High-energy-resolution X-ray monochromator calibration using the detailed-balance principle

Abstract

A new method is presented to calibrate an X-ray energy scale with sub-meV relative accuracy by using the detailed-balance principle of the phonon creation and annihilation. This method is conveniently used to define or verify the energy scale of high-energy-resolution monochromators that are used in inelastic X-ray scattering and nuclear resonant inelastic X-ray scattering instruments at synchrotron radiation facilities. This method does not rely on sample properties and its precision only depends on the statistical data quality. Well calibrated instruments are essential for reliable comparison of data sets obtained at different synchrotron radiation beamlines, of data with theoretical predictions, and of data from other techniques such as neutron or light scattering. The principle of the detailed-balance method is described in this paper and demonstrated experimentally.

Energy calibration issues in nuclear resonant vibrational spectroscopy: observing small spectral shifts and making fast calibrations

“…Omitting the higher-order corrections (Zhao & Sturhahn, 2012), the real energy position can be calculated with E real = (KE obs +ÁE), where E real stands for the real energy, E obs stands for the observed energy, ÁE is the energy position drift and K is the energy scale. The energy calibration thus includes: (i) aligning the nuclear resonant peak to E = 0 to correct for ÁE; (ii) rescaling the energy axis to obtain the correct K value.…”

“…The energy of the high-resolution monochromator (HRM) used for NRVS can be scanned (or altered involuntarily) by changing: (i) the relative scattering angles among the HRM crystals; and/or (ii) the temperature of one back-reflection crystal (Zhao & Sturhahn, 2012). The accuracy for the energy scale therefore relies on the high-precision measurements (and controls) on the angle, the temperature, as well as the thermal gradients for the HRM crystals.…”

“…The error is usually about a few percent of the HRM energy. For higher accuracy, additional calibration is required (Zhao & Sturhahn, 2012). NRVS, especially on biological samples, has a very weak signal level and needs about 24-48 h (Kamali et al, 2013) to obtain a quality spectrum for a dilute sample.…”

“…In a recent publication, Zhao & Sturhahn (2012) reported a successful procedure to calibrate HRM energy using the detailed-balance between the phonon annihilation and the phonon creation in an iron foil (or in any samples), with minor changes in the NRVS measurement set-up. This is a sampleindependent method and does not require a specified standard sample.…”

“…It also provides an accurate energy ruler (including the higher-order corrections) for an interested HRM. However, their procedure takes about 4 h (Zhao & Sturhahn, 2012), which still limits its application as a frequent energy checkup during regular NRVS measurements.…”