# Influence of Surface State in Micro-Welding of Copper by Nd:YAG Laser
## 2 Materials and Methods  
Micro-welding of oxygen-free copper, C1020 was performed by using 1064 nm wavelength Nd:YAG laser (KLY-HP300\(\alpha\), Kataoka Corporation, Kyoto, Japan). The physical properties of copper C1020 are summarized in Table 1[6; 17; 18]. The experimental setup for the measurement of absorption rate is shown in Figure 2. The copper specimen was mounted in an integrating sphere (F100A-IS, Ophir Japan Ltd, Saitama, Japan), which was filled with nitrogen gas to prevent oxidation of the workpiece. The absorption rate was evaluated by measurement of reflected energy inside the integrating sphere. The inner surface of the integrating sphere was coated with barium sulfate, which is a highly reflective material. The specimen was set at the center of the integrating sphere. The detector was located along the inner surface of the integrating sphere, and there were no time dependent variations during the measurement process. To prevent scattering of spatter, the specimen was set in a quartz glass tube with inner diameter of 6.0 mm and outer diameter of 8.0 mm. The opening of the tube was sealed with a 0.3 mm thick cover made of borosilicate glass. The specimen size was 4.0 mm in length, 4.0 mm in width, and 1.0 mm in thickness. To prevent the cover glass from being damaged by plasma pressure or metal vapor generated during processing, a pressure releasing hole was provided in the jig used to fix the specimen. The reflection loss caused by the glass plates was considered when calculating the absorption rate, as shown in Figure 3. \begin{table}
\begin{tabular}{c c} \hline Melting temperature & 1356 K \\ Thermal conductivity & 391.1 W/(m K) \\ Coefficient of thermal expansion & 17.6 \(\times\) 10\({}^{-6}\) (1/K) \\ Specific heat & 380 J/(kg-K) \\ Density & 8.94 g/cm\({}^{3}\) \\ Electrical resistivity & 17.1 n/m \\ Electrical conductivity & 59.1 MS/m \\ Poisson’s ratio & 0.33 \\ Young’s modulus & 120 GPa \\ \hline \end{tabular}
\end{table} 
Table 1: Physical properties of copper C1020. Figure 2: Schematic illustration of experimental setup for measurement of absorption rate. The initial energy from the irradiated laser beam is \(E_{i}\), the energy measured by the sensor in the integrating sphere is \(E_{m}\), and the energy reflected by the specimen is \(E_{r}\). The reflectance of the copper specimen and the glass are \(R_{w}\) and \(R_{g}\), respectively. In this case, the incidence angle was assumed to be at the lower level below 45 degrees, and the reflectivity from air to glass and vice versa was assumed to be of the same value. The incident laser beam is reflected twice by the cover glass before reaching the specimen surface. Thus, the relationship between the incident light energy \(E_{i}\) and the transmitted light energy \(E_{i2}\) is given by Equation (1). \[E_{i2}=E_{i}\big{(}1-R_{g}\big{)}^{2} \tag{1}\]  
The incident energy \(E_{i}\) was measured by irradiating the laser beam inside the integrating sphere with no specimen in place. In addition, the value of transmittance for the cover glass used in this experiment was measured to be 91.8%. Using Equation (1), the reflectance of glass \(R_{g}\) was calculated to be approximately 4%. The energy reflected by the specimen inside the integrating sphere \(E_{r}\) is as expressed by Equation (2). \[E_{r}=R_{w}E_{i}\big{(}1-R_{g}\big{)}^{2} \tag{2}\]  
Considering the reflection loss due to the glass plates, the total reflected energy was computed as shown by Equation (3), while the absorption rate was computed according to Equation (4). Second reflection by the back side of the glass was ignored in the computation since its value was very small, hence negligible.