arXiv subjects

Guglielmo Macrelli

Publications and source records attributed to Guglielmo Macrelli.

9 recordsLinked to original sources

arXiv2026

Strengthened Silicate Glasses by Residual Stress: Depth of Compression and Surface Flaws Stability Conditions

The application of silicate glasses in severe service environments requires a precise evaluation of structural strength under mechanical loads and surface tribological conditions. Because glass strength is governed by surface flaws and microcracks rather than being an intrinsic material property, residual surface compression fields, balanced by interior tensile zones, are widely implemented to inhibit flaw opening. Rather than relying on conventional allowable stress criteria to establish product acceptance, this study adopts a fracture mechanics framework based on the stress intensity factor KI and fundamental material limits: the critical stress intensity factor KIC for rapid fracture and the threshold stress intensity factor KIth for time-delayed static fatigue failure. Using the Weight Function Method (WFM), KI is evaluated across generic surface flaw depths for two-dimensional continuous (2D-Continuous) surface cracks subjected to non-uniform internal residual stress fields and external loads. Flaw stability criteria are established for both zero-risk and moderate-risk design methodologies. Finally, the interaction and superposition of externally applied mechanical and thermal stresses with internal residual stress fields are evaluated.

cond-mat.mtrl-sci↗

arXiv2026

Kinetic Flux Equations for Ion Exchange in Silicate Glasses

Ion exchange kinetic flux equations have been extensively investigated since the mid-twentieth century and continue to provide a fundamental framework for describing mass transport phenomena in solid materials. Despite the maturity of this field, inconsistencies remain in the literature concerning the definition, dimensional consistency, and physical interpretation of the parameters involved. A rigorous and unified treatment of these equations is therefore essential to ensure the reproducibility and comparability of theoretical and experimental studies. The present study aims to establish a coherent and systematic development of ion exchange kinetic flux equations, with particular emphasis on the consistent definition and dimensional formulation of the relevant physical quantities. Beyond refining the theoretical foundations, this study extends the classical formulation by incorporating the influence of mechanical stress on ion transport and considering cross-term interactions within the framework of linear irreversible thermodynamics. This study investigates ion-exchange kinetics within silicate glasses, operating under the Nernst-Planck binary interdiffusion regime. These developments provide a more comprehensive description of ion exchange kinetics, particularly as applied to silicate glasses, where coupling between chemical and mechanical effects plays a crucial role in determining transport behavior and performance.

cond-mat.mtrl-sci↗

arXiv2024

Diffusion in a two Phases System: Application to Ion Exchange in Silicate Glasses

Diffusion in a two-phase system is a classical problem discussed in the literature. The general solution of the one-dimensional case to this problem is revisited and a detailed derivation is proposed. The solution is discussed in relationship with ion exchange in silicate glasses. The general solution is compared with the complementary error function (erfc) solution and the assumptions under which the general solution reduces to the erfc are identified. Interface or glass surface issues related to ion exchange are discussed in terms of the ratio between the diffusion coefficients of the diffusing alkali ions in the glass and in the ion reservoir phases respectively. Another relevant issue can be identified in the assumption of instantaneous equilibrium at the two-phase interface once the contact is established. Even though this last assumption is somehow unphysical it is the common approach used in the technological application of ion exchange in silicate glass which is justified when the contact time (immersion time) of glass with an ion reservoir is much larger than the time to achieve thermodynamic equilibrium at the surface.

cond-mat.mtrl-sci↗

arXiv2024

Thermodynamics and Kinetics of Silicate Glasses submitted to Binary Ion Exchange: Equilibrium Conditions and Interdiffusion Kinetics

