A. R. Cooper

Topologically disordered networks of rigid polytopes

Abstract A condition is derived for the existence of infinitely large d-dimensional topologically disordered networks composed of δ-dimensional rigid vertex-sharing polytopes which is consistent with Zachariasens first two rules. It generalizes these rules to polytopes, network dimensions, polytope dimensions, and vertex coordinations not considered previously.

Thermal healing of cracks in glass

Abstract Vickers indented glass samples were subjected to heat treatments from 525 to 725°C. Subsequently, they were examined microscopically at room temperature. Blunting and pinching of crack tips, rounding and grooving of radial cracks, receding and breaking up of lateral and median cracks, and cylinderization and spheroidization of closed cavities were observed. The morphology change pattern indicates that viscous flow driven by capillarity was operating. When tested for strength in bending at room temperature, samples fractured through the indent if they had experienced only the early stages of healing. Otherwise, fracture occurred elsewhere. Both indented and as-received samples respond to elevated temperature by strengthening followed by weakening. Indented samples strengthened to the level of as-received samples within a narrow time interval, probably due to crack bridging resulting from grooving. As-received samples strengthened gradually with time, suggesting that processes other than viscous flow were responsible for their heating. It is proposed that pre-existing flaws are similar to the reversibly closed macroscopic cracks with hydrogen or cationic bonds. Weakening is rationalized by new flaws development at elevated temperatures.

Numerical calculation of induction times for crystallization of glasses

Abstract The coupled rate equations of classical nucleation theory are solved numirically, and the induction time needed to reach steady state nucleation is calculated. Although the results do not differ significantly from the value obtained from the Kashchiev solution of the Zeldovich equation, the functional dependence of the induction times on the thermodynamic parameters is different. It is shown that, at least in the case of crystallization from glassy melts, nucleation occurs only at undercooling corresponding to small critical clusters such that numerical calculations are possible and convenient.

Oxygen-18 tracer study of the passive thermal oxidation of silicon

This work focuses on the thermal oxidation of silicon near 1273 K using the double-tracer oxidation method. The results confirm that oxidation occurs by the transport of electrically neutral non-network oxygen through the interstitial space of the vitreous silica (ν-SiO2) scale. Simultaneously, self- (or isotopic-) diffusion occurs in the network, resulting in characteristic isotopic fraction distributions near the gas-scale interface. The self-diffusion coefficients calculated from these profiles agree with those reported for tracer diffusion in ν-SiO2, and the diffusion coefficient calculated from the scale growth is consistent with reported O2 permeation data. An important parameter that describes the double-oxidation behavior is the ratio of the value of Δ/√(Dnt′),where Δ is the scale thickness grown during the second oxidation, Dn is the network self-diffusion coefficient for oxygen, and t′ is the time of the second oxidation.

W.H. Zachariasen - the melody lingers on

Abstract “The Atomic Arrangement in Glass” is only a minor part of the extensive contributions of W.H. Zachariasen. Yet, this brief incisive, intuitive theoretical paper. published in 1932 when Zachariasen was only 26 years of age, may be as infuential as his more widely acclaimed works on atomic radii, crystal structure, X-ray theory and practice, and the chemistry of transuranium elements. Speculation regarding the factors that piqued Zachariasens interest in glass will be offered. Some of the many ways in which “The Atomic Arrangement in Glass” has influenced thinking about glass structure over the past half century will be explored. Within his paper, W.H. Zachariasen presented topological conditions (Zachariasens Rules) necessary for easy glass formation. Many modern workers find topology of amorphous atomic networks a fascinating subject. Thus, it seems in order to attempt a generalization of Zachariasens Rules in order to permit their application to some glass forming systems that were not known in 1932.

Electric field buildup and relaxation for chemical diffusion

Abstract By applying Maxwells equation (Poissons law) to the flux equations for ionic diffusion it is shown that analytical solutions for the flux of charge and the compensating electrical field can be derived for the limits t →0 and t →∞. (Actually the long time limit becomes appropriate after a time equivalent to a small multiple of the mean time between successive jumps of all ions.) These expressions permit derivation of the Nernst-Planck equations and their generalization to multi-component systems without any self-contradictory assumptions. They also allow an approximate interpolation between the two limiting time periods so that a close approximation of the field and flux is obtained for the entire time interval. It should be noted that the flux of charge changes sign during the process and tends to zero much more quickly than the electric field. The scaling constants for time, energy and electrical flux are evaluated in general and for conditions relevant to alkali ion exchange in a silicate glass near the glass transition temperature. Values for the time constant, the maximum field, and the maximum flux are of the order of fractional micro-seconds, one megavolt/cm, and one ampere/cm 2 , respectively.

Index variation from field-assisted ion exchange

Concentration distributions produced from the combined effect of a unidirectional electric field and diffusion are presented for a slab and for a hollow cylinder. A field in the direction such that slow ions follow fast ones results in a stationary distribution that moves with a constant or nearly constant velocity. If the field is in the opposite direction, it tends to mix the ions, and an entirely different distribution that never reaches a steady state is obtained. These results are discussed in the context of the production of graded-index optical materials.

An analysis of the suitability of the Lillie Number to characterize the glass transition of real glass-forming substances

Abstract The Lillie Number, the negative product of the cooling rate and the temperature dependence of the structural relaxation time, characterizes the glass transition for systems with a single relaxation time. In this paper the utility of the concept is examined in “real” glasses, where a spectrum of relaxation times is necessary. While the principle is still useful, the simplicity and elegance of the approach are diminished for the “real” glass.

Continuous cooling from a high initial temperature through a freezing-in transition

Abstract The proposal that “freezing-in” transitions occur on cooling when the Lillie Number, ≅ (− B τ)′ ≅ − d Bτ d T ≃ τ ≅ d τ d t , ≡ (−Bτ)′ ≡ − d Bτ/ d T ≅ dot τ ≡ d τ/ d t , where t is time, T is temperature, τ is structural relaxation time, and B ≡ −dT/dt is the cooling rate) is of the order of unity, is examined and tested against the analytical solution of Hutchinson and Kovacs and numerical solutions of Scherer for single relaxation time processes. It is found that in all cases the progress of the transition is determined by the value of i′. Additional considerations of freezing-in processes and a brief consideration of a distribution of relaxation times are presented.

Thermal history effects on electrical relaxation and conductivity for potassium silicate glass with low alkali concentrations

Abstract Electrical response measurements from 10 Hz to 100 kHz between 120 and 540°C were made on potassium silicate glasses with alkali oxide contents of 2, 3, 5 and 10 mol%. Glasses with low alkali content were chosen to reduce the Coulombic interactions between alkali ions to the point that frozen structural effects from the silica network on the electrical response could be observed. Conductivity and electrical relaxation responses for both annealed and quenched glasses of the same composition were compared. Lower dc conductivity, σ dc , activation energies were measured for the quenched glass than for the annealed glasses. All of the glasses exhibited Arrhenius behavior in the log σ dc against 1 T plots. A sharp decrease in σ dc was observed for glasses containing K 2 O concentrations of 5 mol% or less. The frequency at which a maximum occurs, f max , in the modulus loss, M ″, plots, when plotted against 1 T , exhibited Arrhenius behavior for both annealed and quenched samples. The activation energies for these plots closely agreed with the σ dc activation energies. A sharp increase in activation energy was observed for σ dc and f max as the potassium oxide concentration decreased. Changes in the electrical response are attributed to structural effects due to different alkali concentrations.