RECENT APPLICATIONS OFX RAYS IN CONDENSED

MATTER PHYSICSAdvances in x-ray source brightness, detector efficiency, x-ray optics and computingpower promise to make the second century of x-ray applications in condensed matter

physics as exciting as the first.

Jens Als-Nielsen and Gerhard Materlik

ince their discovery by Wilhelm Conrad Rontgen, x rays«Jhave played a significant role in our lives: they makethe unseen in our bodies visible; they enhance our securityin air travel; they make possible nondestructive testing ofa wide variety of materials. And through x-ray diffractionand spectroscopy they make it possible to probe the orderof matter at the atomic level.

The discovery of x-ray diffraction in crystals by Maxvon Laue, Walther Friedrich and Paul Knipping, andWilliam Rragg's subsequent interpretation of the diffrac-tion spots as proof of the wave nature of x rays, laid thefoundation for the field of x-ray crystallography. X-raycrystallography proved essential in relating the atomicstructure of solids to their functions and physical proper-ties. The intensity distribution in the diffraction patternwas found to reveal how electrons were distributed withinthe atom and to give information about how the atoms ina solid vibrated about their equilibrium positions. In morecomplex crystals with unit cells built of molecules, thespot intensities in the regular diffraction pattern weremodulated in a way that directly revealed the atomicstructure of the molecule—a discovery that revolutionizedchemistry and molecular biology. (See the article byWayne Hendrickson on page 42 of this issue.) Diffractionpatterns from the liquid state of matter, while not asdetailed as those from the crystalline state, indicated thecorrelations in the positions of the atoms in the liquid,which formed the basis of the physics of liquids.

Early in the history of x rays, Compton scatteringrevealed the energy and momentum distributions of elec-trons as well as vividly illustrating Heisenberg's uncer-tainty principle. But the real birth of x-ray spectroscopycame with the discovery that Bragg scattering could beused to select x rays of a particular wavelength. Usingthis technique, Moseley found that the discrete linessuperimposed on the continuous bremsstrahlung spectrumvaried systematically with the anode material's atomicnumber, making possible the completion of the periodic

JENS ALS-NlELSEN is a professor at the Niels Bohr Institute,Oersted Laboratory, University of Copenhagen, Denmark.G E R H A R D MATERLIK is associate director at the HamburgSynchrotron Radiation Laboratory (HASYLAB), at theDeutschesElektronen-Synchrotron (DESY) and a professor of experimentalphysics at the University of Hamburg,

table before all the elements had been chemically sepa-rated. X-ray spectroscopy made it possible to determinenondestructively the chemical composition of samples sim-ply by looking at the x-ray fluorescent spectra when theatoms in the sample were excited by x rays or other probes.With a finely focused excitation source, one could deter-mine the chemical composition with very good spatialresolution.

Given the impact x rays had on daily life as well asscience during their first 80 years, it is surprising thatthroughout this time x rays were generated by more or lessthe same principle Rontgen had discovered, and that x-raysource brightness improved by less than a factor of 100.

Undulator synchrotron radiationarticles in a high-energy electron or (positron) accelerator,such as a storage ring, move with a velocity v close to

the speed of light, c ~ 3 X 1010 centimeters per second. Anundulator imposes an alternating, perpendicular magnetic fieldon a straight part of the accelerator, forcing the electron beamto oscillate transversely and to emit broadband monochro-matic electromagnetic radiation. For simplicity, if the mag-netic field has a period of 3 cm, the electron will oscillate at1010 Hz, However, the line-of-sight observer sees the electronoscillations Doppler-shifted by a factor on the order of[1 - (v/c)Yl, or of order y1, where y is the ratio of theelectron's energy to its rest mass energy.

For an electron energy of 5 GeV, y is about 104, andtherefore the electron will radiate in the x-ray range at around1018 Hz. Furthermore, because the Doppler effect diminishesrapidly with the angular deviation from the oscillation axis, thex-ray part of the emission spectrum is confined to a cone aroundthe axis with an opening angle on the order of 1/y, leading toan x-ray beam intensity many orders of magnitude higher thanthat obtainable from an x-ray tube. Additional benefits includethe ability to tune the undulator's fundamental frequency byvarying the magnetic field, and the perfect linear polarizationand the bunched time structure of the x rays.

