Ultrafast Time-Resolved Transient Structures of Solids and Liquids

Ultrafast electron optics: Propagation dynamics of femtosecond electron packets. Bradley J. Siwick , Jason R. Dwyer , Robert E. Jordan , R. J. Dwayne ...
0 downloads 0 Views 159KB Size
Download PDF
J. Phys. Chem. B 1999, 103, 7081-7091

7081

FEATURE ARTICLE Ultrafast Time-Resolved Transient Structures of Solids and Liquids Studied by Means of X-ray Diffraction and EXAFS Ivan V. Tomov, Dmitri A. Oulianov, Peilin Chen,† and Peter M. Rentzepis* Department of Chemistry, UniVersity of California, IrVine, California 92697 ReceiVed: March 10, 1999; In Final Form: June 9, 1999

Picosecond and nanosecond transient structures have been observed directly using time-resolved X-ray diffraction and absorption. These experiments provide insight on the evolution of transient molecular structure on the atomic length scale during the course of a chemical reaction. Recent advances in the generation of short X-ray pulses and detectors have made time-resolved X-ray studies a reality. We discuss a few of the vast number of possible time-resolved structure studies in solids and fluids. Ultrafast relaxation dynamics of crystal lattice structures induced by picosecond and nanosecond laser pulses have been observed by means of time-resolved picosecond and nanosecond X-ray diffraction. Lattice deformation with 10 ps and 10-3 Å resolution have been performed. The picosecond X-ray system, which we have used, is described, and its application to time-resolved ultrafast X-ray diffraction in crystals and EXAFS in liquids is discussed.

1. Introduction Since their discovery, X-rays have been the dominant source for the determination of structure. X-ray diffraction has been the most common and accurate method for the measurement of crystal structures from simple inorganic crystals, such as common salts to large biological molecules, such as DNA, hemoglobin, and rhodopsin.1 X-ray absorption and lately EXAFS studies have made it possible to determine the structure around a specific atom in the liquid state. Lately, the wide use of synchrotrons has resulted in a number of EXAFS studies, which have helped considerably in the effort to elucidate the structure of liquids.2 Electron and neutron diffraction has also been used; however, electrons, because of their short penetration depth, are more useful for surface characterization and gases. Time-resolved electron diffraction was first performed in 1988 in picosecond time-resolved studies of solids3 and nanosecond time-resolved electron diffraction from gases.4 Since then, several publications have appeared and now other groups are also active in this field.5-9 Ultrafast laser spectroscopy has provided the decay and formation kinetics of many transient chemical and biological processes. However, the structures of excited states remain unknown although their identity as single or triplet states, etc., can be deduced from ultrafast optical spectroscopy. This article will be restricted to time-resolved X-ray diffraction and EXAFS, its aim being to introduce this rather new and potentially very important field of science. The vast majority of X-ray structure studies have been performed in the static regime. However, as in the case of lasers, which have been used since the 1960s, the means for timeresolved excited-state research, X-rays, have also started to † Present address: Department of Chemistry, University of California, Berkeley, CA 94720. * Corresponding author.

become instruments for transient structure determination.10 To understand, in depth, the dynamics of even the most well-known physical, chemical, and biological processes, such as bond dissociation and formation, protein folding and unfolding, liquid structures, phase transition, temperature or shock strain in materials, and even the excited-state structure of molecules, time-resolved X-ray studies have become rather mandatory. Normally X-ray structures are determined by averaging the data over the time of the experiment and obtaining a space average of all molecules in the sample. Transient studies, however, must account for the evolution of a structure, which may occur very fast and may even have a varying spatial and temporal distribution within the sample at a given time. Thus transient structure determination is far more challenging. The continuous development in technology has made possible the design, construction and use of time-resolved X-ray systems, which vary from the very powerful, versatile, and often used synchrotron sources, to small benchtop laboratory systems. Before we discuss time-resolved X-ray studies in detail, we will review briefly the basic principles of X-ray interaction with matter.1,2 When X-rays are incident on a material they are scattered by the electrons of the atoms. The typical X-ray photon energy (5-100 keV) is significantly greater than the binding energy of the majority of the electrons although some inner shell electrons (i.e., K-electrons) may have comparable or even higher energy than the X-ray photon. As a first approximation, we may assume that the amplitude of the X-rays scattered from an individual atom is proportional to the total number of electrons in the atom, i.e., the atomic number. The scattered amplitude from an atom, the atomic form factor f can be calculated with reasonable accuracy. Absorption effects can also be included in the atomic form factor by considering it as a complex number. In crystals, the atoms are arranged in a periodic threedimensional crystal lattice. The incident X-rays experience a

10.1021/jp9908449 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/04/1999

7082 J. Phys. Chem. B, Vol. 103, No. 34, 1999

Tomov et al.

three-dimensional arrangement of the electron density and the contour map of this electron density is studied in X-ray scattering experiments. Therefore, an X-ray beam, which impinges on a crystal, sees a periodic structure of planes of atoms and therefore the X-rays scattered by different atoms will interfere with themselves. In the directions of constructive interference a well-defined pattern of scattered X-ray intensities is observed. Bragg’s law gives the condition for diffraction

2dhklsin ΘΒ ) λ where λ is the X-ray wavelength, dhkl is the plane spacing, and ΘΒ is the angle of incidence between the X-ray beam and the lattice plane. For monochromatic X-ray radiation the angle of incidence must satisfy Bragg’s law. If a fixed direction and a X-ray beam with low divergency is used, then by rotating the crystal different sets of diffracting planes can be studied (Bragg diffraction). When polychromatic X-ray radiation is used, the crystal may remain stationary and it will select and diffract radiation of different wavelengths in different directions in order to satisfy Bragg’s law. This method, known as Laue diffraction, makes possible the collection of diffracted radiation from many different planes simultaneously. To avoid overlap of spots, a low divergent beam with small cross section must be used. Both Bragg and Laue diffraction methods are widely employed in X-ray crystallography. To obtain the entire structure of a crystal, a complete set of diffraction data is necessary and in this case the Laue diffraction method allows for faster data collection. In the case of noncrystalline materials, such as gases, liquids, and amorphous solids, where there is an absence of periodic arrangement of atoms, diffraction is also observed but with much less efficiency. Nevertheless, information, on the structure may be obtained. The average intensity of the scattered X-rays from an array of atoms, which may have all orientations in space, is determined by the Debye equation:

Ia )

