Table Of ContentPreface
This book is a part of the series "Analytical Spectroscopy Library" and is devoted to X-ray
analysis by synchrotron radiation. X-ray analysis is one of the oldest and most well
established techniques in analytical chemistry. The method, however, is still on the leading
edge of instrumental analysis. X-rays are nonrestrictive and can be tuned to a very sharp
bandwidth. Their very short wavelength enables high resolution imaging down to a molecular
or atomic scale. These potential capabilities are not well realized in current X-ray analytical
instruments. The largest drawback is the low intensity of an X-ray source. Recent
developments in the synchronotron radiation (SR) X-ray source are the real breakthrough, and
the photon deficiency problem is now being solved. The number of SR facilities, however,
is limited and their distribution is not uniform in the world. Whereas research reports are
circulated in the US and EU countries very well, reports from the orient are often inaccessible
due to language barriers.
This volume is intended to describe various facets of X-ray analytical methods by SR with
some emphasis on Japanese activity. The editors hope that this volume will provide general
perspectives of X-ray analysis by SR, with the added spice of Japanese activity in the Photon
Factory and the future SPring-8 project. Chapter 1 (Mititaka TERASAWA and Motohiro
KIHARA) is a concise introduction to synchrotron facilities and the related basic
instrumentation. The chapter will be helpful to understand the discussion of machine operators
and technicians and to communicate with design people in the planning of a new ring or an
insertion device. In chapter 2 (Hideo SHAISHO and Hideki HASHIMOTO), X-ray
fluorescence analysis is discussed. SR provides tunable excitation which is very effective in
improving a detection limit (DL). The detailed discussion on DL is based on a theoretical
estimation of background and the discussion can be extended to fiJture research planning.
Another important characteristic of SR is natural collimation, which leads to total reflection
analysis. The theoretical treatment in this chapter will be especially useful for thin layer
analysis by XRF. Chapter 3 (Shinjiro HAYAKAWA and Yohichi GOHSHI) covers
microbeam and chemical state analysis. Instrumentation for microbeam optics is completely
dependent on the fabrication technology of optical components which are state of the art. X-
ray analysts, however, can expect better performance of a microbeam optical system with the
knowledge of optical systems described in this chapter. In addition to its imaging capability,
an energy tunable microprobe can speciate analytes. Several sophisticated applications are
discussed. Chapter 4 (Hiroyuki OYANAGI) covers X-ray absorption fine structure, which is
the most widely used technique in the application of SR to material analysis. Instrumentation
vi
in the detection system is included together with a general description of XAFS and a variety
of applications. Chapter 5 (Toshiaki OHTA, Kiyotaka ASAKURA and Toshihiko
YOKOYAMA) covers surface structural analyses. Surface sensitive signal detection is
described, followed by SEXAFS and NEXAFS applications to surface phenomena. Other
important techniques such as surface diffraction, standing wave, and angle resolved
photoemission fine structure are also explained together with several applications. Chapter 6
(Kanji KAJIWARA and Yuzuru HIRAGI), Structure Analysis by Small-angle X-ray
Scattering, describes the powerful traditional method for organic molecules, especially
polymers. Chapter 7 (Fujio IZUMI) explains details of the Rietveld method and its
applications to synchrotron X-ray powder diffraction data. The author has developed much
software for the Rietveld method and his experience contributes to the comprehensive
description given in this chapter. Chapter 8 (Katsuhisa USAMI) and Tatsumi HIRANO), X-
ray Microtomography deals with large scale structural analysis. Energy tunability of the SR
X-ray source adds even more elemental and chemical state information to the tomographic
image of information. Though there is still a gap between atomic scale structural analysis and
mm or gm analysis, this will be bridged by the future SR X-ray method.
The editors H.S. and Y.G. hope that this volume will be of help to research scientists and
students who are interested in materials analysis by X-ray methods. H.S. and Y.G. finally
appreciate the effort and patience of all the authors and the staff at Elsevier Science.
February 1996
Y. GOHSHI
H. SAISHO
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CHAPTER 1
BASIC CHARACTERISTICS OF
SYNCHROTRON RADIATION AND
ITS RELATED FACILITIES AND
INSTRUMENTATION
Mititaka TERASAWA
Himeji Institute of Technology
2167 Shosha, Himeji, Hyogo 671-22, Japan
Motohiro KIHARA
National Laboratory for High Energy Physics (KEK)
Oho, Tsukuba, Ibaraki 305, Japan
1.1. INTRODUCTION
Electromagnetic radiation emitted by charged particles when they move at a highly relativistic
velocity on a circular orbit is called synchrotron radiation, or SR in short- which was named
after the first observation of the radiation in an electron circular accelerator, a synchrotron.