Over the last 20 years the brilliance of synchrotron radia-tion sources has more than doubled every two years! Asynchrotron radiation facility with x-ray undulator sources inthe 1 to 100 keV region is already operating in Europe; anotheris under commission in the United States, and one more isunder construction in Japan.

34 NOVEMBER 1995 PHYSICS TODAY1 1995 American Institute of Phvsics

atomic order

£ph-A£+£bmdl0g

e" energy levels andwavefunction

coherent imageintegral densitysurface topology

angle dispersiveA dispersiveLaue methodmagnetic reflectiontime resolvedSpeckle interferometrymultiple diffractionphase determination

photoemission (XPS)absorption (XAFS, time

resolved)fluorescenceAuger electronsphononsplasmonsluminescenceion and atom desorptionmagnetic statesCompton photonsRaman excitationnuclear resonance

standing wavesDAFSMAD

microscopytomographylithographyfluorescence microprobeangiographyholographyphase contrast

interferometryreflectometry

XAFS tomography2A angiography

diffraction microscopydiffraction tomographytopography

Because today's x-ray sources, in which x-ray beams aregenerated by relativistic electrons or positrons in storagerings (see the box "Undulator synchrotron radiation"), aretrillions of times more brilliant, many expect the impactof the second century of x rays to be at least as great asthat of the first.

In this article we shall briefly survey some of thecurrent trends in imaging, diffraction and spectroscopy(see figure 1), noting that yet another trend is to combinetwo or more of these techniques to form new hybridexperiments.

ImagingFrom Rbntgen's discovery to the present, imaging hasattracted the greatest interest of both the public andspecialists in different fields.1 The penetrating power ofx rays reveals the volume properties of matter rather than

X RAYS IN CONDENSEDMATTER PHYSICS. Whileimaging applications (pink) areprobably best known,diffraction (blue) andspectroscopy (yellow) yieldequally importantinformation. X-raydiffraction is used primarily todetermine the order of matterat the atomic scale.Spectroscopy yieldsinformation about theenergetics of electrons indifferent states of matter.Among the most promisingnew trends are hybridtechniques that combinediffraction with imaging(purple), spectroscopy withdiffraction (green) andspectroscopy with imaging(orange). FIGURE 1

just its outward form. Thelow level of diffuse scatter-ing, the small refractive in-dex (less than 10~4 smallerthan unity) and the strongdependence of absorption onatomic number give rise tohigh contrast and 1:1 imag-ing in absorption radio-graphs. Given sufficientcomputing power, tomo-graphic recording of the ab-sorption's spatial dependenceallows one to reconstruct thestructure of matter down to aspatial resolution of about amicron, with this limit cur-rently set by the resolution ofavailable detectors.

When the photon energyincreases to the point wherecore electrons can be excited,abrupt increases in absorp-tion occur. These "absorp-tion edges" are characteristicfor each element. By choos-ing the appropriate energy

from the continuous synchrotron x-ray spectrum, one canobtain element specific tomographs. Present resolutioneven allows the small energy shift of the edge specific fora particular chemical state of the atom to be mapped out.

Since the minimum distance that can be resolved bya wave of wavelength A is given by a\/NA, where NA isthe numerical aperture seen from the source/object and ais a factor between 0.5 and 1 determined by the sourcecoherence properties, x rays of Angstrom wavelengthshould be able to probe structures at the atomic scale.Up till now, however, the best resolution attained withx-ray imaging has been around 100 A. One reason isthat, because the refractive index is so close to unity,conventional optical schemes do not work for x rays.Instead, one uses diffraction lenses such as Fresnel zoneplates (FZPs) or curved mirrors at extreme glancingangles where figure errors seriously affect performance.

