Structural Correlation Length Research Articles

Local Structures and Structural Relaxation Processes in Supercooled Tetra(ethylene glycol)

Raman spectra of tetra(ethylene glycol) have been measured at near the glass transition temperature, Tg. The spectra from 750 to 950 cm-1 indicate that the conformation in the liquid state depends upon temperature and may approach to that in the crystalline state with decreasing temperature down to Tg. A broad peak known as a boson peak is observed at below 233 K in the low-frequency spectra. The lineshape of the boson peak is reproduced by the extended disorder-induced scattering model and structural correlation length is estimated. The correlation between the local structures of molecules and the structural relaxation processes obtained by sound velocity and dielectric measurements are discussed.

Intermediate range ordering in a network glass

The extent of intermediate range order in a network glass, B 2O 3, has been investigated using the reverse Monte Carlo method and reported neutron diffraction data. The first sharp diffraction peak (FSDP) in the static structure factor, S( Q), which is an experimental signature of intermediate range order, is found to be dependent on the size of the configuration, whereas the remaining part of S( Q) is almost unaffected. Correlations in the range 0.4 to 1 nm are shown to be of particular importance for the shape of the FSDP. The origin of the FSDP in B 2O 3 is a weak correlation between neighbouring segments of BO 3 triangles separated by voids in the structure. This inter-segment correlation produces a damped oscillation with a period of about 0.4 nm in the total pair correlation function. The quasi-periodicity extends out to about 1.5 nm, which thereby is the longest structural correlation length of this glass.

Raman spectroscopic investigations of the effect of the doping metal on the structure of binary tellurium-oxide glasses

Raman studies over the range 10 to 1000 cm −1 have been performed on binary tellurium-oxide glasses (1- x)TeO 2- xMO (M = Pb,Zn or Mg) prepared using a conventional melt technique. The intensities and positions of Raman bands observed in the range above 250 cm −1 were found to depend both on the compound oxide and on the amount of doping. Indeed, the ratio of the intensity of the band around 680 cm −1 (assigned to vibrations of TeO 4 trigonal bipyramids) with respect to that of the component around 750 cm −1 (related to stretching-vibrations in TeO 3+1, TeO 3 and MO groups) are affected in different ways for the glass-modifier MgO and for the intermediate glass-formers PbO and ZnO. Concurrently, an explicit dependence on the compound oxide and amount of doping was also observed on the maximum of the boson peak (BP) in the low-frequency region around 40 cm −1. The structural correlation lengths in the glasses, calculated using the model described by Shuker and Gammon, were found to be about 0.50 nm (1- x)TeO 2- xMgO glasses and around 0.65 nm for (1- x)TeO 2- xMO (M = Pb or Zn) glasses. All these results are interpreted in terms of the effect of the metal oxide on the changes induced in the structural arrangements of 1 χ[TeO 4-TeO 3] chains.

Structural evolution and microscopic interactions in a three-component amphiphilic microemulsion system

Structures and interaction parameters of a three-component amphiphilic microemulsion system consisting of n-decane, water, and an amphiphile AOT (sodium-di-2-ethylhexylsulfosuccinate) have been studied by means of small angle neutron scattering. The scattering curves are fitted with Teubuer and Strey’s formula, from which three structural parameters are extracted; the average periodic distance D between the oil and water, the structural correlation length ξ, and the area aH per amphiphile molecule. The same data are further examined in terms of Gompper and Schick’s formula, from which three interaction parameters are obtained; the strength of segregation J/T among the oil and water, the amphiphilicity L/T of the amphiphile toward the oil and water, and the critical surfactant volume fraction φcs. These interaction parameters have right order of magnitudes and their implications to structural evolution are discussed.

Linearity between Structural Correlation Length and Correlated-Proton Raman Intensity from Amorphous Ice and Supercooled Water up to Dense Supercritical Steam

Linearity between Structural Correlation Length and Correlated-Proton Raman Intensity from Amorphous Ice and Supercooled Water up to Dense Supercritical Steam

Low frequency Raman investigations of lead borate and lead alumino borate glasses

Lead borate and lead alumino borate glasses in the systems xPbO·(100-x)B2O3 (0 ≤ x ≤ 75 mol%) and xPbO·(95-x)B2O3, 5Al2O3 (0 ≤ x ≤ 80 mol%), respectively, have been prepared and investigated by Raman spectroscopy. Using the Martin-Brenig model, structural correlation lengths were determinated from Boson peak positions of temperature reduced Raman spectra and transversal sound velocities. Vv polarized spectra contain information about the nature of the PbO component within the network.

