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X-Ray Photon Correlation Spectroscopy Study of Brownian Motion of Gold Colloids in Glycerol

August 1995
Physical Review Letters 75(3):449-452

August 1995
75(3):449-452

DOI:10.1103/PhysRevLett.75.449

Source
PubMed

Authors:

Ronald Pindak

Brookhaven National Laboratory

Robert M Fleming

Sandia National Laboratories

Show all 5 authorsHide

We report x-ray photon correlation spectroscopy studies of the static structure factor and dynamic correlation function of a gold colloid dispersed in the viscous liquid glycerol. We find a diffusion coefficient for Brownian motion of the gold colloid which agrees well with that extrapolated from measurements made with visible light, but which was determined on an optically opaque sample and in a wave-vector range inaccessible to visible light.

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VOLUME 75, NUMBER 3 PHYSICAL REVIEW LETTERS 17JULY 1995

X-Ray Photon Correlation Spectroscopy Study of Brownian Motion of Gold Colloids in Glycerol

S.B. Dierker,1R. Pindak,2R.M. Fleming,2I.K. Robinson,3and L. Berman4

1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120

2AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974-0636

3Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080

4National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973-5000

(Received 30 November 1994; revised manuscript received 5 May 1995)

We report x-ray photon correlation spectroscopy studies of the static structure factor and dynamic

correlation function of a gold colloid dispersed in the viscous liquid glycerol. We ﬁnd a diffusion

coefﬁcient for Brownian motion of the gold colloid which agrees well with that extrapolated from

measurements made with visible light, but which was determined on an optically opaque sample and in

a wave-vector range inaccessible to visible light.

PACS numbers: 61.10.Lx, 05.40.+j, 42.25.Kb, 82.70.Dd

Photon correlation spectroscopy (PCS) probes the dy-

namics of a material by analyzing the temporal correla-

tions among photons scattered by the material. Visible

light PCS has proven to be an indispensible technique

for studying the long wavelength hydrodynamics of ﬂu-

ids, including simple liquids, liquid mixtures, liquid crys-

tals, polymers, and colloids [1]. However, visible PCS

cannot probe the short wavelength dynamics of materi-

als or opaque materials at all. The new ﬁeld of x-ray PCS

(XPCS) offers an unprecedented opportunity to extend the

range of length scales over which a material’s low fre-

quency (10–3 to 106Hz) dynamics can be probed down to

interatomic spacings. It is clear that demonstration of the

ability to make dynamic XPCS measurements would be a

major step forward in this nascent ﬁeld.

Many of the important problems in the low frequency

dynamics of condensed matter systems for which XPCS

should be uniquely suited arise in disordered materials, in

particular, liquids. These include studies of the dynamic

structure factor of liquids down to interatomic length

scales, density ﬂuctuations in liquids undergoing a glass

transition, internal conformational dynamics and reptation

in polymers, and equilibrium concentration ﬂuctuations

in polymer blends near a phase separation critical point.

Here we report results of equilibrium dynamic measure-

ments on a disordered system using XPCS. Speciﬁcally,

we measured the diffusion coefﬁcient for Brownian mo-

tion of gold colloid particles dispersed in glycerol. Our

results unequivocally demonstrate the feasibility of the

XPCS technique, as well as illustrate the crucial impor-

tance of both matching the longitudinal coherence length

of the x rays to the experimental requirements and the

tremendous beneﬁt of utilizing area detectors in XPCS

measurements.

While the principles of XPCS have been known for

decades, the very low ﬂux of coherent x rays available

with previous sources has, until now, precluded its appli-

cation as a practical technique. The critical development

which has now made XPCS a feasible technique is the

use of insertion devices at second and third generation

synchrotron sources. The work reported here was done

on the wiggler beam line X25 at the Brookhaven National

Synchrotron Light Source (NSLS).

Previous work has consisted of measurements of the

static speckle patterns resulting from the structure of an-

tiphase domains in Cu3Au [2] or from grazing incidence

scattering from gold-coated polymer ﬁlms of inhomoge-

neous thickness [3]. Identiﬁcation of equilibrium critical

ﬂuctuations in Fe3Al with XPCS has also been reported

very recently [4]. These studies beneﬁted either from

the tremendous gain in scattering cross section of Bragg

scattering from essentially well-ordered materials [2,4] or

from the large reﬂectivity at grazing incidence [3]. In

contrast, the scattering typical of highly disordered mate-

rials, such as liquids or glasses, is dramatically weaker.

