Material

As a materials temperature varies, so do its properties. In order to simulate the design’s behaviour correctly, choices with respect to material parameters have been made in order to create a model that overestimates the loss of heat away from the sample. This choice has been made for several reasons. First, assuming that more energy dissipates away from the sample return a specific energy input that is on the safe side. This means that the chosen laser power is greater than strictly necessary and therefore adequate. Second, enabling parts to become hotter than they are in reality creates a safety factor with respect to the cooling; if the cooling is adequate for an assembly temperature of 1000°C, it will also be adequate for lower temperatures.

Looking at the material that is in contact with the sample and the SiC disk, aluminium oxide, the thermal conductivity decreases with increasing temperature. As the initial value of 25W/mK remains constant through the entire simulation, less energy dissipates in reality than in the simulations. In addition because the thermal conductivity decreases, the alumina parts will not heat up as much as they do in the simulation. Since the alumina hood is the hottest part in the assembly, this also means that the cooling is able to extract enough heat from the assembly as it does this adequately in the simulations.

Figure 42: Thermal conductivity of Alumina (Al2O3),Tantalum (Ta), and Zirconia(ZrO2) as a function of temperature [50, 51].

Since the thermal conductivity of tantalum increases with increasing temperature, the largest value is chosen as a constant for the simulation. For zirconia, the initial value is chosen as it behaves in similar fashion to alumina. These two choices have the same effect on the heat dissipation as previously mentioned for alumina.

Page 58 E.2 Heat transfer

While simulations aim to provide a description of a real life problem, some heat transfer parameters are quite cumbersome to determine, therefore assumption are made to simplify the problem while keeping the solution realistic.

As the design is governed by the amount of energy added to the SiC disk and the dissipation of this energy, and by the heating of parts that are able to radiate towards the rest of the SEM, it is beneficial to model the system towards the worst possible outcome. Again, assumptions are made so that the dissipation is modelled larger than it really is, and parts become hotter than they would in reality. One way this is done, is by modelling surface contact as perfect surface to surface couplings.

This means that all surfaces that touch another surface are modelled to be touching perfectly, while in reality this can never be the case. Therefore, the simulated thermal resistances are smaller than in reality. The threshold for this coupling is chosen as 0.1mm; if two elements are closer than 0.1mm, they are modelled as if they were in perfect contact. This also means that the alumina blocks that clamp the sample have a much larger contact area in the simulation than in reality as is depicted in Figure 43 below. Since the surfaces touch perfectly, heat can dissipate much more easily than in the real situation. As heat travels more easily, all non-actively heated parts also become hotter.

Figure 43: While the contact between a curved surface and a rectangle is infinitely small in reality (left), the simulation uses a contact between all points that are closer to each other than a specified threshold, in this case 1mm(right).

With respect to radiative heat transfer, due to the size of the stage, all radiative couplings are modelled to be close parallel plates. Besides the fact that the object surfaces are close together, this coupling technique is supported by the fact that the stage operates in vacuum, where no attenuation of radiative power is present. In addition to all object that “see” each other being from a radiation point of view, all outer surfaces radiate to the environment. Since the heating will occur in vacuum, convective heat transfer to the surroundings is neglected. However, as the system is water cooled, convection does occur in the cooling coil. Since, generally, convection coefficients are determined experimentally, the lowest value found in literature is used in the simulations [52].

Page 59 E.3 Heating Stage

E.3.1 Iterations on the heating stage

In order to arrive at the previously described optimized heating stage, several separate components have been redesigned from the course model as has been described in Chapter 1, section 2.4.2 Thermal SimulationsTo depict the influence of the design changes in more detail than the global changes found in Chapter 1, the major design changes and their influence is shown below.

