\label{sec:procedure} The calibration was carried out at the laboratory for vacuum metrology at the Physikalisch-Technische Bundesanstalt (PTB). In the pressure range from \SI{2.7e+01}{\pascal} to \SI{1.3e+02}{\pascal}, the calibration pressure was established in the primary standard SE3 metrologically linked to the primary standard SE2 of PTB applying the static expansion method. In the range \SI{2.7e+02}{\pascal} to \SI{2.7e+04}{\pascal} the calibration was carried out by direct comparison to a secondary standard consisting of 15 diaphragm gauges. The gas temperature during calibration using the static expansion method with nitrogen was \SI{296.719+-0.031}{\kelvin} at a room temperature of \SI{296.32+-0.09}{\kelvin}. During the calibration by direct comparison with nitrogen the temperature of the gas was \SI{296.3+-1.6}{\kelvin}. Here, the room temperature was \SI{296+-2}{\kelvin}.
<dcc:contentlang="en">\label{sec:procedure} The calibration was carried out at the laboratory for vacuum metrology at the Physikalisch-Technische Bundesanstalt (PTB). In the pressure range from \SI{2.7e+01}{\pascal} to \SI{1.3e+02}{\pascal}, the calibration pressure was established in the primary standard SE3 metrologically linked to the primary standard SE2 of PTB applying the static expansion method. In the range \SI{2.7e+02}{\pascal} to \SI{2.7e+04}{\pascal} the calibration was carried out by direct comparison to a secondary standard consisting of 15 diaphragm gauges. The gas temperature during calibration using the static expansion method with nitrogen was \SI{296.719+-0.031}{\kelvin} at a room temperature of \SI{296.32+-0.09}{\kelvin}. During the calibration by direct comparison with nitrogen the temperature of the gas was \SI{296.3+-1.6}{\kelvin}. Here, the room temperature was \SI{296+-2}{\kelvin}.
The device was operated with the following setup: \begin{itemize}[leftmargin=1cm]
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\end{itemize}
Before each calibration point the offset \(p_\text{r}\) was recorded (5 readings) at the base pressure and subtracted from the subsequent indication \(p_\text{ind}\) to give the corrected indicated value \(p_\text{corr}\). The contribution of the offset scatter to the total uncertainty was $(k=1)$: \begin{itemize} \item[nitrogen, static expansion method:]\, \begin{itemize} \item[\SI{7.6E-02}{\pascal}] entire measurement range \end{itemize} \end{itemize} \begin{itemize} \item[nitrogen, direct comparison method:]\, \begin{itemize} \item[\SI{1.6E-01}{\pascal}] entire measurement range \end{itemize} \end{itemize}
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Before each calibration point the offset \(p_\text{r}\) was recorded (5 readings) at the base pressure and subtracted from the subsequent indication \(p_\text{ind}\) to give the corrected indicated value \(p_\text{corr}\). The contribution of the offset scatter to the total uncertainty was $(k=1)$: \begin{itemize} \item[nitrogen, static expansion method:]\, \begin{itemize} \item[\SI{7.6E-02}{\pascal}] entire measurement range \end{itemize} \end{itemize} \begin{itemize} \item[nitrogen, direct comparison method:]\, \begin{itemize} \item[\SI{1.6E-01}{\pascal}] entire measurement range \end{itemize} \end{itemize}</dcc:content>
</dcc:description>
</dcc:usedMethod>
<dcc:usedMethod>
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<dcc:contentlang="en">Relative error of pressure indication and correction factor</dcc:content>
</dcc:name>
<dcc:description>
<dcc:contentlang="en">
<![CDATA[
The relative error \(e\) of the corrected indicated pressure \(p_\text{corr}\) (with \(p_\text{corr} = p_\text{ind} - p_\text{r}\)) at the time of calibration is defined as:\[e = \frac{p_\text{ind} - p_\text{r}}{p_\text{cal}} - 1\] where \(p_\text{cal}\) denotes the calibration pressure as generated in the primary standard. From this, the real pressure \(p\) can be calculated from the indicated and offset pressure by:\[p = \frac{p_\text{ind} - p_\text{r}}{e + 1}\]
<dcc:contentlang="en">The relative error \(e\) of the corrected indicated pressure \(p_\text{corr}\) (with \(p_\text{corr} = p_\text{ind} - p_\text{r}\)) at the time of calibration is defined as:\[e = \frac{p_\text{ind} - p_\text{r}}{p_\text{cal}} - 1\] where \(p_\text{cal}\) denotes the calibration pressure as generated in the primary standard. From this, the real pressure \(p\) can be calculated from the indicated and offset pressure by:\[p = \frac{p_\text{ind} - p_\text{r}}{e + 1}\]