To demonstrate the difﬁculty of a coherent x-ray beam

by liquids, we estimate its average scattering efﬁciency.

For an incident x-ray beam of cross-sectional area Aiand

power P0(photonsysec) incident on a sample containing

Ntot uncorrelated atoms of charge Z, the fractional detected

count rate sPyP0dscattered into the solid angle DV is [5]

PyP0r2

0NtotZ2DVyAi. Here r0e2ymc22.8 3

10213 cm is the classical Thomson electron radius. In

terms of the density r, molecular weight M, Avogadro’s

number NA, and the scattering volume V, we have Ntot 

rVNAyM. We take VAiymfor a sample of thickness

t1ym, where mrmmis the adsorption length and

mmis the mass absorption coefﬁcient, and make use of the

approximate relationship [5] mmøCZl3NAyM, where C

is a constant. In a speckle experiment, the detector solid

angle of a single speckle is DV øl2yAi. Altogether this

gives PyP0ø8310226ZyClAi. This demonstrates the

beneﬁt of having a high source brightness, i.e., P0yAi.

Aiis set by the transverse coherence length of the x-

ray beam. At X25, this requires a pinhole diameter of

5mm, for which Ai,20 mm2. For the case of liquid Au,

Z79, and taking l1.55 Å at 8 keV, C261 cm–1

for Au at 8 keV, and P0ø43107photonsysec at X25

with DEyE1.5%, we estimate the impracticably small

count rate of P,331024cps.

VOLUME 75, NUMBER 3 PHYSICAL REVIEW LETTERS 17JULY 1995

However, if one had a liquid of Npgold particles, each

with naatoms (whether crystalline or amorphous, regard-

less of orientation), such that NpnaNtot, then the aver-

age scattering in the forward direction would be the sum

of the coherent scattering from Npparticles, i.e., PyP0~

Npn2

aNtotna, instead of Ntot. The qdependence of the

scattering will be that of the particle form factor [5] FsqRd

for a sphere of radius R(in the dilute gas limit at low q,

the structure factor will be unity),

FsqRd∑3hsinsqRd2qR cossqRdj

sqRd3∏2

.(1)

For example, for a Au particle with R200 Å, na,

23106, giving a sufﬁciently large P,600 photonsysec.

A constraint of this approach is that one must work at

very low q, although not so low as to be dominated by the

tail of the Fraunhofer diffraction of the main beam. We

estimate that measurements should be possible at least over

the range 131023,q,331022Å–1. This extends

far beyond the upper qrange of visible light scattering, for

which qmax ,431023Å–1.

Monodisperse gold sols were prepared by reducing

HAuCl4with Na3-citrate [6]. The hydrodynamic radius

RHof the resultant gold colloid particles was determined

to be 335 Å for a small diluted aliquot of the resulting

sol using visible PCS [1]. A cumulant analysis of the dy-

namic correlation functions indicated a polydispersity of

,10%. The hydrophobic gold sol was stabilized against

aggregation by absorbing cold water ﬁsh skin gelatin onto

the surface of the particles [7]. RHand the hydrodynamic

polydispersity were remeasured for the stabilized sol and

determined to be 425 Å and 20%, respectively. The in-

creased magnitude of these quantities presumably reﬂects

the increased drag and statistical size ﬂuctuations of the

“fuzzy” molecular coat covering the spheres.

The as-prepared sol had a gold volume fraction of

2.7 31024%, whereas the XPCS measurements required

a sample with a gold volume fraction of ,1%.At

this concentration, the x-ray absorption of the gold and

the glycerol are approximately equal. Thus, 450 ml

of sol was concentrated by centrifuging, aspirating out

the supernatant, and resuspending in 1.5 ml H2Oby

ultrasonicating. The concentrated sol was remeasured

with visible PCS, and RHand the polydispersity were

determined to be 590 Å and 26%, respectively. The sol

was then centrifuged and the supernatant was aspirated

and resuspended by ultrasonicating in 0.10 ml glycerol

to which 0.4MNaCl had been added in order to screen

out Coulomb interactions between the spheres. This was

repeated twice more. The end result was a concentration

enhancement of 4000:1, giving an estimated gold volume

fraction of 1.3% in a 0.1 ml sol. This concentration was

conﬁrmed by x-ray absorption measurements. We note

that at this high concentration the sample is completely

opaque to visible light, and thus could not be studied with

visible PCS. The 1% Au sample was placed in a 1.0 mm

diameter hole drilled in a 0.6 mm thick aluminum plate,

i.e., about one absorption length thick at 8 keV.

