI, angular particles in the grain size interval 32 to 130 μm are generated that show surface textures dominated by cracks and pitting. The physical process of their generation is described as a brittle process acting at cooling rates of >106 K/s, at stress rates well above 3 GPa/m2, and during ∼700 μs. In this time period the emission of intense shock waves in the megahertz range was detected, releasing kinetic energy of >1000 J. By both experimental methods, three more types of particles were produced in addition, which could be identified and related to the acceleration and ejection history of the melt: spherical particles, elongated particles, and Pele's hair. Abundance and grain size distribution of these particles were found to be proportional to the rate of acceleration and the speed of ejection but were not influenced by the experimental method used. Pele's hair occurred at ejection speeds of >75 m/s.

Journal ArticleDOI
TL;DR: In this paper, the defect properties of nanocrystalline oxides have been investigated and it was shown that defect formation at low energy grain boundary sites is responsible for these properties.
Abstract: We synthesized dense CeO $${2 - x} $$ polycrystals of ∼10 nm grain size and characterized their electrical conductivity, in order to determine whether the defect properties of nanocrystalline solids fundamentally differ from those of conventional materials The nanocrystals exhibit enhanced electronic conductivity, greatly reduced grain boundary impedance, and a heat of reduction more than 24 eV lower per oxygen vacancy compared to their coarse-grained counterparts We propose that defect formation at low energy grain boundary sites is responsible for these properties, and that nanocrystalline oxides represent bulk materials possessing the defect thermodynamics of interfaces

Journal ArticleDOI
TL;DR: In this article, a model for the deformation of nanocrystalline materials based on grain boundary sliding and formation of mesoscopic glide planes is presented, and the experimental result of decreasing hardness with decreasing grain size (inverse Hall-Petch relationship) found in metals and intermetallics with nanometer grain sizes can be described by this model.

Journal ArticleDOI
TL;DR: In this article, a new method for the synthesis of zinc oxide nanoparticles using ethanol-in-oil microemulsions with Zn-DEHSS (diethylhexyl sulfosuccinate) as surfactant was described.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the interface microstructure of the state-of-the-art cathode material for solid oxide fuel cells, SrxLa1-xMnO3 (SLM), with respect to its electrochemical performance.
Abstract: The interface microstructure of the state-of-the-art cathode material for solid oxide fuel cells, SrxLa1–xMnO3 (SLM), was investigated with respect to its electrochemical performance. The interface microstructure was characterized by grain size and coverage of SLM on the electrolyte surface. Variation of the grain size was obtained by using three different sintering temperatures, whereas variation of the coverage was obtained by using two powders with a different morphology. This resulted in a set of six cathode/electrolyte samples with different combinations of grain size and SLM coverage at the interface. The cathode overpotential, as a measure for the electrochemical performance, could not be related to the length of the three-phase boundary. Based on the constriction resistance occurring in the electrolyte a model was developed which provides an estimate for the width of the active three-phase boundary zone.This zone is most likely to extend outside the cathode particle across the zirconia surface. The width calculated in this way was found to vary in the range of 0.03 to 0.07 µm for the different electrode microstructures. It is argued that the actual values may be smaller by one or two orders of magnitude.

Journal ArticleDOI
TL;DR: In this paper, a steady state and laser-flash method was developed for measuring the thermal conductivity of various types of diamond films; single crystal by homoepitaxial growth, single crystal synthesized by a high-pressure and high-temperature (HP/HT) method and polycrystalline film grown by chemical vapor deposition (CVD).

Journal ArticleDOI
TL;DR: In this paper, the effects of clustering on the tetragonal-cubic transformation of barium titanate (BaTiO3) particles are shown in the behavior of the c/a ratio of the particles and the enthalpy change, ΔH, as a function of particle size.
Abstract: Clustering has an important effect on the tetragonal-cubic transformation of barium titanate (BaTiO3) particles. Small particles that would be cubic if they were by themselves can be tetragonal if they are in a cluster. The effects of clustering are shown in the behavior of the c/a ratio of the particles and the enthalpy change, ΔH, of transition as a function of particle size. The c/a ratio and the value of ΔH both decrease at a smaller particle size than those which are observed in samples where clustering is minimal. Our results are consistent with the observation that very small grains in polycrystalline samples can remain tetragonal even though the grain size is so small that it would be cubic if it were an individual particle. The transition temperature, TC, on the other hand, is insensitive to the particle size, which is similar to the observation in polycrystalline BaTiO3 that TC is insensitive to the grain size. The observed clustering effect is suggested to result from the reduction of depolarization energy of particles in clusters.

