• In a typical crystallography experiment, a large number of diffraction peaks or Bragg reflections are recorded on an area detector while rotating or oscillating a crystal specimen. The intensity recorded for each Bragg reflection depends only on the magnitude of its structure factor, but not on its phase, which is also needed to determine the atomic positions in a crystal. This is the fundamental phase problem in diffraction and its general solution remains to be an active area of research. 
• Recently we have developed a phase-sensitive reference-beam diffraction (RBD) technique that has the potential to provide a practical solution to the phase problem in crystallography. The RBD technique is based on the principle of multiple-beam or three-beam diffraction, which has been known to contain structural phase information. In the past the intensity profiles of the three-beam diffraction are measured one-at-a-time in an experiment, which is very inefficient and time-consuming, and seriously limits the practical implications of the 3-beam technique. 
• The new RBD method, on the other hand, incorporates the principle of multiple-beam diffraction into the most common crystallographic data collection technique - the oscillating crystal method, and allows a parallel collection of many three-beam interference profiles. It therefore provides a way to measure both the magnitudes and the phases of a large number of Bragg reflections, in a time period that is similar to existing crystallographic techniques such as multiple-wavelength anomalous diffraction. 
• In collaboration with Nobel Laureate Herbert Hauptman at Hauptman-Woodward Institute in Buffalo, we are applying the RBD technique to solving protein crystal structures in conjunction with the direct methods or with other techniques.  A recent 5-yr NIH award allows us to strengthen our efforts in this exciting area of research.
• Publications:

1. Qun Shen, "Solving the phase problem using reference-beam x-ray diffraction", Phys. Rev. Lett. 80, 3268 (1998).
2. Qun Shen, "Direct measurements of Bragg-reflection phases in x-ray crystallography", Phys. Rev. B 59, 11109-12 (1999).
3. Qun Shen, Stefan Kycia, and Ivan Dobrianov, "Enantiomorph determination using inverse reference-beam diffraction images", Acta Cryst. A 56, 264-267 (2000).
4. Charles M. Weeks, Hongliang Xu, Herbert A. Hauptman, and Qun Shen, "Shake-and-Bake applications using simulated reference-beam data for crambin", Acta Crystallogr. A 56, 280-283 (2000).
5. Qun Shen, Stefan Kycia, and Ivan Dobrianov, "Triplet-phase measurements using reference-beam x-ray diffraction", Acta Cryst. A 56, 268-279 (2000).
6. Qun Shen, S. Kycia, I. Dobrianov, and D. Pringle, “Phase-sensitive data collection in x-ray crystallography using reference-beam diffraction”, SPIE Proceedings 4145, 150-156 (2001).
7. Qun Shen, Daniel Pringle, Marian Szebenyi, and Jun Wang, “Solving the Crystallographic Phase Problem with Reference-Beam Diffraction”, Rev. Sci. Instrum. 73, 1646 (2002).
8. Daniel Pringle and Qun Shen, “New five-circle kappa diffractometer for reference-beam diffraction experiments”, J. Appl. Cryst. 36, 29 (2003).
9. Q. Shen & J. Wang, “Recursive direct phasing of protein structure with reference-beam diffraction”, Acta Cryst. D 59, in press (2003).
10. Q. Shen, “Improved triplet phase accuracy by inverse reference beam measurements on a protein crystal”, submitted to Acta Cryst. A (2003).

• Diffraction of x-rays is a widely-used technique for studying structural information in condensed matter. One of the main advantages of this structural technique is that the diffracted intensities measured in experiments can be easily interpreted by a simple kinematic theory. The kinematic theory, however, is intrinsically limited by the phase problem of diffraction, i.e. it is generally insensitive to the phases of scattering amplitudes even though both the phases and the magnitudes are needed for solving a complex structure. The only existing diffraction theory to date that can be phase-sensitive is the so-called dynamical theory, which includes all possible interactions among multiply-excited Bragg reflection waves inside a crystal. Unfortunately, this theory is rather complicated in its mathematical formulation, especially in the case of multiple Bragg waves, and it is generally viewed as a specialist's theory and is rarely used in everyday crystallography analyses. 
• The practical need for a simple, phase-sensitive, first-principle x-ray diffraction theory is greatly exemplified by the recent experimental innovation of reference-beam diffraction which in principle allows a phase-sensitive intensity data collection of a large number of Bragg reflections using a routine crystallography setup. This experimental development has also inspired a new approach to the theory of x-ray diffraction.
• The new theoretical approach, called an expanded distorted-wave approximation (EDWA), follows closely to the algorithm of the conventional DWA for x-ray scattering from surfaces, with an important revision that a sinusoidal Fourier component G is added to the distorting component of the electric dielectric function. This sinusoidal compo-nent represents a perturbing reference G charge density component for the reference beam, and the resulting distorted wave is in fact composed of two waves, O- and G-waves. Instead of the Fresnel theory, a two-beam dynamical theory is employed to evaluate these distorted waves, while the subsequent scattering of these waves is again handled by the Born approximation. The final result is a simple analytical expression of a phase-sensitive diffracted intensity that is valid for all measured Bragg reflections and for the entire excitation range of the reference reflection G in a reference-beam diffraction experiment.
• Publications: 

