Group leaders: Charles Fadley, LBNL, Berkeley, CA 94720

Gerhard Materlik, DESY, D-22603 Hamburg, Germany

1. Photon correlation spectroscopy (PCS), coherent x-ray diffraction (CXD), or speckle:

These closely related coherence-based measurements involve diffraction experiments in which the scattering volume is contained within the coherence volume of the beam. This can be accomplished in several ways: diffraction can be performed with an intrinsically coherent beam (such as a beam from the LCLS), or a sample smaller than the beam's coherence volume can be used, or an aperture smaller than the spatial coherence area of the beam can be as a spatial filter.

Photon correlation spectroscopy with coherent x-rays provides capabilities complementary to other techniques for studies of dynamics in disordered systems. Inelastic scattering of neutrons and x-rays (including neutron spin-echo) can probe the dynamic properties of matter at frequencies from 1014 Hz down to about 108 Hz and achieve atomic resolution. Scattering wavevectors between 10-2 Å-1 and 10 Å-1 are usually accessible in these experiments. Direct temporal measurements by photon correlation spectroscopy (PCS), on the other hand, can cover the low frequency dynamics (typically up to about 106 Hz) and provide an alternative view useful in understanding processes with time-varying dynamics. To date, PCS has been performed with coherent visible light, allowing study of small scattering wavevectors (q < 4.10-3 Å-1) in materials not absorbing visible light. Only recently have intense coherent x-ray beams from third generation synchrotron radiation sources become available, opening up the possibility for spectroscopies with coherent x-rays. X-ray photon correlation spectroscopy (XPCS) is capable of probing the low frequency dynamics (10-3 Hz to 106 Hz or higher) in a q range from 10-3 Å-1 up to 10 Å-1, with the potential to provide atomic resolution. The LCLS will greatly extend the capabilities of XPCS beyond that possible with existing x-ray sources both by providing unprecedented average coherent flux and providing extremely short pulses to allow stroboscopic measurements in the 106 Hz range.

Since the speckle pattern arises from complex-amplitude addition over the scattering volume with no ensemble averaging, it contains information about the specific configuration of the scatterers. Inversion of the speckle patterns is complicated by the fact that there is no reference wave as in holography. However, numerical algorithms developed in the protein crystallography and noncrystalline diffraction communities show some promise for retrieving the phases of the speckle pattern and producing a real-space image of the scattering volume.

Since the LCLS beam has full transverse coherence, PCS/CXD can be performed using the whole beam, which is especially important with the introduction of focusing or beam compression optics. The peak coherent flux of the LCLS should be 10 orders of magnitude higher than 3rd generation sources (or 3 orders of magnitude time-averaged). A beam such as that provided by the LCLS should make possible experiments requiring full speckle pattern measurements on fairly short time scales. There are also suggestions that entire speckle patterns may be measurable from a single pulse of the LCLS. In future work on the scientific case, a more quantitative estimate of the minimum number of photons necessary for a reliable speckle pattern is needed, including its dependence on the size of the disordered region. This would permit comparing the performance of a 3rd generation source and an LCLS type source for such experiments. Such an estimate will also yield the optimum bunch structure of an LCLS-type source.

Photon correlation spectroscopy using speckle is a form of time-resolved imaging, and therefore the experimental methods that might be used at LCLS are much the same as those discussed by the working group on sub-picosecond time-resolved scattering. In particular, pump/probe or probe/probe experiments using the LCLS x-ray pulse as a final probe and either an x-ray or optical laser initial pulse would be quite interesting.

By splitting the LCLS pulse so as to achieve two x-ray probe pulses with a small adjustable time delay, one could measure the correlation function <I(0,q) I(t,q)> for a large range of momentum transfer vectors q and for a reasonable sample of delay times t in the picosecond-nanosecond range. Fourier transformation of this intensity correlation function would then give the time-dependent autocorrelation of the real-space electron density function <r(x,0)r(x,t)>, where r is the electron density function at each point in the sample (a molecule in a crystal, for example).

However, this analysis does not tell how these fluctuations are coupled from point to point in space, and additional spatial information can be obtained by measuring the non-Bragg scattering that falls between the lattice points. This scattering arises from that part of the structure that is non-periodic, and therefore reflects spatial structural information. This scattering is generically related to the pair correlation function within the electron density function, but is most easily interpreted in terms of the time-dependent structure factor of the contents of one unit cell. From such an approach, dynamical models of fluctuations could be tested by comparing the predicted values of I_diffuse with experiment.