Although the synchrotron radiation was, in its early history, considered simply to be a useless
and harmful by-product generated in circular accelerators, it has become of great interest and is
utilized in materials science as an intense and versatile photon source. At the beginning, the
radiation was used as a powerful photon source for spectroscopy in the wavelengths ranging
from soft X-rays to the vacuum ultra-violet (VUV). From the early 1960s many of the existing
electron synchrotrons in the several hundred MeV class have been modified and turned over to
synchrotron radiation facilities.
In the mid 1970s, an electron storage ring became a normal photon source facility, in place of
the electron synchrotron. The storage rings were originally developed for collision experiments
in high energy physics. In the electron synchrotron, electrons are accelerated and, after the
maximum energy is achieved, are extracted, usually at a rate of several tens per second. In
contrast, in the storage ring the previously accelerated electrons are injected into and stored in
the ring orbit. As a consequence this is greatly superior to the former synchrotron as an intense
and stable radiation source. Recently large storage rings in the multi-GeV class have been
developed and the wavelengths of the radiation have been extended to the hard X-ray range.
The use of such high energy X-rays is now having a great impact in studies on X-ray
scattering, diffraction, inner shell ionization, and even nuclear excitation.
Nowadays the usefulness of synchrotron radiation is well recognized in various research
fields, and many storage tings dedicated to synchrotron radiation research have been
constructed or are currently under construction. Moreover, insertion devices, which allow
radiation of much higher brilliance to be obtained, are well developed and available as practical
facilities. The synchrotron radiation is usually emitted by electrons moving in a circular orbit in
the bending magnet. The radiation from insertion devices such as the undulator and the
multipole wiggler, which are positioned on the straight section of the storage ring, is of
extremely high brilliance -- and also has a shorter wavelength with multipole wigglers than
with bending magnets. The storage tings of recent advanced synchrotron radiation facilities are
designed to have many long straight sections so as to accommodate such insertion devices as
low emittance and high brilliance photon sources. Consequently, the tings always tend to
become larger.
1.1.1. Properties of Synchrotron Radiation
Electrons submitted to an acceleration field emit electromagnetic waves. This phenomenon is
well recognized in a classic antenna where the electrons are travelling in conducting wires, the
acceleration is very weak, and the emission takes place in the radiofrequency range. With
vacuum electron tubes, such as the klystron, it is possible to increase the acceleration on
electrons which are travelling in the vacuum, and to push the emission into the ultra-high
frequency (UHF) range. In these tubes the electron energy is fairly weak. In circular high
energy electron accelerators,~with electron energies up to several giga electron volts (GeV), the
magnetic field in the bending magnets induces a very strong centripetal acceleration in the
highly relativistic electrons, with an energy E >> mc 2 where m is the rest mass of electron. The
acceleration induces an electromagnetic wave emission up to several hundreds keV in the most
energetic machines. This radiation is called synchrotron radiation. Relativistic positrons also
emit synchrotron radiation in the magnetic field by the same principle.
Thus, circular electron- and positron-accelerators and storage rings, in which the particles
move with relativistic energies, have become man-made sources of synchrotron radiation. The
radiation source is basically composed of three component facilities: a linear accelerator, the
synchrotron and the storage ring. Electrons are injected into an electron synchrotron at a
relatively low energy, say several hundred MeV, from the linear accelerator. They are then
accelerated on a fixed circular orbit. The synchrotron consists of an array of magnets for
focusing and bending the electron beam, and straight linear sections for accelerating the
particles. The magnetic field in the deflecting magnets is increased during the acceleration in
order to keep the electrons on the same circular path as their energy is gradually increased.
Finally, when they reach the appropriate energy, the electrons are transferred to the storage
ring. Here the magnetic field remains constant. There are acceleration sections within the
storage ring which compensate for the energy losses due to synchrotron radiation. Around the
storage ring the radiation from the stored electrons can be used for various experiments. This
photon production is of extreme interest for spectroscopy.
Synchrotron radiation has a number of outstanding properties:
(1) A continuous spectrum from the infrared to the X-ray region.
(2) High intensity, owing to the high current electrons accumulated in the storage ring.
(3) Collimation of the emitted radiation in the instantaneous direction of flight of the emitting
particles (the angular spread is of the order of 1 mrad).
(4) Linear polarization, with the electric vector parallel to the plane of the orbit.