1. Qun Shen, "A new approach to multi-beam x-ray diffraction using perturbation theory of scattering", Acta Crystallogr. Sect. A 42, 525-533 (1986).
2. Qun Shen, "Expanded distorted-wave theory for phase-sensitive x-ray diffraction in single crystals", Phys. Rev. Lett. 83, 4784-4787 (1999).
3. Qun Shen, "Dynamical diffraction", in Methods in Materials Research, edited by E. Kaufmann, J. Sanchez, et al. (John Wiley & Sons, New York, 2000).
4. Qun Shen, "A distorted-wave approach for reference-beam x-ray diffraction in transmission cases", Phys. Rev. B 61, 8593-8597 (2000).
5. Qun Shen and Xianrong Huang, “Phase-sensitive x-ray diffraction in the expanded distorted-wave approximation”, Phys. Rev. B 63, 174102 (2001).

 

• Interface and surface induced strain fields in thin-film semiconductor and magnetic materials play an important role in determining the physical properties of mesoscopic-scale crystalline materials of several to a hundred nanometers in size. Although its effect on electronic band structures for bulk and two-dimensional thin-film materials has been known for quite a long time, systematic studies of the strain effects in lateral low-dimensional microstructures, such as quantum wires (QWRs) and quantum dots (QDs), have become available only recently. Recent experimental and theoretical developments on self-organized surface corrugations have further enhanced the scientific interests in studying strain and strain distributions near an interface of dissimilar materials during heteroepitaxial growths. 
• In all these cases it is important to experimentally determine the strain fields in the corrugated surface structures or quantum-confinement structures and to correlate the measured strain with other physical properties such as optical luminescence and the modes of epitaxial growth. In recent years high-resolution x-ray diffraction has been used as a convenient, non-destructive technique to characterize the geometric shape and the lattice strain in periodic nanostructures. Average lattice relaxations have been studied for free-standing multiple-layer quantum wires, and lateral-size-dependent lattice distortions have been observed on a single-layer of 10 nm thick quantum wires of In0.2Ga0.8As buried in a GaAs substrate. 
• We are also interested in studying lattice constant variations in the interfacial region of quantum wire and quantum dot structures. These variations have been difficult to observe in the past, primarily due to the diffuse weak signal from any strain-varying region of a few nanometers in size, until recently. By using an intense synchrotron x-ray beam and by taking advantage of the coherent-grating nature of a quantum wire or dot array, both the longitudinal and the transverse strain gradients can be determined along with the average strain. Our results indicate that a lattice parameter gradient as small as 10-5 Å/Å can be readily detected using the present x-ray analysis. For non-periodic microstructures, such as self-assembled quantum dots by epitaxial growth, diffuse scattering intensities along crystal truncation rods normal to side wall facets can be used to obtain similar information on strain variations in the QDs. 
• Selected Publications: 

