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Droplet interactions in water-in-carbon dioxide (W/C) microemulsions formed with a perfluoropolyether-based surfactant for droplet volume fractions from 0.05 to 0.10 are studied with small-angle neutron scattering (SANS) to understand the mechanism of microemulsion stability. The water-to-surfactant ratio (Wo) is fixed at 12.5. Droplet interactions increase as the upper critical solution pressure is approached with decreasing pressure at constant temperature, increasing temperature at constant pressure, or increasing droplet volume fraction. These interactions are quantified in terms of the structure factor at zero momentum vector, S(0), and the correlation length, ξ, for an Ornstein−Zernicke structure factor, or the square-well depth for the structure factor of a square-well potential. Near the critical solution pressure, the interaction strength (A) approaches the value predicted for a hard-sphere fluid with a van der Waals attractive term. The observed interaction strength between droplets is larger in...

In this paper we report a SANS investigation of micelle formation by fluorocarbon-hydrocarbon block copolymers in supercritical CO2 (scCO2) at 313K. A sharp unimer-micelle transition is obtained due to the tuning of the solvating ability of scCO2 by profiling pressure. At high pressure the copolymer is in a monomeric state with a random coil structure. By lowering the pressure aggregates are formed with the hydrocarbon segments forming the core and the fluorocarbon segments forming the corona of spherical aggregates. This aggregateunimer transition is driven by the gradual penetration of CO2 molecules toward the core of the aggregate and is critically related to the density of the solvent, thus suggesting the definition of a critical micellisation density (CMD).

In this letter we address the long-standing controversy which originated from differences between the experimental and theoretical values of the scaling exponent (n) for the critical amplitude ξ0 of the correlation length in polymer solutions. Using small-angle neutron scattering we examine the dependence of ξ0 on polymer molecular weight in polystyrene-methylcyclohexane-d14 solutions. We find that the experimental values of ncr = 0.195 ± 0.010 in the critical region of phase demixing as well as nmf = 0.255 ± 0.009 in the mean-field domain around the Θ temperature agree with the predictions of scaling theory (ncr = 0.185, nmf = 0.25).

The melt-state phase behavior of isotactic polypropylene (i-PP) blended with a series of poly(ethylene/ethylethylene) random copolymers has been investigated using small-angle neutron scattering (SANS). These PEExx copolymers, where xx is the percentage of ethylethylene (EE) units, were prepared by hydrogenation of anionically polymerized polybutadienes with controlled amounts of 1,2 addition. Random phase approximation (RPA) fits to the scattering data for blends of i-PP with a deuterated, low molecular weight PEE90 at 180 °C indicate a statistical segment length for i-PP that is 10% less than that reported previously. Scattering from blends of i-PP with higher molecular weight PEE90 and PEE73 at 180 °C can be quantitatively fit using the RPA theory with χ as the only adjustable parameter, indicating melt miscibility. PEE46 and PEE62 are strongly and marginally immiscible, respectively, with i-PP at 180 °C. These results establish a “window” in EE content in which these random copolymers can form single ...

We have performed a series of small angle neutron scattering (SANS) experiments on blends of linear and branched polyethylenes to investigate the level of branching that is required to phase separate the system. These results confirm that the mixtures are homogenous for all compositions when the branch content is low (i.e., 2. In each case, the resolution of conventional SANS pinhole cameras (Qmin ∼ 10-3 A-1) is adequate to determine the state of mixing, even for systems with large domains.

The issue of multiple equilibrium phases in compositionally heterogeneous random copolymers has been addressed by a series of small-angle neutron scattering (SANS) experiments. An ethylene−hexene (EH) copolymer, representative of many linear low-density polyethylenes (LLDPE) has been shown to contain a dispersed minority phase (volume fraction, φ ∼ 0.02) consisting of highly branched, amorphous material. The dispersed phase is eliminated to a good approximation by xylene extraction, which removes the low molecular weight and highly branched molecules. The extracted material contains a much higher fraction of branched molecules and hence has a greater proportion of the dispersed phase (φ ∼ 0.2). These findings support the prediction of liquid−liquid phase separation for compositionally polydisperse LLDPEs, whereby the more highly branched molecules in the distribution may phase segregate, even if the overall branch content is low.