The unique LCLS capabilities are most acutely needed for the time delay measurements of <I(0,q)I(t,q)>. The high-brilliance pulses make this possible. Examination of the diffuse background is possible with third generation sources but time correlations in the diffuse scattering would also require the LCLS.

2. Heterodyne Mixing:

Consider two coherent photons of frequency w₀ incident on the sample; one is scattered elastically, one inelastically (with frequency change dw) into a detector at a fixed distance L from the sample. These two waves will beat with each other so that the intensity in the detector as a function of time will be given by

|a₁ exp{i w₀ t}+ a₂ exp{i (w₀ + dw)t}|² = const + A cos (dw t).

The wavevector transfer q of the experiment can be determined by w₀ and the detector angle according to the usual considerations. For several different values of dw scattered by the sample, an addition of the above intensities shows that I(t) measured in the detector is the time Fourier transform of the scattering function S(q, w), called the Intermediate Scattering Function I(q, t).

Some feasibility considerations for this experiment are:

1) There must be a significant occupation of two or more photon states of the same frequency (degeneracy n>>1). Thus these experiments are impossible with present SR sources where n<1.

2) The different "times" t at the detector can be sampled by different delays of the pulse at the sample relative to the detector (e.g. by varying the sample-detector distance, with a 1 cm change in L corresponds to a dw of 30 (nsec)^-1.

3)The random phase shift for photons in each new pulse disappears in the expression for the intensity in the detector.

3. External-Source and Internal-Source (Fluorescence) Holography:

Holography is a well-known method for obtaining 3d images of objects. By now, it can be divided into two categories: external source holography (related to the classic Gabor or in-line geometry, in which a carefully prepared source beam interacts with the sample to be imaged), and internal source holography in which fluorescing atoms in the sample are in some way involved. The spatial resolution is limited by a combination of the imaging wavelength, the source size, and the detector resolution, with the numerical aperture of the final system including all these factors. The wavelength limitation can be overcome by working with higher energy photons or electrons. To overcome the last two limitations, there are several possibilities:

The LCLS offers the exciting possibility of imaging with 1Å resolution using fully coherent diffraction-limited radiation. In more conventional holographic approaches, the radiation is focussed to a diffraction-limited spot and a sample placed in the diverging radiation. The resulting wavefield may be recorded to obtain a highly magnified hologram of the object; this is essentially a conventional Gabor hologram configuration. Techniques developed at the University of Melbourne also permit the near-field diffraction hologram to be phased, thereby eliminating the twin image ambiguity, and a high-resolution holographic image of the sample to be recovered. This technique has been demonstrated to produce 0.1-micron resolution using the Advanced Photon Source.

In the case of the LCLS it will probably not be possible to produce diffraction-limited spots due to limitations in focusing techniques. However, holographic techniques do not require a spherical reference beam, simply a well-characterized field. Thus, with the LCLS the fully coherent radiation could be brought to a controlled, but not point-like, focus and then allowed to diverge. The resulting wavefront could then be fully characterized. An object could be placed in the beam and the resulting field also characterized. The resulting data would permit a diffraction-limited image of the object to be produced.

Techniques of this form allow a number of important imaging problems to be solved. The most obvious of these is the genuine atomic-scale imaging of structures. Atomic-scale holography has been discussed in the past and it has subsequently been pointed out that the combination of the required photon energy and photon density will inflict substantial damage on the structure. One way to mitigate this effect is to image structures with some periodicity, such as a crystal or an orientated array of molecules. The resulting diffraction pattern should permit atomic scale imaging without damaging radiation densities. This high-resolution imaging is only possible with a diffraction-limited coherent x-ray source such as the LCLS.