1. Qun Shen, C.C. Umbach, B. Weselak, and J.M. Blakely, "X-ray diffraction from a coherently illuminated Si (001) grating surface", Phys. Rev. B 48, 17967 (1993).
2. Qun Shen, B. Weselak, and J.M. Blakely, "Structural study of Si (001) grating surface by white beam x-ray Laue photography", Appl. Phys. Lett. 64, 3554 (1994).
3. Qun Shen, C.C. Umbach, B. Weselak, and J.M. Blakely, "Lateral correlation in mesoscopic on silicon (001) surface determined by grating x-ray diffuse scattering", Phys. Rev. B 53, R4237 (1996).
4. Qun Shen, H. Luo, and J.K. Furdyna, "Spatial dependence of exchange interaction in Heisenberg antiferromagnet Zn1-xMnxTe", Phys. Rev. Lett. 75, 2590 (1995).
5. S. Tanaka, C.C. Umbach, Qun Shen, and J.M. Blakely, "Atomic diffusion and strain measurement on Si grating structures by x-ray diffraction", Mat. Res. Soc. Symp. Proc. 380, 61 (1995).
6. Qun Shen, "Study of periodic surface nanosctructures using coherent grating x-ray diffraction (CGXD)", Mat. Res. Soc. Symp. Proc. 405, 371 (1996).
7. So Tanaka, C.C. Umbach, Qun Shen, and J.M. Blakely, "Strain measurement in two-dimensional nanoscale Si gratings by high resolution x-ray diffraction", Mat. Res. Soc. Symp. Proc. 405, 109 (1996).
8. C.C. Umbach, B.W. Weselak, J.M. Blakely, and Qun Shen, "Characterization of large-area arrays of nanoscale Si tips fabricated using thermal oxidation and wet etching of Si pillars", J. Vac. Sci. Tech. 14, 3420 (1996).
9. Qun Shen, S.W. Kycia, W.J. Schaff, E.S. Tentarelli, and L.F. Eastman, "X-ray diffraction study of size-dependent strain in quantum wire structures", Phys. Rev. B 54, 16381 (1996).
10. Qun Shen and Stefan Kycia, "Determination of interfacial strain distribution in quantum wire structures by high-resolution x-ray scattering", Phys. Rev. B 55, 15791 (1997).
11. Qun Shen and S. Kycia, "Interfacial strain-field in thin-film microstructures", Mat. Res. Soc. Symp. Proc. 492, 389-394 (1998).
12. N. Darowski, U. Pietsch, Wang, K.-H.; Forchel, A., Q. Shen, and S. Kycia, "X-ray diffraction analysis of strain relaxation in free standing and buried GaAs/ GaInAs/ GaAs SQW lateral structures", Thin Solid Films 336, 271-6 (1998).
13. Qun Shen and Stefan Kycia, "Determination of coherent strain field in periodic and self-assembled microstructures on crystal surfaces", SPIE Proceedings 3448, 114 (1998).
14. S. Tanaka, C.C. Umbach, Q. Shen, and J.M. Blakely, "Lattice strain in oxidized Si nanostructure arrays from x-ray measurements", Thin Solid Films 343-344, 365-369 (1999).
15. O. Thomas, Q. Shen, P. Schieffer, N. Tournerie, B. Lepine, “Interplay between anisotropic strain relaxation and uniaxial interface magnetic orientation in epitaxial Fe films on (001) GaAs”, Phys. Rev. Lett. 90, 017205 (2003).  

• The ability to completely analyze the polarization of a hard x-ray beam is of practical importance in evaluating the performance of special insertion-device synchrotron sources and crystal phase plate optics. It is also of scientific interests in x-ray absorption and scattering experiments involving spin-dependent magnetic interactions and/or resonant atomic transitions in various materials. For the linear polarization, 90° elastic scattering or Bragg reflections have been widely used and a high precision can be achieved by means of multiply-bounced Bragg reflections. 
• Recently we have proposed and demonstrated a new method of measuring the degree of circular polarization. The new method makes use of phase-sensitive interference and possible polarization mixing in a multiple-beam Bragg diffraction (MBD) process in a single crystal. Because the phase shift between the s and the p wave fields is strictly determined by the crystal structure, independent of crystal thickness and x-ray wavelength, the MBD method has a very broad applicable energy range and a moderate tolerance in angular divergence of the x-ray beam. 
• We have shown that a general x-ray polarization can be determined completely by a measurement of three MBD interference profiles or by a combination of a Bragg-reflection linear polarization measurement and an MBD circular polarization measurement. This can be achieved by using only one single Bragg reflection from a perfect GaAs crystal. It provides a versatile x-ray polarimetry over essentially a continous range of energies from ~2 keV to about 15-20 keV. 
• Selected Publications: 

