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Application of structural phase transitions in x-ray spectroscopy
JOURNALOF X-RAYSCIENCEANDTECHNOLOGY4, 217-220 (1994)
Application of Structural Phase Transitions in X-Ray Spectroscopy U. GEPPERT 1 Max-Planck-Institut far extraterrestrische Physik, Aussenstelle Berlin, Rudower Chaussee 5, D-12489 Berlin, Germany
Received August 12, 1993; revised March 11, 1994 A method is proposed for measuring different energy ranges of x-ray radiation with the same spectrometer crystal employing structural phase transitions. When the crystal temperature is varied beyond the phase transition temperature, the crystal symmetry is altered predictably and reversibly. Thus, with no change in the angle of glancing incidence, the x-ray beam hits in different crystal phases different lattice planes which correspond to different energy ranges. The advantage is that neither large motions nor exchanging the spectrometer crystal is necessary during observations. © 1994AcademicPress,Inc. 1. THE PROBLEM High-energy electromagnetic radiation (x rays and extreme ultraviolet light) is c o m m o n l y analyzed by using periodic structures. Besides gratings, crystals play an important role in high-resolution x-ray spectroscopy (1). Their s y m m e t r y defines certain lattice planes. The distance between those planes, dhkz (h, k, I denote the Miller indices), determines the wavelength X o f the radiation that can be investigated. Both quantities are related by the Bragg equation nX = 2dhk/sin 0,
[1]
where n is an integer representing the order of reflection and 0 is the angle of glancing incidence of the radiation. This is the f u n d a m e n t a l equation for all high-resolution spectroscopic m e a s u r e m e n t devices using crystals. Often, it is very interesting to measure the same source at different energies. Especially in the case o f astrophysical m e a s u r e m e n t s , one needs spectroscopic observations of different lines emitted by an astrophysical object f r o m different elements or f r o m different ionization states of an element. Considerable effort has been m a d e to design spectrometers which are able to measure at different energies. Thus, spectrometer crystals are covered with multilayer structures to allow the use of both the periodic structure o f the layers and the different periodic structure o f the crystal itself for simultaneous m e a s u r e m e n t s at different energies. This is a rather complicated technology. A n o t h e r m e t h o d uses different kinds of crystals in the spectrometer. In the specific case of the objective crystal spectrometer to be flown on the S P E C T R U M - X - G A M M A satellite (2), different natural crystals are used E-mail address: [email protected]. 217
0895-3996/94$6.00 Copyright © 1994 by Academic Press, Inc. All rights of reproduction in any form reserved.
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together with a multilayer structure, allowing for high resolution spectroscopy in four energy bands from N0.1 to ~ 7 keV. The crystals are mechanically rotated relative to the incident beam, depending on the energy of interest. Thus, the crystal-covered panel has to be rotated by 180 ° for observations in the respective other energy range. A drawback of this scheme under space conditions is that all mechanical movements are difficult to manage and could give rise to distortions of the system. Large motions (very small scan motions remain necessary) of the spectrometer in a complex observational setup can obstruct the realization of other measurements. To overcome these problems the following method is proposed. 2. THE PROPOSAL
It is well known that many crystals undergo structural phase transition (PT) if their temperature crosses a transition temperature O. This temperature depends on the composition and symmetry of the crystal. The nature of such second-order transitions can be manifold (order-disorder transitions, displacive transitions, etc.), but every transition is connected with quantitative and, in most cases, with qualitative changes of the crystal structure; i.e., the lengths of the unit cell edges (a, b, e) change in a jump, and the crystal system changes, too. To give an example, varying the crystal temperature may result in the following: 1. The symmetry at T >~ 0 is cubic (index c), at T < O it is tetragonal (index t), then ac = bc = cc and at = bt =Pct, but at 5~ ac. 2. The symmetry at T > / 0 is tetragonal, at T < O it is orthorhombic (index o), then ao =P bo ~ Coand ao = at, bo 4= bt, and Co ~ ct. The aim of not touching the spectrometer crystal requires a constant angle 0. Thus, the effect of the PT