X-Rays are short wavelength electromagnetic radiation produced by the deceleration of
high energy electrons or by electronic transitions of electrons in the inner orbital of atoms.
The wavelength range of X-rays is from about 10-5
Å to 100 Å; conventional X-ray
spectroscopy is largely confined to the region of about 0.1 Å to 25 Å.
X-ray spectroscopy is a form of optical spectroscopy that utilizes emission, absorption,
scattering, fluorescence, and diffraction of X-ray radiation
X-rays are short-wavelength (hence, high frequency, and hence, relatively high
energy) electromagnetic radiation. Two ways to produce X-rays:
1) Deceleration of high-energy electrons
2) Electronic transitions involving inner-orbital (e.g. - d or f) electrons
Approximate wavelength range: 10-6 nm - 10 nm
Wavelength range used in conventional applications: 0.01 nm - 2.5 nm
X-rays are the shortest wavelength, i.e., highest energy, electromagnetic radiation
associated with electronic transitions in atoms. Calculation of the energy states of an atom
is in general, very difficult, except of course in the particular case of the hydrogen atom,
where the problem is readily soluble and the results, shown schematically below, are very
The orbital picture of the H-atom associated with this energy level diagram is readily
extended to multi-electron atoms and the again familiar result is qualitatively represented
Energy levels of many electron atoms in the
periodic table. The insert shows a magnified view
of the order near Z = 20.
An important feature of both the above diagrams is that the differences in orbital energies
decrease as they themselves increase. This means that the energy required for excitation, or
given out on relaxation of an electron from a higher orbital to a lower orbital is greater
when "inner" orbitals are involved and least when "outer" orbitals are involved. Except for
light elements (say, those preceding Na) the innermost orbitals are not significantly
influenced by bonding interactions involving the atom and, hence, their energies may be
regarded as characteristic of that atom regardless of its state of combination. Inner orbital
transitions involve X-rays, and it is for this reason that X-ray spectrometry can be a form of
atom detection and, hence, of non-destructive chemical analysis.
Of course, for a multi-electron atom, a conventional orbital diagram as given above cannot
simply be converted into an energy level diagram. The energy level diagram for any atom is
considerably more complex and depends in detail upon the particular atom. However, for
X-ray emissions of importance in elemental analysis, a simplified treatment is sufficient and
the diagram below is useful.
Partial energy level diagram showing common transitions
leading to X–radiation.
The most intense lines are indicated by the widest arrows.
The orbital shells for which the principal quantum number n = 1,2,3, etc. are labelled the K,
L, M, etc. and, hence, emissions due to a higher energy electron entering these shells are
said to form the K, L, M, etc. series of lines. Generally, only the K and L series of X-rays
are of analytical utility and the wavelengths of these lines for a selection of elements
spanning the Periodic Table are shown below.
Wavelengths/Å for Intense X–ray Emission Lines
Element K Series L Series
a1 b1 a1 b1
Na 11.909 11.617 – –
K 3.742 3.454 – –
Cr 2.290 2.085 21.714 21.323
Rb 0.926 0.829 7.318 7.075
Cs 0.401 0.355 2.892 1.282
W 0.209 0.184 1.476 1.282
U 0.126 0.111 0.911 0.720
(Note that all possible electronic transitions are not of equal
probability, i.e., the nature of a spectrum depends on specific
selection rules, so that the complexity of a spectrum is not as
great as might be expected from first consideration of an energy
The fact that the wavelength of a line of given type decreases as the atomic number of the
element increases is rather important in that it means that an X-ray from a given element
must be able to cause inner shell ionization and, hence, emission of radiation of lower
energy from any lighter element.
For analytical purposes, X-rays are generated in three ways:
1) bombardment of metal target with high-energy electron beam
2) exposure of target material to primary X-ray beam to create a secondary
beam of X-ray fluorescence
3) use of radioactive materials whose decay patterns include X-ray
Synchrotron radiation is an
indispensible tool for x - ray
absorption studies of biological
materials. The XAFS technique
yield information on the
number, type and radial
distribution of ligands
coordinated to a metal are
revealed at subatomic
The oxidation state of a metal
and the effects of substrate
binding or catalysis on the
metal centre can be probed.