Since the sample is the hottest part and must remain hot, it is evident to investigate the possibilities of isolating the sample first. Prior to formulating the coarse design and the optimized design, an initial design has been made that focussed on the conceptual workings of the design and less on temperature. This design used tungsten parts to fixate the sample, i.e. the nest of springs and the base plate, and an Al2O3 hood. For an input power of 100W (which is the maximum power of the laser system), this did not result in a temperature of 1500°C but in 763°C. In order to increase the sample temperature without changing the design or input power, the materials used in the model are investigated and as a result, the tungsten components are replaced by tantalum components.

This led to a sample temperature of a sample temperature of 987°C. The comparison in temperature distribution between the use tungsten and tantalum parts is shown below in Figure 44. In Figure 44a, it can be seen that the gradient in temperature away from the sample is greater than that in Figure 44b. This is caused by the difference in thermal conductivity of the tantalum with respect to tungsten.

Figure 44: (a) Temperature distribution of the heated assembly with and without the alumina hood with a tungsten base plate and nest of springs at 100W. The sample reaches 763°C while the temperature in the legs reaches 150°C. (b) Changing

the tungsten parts to tantalum results in a sample temperature of 987°C and in the legs the temperature becomes 180°C.

Page 60 As the change from tungsten to tantalum resulted in an increased sample temperature and does not add any difficulties or cost to the design, the choice is made to keep tantalum in the design regardless of other possible improvements.

While the material change resulted in a temperature increase, it is not sufficient as the sample temperature remains too low and the temperature in the cooling circuit too high, namely 167°C.

Therefore, another step is taken to isolate the sample from its surroundings by placing small alumina blocks between the sample and the tantalum springs. While other materials exist that have higher application temperatures or have lower coefficients of thermal conductivity, alumina is chosen as its combination of these two parameter is optimal for use at the spring tips.

In addition to the change in spring tips, the heating assembly is better isolated from the cooling circuit as for the previous designs, the heated assembly dissipated energy into the cooling circuit too easily, and the cooling circuit reached temperatures of up to 167°C. Which is too hot as the cooling liquid is water which starts to boil at 100°C. To minimize the conductive heat transfer, the three base plate legs are adapted by reducing their cross-section and using zirconia inserts at the end of the legs. This change does not only result in a decrease of temperature in the cooling circuit down to 50°C, but also in an increased sample temperature to 1650°C at 60W due to less energy dissipation away from the sample.

Figure 45: Changing the legs of the base plate to narrow beams and adding zirconia isolators and alumina spring tips, results in a sample temperature of 1650°C, while the ZrO2 isolators only reach 60°C at 60W.

The final change made to the design if the use of a heatshield located at the back of the heating stage. As the optical fibre is place rather close to the hot parts of the heating stage in the coarse design, the fibre itself also heats up to a temperature of 240°C; well above the allowable 80°C specified by the manufacturer. For this reason, a heatshield is placed in between the fibre and the heated assembly.

As the heatshield is only connected to the other parts via the cooling circuit, no extra energy dissipates away from the sample and no extra sample isolation is added, therefore the sample temperature does not change. The only change is the decrease in temperature of the fibre from 240°C down to 65 °C.

Page 61 E.3.2 Final Model of the heating stage

The combination of the previously mentioned constraints results in a model that, for a given energy flux into the SiC disk, returns a minimum sample temperature and a maximum temperature for all other parts. For 55W, a sample temperature of 1540°C is attained, the frame and outer surfaces of the heatshield and cooling circuit reach a temperature of 48°C, as is depicted in Figure 46 on the left.

Figure 46: Heating stage temperature distribution for a sample temperature of 1540°C for the outside of the stage (left) and the inner parts of the stage (right) at 55W of laser power.

In Figure 46 on the right, the temperature distribution from the sample to the ZiO2 blocks is shown.

While the sample remains hot, the zirconia blocks isolate the base plate from the cooling circuit while the latter allows for the dissipation of the accumulated energy in the zirconia blocks.

Looking at all individual parts, no material reaches their limiting temperatures, where the most critical components are the Al2O3 blocks that may not exceed 1600°C for longer durations. Also, the tantalum only reaches a temperature where it maintains 80% of its strength, thus giving enough bending reaction forces to keep the sample in place [53].

