**3. Special factors to be considered in diffusion welding of micro-devices**

Some aspects relating to micro-structures have already been mentioned in the sections above. From this, it can be concluded that bearing pressure should be kept as low as possible, while, on the other hand, it must be sufficient to deform asperities and to increase the contact area during the bonding process.

The temperature should be sufficient for a high density of vacancies and for filling the pores by volume diffusion, which also depends on the bonding time.

Micro-devices mainly consist of micro-structured multiple sheets. Channels may run in the same direction or cross-wisely, and the load-bearing structures may not proceed over the whole thickness for technical reasons (**Figure 18**).

**Figure 19.** Impact of the cross-section of thin walls. Left: rectangular cross-section of thin walls. Right: self-reinforcing

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The dimension of the walls should exceed the grain size of the material: in most cases, walls should be at least 100–200 μm in width. The aspect ratio should not exceed 1:1 for stability

**3.2. Impact of the design of mechanical micro-structures, the aspect ratio and the number of**

Moreover, the geometry of the micro-structured foils to be proper is important: the ratio between the thickness of the remaining bottom and the width of a trench should not exceed 1:1 to transmit sufficient bearing pressure to the next layer and to prevent lacking fusion

**Figure 20.** Left: 1.4301, T = 1075°C, t = 4 h, p = 8 MPa, incomplete fusion due to insufficient thickness of the bottom in relation to the width of trenches. Right: 1.4876, T = 1250°C, t = 1 h, p = 8 MPa, distortion due to grain boundary sliding

Depending on the application, a grain boundary crossing the remaining thickness of the bottom of a micro-channel should be avoided. In case of corrosion, this would be a favourable path for failure. During diffusion welding it causes local grain boundary sliding and distortion

Another topic is the aspect ratio of the parts to be welded, e.g., due to the different thermal expansion coefficients of the TZM-stamps (see Section 4), and the parts and deformation during the welding process, friction between both occurs. For a high aspect ratio in the range

cross-section due to etched micro-channels.

reasons, e.g., to avoid bending.

**layers on the deformation**

(**Figure 20**, left).

within a thin bottom.

of the mechanical micro-structure (**Figure 20**, right).

Bottom and top are often closed by discs of a few millimetres in thickness, having coarse grains. For thin sheet material, however, the grain size is about one order of magnitude smaller due to cold work hardening and recrystallization. The micro-structured stack and thick plates will deform completely differently and the deformation will be concentrated mostly on the microstructured section. An intelligent design may help achieve reasonable results.

#### **3.1. Shapes of thin walls in micro-structures**

The cross-section of thin walls may be important to the deformation behaviour: if the bearing pressure forces the material to creep, cross-sections of rectangular wall may be bent or deformed to a barrel shape, as can be seen in the left section of **Figure 19**. In the SEM of material with etched micro-channels on the right, however, the part is stabilised, since the bonding cross-section increases when deformation occurs.

**3. Special factors to be considered in diffusion welding of micro-devices**

Some aspects relating to micro-structures have already been mentioned in the sections above. From this, it can be concluded that bearing pressure should be kept as low as possible, while, on the other hand, it must be sufficient to deform asperities and to increase the contact area

The temperature should be sufficient for a high density of vacancies and for filling the pores

Micro-devices mainly consist of micro-structured multiple sheets. Channels may run in the same direction or cross-wisely, and the load-bearing structures may not proceed over the

**Figure 18.** Displaced micro-structure with offsets made of 1.4301 diffusion-welded at locally varying bearing pressure

Bottom and top are often closed by discs of a few millimetres in thickness, having coarse grains. For thin sheet material, however, the grain size is about one order of magnitude smaller due to cold work hardening and recrystallization. The micro-structured stack and thick plates will deform completely differently and the deformation will be concentrated mostly on the micro-

The cross-section of thin walls may be important to the deformation behaviour: if the bearing pressure forces the material to creep, cross-sections of rectangular wall may be bent or deformed to a barrel shape, as can be seen in the left section of **Figure 19**. In the SEM of material with etched micro-channels on the right, however, the part is stabilised, since the bonding

structured section. An intelligent design may help achieve reasonable results.

**3.1. Shapes of thin walls in micro-structures**

cross-section increases when deformation occurs.

by volume diffusion, which also depends on the bonding time.

whole thickness for technical reasons (**Figure 18**).

during the bonding process.

210 Joining Technologies

at T = 1075°C, t = 4 h.