Short and medium range order in ternary borate glasses

Low frequency Raman scattering experiments are described in ternary lithium borate glasses (B 2O 3-0.6 Li 2O yLi n X with n = 1, X = F, Cl, Br and I; or n = 2, X = SO 4). The ‘boson peak’ is analyzed in terms of a correlation length of phonon propagation and of a phonon-photon coupling. The concentration and the chemical composition dependance of the sound velocity, as well those of the structural correlation length deduced from the Raman spectra are discussed. Using a linear dependance for the coupling parameter, the experimental density of vibrational states is obtained and compared with those calculated in binary lithium borate glasses. Two different structural modifications depending on the nature of the anions of the ‘doping salt’ (halide or sulfate ions) are proposed to describe the glass network conformation.

Raman scattering and medium range order in ternary borate glasses

Low frequency Raman scattering associated with sound velocity measurements on ternary borate glasses (B 2O 3-0.6Li 2 O-yLiO- yLi nX with n = 1, X = F, Cl, Br, I or n = 2, X = SO 4 are reported. The “boson peak” is analyzed on the basis of the model proposed by Martin and Brenig. The sound velocity decreases while the structural correlation length (SCL) increases with the lithium salt content and with the anionic radii. As the addition of lithium halide does not change significantly the ration between the BO 3 and BO 4 units, these results indicate that the two basic units are redistributed into the matrix to form larger closed borate entities with BO 4 such as diborate rings. This contributes to the expansion and the softening of the BO network by diminution of its connectivity to incorporate the anionic species in interstitial sites. The small variations of the SCL in the case of sulfoborate glasses, seems to indicate that sulfate ions act as a modifier. The existence in the network, of new sulfoborate units in which the sulfate ions are connected with BO 4 tetrahedra is expected.

Calcium Concentration Dependence of the Intergranular Film Thickness in Silicon Nitride

High‐resolution electron microscopy and nano‐beam analytical electron microscopy have been used to characterize both the intergranular silicate film thickness and its local composition in a series of high‐purity Si3N4 ceramics doped with 0–450 at. ppm Ca. Calcium was detected at both two‐grain junctions and triple junctions, even in the 80‐ppm‐Ca‐doped specimen. The thickness of the intergranular film at two‐grain junctions was found to depend sensitively on Ca content. In undoped material, the thickness was 1.0 ± 0.1 nm. With increasing Ca content, the thickness decreased in the dilute region (80 ppm Ca), but then increased. The variation in film thickness can be qualitatively understood in terms of the balance of three long‐range forces acting normal to the film, namely the van der Waals dispersion force, a structural “steric” force, and an electrical‐double‐layer force. By comparing the measured thicknesses to those predicted, estimates for the structural correlation length and the inverse Debye length can be made. These estimates have values of ∼ 0.22 nm and approximately 0.3–0.5 nm, respectively, for the calcia‐free and 80 ppm calcia materials.

Finite temperature properties of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice.

We have studied the spin-1/2 Heisenberg antiferromagnet on the triangular lattice by high temperature series expansions. From an analysis of the antiferromagnetic structure factor and correlation length, we deduce that the ground state has small but nonzero long range antiferromagnetic order. We also determine the temperature dependence of the uniform susceptibility and the specific heat.

Finite-size effect on the first-order metal-insulator transition in VO2 films grown by metal-organic chemical-vapor deposition.

We studied the finite-size effect on the first-order metal-insulator phase transition and the accompanying tetragonal-to-monoclinic structural transition of ${\mathrm{VO}}_{2}$ films. The ${\mathrm{VO}}_{2}$ films were epitaxially grown by a metal-organic-chemical-vapor-deposition technique on the (101) growth plane of a 125-\AA{}-thick ${\mathrm{TiO}}_{2}$ buffer layer which was also epitaxially predeposited on polished sapphire (112\ifmmode\bar\else\textasciimacron\fi{}0) substrates. The thickness of the ${\mathrm{VO}}_{2}$ films in this study ranges from 60 to 310 \AA{}. We find that ${\mathrm{VO}}_{2}$ films grow isomorphically on the ${\mathrm{TiO}}_{2}$ buffer layer resulting in a high degree of epitaxial ${\mathrm{VO}}_{2}$ films. We determined structural correlation lengths of the ${\mathrm{VO}}_{2}$ films parallel and normal to the growth plane from the x-ray-diffraction widths of ${\mathrm{VO}}_{2}$ reflections at room temperature. The structural order parameter associated with the monoclinic distortion and the change in resistivity associated with the metal-insulator phase transition were simultaneously measured using x-ray-diffraction and resistivity measurements. It was found that the transition temperature, width of the transition, and the estimated electronic gap are dependent on the structural correlation length normal to the growth plane. These dependences are discussed in terms of finite-size and substrate effects on the first-order phase transition.