NOVEMBER 1995 PHYSICS TODAY 35

100 nm

300 nm

I I 1 1 f ti i• • •« 1 1 1 •«

i i i f»• 11I I r I 1 r

LAYERED SEMICONDUCTOR STRUCTURE

with 300 nanometers of InGaAs and a capof 100 nm of InP grown on an InP base

with oxide ridges is shown schematically(a) and imaged (b) to a depth of about 250

nm by a grazing-incidence synchrotronx-ray beam. The fringe contrast in the

x-ray topogram reveals changes in thelattice constant and elemental composition.

(Courtesy D. Novikov.) FIGURE 2

200 n:

EH InPI I InGaAs

I I oxide

In addition, the required beampower is so high that sophisticatedmethods must be applied to avoiddamaging the delicate optical com-ponents. Despite these difficul-ties, several beam focusingschemes have been tested.

Although FZPs are in use atseveral synchrotron radiationsources with A > 15 A, only recentlyhave attempts to produce transmis-sion FZPs for the conventional x-rayrange been reported. So far, Braggreflection FZPs etched directly into the surface of a siliconcrystal have been more successful than transmission FZPsfor this range.

Other strategies avoid optical elements altogether.Contact microscopy—with the specimen lying directly onthe detector—and projection microscopy—with the beamfrom a microspot source diverging through the specimento produce an enlarged picture on the detector—can beused at shorter wavelengths. The detecting media arethe resolution-defining elements, with photoresists havinga resolution of about 100 A.

Another method that avoids using optical elements isx-ray holographic microscopy2 employing the Gabor in-linearrangement, in which the incident wave traveling outsidethe crystal serves as a reference for the phase of the scatteredwave. The crucial step is the registration of the hologramand its sequential reconstruction. After initial unsuccessfulattempts in the early 1950s to reconstruct and magnify theimage with optical light, today's images are stored in pho-toresists, read out by an atomic force microscope and thennumerically reconstructed with a computer. This techniquealso looks promising for conventional x rays with A < 10 A.Conventional x rays not only will allow study of thickerspecimens, but will also enlarge the field of spectromicroscopyto record element and chemical state specific maps for amuch larger range of elements. Yet another benefit of harderx rays is the lower level of radiation damage they cause tothe specimen.

Spectromicroscopy uses scanning techniques, whichrequire small, focused beam spots. At present, FZPs andmirrors are the favored technique for producing spotsdown to 200 A, but specially designed glass capillarieshave successfully generated spots of similar size, and x-raywave guides are currently being developed.

Bragg diffraction can be used to carry out diffractionmicrotomography on textured polycrystalline materials.

,' 3.3 mm

The strongest impact of x-ray imaging on research anddevelopment, however, has resulted from topographic im-ages of the lattice perfection of single crystals. Disloca-tions, strain patterns and lattice-constant inhomogeneitiescan easily be detected by imaging the intensity and angledispersion of a Bragg reflection. In fact, it is hard tooveremphasize the influence this technique has had onour ability to grow perfect single crystals. (See figure 2.)The lateral resolution limit is set by the detector andinherent limits of crystal optics to about one micron.Recently, dark field and differential phase contrast meth-ods have been developed by using the extremely highangular resolving power of single-crystal optical elements.

Very recently, researchers have attempted3 to use thescattering pattern from a single unit of structure insteadof using signal enhancement by translational repetitionof the unit as in crystallography. This diffraction patterncontains geometrical phase information like that in ahologram, but with atomic-scale resolution. Such studiesrequire the full brilliance of modern synchrotron x-radia-tion sources and the development of detectors with highefficiency, high-count-rate capability and high spatial reso-lution. If enough computing power is at hand to rapidlyanalyze the patterns, we can expect great progress in x-rayimaging for several decades to come.