A laterally coherent beam was prepared by passing the

x rays through a 5 mm diameter pinhole. The longitudi-

nal coherence length lcoh of the x-ray beam is given by

lslyDldand was set by using a two crystal WyB4C multi-

layer monochromator, giving lcoh ,100 Å. This resulted

in an incident coherent x-ray ﬂux of 43107photonsysec.

In a transmission geometry, the maximum path length dif-

ference (PLD) is given by 2hsinutanu, where his the

sample thickness. Thus, the requirement [1] that PLD

,lcoh is satisﬁed up to scattering angles 2uof 8 mrad, cor-

responding to q3.2 31022Å–1. We also attempted

measurements using a Si(220) monochromator, for which

lcoh 2mm and the incident coherent ﬂux was only

,23105photonsysec. Data collected under those con-

ditions were of signiﬁcantly poorer quality than those re-

ported here. However, small-angle scattering data col-

lected under incoherent illumination conditions using the

Si(220) monochromator were of good quality, and all such

data presented here (Figs. 1–3) were collected using this

monochromator. This underscores the crucial importance

of not having lcoh any greater than required by PLD in

order to have the maximum intensity available for the

experiment.

X-ray detectors used included a scintillation detector

and a two-dimensional charged couple device (CCD)

area detector operated in the direct detection mode. The

CCD detector was custom-built and used a Kodak KAF-

1400 CCD, which is a front illuminated device having a

512 3768 array of 9 mm square pixels.

Figure 1 shows the measured scattering intensity, both

with and without the colloid. The strong signal centered at

q0is the direct beam transmitted through the sample.

The background scattering without sample is due to small

angle scattering from the slits and pinholes in the beam

line. The overall shape and intensity of the colloid scat-

tering qualitatively matches that expected from Eq. (1).

Measurements of the static structure factor were also

made with the CCD area detector. Figure 2 shows a plot

of a CCD image taken with an 80 mm front pinhole.

The channel cut through the center of the plot is due

to the shadow of a 200 mm diameter gold wire used to

block the main beam, which would have saturated the

FIG. 1. Ssqdas measured with incoherent x rays by scanning

an 80 mm pinhole followed by a scintillation detector. The

incident beam diameter was 200 mm. One contribution to the

background, a Kapton window, is indicated.

450

VOLUME 75, NUMBER 3 PHYSICAL REVIEW LETTERS 17JULY 1995

FIG. 2. Log plot of scattering intensity from the colloid

collected with the CCD camera.

detector. The CCD image was obtained by summing ten

1 sec exposures in order to extend the CCD’s dynamic

range. In comparison, each line scan with the pinhole-

scintillation detector combination over a similar qrange

took more than an hour.

A comparison of the structure factor measured in the

scintillation detector scans with that deduced from radial

averages of the CCD image is shown in Fig. 3. The

data have been scaled to coincide at q,0.015 Å–1.

The scintillation detector and CCD scans show good

general agreement apart from differences in the amount

of forward scatter around the main beam between the two

measurements.

In order to determine the size of the protected colloid

spheres and the degree of polydispersity, the scintillation

detector data shown in Fig. 3 were ﬁt by a model

consisting of a Gaussian distribution of sphere scattering

radii, with each sphere according to Eq. (1), along with

FIG. 3. Comparison of Ssqdderived from scintillator or

pinhole scans with that from the CCD image in Fig. 2. Also

shown are the results of a ﬁt of a model for Ssqdbased on

Eq. (1) and a Gaussian distribution of particle radii.

a constant background. The results indicate that the

mean radius was 270 Å and the standard deviation of

the distribution was 57 Å. These numbers agree well

with the mean hydrodynamic radius and polydispersity

measured on dilute aqueous solutions of the colloid with

visible PCS before protecting them with gelatin. This

suggests that the increased RHmeasured for the protected

colloid results from the added hydrodynamic drag of

the macromolecular coating. The further increase in RH

upon centrifuging presumably results from changes in the

molecular conformation of the gelatin molecules and not

from aggregation of the spheres.

We next turn to consideration of the Brownian motion

dynamics of this system. The Au colloid particles form

a dilute gas having diffusively relaxing concentration

ﬂuctuation with a corresponding diffusion coefﬁcient

given by [1] DkbTy6phRHand a relaxation time at

wave vector qof t1yDq2. Glycerol is a prototypical

glass former with a glass transition at Tg286 ±

C, at

which the shear viscosity happroaches ,1013 P [8].