Low frequency Raman scattering study of liquid-glass transition in propylene glycol

The liquid-glass transition of propylene glycol has been studied by the Raman scattering. When the temperature decreases, the boson peak continuously appears 70° above Tg=172K, in contrast the depolarization ratio is remarkably insensitive from 5cm −1 to 200cm −1, and it hardly depends on temperature. The observed lineshape and the depolarization ratio of the spectra are well explained by the use of the exponential structural correlation function. The structural correlation length is derived to be about 19A.

Low-frequency Raman investigation of the liquid-glass transition in glycerol.

The low-frequency response of glycerol has been studied by polarized Raman scattering. The «boson peak» always appear far above T g =193 K, whereas the depolarization ratio is nearly constant between 5 cm -1 and 200 cm -1 at temperatures from 333 to 90 K. In the analysis of the boson peak, comparisons are made between experimental results and calculations based on the two types of structural correlation function. The typical behavior of line shape and depolarization ratio of the spectra is fitted with an exponential structural correlation function. The structural correlation length is estimated to be about 14 A

A Raman study of B203 through the liquid-glass transition range

The low frequency Raman spectrum of B203 and the boroxol ring vibrational mode at 808 cm-1 have been studied from room temperature to 1273 K as the glass transforms to a melt. Both the low frequeney "boson" peak and the boroxol mode are markedly influenced by the glass transition. Raising the temperature above Tg the strength of the 808 cm-1 mode decreases linearly indicating the Similar behavior of the boroxol ring concentration. The boson peak shows a different temperature behavior, which mirrors that of the sound velo city. The structural correlation length demostrates the same correlation range in the liquid and the glass. The results, when compared with neutron diffraction measurements contradict a recently proposed relation between the "boson correlation length" and the position of the first sharp diffraction peak of the structure factor.

Raman spectroscopic investigation of irreversibly compacted vitreous silica

Polarized, depolarized, isotropic, difference, and reduced Raman spectra were obtained from vitreous silica, irreversibly compacted at 600 °C and 50 kbar, to ambient densities as high as 2.73 g cm−3. The 60 cm−1 ‘‘Boson’’ peak; and, the intense optic, Si–O–Si bending peak at 440 cm−1 including its low-frequency shoulders at ≊210–240 and ≊340 cm−1; were observed to move strongly upward in position, but at two different rates with density rise. The two peak frequencies behave experimentally like spherical transverse acoustic (TA) or shear (S), and spherical longitudinal acoustic (LA) or pressure (P) stress waves of an isotropic elastic solid. In contrast, downward frequency shifts were observed for the transverse optic (TO) 1060 cm−1 and longitudinal optic (LO) 1200 cm−1 modes in the Si–O stretching region, but at absolute rates equal, respectively, to those of the 60 and 440 cm−1 peak frequencies thus linking optic as well as acoustic modes to the elastic modulii. The TO and LO splitting was shown from a phonon coupling model to result from very strong interaction between the optic modes and the low-frequency S and P modes. The frequency decreases of the TO and LO modes indicate a decrease in the Si–O stretching force constants, related to a decrease in the mean Si–O–Si bridging angle, from ≊144° to ≊120°, inferred from frequency increases at 440 and ≊800 cm−1. A decrease in the mean O–2nd-O distance also occurs, but severe distortion of the SiO4 tetrahedra does not seem probable to densities of 2.73 g cm−3. The dilatational P-mode wavelength ≥5 Å corresponds to volume-related distances, e.g., Si–2nd-O, O–2nd-O, or Si–2nd-Si. The shear mode wavelength is larger (≊13 Å) and similar to the structural correlation length, estimated roughly from x-ray data, where G(r)≊1. Both S and P modes involve small coherence volumes, and both may have negligible group velocities, i.e., standing waves. The low-frequency S scattering is weakly to completely depolarized, but the higher-frequency P scattering may be strongly polarized, falling near or just below (BeF2, B2O3, GeO2, SiO2, ZBLAL) the first very strong minimum in the Raman depolarization ratio, located above the S mode. This new criterion locates the actual P mode of fused silica within the ≊200–350 cm−1 shoulder region. This region is intense in the density of states, determined by neutron inelastic scattering (NIS). S and P modes are resolved in the Raman spectra of several glasses, but their relation to the low-order spherical acoustic stress waves of isotropic media has, heretofore, not been widely recognized.