Three dimensional structural
information is obtained when
x - ray absorption data and
protein crystal data are
combined in the 3D - XAFS
Identification and measurement of concentration of elements based on the fact that primary-
emission x-rays emitted by an element excited by an electron beam have a wavelength
characteristic of that element and an intensity related to its concentration. It may be
performed by an electron probe microanalyzer, an electron microscope microanalyzer, or by
an electron microscope, or scanning electron microscope, fitted with an x-ray spectrometer.
Below is a schematic of an X-ray tube.
X-ray sources can emit two forms of X-rays:
1) continuous (white radiation or Bremsstrahlung - “Bremsstrah-
lung” refers to radiation arising from the deceleration of particles)
2) discontinuous (line)
Below is the partial energy-level diagram showing common transitions producing X-rays.
The most intense lines are indicated by wider arrows.
Electron beam sources...
In electron beam sources, X-rays are produced by heating a cathode to produce
high-energy electrons; these electrons are energetic enough to ionize off the cathode and
race towards a metal anode (the target) where, upon collision, X-rays are given off from the
target material in response to the colliding electrons. By varying the conditions, one can
obtain either a continuous spectrum or a discontinuous spectrum.
The reaction between the electron beam and the target material involves
deceleration of the electron and ejection of a target photon and emission of X-rays. The
energy lost by the electron as it smashes into the target material is equal to the energy of the
ejected photon. Since any given electron can be retarded differently by the same target
material, a range of photon energies are possible. The maximum photon energy corresponds
to total stopping of the electron and is given by:
hvo = (hc)/λo = Ve,
where, vo is the maximum frequency,
V = accelerating voltage,
e = electron charge
This is the Duane-Hunt law.
Electron beam source line spectra characteristic...
1. Elements with Z > 23 exhibit two spectral series: a K line (corresponding to
shorter wavelengths) and an L line (corresponding to relatively longer
wavelengths). Elements with Z < 23 exhibit only the K series
2) As Z increases, so too does the minimum amount of energy required for
For all but the lightest elements, the X-ray line spectra are independent of
either physical or chemical states. This is because the electrons involved in
the transition are not participating in any chemical bonds.
Continuum Spectra from Electron Beam Sources…
In an X-ray tube, electrons produced at a heated cathode are accelerated toward a metal
anode by a potential as great as 100kV; upon collision, part of the energy of the electron
beam is converted into X-Rays. Under some conditions only a continuum spectrum is
results. The continuum X-Ray spectrum is characterized by a well-defined, short
wavelength limit, which is dependent upon the accelerating voltage but independent of the
target material. The continuum radiation from an electron beam source results from
collisions between the electrons of the beam and the atoms of the target material.
Figure 1.1: Schematic representation of an AGN continuum spectrum including a possible source for
each emission component.
Line Spectra from Electron Beam Sources…
Bombardment of a molybdenum target produces intense emission lines. The emission
behavior of molybdenum is typical of all elements having atomic numbers greater than 23,
that is, the X-Ray line spectra are similar when compared with ultraviolet emission and
consist of two series of lines.
Line spectra are composed of distinct lines of color, or in the case of our graphs, sharp
peaks of large intensity at a particular wavelength. Line spectra are characteristic of
elements and compounds when excited (energized) under certain conditions. These spectra
helped develop the current atomic theories. Line spectra thus provide a “fingerprint” unique
to each element, and as with continuous spectra, the combination of the prominent lines in
the spectrum produce the observe light color.
The fluorescent lamp’s spectrum is a mixture of line and continuous spectra. Because of the
exact correlation with the principal mercury vapor lines and the fluorescent lamp’s lines, we
can conclude that a major component of the fluorescent lamp is mercury vapor. But what
produced the continuous portion of the fluorescent spectrum?
A phosphor is a substance that can accept energy in one form and emit the
energy in the form of visible light. Fluorescent lights are produced by coating the
inside surface of the glass tube with phosphor particles, which accepts the energy
of ultraviolet photons and emits visible photons. In the case of my lamp, the
phosphor coating emitted relatively high intensities of light ranging from blue to
yellow in color, demonstrated by the continuous peaks between about 480 nm
and 600 nm. Because it is not an atomic source, we should not expect line
spectra from the phosphor particles, and so attribute the continuous portion of the
plot to the activity of the phosphor. The presence of the continuous spectra also
tells us that the mercury vapor is emitting light in the ultraviolet range, which is
beyond the scope of our spectrophotometer to detect directly.
