J. Phys. Chem. 199498, 2782-2796
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Ultrafast Electron Diffraction. 5. Experimental Time Resolution and Applicationst Marcos Dantus,* Scott B. Kim, J. Charles Williamson,! and Ahmed H. Zewail' Arthur Amos Noyes Laboratory of Chemical Physics,ll California Institute of Technology, Pasadena, California 91 125 Received: January 13, 1994'
This paper, the fifth in a series, is concerned with the experimental description of ultrafast electron diffraction and its application to several isolated chemical systems. We present a detailed description of the Caltech apparatus, which consists of a femtosecond laser system, a picosecond electron gun, and a two-dimensional chargecoupled device (CCD) detection system. W e also discuss the analysis of the scattering patterns. Ultrafast diffraction images from several molecules (CClh, 12, CF31, C ~ F ~ I are Z ) reported. For our first study of a chemical reaction in a molecular beam, we show the change in the radial distribution function following the formation of CF3 radical after dissociation of CF31. The total experimental temporal resolution is discussed in terms of the electron pulse width and velocity mismatch. The electron pulse was characterized temporally with a streaking technique that yielded the width as a function of the number of electrons per pulse. Experimental results show that the electron source produces picosecond (or less) pulses at densities of 100 electrons per pulse and 10-ps pulses at 1000 electrons per pulse. We also report our observation of a novel photoionization-induced lensing effect on the undiffracted electron beam, which we have used to establish time zero for UED when reactions are initiated by a laser pulse.
I. Introduction As mentioned in the preceding paper,' our experimental goal in developing ultrafast electron diffraction (UED) was to bring gas-phaseelectron diffraction to the picosecond and femtosecond time scale, such that structures of gas-phase molecules in reactions may be obtained in real time. In a previous Letter, it was experimentally demonstrated that there is sufficient sensitivity to record structures and to discriminate between the reactants and the products when picosecond electron pulses are employed.2 The intent of this article is to provide a more complete description of our apparatus and the technique, paying special attention to the time resolution and thedifferent applications. We also present a novel electron beam lensing technique used to obtain the zero of time for these experiments. After a brief review of gas-phase electron diffraction theory (section 11), we provide two simple, order-of-magnitude calculations that yield estimatesfor thelengthof exposure time required to obtain an electron diffraction pattern given an extremely low incident electron intensity (section 111). In section IV wedescribe the experimental components of our UED apparatus, detailing the laser system, the diffraction chamber, the molecular beam, the electron gun, and the CCD detector. The data analysis procedures for extractingmolecular structuresfrom the diffraction patterns are also presented. Static diffraction patterns of several molecules (CC14,12, CF31,C2F4I2) were recorded with picosecond electron pulses, and the corresponding molecular scattering and radial distribution curves are presented in section V. Structural studies of a laser-induced chemical change, the dissociation of CF31 into CF3 radical and an I atom, is also discussed. On the basis of these observations, the next experimental step is a time-resolved UED experiment, which requires a complete understanding of the total temporal resolution of the apparatus and a method for establishing time zero (the time when the laser pulse and electron pulse simultaneously intersect in the molecular f Thisworkwasalsopresentedat the 1993 PacificConferenceonChemistry and Spectroscopy, Pasadena, CA, U S A . , October 1993. t Present address: Department of Chemistry, Michigan State University, East Lansing, MI 48824-1322. 1 National Science Foundation Pre-Doctoral Fellow. I Contribution No. 8917. Abstract published in Advance ACS Abstracts, March 1, 1994.
0022-3654/94/2098-2182S04.50/0
beam). A detailedtemporal characterizationof theelectron pulse is provided in section VI, with consideration given to velocity mismatch effects. In section VII, we report our first observations of photoionization-induced lensing, a phenomenon that we used experimentally to measure time zero. This lensing serves as a cross-correlation techniquebetween the laser and electron pulses. Section VI11 contains our conclusions and the direction of our future research. 11.
