The peak energies of the fits of individual measured V Kβ spectra

<p><strong>Figure 8.</strong> The peak energies of the fits of individual measured V Kβ spectra. Each of the seven lines represents an independently measured set of results from the full calibration series, derived by methodical stepping of the spectrometer arm length so that the profile stepped across the detector area. The variance is larger than the point precision, indicating sources of systematics. The characterization function drifts off towards the edges of the detector, where vignetting or other loss of efficiency may affect the calibration. Further, some of the linked series have offsets, whether from minor hysteresis or e.g. temperature variations. The overall consistency and hence robustness of the independent measurements yields a final pooled uncertainty of 0.0184 eV or 3.4 ppm.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

The peak energy of the fitted model function of the Ti Kβ spectra as a function of the instrumental broadening

<p><strong>Figure 7.</strong> The peak energy of the fitted model function of the Ti Kβ spectra as a function of the instrumental broadening. The measured broadening of the spectrum of 1.24(4) eV and the asymmetry of the peak leads to a shift of peak position of 0.25 eV or 50 ppm.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

Schematic diagram of experimental setup

<p><strong>Figure 1.</strong> Schematic diagram of experimental setup.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

Characterization of the Ti Kβ spectral profile

<p><b>Table 2.</b> Characterization of the Ti Kβ spectral profile. The profile is fully characterized on an absolute energy scale through a sum of component Lorentzians convolved with a Gaussian instrumental broadening. Integrated areas <em>A_i</em>, centroids <em>C_i</em> and FWHMs <em>W_i</em> of individual components were obtained from a fit of intensity against detector position. The detector position axis was transformed to an absolute energy scale via the calibration procedure. The Gaussian width σ = 1.244(41) eV. The background was <em>B</em> = 831(26) counts. The second and third components are dominant, contributing more than three quarters of the intensity of the spectrum while the fourth component is very weak. The third and fourth component widths are dominated by the Gaussian instrumental width. The first component is very broad relative to the entire Kβ spectrum.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

Error budget for the peak energy of all the spectral profiles of Ti Kβ that go into the final energy determination

<p><b>Table 3.</b> Error budget for the peak energy of all the spectral profiles of Ti Kβ that go into the final energy determination. Since the resultant determined energies show evidence of additional variance, the final energy determination has a larger uncertainty that this ideal 1.6 ppm for an individual spectrum.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

The full characterization of the V Kβ spectral profile on an absolute energy scale

<p><b>Table 4.</b> The full characterization of the V Kβ spectral profile on an absolute energy scale. The parameters in this table are used in equation (<a href="http://iopscience.iop.org/0953-4075/46/14/145601/article#jpb458169eqn05" target="_blank">5</a>). Amplitudes <em>A_i</em>, centroids <em>C_i</em> and widths <em>W_i</em> of individual components were obtained from a fit on the intensity versus detector position axis. The detector position axis was transformed to an absolute energy scale via the calibration procedure. The Gaussian width σ was 0.805(25) eV. The background was 749(24) counts.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

Characteristic radiation peak energy data from Chantler <em>et al</em> [19] and Deslattes <em>et al</em> [6]

<p><b>Table 1.</b> Characteristic radiation peak energy data from Chantler <em>et al</em> [<a href="http://iopscience.iop.org/0953-4075/46/14/145601/article#jpb458169bib19" target="_blank">19</a>] and Deslattes <em>et al</em> [<a href="http://iopscience.iop.org/0953-4075/46/14/145601/article#jpb458169bib06" target="_blank">6</a>]. The peak energy of the Kβ radiation has a larger uncertainty than for Kα radiation by an order of magnitude.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

Typical fit of a Ti Kβ spectrum

<p><strong>Figure 5.</strong> Typical fit of a Ti Kβ spectrum. The crystal clinometer voltage was −1.012 9597(74) V and the peak detector position was 0.8089(14) mm. Fitting parameters are provided in table <a href="http://iopscience.iop.org/0953-4075/46/14/145601/article#jpb458169t2" target="_blank">2</a>.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

The peak energies of the fits of individual measured Ti Kβ spectra

<p><strong>Figure 6.</strong> The peak energies of the fits of individual measured Ti Kβ spectra. Each of the seven lines represents an independently measured set of results from the full calibration series, derived by methodical stepping of the spectrometer arm length so that the profile stepped across the detector area. The variance is larger than the point precision, indicating sources of systematics. The characterization function drifts off towards the edges of the detector, where vignetting or other loss of efficiency may affect the calibration. Further, some of the linked series have offsets, whether from minor hysteresis or e.g. temperature variations. The overall consistency and hence robustness of the independent measurements yields a final pooled uncertainty of 4.5 ppm.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p

The energy shift from Bragg's law predicted by Mosplate, including peak and profile shifts as used in the computation, with an estimated uncertainty of 1.5 ppm

<p><strong>Figure 3.</strong> The energy shift from Bragg's law predicted by Mosplate, including peak and profile shifts as used in the computation, with an estimated uncertainty of 1.5 ppm.</p> <p><strong>Abstract</strong></p> <p>Transition metals have Kα and Kβ characteristic radiation possessing complex asymmetric spectral profiles. Instrumental broadening normally encountered in x-ray experiments shifts features of profiles used for calibration, such as peak energy, by many times the quoted accuracies. We measure and characterize the titanium Kβ spectral profile. The peak energy of the titanium Kβ spectral profile is found to be 4931.966 ± 0.022 eV prior to instrumental broadening. This 4.5 ppm result decreases the uncertainty over the past literature by a factor of 2.6 and is 2.4 standard deviations from the previous standard. The spectrum is analysed and the resolution-free lineshape is extracted and listed for use in other experiments. We also incorporate improvement in analysis applied to earlier results for V Kβ.</p