The effects of the addition of crown ether 1,4,7,10,13,16-hexaoxacyclooctadecane on the structure of aqueous solutions of surfactants sodium dodecyl sulfate and dodecyltrimethylammonium bromide have been studied by small angle neutron scattering. By modeling the scattering intensities, it was possible to derive, simultaneously, both structural properties and information on the distribution of crown ether between the micellar and aqueous phases. In the case of sodium dodecyl sulfate, an appreciable amount of crown ether was found to be localized in the micellar phase, though it was not possible to establish whether it was in the core or in the shell ; there was no evidence of crown ether localization in dodecyltrimethylammonium bromide micelles. The above observations indicate that although, at least in principle, the crown ether methylene groups could interact hydrophobically in the micellar core with the surfactant alkyl chains, the ability of crown ethers to form metal complexes might also lead, in sodium dodecyl sulfate solutions, to electrostatic interactions in the external palisade between the crown ether-sodium ion complex and the surfactant head groups. The absence of crown ether from dodecyltrimethylammonium bromide micelles indicates that the macrocyclic molecules interact with sodium dodecyl sulfate micelles via the formation of a complex between the sodium ion and the crown ether and rules out the possibility of hydrophobic interaction in the micellar core.

The structure of ultrathin cellulose acetate membranes, known as active layer membranes, has been investigated using small-angle neutron scattering. These membranes are known to have structural and functional similarity to the surface or "skin" layer in commercial reverse-osmosis (RO) membranes and hence are useful model systems for understanding the structure of the RO membrane skin layer. Active layer membranes were studied after swelling them with either DzO or CD30D. The results in both cases clearly indicated the presence of very small (10-20 A) porous structures in the membrane. The presence of such pores has been a subject of long-standing controversy in this area. The data was analyzed using a modified Debye-Bueche analysis and the resultant membrane structure was seen to agree well with structural information from electron microscopic studies. Finally, a possible explanation for the differences in scattering observed between the DzO swollen membranes and the CD30D swollen membranes has been presented.

Pore structure in cellulose acetate ultrafiltration (UF) and reverse-osmosis (RO) membranes has been studied using small-angle neutron scattering. Scattering experiments were carried out on dry membranes as well as on membranes swollen with deuterated solvents (D[sub 2]O and CD[sub 3]OD). In addition, the RO membranes were studied both before and after annealing (a process of heating a membrane in a water bath at [approximately]75 C to improve its separation properties). The pore surface in UF membranes was found to be smooth and nonfractal, as evidenced by the fourth power law behavior at high Q. Values of average pore sizes obtained for dry and solvent swollen membranes agree well with pore sizes obtained by other methods. For cellulose acetate RO membranes in their dry state, the unannealed membrane appears to consist of two discrete pore size distributions in the intermediate and high Q region while the annealed membrane contains a much wider distribution of pore sizes. These results give a good account of the changes occurring in the structure of RO membranes as a result of annealing, and agree well with the prediction of other authors.

We report on small angle neutron scattering observations of the flux line lattice (FLL) in a single crystal of YBa[sub 2]Cu[sub 3]O[sub 7]. To probe the mass anisotropy ratio, [ital m][sub 3]/[ital m][sub 1], measurements were made as a function of angle, [Theta], between the 8 kOe applied field and the crystallographic (001) axis for 0[degree][le][Theta][le]80[degree]. With the rotation about an [ital a]/[ital b] (or [ital y]) axis, two symmetry-related distorted hexagonal FLL domains formed. Contrary to theoretical prediction, the lattices formed are consistent with a rotation of the short basis vector, [bold a][sub 1], from the [ital x] axis by 15[degree], after the effects of anisotropy are removed. The mass ratio is 20[plus minus]2, which is slightly lower than published values. The temperature dependence of the intensity is not conventional.

Crystalline morphologies of poly(e-caprolactone) (PCL) and deuterated polycarbonate (d-PC) blends were studied by SANS and SAXS. Measurements were conducted at both room temperature and temperatures above the melting point (60°C) of PCL. Due to the different contrast between the phases for neutrons and X-rays, SANS exhibited a monotonic drop in intensity with increasing scattering angle while SAXS showed lamellar (peak) scattering. A two-correlation length model provided an excellent fit for the SANS data over the entire composition range