Journal ArticleDOI
TL;DR: In this paper, the influence of pulse parameters, namely, pulse on-time, off-time and peak current density on the grain size, surface morphology and crystal orientation was determined.
Abstract: Square-wave cathodic current modulation was used to electrodeposit ultra-fine-grained nickel from an additive-free Watts bath. The influence of pulse parameters, namely, pulse on-time, off-time and peak current density on the grain size, surface morphology and crystal orientation was determined. The study showed that an increase in peak current density resulted in considerable refinement in crystal size of the deposit. The crystal orientation progressively changed from an almost random distribution at the lowest peak current density of 400 mA cm −2 to a strong (200) texture at a peak current density of 1600 mA cm −2 . At constant peak current density and off-time, the crystal size of the deposit was found initially to decrease with pulse on-time before it started to increase with further increase in on-time. The crystal orientation progressively changed from an almost random distribution at the shortest on-time of 1 ms to a strong (200) fibre texture at an on-time of 8 ms. An increase in the pulse off-time at constant on-time and peak current density resulted in a progressive increase in crystal size. However, the crystal orientation remained unaffected with increasing off-time.

Journal ArticleDOI
01 Nov 1997
TL;DR: In this article, the authors measured particle size spectra in Monterey Bay, CA, using six different instruments that examined particles ranging from approximately 1 μm to 10 mm, and they used fractal scaling to piece the results together, deriving fractal dimensions of 2.26-2.36.
Abstract: Particles are responsible for the vertical transport of material in the ocean. Size is an important characteristic of a particle, determining its fall velocity, mass content, scattering crosssection, and food value, as well as other properties. The particle size spectrum describes the distribution of particles in a volume of water as a function of their sizes. We measured particle size spectra in Monterey Bay, CA, using six different instruments that examined particles ranging from approximately 1 μm to 10 mm. Before the results could be combined, they had to be adjusted for the different particle properties actually measured. Results from different optical instruments were similar, although the spectral values were sensitive to minor variations in the diameter assigned to particles. Sample volume was crucial in determining the effective upper size limit for the different techniques. We used fractal scaling to piece the results together, deriving fractal dimensions of 2.26–2.36. Diver observations of visible particles showed that they were composed mostly of aggregated diatoms. The particle size spectra n I were remarkably well fitted with a power law function n I = ad I − b I , where d I is the image diameter and b I = 2.96–3.00 . The equivalent slopes for particles measured with an aperture impedance instrument were 3.50–3.61. The particle volume distribution showed that most of the particle mass was in the 0.1–3 mm range. This volume distribution is consistent with theories that assume particle sizes are controlled by simultaneous coagulation and disaggregation.

Patent
Vasanta Chivukula1, Pak K. Leung1
10 Mar 1997
TL;DR: In this article, a polycrystalline perovskite phase of lead zirconate titanate dielectric material is provided by a low temperature process, by a rapid thermal annealing process.
Abstract: A ferroelectric dielectric for microwave applications is provided including a polycrystalline perovskite phase of lead zirconate titanate dielectric material. Small grain size material is provided by a low temperature process, by a rapid thermal annealing process. A layer of amorphous ferroelectric precursor material is deposited and annealed in an oxygen containing atmosphere in the presence of water vapour, preferably with the addition of a few percent of ozone, and at a temperature of less than 500° C. Advantageously, the method provides for formation of a ferroelectric material including lead zirconate titanate with a grain size less than 20 nm, with low film stress, high dielectric constant and low leakage current, which has excellent ferroelectric characteristics up to 10 GHz. This material has applications for capacitors, as filters, decoupling, coupling, and bypass elements and also for high frequency surface acoustic wave devices.