∑ ∑ fmfn m n

sin krmn krmn

Here k ) 4πsin θ/λ, rmn is the distance between the m- and the nth atom, and θ is the scattering angle. Since atoms have welldefined sizes and closest distances of approach, there is a structure relative to an origin at the center of an average atom. This type of structure is expressed in the form of a radial distribution function. Modulation of the radial distribution function can give information regarding the interatomic distances and molecular structure in liquids and amorphous solids. X-ray absorption by molecules has been used to provide structural information of molecules, including chemical bonding, charge, and the oxidation-reduction state of atoms and molecules. X-ray diffraction provides information regarding the global structure of molecules in the condensed phase. However, the spatial information obtained by X-ray absorption is limited to the local environment of a particular atom. Absorption has the very desirable advantage of being very sensitive only to a particular atom. Therefore, it provides the structure near the selected atom and does not favor large Z atoms as in the case of diffraction. It can be easily used, in principle, to study small Z number molecules composed of H, C, N, O which are of great importance to chemistry and biology. The absorption processes, which can give structural information, are extended X-ray absorption fine structure (EXAFS), near edge resonances, and chemical shifts. EXAFS and near edge

Figure 1. Time scale of transient phenomena, pulsed X-ray sources, and detection techniques.

resonances are displayed as modulation of the absorption spectrum above the X-ray absorption edge. To understand these modulations in the spectrum we can think as follows: when an incident X-ray photon is absorbed by an atom, it, most likely, induces photoionization. The excess energy of the X-ray photon above the ionization potential is carried away by a photoelectron. At very small kinetic energies (less than 50 eV) there is multiple scattering of the electron and interference effects between the electrons of the atom and those of the near neighbor atoms. A full molecular orbital treatment is necessary to describe the electron near edge absorption spectrum. At higher kinetic energies the photoelectron can be treated as a spherical wave leaving the atom which scatters from the electrons of neighboring atoms, and the resulting interference pattern is then a function of a few atomic and molecular parameters. This interference pattern is the EXAFS spectrum which is Fourier transformed to yield structural information such as bond lengths and angles. The chemical shift of the absorption edge is very small (a few eV). It is the result of the charge screening effect of the outer electrons on the inner electrons in the atom. Chemical environment changes the screening effect and results in a characteristic chemical shift for a particular atomic arrangement. 2. Studies of Transient Structures by Means of Time-Resolved X-ray Probing In contrast to the static structure determination, to follow the evolution of the structure, we must take “snapshots” with the probing pulsed X-ray radiation. The duration of the X-ray pulses must be practically as short as the lifetime of the transient structure. The lifetime of the transient structures of interest vary from many seconds to femtoseconds. For example, folding and unfolding of proteins occurs in seconds while the dissociation of chemical bonds may require only femtoseconds. To cover such a wide temporal range, various pulsed X-ray sources, and detection devices have been designed and used. Figure 1 depicts the time scales of typical transient phenomena, X-ray pulse sources, and detection techniques. What transient structural information would we hope to obtain with time-resolved X-ray probing? Essentially any, given the appropriate equipment: from electron-phonon relaxation to the iron movement in hemoglobin. Here we will mention only a few examples from current research.

Feature Article On the atomic and molecular level, time-resolved X-ray data could provide direct information allowing one to reconstruct the motion of atoms during a dynamic process.11 With an experimental X-ray time resolution in the tens of femtoseconds range, it may be possible to observe directly electron-phonon interaction and the evolution of chemical reactions, i.e., formation and dissociation of chemical bonds. In biology, static X-ray crystallography has been very successful in determining the structure of many very important biological macromolecules such as proteins, enzymes, and DNA. To further understand the properties and behavior of these macromolecules under reaction conditions, one must know how their structural changes in time, i.e., identify the structures of intermediate and transition states.12 This information in turn will make the understanding of the reaction mechanism and activation parameters of a particular reaction rather complete. In material science the development of new and improved technological materials requires increased sophistication in structural investigations, including in situ processing with high temporal resolution.13-15 As technology advances, the use of nonequilibrium and artificially structured materials in ultrafast switching devices makes the understanding and knowledge of the temporal properties of these new materials mandatory. These are a few examples of a wide field of time-resolved studies which are important for the advancement of basic science and technology. To achieve this ambitious goal a wide set of experimental X-ray data must be accumulated and theoretical models used in order to determine the time-resolved evolution of the transient structure of matter. In the optical range by application of pump/probe techniques, in which an optical pump pulse initiates a chemical reaction and another delayed optical pulse probes intermediate spectra of the reacting system, a time resolution in the femtosecond range has been achieved. However, optical measurements do not provide information regarding atomic and molecular positions. Time-resolved X-ray studies are necessary in order to measure directly the short-lived transient structure of matter with atomic spatial resolution. Similar pump/probe transient techniques, developed for picosecond spectroscopy, can be applied to time-resolved X-ray studies. Of course, short optical pulses are needed for the initiation of the fast processes to be probed by X-ray pulses. There are three components, which are critical for the successful, execution of time-resolved X-ray experiments: a pulsed X-ray source, reaction initiation, and detection systems. We will briefly discuss each of these components. 2.1. Pulsed X-ray Sources. There are three main types of pulsed X-ray sources, which have been used in time-resolved X-ray studies: electron impact sources, laser-produced plasma, and synchrotrons. There is extensive literature covering the characteristics and operational parameters of each source10,16,17 therefore, here, we will list only some of the most important features related to time-resolved studies. (a) The First X-rays Were Generated by Electron Impact on Metal Anodes. In an impact source, the electrons are produced at the cathode, then accelerated by an electric field and finally impinge on the anode producing X-ray radiation. The spectrum of this radiation consists of a broad continuum and lines characteristic of inner shell ionization of the anode atoms. In a standard, continuous X-ray tube the electrons are usually emitted from heated metal filaments. Submicosecond duration pulses have been achieved by applying electrical pulses to the X-ray diode in which the electrons are generated by the field-emitting cathode. This technique allows for the production of X-ray

