- Email: [email protected]
Wavelength-Modulated Diffraction System
Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
Wavelength-modulated diffraction system T. Koganezawaa, K. Handaa, N. Nakamuraa, Y. Yoshimuraa, H. Iwasakia,*, T. Yamadab, T. Shojib a
Faculty of Science and Engineering, Ritsumeikan University Kusatsu, Shiga 525-8577, Japan b Rigaku Corporation, Takatsuki, Osaka 569-1146, Japan
Abstract A new X-ray diffraction system has been constructed at the SR Center at Ritsumeikan University, in which the wavelength of the incident synchrotron radiation is continually and repeatedly changed over a definite range by rocking a couple of monochromator crystals while rotating a sample crystal and recording the diffraction pattern on a moving imaging plate detector. Bragg reflections appear as elongated spots and, if the wavelength range is chosen in the immediate vicinity of the absorption edge of an atom in the crystal, direct information on the phase of Bragg reflections can be derived from the intensity gradient of the elongated spots with respect to the wavelength. This method of phase determination is simple and free from the problem of intensity scaling encountered in the multi-wavelength diffraction method. When both a sample crystal and the detector are kept stationary while changing the wavelength, a pattern is obtained which is similar to Laue pattern, but there is a definite difference. The wavelength of the radiation that has given rise to the diffraction spot can be uniquely known and the diffraction intensity can be measured from the spectrum of the incident radiation. This method of diffraction has a wide range of applicability. # 2001 Elsevier Science B.V. All rights reserved. PACS: 07.85.Qe; 61.10.Eq Keywords: X-ray diffraction; Anomalous scattering; Phase determination
1. Introduction Iwasaki et al. [1] developed a new diffraction method, in which the wavelength of the incident radiation is continually changed over a definite range in the immediate vicinity of the absorption edge of an atom in the crystal. If a twodimensional detector such as an imaging plate is *Corresponding author. Tel.: +81-77-561-2719; fax: +8177-561-2663. E-mail address: [email protected] (H. Iwasaki).
used, Bragg reflections appear as elongated spots and their intensity profile contains information on the phase of the structure factor. The method, called wavelength-modulated diffraction (WMD) method, is free from the problem of intensity scaling encountered in other methods such as the multi-wavelength diffraction method. Preliminary measurements were made employing a conventional diffraction apparatus on a synchrotron radiation source at Ritsumeikan University and satisfactory results were obtained [2].
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 7 1 8 - 5
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T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
To conduct WMD measurements more effectively and extensively, a new diffraction system has been constructed. Its design and performance are described in the following.
2. Outline of the system The new system has been installed at the beam extraction port BL-1 at the SR center at Ritsumeikan University, where radiation from the compact superconducting storage ring (575 MeV in electron beam energy and 300 mA in initial beam current) is available. Though the electron beam energy is not high, the small radius (0.5 m) of the electron orbit shifts the radiation spectrum to shorter wavelength so that it contains X-ray components usable for diffraction measurements [3]. The radiation beam from the ring is first reflected by a toroidal mirror, made of platinumcoated silicon single crystal, and focused at the sample position, 9 m from the source point.
A monochromator is placed in between the mirror and the sample position. For the WMD measurements, it is essential to have an incident parallel radiation beam of wavelength l changing continually. The doublecrystal monochromator of the Golovchenko-type [4] can provide radiation beam whose position is kept fixed even if the wavelength is changed and is most suited. For systematic recording of as many Bragg reflections as possible in the WMD mode, a diffraction apparatus was designed adopting the Weissenberg camera mechanism with the imaging plate as a detector. It is bent cylindrically to the radius of 127.4 mm, large enough to see intensity profile of elongated spots. The maximum diffraction angle of reflections acceptable is 1408 on one side and 608 on the other side. Layer screen may or may not be inserted depending on the strategy for the intensity data collection. During sample crystal rotation, every reciprocal lattice point intersects the Ewald sphere of changing radius, but the intersection does not occur in the order of increasing or decreasing l. If the number of
Fig. 1. Photograph showing the wavelength-modulated diffraction system at the compact storage ring at Ritsumeikan University.
T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
repetitions of the wavelength change is large, the reciprocal lattice point intersects the sphere of all radii included in the wavelength range Dl and an effective wavelength scan of Bragg reflection is obtained. It is to be noted that the angular velocity of the sample crystal rotation is not synchronous with that of the monochromator crystal rocking; otherwise a systematic intersection occurs. The ‘‘non-systematic’’ nature of the intersection gives such a beneficial effect that intensity variation of the incident radiation is ‘‘averaged out’’ and Bragg reflection profile recorded is not affected by the intensity decay unavoidable for synchrotron radiation source. WMD pattern stored in the imaging plate is automatically read by an attached imaging plate reader and transferred to a hard disc of the personal computer. It can readily be seen on a display. With the present system it is possible to make WMD measurements with the radiation of the wavelength ranging from 0.32 to 0.14 nm. Fig. 1 shows a photograph of the whole diffraction system and the compact storage ring (on the left).
