Alignment of in =E2=80=93 and off-plane reflexes in 6-circle dif= ractometer setup at P10

In case of a *symmetric *reflection, when diffraction planes of a=
reflection are *parallel* to the surface of a crystal, finding the =
reflection is quite easy. Let us consider the vertical scattering geometry =
when the =E2=80=98omega=E2=80=99 circle is used for angular scanning of the=
sample crystal and the =E2=80=98delta=E2=80=99 circle is used for position=
ing the detector.

1) First step is to align the =
crystal in the direct beam. For that both =E2=80=98omega=E2=80=99 and =E2=
=80=98delta=E2=80=99 should be set at 0. The detector slits should be open =
to a size of 5x5 mm^2 and the detector arm (=E2=80=98delta=E2=80=99) has to=
be scanned (without sample in the beam) to define the detector zero-positi=
on d_{0}. For further finding zero-=E2=80=98omega=E2=80=99 position=
, the vertical size of detector slit has to be reduced down to a size of 1 =
mm.

2) The sample (here we suppose=
Si crystal slab with <111> orientation of the surface) should be set=
by =E2=80=98cryoz=E2=80=99 (vertical sample translation) to a half-intensi=
ty position; then the rocking scan by =E2=80=98omega=E2=80=99 should be don=
e and =E2=80=98omega=E2=80=99 position has to be corrected to the peak inte=
nsity position. Above steps (starting from setting a sample to half-intensi=
ty position) should be repeated several times with decreasing stepwidth unt=
il the exact zero-=E2=80=98omega=E2=80=99 position (w_{0}) is defin=
ed.

3) Next is to set the =E2=80=
=98omega=E2=80=99-circle to the position w_{0}+q_{b} and th=
e =E2=80=98delta=E2=80=99-circle to the position d_{0}+2q_{b , where qb is the Bragg angle for the aimed reflection [examp=
le Si(111)] at the working X-ray energy.}

4) In order to find the reflec= tion, one has to scan =E2=80=98omega=E2=80=99 in a reasonable angular range= with a step matching the expected width of the rocking curve; normally the= reflection is found after scanning =E2=80=98omega=E2=80=99 within =C2=B10.= 1=C2=B0 and a step of 0.001=C2=B0.

In case of an *asymmetric *reflection, when diffraction planes of=
a reflection are *not* *parallel* to the surface of a crysta=
l, finding the reflection is a bit more elaborate than for symmetric case. =
The first step is to find out whether the desired reflection is possible fo=
r the actual surface orientation and applied photon energy. As it is illust=
rated in Figure 1, the reflection will be possible to measure (in reflectio=
n geometry) if its Bragg angle is larger than the angle j between the diffr=
action planes and the surface (otherwise the reflection can be measured onl=
y in Laue (transmission) geometry).

Figure 1: Example of lattice planes.

For a cubic lattice the angle j between two planes having Miller indexes=
h_{1}k_{1}l_{1} and h_{2}k_{2}l

cos(j)=3D (h_{1}*h_{2} + k_{1}*k_{2} + l=
_{1}*l_{2} )/(sqrt(h_{1**}2 + k_{1}**2 + l<=
sub>1**2)*sqrt(h_{2}**2 + k_{2}**2+ l_{2}**2)=
)

For example, for the Si(311) reflection and a <111> crystal surfac=
e orientation we have j=3D29.5=C2=B0. For X-ray energy of 8 keV the Bragg a=
ngle of Si(311) reflection is q_{b} =3D 28.2=C2=B0, which means tha=
t this reflection is not accessible in Bragg (reflection) geometry at this =
X-ray energy.

After the measurable reflection is selected, the steps 1) and 2) should =
be applied. As before, in step 3) the detector arm has to be places at d_{b}. But the =E2=80=98omega=E2=80=99 circle should be =
positioned either at q_{b}-j or at q_{b}+j (see Figure 1). =
The case of incident angle equal to q_{b}-j is favourable sin=
ce the intrinsic width is becoming larger due to asymmetry factor; and henc=
e the reflection will be easier to find. After the =E2=80=98delta=E2=80=99 =
and =E2=80=98omega=E2=80=99 circles are brought to their positions, one has=
to start azimuthal scans of the sample using the =E2=80=98phi=E2=80=99 cir=
cle. Scanning of =E2=80=98phi=E2=80=99 motor should be performed in a wide =
angular range of 180=C2=B0 with reasonably small step of 0.01=C2=B0.=
After the reflection is found, one can measure its rocking curve by =
scanning =E2=80=98omega=E2=80=99 as in step 4).

As an example, the rocking curve of Si(111) and Si(444) at E=3D8keV are = displayed.