GED Theory
Several authors have provided detailed descriptions of gasphase electron diffraction theory (see, e.g., refs 3,4, and 5). This section presents the basic formulas which we shall use in the analysis of conventional scattering patterns and internuclear separations. A theoreticaldiscussion of rotationaland vibrational coherence effects and UED is given in the preceding paper.' Electron scattering intensity is typically expressed as a function of s,the magnitudeof the momentum transfer between the incident electron and the elastically scattered electron: s = 21k,,1 sin(6/2)
(1) As eq 1 shows, s depends on the scattering angle 6 and the magnitude of the electron beam wave vector, This magnitude is related to the de Broglie wavelength of the electrons by lkOl= 21r/X, where X = hI(2mg
+ E2/c2)'/2
(2) In this equation, meis the electron mass, E is the electron kinetic energy, h is Planck's constant, and c is the speed of light. As an example, X = 0.0993 A for a 19-keV electron beam and 0.0601 A for 40 keV. Note that s has units of inverse angstroms. The total diffractedintensity is a sum of scatteringcontributions from individual atoms (atomic scattering, ZA) overlaid with interference terms fromall atom-atom pairs (molecular scattering, 1 ~ )The . molecular scattering contribution is of interest because it contains structural information-internuclear separations. If it is assumed that the potentials of each atom are independent, then the isotropic molecular scattering intensity may be written Q 1994 American Chemical Society
Ultrafast Electron Diffraction
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10
5
density of internuclear distances in the molecule. As shown in Figure 1, the modified molecular scattering intensity offered by eq 4 tends to distort the baseline of the radial distribution curve, while the formulation in eq 5 keeps the baseline flat when appropriate atoms a and b are chosen. The availableexperimentalscattering intensity (s-) is limited within some range of smin to s., Typically, the theoretical scattering intensity (sW)is appended from 0 to s- in order to eliminate distortions of the radial distribution baseline. Trun. cation of the integral at smaxintroduces artificial high frequency oscillations in Ar);these may be filtered with an exponential term dependent on sz and damping constant kd
15
s (A-I)
fir) = g"sM(s) exp(-kb2) sin&) ds,
0
2
1
3
Because of the integration process and the approximations listed above, all structural analysis and fitting procedures are best conducted on the experimental molecular scattering function and notf ( r ) . The radial distribution function, however, often contains hints to accelerate the fitting process. Further details of the data analysis (background correction techniques, etc.) are discussed in section VI.
4
Intemuclear Separation (A)
Figure 1. Theoretical scattering curves for.carbon tetrachloride. (a) Molecular intensity I&). The oscillation amplitude decreases rapidly like s4. (b) Modified molecular scattering intensity sM(s). (c) Radial with kd distribution function f i r ) calculated from sM(s) = SIM/~CI~CII 0.01 &and s- = 15 A-l. (d)fir) calculated fromsM(s) = s I t + i / I ~ . Structural parameters are taken from ref 18.
-
as a double sum over all N atoms in the molecule
wherefi is the direct elastic scattering amplitude for atom i, vi is the corresponding phase term, rtj is the internuclear separation between atom i and atomj, 1, is the mean amplitude of vibration, and Cis a proportionality constant. The scattering factorsfand q depend on E, s, and the atomic number Z, and tables off and 7 are available in the literature.6 The total scattering intensity decays by a factor of lo4between s = 0 A-1 and s = 35 a graph of the modified molecular scattering intensity, sM(s), is often plotted instead of I d s ) in order to bring out the oscillatory characteristics at higher values of s (compare parts a and b of Figure 1). The modified molecular scattering intensity is written either as: (4)
or
sM(s) = s-'M")
KIVbl
(ref 5 )
(5)
where a and 6 correspond to two atoms in the molecule (often atoms with high Z). Throughout the text weuse the formulation presented in eq 5 because of its impact on Ar), the radial distribution function:
Ar) = r s M ( s ) sin(sr) ds
(6)
Although all structural information is contained in the molecular scattering function, the radial distribution curve is better suited for qualitative interpretations sinceflr) approximates the relative
111. Electron Intensity Considerations
