## 4 Discussion  
In the deposition process by PVD (Physical Vapor Deposition) and CVD (Chemical Vapor Deposition) coating onto the inner surfaces, the adhesion probability of coating particles is high enough to coat at the vicinity of micro-nozzle inlet but significantly decreases with the distance toward the outlet [17]. Hence, it is very difficult to deposit the inner surfaces of a micro-nozzle hole smaller than 1 mm in diameter and to coat the curved surfaces in the micro-spring with uniform thickness. In the present plasma nitriding, the inner surfaces of the micro-nozzle as well as micro-springs are subjected to the plasma sheath by the hollow cathode effect. Small RF-plasma is confined to the inside of the micro-nozzle by the application of DC-bias. As shown in Figure 5, its inner surface is nitrided and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Microspring-1** & **Microspring-2** \\ \hline Wire diameter (d) & 0.2 & 0.15 \\ Coil diameter (D) & 1.7 & 1.5 \\ Length (L) & 5.7 & 9.5 \\ Number of turns (N) & 10 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometry and dimensions of two micro-springs.  
Figure 8: The load–displacement relationship for the original spring and two nitrided springs.  
hardened up to 1000 HV. This reveals that the tool life of micro-nozzles could be prolonged by mini- and micro-sized plasma control for nitriding of their inner surfaces [12; 13; 18].  
The stiffness of the coil-springs (k) is defined by the following equation,  
\[\mathrm{k}=\mathrm{G}\times\mathrm{d}^{4}/(8\times\mathrm{N}\times\mathrm{D}^{3 }), \tag{1}\]  
where G is the effective shear modulus of the stainless steel wire including the residual stresses in the fabrication of springs from wires and so forth. Since the micro-springs were self-standing on the DC-biased metallic fixture during nitriding, the geometry of coil spring and number of turns are insensitive to the perturbed modification by nitriding; e.g., \(\Delta\mathrm{D}=\Delta\mathrm{N}=0\) in nitriding. The ratio of perturbed stiffness (\(\Delta\mathrm{k}\)) to k is then given by a variation of Equation (1),  
\[\Delta\mathrm{k}/\mathrm{k}=\Delta\mathrm{G}/\mathrm{G}+4\;(\Delta\mathrm{d}/ \mathrm{d}), \tag{2}\]  
where \(\Delta\mathrm{G}\) is a perturbed effective shear modulus and \(\Delta\mathrm{d}\), a perturbed wire diameter.  
Since \(\Delta\mathrm{d}\) is negligibly small in measurement, the main contribution to the increase of (\(\Delta\mathrm{k}/\mathrm{k}\)) in Equation (2) is (\(\Delta\mathrm{G}/\mathrm{G}\)) during nitriding. Consider that the torsional shear strain is induced on the cross-section of the stainless steel wire in the coil spring during its elongation or compression. The inner surface of the micro-coil is hardened by nitriding to reduce this torsional strain even when applying the same load to the micro-springs. This reveals that the equivalent shear modulus of wires is significantly increased up to 8 to 10 % by the inner nitriding to enhance the stiffness of micro-springs. In medical applications, a top-edge of tweezers and forceps as well as these micro-springs might well have higher stiffness to catch and hold the targeted objects precisely in operation. Selective nitriding of these tools by the present system provides a means to control their stiffness in part.