The dynamic correlation function gstdis deﬁned as

gstdknstdns0dlykns0dl2,(2)

where kl represents a time average and nstdis the

detected photon count at time t.gstdshould have a

maximum value of 2 at t0, decaying to 1 at inﬁnite

time. Spatial averaging of the speckles by the detector

can reduce the t0intercept of gstd.

A dramatic increase in collection efﬁciency was ob-

tained by using the CCD detector to measure the scatter-

ing for 6750 pixels simultaneously. Since the dynamics

depend only on the magnitude of q, we can average the

autocorrelation functions measured in all of the pixels in a

band of qvalues. This is equivalent to performing an en-

semble average over pixels, as well as a time average for

each pixel, and should reduce the time needed to measure

the correlation functions with good statistics by the num-

ber of pixels averaged over [9]. With 6750 pixelsyimage,

the reduction is substantial.

Speciﬁcally, we recorded 1920 images of the inten-

sity in two separate 90±arcs corresponding to q’s of

3.3 31023and 5.5 31023Å–1, with widths of 10% of

their average q’s and containing 1750 and 5000 pixels,

respectively (see Fig. 4). The larger qis well above the

maximum value of ,431023Å–1 attainable by visible

PCS. The images were taken once per second for a to-

tal duration of 32 min, with the exact time of exposure

recorded for each image. A total of ,3.4 3106pho-

tons were detected, corresponding to an average count rate

of 0.36 photonsypixel sec. This compares well with the

value of 0.68 derived from our earlier estimate when the

sample transmission (0.35), the ratio of the area of a pixel

to that of a speckle (0.13), the estimated quantum efﬁ-

ciency of the CCD detector (0.05), and Eq. (1) (0.5) are

taken into account.

The time autocorrelation function of each pixel was then

calculated and the ensemble average of the resulting 1750

451

VOLUME 75, NUMBER 3 PHYSICAL REVIEW LETTERS 17JULY 1995

FIG. 4. Autocorrelation functions of colloid scattering inten-

sity as collected with the CCD camera for two different wave

vectors along with single exponential ﬁts and relaxation times,

as indicated. The inset schematically depicts the scattering

“halo,” the beam stop, and the subarrays which were ensem-

ble averaged over. Curve (b) is offset by 0.15 for clarity.

or 5000 correlation functions calculated. The results are

shown in Fig. 4, which is plotted as gstd21. The large

signal-to-noise ratio of the data in Fig. 4 can leave no doubt

that they correspond to dynamic x-ray scattering from

colloid concentration ﬂuctuations. The large amplitude of

the decays is also as expected considering the small size of

the pixels relative to the coherence area for the scattering.

Also shown in Fig. 4 are ﬁts to the data of single

exponential relaxations. They give characteristic decay

times of 43.1 and 24.1 sec for q3.3 31023and 5.5 3

1023Å–1, respectively. The measurements were made at

a temperature of 229 ±

C. The viscosity of pure glycerol

[8] should be 5.5 3103P at this temperature. Thus,

the nominal expected relaxation times are 61 and 22 sec,

which are in good agreement with the measurements.

The deviation of the relaxation rates from a precise

q2dependence may be an indication of the onset of

nonhydrodynamic effects at large wave vector [10].

While these measurements clearly establish the feasi-

bility of XPCS studies, more experiments are called for

in order to fully understand the dynamics of this colloid.

For example, nonhydrodynamic effects at large wave vec-

tor [10] as well as nonlinear relaxation effects predicted

by mode coupling theories [11] near the glass transition

should be fruitful areas of future study with this new

technique.

In conclusion, we have made small angle x-ray scat-

tering measurements of the static structure factor of an

optically opaque gold colloid dispersed in glycerol. We

also reported a determination of dynamic correlation func-

tions and the diffusion coefﬁcient for the Brownian mo-

tion of the colloid particles, at a wavelength inaccessible

to visible PCS, by using the new technique of XPCS. Our

results demonstrate the importance of using a multilayer

monochromator, or just the natural bandwidth of undula-

tor radiation (,1%), in situations where a large lcoh is not

required, such as surface diffraction or small-angle scat-

tering experiments, as well as the beneﬁts of ensemble av-

eraging with CCD area detectors in XPCS measurements.