These three elemental vapor spectra clearly illustrate line spectra. Examining the prominent
lines of neon, I would expect the light to be a deep red-orange color, which is what we
observed. The spectral lines of krypton indicate another red light, however, we observed a
cool blue color. Argon’s prominent lines also imply a red color, which does not match the
observed lavender-purple color. I hypothesize that the difference is because our
spectrophotometer doesn’t detect or plot the very short blue visible wavelengths (near
ultra-violet), which would combine with the red lines in the spectrum to produce the blue
and lavender-blue light seen from krypton and argon vapor lamps.
A neon-helium laser produces a red laser beam, which is correlated on the spectral graph
with a single, sharp peak in the red portion of the spectrum. Because of this single peak, we
can refer to the laser as an extremely monochromatic light source. Careful examination of
the graph reveals a minor peak on the neon vapor spectra at the same wavelength of the
laser beam, which indicates the neon component of the neon-helium laser.
Absorption of X-ray radiation follows Beer’s law like the absorption of other forms
of electromagnetic radiation. For X-ray work, Beer’s law looks like:
ln(Po/P) = µx
where Po = incident beam power,
P = transmitted beam power,
µ = linear absorption coefficient (similar to molar absorbtivity),
x = path length in cm
We can rewrite this to take into account the density of the sample:
ln(Po/P) = µMρx
where µM is the mass absorption coefficient.
Using the mass absorption coefficient, you don’t need to worry about the physical or
chemical state of the sample. Nifty, huh?
And, mass absorption coefficients have the additional convenience of being additive
functions of their weight fractions of sample components:
So, µM, tot = WAµA + WBµB + ... + Wnµn
Like many important scientific discoveries, Fraunhofer's observation of spectral lines was a
complete accident. Fraunhofer wasn't looking for anything of the sort; he was simply testing
some new state-of-the-art prisms he had made. When sunlight was sent through a thin slit
and then through one of the prisms, it formed a rainbow-colored spectrum, just as
Fraunhofer had expected--but, much to his surprise, the spectrum contained a series of dark
Dark lines? That's the opposite of what we've been talking about. You've been telling me
that different elements create a series of bright lines at certain wavelengths.
That's what happens when an element is heated. In terms of the Bohr model, heating the
atoms gives them some extra energy, so some of their electrons can jump up to higher
energy levels. Then, when one of these electrons drops back down to a lower level, it emits
a photon --at one of that element's special frequencies, of course.
And those photons create the bright lines in the spectra you showed me.
Exactly--that's called an emission spectrum. But there is another way in which elements
can produce spectra. Suppose that instead of a heated sample of some element, you have
the element in the form of a relatively cool gas. Now let's say that a source of white light--
containing all visible wavelengths--is shining behind the gas. When photons from the light
source make their way through this gas, some of them can interact with the atoms--
provided that they have just the right frequency to bump an electron of that element up to a
higher energy level. Photons at those particular frequencies are thus absorbed by the gas.
However, as you noted before, the atoms are "transparent" to photons of other
So all those other frequencies would come through okay. Then the spectrum of light that
had been through the gas would just have some gaps in it, at the frequencies that were
That's right. The spectrum with these missing frequencies is called an absorption
spectrum. (Note that the dark lines in an absorption spectrum appear at exactly the same
frequencies as the bright lines in the corresponding emission spectrum.)
And that's what Fraunhofer saw?
Yes. Under very careful examination, the "continuous" spectrum of sunlight turns out to be
an absorption spectrum. In order to reach earth, sunlight needs to pass through the sun's
atmosphere, which is a lot cooler than the part of the sun where light is emitted. Gases in
the atmosphere thus absorb certain frequencies, creating the 600 or so dark lines that
Fraunhofer observed. (They are now called Fraunhofer lines in his honor.)
Fraunhofer was unaware of all this, however. No one offered an explanation of spectral
lines until decades later...
Since X-rays are rather energetic, excitation of sample electrons will give rise to
fluorescence as the sample electrons are excited and return to their ground states in a series
of electronic transitions.
When a primary x-ray excitation source from an x-ray tube or a radioactive source strikes a
sample, the x-ray can either be absorbed by the atom or scattered through the material. The
process in which an x-ray is absorbed by the atom by transferring all of its energy to an
innermost electron is called the "photoelectric effect." During this process, if the primary x-
ray had sufficient energy, electrons are ejected from the inner shells, creating vacancies.
