The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbum... more The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbumps. Even at room temperature, however, intermetallic compounds of Cu 3 Sn and Cu 6 Sn 5 are formed at the interconnection between Cu and Sn, and voids are produced inside the microbump. The formation of compounds and voids deteriorates mechanical and electrical properties of the microbump and thus causes potential reliability issues. Among various root causes of voids in microbumps, the void formation due to Kirkendall effect was examined in the present study. The Kirkendall effect provides the lower limit of the void formation in the Cu/Sn microbump. In order to develop a criterion for the maximum vacancy concentration in the Cu/Sn system, the growth of intermetallic compounds and the formation of Kirkendall vacancy in the binary Cu-Sn system were studied by simulation using an analytical diffusion model and experimental results under an assumption of atomic exchange mechanism for diffusion. The fraction of Kirkendall vacancy was calculated and then plotted against the distance representing the Cu/Cu 3 Sn, Cu 3 Sn/Cu 6 Sn 5 and Cu 6 Sn 5 /Sn interfaces in semi-infinite diffusion couples. Among these three interfaces, a maximum vacancy fraction of about 0.0125 was realised at the location close to the initial Cu/Cu 3 Sn interface at an annealing temperature of T = 473 K for an annealing time of t = 1 h. The penetration depth of vacancy is much greater on the Cu 3 Sn side than on the Cu side. This implies that Kirkendall voids may be predominantly formed on the Cu 3 Sn side of the Cu/Cu 3 Sn interface. To confirm validity of the simulation, the growth behaviour of intermetallic compounds and the formation of Kirkendall voids were experimentally observed using Cu/Sn diffusion couples prepared by an electroplating technique. The fraction of Kirkendall void in the diffusion couple annealed at T = 473 K for t = 1 h was measured by binary large objects (Blob) analysis. According to the observation, a row of Kirkendall voids is formed in Cu 3 Sn along the direction parallel to the Cu/Cu 3 Sn interface, where the measured value of void fraction is 0.0112. If most of Kirkendall vacancies are used to form Kirkendall voids, the void fraction is almost equal to the vacancy fraction. Thus, the simulation satisfactorily reproduces the experiment. The growth behaviour of the intermetallic compounds in the present Cu/Sn diffusion couple well coincides with that observed for a semi-infinite Cu/Sn diffusion couples in a previous study.
The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbum... more The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbumps. Even at room temperature, however, intermetallic compounds of Cu 3 Sn and Cu 6 Sn 5 are formed at the interconnection between Cu and Sn, and voids are produced inside the microbump. The formation of compounds and voids deteriorates mechanical and electrical properties of the microbump and thus causes potential reliability issues. Among various root causes of voids in microbumps, the void formation due to Kirkendall effect was examined in the present study. The Kirkendall effect provides the lower limit of the void formation in the Cu/Sn microbump. In order to develop a criterion for the maximum vacancy concentration in the Cu/Sn system, the growth of intermetallic compounds and the formation of Kirkendall vacancy in the binary Cu-Sn system were studied by simulation using an analytical diffusion model and experimental results under an assumption of atomic exchange mechanism for diffusion. The fraction of Kirkendall vacancy was calculated and then plotted against the distance representing the Cu/Cu 3 Sn, Cu 3 Sn/Cu 6 Sn 5 and Cu 6 Sn 5 /Sn interfaces in semi-infinite diffusion couples. Among these three interfaces, a maximum vacancy fraction of about 0.0125 was realised at the location close to the initial Cu/Cu 3 Sn interface at an annealing temperature of T = 473 K for an annealing time of t = 1 h. The penetration depth of vacancy is much greater on the Cu 3 Sn side than on the Cu side. This implies that Kirkendall voids may be predominantly formed on the Cu 3 Sn side of the Cu/Cu 3 Sn interface. To confirm validity of the simulation, the growth behaviour of intermetallic compounds and the formation of Kirkendall voids were experimentally observed using Cu/Sn diffusion couples prepared by an electroplating technique. The fraction of Kirkendall void in the diffusion couple annealed at T = 473 K for t = 1 h was measured by binary large objects (Blob) analysis. According to the observation, a row of Kirkendall voids is formed in Cu 3 Sn along the direction parallel to the Cu/Cu 3 Sn interface, where the measured value of void fraction is 0.0112. If most of Kirkendall vacancies are used to form Kirkendall voids, the void fraction is almost equal to the vacancy fraction. Thus, the simulation satisfactorily reproduces the experiment. The growth behaviour of the intermetallic compounds in the present Cu/Sn diffusion couple well coincides with that observed for a semi-infinite Cu/Sn diffusion couples in a previous study.
