Calibration and peak positions¶

Calibration determines where a reflection appears on the experimental axis. It can therefore correlate strongly with fitted cell dimensions.

Constant-wavelength position¶

\[2\theta_h=\frac{360}{\pi}\arcsin\left(\frac{\lambda}{2d_h}\right),\qquad x_{\rm corrected}=x_{\rm observed}-z.\]

The angle returned by the position equation is in degrees; \(z\) is calib_twotheta_offset, also in degrees \(2\theta\). The corrected coordinate must remain in the admitted open angular range for calculated points. Wavelength and cell changes both affect reflection positions; check their physical meaning before fitting both freely.

Displacement and transparency shifts¶

The implemented CW reflection-centre shift is

\[\Delta(2\theta_h)=D\cos(2\theta_h)+T\sin(2\theta_h),\]

where \(D\) is calib_sample_displacement and \(T\) is calib_sample_transparency, in degrees \(2\theta\). It is applied to each reflection centre. The zero offset remains on the corrected observed axis. In particular, the displacement term here uses \(\cos2\theta\), not an assumed Bragg–Brentano \(\cos\theta\) formula.

Time-of-flight position¶

\[t_h=z+D_1d_h+D_2d_h^2.\]

\(z\) is in µs, \(D_1\) in µs/Å and \(D_2\) in µs/Å². The physical positive-spacing branch of the inverse quadratic is used; a negative quadratic coefficient does not by itself justify switching to the other mathematical root.

The reciprocal coefficient calib_d_to_tof_reciprocal (\(D_{-1}/d\)) is read and saved, but not used in the calculation.

Fixed bank angle¶

A TOF bank uses its declared scattering angle to determine \(\theta_{\rm bank}\) and \(\lambda_h=2d_h\sin\theta_{\rm bank}\). Keep the bank geometry with calibration and absorption settings when moving or comparing a project.

See instrument parameters, Bragg's law and TOF profiles.