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7083 pulses with several tens of nanosecond duration. Shorter electron pulses with nanosecond and picosecond duration have been generated in photocathodes excited by ultrashort pulses. In section 3 of this paper we will describe in more detail the laser pumped X-ray diodes for the production of nanosecond (ns) and picosecond (ps) hard X-ray pulses. (b) Laser-Produced Plasma. When a powerful laser pulse is focused on a solid target, the energy is deposited in a small spot so fast that there is not sufficient time for heat diffusion to take place, and consequently hot plasma is produced. The temperature of the plasma can reach millions of Kelvin and therefore it expands in the surrounding vacuum. This type of plasma is known to emit a broad spectrum of electromagnetic radiation including X-rays. The amount and properties of the X-ray radiation produced by a laser plasma depends on the plasma processes, but the duration of the X-ray pulses generated closely follows the duration of the excitation laser pulse. This technique has generated nanosecond and picosecond X-ray pulses and is expected to generate pulses in the femtosecond (fs) range. (c) Synchrotrons Produce Electromagnetic Radiation by MoVing Charged Particles in a Circular Orbit at RelatiVistic Velocities. The radiation wavelength and power generated depend on the electron energies and radius of curvature of the bending magnets. The spectral properties of the emitted radiation may be further manipulated by inserting magnetic devices into the ring. The output of the present day advanced synchrotrons is a “bunch” of high power X-ray pulses emitted in a narrow cone angle. The duration of a single pulse in the bunch may be as short as 50 ps. To compare the capabilities of the various X-ray sources, a “spectral brightness” term is used which is defined as the number of photons per second per unit area per unit solid angle per 0.1% bandwidth. By far the brightest sources in the hard X-ray region are the synchrotrons with brightness up to 1017 in the10 keV range, which are several orders of magnitude higher than the X-rays generated in pulsed impact sources. However, the laser plasma and X-ray diode can produce the shortest X-ray pulses. Even though synchrotron facilities are the brightest and have very wide wavelength ranges, they are also the most expensive and least flexible systems. Therefore benchtop-pulsed X-ray sources are also quite useful. 2.2. Reaction Initiation. The reaction, which generates the transient structure to be studied, must be initiated by a short light pulse or other short pulse sources, which are synchronizable with the X-ray probing pulse. In addition, both pump and probe pulses must not damage the sample and must be reproducible. Initiation can be achieved by various means. These include short laser pulses, temperature or pressure jumps, electrical or magnetic pulses, and chemical diffusion. For the nanosecond and shorter time ranges, use of ultrashort laser pulses for initiation seems to be the most practical choice. However, the more rapid the process, the higher the peak power needed for initiation which may be limited by the damage threshold of the sample. In solid samples, excitation by optical pulses invariably leads to crystal heating. In crystals with strong absorption the laser energy is deposited in a thin layer near the entrance surface and then the energy is transferred into the bulk by heat diffusion. Therefore, strain and stress may be generated in the crystal. This effect is not observed and is not of importance in optical spectroscopy; however, because of the lattice constant change caused by the nonequilibrium heating of the sample it is very evident and of importance for the transient structure of the crystal. Strong absorption of the input laser radiation can also

7084 J. Phys. Chem. B, Vol. 103, No. 34, 1999 alter the quality of the crystal. Single-shot experiments require powerful X-ray pulses, which may be difficult to generate, and if used, the high flux of X-ray radiation may cause damage to the sample. “Stroboscopic” experiments, where many shots are accumulated may be more suitable, but require high repetition rate systems with accurate synchronization between pump and probe pulses. In addition, the structural processes studied must be reversible within the time period between excitation pulses, or a new sample must be supplied for every shot. 2.3. Detectors. Most of the detectors used, in the timeresolved X-ray studies, have much slower response than the time resolution needed for many of the processes studied.10 Although there are X-ray streak cameras with picosecond resolution, they require very high X-ray intensities and therefore they have found very limited use. The most common detectors for hard X-rays fall into two categories: integrating detectors and photon-counting detectors. Integrating detectors are used most often, especially in X-ray diffraction. They measure some quantity, which varies with the X-ray intensity to which they are exposed. In the case of chargecoupled devices (CCD) this quantity is the amount of charge accumulated in a single element of the detector (pixel). In the case of phosphor image plates, it is the number of F centers created in the phosphor and in X-ray film the degree of blackening as a function of the numbers of X-ray photons striking the film. These types of detectors integrate the incoming X-ray radiation, are insensitive to the rate at which the X-ray photons arrive and they can record large amounts of X-ray radiation as long as saturation is avoided. CCDs are becoming rapidly the most important integrated detector. Their performance characteristics, such as high dynamic range, versatile readout, data storage modes, and highresolution two-dimensional geometry, have opened new possibilities in data handling and processing. CCD detectors are used in two modes: direct and indirect detection of X-ray radiation. In the direct detection mode, the X-ray photons with energies in the range up to 30 keV are absorbed by the silicon pixel chips; at higher energies the absorption efficiency of silicon becomes too low to be useful. Indirect CCDs use a phosphor screen in front that converts the incoming X-ray radiation into optical photons which in turn are channeled to and detected by the CCD. Frequently, fiber optic tapers are used as faceplates between the phosphor and the indirect CCD detectors. Photon counting detectors distinguish and record each incoming X-ray photon. In these detectors the limitation is determined by the rate at which the photons arrive. Detection of a photon requires some time during which the detector is insensitive to the arrival of further photons. Although they will not count simultaneously, arriving photons some of these detectors are capable of determining the wavelength and position of each photon. There is no perfect detector, all have strengths and weaknesses, and the optimum choice depends on the exact nature of the measurements needed to be performed. Most of the X-ray detectors available measure intensity, but the phase information is lost, and therefore, it is difficult to Fourier transform the experimental data. This is the “phase problem” in X-ray crystallography.1 It is worth noting several of the assumptions on which the time-resolved measurements are based: (1) during the X-ray probing of the sample the structural changes should be sufficiently large to be detectable. As a rule of thumb the faster the process is, the smaller the changes. (2) Structural intermediates may be detected, only if in the time scale of the experiment

Tomov et al.

Figure 2. Experimental system for pump/probe time-resolved X-ray studies. A, anode; C, cathode; (s) laser pulses; (‚‚‚) electron pulses; (- -) X-ray pulses; (-‚-) diffracted X-ray pulses.

there is an appreciable accumulation of intermediates and if their lifetime is longer than the time resolution of the experiment. Also we have to consider the possibilities of several pathways leading to similar intermediate structures. (3) Time dependent changes of the measured X-ray intensities must be reducible to electron density distributions and atomic structure. Thermal and other conformational gradients will occur, and since they are time dependent, care must be taken to either eliminate them or decrease them to a large extent or their influence should be accounted for in the interpretation of the results. Owing to the nonhomogeneous nature of the transient changes, there will always be some degree of spatial and temporal averaging to be made and therefore very often the transient data may not be defined exactly as in the steady-state experiments. These are some of the problems we encounter when processing the experimental time-resolved transient structure data. Continuous improvement of the data processing techniques is necessary for the determination of the exact transient structures of complex molecules. 3. Time-Resolved Studies with Nanosecond and Picosecond X-ray Pulses We have developed a laser driven X-ray diode which generates nanosecond and picosecond hard X-ray pulses.18,19 This system has allowed us to carry out a number of timeresolved X-ray studies. A laser driven X-ray diode is similar to the conventional X-ray diode in which the thermal cathode is replaced with a photocathode. Thus, by illuminating the photocathode with short laser pulses, short electron pulses are generated at the cathode surface and then accelerated by high voltage applied to the diode. When the accelerated electron pulse impinges on the anode a X-ray pulse is generated (see Figure 2). The operation of the X-ray diode with a photocathode is similar to that of a conventional X-ray tube where the output X-ray spectrum is determined by the anode material and the electron energy. The duration of the X-ray pulse produced by a diode is determined by the duration of the electron pulse impinging on the anode. To maximize the output X-ray flux, high peak current electron pulses have to be generated and subsequently propagated through the X-ray diode. The space charge effects in the diode place a limit on the maximum output flux, as well as on the shortest X-ray pulse duration that may be emitted by the diode. Using this approach and ultrashort laser pulses X-ray pulses with nanosecond to femtosecond duration can be generated. Because of isotropic space distribution of the X-ray radiation generated on the anode surface and lack of focusing optics for hard X-rays, only a small portion of the X-ray output can be collimated and used in experiments. A high