(5) Circular polarization above and below the plane of the orbit.
(6) High brilliance of the source, because of the small cross section of the electron beam and the
high degree of collimation of the radiation.
(7) A time structure with pulse lengths down to 100 ps.
(8) Absolute calculability of all the properties of the source.
(9) Cleanliness of the source, since the light emission takes place in an ultra-high vacuum, in
contrast to the situation in gas discharge or spark lamps.
1.1.2. Historical Remarks
Although synchrotron radiation was first observed directly by Elder and his co-workers 1 at
the General Electric 70 MeV synchrotron in 1947, the theoretical consideration of radiation by
charged particles in circular motion goes back to the work of Lienard in 1898 2. Further
theoretical work was made by Schott 3, Jassinsky 4, Kerst 5, Ivanenko and Pomeranchuk
6, Arzimovitch and Pomeranchuk 7 and others through to 1946. Blewett 8 was one of the
first to be concerned with the effects of the radiation on the operation of electron accelerators
and he observed the effects on the electron orbit in 1945, although he did not detect the radiation
itself.
After the observation of the radiation by Elder and his co-workers in 1947 the interest in
synchrotron radiation was renewed. Comprehensive theoretical treatments were presented by
Sokolov and his co-workers 9 and by Schwinger 10 in the late 1940s and later. With these
works the theory was fully developed so that accurate predictions could be made regarding the
intensity, spectral and angular distributions, polarization, and so on. Following the first
observation Elder and his co-workers carded out experimental investigations in the late 1940s
on the properties of the radiation, using the General Electric 70 MeV synchrotron.
In the 1950s studies of synchrotron radiation were extended by several groups 11, using the
250 MeV synchrotron at the Lebedev Institute in Moskow, by Corson 12 and Tomboulian and
his co-workers 13 using the Comell 300 MeV synchrotron, and by Codling and Madden 14
using the 180 MeV synchrotron at the National Bureau of Standards (NBS) in Washington
D.C. In the mid-1960s Haensel and his co-workers 51 were the first to utilize radiation from
a multi-GeV accelerator, the 6 GeV synchrotron in Hamburg. The investigations mentioned
above confirmed the basic theoretical predictions and provided much useful data and experience
in the use of the radiation.
1.2. PRINCIPLE OF SYNCHROTRON RADIATION EMISSION
1. 2. 1. Principle of Synchrotron Radiation Emission
The properties of synchrotron radiation (SR) can be derived by applying the methods of
classical electrodynamics to the motion of relativistic electrons and positrons in circular orbits.
Hereafter we confine the following discussion to the radiation emission only by electrons,
because the principle of the emission by positrons is the same.
First of all, we consider the circular motion of an electron with momentum p in a magnetic
field B. The radius of the electron orbit, p, is given by the following equation.
pc = Bep (1-1)
where e is the electron charge and c is the speed of light. For relativistic electrons,
E 2 = p2c2+m2c 4 ~ p2c2 (1-2)
where E is electron total energy and m is the electron rest-mass. From Eqns. (1-1) and (1-2),
E = Bep (1-3)
This relation is described using practical units, by Eqn. (1-4).
Btesla pm = 3.336 EGeV (1-4)
Angular distribution of SR
When an electron is non-relativistic (fl = v/c << )1 and the velocity is significantly low
compared to the speed of light, the electron on a circular orbit is accelerated toward the center of
the orbit, and emits a dipole radiation whose axis is in the direction of the acceleration. The
radiation power per unit solid angle, which is the energy of the electromagnetic wave emitted in
unit time from the electron with the acceleration of dv/dt, is given by
dP(z)= e 2 (~t)2sin2z
dO cr~4 2 (1-5)
where Z is the angle between the directions of the acceleration and electromagnetic wave
transmission. Therefore the angular distribution of the radiation power based on a dipole
radiation shows the typical pattern of sin2z. As shown in Fig. 1-1, the radiation emission is at
maximum in a direction normal to the acceleration (2' = 7r/2), and there is no emission at the two
acceleration directions of Z = 0 and 72 = .r7
tibrO- ---....~
dv ) noitareleccA /--~~)~'~Ujt J'
at
oT
v spectrograph
)a( )b(
Fig. 1-1. Radiation patterns of electrons in circular motion at low velocity.
K K'
P
,-x-(x, y, z, t)
(x', y', z', t')
Otl
vt Z IJ" 'Z
I
Fig. 1-2. Coordinate systems showing Lorentz transformation. Electrons moving at the
velocity v are on the system K', and the radiations are observed on the system K.