These vacancies present an unstable condition for the atom. As the atom returns to its stable
condition, electrons from the outer shells are transferred to the inner shells and in the
process give off a characteristic x-ray whose energy is the difference between the two
binding energies of the corresponding shells. Because each element has a unique set of
energy levels, each element produces x-rays at a unique set of energies, allowing one to
non-destructively measure the elemental composition of a sample. The process of emissions
of characteristic x-rays is called "X-ray Fluorescence," or XRF. Analysis using x-ray
fluorescence is called "X-ray Fluorescence Spectroscopy." In most cases the innermost K
and L shells are involved in XRF detection. A typical x-ray spectrum from an irradiated
sample will display multiple peaks of different intensities.
Spectrum taken using Amptek XR-100CR 25mm2
X500µm X-Ray Detector (20µs shaping
time - optional feature) and Amptek MCA8000A Multichannel Analyzer.
The characteristic x-rays are labeled as K, L, M or N to denote the shells they originated
from. Another designation alpha (a), beta (b) or gamma (g) is made to mark the x-rays that
originated from the transitions of electrons from higher shells. Hence, a Ka x-ray is
produced from a transition of an electron from the L to the K shell, and a Kb x-ray is
produced from a transition of an electron from the M to a K shell, etc. Since within the
shells there are multiple orbits of higher and lower binding energy electrons, a further
designation is made as a1, a2 or b1, b2, etc. to denote transitions of electrons from these
orbits into the same lower shell.
The XRF method is widely used to measure the elemental composition of materials. Since
this method is fast and non-destructive to the sample, it is the method of choice for field
applications and industrial production for control of materials. Depending on the
application, XRF can be produced by using not only x-rays but also other primary excitation
sources like alpha particles, protons or high energy electron beams.
Sometimes, as the atom returns to its stable condition, instead of emitting a characteristic x-
ray it transfers the excitation energy directly to one of the outer electrons, causing it to be
ejected from the atom. The ejected electron is called an "Auger" electron. This process is a
competing process to XRF. Auger electrons are more probable in the low Z elements than
in the high Z elements.
Like other forms of electromagnetic radiation, X-rays are also susceptible to
diffraction. This property is most useful in determining the structure of single crystal
samples. Here’s the basic idea:
In crystals, we have an essentially infinitely repeating sequence of atoms that are
usually layered one on top of another. In X-ray diffraction, parallel beams of X-rays are sent
into a sample; some will immediately be reflected by the surface layer; some will penetrate
into inner layers. As the X-rays travel into the inner layers, some will be reflected and some
will continue through the sample and so. We now have a series of reflected X-rays that can
form an interference pattern with each other; we will obtain an interference pattern where
dark regions correspond to destructive interference and light regions correspond to
constructive interference. The Bragg equation gives the angle of incidence where
constructive interference occurs in terms of the interatomic distance between crystal planes:
sin θ = (nλ)/2d
where, θ= angle of incidence
λ = wavelength
d = interplane distance of crystal
Below is a figure of the diffraction of X-rays by a crystal.
Diffraction and Bragg's Law
Diffraction occurs as waves interact with a regular structure whose repeat distance is about
the same as the wavelength. The phenomenon is common in the natural world, and occurs
across a broad range of scales. For example, light can be diffracted by a grating having
scribed lines spaced on the order of a few thousand angstroms, about the wavelength of
It happens that X-rays have wavelengths on the order of a few angstroms, the same as
typical interatomic distances in crystalline solids. That means X-rays can be diffracted from
minerals which, by definition, are crystalline and have regularly repeating atomic structures.
When certain geometric requirements are met, X-rays scattered from a crystalline solid can
constructively interfere, producing a diffracted beam. In 1912, W. L. Bragg recognized a
predicatable relationship among several factors.
1. The distance between similar atomic planes in a mineral (the interatomic spacing) which
we call the d-spacing and measure in angstroms.
2. The angle of diffraction which we call the theta angle and measure in degrees. For
practical reasons the diffractometer measures an angle twice that of the theta angle. Not
surprisingly, we call the measured angle '2-theta'.
3. The wavelength of the incident X-radiation, symbolized by the Greek letter lambda and,
in our case, equal to 1.54 angstroms.
A diffractometer can be used to make a diffraction pattern of any crystalline solid. With a
diffraction pattern an investigator can identify an unknown mineral, or characterize the
atomic-scale structure of an already identified mineral.
