Oxidation kinetics of thin copper films and wetting behaviour of copper and Organic Solderability Preservatives (OSP) with lead-free solder

The oxide formation on thin copper films deposited on Si wafer was studied by XPS, SEM and Sequential Electrochemical Reduction Analysis SERA. The surfaces were oxidized in air with a reflow oven as used in electronic assembly at temperatures of 100 °C, 155 °C, 200 °C, 230 °C and 260 °C. The SERA analyses detected only the formation of Cu₂O but the XPS analysis done for the calibration of the SERA equipment proved also the presence of a CuO layer smaller than 2 nm above the Cu₂O oxide. The oxide growth follows a power-law dependence on time within this temperature range and an activation energy of 33.1 kJ/mol was obtained. The wettability of these surfaces was also determined by measuring the contact angle between solder and copper substrate after the soldering process. A correlation between oxide thickness and wetting angle was established. It was found that the wetting is acceptable only when the oxide thickness is smaller than 16 nm. An activation energy of 27 kJ/mol was acquired for the spreading of lead free solder on oxidized copper surfaces.From wetting tests on copper surfaces protected by Organic Solderability Preservatives (OSP), it was possible to calculate the activation energy for the thermal decomposition of these protective layers.     

Fierz–Pauli equation for massive gravitons from Induced Matter theory of gravity

Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on a 4D curved spacetime which has the form of a Fierz–Pauli one. In our model the mass of gravitons mg$m_g$ is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz–Pauli one.     

The effect of solute on ultrasonic grain refinement of magnesium alloys

An experimental study has been conducted to assess the structural refinement of magnesium and its alloys by ultrasonic irradiation during solidification. It is shown that (i) ultrasonic irradiation leads to significant refinement only in the presence of adequate solute, which is alloy dependent; (ii) the attendant grain density increases linearly with increase in solute content at a given irradiation level; (iii) increasing the solute content at a low irradiation level above the cavitation threshold is more effective than substantially increasing the irradiation intensity; and (iv) the difference in the grain size between two ultrasonicated magnesium alloys is mainly determined by the solute content rather than the irradiation intensity. In view of these, the effect of ultrasonic irradiation on solute redistribution in a solidifying magnesium alloy seems rather limited even at a substantial intensity level such as 1700 W cm⁻². The implications of these findings are discussed and a mechanism is proposed to account for the experimental observations.     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Big rational surfaces

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of \mathbbP²{\mathbb{P}^2} at distinct points lying on a (possibly reducible) cubic.