Materials science & engineering. C, Materials for biological applications, 2017
In this work the microstructure and degradation behavior of several as-cast alloy compositions be... more In this work the microstructure and degradation behavior of several as-cast alloy compositions belonging to the Mg rich corner of the Mg-Si-Sr system are presented and related. The intermetallic phases are identified and analyzed describing the microstructure evolution during solidification. It is intended in this work to obtain insight in the behavior of the ternary alloys in in vitro tests and to analyze the degradation behavior of the alloys under physiologically relevant conditions. The as-cast specimens have been exposed to immersion tests, both mass loss (ML) and potentiodynamic polarization (PDP). The degradation rate (DR) have been assessed and correlated to microstructure features, impurity levels and alloy composition. The initial reactions resulted to be more severe while the degradation stabilizes with time. A higher DR is related with a high content of the Mg17Sr2 phase and with the presence of coarse particles of the intermetallics Mg2Si, MgSiSr and MgSi2Sr. Specimens ...
Diffusion and Defect Data Solid State Data Part B Solid State Phenomena, 2007
A phase field model for simulating grain growth and thermal grooving in thin films is presented. ... more A phase field model for simulating grain growth and thermal grooving in thin films is presented. Orientation dependence of the surface free energy and misorientation dependence of the grain boundary free energy are included in the model. Moreover, the model can treat different mechanisms for groove formation, namely through volume diffusion, surface diffusion, evaporation-condensation, or a combination of these mechanisms. The evolution of a groove between two grains has been simulated for different surface and grain boundary energies and different groove formation mechanisms.
Phase-field modeling has proven to be a versatile tool for simulating microstructural evolution p... more Phase-field modeling has proven to be a versatile tool for simulating microstructural evolution phenomena, such as grain growth in polycrystalline materials. However, the computing time and computing memory requirements of a phase-field model pose severe limitations on the number of phase-field variables that can be taken into account in a practical implementation. In this paper, a sparse bounding box algorithm is proposed that allows the use of a large number of phase-field variables without excessive memory usage or computational requirements. The algorithm is applied to a three-dimensional model for grain growth in the presence of second-phase particles.
A sparse bounding box algorithm is extended to perform efficient phase field simulations of grain... more A sparse bounding box algorithm is extended to perform efficient phase field simulations of grain growth in anisotropic systems. The extended bounding box framework allows to attribute different properties to different grain boundary types of a polycrystalline microstructure and can be combined with explicit, implicit or semi-implicit time stepping strategies. To illustrate the applicability of the software, the simulation results of a case study are analysed. They indicate the impact of a misorientation dependent boundary energy formulation on the evolution of the misorientation distribution of the grain boundary types and on the individual growth rates of the grains as a function of the number of grain faces.
The aimed properties of the interpolation functions used in quantitative phase-field models for t... more The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu-Sn systems as a function of R/', with R grain size and ' diffuse interface width.
The evolution of fibre textured structures is simulated in two dimensions using a generalised pha... more The evolution of fibre textured structures is simulated in two dimensions using a generalised phase field model assuming two forms for the misorientation dependence of the grain boundary energy. In each case, a steady-state regime is reached after a finite amount of grain growth, where the number and length weighted misorientation distribution functions (MDF) are constant in time, and the mean grain area A as a function of time t follows a power growth law A - A 0 = kt n with n close to 1 and A 0 the initial mean grain area. The final shape of the MDF and value of the prefactor k in the power growth law clearly correlate with the misorientation dependence of the grain boundary energy. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with non-uniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results. In previous studies on grain growth in anisotropic fibre textured systems, this steady-state regime was often not reached, which resulted in wrong conclusions on the growth exponent n and evolution of the MDF.
The Bi-In-Sn-Zn system is an important alloy system in lead-free soldering. Thermodynamic descrip... more The Bi-In-Sn-Zn system is an important alloy system in lead-free soldering. Thermodynamic descriptions for the ternary systems Bi-In-Sn, Bi-In-Zn, Bi-Sn-Zn and In-Sn-Zn are optimized, using the CALPHAD method and combined to obtain a description of the quaternary Bi-In-Sn-Zn. All available experimental data from the literature are taken into consideration in the optimization. Calculated liquidi, isothermal and vertical sections and thermodynamic properties are compared with experimental data. Ternary and quaternary invariant reactions are also calculated.
A phase field model for grain growth in materials containing inert, immobile particles has been i... more A phase field model for grain growth in materials containing inert, immobile particles has been implemented. Large scale 2D-simulations were performed for different sizes and volume fractions of the second-phase particles and different initial grain sizes of the matrix phase. For all simulations the mean grain size and the number of particles located on grain boundaries as a function of time were determined. The agreement with Monte Carlo and front-tracking simulations is very good. From comparison with experiments suggestions for further improvement of the simulations are made.
