Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM)
Background – from Klein and Hurlbut, Manual of Mineralogy, 22nd Edition (1989) and other
sources

History – the discovery of a mysterious new way to observe Mrs. Roentgen’s hand
1895 – Wilhelm Conrad Roentgen, a professor of physics at the University of Freiberg,
Germany, accidentally discovered “X-radiation”. Roentgen was unsuccessful in his efforts to
measure the wavelength of X-rays but he was successful in showing that X-rays penetrate
matter, including human flesh and show density contrasts. He recorded the x-ray image of
his wife’s hand, for example (see below). He was awarded the first Nobel Prize in Physics in
1901 for his discovery of this mysterious new form of highly penetrating radiation.
Wilhelm Conrad Roentgen Mrs. Roentgen’s Hand
A Simple X-ray Diffraction Experiment

1912 – Max von Laue, a professor of physics at the University of Munich in Germany,
suggested to one of his research assistants (Walter Friedrich) and a doctoral student (Paul
Knipping) that they use X-rays in the first diffraction experiment. The crystal used for this
pioneering experiment was copper sulfate. Von Laue’s reasoning was that X-rays have a
wavelength similar to the interatomic distances in crystals, and as a result, the crystal should
act as a 3-D diffraction grating. He was able to demonstrate in a later experiment on
sphalerite (ZnS) that the pattern recorded by Friedrich and Knipping for copper sulfate on
photographic film was due to diffraction of very short wavelength electromagnetic radiation
(about 1.5 Å, where 1Å = 10-8 cm) from a regular arrangement of atoms in the ZnS crystal.
If the interatomic distances in the crystal are known (as they were in cubic ZnS), then the
wavelength of the X-rays can be measured, or alternatively, if the wavelength is known,
diffraction experiments can be used to determine the interplanar spacings of a crystal. Von
Laue, as well as Friedrich and Knipping were awarded Nobel Prizes in Physics for their
discoveries involving X-ray diffraction.

1913 – William H. Bragg and his son William L. Bragg (University of Manchester, England)
determined the first mineral structure (NaCl) from XRD, and also determined the atomiclevel structure of many more minerals including those of pyrite (FeS2), fluorite (CaF2), and
calcite (CaCO3). They also simplified von Laue’s mathematical generalization and
introduced the now famous Bragg equation ( = 2d sin), which describes the condition for
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
diffraction to occur in terms of the wavelength of the x-radiation (), the interplanar (“d”)
spacings of the crystal, and the angle of incidence of the radiation with respect to the crystal
planes (). Father and son Bragg shared the Nobel Prize in Physics for their contributions to
this new field, which became known as x-ray crystallography.
The Electromagnetic Spectrum, generation of X-rays, and the Braggs’ Equation
 Nature of X-rays: X-rays can be thought of as waves with wavelengths on the order of 0.1 Å to
~10 Å. The shorter the wavelength, the more energetic the wave. Because of the relatively
short wavelengths of electromagnetic radiation in the X-ray region, X-rays are high energy
waves and are much more penetrating compared to UV, visible, IR, or radio waves. The
conversion between energy, frequency, and wavelength is the well-known de Broglie
relationship: E = h = hc/, where  is the frequency, h is Planck’s constant (6.62 x 10-34
joule-second), c is the speed of light (2.998 x 108m/sec), and  is the wavelength of the
radiation (in m).

Generation of X-rays: When electrons strike a metal anode with sufficient energy, X-rays are
produced. This process is typically accomplished using a sealed x-ray tube, which consists
of a metal target (often copper metal) and a tungsten metal filament, which can be heated by
passing a current through it (typically 10-15 mA), resulting in the “boiling off” of electrons
from the hot tungsten metal surface. These “hot” electrons are accelerated from the tungsten
filament (negative bias) to the metal target (positive bias) by an applied voltage (typically 1530 kilovolts). The collision between these energetic electrons and electrons in the target
atoms results in electron from target atoms being excited out of their core-level orbitals,
placing the atom in a short-lived excited state. The atom returns to its ground state by having
electrons from lower binding energy levels (i.e. levels further from the nucleus) make
transitions to the empty core levels. The difference in energy between these lower and higher
binding energy levels is radiated in the form of X-rays. This process results in the production
of characteristic X-rays (i.e. X-rays whose energies are unique to the target metal due to the
quantized nature of the electron energy levels of each atom and the unique energies of these
energy levels) [Cu K (L3 to K electronic
transition: E = 8047.78 eV,  = 1.54051 Å), Cu
K (L2 to K electronic transition: E = 8027.83
eV,  = 1.54433 Å), Cu K1 (M3 to K electronic
transition: E = 8905.29 eV,  = 1.39217 Å)]. Thus
X-rays provide a convenient means of
determining what elements are present in a
sample because of the unique wavelengths
produced by each unique element. A lower energy
process that involves the interaction of electrons
with the nucleus of an atom in the target metal
produces a continuum of lower intensity Xradiation over a broad energy range known as
Bremstrahllung. As the voltage on an X-ray tube
is increased, the characteristic line spectra of the
target element are superimposed upon the
continuous spectrum (at right).
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration

X-ray diffraction: Crystals are ordered,
three-dimensional arrangements of
atoms with characteristic periodicities.
As the spacing between atoms is on
the same order as X-ray wavelengths
(1-3 Å), crystals can diffract the
radiation when the diffracted beams
are in-phase. The Bragg equation is
given as n = 2dsin. For a given
wavelength (), diffraction can only
occur at a certain angle () for a given
d-spacing. (Figures from; http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
Diffraction
 Single Crystal (Laue) Diffraction – a beam of X-rays of all
wavelengths is directed at a single crystal, which sits stationary
in front of a photographic plate. A series of diffraction spots
surround the central point of the beam, corresponding to
diffraction from a given series of atomic planes (at right).
 Powder Diffraction – a powder is used to ensure completely
random crystal orientation to get diffraction from all possible
planes. The diffraction pattern can be recorded on a flat
photographic film or on a CRT (cathode ray tube). When the
incident beam satisfies the Bragg condition, a set of planes
forms a cone of diffracted radiation at an angle  to the sample. Since the cone of X-rays
intersects the flat photographic filmstrip in two arcs equally spaced from the direct X-ray
beam, two curved lines will be recorded on the photographic film. The distance of the lines
from the center can be used to determine the angle , which can then be used to determine the
interplanar d spacing. X-ray powder diffractometers record all reflections using a scintillation
detector (in counts per second of X-rays). The pattern of diffracted X-rays is unique for a
particular structure type and can be used as a “fingerprint” to identify the structure type.
Different minerals have different structure types, thus X-ray diffraction is an ideal tool for
identifying different minerals.
Above at left; powder film of (a) spodumene (LiAlSi2O6), (b) aragonite (CaCO3), (c) feldspar
(KAlSi3O8) and (d) alpha-quartz (SiO2). At right, a diffraction pattern from a mixture of
magnetite
and
hematite
using
a
XRD
powder
diffractometer.
(from;
http://spade.ncl.ac.uk/materials/materials/services/xrd.html)
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
Primary Uses
Limitations
X-rays have made it possible to measure the
distance between successive atomic planes and XRD can only work with crystalline materials,
positions of atoms or ions within a crystal, hence glasses and partially crystalline materials
allowing for the determination of crystal cannot be identified using this method.
structure.
Powder XRD can be used to fingerprint Phases that comprise less than about 3-5 wt.%
minerals without any prior knowledge of (depending on crystal symmetry) of a sample
crystal structure or symmetry.
will not be detected using a bench-top XRD.
Relative proportions of mineral mixtures can Mixtures of phases with low symmetry will be
be obtained by comparing diffraction line difficult to differentiate due to the larger
intensity.
number of diffraction peaks.
Example I: Name that biomineral
This sample is from an equine enterolith (an intestinal
stone that was almost fatal for Gordon’s wife’s horse Ripley).
This condition has been found to be particularly common in
California, due to the type of alfalfa the horses eat (Hintz,
2001). Chemical breakdown of the grain causes the usually
acidic environment in the intestinal track to become more
alkaline. This causes salts of magnesium, ammonium, and
phosphate to precipitate, typically nucleating on a foreign
object (such as a piece of plastic, wood, gravel, etc.) (at right).
As precipitation proceeds, the stone can become large enough to block the intestinal track (up to
20 cm in diameter) and become fatal. However, enteroliths can be easily removed with surgery
if detected soon enough. We will attempt to identify the major phase(s) that comprise this
enterolith.
Some questions to consider
How many phases are present? Does the line pattern for struvite account for all pattern
features?
 If you think there is more than one phase, which one dominates the sample?
 Given the composition of the enterolith, how might the enterolith sequester other metals or
molecules? Struvite can also be found clogging wastewater treatment pipes. Think about what
ions could substitute into the mineral structures in the horse’s gut, or in the water pipe.

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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
Example II: Beach Sand – an aquifer analog
Setting: An environmental consulting firm has asked you to characterize the mineralogy of a
groundwater aquifer. There has been a recent industrial spill, and they want to know if metals
like Pb and Cd will be retarded due to mineral surface interactions.
XRD pattern – what do you see?
This pattern looks pretty clean, and the sample may only be comprised of one or two
phases. There is no large amorphous background, so the phases are probably all crystalline.