In order to be able to validate the thermal simulations and to be able to predict sample temperatures for a given input power, the model is simulated for a range of powers from 0 to 100 W. While the graph below shows the temperature reaching its goal at around 55W, inputting 55W will not let the sample reach the given temperature due to losses and reflections in the laser delivery system.

Figure 47: Power versus sample temperature calculated from simulations, in reality the curve will shift to the right due to losses in the light delivery system.

Page 62 E.4 Tensile Stage

E.4.1 Iterations on the tensile heating module

Similarly to the design process that has been gone through for the dedicated heating stage, the tensile heating module has also undergone several iterations. Again, prior to investigating the temperature distributions within the model, first the conceptual design is made to obtain a working principle. This resulted in a model where two tantalum hooks were used in combination with a heatshield. While the heatshield showed to adequately remove energy for it not to heat up (and therefore is not changed from the original design), the hook showed to be too thermally conductive for the sample to reach the goal temperature, see Figure 48a. To solve this problem, alumina inserts were modelled in between the sample and the tantalum hooks. While this resulted in a sample temperature increase from 990°C tot 1200°C, this still isn’t enough. In addition, the temperature in the cooling conduits of the clamps is only decreased from 335°C for the tantalum hooks, to 290°C with the alumina inserts. The change in temperature distribution between the situation with and without inserts is shown in Figure 48a and Figure 48b below.

Figure 48: (a) Temperature distribution in the hooks for hooks manufactured from tantalum resulting in a sample temperature of 990°C, (b) Temperature distribution for the change to alumina inserts resulting in a sample temperature of

1200°C, (c) Temperature distribution for the change to zirconia inserts resulting in a sample temperature of 1400°C

Page 63 As the goal for the sample temperature is not reached with the alumina inserts, other solutions are investigated. Since the temperature of the sample at the edges is equal to 1050°C, it is possible to use zirconia for the inserts. The resulting sample temperature increase from 1200°C to 1410°C is shown in Figure 48c. While this increase in temperature is good, the temperature in the cooling circuit of the clamps remains too high at 210°C Since the combination of maximum temperature and cooling circuit does not meet the design requirements, the hooks are redesigned. This redesign results in the hooks of the optimised design.

In order to better isolate the sample, the shape of both the hooks and the inserts is changed. Where the contact area between the sample and the zirconia inserts remains approximately the same, the contact area between the hook and the inserts is reduced. In addition, the thickness of the inserts, i.e. the distance from sample to hook, is approximately doubled. The change in hook design and insert shape, results in temperature of 1540°C for the sample, 75°C in the cooling circuit and 1010°C for the zirconia inserts. With this temperature distribution, shown in Figure 49, the system meets the set requirements.

Figure 49: Thermal simulation of the optimized design of the hooks. The zirconia inserts remain below 1170°C, the sample reaches a temperature of 1540°C and the cooling of the hooks reaches 75°C.

Figure 50: (a) The initial heating assembly design making use of a suspension and with that reaching an inadequate sample temperature of 1410°C, (b) Heating assembly at 65W with a heated rod temperature of 1650°C which enables the sample

to reach 1540°C.

In addition to the iterations performed on the hooks, the heating system is also iterated upon. As the initial design did not allow the sample to reach temperatures of 1500°C and the plate to which the suspension was fixed to reached 1000°C (see Figure 50a) , it has been concluded that the thermal coupling between laser and sample can be improved upon. For this reason the suspension is changed into a spring system; the contact area between the SiC disk and the heating assembly is minimized by

Page 64 using a tantalum spring, centred by a thin tube that also serves as light guide for the laser. This spring presses against the SiC on one side, and against a steel plate on the other. As this plate is connected to the actively cooled water circuit, the plate doesn’t become hot. Additionally, the use of this plate also keeps the optical fibre away from the heated assembly, allowing the use of a commercial fibre.

