Units are a set of small classes in Mantid that define a unit of measure, and the conversions between various units.
The Unit Factory is a :ref:`Dynamic Factory <Dynamic Factory>` that creates and hands out instances of Mantid Unit objects.
The following units are available in the default Mantid distribution. These units are TOF convertible.
| Name | ID (as known by Unit Factory) | Unit | Relevant equation |
|---|---|---|---|
| Time of flight | TOF | \mu s | TOF |
| Wavelength | Wavelength | \mathrm{\AA} | \lambda = \frac{h}{p} = \frac{h \times \mathrm{tof}}{m_N \times L_{tot}} (see below) |
| Energy | Energy | meV | E = \frac{1}{2} mv^2 = \frac{m_N}{2} \left ( \frac{L_{tot}}{\mathrm{tof}} \right )^2 |
| Energy in wavenumber | Energy_inWavenumber | cm^{-1} | 8.06554465 \times E |
| Momentum (k) | Momentum | \mathrm{\AA}^{-1} | k = \frac{2 \pi }{\lambda}=\frac{2 \pi \times m_N \times L_{tot}}{h \times \mathrm{tof}} |
| d-spacing | dSpacing | \mathrm{\AA} | TOF = DIFA \, d^2 + DIFC d + TZERO (see below) |
| Momentum transfer (Q) | MomentumTransfer | \mathrm{\AA}^{-1} | Q = 2 \, k \, sin \, \theta = \frac{4 \pi sin \theta}{\lambda} |
| Momentum transfer squared (Q^2) | QSquared | \mathrm{\AA}^{-2} | Q^2 \frac{}{} |
| Energy transfer | DeltaE | meV | \Delta E = E_{i}-\frac{1}{2}m_N \left ( \frac{L_2}{\mathrm{tof}-L_1\sqrt{\frac{m_N}{2E_i}}} \right )^2 |
| Energy transfer in wavenumber | DeltaE_inWavenumber | cm^{-1} | 8.06554465 \times \Delta E |
| Spin Echo Length | SpinEchoLength | nm | constant \times \lambda^2
The constant is supplied in eFixed
|
| Spin Echo Time | SpinEchoTime | ns | constant \times \lambda^3
The constant is supplied in eFixed
|
| d-spacingPerpendicular | dSpacingPerpendicular | \mathrm{\AA} | d_{\perp} = \sqrt{\lambda^2 - 2\log\cos\theta} |
Where L_1 and L_2 are sample to the source and sample to detector distances respectively, L_{tot} = L_1+L_2 and E_i is the energy of neutrons leaving the source. \theta here is the Bragg scattering angle (e.g. half of the \theta-angle used in spherical coordinate system directed along Mantid z-axis)
Note on Wavelength: If the emode property in :ref:`ConvertUnits <algm-ConvertUnits>` is specified as inelastic Direct/Indirect (inelastic) then the conversion to wavelength will take into account the fixed initial/final energy respectively. Units conversion into elastic momentum transfer (MomentumTransfer) will throw in elastic mode (emode=0) on inelastic workspace (when energy transfer is specified along x-axis)
Note on d-spacing: The coefficients DIFA, DIFC and TZERO may be obtained via calibration of a TOF diffraction instrument. In the absence of a calibration, DIFA=TZERO=0 and the default value of DIFC is:
DIFC = 10^{-4} \frac{m_N}{h} (L_1 + L_2) 2 \sin(\theta)
where the scaling factor adjusts for the fact that DIFC is required in units of \mu s per \mathrm{\AA}.
d-spacingPerpendicular is a unit invented in J. Appl. Cryst. (2015) 48, pp. 1627--1636 for 2D Rietveld refinement of angular and wavelength-dispersive neutron time-of-flight powder diffraction data. Together with the d-Spacing d, d-SpacingPerpendicular d_{\perp} forms a new orthogonal coordinate system.
The following units are available in the default Mantid distribution. These units cannot be converted to or from TOF.
| Name | ID (as known by Unit Factory) | Unit | Description |
|---|---|---|---|
| Empty | No unit | An empty label | |
| t | Time | s | An independent unit of time not related to energy or TOF |
| Scattering angle | Degrees | degrees | Degrees is a measurement of angular position |
| Temperature | Temperature | K | Temperature in Kelvin |
Units on MatrixWorkspaces are accessed via the Axis.
.. testcode:: UnitWorkspaceAxes
ws = CreateSampleWorkspace()
for i in range(ws.axes()):
axis = ws.getAxis(i)
print("Axis {0} is a {1}{2}{3}".format(i,
"Spectrum Axis" if axis.isSpectra() else "",
"Text Axis" if axis.isText() else "",
"Numeric Axis" if axis.isNumeric() else ""))
unit = axis.getUnit()
print("\t caption:{0}".format(unit.caption()))
print("\t symbol:{0}".format(unit.symbol()))
Output:
.. testoutput:: UnitWorkspaceAxes
:options: +NORMALIZE_WHITESPACE
Axis 0 is a Numeric Axis
caption:Time-of-flight
symbol:microsecond
Axis 1 is a Spectrum Axis
caption:Spectrum
symbol:
.. testcode:: UnitAxesLabel
ws = CreateSampleWorkspace()
axis = ws.getAxis(1)
# Create a new axis
axis.setUnit("Label").setLabel('Temperature', 'K')
unit = axis.getUnit()
print("New caption:{0}".format(unit.caption()))
print("New symbol:{0}".format(unit.symbol()))
Output:
.. testoutput:: UnitAxesLabel :options: +ELLIPSIS,+NORMALIZE_WHITESPACE New caption:Temperature New symbol:K
Writing and adding a new unit is relatively straightforward. Instructions will appear here in due course. In the meantime if a unit that you require is missing, then please contact the development team and we will add it to the default Mantid library.
.. categories:: Concepts