Fitting – how many phases are present?
When we fit the XRD pattern, the characteristic quartz lines account for all peaks in the
pattern. There are no extra peaks to fit. From the XRD pattern, we might deduce that the sample
is 100% quartz.

Visual Observation – what can you see with your eyes?
Just by looking at the sample, we can see that there is more than quartz in the sand.
Other mineral phases include Fe-oxides, feldspar, mica, and calcite. These phases are likely less
than ~2 wt.% of the bulk sample.

Some questions to consider
 Why do you think the XRD pattern only showed the quartz peaks?

Are these other phases significant? What is the difference in reporting that the aquifer is 100%
versus 99% quartz?

Do the other phases behave differently versus quartz with respect to surface sorption of metals?

What other techniques might you use to better characterize this sample?

If you were interested in a different problem, like flow dynamics, would XRD have been
sufficient enough to determine the mineralogy?
Conclusions
XRD is a very powerful determinative method in the mineral and materials sciences.
There are some limitations, but X-ray diffraction can also be a very straightforward and easy to
use method to determine the identity of minerals. Some finals questions to ponder:

How well does XRD characterize the chemical nature of a sample?

Did we learn enough from the XRD patterns alone to understand the mineralogy that
dominates reactivity with the enterolith, or the sand?

XRD is nearly 100 years old, and still not “out of style”. What would you do to try and
improve the technique?
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
XRD patterns
Example 1 – equine enterolith
Example 2 – beach sand
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
Scanning Electron Microscopy (SEM) Background
Good Reference: J.I. Goldstein, D.E. Newbury, D.C. Joy, C.E. Lyman, P. Echlin, E.
Lifshin, L.C. Sawyer, and J.R. Michael (2003) Scanning Electron Microscopy and X-ray
Microanalysis, 3rd Ed., Springer: New York, 689 p.
The scanning electron microscope (SEM) “sees” low kinetic energy secondary electrons
from solid surfaces. When an electron beam interacts with a solid, various types of elastic and
inelastic processes occur, including electron scattering and excitation, which produces (1)
secondary electrons, (2) backscattered electrons, (3) Auger electrons, (4) characteristic x-rays,
(5) bremsstrahlung or continuous x-rays, and (6) photons of various energies, including those in
the infrared, visible, and ultraviolet. The fraction of energy deposited by an electron beam in a
sample associated with these different processes is dependent on the sample. Secondary and
Auger electrons can only be observed when they come from the near-surface region of a solid
(typically < 500 Å for insulators, such as silicate minerals, and < 100 Å for metals such as gold).
Thus, measurements involving these types of electrons are “surface sensitive”. The reason for
the greater escape depth of secondary electron from insulators relative to metals is that inelastic
scattering of secondary electron takes place mainly through interactions with conduction-band
electrons, which are abundant in metals and significantly less abundant in insulators. Secondary
electrons are generated by the primary electron beam as it enters a sample as well as by
backscattered electrons as they exit a sample. Secondary electrons, which typically have kinetic
energies < 50 eV, are sensitive enough to differences in surface topology that they can be readily
observed from the surface of a sample. Such electrons form the basis of scanning electron
microscopy. In order to enhance the number of secondary electrons from an insulating sample,
the sample is often coated with a thin layer of gold-palladium alloy or another electron-rich
conducting material that produces abundant secondary electrons when struck by a focused
electron beam. A thin metal coating will not mask surface features or the overall topology of the
underlying sample. The gold-palladium coating also conducts electrons away, so that the sample
does not develop a significant charge when it loses secondary electrons and other types of
electrons. This type of coating is essential for insulator samples, which don’t conduct charged
particles. Such samples, if uncoated, would be difficult to image using an SEM because of the
fact that they would develop a negative charge (due to build-up of electrons), which would cause
the image to become defocused due to deflection of the exciting electron beam.
Several figures on the next page show secondary and backscattered electron energy
distributions and their paths in solids as well as a schematic of a typical SEM.
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
SEM Images of meteoritic orthopyroxene surface which has been populated by a filamentous
microorganism. A blow-up of a portion of the surface shows rod-shaped calcite crystals, which
were originally incorrectly interpreted as nanobacteria. They are instead nano-crystals of calcite.
(from Benzerara et al., 2005).
mm m
SEM image of Acidothiobacillus ferrooxidans on a pyrite surface, showing ferrihydrite
precipitate to mthe right and an oxidation rim, which is shown in close-up on the next page.
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Stanford EMSI Science Teachers Workshop – July 2006: XRD Tutorial and Demonstration
SEM lose-up of oxidation rim around A. ferrooxidans showing goethite crystals (smooth laths)
and schwertmannite crystals (clusters). The goethite crystals are about 200 nm long.
2 m
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