The changes made to the heating assembly results in the tip of the heated rod to reach a temperature of 1650°C at 65W, for which the temperature distribution is shown in Figure 50b above.

Taking the previously mentioned constraints and simplification into account results in a model that, similarly to the dedicated heating stage model, returns a minimum sample temperature and a maximum temperature for all other parts for a given energy flux into the SiC. For a sample temperature of 1540°C, the zirconia inserts reach 1010°C and the cooling circuit 75°C, as is depicted in Figure 51b.

E.4.2 Final Model of the tensile heating module

In Figure 51, the entire heating module is shown. As can be seen, the shielding around the hooks and heating rod remains relatively cold with a temperature of 40°C. The sample reaches a temperature of 1540°C, which meets the set requirements. Looking at all individual parts, no material reaches their limiting temperatures. Where the most critical parts are the zirconia blocks that may not exceed 1170°C [54], they remain at 1010°C which is well below the limit. In addition, the constraints of the cooling water temperature are not violated either with a temperature of 75°C in the clamp cooling conduit.

Figure 51: Cross section of the final model without the top cover for 65W. The sample temperature reaches 1540°C while the cooling reaches only 75°C and the plate reaches 450°C.

In order to be able to validate the thermal simulations and to be able to predict sample temperatures for a given input power, the model is simulated for a range of powers from 0 to 100W. While the graph below shows the temperature reaching its goal at around 65W, inputting 65W will not let the sample reach the given temperature due to losses and reflections in the laser delivery system.

Page 65

Figure 52: Power versus sample temperature calculated from simulations, in reality the curve will shift to the right due to losses in the light delivery system.

0 500 1000 1500 2000 2500

0 20 40 60 80 100

Page 66 E.5 Detector Screen Cooling

While various assumptions and simplifications have been made both for the dedicated heating stage and the tensile stage with respect to thermal simulations, the detector screen cooling doesn’t need this: the problem is well defined by being fabricated solely from glass and having a easily definable maximum heat load.

As thermal conductivity increases for increasing temperatures , the energy dissipation occurring from the front of the screen, through the glass, and into the cooling water also increases for increasing temperature [55]. Therefore, modelling the detector cooling with thermal properties, valid at room temperature, ensures that the cooling will be sufficient.

As, both for the dedicated heating stage and tensile heating module, the heatshield limits the exiting thermal radiation. With this, the phosphor screen position for which the incident radiation is maximal, is the position for which the outgoing electron cone fully shines on the detector. Moving the screen away from the sample results in less radiation while moving the screen towards the sample only decreases the area where the radiation hits the detector but not the amount of energy.

As the latter decreases the quality of the acquired data, the second case is evaluated in the thermal simulations. The amount of radiation incident on the screen is determined to be 15W. The result for which is shown below in Figure 53. The amount of radiation is determined by calculating the amount of energy per unit area that the sample emits as a black body, and subsequently multiplying it by the visible area of the sample. As the sample emits radiation in all directions, the energy that is blocked by the heatshield amounts to 40% of total radiated energy of 25W, resulting in a heat load of 15W on the sample.

Figure 53: Thermal simulation of the phosphor screen for a sample temperature of 1500°C

From Figure 53, it can be seen that the temperature distribution is quite homogenous in the area where the phosphor screen has been deposited. Outside of this area, the temperature gradient is quite large and the temperature decreases rapidly moving away from this phosphor screen. The maximum temperature is found in the middle of the screen, which is according to expectations as the incoming energy is the largest there. The maximum temperature is 35°C on the screen, and 21°C on the rear of the assembly, both temperatures are within operational values of the materials thermal properties and below values where negative effects such as thermal noise start to occur [23].

Page 67

F. Sample preparation

In order to achieve high quality kikuchi patterns and therefore high quality EBSD results, sample

In order to achieve high quality kikuchi patterns and therefore high quality EBSD results, sample