1055
Fig. 2. Wavelength-modulated diffraction pattern of a C36H32O7Fe crystal, space group P21/a (centrosymmetric). Dl was set to be from 0.1722 to 0.1797 nm, K-absorption edge of the Fe atoms being at 0.1743 nm.
lengths and the positions of the anomalous scatterers are known or properly assumed, A(hkl) and B(hkl) are obtained by solving two simultaneous linear equations, leading to the phase The situation jðhklÞ ¼ tan1 {B(hkl)/A(hkl)}. becomes particularly simple when the crystal has the center of symmetry and only one measurement of the intensity gradient yields the sign of A(hkl). 3. Application of wavelength-modulated diffraction Fig. 2 shows a WMD pattern of a C36H32O7Fe crystal, space group P21/a (centrosymmetric) [5], Anomalous diffraction phenomenon gives rise in which the Fe atoms acted as anomalous to an abrupt change in the atomic scattering factor scatterers (l of the K-absorption edge is for the wavelength in the vicinity of the absorption 0.1743 nm). Dl was set to straddle the edge, edge and, when viewed through WMD, the change 0.1722–0.1797 nm. The number of repetition of is reflected in an intensity profile of Bragg the wavelength change was 104 and time of reflections. As shown by Iwasaki, Yurugi and exposure was 4 h. It can be seen that there are a Yoshimura [1], the intensity gradient with respect number of Bragg reflection spots elongated in the to the wavelength, qIðhklÞ=ql, is related to the real radial direction. Fig. 3 shows the intensity profile part A(hkl) and imaginary part BðhklÞ of the of the 0 2 1 5 reflection1. On the long wavelength structure factor as follows: n X X o qIðhklÞ=ql ¼ 2 ðqfH0 =qlÞ cos WH ðqfH00 =qlÞ sin WH AðhklÞ H
H
X X o n sin WH þðqfH00 =qlÞ cos WH BðhklÞ þ 2 ðqfH0 =qlÞ H
fH0
H
fH00
where and are, respectively the real and imaginary part of the anomalous scattering factor of a heavy atom. WH ¼ 2pðhxH þ kyH þ lzH Þ and the sum is taken over the coordinates of those atoms. If qIðhklÞ=ql is measured at two wave-
1
Owing to the finite wavelength width of the incident radiation, the modulation range of l in Fig. 3 appears to be slightly different from that 0.1722–0.1797 nm.
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T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
Fig. 3. Intensity profile of the 0 2 1 5 reflection plotted against the wavelength. Intensity gradient on the long wavelength side of the absorption edge is positive. Note that, owing to the finite wavelength width of the incident radiation, the modulation range of l appears to be slightly different from that described in the text.
side of the edge, the gradient P is positive, while qfH0 =ql is positive on this side. H cos WH calculated from the positions of the peaks in the Patterson map is positive. Then, the sign of the structure factor of that reflection is positive. In this way the sign (phase) has been determined for 102 reflections, of which 99 reflections are given signs consistent with the structure model of the compound [5]. The WMD method can also be applied to structural study of a crystal sample which is fixed in a solid block or kept under non-ambient conditions. Although the sample crystal is not rotated, the wavelength of radiation is changed continually and the Bragg condition is satisfied for many reflections. The diffraction pattern thus obtained looks like a Laue pattern, but there is a definite difference between them. The wavelength range is exactly known for the WMD pattern and it is possible to assign without ambiguity the
wavelength of the radiation which has given rise to each diffraction spot. The present work was supported by the fund from New Energy and Industrial Technology Development Organization.
References [1] H. Iwasaki, T. Yurugi, Y. Yoshimura, Acta Crystallogr. A55 (1999) 864. [2] K. Handa, T. Koganezawa, M. Kato, Y. Yoshimura, N. Nakamura, H. Iwasaki, T. Yamada, Abstract Meeting Japan Physics Society (2000) 838. [3] H. Iwasaki, N. Kurosawa, S. Masui, S. Fujita, T. Yurugi, Y. Yoshimura, N. Nakamura, J. Synchrotron Radiat. 5 (1998) 333. [4] J.A. Golovchenko, R.A. Levesque, P.L. Cowan, Rev. Sci. Instrum. 52 (1981) 509. [5] N. Nakamura, S. Setodoi, Mol. Cryst. Liq. Cryst. 319 (1998) 173.