Mini-emulsified lateres of anionically polymerized deuterated and protonated polystyrene (DPS=185 000, HPS= 00 000) were prepared by direct mini-emulsification. Films containing 6% deuterated particle were annealed at 144 o C for various periods of time. The average depth of penetration of the deuterated polystyrene chains and tensile strength buildup were characterized during the course of annealing. When the present results were compared with those of the conventional emulsion polymerized system, the directly mini-emulsified later had greater interdiffusion rates and higher tensile strength than the emulsion polymerized latex system at similar annealing times

Neutron diffraction has been used to measure the vortex lattice scattering for YBa2Cu3O7. A square pattern is found when the field is applied along the c axis, while a triangular pattern is found when the field is applied well away from the c axis. High‐resolution measurements for the square pattern show that the vortex lattice has long‐range orientational order but only short‐range positional order. The temperature dependence of the penetration depth is not that expected for a superconductor with a conventional s‐wave BCS‐type gap. Preliminary measurements for temperatures near the irreversibility line are consistent with the occurrence of melting of the vortex lattice or glass phase.

A small-angle neutron study of vortex lattices in YBa 2 Cu 3 O 7 showed a diffraction pattern with square symmetry when the applied field was along the c axis with the four main spots aligned with the crystallographic {110} directions. With the field 30 o from the c axis, a hexagonal lattice exists. At intermediate angles, a fraction of the flux lines follow the c axis and the two lattices coexist. The temperature dependence of the intensity deviates markedly from conventional predictions

Experimentally measured scattering data differ from theoretical curves because of departures from point geometry in a real instrument. In a small-angle scattering instrument there are three contributions to the smearing of an ideal curve: (1) the angular divergence of the beam; (2) the finite resolution of the detector; and (3) the polychromatic nature of the beam. In general, instrumental-resolution (smearing) effects are smaller for small-angle neutron scattering (SANS) than for small-angle X-ray scattering (SAXS). This is because most SANS experiments are performed in point geometry (with pinhole collimation) whereas a significant proportion of X-ray experiments have used long-slit sources where smearing effects are much larger, particularly at small angles. Hence, corrections to the measured curve are often applied in SAXS experiments to compensate for angular smearing. Less attention has been given to the effects of wavelength smearing in SAXS which is often assumed to be negligible. Similarly, SANS data are routinely analyzed without reference to instrumental smearing effects. The circumstances under which the above assumptions break down are illustrated by a range of experiments comparing data taken from the same samples, run on different types of SAXS and SANS facilities. These experiments indicate some circumstances under which the above effects cannot be neglected.

SANS measurements of deuterated polystyrene in undeuterated polystyrene solvents that vary in molecular weight are reported. The second virial coefficients decrease with increasing molecular weight of the solvent as is expected, but the functional dependence of this decrease is not in accord with Flory-Huggins theory or simple modifications of it. The results are qualitatively similar to earlier work of Kirste and Lehnen on the poly(dimethylsiloxane) system

A series of experiments have been undertaken on the Oak Ridge National Laboratory (ORNL) 10 m small-angle X-ray scattering (SAXS) camera to provide quantitative data on the level of background (parasitic) scattering generated by different types of bevelled collimating slits. The addition of a third (guard) slit, positioned close to the sample, resulted in a reduction of over an order of magnitude in the parasitic background generated by the best two-slit combination of collimating slits. This made it possible to reduce the size of the beamstop, permitting useful data to be collected down to a value of the scattering vector Q = 4πλ−1sinθ ≃ 3 × 10−3 A−1, where λ is the wavelength, and 2θ is the angle of scatter. This permits the resolution of distances d ~ 2π/Q up to 2000 A.

Under monomer starved feed conditions, emulsion polymerization of perdeuterated methyl methac-rylate and styrene in the presence of preformed polymethylmethacrylate latexes resulted in particles with a core-shell morphology, as determined by small-angle neutron scattering (SANS) analysis for a hollow sphere. The locus of polymerization of the added deuterated monomer is therefore at the particle surface. In similar measurements a statistical copolymer of styrene and methyl methacrylate was used as seed particles for further polymerization of trideuteromethyl methacrylate. The resulting polymer latex was again shown to have a core-shell morphological structure as determined by SANS. In both studies the overall size of the particle was in excellent agreement with the values obtained by other techniques (light-scattering, transmission electron microscopy, etc.). SANS experiments were also undertaken on polystyrene latexes polymerized by equilibrium swelling methods, with deuterated polymer forming t...