on the reflection of the x-ray beam depends on which reflecting lattice plane has been selected in the high-symmetry phase. If it was, e.g., the (110) plane in the cubic phase before PT, then after the PT into the tetragonal phase the beam hits the (110) plane again. According to Eq. [1], the change in the distance between successive lattice planes is inversely proportional to that between the x-ray energies, which obey the Bragg condition. Since the jump of the length of the unit cell edges is in many PTs of the order of percent (or less), which is often of the order of the width of the x-ray lines, this effect is not suited for observing x-ray lines with greatly different wavelengths. However, if in this example the high-symmetry-phase reflecting plane is the (101) plane and at the PT the symmetry changes from tetragonal to orthorhombic, the beam will hit another lattice plane beyond the PT. Here the symmetry breaking is due to relatively small, but different, changes of the three lattice constants, which results in large variations of the x-ray wavelength that obeys the Bragg condition at constant angle 0. Thus, for example, if the incident beam hits in the high-temperature phase on lattice planes indicated by small Miller indices (i.e., large distances between the planes), the same beam hits, as a rule, lattice planes with much larger Miller indices in the lowtemperature phase. Hence, x rays of much higher energies obey the Bragg condition
STRUCTURAL PHASE TRANSITIONS AND X-RAY SPECTROSCOPY
219
and can be observed with the same spectrometer in the low-temperature phase without any motion of the crystal or of the whole spectrometer. Of course, crystallographic knowledge and experience are necessary to select specific crystals with crystal systems and lattice constants above and below the PT which are appropriate for the designed energy ranges. Especially, the Miller indices in the lowtemperature phase should be not too large, since the reflectivity decreases with decreasing occupation number density of the reflecting planes. The design of such a setup requires the possibility of heating and cooling the whole crystal with high temporal and spatial precision. To avoid significant thermal expansion effects as a consequence of temperature variations, the temperature of the crystal has to be maintained close to the transition temperature, say 2 K below or above. A small temperature difference between both states also shortens the switch-over time from one state to the other. 3. EXAMPLE Since there is a large variety of crystals which undergo a structural PT, many lattice planes exist which are suitable for reflection of x-ray radiation. Let us consider a hypothetical crystal to demonstrate the method. This crystal should undergo two PTs, at Ol from the cubic to the tetragonal phase and a t O 2 from the tetragonal to the orthorhombic phase. The following lattice constants are assumed: ac = bc = Cc = 3.9
A, at= bt=4 A, ct=4.1A, ao=4 A, bo= 5.6 A, Co= 5.7 A. The distance between successive lattice planes is given by
[2]
Choosing the (110) plane as the reflecting plane in the cubic phase, we find 2dl10 = 5.515 A. In the tetragonal phase, the x-ray radiation hits under the same angle 0 the same (110) plane, whose 2dllo = 5.657 A. Assuming the glancing angle 0 = 45 °, radiation with an energy of 3.18 keV obeys the Bragg condition in the cubic phase, whereas in the tetragonal phase the energy is 3.10 keV. Thus, using this plane and this PT, only very narrow and neighboring lines could be observed. The opposite case happens if the (110) plane in the tetragonal phase is selected and the PT to the orthorhombic phase is used. Then, the incident beam does not hit the (110) plane but rather the (750) plane of the orthorhombic crystal, with 2d750 = 1.018 A and, while 0 is still 45 °, the energy of the Bragg reflecting x rays becomes 17.24 keV. Of course, the reflectivity of this plane is smaller than the reflectivity of the (110) plane. The hypothetical crystal above is similar to BaTiO3 (3) with two PTs, occurring at 120°C (ferroelectric PT, cubic --~ tetragonal, easy to realize under terrestrial conditions only) and at 5°C (tetragonal --~ orthorhombic). 4. CONCLUSIONS The example demonstrates that, using structural PTs in properly selected crystals, with the help of temperature changes alone one can achieve both observation of neigh-
220
u. GEPPERT
