# Djurleite Twinning (pseudohexagonal)

**Djurleite:** Cu_{1.97}S

## Situation

Besides the general features of twinning we find:

Large hexagonal *twin lattice*. Many reflections weak or missing. All
strong reflections obey the conditions:

h = 0 mod 4

k = 0 mod 4

l = 0 mod 2

(The converse is not true: some reflections whose indices obey these criteria
are not strong.)

## Solution

The orthorhombic unit cell has the cell parameters

a = 26.92 Å, b = 15.71 Å, c=13.56 Å

a is approx. sqrt(3)*b
From the systematic extinctions, the extinction symbol is P-n-, which is
compatible with the space groups Pmnm, P2_{1}nm or Pmn2_{1}.

By applying the transformation matrix

(0.00 2.00 0.00)

(0.00 -1.00 2.00)

(1.00 0.00 0.00)

you get the pseudohexagonal unit cell

a = 31.42 Å, b = 31.34 Å, c= 26.92 Å,
al = 90.0°, be = 90.0°, ga = 120.08°

Graphics

**Note:** A valuable tool for finding sub-/supercells is the PC version of
the program
LEPAGE. The
program LEPAGE is also implemented in the program
PLATON.
PLATON also contains the routine
LePageTwin.

## Twin Index

The determinant of the transformation matrix is 4. Therefore the twin index is
4.

## Twin Law

The operations of pseudo-symmetry in the (pseudo-hexagonal) *twin lattice*
are the possible twin operations.

If you rotate the orthorhombic lattice about [100] counterclockwise
through 120° and 300°,
you end up with the pseudo-hexagonal twin lattice. So, the twin lattice
consists of three orthorhombic cells.

## Solid State Chemistry

The crystal structure of djurleite Cu_{1.97}S can be derived from the
high temperature structure of chalcocite Cu_{2}S. In the high chalcocite
structure the sulfide ions form a hexagonal-close packed framework, in which
half of the triangle centers are occupied alternately by copper ions. Space
group is P6_{3}/mmc and the cell parameters are
a = 3.96 Å, c = 6.72 Å (Evans, 1979).

## Final Remark

By the crystal structure determination on an untwinned single crystal,
the space group turned out to be
monoclinic P2_{1}/n with a beta-angle of 90.13(3)°(Evans, 1979).

## References

H. Takeda, J.D.H. Donnay, D.E. Appleman, *Z. Krist.* (1967) 125, 414-422.

A. Santoro, *Acta Cryst.* (1974) A30, 224-231.

H.T. Evans, jr., *Z. Krist.* (1979) 150, 299-320.

Page maintained by Martin Lutz. Last change 4-FEB-2021.

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