Wavelength-modulated diffraction system T. Koganezawaa, K. Handaa, N. Nakamuraa, Y. Yoshimuraa, H. Iwasakia,*, T. Yamadab, T. Shojib a
Faculty of Science and Engineering, Ritsumeikan University Kusatsu, Shiga 525-8577, Japan b Rigaku Corporation, Takatsuki, Osaka 569-1146, Japan
Abstract A new X-ray diffraction system has been constructed at the SR Center at Ritsumeikan University, in which the wavelength of the incident synchrotron radiation is continually and repeatedly changed over a definite range by rocking a couple of monochromator crystals while rotating a sample crystal and recording the diffraction pattern on a moving imaging plate detector. Bragg reflections appear as elongated spots and, if the wavelength range is chosen in the immediate vicinity of the absorption edge of an atom in the crystal, direct information on the phase of Bragg reflections can be derived from the intensity gradient of the elongated spots with respect to the wavelength. This method of phase determination is simple and free from the problem of intensity scaling encountered in the multi-wavelength diffraction method. When both a sample crystal and the detector are kept stationary while changing the wavelength, a pattern is obtained which is similar to Laue pattern, but there is a definite difference. The wavelength of the radiation that has given rise to the diffraction spot can be uniquely known and the diffraction intensity can be measured from the spectrum of the incident radiation. This method of diffraction has a wide range of applicability. # 2001 Elsevier Science B.V. All rights reserved. PACS: 07.85.Qe; 61.10.Eq Keywords: X-ray diffraction; Anomalous scattering; Phase determination
1. Introduction Iwasaki et al. [1] developed a new diffraction method, in which the wavelength of the incident radiation is continually changed over a definite range in the immediate vicinity of the absorption edge of an atom in the crystal. If a twodimensional detector such as an imaging plate is *Corresponding author. Tel.: +81-77-561-2719; fax: +8177-561-2663. E-mail address: [email protected] (H. Iwasaki).
used, Bragg reflections appear as elongated spots and their intensity profile contains information on the phase of the structure factor. The method, called wavelength-modulated diffraction (WMD) method, is free from the problem of intensity scaling encountered in other methods such as the multi-wavelength diffraction method. Preliminary measurements were made employing a conventional diffraction apparatus on a synchrotron radiation source at Ritsumeikan University and satisfactory results were obtained [2].
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 7 1 8 - 5
1054
T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
To conduct WMD measurements more effectively and extensively, a new diffraction system has been constructed. Its design and performance are described in the following.
2. Outline of the system The new system has been installed at the beam extraction port BL-1 at the SR center at Ritsumeikan University, where radiation from the compact superconducting storage ring (575 MeV in electron beam energy and 300 mA in initial beam current) is available. Though the electron beam energy is not high, the small radius (0.5 m) of the electron orbit shifts the radiation spectrum to shorter wavelength so that it contains X-ray components usable for diffraction measurements [3]. The radiation beam from the ring is first reflected by a toroidal mirror, made of platinumcoated silicon single crystal, and focused at the sample position, 9 m from the source point.
A monochromator is placed in between the mirror and the sample position. For the WMD measurements, it is essential to have an incident parallel radiation beam of wavelength l changing continually. The doublecrystal monochromator of the Golovchenko-type [4] can provide radiation beam whose position is kept fixed even if the wavelength is changed and is most suited. For systematic recording of as many Bragg reflections as possible in the WMD mode, a diffraction apparatus was designed adopting the Weissenberg camera mechanism with the imaging plate as a detector. It is bent cylindrically to the radius of 127.4 mm, large enough to see intensity profile of elongated spots. The maximum diffraction angle of reflections acceptable is 1408 on one side and 608 on the other side. Layer screen may or may not be inserted depending on the strategy for the intensity data collection. During sample crystal rotation, every reciprocal lattice point intersects the Ewald sphere of changing radius, but the intersection does not occur in the order of increasing or decreasing l. If the number of
Fig. 1. Photograph showing the wavelength-modulated diffraction system at the compact storage ring at Ritsumeikan University.
T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
repetitions of the wavelength change is large, the reciprocal lattice point intersects the sphere of all radii included in the wavelength range Dl and an effective wavelength scan of Bragg reflection is obtained. It is to be noted that the angular velocity of the sample crystal rotation is not synchronous with that of the monochromator crystal rocking; otherwise a systematic intersection occurs. The ‘‘non-systematic’’ nature of the intersection gives such a beneficial effect that intensity variation of the incident radiation is ‘‘averaged out’’ and Bragg reflection profile recorded is not affected by the intensity decay unavoidable for synchrotron radiation source. WMD pattern stored in the imaging plate is automatically read by an attached imaging plate reader and transferred to a hard disc of the personal computer. It can readily be seen on a display. With the present system it is possible to make WMD measurements with the radiation of the wavelength ranging from 0.32 to 0.14 nm. Fig. 1 shows a photograph of the whole diffraction system and the compact storage ring (on the left).
