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The Goniometer allows to figure out what angles to apply to a double-tilt or tilt-rotation
specimen holder in order to align a particular [uvw] crystallographic zone axis with the
microscope optical axis. Note that, in the Oxyz reference frame, Oz points up (anti-parallel
to the optical axis of a conventional TEM).

Figure 1 Double tilt specimen holder.
The tool buttons (from left to right) allows to:
Print the window.
Save the window.
Tranfer window to clipboard.
Show Specimen settings.
Show 3-D crystal.
Show HAADF image.
Show SAED pattern.
Display more [uvw].
Display less [uvw].
Show [uvw] or (hkl) indices.
Tabulate [uvw] zone axis.
Show toolbox
Show this help file.
Aligning a crystal with reference to the TEM optical axis requires to figure out the value
of 3 angles of rotations defined as follow:
Double-Tilt (DT): α rotation axis defined by the specimen holder axis (perpendicular
to the microscope optical axis), β rotation perpendicular to the specimen holder axis and θ is along the
[uvw]1 crystallographic direction (Fig. 1).
Tilt-Rotation (TR): α rotation along the specimen holder axis, θ perpendicular
to α along the microscope optical axis when α = 0 and φ also of [uvw] crystallographic
direction (Fig. 7).
With the help of the procedure described in this document the alignment of the crystal in any accessible [uvw] crystallographic
direction is made simpler and faster. One procedure defines the orientation of the crystal with respect to
the microscope reference frame using 2 [uvw] identified crystallographic zone axes while the other is
using one zone axis and the angle of its attached SAED with the specimen holder axis direction (Ox).
It should be noted that the proposed alignment procedure using 2 crystallographic zone axes
offers a way to improve the crystal orientation settings recursively, since identifying two crystallographic
directions separated by a larger angle renders the crystal orientation more accurate.
Since the alignment procedure using a DT or specimen holder are almost identical only
the procedure for orienting a crystal on a Double-Tilt specimen holder will be detailed.
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Double-Tilt specimen holder
The goniometer allows to compute the (α, β) angles necessary to align (anti - parallelly to the
electron beam) a particular zone axis. The alignment requires to specify the 2 angles (α, β) and
a third angle θ to fully orientate the crystal with reference to the microscope optical axis (Oz)
and the specimen holder Ox and Oy axes (with Ox being the specimen holder axial
direction and Oy perpendicular to Ox).
With (α, β) = (0, 0) the Oz axis is marked by a red circle at the stereogram centre.
The red arrows labeled α and β define the Ox axis (α tilt axis)
and the perpendicular Oy axis (β tilt axis). Note that only when α = 0 the arrow β is in the plane of
the figure,
The crystal orientation can be specified using either 2 identified crystallographic zone axes or a single one and the rotation of its
associated SAED pattern with respect to Ox. Here zone axis 1, [1,2,3]1, is aligned with Oz
when (α, β) = (20, 12) and zone axis 2, [0,1,1]2 is aligned when
(α, β, θ) = (4.8, 0, -126) (Figures 1, 2).
The [uvw] zone axis indices [−7, 189, 162] of the oriented crystal
are shown below the stereogram. Note that they are pretty close to [0,1,1]
as it should be.

Figure 2 Crystallographic axis [1,2,3] is aligned when (α, β) = (20, 12).

Figure 3 Crystallographic axis [0,1,1] is aligned when (α, β, θ) =
(4.8, 0, -126).

Figure 3a Goniometer plot at (α, β, θ) =
(0, 0, -126).
The keyboard arrows ←, →, ↑ and ↓ can be used to tilt the crystal or
to change the angle values displayed by the controls. Also after selecting a slider, the displayed
value can be modified using the ↑, ↓ arrows (this jems feature is available for slider controls).
Orientating the crystal using a single identified crystallographic zone axes and its associated SAED is similar:
Rotate the specimen holder in order to align (anti-parallel to the electron beam) a
particular crystal zone axis (here [1,2,3]). Put the zone axis [uvw]1 indices and
the (α, β) angles provided by the specimen holder into the controls of panel labelled
Zone axis of tab Crystal orientation. (Fig. 4).
Measure the angle between a single or a line of identified reflections and
the specimen holder Ox axis.
Select tab Reflection and put the (hkl) indices of the identified
reflection into text field (h,k,l). The reflection must belong to the Zero-Order Laue Zone.
The [uvw]1 SAED pattern is now plotted over the stereogram (Fig. 4a).
The θ control rotates the stereogram (rotation of axis [uvw]1). θ should be set to
the measured angle. The diffraction parameters, i.e. camera length, beam half-convergence, etc, as well as
thresholds used to filter out Kikuchi, HOLZ lines or diffraction spots are modified using the popup menu item
Show diffraction parameters.
Using the (β, β) controls of the tab Goniometer settings, the stereogram can be rotated in
order to align a particular [uvw] crystallographic zone axis with the microscope optical axis (Oz-axis).
When the orientation of the crystal is completed use the buttons:
- Done to freeze the orientation.
- Modify to modify the orientation settings.
- Reset to reset the angles.

Figure 4 SAED is oriented using the θ rotation (Double-tilt) or φ
(Tilt-Rotation).

Figure 4a SAED plotted on the oriented stereogram.
The popup menu attached to the stereogram or the tool buttons allows to display SAED or/and HAADF
images in the stereogram corners (Figures 5, 6).

Figure 5 SAED pattern displayed at the bottom left corner of the stereogram.

Figure 6 HAADF image displayed at the bottom left corner of the stereogram.
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Tilt-Rotation specimen holder
The Tilt-Rotation goniometer (Fig. 7) is pretty similar except that the
orientation is given by α specimen holder axis, θ parallel to Oz when α = 0
and φ is parallel to [uvw]1.

Figure 7 Tilt-Rotation specimen holder.