boring and observation of distant in energy narrow spectral lines, while the crystal itself need not be moved. The complicated exchange of crystals within the spectrometer or the use of expensive multilayer structures can be avoided. After the PT the whole crystal surface of the spectrometer is available again for high resolution spectroscopy in another energy range. It should be emphasized that the above-considered hypothetical crystal is only an example which shows that the PT effect can be used in principle. The probability of finding appropriate crystals for every special purpose seems to be rather large because of the huge number of crystals which undergo structural PTs. However, at least two problems have to be solved before this principle can be used in x-ray spectroscopy. The first is finding real crystals to look at particular combinations of lines. Here, the main problem is getting a good compromise between the distances of the energy ranges and the reflectivity of the lattice planes, which decreases considerably with increasing Miller indices. The second is ensuring that the switching between both phases really happens reversibly and avoiding defects or other distortions which can destroy the well-defined crystal structure necessary for high resolution spectroscopy. At present, experimental investigations aimed at solving these problems are being performed. The results will be reported in a forthcoming paper. ACKNOWLEDGMENTS Discussions with F. E. Christensen(Danish Space Research Institute) are gratefullyacknowledged. I also thank my colleaguesH.-J. Wiebickeand I. Halm for discussions and for carefullyreading the manuscript. REFERENCES 1. D. VAUGHAN(Ed.), "X-ray Data Booklet," LawrenceBerkeleyLaboratory,University of California, Berkeley,CA, Apr. 1986. 2. F.E. CHRISTENSEN,B. P. BYRNAK,A. HORNSTRUP,Z. SHOU-HUA,ANDH. W. SCHNOPPER,"Objective Crystal Spectrometer(OXS) for the SPECTRUM-X-GAMMASatellite,"in Proceedingsof SPIE, Vol. 1344, p. 14, SPIE--The InternationalSocietyfor Optical Engineering,Bellingham,WA, 1990. 3. "Landolt-Brrnstein Numerical Data and Functional Relationships in Science and Technology,New Series,"Group IlI, Vol. 28B, Springer-Verlag,Berlin/Heidelberg/NewYork, 1990,and citationstherein.
Application of Structural Phase Transitions in X-Ray Spectroscopy U. GEPPERT 1 Max-Planck-Institut far extraterrestrische Physik, Aussenstelle Berlin, Rudower Chaussee 5, D-12489 Berlin, Germany
Received August 12, 1993; revised March 11, 1994 A method is proposed for measuring different energy ranges of x-ray radiation with the same spectrometer crystal employing structural phase transitions. When the crystal temperature is varied beyond the phase transition temperature, the crystal symmetry is altered predictably and reversibly. Thus, with no change in the angle of glancing incidence, the x-ray beam hits in different crystal phases different lattice planes which correspond to different energy ranges. The advantage is that neither large motions nor exchanging the spectrometer crystal is necessary during observations. © 1994AcademicPress,Inc. 1. THE PROBLEM High-energy electromagnetic radiation (x rays and extreme ultraviolet light) is c o m m o n l y analyzed by using periodic structures. Besides gratings, crystals play an important role in high-resolution x-ray spectroscopy (1). Their s y m m e t r y defines certain lattice planes. The distance between those planes, dhkz (h, k, I denote the Miller indices), determines the wavelength X o f the radiation that can be investigated. Both quantities are related by the Bragg equation nX = 2dhk/sin 0,
[1]
where n is an integer representing the order of reflection and 0 is the angle of glancing incidence of the radiation. This is the f u n d a m e n t a l equation for all high-resolution spectroscopic m e a s u r e m e n t devices using crystals. Often, it is very interesting to measure the same source at different energies. Especially in the case o f astrophysical m e a s u r e m e n t s , one needs spectroscopic observations of different lines emitted by an astrophysical object f r o m different elements or f r o m different ionization states of an element. Considerable effort has been m a d e to design spectrometers which are able to measure at different energies. Thus, spectrometer crystals are covered with multilayer structures to allow the use of both the periodic structure o f the layers and the different periodic structure o f the crystal itself for simultaneous m e a s u r e m e n t s at different energies. This is a rather complicated technology. A n o t h e r m e t h o d uses different kinds of crystals in the spectrometer. In the specific case of the objective crystal spectrometer to be flown on the S P E C T R U M - X - G A M M A satellite (2), different natural crystals are used E-mail address: [email protected]. 217
0895-3996/94$6.00 Copyright © 1994 by Academic Press, Inc. All rights of reproduction in any form reserved.