DiffractionIn addition to increasing the resolution attainable indiffraction studies, the increasing brightness of synchro-tron radiation sources also makes it possible to studysmaller samples. Many crystals can be grown only inminute sizes. Some experiments may require a highdegree of crystalline perfection, which as a rule is moreeasily realizable in a small crystal or by illuminatingminute areas of a larger crystal. A tiny amount of mattercan be studied under pressures comparable to those deep

36 NOVEMBER 1995 PHYSICS TODAY

ALGEBRAIC DECAY. Many, diverse systems exhibit neitherlong-range order, in which the pair correlation function of thesystem's order parameter is constant, nor short-range order, in

which the the pair correlation function decays exponentialywith r. Rather, the pair correlation function of such systems

decays algebraically, as r~'" ">, where 77 is the characteristicexponent. In x-ray diffraction, long-range order producessharp Bragg peaks and short-range order produces diffuse,

Lorentzian-shaped diffraction peaks. Algebraic decay producespseudo-Bragg peaks with broad wings, from which 17 can be

determined, a: The binary alloy Fe,Al undergoes a transitionfrom an ordered phase, in which Fe and Al atoms occupy in aperfectly ordered way the corners of a cubic unit cell with an

Fe atom at the center, to a disordered phase, in which thecorners are occupied by either Fe or Al with equal

probability. For temperatures very near the criticaltemperature and at shallow depths, the alloy exhibits algebraicdecay in agreement with predictions of renormalization group

theory (from ref. 6). b: The surface of a liquid remainssmooth, resisting fluctuations in its height, because of its

surface tension. Plotting the intensity of the scattered x raysversus qy, the component of the x-ray scattering vector parallel

to the surface, results in a curve with pseudo-Bragg peaks andbroad wings indicative of algebraic decay. 77 is inversely

proportional to the surface tension and proportional to thesquare of qz, the perpendicular component of the scatteringvector (red and blue curves). (Adapted from ref. 7.) c: In a

stack of surfactant membranes, the neighbors limit the spaceavailable for fluctuations, causing an entropic repulsion, for

which 77 depends on the intermembrane distance d. In aternary system of oil, water and surfactant, 77 was measured as

a function of d (red), which was varied by changing the oilconcentration, and found to agree with the theoretical

treatment by Wolfgang Helfrich. If the surfactant's polar headgroups are charged, the entropic interaction is overwhelmed

and 77 decreases (blue). (Adapted from ref. 8.) FIGURE 3

in the Earth and other planets. Finally, an increasinglyimportant special case of diffraction by a small sample isthe study of atoms or molecules confined to a surface orinterface.

Shining x rays onto a surface at close to the criticalangle of total reflection and detecting the specularly re-flected intensity yields a wealth of information.4 For asharp but laterally rough surface, this x-ray reflectivity(XR) measurement gives the correlation in heights acrossthe surface. As an example, consider a single crystal cutso the surface is at a small angle relative to atomic netplanes. The resulting surface profile is like a staircasewhere the steps coincide with the atomic net planes.Recent XR studies of such surfaces in a silicon crystalhave shown that the step morphology changes with tem-perature from a high-temperature, uniform phase withsmall steps to separated phases of large facets and highsteps at low temperatures. This phase separation isanalogous to the case of a mixture of two liquids that mixperfectly at high temperatures, but phase-separate at lowtemperatures.

The complementary case to the sharp but roughsurface is that for which the density changes gradually inthe normal direction across a smooth surface. Here XRdetermines in a very direct way the average density acrossthe surface. Experiments on simple liquids, such as waterand ethanol, showed that the fuzziness of the liquid-vaporinterface was fully accounted for by thermally excitedcapillary waves. In other simple liquids, such as mercuryand gallium, as well as liquid crystals in the isotropic

2500

0 50 100 150 200INTERMEMBRANE DISTANCE d (A)

phase, it was discovered that a few well ordered layersform on top of the isotropic liquid.

In heterogeneous systems, such as Langmuir films4

(a single molecular layer of amphiphilic molecules depos-ited on a water substrate), one can accurately measurethe thickness of the film and thereby the possible tilt ofthe molecules with respect to the water surface. Also, onecan study how charged polar head groups in the Langmuirfilm attract ions or how the head groups attract solutemolecules, forming nuclei for three-dimensional crystalgrowth under the film.