The evolution of microstructure of shaly source rocks occuring during the natural oil generation is studied by the small-angle neutron and x-ray scattering for length scales 50-2000 \AA{}. The study is performed on a set of rocks with several weight percent organic matter content, forming a natural maturity sequence for hydrocarbon generation. These rocks have been previously analyzed using various geochemical methods. The applicability of small-angle scattering techniques for the quantitative source rock studies is also tested using the laboratory-prepared rocks containing hydrogenated or deuterated eicosane. Although the natural source rocks are five-phase systems, they are perceived by neutrons as quasi-two-phase, which enables straightforward interpretation of the SANS data. The surfaces of immature source rocks are fractal ($D=2.5\frac{+}{\ensuremath{-}}0.1$) within the entire length scale region, regardless of the organic content. Upon maturation, two distinct fractal regimes develop ($D=2.8\frac{+}{\ensuremath{-}}0.1$ and $D=2.0\frac{+}{\ensuremath{-}}0.05$) for the length scales below and above 600 \AA{}, respectively. The SAXS and SANS data are compared with the geochemical thermal maturity indicators and a model of source rock structural evolution is presented. Our data suggest an oil generation scenario according to which hydrocarbons are produced from macerals finely dispersed inside the bulk of the rock and also concentrated on the grain boundaries for grain sizes larger than 600 \AA{}. Upon reaching the thermal conditions necessary for oil generation the small grains crack and release oil into these microfractures, whereas the intergranular macerals produce oil and also wet the interface, thus forming an oil-wet network of conduits for primary migration.

We have made precise measurements of the unperturbed radius of gyration 〈S2〉1/20 of polystyrene and polymethylmethacrylate molecules in the melt over the temperature range 120 °C–240 °C by small‐angle neutron scattering. Contrary to most previous reports, based on dilute solution measurements, we find that neither polymer exhibits a significant change in dimensions with temperature, and we deduce temperature coefficients, κ=d ln〈S2〉0/dT, of (0.0±0.1)×10−3 K−1 for polystyrene and (0.1±0.1)×10−3 K−1 for polymethylmethacrylate. These κ values are close to those given by thermoelastic measurements, but are difficult to reconcile with predictions obtained from the rotational isomeric state model.

We describe small-angle neutron scattering (SANS) studies of vortex structures in the high T c superconductor YBa 2 Cu 3 O 7 in the mixed state. The SANS technique is a unique tool for probing the crystallography of a flux line arrangement in the bulk sample that can measure the values of the characteristic lengths and the effect of defects on lattice arrangement and orientation extremely accurately. The effects of crystal anisotropy on the field distribution in a vortex line is the topic of this paper

Four samples of polyethylene terephthalate (PET), with different thermal histories were investigated by radial distribution function (RDF) methods. Intramolecular distances in the polymer repeat unit were successfully attributed to peaks in the RDF plot up to values of r ∼ 5 A. A broad peak at ∼ 4 A was attributed to nearest neighbour intermolecular ordering, but there was no evidence of ordering beyond this distance in samples annealed for prolonged periods at temperatures close to the polymer Tg. This evidence does not support previous models proposing the presence of extensive para-crystalline ordering in amorphous PET. Low frequency broad peaks, with a periodicity of ∼ 4 A, were resolved out to values of r ∼ 20 A in the RDF plot for a sample with a density crystallinity index of ∼ 20%, thus confirming the sensitivity of the RDF analysis to short range intermolecular ordering.

Bulk polystyrene film samples were made from a 50% deuterated latex with a molecular weight of 5.85 × 106 g/mol and 38 nm particle diameter. Because of the high molecular weight and small particle ...

