Femtosecond X-ray powder diffraction
X-ray diffraction from polycrystalline powder samples, the
Debye Scherrer diffraction technique, is a standard method
for determining equilibrium structures. The different crystallite
orientations with respect to the incoming monochromatic
x-ray beam result in a distribution of the angles of incidence
q and a cone of diffracted x-rays with an opening angle
2θ . When recorded on a planar detector, they form
a characteristic ring-like patterns. The intensity of the
rings are determined mainly by the respective x-ray structure
factor Fhkl(t), which represents the Fourier transform of
the spatial electron density ρe(x;y; z; t) for a particular
reciprocal lattice vector, i.e., set of lattice planes.
This is true also for transient electronic configurations
in the unit cell. Thus, the knowledge of the temporal evolution
of the intensities of the different rings allows for a reconstruction
of the transient electron density distribution inside the
unit cell.
However, the intensity is connected to the structure factor
with the following formula Ihkl=C|Fhkl|2, where C contains
factors that can be easily calculated. F is in general a
complex number: the intensity gives no information about
the phase of the structure factor. If the crystal structure
under investigations is inversion symmetric then F is real-valued
and, under the reasonable assumption that upon pumping the
crystal does not change its symmetry, the phase problem
is greatly simplified by assuming that the phase is constant
(with possible values 0° or 180°).
In this way, variations of the diffracted intensities for
the different reflections can be directly translated into
changes of the electron density distribution inside the
unit cell via Fourier transform. Prerequisite for the application
of this method is the precise knowledge of the static structure.
Fig.1. Schematic of the experimental setup and Debye-Scherrer
diffraction pattern from an ammonium sulfate sample.
Recently, ultrafast, time-resolved ring patterns
were acquired by applying the optical pump / X-ray probe scheme
to ammonium sulfate (AS) powder (see Fig.1). AS is a hydrogen-bonded
ionic crystal with orthorhombic structure. At room temperature
(T=300 K), the material is in a paraelectric phase affiliated
with the space group Pnam. Under equilibrium conditions, AS
undergoes different structural phase transitions. By applying
the above-described procedure to the measured intensity changes
(Fig.2) we could extract information about the transient structure.
Fig.2. (a) Upper panel: calculated (red dots) and measured
(solid line) powder pattern after along-the-ring integration.
Lower panel: angle-resolved intensity changes at delay t =
50 fs. (b) Angle vs. delay plot of the measured data
Equilibrium and transient charge density maps of AS are presented
in Fig. 3. The changes Δρderived from our diffraction data
for a delay time of 50 fs are presented in Fig. 3c. One observes
a pronounced increase of electron density in a new highly
confined area in the center of the map.
This area is a channel-like volume of enhanced electron density
parallel to the c axis. This behavior is borne out in more
detail by the transient charge density maps in Fig.4. A detailed
analysis including other planes in the unit cell shows a marked
decrease of electron density on the sulfur and - to lesser
extent - on the nitrogen and oxygen atoms, i.e., a migration
of charge from these atoms to the channel is observed
Fig.3. (a) Unit cell of AS. The shaded plane
is parallel to the z-axis and go through (0.5a, 0.5b, 0.5c)
and is tilted by 60° with respect to the x-axis. It includes
the line connecting the hydrogen atoms of opposite NH+4 groups.
(b) Equilibrium electron density on this plane calculated
from literature data. (c) Electron density map of the time-resolved
changes Δρ(x,y,z,t) for delay t = +50 fs.
Fig.4. Δρ(x,y,z,t) on the plane
shown in Fig.3 for different time delays. The position of
opposite NH+4 groups, through which
the plane goes, are marked with a dashed circle.
The electron density behavior in this plane
can be also more clearly observed in this small
movie, obtained by putting together a series of snapshots.
In this work we demonstrate the potential
of femtosecond x-ray powder diffraction. The technique can
be applied to many other systems, for instance for investigating
molecular magnets or for monitoring electron motions in (bio)molecular
light harvesting complexes used in solar cells.
F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, Femtosecond
powder diffraction with a laser-driven hard X-ray source,
Opt. Express 18, 947 (2010).Free
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M. Woerner, F. Zamponi, Z. Ansari, J. Dreyer, B. Freyer, M.
Prémont-Schwarz, and T. Elsaesser, Concerted electron
and proton transfer in ionic crystals mapped by femtosecond
x-ray powder diffraction, J. Chem. Phys. 133, 064509 (2010).
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Search and Discovery article of Johanna Miller in
Physics Today
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M. Wörner