X-ray diffraction can also reveal the lateral structurewithin the interface.5 By using an incident x-ray beamat glancing angles near the angle for total external reflec-tion, one creates an evanescent wave with a field whoseamplitude decays exponentially perpendicular to thesurface. An important feature of this grazing incidence

NOVEMBER 1995 PHYSICS TODAY 37

DRAMATIC IMPROVEMENT in the resolution of x-ray spectralfeatures is evident from comparison of a state-of-the-art

K-absorption edge plot for gaseous argon from 196710 (top)and an expanded plot made in 1984 (bottom; courtesy

R. Frahm) using a much shorter exposure to synchrotron xrays. The dominant feature in the 1967 plot corresponded toa Is electron being excited to unoccupied states. The feature

around 3.222 keV, barely visible in the 1967 plot, results frommultielectron excitations, about which the 1984 plot revealsmuch more detail. Current theoretical calculations11 (blue)

reproduce the overall shape of the 1984 plot but varyconsiderably in many details. FIGURE 4

diffraction (GID) technique is that the probing depth ofthe evanescent wave can be varied from about a coupleof nanometers to tens of nanometers by minute changesof the glancing angle. In contrast to low-energy electrondiffraction, the interpretation of the diffraction data isstraightforward because the x-ray photon is a weak probeand multiple scattering can be neglected.

Applications of this technique include the reconstruc-tion of many clean metal and semiconductor interfaces inultrahigh vacuum as well as the study of chemisorptionof, for example, oxygen atoms on a copper surface andresearch on the liquid interface in an electrolyte, whereone has been able to see how the surface of a metalelectrode changes with an applied voltage over the elec-trolytic cell.

In the past, the rich phase diagrams of Langmuirlayers were studied by classical methods, such as pres-sure-area isotherms, but modern x-ray diffraction tech-niques were necessary to determine the nature and inter-action of these phases. Although Langmuir films aretwo-dimensional powders, usually with a lateral grain sizeof some tens of microns, synchrotron radiation beams areintense enough to produce diffraction patterns with suffi-cient detail to resolve molecular packing at near-atomicscales. The molecular packing in free-standing, self-sup-porting films only a few monolayers thick has also beenanalyzed, yielding new insights into the basic structuralfeatures in the transition from two to three dimensions.

Phase transitions at interfaces may be quite differentfrom those in bulk. Melting-solidification, perhaps themost ubiquitous phase transition in nature, has beenstudied a great deal using a variety of experimentaltechniques, computer simulations and theoretical calcula-tions. Ion scattering experiments have shown that thetop atomic layers of a Pb crystal's (1,1,0) face lose crys-talline order tens of degrees below the bulk meltingtemperature. This astonishing result has been confirmedby GID x-ray diffraction. Surface melting has now beenobserved in metals, semiconductors, rare gas films, ice andother molecular crystals.

The opposite phenomenon, surface crystallization,also occurs in Nature. One example is the solidificationof alkanes—simple hydrocarbon chain molecules terminat-ing in a methyl group at both ends, CH3(CH2)n_2CH3. XRand GID measurements reveal that, at about 3 °C aboveand persisting down to the bulk solidification temperature,the surface of alkanes forms a single crystalline monolayer.The monolayer has a two-dimensional hexagonal latticeand the molecular axis is perpendicular to the surface.

In melting-solidification, the phenomenon of super-cooling is well known, as in, for example, a glaze of frostforming on a road in Winter. Superheating is much lesscommon. One example is the melting of small Pb crystalsembedded in an aluminum crystal matrix. Transmissionelectron microscopy shows that nanometer-sized Pb crys-tals form close-packed (1,1,1) face octahedra, truncated in

3000

e 2000

1000

n

I K excitation

-Si

3.20 3.22ENERGY (keV)

3.22 3.24 3.26ENERGY (keV)

3.28 3.30

smaller (1,0,0) faces co-aligned with the single crystal Almatrix. As the temperature approaches the melting pointfrom below, x-ray experiments have shown that the (1,0,0)faces become rough while the (1,1,1) faces stay atomicallysmooth, even at temperatures well above the bulk meltingtemperature of Pb. Upon melting, the inclusion becomesspherical.