Feature Article

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7085

repetition rate system is therefore extremely important to make up for this deficiency in X-ray flux. Our laser driven X-ray diode can operate in the kHz range and its repetition rate is determined, mainly, by the pulse rate of the pump laser. The most efficient photocathodes for optical radiation are the bialkali or semiconductor devices; however, they degrade at high photocurrent density and high repetition rates and also require high vacuum for prolonged life. We have found that pure metal photocathodes are preferable for use in laser driven X-ray diodes. Using powerful ultraviolet (UV) laser radiation and low vacuum compensate for their low efficiency and high work function. Our X-ray diode employs an aluminum photocathode and a copper anode; however, different X-ray wavelengths can be emitted by changing the anode material. The laser system, which has been used to drive the X-ray diode, generates 193 nm pulses at a repetition rate of 300 Hz. The UV pulse duration was varied from ps to ns depending on the studies to be performed. In both modes of operation the UV pulse energy delivered by the laser system was higher than needed for driving the diode. The excess UV energy was used to form the pump pulse. To achieve this, the output of the laser system was split into two parts one used to drive the X-ray diode and the other was used to pump the sample. This approach has another major advantage, which is the very high degree of synchronization between the laser pump and the X-ray probe pulses. The excellent synchronization makes it possible for us to accumulate the signal from many shots with high-resolution accuracy. Changes in the structure of materials, following pulsed laser irradiation, have been studied for the last two decades. The motivation for these studies has been to understand ultrafast system disorder such as melting and induced phase transitions. Depending on the time scale of the experiments, insight into different phenomena has been obtained. In the nanosecond and picosecond time scale, crystal structure dynamics of thermally induced melting, shock propagation, strain, heat diffusion, crystal regrowth, and annealing have been determined.10 We have used our pulsed X-ray system to study the lattice dynamics of metal and semiconductor crystals heated by nano and picosecond laser pulses. The standard pump/probe set up is shown in Figure 2. The laser pulse absorbed by a thin layer of the sample induces heat, which in turn alters the lattice structure. The transient structure generates changes in the scattered X-rays recorded by the CCD camera. The recorded signal is essentially a convolution of the material response with the probing X-ray pulse. The time resolution that can be obtained from these experiments depends not only on the duration of the pump and probe pulses but also on the material response, as well as the propagation time of these pulses in the bulk of the sample. It has been shown that the thickness of the sample places a limit on the X-ray time resolution.20 It is known that the diffraction of monochromatic X-ray radiation from a crystal is governed by Bragg’s law. When even small changes in the interatomic spacing of a crystal occur, the Bragg condition changes resulting in a shift in the diffracted angle. The relation between the angle shift ∆θ and the lattice spacing d is given by differentiation of Bragg’s equation

∆d/d ) - ∆θ/tan θ The angle shift, therefore, is a measure of the change in the spacing of the diffracting planes of the crystal. When the laser radiation is absorbed by a very thin surface layer the temperature distribution and the associated stress in the bulk of the crystal will be nonuniform causing a distortion in lattice spacing. Figure 3 shows a schematic diagram of an experiment where a

Figure 3. Schematic diagram of Bragg diffraction from (a) single crystal and (b) deformed single crystal.

divergent monochromatic X-ray beam is diffracted by a single crystal in which the plane spacing has a gradient. When a nonuniform lattice spacing distribution inside the crystal is induced, the diffracted signal will be composed of signals scattered over the range of angles corresponding to the lattice spacing. If the divergence of the incoming X-ray beam covers all of these angles, then the recorded signal will contain all of the information about the distribution of the lattice space changes which will be obtained at different positions and at different times. Experimentally, a whole rocking curve may be recorded with a single shot by illuminating the crystal with a divergent beam and using a CCD detector which can record the reflected X-ray radiation over the entire scattered angle. To calculate the angle dependent diffracted intensity two different theoretical approaches are employed: dynamical and kinematical theory.1,21-23 These two theories describe the X-ray diffraction from perfect and ideally imperfect crystals, respectively. The probed depth of the X-ray radiation in a perfect crystal is determined by its extinction length, which is defined as

Am ) 2

( )

V x|γoγh| e2 λ|Fh| mc2

-1

Here e2/mc2 is the classical electron radius; λ, X-ray wavelength; Fh, structure factor for reflection; and V, volume of unit cell. Directional cosines of the incident and diffracted wave are: γo ) sin (φ+θ) and γh ) sin (φ-θ), here θ is the Bragg angle and φ is the inclination of the reflecting plane to the surface. Usually the extinction length is shorter than the absorption length. In a mosaic or imperfect crystal the scattered radiation is effectively decoupled from the incident radiation and the X-rays are attenuated by the photoelectric absorption. In practice, most crystals are somewhere between these two extremes; however, for good quality, semiconductor crystals, such as Si and GaAs and others with relatively small flows, the crystal may be considered perfect and therefore the dynamical theory is still applicable. 3.1. Picosecond Time-Resolved Diffraction. In the picosecond mode of operation, the laser system used for these studies