The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbum... more The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbumps. Even at room temperature, however, intermetallic compounds of Cu 3 Sn and Cu 6 Sn 5 are formed at the interconnection between Cu and Sn, and voids are produced inside the microbump. The formation of compounds and voids deteriorates mechanical and electrical properties of the microbump and thus causes potential reliability issues. Among various root causes of voids in microbumps, the void formation due to Kirkendall effect was examined in the present study. The Kirkendall effect provides the lower limit of the void formation in the Cu/Sn microbump. In order to develop a criterion for the maximum vacancy concentration in the Cu/Sn system, the growth of intermetallic compounds and the formation of Kirkendall vacancy in the binary Cu-Sn system were studied by simulation using an analytical diffusion model and experimental results under an assumption of atomic exchange mechanism for diffusion. The fraction of Kirkendall vacancy was calculated and then plotted against the distance representing the Cu/Cu 3 Sn, Cu 3 Sn/Cu 6 Sn 5 and Cu 6 Sn 5 /Sn interfaces in semi-infinite diffusion couples. Among these three interfaces, a maximum vacancy fraction of about 0.0125 was realised at the location close to the initial Cu/Cu 3 Sn interface at an annealing temperature of T = 473 K for an annealing time of t = 1 h. The penetration depth of vacancy is much greater on the Cu 3 Sn side than on the Cu side. This implies that Kirkendall voids may be predominantly formed on the Cu 3 Sn side of the Cu/Cu 3 Sn interface. To confirm validity of the simulation, the growth behaviour of intermetallic compounds and the formation of Kirkendall voids were experimentally observed using Cu/Sn diffusion couples prepared by an electroplating technique. The fraction of Kirkendall void in the diffusion couple annealed at T = 473 K for t = 1 h was measured by binary large objects (Blob) analysis. According to the observation, a row of Kirkendall voids is formed in Cu 3 Sn along the direction parallel to the Cu/Cu 3 Sn interface, where the measured value of void fraction is 0.0112. If most of Kirkendall vacancies are used to form Kirkendall voids, the void fraction is almost equal to the vacancy fraction. Thus, the simulation satisfactorily reproduces the experiment. The growth behaviour of the intermetallic compounds in the present Cu/Sn diffusion couple well coincides with that observed for a semi-infinite Cu/Sn diffusion couples in a previous study.
The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbum... more The Cu/Sn system is one of the simplest metallurgical options for three-dimensional (3D) microbumps. Even at room temperature, however, intermetallic compounds of Cu 3 Sn and Cu 6 Sn 5 are formed at the interconnection between Cu and Sn, and voids are produced inside the microbump. The formation of compounds and voids deteriorates mechanical and electrical properties of the microbump and thus causes potential reliability issues. Among various root causes of voids in microbumps, the void formation due to Kirkendall effect was examined in the present study. The Kirkendall effect provides the lower limit of the void formation in the Cu/Sn microbump. In order to develop a criterion for the maximum vacancy concentration in the Cu/Sn system, the growth of intermetallic compounds and the formation of Kirkendall vacancy in the binary Cu-Sn system were studied by simulation using an analytical diffusion model and experimental results under an assumption of atomic exchange mechanism for diffusion. The fraction of Kirkendall vacancy was calculated and then plotted against the distance representing the Cu/Cu 3 Sn, Cu 3 Sn/Cu 6 Sn 5 and Cu 6 Sn 5 /Sn interfaces in semi-infinite diffusion couples. Among these three interfaces, a maximum vacancy fraction of about 0.0125 was realised at the location close to the initial Cu/Cu 3 Sn interface at an annealing temperature of T = 473 K for an annealing time of t = 1 h. The penetration depth of vacancy is much greater on the Cu 3 Sn side than on the Cu side. This implies that Kirkendall voids may be predominantly formed on the Cu 3 Sn side of the Cu/Cu 3 Sn interface. To confirm validity of the simulation, the growth behaviour of intermetallic compounds and the formation of Kirkendall voids were experimentally observed using Cu/Sn diffusion couples prepared by an electroplating technique. The fraction of Kirkendall void in the diffusion couple annealed at T = 473 K for t = 1 h was measured by binary large objects (Blob) analysis. According to the observation, a row of Kirkendall voids is formed in Cu 3 Sn along the direction parallel to the Cu/Cu 3 Sn interface, where the measured value of void fraction is 0.0112. If most of Kirkendall vacancies are used to form Kirkendall voids, the void fraction is almost equal to the vacancy fraction. Thus, the simulation satisfactorily reproduces the experiment. The growth behaviour of the intermetallic compounds in the present Cu/Sn diffusion couple well coincides with that observed for a semi-infinite Cu/Sn diffusion couples in a previous study.