The laser pulses employed in femtosecond transition-state spectroscopy (FTS) are typically 50 fs in duration and 100 pJ in energy. Such 620-nm pulses have a peak power of 2 X 109 W and contain 3 X 1014photons each. The temporal resolution is independent of the number of photons. In an ultrafast electron pulse, however, electron4ectron repulsion takes place. These space-chargeeffects broaden the pulse duration over time, leading to a trade-off between temporal resolution and the electron pulse density.' Picosecond electron pulses typically contain 1000 electrons or less; consequently, the total scattering intensity is very low compared with conventional GED experiments, and the purpose of this section is to estimate the range of scattering intensity (in A-l) which may be measured by ultrafast diffraction for a given exposure time. This calculation will be conducted in two ways: (1) by an order-of-magnitude comparison with the total intensity in continuous-beam GED and (2) by estimating the number of electrons which must be detected to generate a diffraction pattern. The beam current in a conventional gas-phase electron diffraction experiment is on the order of 1 PA, and the detector (a photographic plate) is exposed to scattering from this beam for less than a ~ e c o n d .Mounted ~ in front of the photographic plate is a rotating sector, which serves two purposes. Approximately 1% of the incident electrons are scattered; the rotating sector contains a Faraday cup to monitor the total beam current and prevent the undiffracted electrons from overexposing the detector. The sector itself is a spinning shield crafted to block most of the scattered electron intensity at low values of s, while letting all the scattered electrons strike the photographic plate at high values of s. This compensates for the s4 decay of the scattered electron intensity and allows a wide range of s to be recorded even though the detector may have a relatively small dynamic range. Scattering intensity is measured out to 30-40 A-1, which is sufficient to provide structural resolution on the order of f0.005 A. Our laser system has a repetition rate of 30 Hz. If each electron pulse contains 1000electrons, then the total beam current is 10 fA. This 8 order-of-magnitude difference relative to the beam current in a conventional experiment must be accounted for by the length of the exposure and the detector construction. Realistically, exposure times must have an upper limit on the order of an hour or two given that several diffraction patterns,
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with different time delays between the laser and electron pulse, are to be taken in one session. Increasing the exposure time to 1 h provides 4 more orders-of-magnitude in the signal intensity. Single-electrondetectioncompensatesfor roughly 2 moreordersof-magnitude,andtothisend wehaveemployedacharge-coupled device (CCD), operating in direct electron-bombardment mode, insteadofa photographic plate. Tberotatingsector throwsaway scattered electron intensity and therefore is not used. The undiffracted beam must still be blocked, however, and this is achieved by applying a 2-pm aluminum coating to a small region of the CCD. The 2-order-of-magnitude intensity deficit which remains after these modifications means that the range of scattered electron intensity detected by UED is curtailed. Fortunately, the Z scattered intensity falloff keeps this from being a devastating loss, and a range of 10-15 A-l may actually be detected. The estimated structural resolution of UED is then *0.05 A, which is sufficient to identify the pronounced structural changes that might he expected during the time evolution of a reaction. In the future, this rangecan beincreased by,e.g.,increa.sing therepetition rate of the laser system. An alternative approach for evaluating the sensitivity of UED is to calculate the total number of scattered electrons required to generate a diffraction pattern with a defined signal-to-noise ratio (SNR) at some value of s. The ratio of the molecular scattering signal to theatomicscattering signal for a homonuclear diatomic molecule is approximated by
where the amplitude of sin(sr) ranges from + I to -1. In the first estimation described above, s, is on the order of 10 A-1, so according to eq 8 the molecular scattering signal at this position is approximately 10%of the total signal for a molecule with r = 2.0 A. Therefore, a signal-to-noise ratio of 2 1 would he achieved if 400 scattered electrons were detected at smn..assuming that there is no additional noise present in the detector system. These electrons would actually fall in a small window of s since the
CCDpixeldimensionsareontheorderofO.O2A-'inourdetection geometry. Thetotalnumberofscatteredelectronsmaybeestimatedusing the 1(rfalloffbetweenOand35A-1;thescatteredelectronintensity is written as
d = 3.88
(9)
and the number of scattered electrons within a range of s on the two-dimensional detector is
If Nc = 400 c in the range sI = 9.99 A-1 to s2 = 10.01 A-1, then the total number of scattered electrons (from sI= 0 A-1 to s2 = -)is -8 X IO'. With lOOOelectronsperpuIse,a30-Hzrepetition rate, and a scattering probability of I%, the exposure time necessarytogivea signal-to-noiseratioof2:1at I0A-I is therefore estimated to be 45 min. Note that the SNR a1 2 A-l for this exposure is -161; a 2 1 ratio at 2 A-I is achieved with only a 40-s exposure. Experimentally, as discussed below, we observed the emergence of the first few rings of a diffraction pattern (out to -6 A-l) with reasonable SNR in exposures of