7086 J. Phys. Chem. B, Vol. 103, No. 34, 1999 was generating UV pulses with 1.8 ps duration and up to 1 mJ energy. About 100 µJ of 193 nm radiation was used to pump and saturate the X-ray diode. When a voltage of 75 kV was applied to the anode, the output X-ray pulse was measured to be 8 ps.24 The photoemission from the metal cathode is in the subpicosecond time domain; therefore, we may assume that the electron pulse generated at the cathode surface has the duration of the excitation laser pulse. However, at high current densities, because of space charge effects the electron pulse is broadened before it reaches the anode. Operation of the diode at low current density allows for the generation of X-ray pulses with duration equal to the excitation laser pulse but at the cost of much smaller X-ray output flux. The X-ray spectrum emitted by the diode with a Cu anode consists mainly of Cu KR, λ ) 1.54 Å, characteristic radiation. This radiation was measured with a large area CCD camera designed specifically for direct X-ray imaging. Our 16 bit X-ray CCD camera consists of a 2048 × 2048 CCD chip (15 µm pixel) interfaced to a Macintosh computer. The active area of the CCD is 30 × 30 mm2; and when cooled below -100 °C, it is capable of single-photon detection. The X-ray pulses produced, by the system described above, were used to study the deformation of a gold (111) single-crystal lattice heated by 1.8 ps, 193 nm, laser pulses. The experimental system is shown in Figure 2. The 193 nm pulses generated by the laser were split into two parts: one part, after passing a variable delay line, was focused by a 35 cm lens on the Au crystal to a 3.5 mm diameter spot size having an average energy density of 1.6 mJ/cm2. The rest of the 193 nm pulse energy was used to drive the X-ray diode. Two vertical slits formed a X-ray beam with 3 mrad divergence, which is enough to cover the rocking curve of the crystal. With this set up about 105 Cu KR photons per cm2 per second were impinging upon the crystal. Taking into account the geometry of the experiment, we find that there is an experimental time resolution, imposed by the slit widths and their separation, anode takes off angle and crystal Bragg angle. In these experiments, the estimated geometrical resolution is about 10 ps, which is longer than the X-ray pulse duration. The gold crystal was L ) 150 nm thick, grown on a 100 µm thick mica crystal. Electron diffraction patterns showed a well ordered Au (111) crystal over several mm parallel to the surface. Thus we assume that there is a mosaic structure along the surface, but along the thickness it is practically a single crystal. The diffracted X-ray radiation from the heated and unheated area of the crystal was detected simultaneously in a twodimensional pattern by the CCD camera. In the measurements reported here two consecutive exposures were carried out. The first one with the selected part of the crystal under UV irradiation and the following without UV heating. Then a comparison of these two exposures was made. The heating of solid materials with picosecond laser pulses, when neither melting nor vaporization were induced, has been studied theoretically in detail.25 We have calculated the heat distribution in the gold crystal using the optical, thermal, and other properties of gold and mica, which are relevant for our experiment. From these data we find that for a 1.8 ps laser pulse, the diffusion length is Ld ) 22 nm. This length represents the crystal depth heated during the pulse illumination. From the above calculations we find that 0.1 mJ of absorbed energy in a spot size of S ) 0.1 cm2 will increase the temperature of the volume SLd of gold by about 190 °C. The heat from this volume spreads within picoseconds to the rest of the 150 nm thick crystal. According to the heat diffusion theory it takes about

Tomov et al.

Figure 4. Time-resolved X-ray diffraction Bragg profile curves for Au(111) crystal. The solid lines represent calculated results; dots depict experimental data.

90 ps for heat equilibrium to be established inside the SL crystal volume. The heat dissipation from this volume may take three directions: along the gold film, into the air, or through the mica substrate. The above estimates show that, for the first 100 ps after the laser pulse, the UV irradiated area of the crystal is in a nonequilibrium transient stage. Inside the crystal there is a thermal strain associated with a heated surface layer. Since the heated spot is much larger than the crystal thickness, a onedimensional strain distribution is reasonable to assume. The strain normal to the heated surface layer as a function of depth is calculated from

Φ(z,t) )

∫TT(z,t) R(T)η(h,k,l)dT 0

where T0 is the temperature of the unheated part of the crystal and R(T) is the linear thermal expansion coefficient. η(h,k,l) is a factor that takes into account the one-dimensional nature of the strain.26 A temperature gradient generated in the crystal lattice will alter the X-ray diffracted pattern. In our experiments the X-ray pulse is probing the entire thickness of the crystal. The absorption loss, for the diffracted X-rays, traveled the longest distance through the gold crystal is about 30%. Therefore, the recorded diffracted pattern is an integration, over the probed crystal volume, for the time of the X-ray pulse duration. We used the theory of X-ray scattering from a one-dimensionally strained crystal to calculate the diffracted X-ray intensity for a given temperature distribution. The results for the calculated curves, at several different time delays and a heating UV pulse with an energy of 120 µJ, are presented in Figure 4 (solid line). Negative delay times mean that the peak of the X-ray pulse arrives on the crystal earlier than the UV heating pulse. In the experiment described here, we have studied the diffracted X-ray signal as a function of the delay between the heating UV laser pulse and the probe X-ray pulse. For every delay point two consecutive 1 h exposures were made. The first one with UV radiation heating a selected part of the Au crystal and the second one without UV heating. Both X-ray patterns are compared to ensure that there is no change due to any effects other than those induced by the laser pulse. To compare the experimental results with the calculated ones, a fit to the

Feature Article

Figure 5. Shift of the rocking curve peak as a function of delay time.

experimental points is made using a Gaussian shape for the diffraction signal. The experimental data curves are normalized to their peak value and compared with the corresponding normalized theoretical curves. In this experiment, the time delay was varied in 10 ps steps in the range of -40 to +100 ps and larger steps at longer times outside this range. The experimental and calculated results for several delay times are depicted in Figure 4. The delay time of -20 ps corresponds to a cold crystal; at t ) 0, actually half of the UV pulse energy has been absorbed by the crystal and the change of the rocking curve is timeresolved and clearly observed. While the temperature distribution in the crystal is inhomogenious the scattered X-ray signal is a combination of the signals from the heated and cold parts of the crystal. After 100 ps, thermal equilibrium has been established and we observe a shift of the rocking curve toward larger Bragg angles. In Figure 5, the shift of the peak of the rocking curve as a function of delay time is shown. These data are the average of five runs at delay times between -100 and 500 ps. The transition through a thermally nonuniform crystal lattice, in the first 50 ps, is clearly seen. In this transition time, the width of the rocking curve is also slightly larger than the one at equilibrium. The spread of the experimental points is partially due to the shot to shot fluctuations in the UV pulse energy which results from the jitter in the triggering of the excimer amplifier. After about 100 ps and up to 500 ps, which was the longest delay used in this experiment, no change in the shift was observed. These measurements show conclusively that our experimental system is capable of 10 ps time resolution and can easily detect transient lattice structure deformations caused by temperature changes of about 20 °C. 3.2. Nanosecond Time-Resolved X-ray Diffraction. Pulsed laser processing of materials especially semiconductors is done, more often, using nanosecond rather than picosecond pulses. Therefore understanding crystal lattice dynamics in the nanosecond time scale has not only scientific but also technological importance. For these reasons we have performed nanosecond time-resolved X-ray diffraction experiments which were aimed at recording the evolution of lattice deformation in semiconductors and metals such as GaAs(111) and Pt(111) crystals, after nanosecond-pulsed UV laser irradiation. In these studies, the laser system generated 12 ns, 193 nm pulses at a repetition rate of 300 Hz and crystals of Pt and GaAs, cut with their surface parallel to the (111) plane were used.27 Both of these crystals absorb strongly 193 nm radiation, and because only 10 nm of