There exists systematic X-ray diffraction data for thousands of mineral species. Much of
these data are gathered together and published by the JCPDS-International Centre for
The diffractometer in the IPFW Geosciences Department is a Philips APD3520 built in
1986. It consists of several parts.
A. The chiller provides a source of clean water to cool the X-ray tube.
B. The regulator smooths our building current to provide a steady and dependable source of
electricity to the diffractometer and its peripherals.
C. The computer sends commands to the diffractometer and records the output from an
analysis. We are currently using a 486-100 running DR-DOS7 to run the diffractometer,
and provide interfacing with this web page. We process most of the information digitally,
although we can make hardcopy analog patterns directly on the;
D. Strip-chart recorder.
E. The tube provides an X-ray source. (An old tube, shown upside down, is on the counter
top.) Inside there is a 40,000 volt difference between a tungsten filament and copper target.
Electrons from the filament are accelerated by this voltage difference and hit the copper
target with enough energy to produce the characteristic X-rays of copper. We use one part
of the copper spectrum (with a wavelength of 1.54 angstrom) to make the diffraction
pattern. The radiation is monochromatized by a graphite crystal mounted just ahead of the
F. The theta compensating slit collimates the X-rays before they reach the sample.
G. The sample chamber holds the specimen. We grind our samples to a fine powder before
mounting them in the diffractometer, and then close the chamber to allow the collimated X-
rays to enter from the left. The X-rays hit and scatter from the sample. The diffracted beams
leave the chamber to the right where they can be detected by the;
H. Scintillation counter which measures the X-ray intensity. It is mounted on the;
I. Goniometer which literally means angle-measuring device. The goniometer is motorized
and moves through a range of 2-theta angles. Because the scintillation counter is connected
to the goniomter we can measure the X-ray intensity at any angle to the specimen. That's
how we determine the 2-theta angles for Braggs's Law.
A diffraction pattern records the X-ray intensity as a function of 2-theta angle. All the
diffraction patterns you'll see on this web site were prepared as step-scans. To run a step-
scan we mount a specimen, set the tube voltage and current, and enter the following
--A starting 2-theta angle.
--A step-size (typically 0.005 degrees).
--A count time per step (typically 0.05-1 second).
--An ending 2-theta angle.
Once started, the goniometer moves through its range, stopping at each step for the alotted
time. The X-ray counts at each step are saved to a file on the computer. Once finished, the
data are smoothed with a weighted moving average and a diffractogram like the one below
is printed or displayed.
Consider the following areas on the diffractogram.
A. The diffraction pattern is labelled with the sample name and other information pertinent
to the experiment. This happens to be a pattern of ground calcite from the France Stone
Quarry in Fort Wayne, Indiana. The sample was randomly mounted using the backpack
technique. The diffraction pattern was prepared on March 24, 1993. The diffractometer was
running at 40 kv and 30 ma. Steps were in increments of 0.005 degrees, and counts were
collected for 0.25 seconds at each step. The data were smoothed with a 15-pt (weighted,
moving average) filter.
B. The vertical axis records X-ray intensity. The horizontal axis records angles in degrees 2-
theta. Low angles (large d-spacings) lie to the right.
C. This is one of the X-ray peaks. It happens to be the one with the smallest angle which I
measured as 23.04 degrees. Solving Bragg's Law (with n=1 and wavelength=1.54 ang) we
find that 23.04 degrees 2-theta corresponds to a d-spacing of 3.86 angstrom.
D. This is another peak picked for no special reason. I measured the peak at 39.37 degrees
2-theta. This corresponds to a d-spacing of 2.287 angstrom.
E. This is the largest peak on the pattern. It actually extends several times the height of this
image. Many factors affect the intensity of a given peak. Some of these factors are intrinsic
to the mineral under study; some of these factors are peculiar to the way a specimen is
mounted in the diffractometer. (The random/backpack mounting method limits, but does
not eliminate, these peculiarities).
When solving scientific problems it is often useful to ask three questions: What do I Know?
What can I measure? What do I want to find out?
In Bragg's law:
1. we know lambda (the wavelength) = 1.54 angstrom and we assume n=1.
2. We can measure 2-theta from the diffraction pattern. Divided by 2, these values become
3. That leaves us with an equation with one unknown -d- the d-spacing we want to find out.
Instruments for X-ray absorption, emission, fluorescence, and diffraction are all
similar to other optical spectroscopy instruments. Thus, the basic components will be a
source (X-ray tube, radioisotopes, or secondary fluorescent sources), a filter system (i.e.
monochromators), sample holder, detector/transducer, signal processor, and output device.
