This document discusses systematically absent reflections in crystal structures. It provides the following key points: 1) Systematically absent reflections occur due to the symmetry and lattice type of a crystal structure, which results in certain planes of atoms reflecting X-rays completely out of phase and thus interfering destructively. 2) Common symmetry elements that lead to systematically absent reflections include translational symmetry, glide planes, screw axes, and lattice centering. Different lattice types like body-centered and face-centered cubic have characteristic formulas for systematic absences. 3) Examples are provided of systematically absent reflections in common crystal structures like NaCl, KCl, CsCl, iron, and copper to illustrate how lattice type and symmetry affect

1. SUBMITTED BY:
Aysha fatima
M.Sc
TOPIC:
SYSTEMATICALLY
ABSCENT REFLECTIONS

2. SYSTEMATICALLY ABSCENT
REFLECTIONS
• Each set of plane in a crystal should diffract
X rays but in many cases interference of
waves causes the resultant intensity to be
zero.
• These abscent reflections may be divided into
two groups:
a) those that are abscent due to some quirk in
the structure
b)And those that are abscent due to symmetry
or type of lattice possessed by structure.
The latter are known as systematic abscences.

3. • The presence of translational symmetry
elements and centering in the real
lattice causes some series of reflections
to be absent
• Translational symmetry of an object
means that a particular translation does
not change the object
• Translation repeats objects by
movement along a line at specific
distances and angles

4. Translational symmetry elements
include glide lines and planes, and
screw axes.
• Glide Planes: a combination of mirror
operations and translation.
• Screw Axes: a combination of rotation axes
and translation.

5. A screw axis is a translational symmetry
element and consists of a rotation
followed by a translation.
Screw axes exist for each rotation axis.
The presence of systematic absences can
be understood in a simple way from
Bragg’s Law

6. • If a set of lattice planes occupy a position
such that they reflect X- rays completely
out-of-phase with another set of lattice
planes, then no reflection will be observed.
i.e. although the Bragg condition is satisfied
for the sets of planes ,
• the destructive interference “extinguishes”
the reflection.
• This situation only arises if there are
translational symmetry elements or centering
in the crystal lattice

7. e.g. the (001) reflection in a cubic lattice (BCC) is absent.
Consider the additional path lengths vs. beam “1”:
For “2” it is 2d sin(q); for “3” it is 2(d/2) sin(q), thus the rays
from “3” will be exactly out-of-phase with those of “2” and no
reflection will be observed.

8. • Systematic abscences arise if either the lattice
type is non primitive (BCC ,FCC)or if elements of
space symmetry (screw axis,glide planes) are
present
• These systematic absences (or “systematic
extinctions”) thus indicate the presence of
centering and/or specific symmetry elements in
the lattice and provide us with information about
the space group of the crystal.
• the conditions for reflections or absences are
reported as simple equations in which “n”
indicates any integer.

9. • E.g. if for reflections of the type
(h00), h = 2n + 1 are absent (this
means that if h is odd, then the
reflection will not be observed)
• Conversely, this means that the limiting
condition for such reflections to be
observed is: for (h00), h = 2n (i.e.
reflections are only observed when h is
even)

10. E.g. for C centered cells, such as the one
pictured above, (hkl) reflections are
systematically absent when: h + k = 2n + 1
(if the sum of h and k is odd)

11. Symmetry Element reflection absence conditions
• A centered Lattice (A) hkl k+l = 2n+1
• B centered Lattice (B) h+l = 2n+1
• C centered Lattice (C) h+k = 2n+1
• face-centered Lattice (F) hkl h+k = 2n+1
h+l = 2n+1
k+l = 2n+1
• Body centered Lattice (I) hkl h+k+l = 2n+1

12. EXAMPLE(absence due to lattice type) Iron
• Iron is BCC. (-Fe)
• Reflections from (100)has zero intensity &
is systematically abscent.
• Strong 200 reflections is observed because
all atoms lie on (200) planes & there are no
atoms lying between (200) planes to cause destructive
interference.

13. • 110 reflection is observed whereas 111
is systematically abscent in -Fe.
• For each non primitive lattice type there
is a simple characteristic formula for
systemic abscences .
• For BCC reflections for which (h+k+l) is
odd are abscent such as 100,111,320
etc are systematically abscent

14. Iron (bcc)
alpha-Iron (Hull, A.W. (1917) Phys Rev 10, 661)
Lambda: 1.54180 Magnif : 1.0 FWHM: 0.300
Space grp: I m -3 m Direct cell: 2.8660 2.8660 2.8660 90.00 90.00 90.00
0 1 1
0 0 2
1 1 2
0 2 2
0 1 3
2 2 2
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

15. Example: NaCl
• NaCl is face centred
cubic.
• Only those reflection
may observed for which
hkl are either all odd or
all even .
• 110 is systemetically
abscent but 111 may be
observed.
:

16. Comparison: NaCl vs KCl
NaCl (Hull, A.W. 1919)
Lambda: 1.54178 Magnif : 1.0 FWHM: 0.200
Space grp: F m -3 m Direct cell: 5.6400 5.6400 5.6400 90.00 90.00 90.00
Fhkl = 4fNa + 4fCl if h,k,l all even
Fhkl = 4fNa - 4fCl if h,k,l all odd
1 1 1
0 0 2
0 2 2
1 1 3
2 2 2
0 0 4
1 3 3
0 2 4
2 2 4
1 13 53 3
NaCl
20 30 40 50 60 70 80 90 100
KCl (Hull, A.W. 1919)
Lambda: 1.54178 Magnif : 1.0 FWHM: 0.200
Space grp: F m -3 m Direct cell: 6.2800 6.2800 6.2800 90.00 90.00 90.00
KCl , K+ and Cl- are isoelectronic
1 1 1
0 0 2
0 2 2
1 1 3
2 2 2
0 0 4
1 3 3
0 2 4
2 2 4
1 13 5 3 3
0 4 4
1 3 5
0 0 62 4 4
20 30 40 50 60 70 80 90 100

17. KCl
• 111 intensity is zero since K+ & Cl- are
isoelectronic
• Intensity should decrease in the order
KCl <KF < KBr< KI

18. Example: CsCl
• CsCl is primitive cubic.
• if difference between Cs and Cl is ignored
The atomic positions are same as in BCC α Fe
• 100 is abscent in α Fe but is an observed
reflection with CsCl because scattering
powers of Cs and Cl are different
So weak/strong reflections

19. Example: Copper
• Copper is face centred cubic.
• Atoms at (0,0,0), (½,½,0), (½,0,½),
(0,½,½)
Three cases to consider
h,k,l all odd
h,k,l all even
h,k,l mixed (2 odd, 1 even or 2 even, 1 odd)
Thus, reflections present when …
Generally true for all face centred structures

20. THANK YOU