SCA 302: INSTRUMENTAL METHODS OF ANALYSIS II
COURSE OUTLINE
1. MASS SPECTROMETRY




Principles involved in the use of electric and magnetic fields for mass analysis
Ionization methods
Applications of mass spectrometric analysis in identification and quantitation of chemical
compounds
Theory, practice, instrumentation, quantitation and characterization
2. RADIOCHEMICAL METHODS OF ANALYSIS



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
Fundamental concepts of radiochemistry
Principles of radioactive decay processes and counting techniques
In-depth treatment of radio-analytical techniques especially Neutron Activation and
Isotope Dilution Methods
Decay processes as sources of X-rays
The use of synchrotron radiation in analytical chemistry
3. PRINCIPLE, THEORY AND APPLICATIONS OF X-RAY PHOTOELECTRON,
AUGER ELECTRON AND ELECTRON SPIN RESONANCE SPECTROSCOPIC
TECHNIQUES (ESCA)
4. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY



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
Magnetic properties of 1H, 13C, 19F, 31P
Radiofrequency radiation
Nuclear Magnetic Resonance spectrometer
Chemical shift
Low and high-resolution NMR spectra
Deuterium exchange in NMR
Combined techniques in identification and structural determination
Confirmation of a structure
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MASS SPECTROMETRY
Mass spectrometry provides qualitative and quantitative information about the atomic and
molecular composition of inorganic and organic materials.
The mass spectrometer produces charged particles that consist of the parent ion and ionic
fragments of the original molecule, and it sorts these ions according to their mass to charge ratio
(m/e or m/z). The mass spectrum is a record of the relative numbers (abundance) of different
kinds of ions and is characteristic of every compound, including isomers.
High resolution mass spectrometry can provide the elemental composition of the molecular and
fragment ions.
Mass spectrometry can be used together with data from IR, UV-Vis and NMR spectra to arrive at
a definite identification or structure assignment of compounds. Advantages of mass spectrometry
are:

Increased sensitivity over most other analytical techniques and

Specificity in identifying unknowns or confirming the presence of suspected compounds
Sensitivity: Sample size requirements for solids and liquids range from a few milligrams to
subnanogram quantities as long as the material can exist in the gaseous state at the temperature
and pressure in the ion source.
The excellent specificity results from characteristic fragmentation patterns, which can give
information about molecular weight and molecular structure.
Mass spectrometry has also contributed to a more detailed understanding of kinetics and
mechanisms of unimolecular decomposition of molecules.
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SAMPLE FLOW IN A MASS SPECTROMETER
All mass spectrometers perform 3 basic tasks:
(i) Creating gaseous ion fragments from the sample
(ii) Separating these ions according to mass (mass/charge ratio)
(iii) Measuring the relative abundance of ion fragments of each mass
Volatile and gaseous samples enter the ionization chamber (ion source) through a “leak”. Once
formed, ions are sorted into discrete mass/energy arrays based on 3 properties that can be
determined with relative ease: energy, momentum and velocity. A measurement of any two of
these allows m/e ratio to be determined. For many years energy and momentum was used.
The operation of the spectrometer requires a collision-free path for the ions. To achieve this, the
pressure in the spectrometer should be less than 10-6 torr.
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SAMPLE INLET SYSTEM
Gas samples
Introduction of gases involves transfer of the sample from small containers of known volumes
(approx. 3 ml) coupled to a Hg manometer. The sample is then expanded into a reservoir (3 – 5
Litres) immediately ahead of the sample “leak”.
Liquids
Are introduced in various ways:
1. Break-off devices
2. By touching a micropipette to a sintered glass disk under a layer of molten gallium
3. By hypodermic needle injection through a silicone rubber septum. The low pressure in
the reservoir draws in the liquid and vaporizes it instantly.
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Solids
Solids with very low vapour pressure can be introduced directly into an entrance to the ionization
chamber on a silica or platinum probe and then volatilized by gently heating the probe until
sufficient vapour pressure is attained (indicated by appearance of a spectrum).
Often a simple chemical reaction is enough to convert a non-volatile compound into a derivative
that still retains all the important structural features but now has sufficient vapour pressure (or is
volatilizable).
Heated inlet systems
These extend the usefulness of mass spectrometry to polar materials, which tend to be adsorbed
on the walls of the chambers at room temperature, and also to less volatile compounds.
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The Molecular Leak
From the inlet system the gases diffuse through a molecular leak into the ion source. The leak is
a pin-hole restriction about 0.013 – 0.050 mm in diameter in a gold foil.
The preferred type of flow into the ion source depends on the purpose for which the instrument is
intended:


For analytical work:- conditions for molecular flow are usually used in which collisions
between molecules and the walls are much more frequent than collisions between
molecules themselves.
For isotope studies:- viscous flow is preferred in which a gas molecule is more likely to
collide with other gas molecules than with the surfaces of the container; thus, there is no
tendency for various components to flow differently from the others and adversely affect
the relative concentrations of an isotope cluster.
Viscous flow occurs when the mean free path is smaller than the tube diameter and the molecular
flow when it is greater than the tube diameter.
IONIZATION METHODS IN MASS SPECTROMETRY
•
There are two different kinds of ion sources, the hard ion sources and the soft ion
sources.
•
The hard ion sources leave excess energy in a molecule which leads to extensive
fragmentation.
•
Soft ion sources leave little excess energy in a molecule which leads to reduced
fragmentation.
•
They are also divided into gas-phase ionization techniques and desorption techniques.
•
Gas-phase techniques deal with substances that are volatile and volatilizable. The sample
is vaporized outside the ion source and then ionization done in the gas phase using
unimolecular (electron impact ionization and field ionization) or bimolecular (chemical
ionization) methods.
•
Desorption techniques include field desorption, fast atom or ion bombardments and laser
desorption.
•
In these techniques ions are formed from samples in the condensed phase inside the ion
source
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•
Ion sources have the dual function of producing ions without mass discrimination from
the sample and accelerating them into the mass analyzer with a small spread of kinetic
energies prior to acceleration.
ELECTRON IMPACT IONIZATION
The electron impact ion source is the most commonly used and highly developed ionization
method.
Once out of the molecular leak, the neutral molecules enter a chamber that is maintained at a
pressure of 0.005 torr and a temperature of 200 ± 0.25 0C. An electron gun (filament) is located
perpendicular to the incoming gas stream. Electrons emitted from a glowing filament (Rherium,
Thoriated Iridium, or carbonized tungsten) are drawn off by a pair of positively charged slits
through which the electrons pass into the body of the chamber. An electric field maintained
between these slits accelerates the electrons. The ionizing electrons from the cathode are formed
into a tight helical beam by a small magnetic field, in the order of 100 Gauss, which is confined
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in the ionization region. The number of electrons is controlled by the filament temperature,
whereas the energy of the electrons is controlled by the filament potential.
Ions are formed by the exchange of energy during the collision of the electron beam and sample
molecules. The product is a molecular ion in a high state of electronic and vibrational excitation.
The filament potential is variable. A range of 6 – 14 V is used in molecular weight determination
when it is desirable to avoid fragmentation. An ion source operating at 70 V, the conventional
operating potential, provides sufficient energy to ionize and cause the characteristic
fragmentation of sample molecules. Fragmentation provides positive identification of an
unknown.
The positive ions formed in the ionization chamber are drawn out by a small electric field
between the large repeller plate (charged positive) behind them and the first accelerating slit
(charged negative). A strong electrostatic field between the first and second accelerating slits of
400-4000V accelerates the ions of masses m1, m2, m3 etc to their final velocities. The ions
emerge from the final accelerating slit as a collimated ribbon of ions with velocities and kinetic
energies given by
𝑧𝑉 =
1
1
1
𝑚1 𝑣12 = 𝑚2 𝑣22 = 𝑚3 𝑣32 … … ..
2
2
2
Where z is the charge of the ion. Many compounds do not give a molecular ion in an electron
impact source because of the excess ionization energy imparted to the molecule during the
ionization step. This can be considered as a disadvantage of this source.
CHEMICAL IONIZATION
This results from ion-molecule chemical interactions involving a small amount of sample with an
extremely large amount of a reagent gas.
Positive Chemical Ionization
A two part process occurs. In the first step a reagent gas is ionized by electron impact ionization
in the source:
CH4 + e8|Page
CH4+ + 2e- (CH+3, CH2+….)
The electrons energy must be 200 – 500 V to ensure penetration into the active volume. This is
followed by reaction of the primary ion with additional reagent gas molecules to produce a
stabilized reagent ion plasma.
The second part of the chemical ionization process occurs when a reagent ion (CH5+ or C2H5+)
encounters a sample molecule (MH). The reagent ion and sample molecule will react through
any of the following:
Proton transfer: CH5+ + MH
Hydride abstraction: CH3+ + MH
Charge transfer: CH4+ + MH
CH4 + MH2+
CH4 + M+