Below is the figure of an X-ray monochromator and detector.
X-ray fluorescence (XFR) is one of the most widely used of all analytical methods
for qualitative identification of elements with Z>8. (Skoog, Leary, p. 373) Below is a
diagram of a XFR.
Below is a X-Ray fluorescence spectrum.
X-ray absorption is not too convenient and is relatively awkward and time-
consuming with respect to X-ray fluorescence methods. Also, X-ray absorption tends to
give spectra with lots of peaks; to make this technique useful, absorption is often restricted
to analysis of single, heavy components in a matrix of relatively lighter components. For
example, X-ray absorption is used to determine the amount of lead in gasoline or the
amount of sulfur/halogens in hydrocarbons.
X-ray diffraction is most powerful when used for crystal structure determination.
Structurally complex compounds, such as steroids, vitamins, and antibiotics are being
studied via X-ray diffraction. In addition to natural products, X-ray diffraction is also good
for qualitative identification of crystalline compounds via the X-ray powder diffraction
method. This method is distinct in that it is the only analytical method capable of providing
both qualitative and quantitative information about the components within a solid sample.
X-ray powder diffraction works on the basis that every compound has a unique X-ray
The electron microprobe is an X-ray emission technique that is used to gather
information about the chemical and physical nature of surfaces. It can provide both
qualitative and quantitative information. It works by focusing a narrow beam of electrons
onto a surface, giving rise to X-ray emission; the emitted X-rays are then detected via
wavelength- or energy-dispersive spectrometers and then analyzed.
Figure 1.2: Schematic diagram displaying the key features of a Seyfert 1 X-ray spectrum
(from Fabian 1998b).(eps)
To first order, the X-ray spectra of AGN are power laws of the form S -
with ~ 0.7,
modified by photoelectric absorption at soft energies (Mushotzky 1980, Halpern 1982,
Rothschild et al. 1983). ROSAT and Ginga, sensitive in the ranges 0.1 - 2 and 2 - 30 keV
respectively, revealed a more complicated structure with a softer underlying power law of
~ 0.9. Superimposed on this continuum are a number of features illustrated in figure 1.2. A
strong emission line is seen at a rest frame energy of ~ 6.4 keV (e.g. Pounds et al. 1990).
This is interpreted as fluorescent Fe K emission, but with an equivalent width too great to
be the result of absorbing material in the line of sight (Makishima 1986). The spectra are
seen to harden beyond this feature to form a bump peaking at ~ 30 keV. This can be
explained by a reprocessing (Compton scattering or `reflection') of the X-ray power law
within optically thick material (e.g. George & Fabian 1991). The intensity of this
component is consistent with the reflector subtending a solid angle of 2 (Nandra et
al. 1991), most likely the accretion disc itself. Photoelectric absorption by elements within
the disc result in Compton reflection only becoming dominant beyond the absorption edge
of iron. Beyond the peak at ~ 30 keV the spectrum steepens due to the effects of energy
loss to electron recoil and reduction in the scattering cross-section.
At soft X-ray energies, the power law continuum is often absorbed by ionised material in
the line of sight. This is known as the `warm absorber' and is generally characterised by the
K-shell absorption edges of ionised oxygen which fall within the ROSAT and ASCA
bandpasses. Absorption by cold material is also seen in some objects although these are
usually classified as obscured AGN (see section 1.2). Photoelectric absorption may often
mask the presence of the `soft excess'. Identification of this feature is also hampered by its
position at the bottom of the bandpass for most X-ray telescopes. However, recent XMM-
Newton spectra of a sample of 6 Seyfert I galaxies reveals an excess soft emission
component in each case (Pounds & Reeves 2002).
A final important aspect of AGN high energy spectra is an exponential cut-off at ~ 200 keV
(e.g. Seyfert I galaxy IC 4329a, Madejski et al. 1995). Although the exact energy of this
cut-off is uncertain, no radio-quiet AGN has been detected beyond several hundred keV.
Models for the X-ray spectra of AGN generally attempt to explain the underlying power
law and high energy cut-off, considering the remaining spectral features to be due to the
effects of reprocessing. The majority ascribe the power law to the inverse Compton
scattering of soft photons in a bath of `hot' electrons. Variations in this model depend on the
energy distribution of these electrons and their location in relation to the accretion disc.