It has also recently been demonstrated that one can use the atoms that are inside the crystal either as sources in what has been termed x-ray fluorescence holography (XFH) or as detectors in what has been called inverse XFH, or multi-energy x-ray holography (MEXH. That is, in XFH, an excited atom emits a spherical wave that can either reach the detector directly or be scattered by one of the neighboring atoms and reach the detector with a different phase. This produces an interference pattern (hologram) that can be used to reconstruct the 3-D arrangement of the crystal. This is a real hologram that can be recorded by measuring fluorescent intensity fluctuations in the far field from the sample. Inverse XFH or MEXH is the optical reciprocal of the latter method in which one has to measure the outgoing intensity fluctuations as a function of the direction of the incident beam. The latter method is well suited for 3^rd generation sources, providing images with much less aberration due to its potential for multi-energy imaging, but the necessity of moving the sample makes it less interesting for ultra high intensity sources such as the LCLS. Some relevant numbers for experimental feasibility are: intensity fluctuations in the holograms are ~10^-3, with features a few degrees wide, so that the total number of photons to be counted is ~10⁷ counts x 10³ directions = 10¹⁰. This means that there is in principle a sufficient number of photons in each LCLS pulse for a measurement in a single shot. This would permit time-dependent and pump-probe measurements of atomic structure and dynamics. Another reason for the need of single-shot measurements is likely that the small cluster of atoms imaged will only have a short lifetime due to interactions with the intense radiation, necessitating some kind of sample renewal or translation during measurement.

Some additional remarks on this type of experiment are: how can one measure 10¹⁰ photons over ~2p solid angle with ~10⁴-10³ pixels, with enough energy resolution to discriminate fluorescent from elastic scattering? Detector development is surely needed here. How small can the actual volume of sample illuminated be, since at least 10¹⁰ atoms are needed to generate 10¹⁰ fluorescent photons? If one is able to focus the beam to the diffraction limit, standard holography would approach atomic resolution, although the numerical aperture of the hologram would be low due to the forward scattering nature of the incoming beam.

Finally, it has been pointed out that experiments which in some sense bridge between holography and classic x-ray diffraction will be possible. In particular, using one "known" part of a molecule or unit cell or sample to generate a reference wave which then scatters from the "unknown" or "dynamic" or "perturbed" part can lead to a new type of holography and time-resolved x-ray crystallography, while avoiding the well-known phase problem. Doing such measurements at multiple energies would further increase the accuracy of such atomic images.

Beyond the various possible applications discussed above, a few additional future uses of an LCLS are worthy of mention:

Speckle with soft x-rays offers some unique advantages for the study of surfaces or ultrathin films. Currently there is a large interest in complex multi-element magnetic layer systems for the new magnetic sensors or MRAM applications. In these specially designed magnetic multilayers, the magnetic microstructure of individual layers could be investigated using the various absorption edges to selectively enhance the element sensitivity. Furthermore, time-dependent studies could be carried out following an external stimulus such as a fast magnetic pulse or a laser pulse "heating" the sample. Thus new time-dependent information would become available about the microscopic magnetic structure of these layer systems, which is extremely relevant for the writing process in MRAM applications. As one example system that has been studied via speckle, we consider Cu₃Au. Below its critical temperature, T_c = 390° C, it forms four types of chemically-ordered antiphase domains which differ from one another by stacking order. At a superstructure Bragg reflection (having mixed even and odd indices hkl), half of the domains have a structure factor differing in sign from the other half. As a result, Cu₃Au presents a phase object to the beam. CXD "speckle patterns" measured with a 5 µm by 5 µm, 8.5 keV beam at the APS have been measured. The speckle contrast (s_I / <I>) was seen to drop roughly exponentially as the horizontal slit size was increased, with a characteristic length approximately equal to the 5 µm coherence length. Also, the Cu₃Au speckle patterns were seen to become strongly streaked near grazing exit; this effect can be explained by the Ewald construction. The measurements of Cu₃Au speckle patterns required exposure times of around 1800 seconds, so a beam such as that provided by the LCLS should make experiments requiring full speckle pattern measurements on fairly short time scales possible.

Speckle with hard x-rays (XPCS) has the potential to impact many areas of statistical physics and promises access to a variety of important phenomena in soft condensed matter physics. We list in the following a selection of examples which were put forward at this and previous workshops:

