Home
Goniometer

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).

Figure1

Figure 1 Double tilt specimen holder.


The tool buttons (from left to right) allows to:

Aligning a crystal with reference to the TEM optical axis requires to figure out the value of 3 angles of rotations defined as follow:

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.

Top
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.

Figure2

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

Figure3

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

Figure3a

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:

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:

Figure4

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

Figure4a

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).

Figure5

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

Figure6

Figure 6 HAADF image displayed at the bottom left corner of the stereogram.

Top
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.

Figure7

Figure 7 Tilt-Rotation specimen holder.