In the `non-thermal' model (Zdziarski et al. 1990, Zdziarski & Coppi 1991), electrons are
accelerated to relativistic energies, perhaps due to magnetic reconnection events. Collisions
with photons and other electrons cause a `pair cascade' which then Comptonise UV and
optical photons from the disc. The pairs then thermalise to temperatures of a few keV
resulting in further upscattering of UV photons to form the soft excess. A major problem
with this model is that the pairs should eventually annihilate to produce a strong emission
line at 511 keV. This line has never been observed. It is therefore thought likely that the
scattering electrons have a thermal (`Maxwellian') energy distribution. This would predict a
high energy cut-off (Ec) at Ec/1.6 kTplasma for a Comptonising plasma at temperature Tplasma
(e.g. Pietrini & Krolik 1995).
The geometry of this Comptonising plasma remains uncertain. A simple `sandwich' model
describes a cool, optically thick accretion disc covered by a hot optically thin layer (e.g.
Maraschi & Haardt 1996). A certain fraction (f) of the gravitational energy is dissipated in
the hot corona, with the remainder (1-f) dissipated in the disc. Isotropic Comptonisation
results in half the emission escaping directly from the corona. Of the half which impinges on
the disc, 10 - 20% is reflected to produce the Compton reflection bump and the Fe K
fluorescence line. The remaining 80 - 90% is photoelectrically absorbed and eventually
reemitted as thermal radiation in the `big blue bump'.
Problems with this model geometry arise on attempting to fit the slope of the X-ray spectra.
It is found the fraction, f, needs to be 1 or too many soft `seed' photons will be produced.
This would require the entire optical-UV bump to be reprocessed emission. In reality UV
luminosities appear to be larger than bolometrically corrected X-ray luminosities for Seyfert
galaxies (Walter & Fink 1993). An alternative geometry consists of the `patchy corona'
model. Here the magnetic field releases energy into the corona in discrete active, or flaring
regions (Galeev, Rosner & Vaiana 1979). In these regions f 1 while elsewhere on the disc
f 0 and the primary UV emission is relatively unimpeded. This model is supported by
observations of continuum variability. The reprocessed contribution to the UV bump would
be expected to vary simultaneously with the X-ray, while the primary thermal disc emission
would vary much more slowly. Variations in the optical-UV and medium X-ray on
timescales of weeks to months, have been observed to be well correlated in a number of
AGN (NGC 4151: Warwick et al. 1996, NGC 5548: Tagliaferri et al. 1996). The UV and
X-ray variations are, however, not perfectly correlated as required by the `sandwich' model
These models still do not explain the source of the soft X-ray excess. The emission process
is poorly constrained due to the large gap in the data between the UV and soft X-ray. An
early candidate was the tail end of a multi-temperature thermal accretion disc spectrum, the
cool end of which is the `big blue bump'. However this requires an extremely high
temperature which appears unlikely, even for the inner edge of the disc. In the case of NGC
5548 at least, the soft excess requires an entirely separate spectral component in order to fit
the data (Magdziarz et al. 1998). Other models include blended soft X-ray line emission
(e.g. Turner et al. 1991), or reprocessed Comptonised emission from the surface layers of
the disc. However, none of these models is completely satisfactory. In particular, recent
evidence that variations in the soft excess may lead variations in the medium X-ray band
(Chiang et al. 2000) causes major problems for the reprocessing scenario.
A feature of AGN X-ray spectra that appears to manifest well beyond the accretion disc is
the signature of the `warm absorber'. Absorption edges of O VII at 739 eV and O VIII at
870 eV are found in at least half of all Seyfert Is and a few quasars (Mathur et al. 1994). In
the same objects, UV and optical absorption features are also typically found although the
warm absorber has a higher ionisation state (Crenshaw et al. 1999). In all cases, absorption
features are blue shifted indicating an outflow of material. For the X-ray absorption lines
typical velocities are hundreds to several thousand km s-1
(e.g. Kaastra et al. 2000, Kaspi et
al. 2001, Collinge et al. 2001), considerably slower than the broad-line region clouds. The
warm absorber is thought to be an ionised wind, (perhaps evaporated off the inner edge of a
dusty torus, Krolik & Kriss 2001) which may also be responsible for scattering the nuclear
light in obscured AGN.