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7087 the surface is penetrated by the UV photons, the bulk of the crystal is heated by diffusion. The energy of the heating laser pulse on the crystal surface was about 3 mJ corresponding to an energy density of 30 mJ/cm2. (A) GaAs Crystal.28 Only very high quality GaAs(111) crystals were used in the experiment described here. Several crystals of varying sizes were cut from a 0.5 mm thick, 50 mm diameter GaAs wafer. The output from the X-ray diode consisted of 12 ns Cu KR X-ray pulses which passed through two slits and then were directed to the GaAs crystal at the Bragg angle. The divergence of the input X-ray beam was large enough to cover all the changes in the Bragg angle induced by the lattice changes occurring as a result of laser heating. The experimental procedure was similar to the one used in the picosecond X-ray experiment described above. The energy of the heating UV pulse, as much as 3 mJ, was deposited in a 0.1 cm2 spot. We note that in our studies the maximum energy density was less than 50 mJ/cm2. This is several times smaller than the melting threshold of GaAs (a 225 mJ/cm2 melting threshold was reported for nanosecond pulses at 193 nm29). The size of the UV spot on the crystal was much larger than the X-ray penetration depth in the crystal; therefore, as previously, one-dimensional distribution of the temperature and stress in the probed bulk of the crystal was assumed. To calculate the rocking curves for the laser heated crystal we use the dynamical equations for slightly deformed crystals.22,23 We divided the strained part of the crystal into an arbitrary number of parallel layers and an average strain (temperature) was assumed for each particular layer. This kind of calculation has been shown to be accurate for steady-state X-ray diffraction.23 Additional approximations are necessary for a crystal under transient conditions. In this case, the calculations are carried out by slicing the probing X-ray pulse into a set of micropulses with picosecond duration and then performing the corresponding calculations for every micropulse. During the passage of each micropulse, the temperature distribution and related strain in the crystal is assumed to be constant but evolves with each subsequent micropulse. Thus, for each micropulse the diffraction process may be treated as being in a steadystate condition. With this approximation, we have calculated first the temperature distribution T(z,t) in the crystal and then the thermal strain Φ(z,t) associated with a specific T(z,t). Then we calculated the X-ray diffracted signal for each micropulse and the overall diffracted X-ray signal was obtained by integrating over the entire X-ray pulse envelope. Figure 6 shows the calculated rocking curves for GaAs(111) symmetric Bragg reflection at different time delays. In practice the calculated rocking curve needs to be convoluted with the instrumental broadening function. For our experimental setup the instrumental broadening function was derived from the static X-ray rocking curve and then convoluted with the calculated Bragg profiles. Although the simulated rocking curves (Figure 6) showed some shape change and broadening around zero time delay, when convoluted with the instrumental broadening function the rocking curve became more symmetric. The integration of the rocking curve gives us the integrated intensity of the scattered X-ray radiation. In Figure 7 (solid line) we show the calculated integrated reflecting power as a function of the delay between the UV heating pulse and the probing X-ray pulse. As seen, the integrated reflected power increases around zero delay. Qualitatively we can expect such an effect, because weak heating of the crystal generates layers of the crystal with different temperatures and therefore slightly different lattice spacings. This distortion in the lattice leads to an increase in the

7088 J. Phys. Chem. B, Vol. 103, No. 34, 1999

Tomov et al.

Figure 8. Lattice spacing evolution within the GaAs(111) crystal heated by a 12 ns laser pulse. Figure 6. Dynamical diffraction theory calculations of the rocking curve at different delay times for a 12 ns X-ray pulse reflected from a heated GaAs(111) crystal.

Figure 7. Calculated integrated reflectivity of laser-pulse-heated GaAs(111) crystal as a function of time. The dots represent experimental data.

acceptance angle for Bragg reflection and therefore increases the integrated reflectivity. We note that, in this case, the crystal is still practically perfect and the dynamical theory is applicable. As the crystal is disturbed more aggressively, by more powerful laser pulses, the crystal structure may revert to a “mosaic” one and then an even higher increase of the integrated reflectivity is expected. We estimate, using the expressions for ideally perfect and ideally mosaic crystals,1 that the integrated reflectivity of a mosaic crystal is higher by a factor of 5 than that of an ideally perfect crystal. These measurements suggest that transient reflectivity may be used as a diagnostic tool for determining the changes in structure which the semiconductor crystal experiences during processing. For a GaAs(111) crystal the penetration depth determined by the absorption of the X-ray radiation in the crystal is 6 µm and the corresponding extinction length is Am(111) ) 1 µm. The angular width of the rocking curve for symmetric Bragg(111) reflection from a GaAs(111) single crystal using Cu KR radiation is ∆θ ) 38 µrad. An angular shift of the rocking curve of this size can be achieved if the crystal temperature is increased

by about 20 °C. Experimentally, we have detected small rocking curve shape changes occurring only at the 10 ns delay time which are due to the temperature gradient in the crystal. For the other delay times, only the shift in the rocking curve and the increase in the reflected intensity were clearly seen. The corresponding measured integrated reflectivity is shown in Figure 7 (points), where we see an increase in the integrated reflectivity in the time window of about 50 ns. Physically, this means that small deformations in the lattice structure lead to an increase in the acceptance angle and therefore a larger part of the incoming divergent beam will be effectively reflected. We note that the experimental points correspond to the average reflectivity over 12 ns and the probed depth within the crystal. These data shows directly a histogram of the evolution of the transient structure of the crystal and its eventual return to the original lattice spacing. The experimental data also indicates that this small light energy flux, supplied by the laser pulse to the crystal, causes only transient structural changes and strain and not a permanent change in the crystal structure. However, higher power laser pulses produce permanent changes in the structure. By fitting the calculated and experimental rocking curves, a profile of the evolution of lattice deformation in the crystal over a 100 ns time window was obtained. The X-ray scattering calculations were fitted to the measured data using the thermally induced lattice strain as a function of depth. Since the GaAs crystal was assumed to satisfy the dynamical theory, the penetration depth of the X-ray radiation is governed by the extinction length. Therefore, the fitting was limited to a depth of less than 1.5 µm. The temperature profile for larger depths was determined using heat flow calculations.25 Figure 8 shows the results of the best fitting procedure for the lattice evolution. We see that the maximum expansion of the lattice spacing takes place at the end of the heating pulse. For a heating energy density of about 20 mJ/cm2 the lattice expansion in a 1µm layer is of the order of 8 × 10-4 A. (B) Platinum Crystal.30 Time-resolved X-ray diffraction studies were carried out also on a Pt(111) crystal, 6.5 mm in diameter and 0.5 mm in thickness. The main difference between the GaAs and Pt crystals was that while the GaAs was a practically perfect crystal, the Pt crystal had mosaic structure. From the thermal properties of Pt we calculate that for a 12 ns heating pulse the diffusion length is 776 nm. This length represents the crystal depth heated during single pulse illumination, and it is comparable to the penetration depth (800 nm) of the X-ray radiation in the bulk of the Pt crystal. For a 2 mJ UV