The present results clearly show that XPCS is a fea-

sible technique and can have wide application to cer-

tain classes of systems, especially complex ﬂuids and

surfaces, even using existing 2nd generation synchrotron

x-ray sources such as the NSLS. This is particularly

true given several signiﬁcant forthcoming enhancements:

(1) Optimization of the use of an area detector for making

ensemble measurements of gstd:3101–102. (2) Beam-

line optics which utilize the full coherent output of the

undulator in both the vertical and horizontal directions:

310. (3) Introduction of undulator sources such as the

Prototype Small Gap Undulator recently installed at the

NSLS: 310. These will enhance the data collection efﬁ-

ciency by 103and 104, relative to the current experiment.

Those classes of problems demanding the utmost coherent

incident x-ray ﬂux will require the 3rd generation undula-

tor sources at the European Synchrotron Radiation Facility

and the Advanced Photon Source: 310 2–103, for a total

gain of 104–106, relative to the current experiment. When

these developments come to fruition, XPCS will realize its

full potential as a unique and important new technique.

It is a pleasure to acknowledge the assistance and

advice of Christoph Schmidt on the preparation of the

gold colloids. Robert MacHarrie assisted in the x-

ray measurements. S.B. D. acknowledges support under

NSF Grant No. DMR 92-17956 and also the donors

of the Petroleum Research Fund, administered by the

American Chemical Society, for the partial support of this

research under Grant ACS-PRF No. 26389-AC9. I. K. R.

acknowledges support under NSF Grant No. DMR 93-

15691. The NSLS is supported by the U.S. Department

of Energy under Contract No. DE-AC02-76CH00016.

[1] See, for example, Benjamin Chu, Laser Light Scattering:

Basic Principles and Practices (Academic Press, San

Diego, 1991), 2nd ed.

[2] M. Sutton et al., Nature (London) 352, 608 (1991).

[3] Z.H. Cai et al., Phys. Rev. Lett. 73, 82 (1994).

[4] S. Brauer et al., Phys. Rev. Lett. 74, 2010 (1995).

[5] G.B. E. Warren, X-Ray Diffraction (Addison-Wesley,

New York, 1968).

[6] G. Frens, Nature (London) 241, 20 (1973).

[7] Colloidal Gold: Principles, Methods, and Applications,

edited by M.A. Hayat (Academic Press, San Diego,

1989).

[8] M.L. Williams et al., J. Phys. Chem. 77, 3701 (1955).

[9] Apollo P.Y. Wong and P. Wiltzius, Rev. Sci. Instrum. 64,

2547 (1993).

[10] W. Hess and R. Klein, Adv. Phys. 32, 214 (1983).

[11] J. Jackle, J. Phys. Condens. Matter 1, 267 (1989).

452

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In conventional frame-based image sensors, every pixel records brightness information and sends this information to a receiver serially in a scanning fashion. This full-frame readout approach suffers from high bandwidth requirements and increased power consumption with the increasing size of the pixel array. Event-based image sensors are gaining popularity for reducing the bandwidth and power requirements by sending only meaningful data in an event-driven approach with the help of address-event representation (AER) communication protocol. However, the event-based readout suffers from increased latency and timing error when the number of pixels with an event increase. In this paper, we introduce a new field-programmable AER (FP-AER) encoding scheme which offers benefits of both frame-based and event-based approaches. The readout design can be configured “in the field” using configuration bits. We also compare the performance of the proposed design against existing AER-based approaches for imaging applications and show that FP-AER performs best in both scanning and event-based readout.

Nanoparticle Transport Through Polymers and Along Interfaces

Chapter

Mar 2022

Transport of nanoparticles has received increasing attention for both fundamental interest to test prevailing models as well as practical interest in separations and self‐healing applications. Methods for measuring particle dynamics are briefly reviewed to orient the reader to different methodologies. The transport of nanoparticles through polymer melts, solutions, and cross‐linked networks is described with emphasis on systems where the nanoparticle is on the length scale of the defining structure including the tube size, correlation length, and mesh size, respectively. Because nanoparticles can interact with the different mediums, the interactions between nanoparticles and polymer and the subsequent impacts on dynamics are described. The transport of particles at liquid–solid (polymer brush) interfaces is addressed due to growing interest in applications ranging from understanding dynamics in porous media to the translocation of DNA. Both hard particles and polymer grafted particles (soft particles) are described. The objective of this article is to provide the reader with fundamental descriptions of phenomena while reviewing the current state of understanding. Further directions will leverage advances in inorganic chemistry to prepare monodisperse, functional nanoparticles as well as polymer chemistry to create novel media, such as networks with monodisperse mesh size.