218
u. GEPPERT
together with a multilayer structure, allowing for high resolution spectroscopy in four energy bands from N0.1 to ~ 7 keV. The crystals are mechanically rotated relative to the incident beam, depending on the energy of interest. Thus, the crystal-covered panel has to be rotated by 180 ° for observations in the respective other energy range. A drawback of this scheme under space conditions is that all mechanical movements are difficult to manage and could give rise to distortions of the system. Large motions (very small scan motions remain necessary) of the spectrometer in a complex observational setup can obstruct the realization of other measurements. To overcome these problems the following method is proposed. 2. THE PROPOSAL
It is well known that many crystals undergo structural phase transition (PT) if their temperature crosses a transition temperature O. This temperature depends on the composition and symmetry of the crystal. The nature of such second-order transitions can be manifold (order-disorder transitions, displacive transitions, etc.), but every transition is connected with quantitative and, in most cases, with qualitative changes of the crystal structure; i.e., the lengths of the unit cell edges (a, b, e) change in a jump, and the crystal system changes, too. To give an example, varying the crystal temperature may result in the following: 1. The symmetry at T >~ 0 is cubic (index c), at T < O it is tetragonal (index t), then ac = bc = cc and at = bt =Pct, but at 5~ ac. 2. The symmetry at T > / 0 is tetragonal, at T < O it is orthorhombic (index o), then ao =P bo ~ Coand ao = at, bo 4= bt, and Co ~ ct. The aim of not touching the spectrometer crystal requires a constant angle 0. Thus, the effect of the PT on the reflection of the x-ray beam depends on which reflecting lattice plane has been selected in the high-symmetry phase. If it was, e.g., the (110) plane in the cubic phase before PT, then after the PT into the tetragonal phase the beam hits the (110) plane again. According to Eq. [1], the change in the distance between successive lattice planes is inversely proportional to that between the x-ray energies, which obey the Bragg condition. Since the jump of the length of the unit cell edges is in many PTs of the order of percent (or less), which is often of the order of the width of the x-ray lines, this effect is not suited for observing x-ray lines with greatly different wavelengths. However, if in this example the high-symmetry-phase reflecting plane is the (101) plane and at the PT the symmetry changes from tetragonal to orthorhombic, the beam will hit another lattice plane beyond the PT. Here the symmetry breaking is due to relatively small, but different, changes of the three lattice constants, which results in large variations of the x-ray wavelength that obeys the Bragg condition at constant angle 0. Thus, for example, if the incident beam hits in the high-temperature phase on lattice planes indicated by small Miller indices (i.e., large distances between the planes), the same beam hits, as a rule, lattice planes with much larger Miller indices in the lowtemperature phase. Hence, x rays of much higher energies obey the Bragg condition
STRUCTURAL PHASE TRANSITIONS AND X-RAY SPECTROSCOPY
219
and can be observed with the same spectrometer in the low-temperature phase without any motion of the crystal or of the whole spectrometer. Of course, crystallographic knowledge and experience are necessary to select specific crystals with crystal systems and lattice constants above and below the PT which are appropriate for the designed energy ranges. Especially, the Miller indices in the lowtemperature phase should be not too large, since the reflectivity decreases with decreasing occupation number density of the reflecting planes. The design of such a setup requires the possibility of heating and cooling the whole crystal with high temporal and spatial precision. To avoid significant thermal expansion effects as a consequence of temperature variations, the temperature of the crystal has to be maintained close to the transition temperature, say 2 K below or above. A small temperature difference between both states also shortens the switch-over time from one state to the other. 3. EXAMPLE Since there is a large variety of crystals which undergo a structural PT, many lattice planes exist which are suitable for reflection of x-ray radiation. Let us consider a hypothetical crystal to demonstrate the method. This crystal should undergo two PTs, at Ol from the cubic to the tetragonal phase and a t O 2 from the tetragonal to the orthorhombic phase. The following lattice constants are assumed: ac = bc = Cc = 3.9