Feature Article

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7089

Figure 10. Schematic diagram of the dispersive X-ray spectrometer for time-resolved studies. Figure 9. Evolution of strain in a Pt crystal as a function of time calculated using the kinematical model (solid curve). Points represent the X-ray rocking-curve experimental data.

pulse energy deposited in a 0.1 cm2 spot, the temperature of the Pt crystal, in this area and diffusion depth, will increase by 70 °C during laser pulse irradiation. Estimates suggest that for the first 100 ns after laser pulse excitation, the UV irradiated area of the crystal is in a nonequilibrium transient stage. In the bulk of the crystal there is a thermal strain associated with the heated surface layer. The time necessary to establish the strain profile is roughly equal to the heat diffusion length divided by the speed of sound in the crystal. For this case it is shorter than 1 ns; consequently, the time lag between the establishment of the temperature distribution and strain profiles in the crystal can be neglected. To calculate the amplitude of the diffracted X-rays we assume the kinematical approximation, which is appropriate for the mosaic Pt crystal structure. The time delay of the experiment was varied between -15 and +50 ns. At each time delay the strain distribution can be obtained by the best match of the calculated and measured X-ray rocking curves. The experimental and calculated results for the heat induced strain in the crystal, at several delay times is shown in Figure 9. The value measured is the average strain over 12 ns and the probed depth (800 nm) of the crystal. The lattice spacing were found to suffer a transient change from 2.2653 to 2.2695 Å, and the strain reached its maximum value 10 ns after laser irradiation. These studies show that time-resolved X-ray experiments detect the strain caused structural changes even in mosaic, imperfect crystals. Also the experimental transient structure agrees very well with the theoretical prediction for both perfect and imperfect crystals in both nanosecond and picosecond ranges. 4. Time-Resolved EXAFS For liquids, X-ray diffraction is not well suited because the diffracted signal originates from all atoms in the liquid solution; small Z number atoms do not scatter with high efficiency and the periodic order of the crystal is absent. There have been of course X-ray diffraction studies of pure liquids, but to our knowledge no time resolved data have been reported. Most chemical and biological reactions and systems of interest and importance take place in solutions. Even in concentrated solutions, the solvent concentration is 100 to 10000 times larger than the molecule of interest to be studied therefore its diffracted signal may be easily masked by the diffracted “noise” signal of the solvent. In addition the short range order of the solution

and the fact that many of the important molecules are composed of low Z number atoms, such as C, H, N, and O, make X-ray diffraction a rather difficult technique to be used for the determination of transient structures in pure liquids or solution. We have used our system, in the nanosecond mode of operation and presently in picosecond range, to record diffraction signals from a number of liquids and powder material. However, to overcome some of the diffraction disadvantages we are applying time-resolved EXAFS techniques for the determination of the evolution of transient structures in liquids. EXAFS, to our knowledge, has never been used before for ultrafast time-resolved studies. EXAFS spectroscopy measures the absorption spectra in the vicinity of the absorption edge of a selected atom in the liquid or solid state. By selecting the energy of the probing X-ray continuum to be in the region of the X-ray edge of a particular atom, the structure of the first few coordination layers around this atom can be measured. The structural information obtainable by EXAFS consists of bond distances and angles. EXAFS may also provide a measure of disorder in bond distances caused by any means including optical and thermal pulses. The majority of the reported results in EXAFS studies have been obtained by means of point by point measurement.2 This approach has limitations when applied to time-resolved studies of molecular systems where structural changes are fast, because each data point of the spectrum is collected at a different time. Also the time needed to collect a large number of points requires proportionally long exposures. To eliminate these disadvantages we have utilized a dispersive method for EXAFS measurements.31 Some of the most important advantages of this approach are 1. The entire EXAFS spectrum of interest is recorded simultaneously. Therefore, fluctuations in the incident X-ray beam intensity do not influence the quality of the EXAFS spectra. In addition the time of X-ray exposure is greatly reduced. 2. There are no moving parts in this spectrometer, and the X-ray path length is kept short; therefore, less powerful X-ray sources than synchrotrons can be successfully employed. 3. Use of a large size X-ray CCD makes possible the simultaneous recording of both the EXAFS spectrum of the sample and the incident X-ray radiation reference signal. Figure 10 shows a schematic representation of our timeresolved EXAFS experimental system. A 20 cm diameter Si(100) crystal oriented for the nonsymmetric (511) reflection is used for the dispersion of the X-ray radiation signals. Both

7090 J. Phys. Chem. B, Vol. 103, No. 34, 1999

Figure 11. EXAFS spectra of Cu K-edge of copper foil (10 µm) and Cu2+ ion in a solution of CuBr2 in water.

Tomov et al. measure directly time-resolved transient structural changes taking place in a molecule and its immediate neighborhood during and after illumination with ultrashort UV pulses such as dissociation or dipole formation in a molecule and the subsequent solvent structural reorientation. We use the same ultrashort UV pulses to both excite the molecule and pump the X-ray diode. Therefore, we achieve here also excellent synchronization between the laser pump and X-ray probe pulses, which is mandatory for accurate time resolution in the picosecond and subpicosecond range. To avoid thermal effects the solution is circulated. The above experiment is just one example and is presented for the purpose of showing that indeed we can perform pulsed EXAFS and therefore time-resolved experiments with nanosecond and picosecond resolution. This method, we believe opens a new, vast and as of now unexplored, area for the study of transient structure evolution in the liquid or solid state using any chemical and biological molecules of interest. 5. Conclusion

Figure 12. Br edge EXAFS spectrum of CBr4 in alcohol. (a) Before UV irradiation. (b) 10 ns after UV pulse irradiation. Insert is Fourier transform of the experimental data.

