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# Units¶

## What are units?¶

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 Dynamic Factory that creates and hands out instances of Mantid Unit objects.

## Available TOF Convertible units¶

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 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.

## Available non-TOF Convertible units¶

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

## Working with Units in Python¶

### Accessing units on workspaces¶

Units on MatrixWorkspaces are accessed via the Axis.

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:

Axis 0 is a Numeric Axis
caption:Time-of-flight
symbol:microsecond
Axis 1 is a Spectrum Axis
caption:Spectrum
symbol:


### Setting the axisLabel to a Label of your choice¶

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:

New caption:Temperature
New symbol:K