Measurement I1: Minimizing interfering influences

To rule out as many interfering influences as possible, a measurement was performed with an unused filament and a new crucible filled with chemically clean lead. Additionally no thermocouples were attached.

While assembling the oven, the heat reflective tantalum foil that is part of its setup had to be shortened by cutting off a piece of approximately 1 cm as it was damaged and would not fit into the assembly otherwise. The power was adjusted manually to keep a stable evaporation rate. When the rate dropped notably it was raised until the evaporation rate recovered.

Results

The measured evaporation rate together with the power is presented in figure 5.20.

At a power of 9 W the evaporation rate rose to a value of around 5 mg h⁻¹and stayed stable for more than 60 h at a constant power value. Then it dropped suddenly, which led

5.3. Unstable evaporation rates

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 0

2 4 6

0 10 20 D1 D2 30

t [h]

R[mgh−1] P[W]

Evaporation rate,R Uncertainty Oven power,P

Figure 5.20.:Evaporation rate and power during measurement I1, with chemically clean lead, a reduced tantalum foil and without external thermocouples. Two time windows, D1 and D2 are further discussed, see figure 5.21.

to the decision to raise the oven power. A second drop of the evaporation rate followed and made an additional raise of the power necessary.

In the second half the evaporation rate decreased over time when the power stayed constant. By raising the oven power several times the evaporation rate could be stopped from dropping below 3 mg h⁻¹for around 80 h. Then it dropped further and it was decided to stop the measurement. During this measurement the evaporation rate was stable over longer times than what was observed before.

Evaporation and resistance changes

Two distinctive drops of the evaporation rate can be seen and only an increase of the oven power could restore a comparable rate as before. The time frames of the drops are marked in grey in figure 5.20, calling them ’D1’ and ’D2’.

It was observed that during the evaporation decrease the oven filament resistance,r, displayed a similar decrease over time as the evaporation rate. Figure 5.21 shows the evaporation rate during these time frames, together with the filament resistance.

In both time frames the evaporation is not changing more than 1 mg h⁻¹over a time of approximately 10 h and then suddenly drops, in the frame D1 1.5 mg h⁻¹in 4 h and in frame D2 2.5 mg h⁻¹ in less than 4 h. In the two time frames the resistance of the oven filament showed a similar temporal profile as the evaporation rate.

The visible fluctuation of the filament resistance is due to the numerical precision of the

1.945 1.95 1.955 1.96 1.965 1.97 1.975

104 106 108 110 112 114 116 118 120

2 2.5 3 3.5 4 4.5 5

1.92 1.94 1.96 1.98 2

124 126 128 130 132 134 136 138 140 142 144 1

2 3 4

r[Ω]

D1

t [h]

R[mgh−1 ] r[Ω]

t [h]

R[mgh−1]

D2

Fil. resistance,r Evaporation rate,R

Figure 5.21.:Evaporation rate and filament resistancer plotted for the two time windows D1 and D2 as shown in figure 5.20. Both drops of the evaporation rate happened while the oven power was constant.

5.3. Unstable evaporation rates

PLC that calculates the resistance from the current and voltage values of the power supply.

The change of the resistance especially in the first case (D1) is more easily visible by smoothing the data, as the change is within the range of the noise fluctuation. For this purpose the resistance data was smoothed using a Gaussian filter.

In both graphs of figure 5.21 the measured resistance is convoluted with a Gaussian function in the time domain, whose width isσ=20 min. The smoothed values are shown as a solid line while the raw resistance data is included as unconnected marks.

Resistance derivation

Plotting the resistance together with the evaporation rate for the complete run in a similar way as done with the oven power in figure 5.20 makes it difficult to see any drops in the resistance, as e.g. the change during the time window D1 is smaller than the resistance increase during a typical power increase.

To still get an overview of the local resistance behaviour in comparison to the evaporation rate, a time derivation of the resistance values can be used. In the two presented cases the resistance is decreasing together with the evaporation. To focus on such events one can look at a value representing the negative derivation:

|r_neg⁰ |=H



−∂r

∂t

‹

∂r

∂t

, (5.3)

whereH is the Heaviside step function in this case setting positive results to zero and

∂r

∂t the derivative of the resistancer with respect to timet. Equation 5.3 gives a value that is positive if the resistance drops and zero if it does not change or if it grows.

Figure 5.22 shows the value of|r_neg⁰ |calculated from the smoothed resistance data to-gether with the evaporation rate. The values were normalized, becoming|r_neg,norm⁰ |. Addi-tionally the resistance data were cut off before the power was set to zero, as the resulting peak of |r_neg⁰ |would otherwise overshadow all other resistance drops. As a last step all values of|r_neg,norm⁰ |smaller than 0.05 were set to zero simply to make the resulting plot clearer.

The result shows that several times the resistance drops over the duration of the measure-ment and in the time of the three largest decreases of the resistance also the evaporation rate dropped, which is visible as peaks of the|r_neg,norm⁰ |value.

0 50 100 150 200 250 300 0

2 4 6

0 0.2 0.4 0.6 0.8 1

t [h]

R[mgh−1] |r0 neg,norm|[a.u.]

Evaporation rate,R res. derivation,|r_neg,norm⁰ |

Figure 5.22.:The evaporation rate together with|r_neg,norm⁰ |which indicates a negative derivation of the filaments resistance.