Steve W. Martin

Relaxation in glassforming liquids and amorphous solids

The field of viscous liquid and glassy solid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg , and a fourth dealing with ‘‘short time processes.’’ The first part tackles the high temperature regime T.Tg ,i n which the system is ergodic and the evolution of the viscous liquid toward the condition at Tg is in focus. The second part deals with the regime T;Tg , where the system is nonergodic except for very long annealing times, hence has time-dependent properties ~aging and annealing!. The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for ‘‘superionic’’ conductivity, and dopart mobility in amorphous silicon, remain active. In the fourth part we focus on the behavior of the system at the crossover between the low frequency vibrational components of the molecular motion and its high frequency relaxational components, paying particular attention to very recent developments in the short time dielectric response and the high Q mechanical response.

Dc and ac conductivity in wide composition range Li2OP2O5 glasses

The electrical conductivity of lithium phosphate glasses has been studied over wide frequency and temperature ranges, using a fully automated system capable of yielding data of high precision. Due to a “total drybox” sample preparation facility, samples containing P2O5 contents up to 65 mol% have been included without sacrifice of data quality. Comparisons with the behavior of the corresponding silicate, borate and boroaluminate glasses have been made and analyzed in terms of microscopic models. At the other composition extreme, measurements have been extended to 62.5 mol% Li2O without finding a conductivity maximum. The ac conductivity data have been analyzed using the modulus formalism, and systematic trends in the Kohlrausch parameter β with composition have been recorded. β decreases from 0.60 to 0.49 over the composition range 37–62.5 mol% li2O and seems to correlate best with the isothermal conductivity. Attention is drawn to anomalous structuring effects in P2O5-rich glasses.

Raman Spectroscopy Study of the Structure of Lithium and Sodium Ultraphosphate Glasses

Anhydrous binary phosphate glasses containing from 0 to 50 mol% Li2O or Na2O have been prepared and examined by Raman scattering spectroscopy. The unpolarized Raman spectrum of vitreous P2O5 has intense bands near 640 cm−1, attributed to the symmetric stretching mode of POP bridging oxygens, (POP)sym, between Q3 phosphate tetrahedra, and at 1390 cm−1 due to the symmetric stretch of the PO terminal oxygens, (PO)sym. With the addition of alkali oxide to P2O5, a new feature appears in the Raman spectra near 1160 cm−1 indicating the formation of Q2 phosphate tetrahedra with two bridging and two non-bridging oxygens. The increase in relative amplitude of this new (PO2)sym band with increasing modifier content is consistent with a simple depolymerization of the phosphate network. From 20 to 50 mol% alkali oxide, the position of the (PO)sym Raman band decreases by ∼ 130 cm−1 whereas the frequency of the (POP)sym band increases by ∼ 60 cm−1. These frequency shifts are the result of π-bond delocalization on Q3 species that effectively lengthens the PO terminal oxygen bond and strengthens the POP linkages with increasing alkali oxide content. The compositional dependence of the π-bond delocalization on Q3 tetrahedra is described by considering the interconnections between neighboring Q3 and Q2 tetrahedra. The onset of π-bond delocalization on Q3 species corresponds with the anomalous Tg minimum at 20 mol% alkali oxide in alkali ultraphosphate glasses. The increase in Tg between 20 and 50 mol% alkali oxide is attributed to the increased ionic interconnection of what becomes a chain-like phosphate network at higher alkali contents. Finally, the Raman spectra of several alkali ultraphosphate glasses show high frequency shoulders on the Raman bands attributed to the (PO2)sym and (PO2)asym vibrational modes. These shoulders represent the presence of strained structural units, possibly three- or four-membered rings.

The short-range structure of sodium ultraphosphate glasses

Anhydrous sodium ultraphosphate glasses were prepared with Na2O contents between 0 and 50 mol% and were characterized by several structurally sensitive spectroscopic probes to determine the nature of the phosphate tetrahedra that constitute the short-range glass structure. Solid state 31P magic angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy reveals that Na2O depolymerizes the branched (Q3) P-O network of P2O5 to form metaphosphate (Q2) sites, in quantitative agreement with Van Wazers ‘chemically simple’ model. X-ray photoelectron spectroscopy reveals that the concomitant increase in non-bridging oxygen with increasing Na2O content is also in quantitative agreement with this structural model. Raman spectroscopic analyses of glasses with approximately 40 mol% Na2O suggest that some intermediate-range order, perhaps associated with strained rings, also exists within the glass network. Strained sites are eliminated when the solid glass is heated to melt temperatures.

The structure of some simple amorphous network solids revisited

Abstract The amorphographic relationships between the structures of a number of single component amorphous network solids are discussed. New neutron diffraction data are introduced for several of the materials including vitreous P 2 O 5 which has not previously been studied by neutron diffraction. These data suggest that network connectivity is more important than structural unit stereochemistry in determining intermediate range order. Previous neutron data for amorphous Ge and vitreous SiO 2 are compared with bith random network and crystal based models and criteria are proposed for the minimum size of model required to accurately predict the shape of the first diffraction peak, which for a number of amorphous network solids is found to be Lorentzian. It is concluded that new computer modelling techniques are capable of generating models in good agreement with modern diffraction data and should considerably enhance present understanding of the structure of amorphous solids.