The correction factor \(CF\) is defined by: \[CF =\frac{p_\text{cal}}{p_\text{ind} - p_\text{r}}\] and can be used to calculate the real pressure \(p\) by: \[p = CF (p_\text{ind} - p_\text{r})\]
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The correction factor \(CF\) is defined by: \[CF =\frac{p_\text{cal}}{p_\text{ind} - p_\text{r}}\] and can be used to calculate the real pressure \(p\) by: \[p = CF (p_\text{ind} - p_\text{r})\]</dcc:content>
</dcc:description>
</dcc:usedMethod>
<dcc:usedMethod>
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<dcc:contentlang="en">Result of the calibration</dcc:content>
</dcc:name>
<dcc:description>
<dcc:contentlang="en">
<![CDATA[
The results of the measurements are given in the following table. \(U(e)\) is the uncertainty of the relative error and \(U(CF)\) the uncertainty of the correction factor. Included is the repeatability of the measurement under otherwise identical conditions (\(p_\text{cal}\), \(T\)). \printResultTable
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<dcc:contentlang="en">The results of the measurements are given in the following table. \(U(e)\) is the uncertainty of the relative error and \(U(CF)\) the uncertainty of the correction factor. Included is the repeatability of the measurement under otherwise identical conditions (\(p_\text{cal}\), \(T\)). \printResultTable</dcc:content>
</dcc:description>
</dcc:usedMethod>
<dcc:usedMethod>
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<dcc:contentlang="en">Uncertainty</dcc:content>
</dcc:name>
<dcc:description>
<dcc:contentlang="en">
<![CDATA[
The uncertainty stated is the expanded measurement uncertainty obtained by multiplying the standard measurement uncertainty by the coverage factor \(k=2\). It has been determined in accordance with the “Guide to the Expression of Uncertainty in Measurement (GUM)”. The value of the measurand then normally lies, with a probability of approximately \SI{95}{\percent}, within the attributed coverage interval.
]]></dcc:content>
<dcc:contentlang="en">The uncertainty stated is the expanded measurement uncertainty obtained by multiplying the standard measurement uncertainty by the coverage factor \(k=2\). It has been determined in accordance with the “Guide to the Expression of Uncertainty in Measurement (GUM)”. The value of the measurand then normally lies, with a probability of approximately \SI{95}{\percent}, within the attributed coverage interval.</dcc:content>
</dcc:description>
</dcc:usedMethod>
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<dcc:contentlang="de">Temperatur des Messgases</dcc:content>
\label{sec:procedure} The effective accommodation coefficient \(\sigma(p)\) was determined between \SI{0.1}{\pascal} and \SI{1}{\pascal} by using the pressures generated in the PTB primary standard SE3 metrologically linked to the primary standard SE2, which is based on the static expansion method. The extrapolated effective accommodation coefficient \(\sigma_0\) (\(p < \SI{1E-2}{\pascal}\)) was determined by extrapolation for \(p \rightarrow 0\) of the linear regression analysis of the data. A run-in-time of at least 12 h was provided before calibration.\par The measurements were performed with 6 readings for each of the 5 target points.\par The gas temperature \(T\) during calibration using the static expansion method with nitrogen was \SI{295.849+-0.033}{\kelvin} at a room temperature of \SI{296.16+-0.04}{\kelvin}.
<dcc:contentlang="en">\label{sec:procedure} The effective accommodation coefficient \(\sigma(p)\) was determined between \SI{0.1}{\pascal} and \SI{1}{\pascal} by using the pressures generated in the PTB primary standard SE3 metrologically linked to the primary standard SE2, which is based on the static expansion method. The extrapolated effective accommodation coefficient \(\sigma_0\) (\(p < \SI{1E-2}{\pascal}\)) was determined by extrapolation for \(p \rightarrow 0\) of the linear regression analysis of the data. A run-in-time of at least 12 h was provided before calibration.\par The measurements were performed with 6 readings for each of the 5 target points.\par The gas temperature \(T\) during calibration using the static expansion method with nitrogen was \SI{295.849+-0.033}{\kelvin} at a room temperature of \SI{296.16+-0.04}{\kelvin}.