- Dynamics of Disordered Systems

XPCS offers the possibility to study the time dependence of critical fluctuations. Several experimental attempts have been made to study critical fluctuations at order-disorder transitions in binary alloys with emphasis on the determination of dynamic critical exponents. The most advanced example so far is Fe3Al where critical dynamics and correlation functions consistent with theory have been observed. Other examples that are potentially within reach are thermal fluctuations at the nematic-smectic A transition of thermotropic and lyotropic liquid crystals which are regarded as model systems for 1-D ordering. These systems involve smaller q-vectors (typically 10-2 Å-1) but probably also shorter correlation times (1 ms < t < 1 s). The dynamic behavior of liquid crystal films has recently been addressed by using 40 Å coherent soft x-rays at the ALS. A variety of systems is expected to show slow equilibrium and non-equilibrium dynamics. Among them are disordered systems such as quasicrystals [14], glasses and alloys, subject to phase separation, and ferroelectrics. Of interest are also the dynamics of domain walls in incommensurate systems, (sliding) charge-density waves and dynamic phenomena on surfaces (e.g. facetting kinetics of miscut surfaces).

- Dynamic Structure Factor of Liquids and Soft Matter Systems

The most advanced examples are the observation of translational dynamics in metal colloids. Q-vectors up to 10-2 Å-1 and correlation times down to 1 msec have been reached. The interest is focussing now on the dynamics of (highly) concentrated, aggregated (fractal) systems with emphasis on translational and rotational dynamics as well as nonhydrodynamic effects that might exist at high momentum transfers. Further topics are the study of slow dynamics in charged and magnetic colloids. Evidence for charge induced crystallization has been seen in colloidal gold. Magnetic relaxations in ferrrofluids are also within the scope of XPCS and attempts to apply the technique to less strongly scattering, non-metallic colloidal suspensions (silica, ludox, laponites) are in progress.

General interest has also been expressed to use coherent x-rays for the investigation of the dynamics of "mesoscopic" soft condensed matter systems such as polymers, polymer blends, polyelectrolytes, block coploymers and micellar systems. Important progress has been achieved recently at ESRF in a study of polystyrene-polyisoprene micelles. A particular feature of spectroscopies with coherent x-rays is their potential to achieve atomic resolution and to eventually gain inside into the internal modes of these systems. Further interest exists in the measurement of rotational and intramolecular relaxation times for stiff and rodlike polymers.

Interesting applications in Biophysics and Biology might involve the study of soft intramolecular and intermolecular modes in DNA (bend- and twist-elasticity of DNA, twist fluctuations, base pair opening processes). Further topics involve conformational dynamics in proteins. The necessary q-range is accessible as shown by SAXS measurements and dynamics in the 1 ms to 1 s time-range is accessible to XPCS. The dynamics of membranes (e.g. multilayers of phospholipid membranes) has already been addressed by Neutron Spin Echo (NSE) measurements and XPCS could provide important complementary information in the low frequency regime.

Neutron spin echo has given important insights in the dynamics of glass forming liquids down to frequencies of about 108 Hz. Spectroscopies with coherent x-rays offer here the possibility to access the large unexplored time/temperature range around the the glass transition temperature, where the characteristic relaxation time is typically 100 s.

Other topics might include porous media (e.g. aerogels) and the investigation of liquids in confined geometries which may induce density and positional order. Liquids in confined geometries might be addressed experimentally by x-ray waveguides capable of producing submicron coherent x-ray beams.

It is already clear today that many of the mentioned phenomena will be at the limit of what can be achieved with XPCS even at third generation sources. This is valid in particular for system that require a momentum transfer bigger than about 5.10-2 Å-1 and involve dynamics faster than 103 Hz. Such system would benefit from new, brighter sources.

The LCLS may also make possible new capabilities for studying the dynamical behavior of protein molecules by examining the time variation of the Bragg reflections, and by measuring the quasi-elastic diffuse scattering that falls between the Bragg maxima in reciprocal space.

Finally, time resolved holography could be used to study nuclear motion in chemical reactions. To do this, the molecules would need to be oriented, and this could be done either by adsorbing the molecules onto a surface, or by brute force alignment of pendular states formed in a strong electric field. There is also a possibility of creating orientation using a strong laser field, but the laser orienting field may affect the subsequent dynamics. Once isolated molecules are oriented, dynamics could be initiated by an optical pulse, following which a delayed x-ray pulse could be used to study the nuclear motions.

Subpicosecond Time-resolved X-ray Measurements

Photon Correlation Spectroscopy and Holography

Non-Linear X-Ray Optical Processes

High Field Physics and Non-linear Quantum Electrodynamics with the LCLS

Content Owner: J. Arthur
Page Master: L. Dunn
Last Update: 16 Nov 1999