An investigation of the molecular structure of amorphous aluminium phosphate, prepared from a recently discovered complex (AlPO4 · HCl · 4C2H5OH), has been carried out using radial distribution function (RDF) techniques. Studies were made on two samples, one prepared by decomposing the solid complex and the other from powder produced by evaporating to dryness a solution of the complex in methanol and then decomposing and grinding the solid obtained. RDF curves were obtained from both samples, and were found to closely resemble that previously reported for vitreous silica. The short range order in both samples is similar to that in vitreous silica, with aluminium and phosphorous atoms occupying positions in aluminium phosphate similar to the positions of silicon atoms in silica. This structure is consistent with the crystal chemistry of aluminium phosphate. It is possible to assign all the peaks in the RDF plots out to values of r∼5 A to known inter-atomic distances. The peak at 1.6 A represents the Al-O and Al-P bond lengths, and is broader than the corresponding Si-O peak in vitreous silica, as the Al-O and P-O bonds are respectively slightly longer (Al-O) and shorter (P-O) than the equivalent Si-O bonds. Subsequent peaks result from the O-O distances (∼ 2.6 A); the Al-Al, Al-P and P-P distances (∼ 3.1A); the Al-second O and P-second O distances (∼ 4.2 A), and O-second O, Al-second Al, P-second P and Al-second P distances (∼ 5.0 A). The sample prepared from the methanolic solution shows some small additional peaks in the region 4 to 5 A, indicating more order in the second neighbour distances. Analysis of the P-O and Al-O peak area indicates that both P and Al atoms are co-ordinated to four network oxygen atoms at a distance ∼ 1.6A, and that absorbed water also co-ordinates to one or both atoms with a P-O and/or Al-O distance of ∼ 1.6 A.

The effects of collimation distortion on the measured diffraction curves from `amorphous' solids and liquids are discussed. It is shown how the parameters governing the range of angular divergence may be obtained and how the `permissible' range of scatter angles may be established. Model calculations and experiments were performed to show some of the distortion effects which can occur in the measured interference function if the permissible range of scatter angles is exceeded. It is shown that distortion effects are potentially most severe where line sources are employed, and it is therefore recommended that in future, collimation limits are calculated and stated. If it proves necessary to use collimation limits which distort the data in order to achieve satisfactory intensity, then these limits should be chosen so that analytical correction procedures to correct the data are possible.

Melange de PEO avec PMMA protone ou deuterie. PMMA est incorpore dans la phase amorphe entre les lamelles cristallines

Small-angle neutron scattering (SANS) experiments on solutions of polystyrene (PSH) and its deuterated homologue (PSD) in deuterated toluene have been performed over a wide range of concentration. Several redundant measurements demonstrated that the high-concentration technique of extracting single-chain scattering functions is highly reliable. Radii of gyration and screening lengths were fitted to power laws and were found to be R/sub g//sup 2/ approx. c/sup -0.156/ and xi approx. c/sup -0.70/. The results differ significantly from predictions by scaling theory, though the dependence of xi on c is in good accord with that previously found by other researchers. These experiments were also analyzed by using recent theoretical results of Muthukumar and Edwards. Measurements at different concentrations yielded a reasonably consistent value of the excluded volume interaction parameter. 41 references, 10 figures, 7 tables.

Small-angle neutron scattering (SANS) analyses of poly(methyl methacrylate) (PMMA) latexes yielded particle sizes that agree with those determined by a light-scattering technique. Emulsion polymerization of perdeuterated methyl methacrylate (d-MMA) and styrene (d-S) in the presence of preformed PMMA latexes resulted in particles with a core—shell morphology, as determined by SANS analysis for a hollow sphere. The locus of polymerization of the added deuterated monomer is therefore at the particle surface. Shells of d-S were less uniform in thickness than those of d-MMA.

Numerical estimates of double scattering of X-rays have been made in cylindrical and parallel-plate geometries for fluid argon in two states. For the cylindrical geometry the ratio of double scattering to single scattering is ~0.01 and independent of scatter angle to a first approximation, and thus does not seriously effect estimates of the radial distribution function. For the parallel-plate geometry the ratio is to a first approximation linear with angle and increases to ~0.15 at high angles; it thus seriously effects estimates of the radial distribution function and direct correlation function. The ratio can reach very high levels at low scatter angles if primary scattering is low.

Experimentally measured scattering data differ from theoretical curves because of departures from point geometry in a real instrument. In a small-angle neutron scattering (SANS) instrument, there are essentially three contributions to the smearing of an ideal curve: (1) the finite divergence of the beam, (2) the finite resolution of the detector, and (3) the poly chromatic nature of the beam. Where the scattering is azimuthally symmetric about the incident beam, indirect Fourier transform (IFT) methods may be used not only to smear an ideal scattering curve, but also to desmear an observed pattern. For experiments where the assumption of azimuthal symmetry cannot be made, alternative procedures based on Monte Carlo (MC) techniques have been developed which simulate the smearing of a given theoretical scattering function. This procedure permits the evaluation of smearing effects in anisotropic systems. Both IFT and MC procedures are illustrated with a range of applications from data taken on the 30 m SANS facility at Oak Ridge National Laboratory. It is shown that for experiments with scattering dimensions < 200 A smearing effects are small (< 5%) and that dimensions up to ~ 1200 A may be accurately resolved after proper evaluation of resolution effects. The procedures described may also be extended to include small-angle X-ray scattering, and an example of one such application is given.