When an electron moves near the light speed, the properties of SR from the electron are
described by relativistic electrodynamics. If an observer is in a fixed coordinate system located
on the electron, he observes the same angular distribution of sin2z as for the non-relativistic
case mentioned above, even if the electron moves relativistically. However, if an observer is in
the stationary coordinate system, the angular distribution becomes distorted due to the
relativistic effect.
Let us take a stationary coordinate system K(x,y,z,t), and another coordinate system
K' (x ,' y z," ',t )" which is moving at speed v along the direction of the z axis. The relationship
between the two systems is given by the Lorentz transformation,
z = 7(z' + vt')
X'- X'
y=y'
t= 7 (t' + flz'/c) (1-6)
where fl = v/c and,
1
r 41_/32
(1-7)
_ E
mc 2 (1-8)
= 1957 EGeV (1-9)
Here, ?'is the energy of the electron represented in units of the electron's rest mass energy, that
is mc 2 = 511 keV. For example, fl = 0.999999868 and ?' = 1957 for E = 1.0 GeV. The
electron mass becomes 1957 times the rest mass, which means that the acceleration of
relativistic particles increases the mass, while changing the velocity little, because it is almost
the speed of light. As shown in Fig. 1-2, if the SR, which is emitted at angle 0' from the z'
coordinate from an electron fixed at the K' system is observed at angle 0 from the z coordinate,
the following relationship is obtained, using the Lorentz transformation for velocity.
cos0'+ fl
SOC 0 =
1 + fl cosO' (1-10)
sinO'
sin0 =
y(1 + fl cosO') (1-11)
then,
tanO=l sinO'
?'cosO'+ fl (1-12)
The angle 0'= + nr/2 in the K' system, at which no radiation is emitted, is proved to
correspond to 0 = + 1/Tin the K system, according to Eqn. (1-12). The sin2z angular
distribution of radiation emission is extremely distorted and a forward focusing, in which the
radiation is concentrated within a sharp cone with its axis tangential to the electron circular orbit,
is observed, as shown in Fig. 1-3.
.... Orbit .....
dv noitareleccA ,
dt
"oT
spectrograph
V
(a) (b)
Fig. 1-3. Radiation patterns of electrons in circular motion at velocity approaching that of light.
The root mean square (r.m.s.) of the radiation emission angle, which corresponds to half the
cone angle, is expressed as follows for the radiations near the emission spectrum center;
(i//2)1/2 = 1
7 (1-13)
For example, 1/7 = 0.064 mrad for E = 8.0 GeV, which means only 6.4 mm spread of the
radiation 100 m from the source point. It is understood that the SR is an ideal collimated beam.
Actually, the intensity of the radiation drops rapidly with increase in the angle ~in the direction
vertical to the electron orbit plane, while the plane is filled with the radiation because electrons
are emitting their radiation all the way round.
Spectra
In the case when an electron moves non-relativistically on a circular orbit with radius p, an
angular frequency of radiation is equal to an electron revolution frequency, oc o = v/p. When an
electron moves relativistically, the main frequency components of the radiation are significantly
higher harmonics of the revolution frequency too. Let us consider an observer standing on a
line tangential to the electron orbit, as shown in Fig. 1-4. The observer will be subjected to the
radiation which is emitted by the electrons moving between A and B on the circular arc, the
length of the arc being 2p/7' because the radiation emission angle is about 2/7,. The time
interval of the radiation to which the observer is exposed will be the time that the radiation
travels from A to B, subtracted from the time that the electron moves along the arc AB, that is,
2p 2p sin~ 2p
At = v)' c = (-~U- c- )1 (1-14)
Adopting
v/c = fl= 1 - 1/(2 '7 )2 (1-15)
At= p = 1
C7' 3 too7' 3 (1-16)
The radiation is confined to an extremely short pulse, since this time interval is in inverse
proportion to ),3. For example, At = 3.48 x 10 -20 sec in the case of E = 8.0 GeV and p = 40.1
m.
revresbo
Fig. 1-4. Electrons in circular motion and synchrotron radiation emitted by the electrons in
a tangential direction.
An electric field of pulsed radiation as a function of frequency, E(to), is derived as the Fourier
transformation of the time-dependent electric field, E(t). The power-spectrum of SR is
determined by E(to) .2 In the present case, E(t) is a periodic pulse with the pulse width of
,)3"7c(/p and the pulse interval ,c/pr72 as shown schematically in Fig. 1-5a. The quantity E(to) 2
consists of a vast number of higher harmonics of the basic angular frequency to o = c/p,