The patterns observed in x-ray diffraction reflect themicroscopic structure of different phases of matter in thesample. Crystalline phases produce sharp Bragg diffrac-tion spots, corresponding to long-range order of thousandsof angstroms, while liquids give broad diffuse rings indi-cating short-range order over only a few angstroms. Re-cent experiments have looked at a state of matter thatexhibits neither long-range nor short-range order, butrather the pair correlation function of atomic positionsexhibits a peculiar algebraic decay characterized by anexponent, 77. In the diffraction pattern, this state givespseudo-Bragg peaks with broad wings from which theexponent 17 can be determined. Figure 3 shows data forthree such systems, all seemingly quite different. Evenstudies of two-dimensional "crystalline" order have re-vealed that such systems actually exhibit algebraic decay.

A particularly advanced application of x-ray diffrac-tion involves the use of x-ray standing wave fields andhas become practical only with the availability of suffi-ciently perfect crystals. In such experiments, one looksnot just at the elastically reflected "far-field" intensity farfrom the crystal, but also at the "near-field" intensity nearthe surface and inside the dynamically diffracting crystal.Such near-field measurements probe the spatial peri-odicities of elemental distributions within the bulk andon the surface of the sample. This technique, which isused to measure the positions of foreign atoms inside andon the surfaces of crystals, circumvents the phase problemof kinematical diffraction measurements by using the hostlattice as an absolute reference for the position of thepattern.9 As one moves the varying electric field of thewave-field nodal planes through the sample, the foreignatom reveals its position by giving off fluorescence

38 NOVEMBER 1995 PHYSICS TODAY

opaiOVJ1

4 -

3 -

Z0piw

ABSORPTION ANDSCATTERING givecomplementary informationabout a sample, a: Theoscillations following theK-absorption edge forcrystalline Ni result frombackscattering of thephotoelectron by neighboringatoms. These oscillations canbe analyzed to find the radiiand number of atomsoccupying neighbor shells aswell as more subtle details,such as vibration amplitudes.b: In the vicinity of the K-edgeresonance, dispersion decreasessharply from its off-resonancevalue, which is equal to theatomic number of thescattering atom. K-edgefrequencies vary for differentelements, allowing one to varythe contrast between elementsin a sample by varying thephoton energy. (Courtesy R.Frahm.) FIGURE 5

PHOTON ENERGY (keV)

photons, Auger electrons, photoelectrons or by desorbing.One application of this technique has been in situ char-acterization of the lattice sites of deposited ions on anelectrode in an electrolyte as a function of the appliedpotential and electrolyte conditions. This coupling of x-rayinterference and spectroscopy is another excellent exampleof the exciting possibilities offered by new hybrid methods.

SpectroscopyMost of what we know about the electrons in differentstates of matter has been revealed by elastic or inelasticscattering of photons. Prior to the 1950s, x rays playeda decisive role in characterizing materials and elucidat-ing atomic structure and the nature of electron-photoninteractions. Since the 1950s, new detectors, perfectcrystal optics, increased computer power and synchro-tron x rays have allowed fundamentally new uses ofx-ray spectroscopy.

Figure 4 illustrates the improvement in a state-of-the-art absorption spectrum for argon gas from 1967 to1984. The additional spectral features in the 1984 spec-trum provide information about multielectron interactionsin the ground state, the excitation and its subsequentdecay. This information can be used to test multielectronrelativistic and quantum electrodynamic effects to preci-sions of better than 10~6 of the total binding energy. Suchadvances are also important for condensed matter physics,because atomic physics forms the basis of condensed mat-ter physics. Figure 5 shows the variation of the real part(associated with scattering amplitude) and the imaginarypart (associated with absorption) of the scattering factorof an Ni atom inside a Ni crystal as a function of the

photon energy. Note that because of interac-tions between the electrons and the crystallinelattice, the oscillating structure above the bind-ing energy extends much further than the os-cillating structure for the gas phase in figure4a. This additional structure gives informationabout the radius and number of atoms in aneighbor shell.9

Over the past 20 years, x-ray absorptionedge fine structure (XAFS) has proved invalu-able in many structural studies. For energiesjust exceeding the binding energy, the outgoingphotoelectron is affected by the spin and angu-lar momentum dependence of the unoccupiedstates, because selection rules must be satisfiedfor energy, angular momentum and spin. Thisgives information about the bonds and exchangeinteractions between neighbors. At higher en-ergies, the transition matrix element reflectsthe chemical and geometrical surroundings ofthe excited atom. Because XAFS does not re-quire long-range crystalline order, it has beenused with great success in fields such as cataly-sis research, often performed in situ duringreactions. Considerable progress has beenmade in relating atomic-scale structural fea-tures revealed by XAFS spectra to the overallfunction of the catalyst.