Ion exchange processes between an ion reservoir and a solid matrix are modeled under the assumption that near interface volumes reach equilibrium in a much faster time than the overall ion exchange process time while, in the bulk of the solid matrix, ions are transported by an interdiffusion kinetic process. Ion exchange equilibrium conditions are initially established according to classical thermodynamics. The result is defined in terms of the chemical potentials of exchanging ionic species. The proposed original derivation is performed making use of the thermodynamics of subsystems to determine near-surface equilibrium concentrations and ion exchange isotherms. Interaction energies of the exchanging ions in the glass are determined through the thermodynamic factor n, which is a parameter of the ion exchange isotherm. The kinetics of the ion exchange process in silicate glass is discussed to find connections with the near-surface equilibrium condition. The flux equation for the incoming ions in the glass is written in the form of a Fick equation with a concentration-dependent interdiffusion coefficient incorporating the thermodynamic factor n. It has been found that the thermodynamic factor of the interdiffusion coefficient is related to the interaction energy of the exchanging ions in the glass allowing a new approach to the interpretation of past experimental results. Surface concentration has been found substantially connected to the second parameter of the ion-exchange isotherm which is the equilibrium constant K and significatively influenced by the chemical composition of the ion reservoir (the molten salt bath). Further treatment of kinetics of ion-exchange within the framework of non-equilibrium thermodynamics allows the interpretation of the thermodynamic factor as a function of incoming ions concentration in the glass matrix.

cond-mat.mtrl-sci↗

arXiv2023

Thermodynamic of Glass Indentation: Dissipative Aspects

A criterium is derived to understand the relevance of thermal effects resulting from high rate mechanical actions on glass surface. The criterium is based on the concept of characteristic contact time of the load to the glass surface. This criterium is of particular relevance to impact phenomena. A general discussion about dissipative aspects of indentation on glass surface is presented and a thermodynamic approach is suggested to evaluate the energetic of the process. Further generalization is proposed based on the thermodynamics of continuous media.

cond-mat.mtrl-sci↗

arXiv2023

Mathematical theory of diffusion in solids: solutions in the semi-infinite body and solution to a diffusion problem with a variable boundary condition

A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step characterized by a Dirichlet constant concentration condition and the second step by a Neumann condition.

cond-mat.mtrl-sci↗

arXiv2022

Ion exchange in silicate glass: mass average interdiffusion coefficient determination

The mass average interdiffusion coefficient DM is an approximated constant value of the interdiffusion coefficient which is relevant in the kinetics of ion exchange in silicate glasses. In this study, it is presented a simple technique for its determination based on the weight change of a glass sample after ion exchange. The theoretical basis of the method is presented in detail together with the approximations assumed in considering the constancy of the DM . Experimental results are presented for soda-lime silicate glasses and it is demonstrated the correlation of DM with the ion exchange temperature following an Arrhenius-type equation with an energy activation barrier and a pre-exponential factor. The determination of the mass average interdiffusion coefficient allows the estimation of the compression layer depth when a stress profile is build-up as a consequence of ion exchange. The estimated values of the compression layer depth have been compared with the ones measured by an optical technique based on differential surface refractometry (DSR). Values have been found quite compatible with the uncertainty limits indicated by the DSR method.

cond-mat.mtrl-sci↗

arXiv2022

The Mathematical Theory Of Diffusion In Solids: Time Dependent First Kind Boundary Conditions

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be helpful in the treatment of diffusion processes where the overall time of diffusion is comparable with the time taken by the surface of the solid body to saturate achieving a dynamical equilibrium between the diffusing elements supplied by the external source and the ones transferred internally through the diffusion kinetic mechanisms. Worked examples for constant diffusion coefficient are presented and discussed.

cond-mat.mtrl-sci↗

arXiv2020

Ion Exchange in Silicate Glasses: Physics of Ion Concentration, Residual Stress, and Refractive Index Profiles

A systematic review of main physical effects generated by ion exchange in silicate glasses is presented. Ion concentration distributions, residual stress profiles, and refractive index effects are discussed with particular attention on the physical and mathematical underpinnings of the ion exchange process. The study has the purpose of presenting a scientific foundation to enable future developments in the field. In this respect, the objective of this article is more educational than to present new research results. Appendixes are included to consider the detail of some specific topics without disrupting the continuity of the overall discussion. Despite the review approach of this study, some original topics are included, such as the concentration distribution with variable boundary conditions and residual stress profile with anomalies due to different relaxation mechanisms, viz., either isochoric and non-isochoric and stress driven or free energy driven. The time scale of the different relaxation mechanisms results, for some specific glass chemical compositions, in the appearance of a subsurface compression maximum progressively moving apart from glass surface and eventually turning in a reversal from compression into tensile state upon prolonged ion exchange processes. Finally, a broad discussion on optical effects induced by ion exchange is presented, paying particular attention to the possibility of experimental determination of residual stress profile.

cond-mat.mtrl-sci↗