**Figure 19.** Impact of the cross-section of thin walls. Left: rectangular cross-section of thin walls. Right: self-reinforcing cross-section due to etched micro-channels.

The dimension of the walls should exceed the grain size of the material: in most cases, walls should be at least 100–200 μm in width. The aspect ratio should not exceed 1:1 for stability reasons, e.g., to avoid bending.

#### **3.2. Impact of the design of mechanical micro-structures, the aspect ratio and the number of layers on the deformation**

Moreover, the geometry of the micro-structured foils to be proper is important: the ratio between the thickness of the remaining bottom and the width of a trench should not exceed 1:1 to transmit sufficient bearing pressure to the next layer and to prevent lacking fusion (**Figure 20**, left).

**Figure 20.** Left: 1.4301, T = 1075°C, t = 4 h, p = 8 MPa, incomplete fusion due to insufficient thickness of the bottom in relation to the width of trenches. Right: 1.4876, T = 1250°C, t = 1 h, p = 8 MPa, distortion due to grain boundary sliding within a thin bottom.

Depending on the application, a grain boundary crossing the remaining thickness of the bottom of a micro-channel should be avoided. In case of corrosion, this would be a favourable path for failure. During diffusion welding it causes local grain boundary sliding and distortion of the mechanical micro-structure (**Figure 20**, right).

Another topic is the aspect ratio of the parts to be welded, e.g., due to the different thermal expansion coefficients of the TZM-stamps (see Section 4), and the parts and deformation during the welding process, friction between both occurs. For a high aspect ratio in the range of one or more, a barrel-shaped profile results, accompanied by a high percentaged deforma‐ tion. Flat parts, however, possess a low deformation at the same conditions. For example, for disks of 160 mm in diameter, a deformation of 10% was obtained for a height of 10 mm for *T* = 1075°C, *t* = 4 h, *p* = 25 MPa. For a height of 150 mm, however, the deformation was more than 33% [22].

e.g., PVA TePla AG, FormTech GmbH, TAV VACUUM FURNACES SPA and Centorr Vacuum Industries. Other companies such as MAYTEC Mess- und Regeltechnik GmbH and SYSTEC Vacuum Systems GmbH & Co.KG modify equipment like tensile testing machines or produce equipment for special needs (**Figure 22**). For this, a water-cooled vessel with a vacuum-sealed feedthrough for the dies is installed. The oven is heated indirectly by metallic heaters, and a vacuum in the order of 1E-05 Pa must be maintained for the protection of the heaters. Tem‐ peratures of not more than 1400°C are sufficient for the most commonly used materials.

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**Figure 22.** Diffusion bonding furnaces. Left: Maytec diffusion bonding furnace, maximum force 20 kN. Right: Systec

The stamps are often made of TZM, a molybdenum ODS-alloy, possessing still a high me‐ chanical stiffness at high temperatures [24]. However, the stability also depends on the thickness-to-diameter ratio and must be adapted to the forces transferred to the sample to

Due to the thermal mass of the equipment and to limit thermal stress, the heating rate and especially the cooling rate are low. PVA TePla AG also offers a rapid cooling technology for

During diffusion welding of stainless steel and nickel-based alloys under vacuum, chromium depletion takes place at the surface due to high partial pressure of chromium oxide [26, 27]. Hence, corrosion properties differ from a heat treatment in inert gas or air. For these materials, also enrichment of carbon must be prevented. Hence, unshielded heaters made of graphite are

Diffusion welding is the only welding process allowing for full cross-sectional welding, mostly without any liquid phase formation. Since the whole part is subjected to a heat treatment, attention must be paid to undesired material changes. Any cold work hardening effect

With reasonable efforts, high-melting metals, e.g., tungsten or tantalum, cannot be welded.

diffusion bonding furnace, maximum force: 2 MN.

decreasing the cycle time [25].

**5. Discussion and outlook**

unsuitable.

prevent irregular deformation of the parts to be welded.

disappears and the grain size will be larger than before.

The number of layers affects the deformation obtained at the same conditions since the roughness of more surfaces must be levelled. For example, a conical sample consisting of 51 layers had a deformation more than 30% higher than the same sample geometry consisting of five segments only (**Figure 21**).

**Figure 21.** Conical samples made of 1.4301, T = 1000°C, t = 4 h, F = 17.55 kN, corresponding to 15–25 MPa. Left: Before diffusion welding. Middle: Five segments, deformation: 5.41 and 5.11%, respectively. Right: Sample made of 51 layers; deformation: 8.34% [6].
