Inelastic Scattering: of X-Rays with Very High Energy Resolution

119 Pages·1991·1.624 MB·English

by  Dr. habil. Eberhard Burkel (eds.)

Springer Tracts in Modern Physics
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521 Inelastic Scattering of X-Rays with Very High Energy Resolution
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Eberhard Burkel
Inelastic Scattering
of X-Rays
with Very High Energy Resolution
With 70 Figures
galreV-regnirpS
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Dr. habil. Eberhard Burkel
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Preface
X-rays are an established tool for investigations of condensed matter in solid
state physics and crystallography. The standard analysis of the elastically
scattered X-rays reveals the short and the long range order of atoms. It gives
information on the structure of atoms as well as on their local displacements.
In these studies, the high intensity of the new generation of X-ray sources
synchrotrons and storage rings - has opened fantastic new research areas.
-
In particular, scattering experiments with X-rays can be performed with reso-
lutions in energy, space and time which were not thinkable before the advent
of these sources.
In general, textbooks on solid state physics dealing with lattice dynamics
come to the conclusion that lattice vibrations cannot be resolved directly with
X-rays. About 001 years after the discovery of X-rays it has now become pos-
sible to achieve sufficiently high energy resolution for the direct observation
of the small energy shifts of the photons due to the creation or annihilation
of lattice vibrations in an inelastic scattering experiment.
The aim of this review is to report on the recent progress in the field
of inelastic scattering of X-rays with very high energy resolution, which is
directly correlated with the development of the spectrometer INELAX. This
instrument uses the backscattering technique (Bragg angles close to 09 ~ of
X-rays at the storage ring DORIS at HASYLAB, DESY in Hamburg, and
has recently yielded an energy resolution of 9 meV, which corresponds to a
relative energy resolution of about 5 (cid:12)9 01 -r.
After short historic comments and a comparison between different probes
for inelastic investigations for condensed matter excitations, the basic princi-
ples of the backscattering technique are described. The technical realization
of the spectrometer INELAX is discussed in detail. Similar attempts of in-
strumental set-ups undertaken in other laboratories are reported, too.
The second half of the review covers the first applications of the inelastic
scattering technique. The selection of the different examples aimed for a broad
spectrum of problems in order to demonstrate the flexibility and power of this
rapidly growing research field.
The feasibility of the determination of phonon dispersion curves in single
crystals is demonstrated on single crystals of beryllium and diamond. The
results on the longitudinal and transverse modes from X-ray scattering are
in excellent agreement with the results from thermal neutron scattering, the
conventional method for measuring phonon dispersion curves.
IV ecaferP
The application of this new method to the field of biology is certainly a
challenging aspect. The power of the technique is shown by the measurements
of internal and external modes of vibrations in the crystallized amino acids
alanine and glycine up to energy transfers of 005 meV.
Collective excitations in liquids will be a dominating research area for
inelastic X-ray scattering. First observations of the dispersion of such excita-
tions in liquid lithium are discussed as well.
The high energy resolution will certainly give new impulse to study the
electronic excitations in solids and liquids, too. Measurements of such excita-
tions in single crystals of lithium up to energy transfers of 5 eV, for instance,
provide information on the dispersion of the so-called zone boundary collec-
tive states.
The final discussion considers the further applications of inelastic X-ray
scattering that would become possible with continued technological improve-
ments.
Munich, August 1991 Eberhard Burkel
Acknowlegements
The author thanks J. Peisl and B. Dorner for fruitful discussions and encour-
aging support and all members of the INELAX team for their productive
collaboration over the years, especially Th. Illini for his enthusiasm in com-
pleting the computer software.
HASYLAB provided hospitality and technical assistance, which is highly
appreciated.
The support and hospitality of M. Bartunik and his group at the Max-
Planck Institute at DESY is appreciated.
The excellent collaboration with .S Lederle in the construction of instru-