The device was operated with the following setup: \begin{quote} \sisetup{detect-all} \begin{tabular}{@{}>{}r@{:~}l@{}} Diameter of the rotor (\(d\))& \SI{4.5}{\milli\metre} \\ Density of the rotor (\(\rho\)) & \SI{7.7}{\gram\per\centi\metre\tothe{3}} \\ Sigma & \num{1.0} \\ Viscosity & \num{0} \\ Unit & 1/s (DCR) \end{tabular} \end{quote} For the measurement with nitrogen, a molar mass (\(M\)) of \( \SI{28.013}{\gram\per\mol} \) was used.
The device was operated with the following setup: \begin{quote} \sisetup{detect-all} \begin{tabular}{@{}>{}r@{:~}l@{}} Diameter of the rotor (\(d\))& \SI{4.5}{\milli\metre} \\ Density of the rotor (\(\rho\)) & \SI{7.7}{\gram\per\centi\metre\tothe{3}} \\ Sigma & \num{1.0} \\ Viscosity & \num{0} \\ Unit & 1/s (DCR) \end{tabular} \end{quote} For the measurement with nitrogen, a molar mass (\(M\)) of \( \SI{28.013}{\gram\per\mol} \) was used.
A sample of the residual drag (RD) including its scatter was measured before the calibration at a base pressure below \(\SI{1E-6}{\pascal}\). Before the measurement with the calibration gas nitrogen, a RD of \SI{1.5429E-06}{\per\second} with a standard deviation of \SI{8.0E-10}{\per\second} was determined. Before each calibration point, RD (6 readings) was checked at the base pressure and subtracted from the subsequent measurement of the relative deceleration rate.
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</dcc:content>
A sample of the residual drag (RD) including its scatter was measured before the calibration at a base pressure below \(\SI{1E-6}{\pascal}\). Before the measurement with the calibration gas nitrogen, a RD of \SI{1.5429E-06}{\per\second} with a standard deviation of \SI{8.0E-10}{\per\second} was determined. Before each calibration point, RD (6 readings) was checked at the base pressure and subtracted from the subsequent measurement of the relative deceleration rate.</dcc:content>
The effective accommodation coefficient was obtained by: \[ \sigma(p_\text{cal}) = \frac{1}{p_\text{cal}} \frac{\pi\rho d}{20} \sqrt{\frac{8 R T}{\pi M}} \left( -\frac{\dot{\!\omega}}{\!\omega} - \text{RD}(\omega) \right) \] with \(R\) the gas constant, \(-\,\dot{\!\omega}/\omega\) the relative deceleration rate and \(p_\text{cal}\) the calibration pressure generated by the primary standard. For the calibration with the measurement gas nitrogen the extrapolated effective accommodation coefficient \(\sigma_0\) for \(p < \SI{1E-2}{\pascal}\) was: \[ \sigma_0 = \lim_{p_\text{cal}\rightarrow 0} \sigma(p_\text{cal}) = \SI{0.9555}{}\quad (\text{nitrogen}) \] With this \(\sigma_0\) together with \(d\) and \(\rho\) from the parameter set under section \ref{sec:procedure}, the SRG controller will give the correct reading of pressure within the measurement uncertainties according to this calibration for pressures \(p < \SI{1E-2}{\pascal}\). Alternatively, the pressure can be calculated from the relative deceleration rate according to \[ p_\text{ind} = \frac{\pi\rho d}{20 \sigma_0} \sqrt{\frac{8 R T}{\pi M}} \left( -\frac{\dot{\!\omega}}{\!\omega} - \text{RD}(\omega) \right)\,. \] In both cases offset and temperature have to be determined for each measurement.\par In the pressure range \(p > \SI{1E-2}{\pascal}\) up to \(p = \SI{2}{\pascal}\), the real pressure \(p\) will be received by multiplication of the indicated pressure \(p_{\text{ind}}\) with a correction factor \(f(p_{\text{ind}})\): \[ p = p_{\text{ind}} f(p_{\text{ind}}) \] and viscosity = 0 entered in the controller. From our calibration, \(f(p_{\text{ind}})\) was obtained for this rotor by the following equation: \[ f(p_{\text{ind}}) = (1 + ( \SI{0.01796+-0.0006}{\per\pascal} ) \cdot p_{\text{ind}}) \quad (\text{nitrogen}) \]