A, at= bt=4 A, ct=4.1A, ao=4 A, bo= 5.6 A, Co= 5.7 A. The distance between successive lattice planes is given by
[2]
Choosing the (110) plane as the reflecting plane in the cubic phase, we find 2dl10 = 5.515 A. In the tetragonal phase, the x-ray radiation hits under the same angle 0 the same (110) plane, whose 2dllo = 5.657 A. Assuming the glancing angle 0 = 45 °, radiation with an energy of 3.18 keV obeys the Bragg condition in the cubic phase, whereas in the tetragonal phase the energy is 3.10 keV. Thus, using this plane and this PT, only very narrow and neighboring lines could be observed. The opposite case happens if the (110) plane in the tetragonal phase is selected and the PT to the orthorhombic phase is used. Then, the incident beam does not hit the (110) plane but rather the (750) plane of the orthorhombic crystal, with 2d750 = 1.018 A and, while 0 is still 45 °, the energy of the Bragg reflecting x rays becomes 17.24 keV. Of course, the reflectivity of this plane is smaller than the reflectivity of the (110) plane. The hypothetical crystal above is similar to BaTiO3 (3) with two PTs, occurring at 120°C (ferroelectric PT, cubic --~ tetragonal, easy to realize under terrestrial conditions only) and at 5°C (tetragonal --~ orthorhombic). 4. CONCLUSIONS The example demonstrates that, using structural PTs in properly selected crystals, with the help of temperature changes alone one can achieve both observation of neigh-
220
u. GEPPERT
boring and observation of distant in energy narrow spectral lines, while the crystal itself need not be moved. The complicated exchange of crystals within the spectrometer or the use of expensive multilayer structures can be avoided. After the PT the whole crystal surface of the spectrometer is available again for high resolution spectroscopy in another energy range. It should be emphasized that the above-considered hypothetical crystal is only an example which shows that the PT effect can be used in principle. The probability of finding appropriate crystals for every special purpose seems to be rather large because of the huge number of crystals which undergo structural PTs. However, at least two problems have to be solved before this principle can be used in x-ray spectroscopy. The first is finding real crystals to look at particular combinations of lines. Here, the main problem is getting a good compromise between the distances of the energy ranges and the reflectivity of the lattice planes, which decreases considerably with increasing Miller indices. The second is ensuring that the switching between both phases really happens reversibly and avoiding defects or other distortions which can destroy the well-defined crystal structure necessary for high resolution spectroscopy. At present, experimental investigations aimed at solving these problems are being performed. The results will be reported in a forthcoming paper. ACKNOWLEDGMENTS Discussions with F. E. Christensen(Danish Space Research Institute) are gratefullyacknowledged. I also thank my colleaguesH.-J. Wiebickeand I. Halm for discussions and for carefullyreading the manuscript. REFERENCES 1. D. VAUGHAN(Ed.), "X-ray Data Booklet," LawrenceBerkeleyLaboratory,University of California, Berkeley,CA, Apr. 1986. 2. F.E. CHRISTENSEN,B. P. BYRNAK,A. HORNSTRUP,Z. SHOU-HUA,ANDH. W. SCHNOPPER,"Objective Crystal Spectrometer(OXS) for the SPECTRUM-X-GAMMASatellite,"in Proceedingsof SPIE, Vol. 1344, p. 14, SPIE--The InternationalSocietyfor Optical Engineering,Bellingham,WA, 1990. 3. "Landolt-Brrnstein Numerical Data and Functional Relationships in Science and Technology,New Series,"Group IlI, Vol. 28B, Springer-Verlag,Berlin/Heidelberg/NewYork, 1990,and citationstherein.