ment components was very productive. The instrument was built with the
technical support of A. EbenbSck and his crew at the machine shop of the
Sektion Physik of the University of Munich. Special thanks to them and to
all who contributed to the success of INELAX.
The author thanks .S Motz for drawing the figures of this review and
he greatly appreciates the careful reading of the manuscript by G. Materlik,
W. Sch/ilke, H. Sinn and by A. M. KShler whose encouragement is especially
appreciated.
This project is supported by the Bundesministerium f/it Forschung und
Technologic under the project number 30 PE1 LMU .2
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 X-ray Diffraction ......................... 1
1.2 Probes for Inelastic Scattering with High Energy Resolution 2
1.3 The Use of Backscattering Geometry .............. 4
Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Scattering Cross Section ..................... 7
2.1.1 Scattering Function .................... 8
2.1.2 Intrinsic Scattering Cross Section for Different Probes . 10
2.2 Instrumental Principle ...................... 13
2.3 Energy Resolution ........................ 14
2.3.1 Crystal Contribution ................... 14
2.3.2 Scattering Geometry and Crystal Optics ........ 17
2.4 Momentum Resolution ...................... 20
2.5 Focusing Elements ........................ 21
X-ray Sources ............................ 25
3.1 Conventional X-ray Generator .................. 25
3.2 Synchrotron Radiation ...................... 26
3.3 Insertion Devices ......................... 29
4 The INELAX Instrument ..................... 33
4.1 The Main Components ...................... 34
4.1.1 Premonochromator .................... 34
4.1.2 Monochromator ...................... 38
4.1.3 Analyzer .......................... 39
4.1.4 Overview of the Network of INELAX Instrumentation. 41
4.2 The Technique for Inelastic X-ray Measurements
with INELAX ........................... 41
4.2.1 Energy Calibration .................... 41
4.2.2 Energy Transfer ...................... 43
4.2.3 Energy Resolution .................... 45
4.3 Experimental Parameters of INELAX .............. 48
X Contents
Other Approaches to Inelastic X-ray Scattering ....... 51
5.1 Activities Using a Conventional Source ............. 51
5.2 Activities Using an Undulator .................. 54
6 Applications of Inelastic X-ray Scattering ........... 57
6.1 Phonons in Single Crystals .................... 57
6.1.1 Beryllium . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.1.2 Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.1.3 High Temperature Superconductor ........... 64
6.2 Vibrational Excitations in Non-single-crystal Systems ..... 66
6.2.1 Polycrystalline Lithium .................. 67
6.2.2 Pyrolytic Graphite ......... ........... 69
6.2.3 Liquid Lithium ...................... 71
6.3 Molecular Vibrations in Amino Acids .............. 77
6.4 Investigations of Electronic Excitations ............. 82
7 The Future of the Technique ................... 91
7.1 Further Applications . . . . . . . . . . . . . . . . . . . . . . . 91
7.1.1 Elastic Scattering with High Energy Resolution .... 91
7.1.2 Inelastic Scattering Under High Pressure ........ 91
7.1.3 Anomalous Inelastic X-ray Scattering .......... 92
7.1.4 Inelastic Scattering with Polarization Analysis ..... 92
7.1.5 Inelastic Scattering Under Grazing Incidence ...... 94
7.2 The Next Generation of INELAX ................ 94
8 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Abbreviations and Symbols
lattice parameter
a0
A mismatch factor; (5.1)
A Thomson part of scattering amplitude; (7.5)
b scattering length of nucleus
B bulk modulus
BCS Bardeen-Cooper- Schriefer theory
c velocity of light
oC calibration constant; (4.2)
constants; (4.3)
1C ~ • . . ~ C4
elastic constants
Cll : 44C
C prefactor in scattering amplitude; (7.6)
constant-Q scan scan with fixed momentum transfer
constant-E scan scan with fixed energy transfer
d, d; distance between two beams
lattice spacing for (h k l) reflection
dhkl
D diameter of spherical crystal
Dhor, Dyer horizontal and vertical beam sizes at monochromator
! t horizontal and vertical beam sizes at analyzer
Dhor, Dyer
DESY Deutsches Elektronen Synchrotron
DORIS electron-positron storage ring at DESY, Hamburg
2~d solid angle element
(da/dD)o intrinsic scattering cross section
Thomson scattering cross section
( d6t / d~ )Th
htuR)2gd/~cd( Rutherford scattering cross section
2d a / ( fwd2~d ) double differential scattering cross section; (2.1)
e charge of electron
eV electron Volt
ed(q,j) normalized phonon eigenvector of mode j with
phonon wavevector q for atom d
initial and final polarization of the photon beam
e ~i ef
E energy transfer in the scattering process; (2.2)