]]></dcc:content>
<dcc:contentlang="en">The effective accommodation coefficient was obtained by: \[ \sigma(p_\text{cal}) = \frac{1}{p_\text{cal}} \frac{\pi\rho d}{20} \sqrt{\frac{8 R T}{\pi M}} \left( -\frac{\dot{\!\omega}}{\!\omega} - \text{RD}(\omega) \right) \] with \(R\) the gas constant, \(-\,\dot{\!\omega}/\omega\) the relative deceleration rate and \(p_\text{cal}\) the calibration pressure generated by the primary standard. For the calibration with the measurement gas nitrogen the extrapolated effective accommodation coefficient \(\sigma_0\) for \(p < \SI{1E-2}{\pascal}\) was: \[ \sigma_0 = \lim_{p_\text{cal}\rightarrow 0} \sigma(p_\text{cal}) = \SI{0.9555}{}\quad (\text{nitrogen}) \] With this \(\sigma_0\) together with \(d\) and \(\rho\) from the parameter set under section \ref{sec:procedure}, the SRG controller will give the correct reading of pressure within the measurement uncertainties according to this calibration for pressures \(p < \SI{1E-2}{\pascal}\). Alternatively, the pressure can be calculated from the relative deceleration rate according to \[ p_\text{ind} = \frac{\pi\rho d}{20 \sigma_0} \sqrt{\frac{8 R T}{\pi M}} \left( -\frac{\dot{\!\omega}}{\!\omega} - \text{RD}(\omega) \right)\,. \] In both cases offset and temperature have to be determined for each measurement.\par In the pressure range \(p > \SI{1E-2}{\pascal}\) up to \(p = \SI{2}{\pascal}\), the real pressure \(p\) will be received by multiplication of the indicated pressure \(p_{\text{ind}}\) with a correction factor \(f(p_{\text{ind}})\): \[ p = p_{\text{ind}} f(p_{\text{ind}}) \] and viscosity = 0 entered in the controller. From our calibration, \(f(p_{\text{ind}})\) was obtained for this rotor by the following equation: \[ f(p_{\text{ind}}) = (1 + ( \SI{0.01796+-0.0006}{\per\pascal} ) \cdot p_{\text{ind}}) \quad (\text{nitrogen}) \]</dcc:content>
</dcc:description>
</dcc:usedMethod>
<dcc:usedMethod>
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<dcc:contentlang="en">Uncertainty</dcc:content>
</dcc:name>
<dcc:description>
<dcc:contentlang="en">
<![CDATA[
The uncertainty of \(\sigma_0\) at the time of calibration is estimated to \SI{0.26}{\percent} (this includes the relative deviation of \(\sigma_0\) with different orientations after a new suspension). The uncertainty stated is the expanded measurement uncertainty obtained by multiplying the standard measurement uncertainty by the coverage factor \(k=2\). It has been determined in accordance with the “Guide to the Expression of Uncertainty in Measurement (GUM)”. The value of the measurand then normally lies, with a probability of approximately \SI{95}{\percent}, within the attributed coverage interval.
]]></dcc:content>
<dcc:contentlang="en">The uncertainty of \(\sigma_0\) at the time of calibration is estimated to \SI{0.26}{\percent} (this includes the relative deviation of \(\sigma_0\) with different orientations after a new suspension). The uncertainty stated is the expanded measurement uncertainty obtained by multiplying the standard measurement uncertainty by the coverage factor \(k=2\). It has been determined in accordance with the “Guide to the Expression of Uncertainty in Measurement (GUM)”. The value of the measurand then normally lies, with a probability of approximately \SI{95}{\percent}, within the attributed coverage interval.</dcc:content>
</dcc:description>
</dcc:usedMethod>
</dcc:usedMethods>
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<dcc:contentlang="de">Temperatur des Messgases</dcc:content>
