class CrystallographicDirection: use uvw for direct and hkl for reciprocal space direction!

[oliverbierwagen]

Define another class for uvw "direction indices" of direct space similar to Miller indices for reciprocal space.
see: https://dictionary.iucr.org/Direction_indices

Use this class for subsection uvw_direct (not hkl_direct) in class CrystallographicDirection(ArchiveSection).

class BravaisMillerIndices(MillerIndices):
"""
With hexagonal and rhombohedral lattice systems, it is possible to use the
Bravais-Miller system, which uses four indices (h k i l) that obey the constraint
h + k + i = 0.
"""

m_def = Section(
    description='A component added to the solution.',
    a_eln=ELNAnnotation(
        properties=SectionProperties(
            order=[
                'h_index',
                'k_index',
                'i_index',
                'l_index',
            ],
        ),
    ),
)
i = Quantity(
    type=float,
    description='The Miller index i.',
    a_eln=ELNAnnotation(
        component=ELNComponentEnum.NumberEditQuantity,
    ),
)

class CrystallographicDirection(ArchiveSection):
"""
A specific crystallographic plane or direction within a crystal structure.
The same property can be described in the direct (or real) space or in the
reciprocal space.

The (hkl) indices in direct space and [hkl] indices in reciprocal space describe
the same set of crystallographic planes,
but their interpretation differs between the two spaces.
In direct space,
(hkl) indices describe the orientation of a plane within the crystal.
In reciprocal space,
[hkl] indices describe a point in the reciprocal lattice that is perpendicular
to the corresponding (hkl) plane in direct space.
"""

hkl_reciprocal = SubSection(
    section_def=MillerIndices,
    description="""
    The reciprocal lattice vector associated with the family of lattice planes is
    OH = h a* + k b* + l c*, where a*, b*, c* are the reciprocal lattice basis
    vectors. OH is perpendicular to the family of lattice planes and OH = 1/d where
    d is the lattice spacing of the family.
    Ref. https://dictionary.iucr.org/Miller_indices""",
)
hkl_direct = SubSection(
    section_def=MillerIndices,
    description="""
    In three-dimensional space, the direction passing through the origin and the
    lattice nodes nh,nk,nl, where n is an integer, has direction indices [hkl].
    This corresponds to taking the coordinates of the first lattice node on that
    direction after the origin as direction indices.
    When a primitive unit cell is used, the direction indices are all integer;
    they may instead be rational when a centred unit cell is adopted.
    Ref. https://dictionary.iucr.org/Direction_indices""",
)