1055
Fig. 2. Wavelength-modulated diffraction pattern of a C36H32O7Fe crystal, space group P21/a (centrosymmetric). Dl was set to be from 0.1722 to 0.1797 nm, K-absorption edge of the Fe atoms being at 0.1743 nm.
lengths and the positions of the anomalous scatterers are known or properly assumed, A(hkl) and B(hkl) are obtained by solving two simultaneous linear equations, leading to the phase The situation jðhklÞ ¼ tan1 {B(hkl)/A(hkl)}. becomes particularly simple when the crystal has the center of symmetry and only one measurement of the intensity gradient yields the sign of A(hkl). 3. Application of wavelength-modulated diffraction Fig. 2 shows a WMD pattern of a C36H32O7Fe crystal, space group P21/a (centrosymmetric) [5], Anomalous diffraction phenomenon gives rise in which the Fe atoms acted as anomalous to an abrupt change in the atomic scattering factor scatterers (l of the K-absorption edge is for the wavelength in the vicinity of the absorption 0.1743 nm). Dl was set to straddle the edge, edge and, when viewed through WMD, the change 0.1722–0.1797 nm. The number of repetition of is reflected in an intensity profile of Bragg the wavelength change was 104 and time of reflections. As shown by Iwasaki, Yurugi and exposure was 4 h. It can be seen that there are a Yoshimura [1], the intensity gradient with respect number of Bragg reflection spots elongated in the to the wavelength, qIðhklÞ=ql, is related to the real radial direction. Fig. 3 shows the intensity profile part A(hkl) and imaginary part BðhklÞ of the of the 0 2 1 5 reflection1. On the long wavelength structure factor as follows: n X X o qIðhklÞ=ql ¼ 2 ðqfH0 =qlÞ cos WH ðqfH00 =qlÞ sin WH AðhklÞ H
H
X X o n sin WH þðqfH00 =qlÞ cos WH BðhklÞ þ 2 ðqfH0 =qlÞ H
fH0
H
fH00
where and are, respectively the real and imaginary part of the anomalous scattering factor of a heavy atom. WH ¼ 2pðhxH þ kyH þ lzH Þ and the sum is taken over the coordinates of those atoms. If qIðhklÞ=ql is measured at two wave-
1
Owing to the finite wavelength width of the incident radiation, the modulation range of l in Fig. 3 appears to be slightly different from that 0.1722–0.1797 nm.
1056
T. Koganezawa et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1053–1056
Fig. 3. Intensity profile of the 0 2 1 5 reflection plotted against the wavelength. Intensity gradient on the long wavelength side of the absorption edge is positive. Note that, owing to the finite wavelength width of the incident radiation, the modulation range of l appears to be slightly different from that described in the text.
side of the edge, the gradient P is positive, while qfH0 =ql is positive on this side. H cos WH calculated from the positions of the peaks in the Patterson map is positive. Then, the sign of the structure factor of that reflection is positive. In this way the sign (phase) has been determined for 102 reflections, of which 99 reflections are given signs consistent with the structure model of the compound [5]. The WMD method can also be applied to structural study of a crystal sample which is fixed in a solid block or kept under non-ambient conditions. Although the sample crystal is not rotated, the wavelength of radiation is changed continually and the Bragg condition is satisfied for many reflections. The diffraction pattern thus obtained looks like a Laue pattern, but there is a definite difference between them. The wavelength range is exactly known for the WMD pattern and it is possible to assign without ambiguity the
wavelength of the radiation which has given rise to each diffraction spot. The present work was supported by the fund from New Energy and Industrial Technology Development Organization.
References [1] H. Iwasaki, T. Yurugi, Y. Yoshimura, Acta Crystallogr. A55 (1999) 864. [2] K. Handa, T. Koganezawa, M. Kato, Y. Yoshimura, N. Nakamura, H. Iwasaki, T. Yamada, Abstract Meeting Japan Physics Society (2000) 838. [3] H. Iwasaki, N. Kurosawa, S. Masui, S. Fujita, T. Yurugi, Y. Yoshimura, N. Nakamura, J. Synchrotron Radiat. 5 (1998) 333. [4] J.A. Golovchenko, R.A. Levesque, P.L. Cowan, Rev. Sci. Instrum. 52 (1981) 509. [5] N. Nakamura, S. Setodoi, Mol. Cryst. Liq. Cryst. 319 (1998) 173.