Glass formation and transition temperatures in sodium and lithium borate and aluminoborate melts up to 72 mol.% alkali

Abstract We report continuous glass formation and glass transition temperatures T g for the pseudo-binary systems x M 2 O (1 − x ) (0.87B 2 O 3 0.13Al 2 O 3 ) to x = 0.675 for M = Na and 0.575 for M = Li. A dependence of both T g and glass-forming range on starting materials is found at high alkali contents, and attributed to retained CO 2 . Maxima in T g for both binary and pseudo-binary systems are quantitatively described in terms of two effects: (i) creation of 4-coordinated borons (increasing T g ), and (ii) creation of non-bridging [BO 3 ] oxygens (decreasing T g . To first approximation we find the latter imparting a stronger effect on T g .

A new problem in the correlation of nuclear-spin relaxation and ionic conductivity in superionic glasses

Following the recent resolution of the longstanding problem of reconciling constant frequency nuclear‐spin lattice relaxation (SLR) activation energies and d.c. conductivity activity energies in ion conducting glasses, we point out a new problem which seems not to have been discussed previously. We report conductivity data measured at a series of fixed frequencies and variable temperatures on a lithium chloroborate glass and compare them with SLR data on identically prepared samples, also using different fixed frequencies. While phenomenological similarities due to comparable departures from exponential relaxation are found in each case, pronounced differences in the most probable relaxation times themselves are observed. The conductivity relaxation at 500 K occurs on a time scale shorter by some 2 orders of magnitude than the 7Li SLR correlation, and has a significantly lower activation energy. We show from a literature review that this distinction is a common but unreported finding for highly decoupled ...

Quantitative study of the short range order in B2O3 and B2S3 by MAS and two-dimensional triple-quantum MAS 11B NMR.

Two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR and MAS NMR of 11B at various magnetic fields, were applied to elucidate the structure of vitreous (glassy) boron trioxide (v-B2O3), vitreous boron trisulfide (v-B2S3) and crystalline boron trisulfide (c-B2S3). These techniques, when combined with computer simulations of the resulting spectra, provide the isotropic chemical shifts and the quadrupole parameters, as well as a quantitative measure of the intensities of various boron resonances. The MAS NMR of v-B2O3 produced overlapping anisotropic lineshapes corresponding to the -1/2<-->1/2 transition in two distinct types of BO3 units with 3(+/-0.08):] intensity ratio. A combination of MAS and the multiple-quantum method resulted in a better resolved, isotropic 11B spectrum of v-B2O3. A remarkable enhancement of resolution of the MQMAS NMR proved instrumental in finding and identifying various impurities present in v-B2S3 and c-B2S3. In addition to the resonances from boron in two types of BS3 groups, four other structural units, BOS2, BO2S, BO3 and BS4, were elucidated from the spectra of vitreous and crystalline samples. The effects of various experimental parameters, such as the magnitude of the B0 and B1 fields, on the resolution of the MAS and MQMAS techniques are also shown.

109Ag NMR investigations of the superionic glasses (AgI)x·(Ag2O·2B2O3)1−x

Abstract The first measurements of the 109 Ag NMR relaxation times and linewidths and of the self-diffusion coefficient in ( AgI ) x ·( Ag 2 O ·2 B 2 O 3 ) 1− x are reported. The initial findings indicate that at lower temperatures (which decreases with increasing x) two distinct Ag + populations, mobile and static, can be detected. At high temperatures all cations appear to be mobile. For the x =0.65 sample, the diffusion measurements give an activation energy of 0.36±0.11 eV . The Ag local motions as probed by relaxation and linewidth measurements are associated with activation energies of about 0.10 eV.

7Li and 11B nuclear spin lattice relaxation in B2O3+0.7Li2O+XLiCl glassy fast ionic conductors

Nuclear spin-lattice relaxation rates, R 1 , are reported for lithium chloro-borate glassy fast ionic conductors for both the mobile 7 Li nuclei and the stationary 11 B nuclei, as functions of temperature and NMR resonance frequency. The 7 Li relaxation is driven by the lithium diffusion via quadrupole interactions. The data for all frequencies can be fitted by assuming a single correlation function of the form exp(−( t / τ c *) β ). In the fit a thermally activated correlation time, τ c *, is assumed with an effective activation energy E a * = 7400 K, higher than the one deduced from dc conductivity measurements. It is argued that the correlation function (CF) which determines the conductivity and the CF which determines the NMR relaxation may differ in the presence of collective effects in the lithium diffusion. The 11 B data indicate that the nuclear relaxation proceeds via a Raman two phonon process involving internal vibrational modes of the BO 4 units heavily damped by reorientational motion. The data are fitted by an expression for R 1 derived from an extension of the Van Kranendonk two phonon relaxation mechanism in insulators. The activation energy for the damping frequency is compared with E a = β E a * which should represent the ‘single particle’ energy barrier for the lithium motion.