Mixtures of model crystallizable copolymers, hydrogenated polybutadiene (HPB) and deuterated polybutadiene (DPB), were investigated by SANS in the intermediate q range (0.02 < q < 0.18 ,~-l). Linear and three-arm-star polymers were crystallized by quenching and slow cooling at rates differing by 3000fold. Care was taken in subtracting the incoherent background scattering. The coherent cross section shows a q-2 dependence which results in a constant Kratky plateau. Absolute SANS intensity is slightly greater than predicted for amorphous chains and is very insensitive to crystallization conditions in these polymers, changing by less than 10%. These observations are interpreted in terms of the gambler's-ruin model for chain configurations in semicrystalline polymers.

Polystyrene latexes with 40-60 nm diameter and molecular weights ranging from 6 × 104 to 6 × 106 g/mol were synthesized by a two-step equilibrium swelling method, with deuterated polymer forming either the first or second step. Below about 1 × 106 g/mol, small-angle neutron scattering gave zero-angle scattering intensities much higher than expected on the basis of gel permeation chromatography molecular weights. Several models were examined, the leading model based on a core-shell latex structure. The development of such structure was found to depend on the ratio of the radius of gyration of the polymer chain to that of the diameter of the latex particle, reaching a maximum in the range where the polymer chain dimensions are about half that of the latex particle. For the highest molecular weights, normal scattering intensities were found. These results lead to the finding that the polymer chains were compressed in the latex particles with constraining in the range of one to four, for this molecul...

Some experimental and theoretical comparisons have been made of the effectiveness of four techniques which have been commonly used for monochromatizing X-radiation for use in diffraction studies of liquids: monochromator crystals, curved or flat; fl-filter and pulse-height analyzer; balanced dual filters. The fl-filter/pulse-height analyzer system alone results in unacceptable error, at both low and high s(s=47r2 -I sin 0). Dual filters can be made quite effective, actually approaching the resolution possible with monochromator crystals.

Critical opalescence in mixtures of Bi-Zn, Pb-Ga and Bi-Ga has been observed in the scattering of 53 A neutrons. Separation of quasi-elastic from inelastic scattering has been used to separate the long-range concentration fluctuation part of the cross section from other effects. To a first approximation, this cross section agrees with the Ornstein-Zernike theory of critical scattering.

The temperature dependence of co-operative modes of motion in liquid lead has been observed in the range 336-725 ?c, using the inelastic scattering of cold neutrons. The positions and widths of modes near a frequency of 12?5 ? 1012 rad s-1 do not change significantly with temperature. However, the width of the non-propagating mode at Q = 2?2 ?-1 increases with temperature in a manner suggestive of single-particle motion. Simple models are employed to discuss these processes, although further theoretical work is needed to explain the data fully.

Relative values for the Pauli susceptibility of solid and liquid lithium have been obtained by using conduction electron spin resonance. A marginal oscillator operating at 16 Mc/s was used and by c...

For pt. I, see abstr. A48149 of 1968. A study of the temperature dependence of critical opalescence in the Bi-Ga system has been made for solutions of five different concentrations, by means of the inelastic scattering of slow neutrons. At each concentration the spectra of neutrons scattered from the solution are separable into a Q-dependent quasi-elastic region and an inelastic region largely independent of Q. The former are associated with scattering from the concentration fluctuations and the latter with the high frequency cooperative modes of the system. The inelastic regions of the spectra are largely independent of temperature and the concentration of the solution, whereas the elastic regions are sensitive to both these parameters. The critical indices eta and delta are evaluated.

A microscopical technique has been used to determine rates of crystallization (devitrification) of some lead phosphate and potash lead phosphate glasses. The devitrification rate is viscosity dependent, and compositional effects were resolved from viscosity effects by the use of isoviscous rate plots, which were obtained by plotting the half-time of crystallization against ΔT, where ΔT is the difference between the crystallization temperature and the transformation temperature of the glass.