Low-frequency Raman spectroscopy of alkali-borate glasses

Low-frequency Raman spectra of glasses of the types (B 2O 3) 1− x (Li 2O) x , (B 2O 3) 1− x (Rb 2O) x and (B 2O 3) 1 − x − y (Li 2O) x -(Li 2Cl 2) y are presented. The temperature-reduced spectra show a peak at 50 cm −1 and a peak at about 130 cm −1. The peak at 50 cm −1 appears to be a common property of oxide glasses and arises because the limited structural correlation length of the glass network causes a non-zero maximum of the frequency-dependent Raman coupling coefficient. The 130 cm −1 band can be attributed to librational modes of BO 3 and BO 4 units. For v-B 2O 3, a structural correlation length equal to the size of a pair of BO 3 triangles is found. Addition of alkali oxide leads to a decrease of this correlation length. The extra oxygens are mostly incorporated in BO 4 units but larger ions such as Rb + will also enhance the number of non-bridging oxygens. Addition of LiCl does not produce major changes in the Raman spectra and consequently does not change the ratio of the numbers of BO 3 and BO 4 units. The Cl − ions are incorporated in interstitial vacancies of the network, which leads to an expansion of the B-O network structure.

Phonon localization in aggregates.

Experiments on the transport of thermal energy through aggregates of small particles at low temperature are discussed. A transition to a weakly-temperature-dependent thermal conductivity, or plateau, appears at the temperature at which the thermal phonon wavelength equals the particle size. This is interpreted as evidence of phonon localization on a length scale determined by the structural correlation length.

Phonon localization in glasses.

A universal but unexplained characteristic of glasses is the temperature-independent region or plateau in the thermal conductivity for temperatures 1--30 K. Examination of low-temperature thermal conductivity data for a wide variety of glasses indicates that the mean free path of the average thermal phonon becomes less than the phonon wavelength at temperatures in the vicinity of the plateau. Comparison with similar data in aggregates suggests that Ioffe-Regel localization of the vibrational modes occurs for phonons whose wavelength and mean free path are on the order of a structural correlation length of the material. Typical correlation lengths in glasses determined by this argument are 20--50 A\r{}. The universal plateau in bulk glasses is therefore associated with phonon localization due to strong scattering from inhomogeneities on this length scale.

Low-frequency Raman investigation of lead-containing fluorozirconate glasses and melts

Raman measurements of fluorozirconate glasses and melts were conducted from −265 (8.5 K) to ∼800 °C for numerous compositions, e.g., from 30 mol % BaF2 (no PbF2) to 35 mol % PbF2 (no BaF2), at nearly constant ZrF4 content. The normalized amplitude of the nominal 45 cm−1 peak was found to increase linearly with increasing PbF2 from 0–35 mol %, as the peak frequency decreased slightly, from ∼47 to ∼43 cm−1. From these observations, depolarization ratios, Pb–F force constants, etc., it was concluded that the 45 cm−1 peak involves a correlated motion of second-neighbor Pb2++Zr4+ or Ba2++Zr4+ cations vibrating against their edge- (or corner-) shared coordination cages of F− anions. Martin–Brenig-type analysis of the band shape below ∼50 cm−1 (at −265 °C) yielded a structural correlation length, SCL=2σ=6.2±0.2 Å (0–15 mol % PbF2). This SCL corresponds to a repeat distance, e.g., the Ba–Zr separation of the Ba(F2)Zr edge-sharing, 4.1–4.2 Å, plus the Zr–F bond length, 2.1 Å, of the ZrF4−nn polyhedra, 5<n<7, and n=CN. Normalized Bose–Einstein corrected difference spectra, I35%–I0% (mol % PbF2), and for 5 mol % PbF2, I635–I25 (°C), show common frequencies between ∼200–500 cm−1 which refer mainly to edge or corner sharing between the ZrF4−nn , PbF2−ll , and BaF2−mm polyhedra, l, m=CN. The 45 cm−1 peak frequency decreases sigmoidally with temperature rise, dropping steeply near TG, and reaching a ∼5 cm−1 limit in the melt. This and the rough density modulation observed for the mode frequency are indicative of viscoelasticity. The virtual absence of the low-frequency mode in the melt due to the Pb+Zr and Ba+Zr vs F cage motions occurs simultaneously with the disappearance of the F sharing modes. For a total stoichiometric F/Zr mole ratio of 5.5 for the melt, nearly free ZrF−5 , ZrF2−6 , and ZrF3−7 anions are indicated.