Spectroscopy and diffraction yield comple-mentary information that is necessary for a fullunderstanding of the structure and dynamics ofa solid. Information about local structure asrevealed by XAFS has also been instrumentalin understanding alloys, helping to place incontext knowledge of the average structure re-vealed by diffraction. (See figure 6.) Combiningboth the diffraction and absorption spectra canreveal, for example, a special symmetry of a

noncentrosymmetric crystal, such as a-Fe2O3, that theabsorption spectrum alone would miss.

Resonances can also be useful for studying systemsthat normally interact only weakly with x rays. Forexample, with respect to charge scattering, magnetic x-rayscattering is suppressed by a factor of (hv/mc2)2, wherev is the x-ray frequency and m the electron rest mass.This suppression, coupled with the relatively small frac-tion of electrons that contribute to magnetism, means thatmagnetic interactions are normally too weak to be probedby x rays, unless one uses very hard x rays—an areaunder active development—or unless one tunes the photonenergy to a resonance. The L-edges of rare earth elementsand the M-edges of actinides have shown resonance en-hancements of several orders of magnitude. As such, onecan label magnetic atoms in alloys of such materials anddetermine the contribution of these atoms. X-ray mag-netic scattering provides information that complementsthat obtained from magnetic neutron scattering, becausethe selection rules for magnetic x-ray scattering are dif-ferent from those for magnetic neutron scattering. Thus,for example, the influence of electron spin and momentumon the scattering could be studied separately.

Another outstanding resonance enhancement resultsfrom exciting nuclear levels with synchrotron x-ray radia-tion. Mossbauer photons emitted from stimulated nuclei,such as 57Fe, are available with resolutions ranging frommeV to neV with photon intensities on the order of 104

per second into a narrow angle.If the photon energy is very close to an excitation

energy, the final state can consist of a hole, a photo-electron and an energy-shifted outgoing photon or of a

NOVEMBER 1995 PHYSICS TODAY 39

2.60

u<H

sOS

go3oi<

2.55 —

2.50 -

2.45

-

/

1

In-As

XAFS

Diffraction /

/

1

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Ga-As

1 1

0.2 0.4 0.6 0.8COMPOSITION [x in Ga^Jto^As)

1.0

photoelectron and an Auger electron with two holes.These are Raman transitions, which are well known fromthe optical regime. The atom passes from the groundstate resonantly through virtual intermediate states tothis final state. Precise measurements of the energy-shifted photon, the photoelectrons and the Auger electronsnot only reveal the nature of this process but also providedetails of the involved final and intermediate states. Eveninelastic scattering processes connected with additionalexcitations of valence electrons can be resonantly en-hanced. The rotation of the optical plane of the x raysby non-centrosymmetric structures—optical activity—hasbeen measured, as has rotation by an external magneticfield—Faraday rotation.

Spin-polarized XAFS, which provides the possibilityof studying the magnetic structure around an atom byusing circularly polarized x rays, also appears to be apromising technique for future studies.

Inelastic scattering of off-resonance photons is nowused to study plasmons and phonons. Among the excitingrecent results is the observation of fast sound in water(3300 meters per second, which is comparable to soundspeed in ice) over a large energy-momentum region. Forsuch experiments, one needs highly perfect crystal opticalelements to furnish the resolution and a bright source toget enough photons within a bandwidth sufficiently nar-row to separate the excitation from noise.

