Multi-scale study of the mineral porosity of veined gneiss and pegmatitic granite from Olkiluoto,Western Finland

The purpose of this work was to support the long-term experiments for investigation of rock matrix retention properties at the spent nuclear fuel repository site ONKALO, in Olkiluoto, Western Finland. Towards this end, rock samples were characterised in terms of porosity connected to mineralogy, with emphasis on pore sizes, and fillings. Both filled and unfilled pores were found with unfilled pores being majority in the pegmatitic granite veins of the mostly veined gneiss samples. It was found that the fillings were often connected to local alteration and the alteration caused variation in the range of pore sizes.     

Solutions to and Validation of Matrix-Diffusion Models

A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracture-column experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.     

Diffusion of Tracer in Altered Tonalite: Experiments and Simulations with Heterogeneous Distribution of Porosity

Numerical time-domain-diffusion simulations were used for studying the diffusion behavior of tracer molecules in rock matrix with homogeneous and heterogeneous porosity. As the heterogeneous sample in these simulations, a 3D tomographic image of altered tonalite was used, in which the mineral components and the pores resolved by X-ray microtomography were represented by their respective intragranular porosities determined previously by the ¹⁴C-PMMA method. The apparent diffusion coefficient of a tracer in altered tonalite was determined experimentally, and was then used in the simulations. In the altered tonalite analyzed, inclusion of heterogeneity in the porosity increased the diffusion coefficient by 16 %. Altered and pristine feldspar was the main mineral component in the sample (72 %), and it also provided the dominant contribution to tracer diffusion, explaining alone 52 % of the diffusion coefficient. The large pores resolved by microtomography (6 %) and altered and pristine mica (22 %) gave an equal contribution to the diffusion coefficient. The simulation method applied was also validated by comparing the results to both an analytical and a numerical solution to the diffusion equation in a homogenous medium. In addition, the method was compared to discrete-time random-walk simulations in the case of randomly placed overlapping spheres.     

A prognostic method for the embedded failure monitoring of solder interconnections with 1149.4 test bus architecture

This paper describes the feasibility of accurate low frequency measurements in predicting the breakdown of modern lead free ball grid array (BGA) interconnections. In these measurements, performed partly with 1149.4 analogue boundary scan, ceramic BGA modules measuring 15×15 mm in width, with 9×9 ball matrixes, were attached on an FR-4 printed wiring board (PWB) and thermally cycled over a temperature range of −40 to +125 °C. The condition of corner interconnections was monitored using the developed measurement methods and construction. In-situ measurements were performed with a datalogger during temperature cycling, accompanied with 1149.4 mixed-signal test bus measurements of corner interconnections performed between cycling intervals. In addition, the measurements were complemented by scanning acoustic microscopy and, X-ray. Monitoring corner interconnections by a simple, low-frequency voltage measurement method with embedded test constructions gives an early warning indication well before the electrical interconnection failures. Of two studied interconnection compositions, the ones with plastic core solder balls (PCSB) proved to be more reliable than the ones with 90/10 PbSn balls.     

Solder interconnection failure time estimation based on the embedded precursor behaviour modelling

This article presents a method for estimating solder interconnection failure times based on nonlinear parameter estimation techniques in conjunction with the Levenberg-Marquardt Algorithm (LMA). The LMA algorithm is applied to precursor measurements, from which failure time estimations are deduced using nonlinear estimation parameters. An electrical behavioural model is also proposed for precursors indicating weakening of solder interconnections. This model is divided into three sections: linear region, conversion region and nonlinear portion. Results obtained from experimental studies are presented and discussed in detail. In addition, an error estimation of the results is conducted to obtain knowledge of the most critical parameters in the estimation problem.The results suggest that the proposed method is capable of predicting solder interconnection failure times in advance, provided that the precursor describing electronic fatigue damage in interconnections obeys the exponential growth model during the wear-out period of the interconnection life-cycle. The obtained prognostic distances (PDs) varied between 15% and 38%, and failure times were predicted 15-25% before the actual failure occurred with an error rate of less than 10%. To show the generality of the proposed method, experimental results are presented for several samples with both lead and lead-free solders.