Observation of speckle by diffraction with coherent X-rays

Article

Aug 1991
NATURE

REFLECTED light from a coherent light source such as a laser shows a graininess known as speckle. In general, a speckle pattern is produced whenever randomly distributed regions of a material introduce different phase shifts into the scattering of coherent incident light. If the arrangement of the regions evolves with time, the speckle pattern will also change. Observation of the intensity fluctuations at a single point in the speckle pattern provides a direct measure of the time correlation function of the inhomogeneity. This leads to a technique1,2, alternatively called light-beating spectroscopy, dynamic light scattering or intensity fluctuation spectroscopy, which has been widely used with visible light to study processes such as critical fluctuations near phase transitions in fluids and the diffusion of particles in liquids. But it is not possible to study processes involving length scales less than about 200 nm, or those in opaque materials, using visible light. If intensity fluctuation spectroscopy could be carried out using coherent X-rays, however, one could probe the dynamics of processes involving atomic length scales in a wide range of materials. Here we show that by using a high-brilliance X-ray source it should be possible to perform this type of measurement using radiation of wavelength ~0.15nm. Specifically, we have observed a speckle pattern in the diffraction of coherent X-rays from randomly arranged antiphase domains in a single crystal of the binary alloy Cu3Au.

Generalized hydrodynamics of systems of Brownian particles

Article

Jan 1983

A generalized hydrodynamic theory is developed for systems of interacting Brownian particles on the basis of a Fokker-Planck equation. General results are derived for correlation functions, frequency- and wave-vector dependent transport coefficients. Explicit expressions for moments, cumulants and the hydrodynamic limits of the transport coefficients are given. For the special cases of overdamped systems with and without hydrodynamic interaction the general results are simplified. As an example for the application of this approach the system of charged spherical polystyrene spheres in aqueous solution is treated in detail. The generalized transport functions are evaluated in mode-mode coupling approximation and detailed numerical results are presented for various collective and single-particle properties. Finally, the relationship to a corresponding Smoluchowski approach is discussed.

X-Ray Intensity Fluctuations Spectroscopy Observations of Critical Dynamics in Fe$_3$Al

Article

Jan 1995

Controlled Nucleation for Regulation of Particle-Size in Monodisperse Gold Suspensions

Article

Jan 1973

G. Frens

MANY properties of colloids and suspensions depend on the particle size. Series of monodisperse suspensions of the same chemical composition but of rather different particle sizes may be used to study particle size dependent phenomena, such as Brownian motion, light scattering, sedimentation and electrophoresis of small particles. We have used such series to demonstrate the increased tendency of metal suspensions to coagulate in the presence of electrolytes as the radius of the particles increases1.

Dynamic light scattering with a CCD camera

Article

Oct 1993

We have successfully implemented a method to measure intensity autocorrelation functions with a CCD camera and a fast computer. We report light scattering experiments on solutions of diffusing latex spheres in glycerol and compare our results to those obtained with a conventional hardwired electronic correlator. Averaging allows significant reduction of measurement times and makes this technique suitable for the study of systems with very long time scales. Moreover, the CCD setup allows measurement of two‐time correlation functions under nonequilibrium conditions where conventional correlators which rely on time‐averaging fail. The new method may offer significant advantage for low‐intensity applications like x‐ray correlation spectroscopy.

Observation of X-Ray Speckle by Coherent Scattering at Grazing Incidence

Article

Aug 1994
PHYS REV LETT

We have observed x-ray speckle at grazing incidence from gold-coated films of symmetric diblock copolymers of polystyrene (PS) and polymethylmethacrylate (PMMA). The polymer films consisted of micron-sized islands on a uniform surface. Coherent 6-keV photons were selected by monochromatizing and collimating the x-ray beam from a bending magnet synchrotron source. The visibility of the speckle patterns was enhanced with increasing degrees of spatial coherence of the photons. Speckles due to coherent scattering from islands with length scales up to 100 [mu]m were clearly identified.

X-Ray Intensity Fluctuation Spectroscopy Observations of Critical Dynamics in Fe3Al

Article

Apr 1995
PHYS REV LETT

We have carried out intensity fluctuation spectroscopy measurements using coherent x rays to study the dynamics of critical fluctuations in a binary alloy at equilibrium. An intense coherent hard x-ray beam, produced from an undulator source, was scattered from a single crystal of Fe3Al held at temperatures near the B2-DO3 order-disorder transition. A speckle pattern was observed at the $12 12 12$ superlattice reflection. Below Tc it was essentially static, while above Tc it fluctuated in time. The behavior of the normalized time correlation function is consistent with predictions of theory.