tungsten and molybdenum anodes have been used, in the X-ray diode, to generate the X-ray continuum. A X-ray CCD detector (1242 × 1152 pixels, 22.5 µm pixel) was situated 43 cm away from the crystal. With this experimental system a 1000 eV EXAFS spectrum in the 13.5 keV, Br edge, region is spread 44 mm along the Bragg angle direction. In our pulsed X-ray system the CCD records about 500 eV of the spectrum simultaneously. In the course of the experiment, one-half of the X-ray beam passes through the sample while the other half propagates through air only and is used as a reference. This arrangement makes possible the simultaneous recording of both the sample and reference X-ray spectrum. Using W Lγ lines for calibration, this dispersive system achieved better than 8 eV resolution at 13.5 keV and 5 eVfor the 9 keV Cu edge. Figure 11 shows the EXAFS spectra of Cu metal foil and Cu2+ ion in a solution of CuBr2 in water, recorded by our EXAFS spectrometer. The time resolution measurements are performed by the pump/probe method described above. Using our time-resolved EXAFS system, we have recorded, first, the spectrum of CBr4 dissolved in alcohol, then exposed this solution to pulsed UV radiation and again recorded the EXAFS spectrum 10 ns after excitation. These preliminary results (Figure 12) display the structural changes in the EXAFS spectrum before and after photodissosiation of the CBr4 molecule. We have shown that we can obtain EXAFS spectra, in liquids, with nanosecond resolution and record transient structures. We are in the process of measuring this, CBr4, and other molecular reactions in the liquid phase, with picosecond resolution, using our EXAFS system. These experiments will reveal directly their intermediate excited state structures and bond length changes as function of time. To our knowledge this is the first description ever of fast time resolved EXAFS experiment. One of our goals is to

The field of time-resolved X-ray spectroscopy has made significant progress in the past decade. The recent advances in source technology have stimulated a wide variety of novel experiments using both synchrotrons and smaller laboratory size systems. These facilities make it possible to measure directly the histogram of the transient structures and states occurring during the course of a chemical or biological reaction. Most important, these time-resolved X-ray facilities are making possible the direct detection and assignment of ultrafast transient structures during the course of a photophysical, chemical, or biological process which have never been seen with any other method. Time-resolved X-ray diffraction and absorption promise to provide real time “snapshots” of the structure evolution of ultrashort excited states and intermediates which were impossible to detect previously by other experimental methods. Acknowledgment. This work was supported in part by the National Science Foundation Grant CHE-9501388 and the W. M. Keck Foundation. References and Notes (1) Warren, B. E. X-ray Diffraction; Dover Publishers, Inc.: New York, 1990. (2) Koningsberger, D. C., Prins, R. Eds. X-ray Absorption; John Wiley & Sons: New York, 1988. (3) Elsayed-Ali, H. E.; Mourou, G. Appl. Phys. Lett. 1988, 52, 103. (4) Schafer, L.; Ewbank, J. D. Acta Chem. Scand. 1988, A42, 358. (5) Cao, J.; Ihee, I.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 338. (6) Ischencko, A. A.; Schafer, L.; Ewbank, J. D. J. Phys. Chem. A 1998, 102, 7329. (7) Schelev, M. Y.; Bryukhnevich, G. I.; Lozovoi, V. I.; Monastirski, M. A.; Proharov, A. M.; Smirnov, A. V.; Vorobiev, N. S. Opt. Eng. 1998, 37, 2249. (8) Geiser, J. D.; Weber, P. M. SPIE 1995, 2521, 136. (9) Liu, W. K.; Lin, S. H. Phys. ReV. A 1997, 55, 641. (10) Helliwell J. R., Rentzepis P. M., Eds. Time ResolVed Diffraction; Oxford University Press: Oxford, 1997. (11) Raksi, F.; Wilson, K. R.; Jiang, Z.; Ikhlef, A.; Cote, C. Y.; Kieffer, J. C. J. Chem. Phys. 1996, 104, 6066. (12) Moffat, K.; Chen Y.; Ng K.; McRee D.; Getzoff E. D. Philos. Trans. R. Soc. London 1992, A340, 175. (13) Larson, B. C.; Tischler, J. Z.; Mills, D. M. J. Mater. Res. 1986, 1, 144. (14) Wark, J. S.; Whitlock, R. R.; Hauer, A. A.; Swain, J. E.; Solone, P. J. Phys. ReV. B 1989, 40, 5705. (15) Laesson, J.; Heimann, P. A.; Lindenberg, A. M.; Schuck, P. J.; Bucksbaum, P. H.; Lee, R. W.; Padmore, H. A.; Wark, J. S.; Falcone, R. W. Appl. Phys. A 1998, 66, 587.

Feature Article (16) Rentzepis, P. M., Ed. Time ResolVed Electron and X-ray Diffraction; SPIE: Bellingham, WA, 1995; Vol. 2521. (17) Germer, R. J. Phys. E: Sci. Instrum. 1979, 12, 336. (18) Van Wonterghem, B.; Rentzepis, P. M. SPIE, 1990, 1204, 784. Van Wonterghem, B.; Rentzepis, P. M. Laser Int. 1989, 89, 16. (19) Tomov, I. V.; Anderson, T.; Rentzepis, P. M. J. X-ray Sci. Technol. 1993, 4, 44. (20) Tomov, I. V.; Chen P.; Rentzepis, P. M. J. Appl. Phys. 1998, 83, 5546. (21) Zachariasen, W. H. Theory of X-ray Diffraction in Crystals; Wiley: New York, 1945. (22) Taupin, D. Bull. Soc. Fr. Miner. Cryst. 1964, 87, 469. (23) Wie, C. R.; Tombrello, T. A.; Vreeeland, T., Jr. J. Appl. Phys. 1986, 59, 3743.

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7091 (24) Chen, P.; Tomov, I. V.; Rentzepis, P. M. J. Chem. Phys. 1996, 104, 10001. (25) Bechtel, J. H. J. Appl. Phys., 1975, 46, 1585. (26) Fukuhara, A.; Takano, Y. Acta Crystallogr. A 1977, 33, 137. (27) Tomov, I. V.; Chen P.; Rentzepis P. M. ReV. Sci. Instrum. 1995, 66, 5214. (28) Chen, P.; Tomov, I. V.; Rentzepis, P. M. J. Phys. Chem. A, 1999, 103, 2359. (29) Solis, J.; Afonso, C. N.; Piqueras, J. J. Appl. Phys. 1992, 71, 1032. (30) Chen, P.; Tomov, I. V.; Rentzepis, P. M. J. Appl. Chryst. 1999, 32, 82. (31) Medea, H.; Terauchi, H.; Tanabe, K.; Kamijo, N.; Hida, M.; Kawamura, H. Jpn. J. Appl. Phys. 1982, 21, 1342.