1. Qun Shen, "Polarization state mixing in multiple beam diffraction and its application to solving the phase problem", SPIE Proceedings. 1550, 27-33 (1991).
2. Qun Shen and K.D. Finkelstein, "Complete determination of x-ray polarization using multiple-beam Bragg diffraction", Phys. Rev. B 45, 5075-5078 (1992).
3. K.D. Finkelstein, Qun Shen, and S. Shastri, "Resonant X-ray diffraction near the iron K edge in hematite (a-Fe2O3)", Phys. Rev. Lett. 69, 1612-1615 (1992).
4. Qun Shen, "Effects of a general x-ray polarization in multiple-beam Bragg diffraction", Acta Crystallogr. Sect. A 49, 605 (1993).
5. K.D. Finkelstein, M. Hamrick, and Qun Shen, "Resonant X-ray diffraction in transition metal oxides", in Proceedings of the Int. Cryst. Anomalous Scattering Conference, Hamburg, Germany, edited by K. Fischer, G. Materlik, and C.J. Sparks (Elsevier Science Publishers B.V., New York, 1993).
6. Qun Shen and K.D. Finkelstein, "A complete characterization of x-ray polarization state by combination of single and multiple Bragg reflections", Rev. Sci. Instrum. 64, 3451 (1993).
7. K.D. Finkelstein, C. Staffa, and Qun Shen, "A multi-purpose polarimeter for x-ray studies", Nucl. Instrum. Meth. A 347, 124 (1994).
8. Qun Shen, S. Shastri, and K.D. Finkelstein, "Stokes polarimetry for x-rays using multiple-beam diffraction", Rev. Sci. Instrum. 66, 1610 (1995). 
9. S.D. Shastri, K.D. Finkelstein, Qun Shen, B.W. Batterman, and D.A. Walko, "Undulator test of a Bragg-reflection elliptical polarizer at 7.1 keV", Rev. Sci. Instrum. 66, 1581 (1995).
10. Qun Shen, "Polarization Optics for High-Brightness Synchrotron X-rays", SPIE Proceedings 2856, 82 (1996). 
11. K. Hirano, T. Mori, A. Iida, R. Colella, S. Sasaki, and Qun Shen, "Determination of the Stokes-Poincaré parameters for a synchrotron x-ray beam by multiple Bragg scattering", Jpn. J. Appl. Phys. 35, 5550 (1996).
12. Lonny E. Berman, Qun Shen, Ken D. Finkelstein, Park Doing, Zhijian Yin, and Guoqiang Pan, “Characterization of a diamond crystal x-ray phase retarder”, Rev. Sci. Instrum.73, 1502 (2002).

• Combining circularly polarized x-rays with multiple-beam diffraction (the Renninger effect) in a crystal can produce an interference intensity that involves both the phases of the structure factors and the phase difference between the s and the p components of the incident x-ray beam. This research has resulted in two main areas of applications: circular polarimetry (as described above), and noncentrosymmetry determination for acentric crystals.
• An experiment on a GaAs crystal has demonstrated that determination of the polarity or the chirality of a noncentrosymmetric crystal is possible by using both right and left-handed elliptically polarized synchrotron radiation. Similar experiments have been performed, in collaboration with Professor R. Colella's group at Purdue University, to explore the noncentrosymmetry in Al-Cu-Fe and AlPdMn quasicrystals. We are hoping to provide experimental evidence on the interesting question of whether it is possible for a quasi crystal not to have an inversion center in its structure, which is a fundamental question in quasicrystal physics. 
• Publications: 

1. Qun Shen and K.D. Finkelstein, "Solving the phase problem with multi-beam diffraction and elliptically polarized x-rays", Phys. Rev. Lett. 65, 3337-3340 (1990).
2. H. Lee, R. Colella, and Qun Shen, "Multiple Bragg diffraction in quasicrystals: The issue of centrosymmetry in Al-Pd-Mn", Phys. Rev. B 54, 214 (1996).
3. Y. Zhang, R. Colella, Q. Shen, and S.W. Kycia, "Dynamical three-beam diffraction in a quasicrystal",in Proc. 6th Int. Conf. on Quasicrystals, (1997). 
4. Y. Zhang, R. Colella, Q. Shen, and S.W. Kycia, "Dynamical three-beam diffraction in a quasicrystal", Acta Crystallogr. Section A 54, pt.4, p. 411-15 (1998).

Special 5-circle Kappa-diffractometer 
for phase sensitive x-ray diffraction

• At Cornell High Energy Synchrotron Source (CHESS) we have designed and implemented a novel compact five-circle k diffractometer to perform the necessary tasks for reference-beam diffraction experiments.  As shown in Figure at left, the key feature in the new instrument, as compared to a standard k diffractometer, is an oscillation axis y inserted between the k and the w axes to provide the needed extra degree of freedom for three-beam diffraction experiments.
• Several reference-beam diffraction experiments have been conducted at CHESS on protein crystals using the new k-diffractomter.  The geometry calculations described in the following paper have been implemented and tested.  Based on these test runs, an experimental procedure has been established for direct measurements of triplet phases on protein crystals using reference-beam diffraction. 
• Publications: 

1. Daniel Pringle and Qun Shen, “New five-circle kappa diffractometer for reference-beam diffraction experiments”, J. Appl. Cryst. 36, 29 (2003).