An experiment performed by detecting inelastically scat-tered photons as the nodes of the standing x-ray wave-fieldmove through regions dominated, respectively, by core andvalence electrons demonstrated the existence of plasmonbands and of plasmon band gaps. This indicates that amean-field approach to calculating the dielectric response ofthe semiconductor—that is, an approximation assuming afree electron gas oscillating relative to a positive ion core—cannot fully describe the plasmon excitation in covalentcrystals, because the periodicity of the positive core potentialchanges the plasmon collective excitation.

LOCAL STRUCTURE REVEALED by x-ray absorptionfine-structure spectroscopy complements the average structureinformation as revealed by diffraction.12 In a crystal ofGaj.jInjAs, the band structure can be successfully calculatedusing Vegard's law, which assumes a perfect lattice with anaverage lattice that varies linearly with X. This dependence isconsistent with diffraction measurements of the averagenearest-neighbor spacing (red), but is at variance with XAFSdata that show that In-As and Ga-As lattice spacings (blueand green, respectively) are close to those for pure InAs andGaAs, respectively, and depend only weakly on x. FIGURE 6

A brighter futureTraditionally, condensed matter physics has been consid-ered "small science," with projects carried out by smallgroups of scientists using equipment that fits into astandard laboratory space. Synchrotron radiation sourcesoffer such overwhelming advantages over traditional x-raysources that they are rapidly moving condensed matterphysics out of the realm of tabletop physics. In so doing,the synchrotron radiation facility is changing not just thetools of condensed matter physics, but also its sociology.At synchrotron radiation facilities, many comparativelysmall groups of physicists, chemists, biologists and otherresearchers are constantly interacting, creating a stimu-lating atmosphere conducive to cross fertilization of ideasand techniques.

Among the results of this atmosphere are new com-bined x-ray techniques that cross the traditional divisionsof x-ray techniques: imaging, diffraction and spectroscopy.In many ways, the new possibilities offered by synchrotronx-ray sources and the combined techniques have made thepresent as exciting as the pioneering period of x-rayresearch at the beginning of the century.

AcknowledgmentSpace restrictions for this article have forced us to selectonly a few dozen of the hundreds of important topics pub-lished in this field over the past two decades. Such aselection procedure is always open to criticism. The respon-sibility for any oversight rests entirely with us. We wouldlike to express our appreciation to the following people fortheir many helpful and stimulating ideas: B. Batterman,M. Blume, P. Eisenberger, W. Graeff, F. Grey, C. Kunz, L.Leiserowitz, B. Lengeler, A. R. Mackintosh, S. Mochrie, D.Moncton, I. Robinson, W. Schulke, S. K Sinha, A. SnigirevB. Sonntag, E. Stern and G. H. Via.

References1. J. Kirz, C. Jacobsen, M. Howells, Quarterly Reviews of Bio-

physics 28, 1 (1995), p. 33.2. S. Lindaas, M. Howells, C. Jacobsen, A. Kalinovsky, J. Opt.

Soc. of America, (submitted).D. Sayre and H. N. Chapman, Acta Cryst. A 51, 237 (1995)J. Als-Nielsen et al, Phys. Reports 246, 251 (1994).I. K. Robinson, D. J. Tweet, Rep. Prog. Phys. 55, 599 (1992).H. Dosch et al, Surface Science 279, 367 (1992).M. K. Sanyal, S. K. Sinha, K. G. Huang, B. M. Ocko Phys RevLett. 66, 628(1991).C. R Safinya, in Phase Transitions in Soft Condensed Matter,T. Riste, D. Sherrington, eds., Plenum, New York (1989)'p. 249.Resonant Anomalous X-Ray Scattering, G. Materlik, C. J.Sparks, K. Fischer, eds., North-Holland, Amsterdam, 1994.

10. H. W. Schnopper, Phys. Rev. 154, 114 (1967).11. V. L. Sikhorukov, A. N. Hopersky, I. D. Petrov, V. A. Yavna, V. F

Demeknin, J. Physique 48, 1667 (1987).12. J. C. Mikkelsen Jr, J. B. Boyce, Phys. Rev. B 28, 7130 (1983). •

3.4.5.6.7.

9

40 NOVEMBER 1995 PHYSICS TODAY