Materials science & engineering. C, Materials for biological applications, 2017
In this work the microstructure and degradation behavior of several as-cast alloy compositions be... more In this work the microstructure and degradation behavior of several as-cast alloy compositions belonging to the Mg rich corner of the Mg-Si-Sr system are presented and related. The intermetallic phases are identified and analyzed describing the microstructure evolution during solidification. It is intended in this work to obtain insight in the behavior of the ternary alloys in in vitro tests and to analyze the degradation behavior of the alloys under physiologically relevant conditions. The as-cast specimens have been exposed to immersion tests, both mass loss (ML) and potentiodynamic polarization (PDP). The degradation rate (DR) have been assessed and correlated to microstructure features, impurity levels and alloy composition. The initial reactions resulted to be more severe while the degradation stabilizes with time. A higher DR is related with a high content of the Mg17Sr2 phase and with the presence of coarse particles of the intermetallics Mg2Si, MgSiSr and MgSi2Sr. Specimens ...
Diffusion and Defect Data Solid State Data Part B Solid State Phenomena, 2007
A phase field model for simulating grain growth and thermal grooving in thin films is presented. ... more A phase field model for simulating grain growth and thermal grooving in thin films is presented. Orientation dependence of the surface free energy and misorientation dependence of the grain boundary free energy are included in the model. Moreover, the model can treat different mechanisms for groove formation, namely through volume diffusion, surface diffusion, evaporation-condensation, or a combination of these mechanisms. The evolution of a groove between two grains has been simulated for different surface and grain boundary energies and different groove formation mechanisms.
Phase-field modeling has proven to be a versatile tool for simulating microstructural evolution p... more Phase-field modeling has proven to be a versatile tool for simulating microstructural evolution phenomena, such as grain growth in polycrystalline materials. However, the computing time and computing memory requirements of a phase-field model pose severe limitations on the number of phase-field variables that can be taken into account in a practical implementation. In this paper, a sparse bounding box algorithm is proposed that allows the use of a large number of phase-field variables without excessive memory usage or computational requirements. The algorithm is applied to a three-dimensional model for grain growth in the presence of second-phase particles.
A sparse bounding box algorithm is extended to perform efficient phase field simulations of grain... more A sparse bounding box algorithm is extended to perform efficient phase field simulations of grain growth in anisotropic systems. The extended bounding box framework allows to attribute different properties to different grain boundary types of a polycrystalline microstructure and can be combined with explicit, implicit or semi-implicit time stepping strategies. To illustrate the applicability of the software, the simulation results of a case study are analysed. They indicate the impact of a misorientation dependent boundary energy formulation on the evolution of the misorientation distribution of the grain boundary types and on the individual growth rates of the grains as a function of the number of grain faces.
The aimed properties of the interpolation functions used in quantitative phase-field models for t... more The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu-Sn systems as a function of R/', with R grain size and ' diffuse interface width.
The evolution of fibre textured structures is simulated in two dimensions using a generalised pha... more The evolution of fibre textured structures is simulated in two dimensions using a generalised phase field model assuming two forms for the misorientation dependence of the grain boundary energy. In each case, a steady-state regime is reached after a finite amount of grain growth, where the number and length weighted misorientation distribution functions (MDF) are constant in time, and the mean grain area A as a function of time t follows a power growth law A - A 0 = kt n with n close to 1 and A 0 the initial mean grain area. The final shape of the MDF and value of the prefactor k in the power growth law clearly correlate with the misorientation dependence of the grain boundary energy. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with non-uniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results. In previous studies on grain growth in anisotropic fibre textured systems, this steady-state regime was often not reached, which resulted in wrong conclusions on the growth exponent n and evolution of the MDF.
The Bi-In-Sn-Zn system is an important alloy system in lead-free soldering. Thermodynamic descrip... more The Bi-In-Sn-Zn system is an important alloy system in lead-free soldering. Thermodynamic descriptions for the ternary systems Bi-In-Sn, Bi-In-Zn, Bi-Sn-Zn and In-Sn-Zn are optimized, using the CALPHAD method and combined to obtain a description of the quaternary Bi-In-Sn-Zn. All available experimental data from the literature are taken into consideration in the optimization. Calculated liquidi, isothermal and vertical sections and thermodynamic properties are compared with experimental data. Ternary and quaternary invariant reactions are also calculated.
A phase field model for grain growth in materials containing inert, immobile particles has been i... more A phase field model for grain growth in materials containing inert, immobile particles has been implemented. Large scale 2D-simulations were performed for different sizes and volume fractions of the second-phase particles and different initial grain sizes of the matrix phase. For all simulations the mean grain size and the number of particles located on grain boundaries as a function of time were determined. The agreement with Monte Carlo and front-tracking simulations is very good. From comparison with experiments suggestions for further improvement of the simulations are made.
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