CH4 + MH+
Negative Chemical Ionization
Typical negative ion-forming reactions are:
[Resonance capture of electron] M + e[Dissociative capture of electron] RCl + eH2O + e-
MR. + Cl-
H. + OH-
Ion-molecule reactions also occur between negative ions formed in the ion source and neutral
sample molecules. The reactions include: charge transfer, hydride transfer and anion-molecule
adduct formation.
The reactions of the hydroxide ion are mimicked by methoxide and amide reagents.
Fluorocarbons produce the fluoride ion.
Reagent Gases
Different gases are specific for certain functional groups and provide excellent control of sample
ion fragmentation.
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When the interest is primarily to determine the molecular weight of a compound or to confirm it
as one of a small set of compounds, a low energy reactant , such as tert – C4H9+ (from isobutane) is frequently used. An even weaker protonating agent such as NH 4+ generates (M + H)+
and (M + NH4)+ ions, useful in characterizing polyhydroxy compounds like sugars.
Deuterium oxide is used to determine the presence of active hydrogen.
Oxygen and hydrogen are used as reagent gases in negative chemical ionization mass
spectrometry.
Competition between localized chemical ionization induced reactions at various sites in a
molecule produces structural information that is often absent from the electron impact spectrum
e.g. with NO as the reagent gas, alcohols give ions at (M – 17), but only primary and secondary
alcohols give additional ions at (M -1) and (M + 30 – 2).
Argon, Helium and Nitrogen, as reagent gases produce fragmentation patterns essentially
identical to electron impact ionization but with increased sensitivity.
Helium because of its use as a carrier gas in gas-liquid chromatography, has been used as a
reagent gas for charge exchange reactions.
FIELD IONIZATION AND FIELD DESORPTION
The unique properties of a field ionization source arise from the behavior of chemical
compounds under high potential fields. When a molecule is brought between two closely spaced
electrodes in the presence of a high electric field (107 – 108 Vcm-1), it experiences an
electrostatic force and if the metal surface (anode) has the proper geometry, either a sharp tip or
tips (or a thin wire) and under high vacuum (10-6 torr), this force can be sufficient to remove an
electron from the molecule without imparting much excess energy. In the absence of electron
collisions there is little or no fragmentation of the ion. However sensitivities are below those of
electron-impact ionization.
In construction a thin needle of a few micrometers diameter constitutes the anode which is
located 1 mm away and immediately behind the exit slit of the ion chamber. The exit slit serves
as the cathode and opposite field forming member. The remainder of the source consists of the
focusing slits common to all ion sources.
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Field desorption
This is a variant of field ionization. In field desorption an activated field ionization emitter wire
is dipped into or has deposited on it a solution of the sample under study. The emitter wire is
then gradually heated with an electric current while it is at the high voltage field ionization
conditions.
Field desorption is a valuable technique for studying surface phenomena, such as adsorbed
species and trapped samples, and the results of chemical reactions on surfaces. Due to the nonhomogeneity of the micro-needle (or wire) size and directional orientation, the surface ions
generated during the field desorption possess an energy distribution and thus spread over a small
angle. This necessitates refocusing of the mass spectrometer after repetitive scans for good field
desorption spectra.
THERMAL (SURFACE) IONIZATION
The thermal or surface ionization source is useful for inorganic solid materials. Samples are
coated on a tungsten ribbon filament and then heated until they evaporate. When an atom or
molecule is evaporated from a surface (at approx. 2000oC) it has a certain probability of being
evaporated as a positive ion. This probability is predictableand is a function of the ionization
potential, εi of the sample and the work function , ϕ, of the filament material. The relationship for
the ratio of ions n+, to neutral species, no, is given by the Langmuir-Saha equation:
𝑛+
𝑒(∅ − 𝜀𝑖 )
=
exp
[
]
𝑛𝑜
𝑘𝑇
Where e = electronic charge.
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This technique is appropriate for inorganic compounds that generally have low ionization
potentials (3 – 6 eV). Surface ionization is especially useful in determining isotope ratios in
inorganic compounds. The advantage of this method is that no ionization of the background
gases in the mass spectrometer occurs.
However, surface ionization is inefficient for organic compounds whose ionization potentials
usually lie in the range from 7 to 16 eV. The energy spread of the ions is small, thus a single
focusing mass spectrometer is needed.
Other types of ionization include:



Ionization by particle bombardment (Fast Atom Bombardment and Secondary ion Mass
Spectroscopy)
Electrospray ionization (ESI)
Matrix-Assisted Laser Desorption Ionization (MALDI)
MASS ANALYSERS (IN MASS SPECTROMETRY)
Several devices are available for separating ions with different mass-to-charge ratios.
The capability of a mass spectrometer to differentiate between masses is usually stated in terms
of its resolution, R, defined as:
𝑅 = 𝑚⁄∆𝑚
Δm is the mass difference between two adjacent peaks that are just resolved.
m= nominal mass of the first peak (the mean mass of the two peaks is sometimes used instead)
Two peaks are considered to be separated if the height of the valley between them is no more
than a given fraction of their height (often 10%). Thus a spectrometer with a resolution of 4000
would resolve peaks occurring at m/z values of 400.0 and 400.1 (or 40.00 and 40.01).
The resolution needed in a mass spectrometer depends greatly upon its applications e.g
discrimination among ions of the same nominal mass such as C2H4+, CH2N+, N2+, and CO+ (all
ions of nominal mass 28 but exact masses of 28.0313, 28.0187, 28.0061, and 27.9949
respectively) requires an instrument with a resolution of several thousand. On the other hand,
low-molecular weight ions differing by a unit mass or more NH3+ (m = 17) and CH4+ (m = 16),
for example can be distinguished with an instrument having a resolution smaller than 50.
Commercial spectrometers are available with resolutions ranging from about 500 to 500,000.
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Example
What resolution is needed to separate C2H4 + (28.0187) and CH2N + (28.0313)
Δm = 28.0313 – 28.0187 = 0.0126
R = m/Δm = 28.025/0.0126 = 2.22 × 103
28.025 is the mean mass of the two species.
MAGNETIC SECTOR ANALYZER
These analyzers employ a permanent magnet or an electromagnet to cause the beam from the ion
source to travel in a circular path (most commonly of 180, 90, or 60 degrees).
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The figure above shows a 90 degree sector instrument in which ions formed by electron impact
are accelerated through slit B into the metal analyser tube, which is maintained at an internal
pressure of about 10-7 torr.
Ions of different mass can be scanned across the exit slit by varying the field strength of the
magnet or the accelerating potential between slits A and B. The ions passing through the exit slit
fall on a collector electrode, resulting in an ion current that is amplified and recorded. The kinetic
energy (K.E) of an ion of mass, m, bearing a charge z, upon exiting slit B is given by:
……….. (1)
V = voltage between A and B.
v = velocity of the ion after acceleration (m/s)
e = electronic charge, 1.60 × 10-19 C. (C = coulombs)
It is assumed that all ions having the same number of charges z, have the same kinetic energy
after acceleration regardless of their mass. Because all ions leaving the slit have approximately
the same kinetic energy, the heavier ions must travel through the magnetic sector at lower
velocities. The path in the sector described by ions of a given mass and charge represents a
balance between two forces acting upon them; the magnetic force (FM) and the centripetal force
(FC).
FC
FM
ION
The magnetic force is given by:
FM = Bzeν……… (2)
B = magnetic field strength
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And the centripetal force is given by:
FC =
𝑚𝜈 2
………. (3)
𝑟
r = radius of curvature of the magnetic sector.
In order for an ion to traverse the circular path to the collector, FM and FC must be equal.
Equating FM and FC gives:
𝐵𝑧𝑒𝜈 =
𝑚𝜈 2
𝑟
…… (4)
Which can be rearranged to give:
𝜈=
𝐵𝑧𝑒𝑟
𝑚
…….. (5)
Substituting equation 5 to equation 1 gives:
𝑚
𝑧
=
𝐵2 𝑟 2 𝑒
2𝑉
…….. (6)
Equation 6 reveals that mass spectra can be acquired by varying one of the three variables (B, V,
or r) while holding the other 2 constants.
Most modern sector mass spectrometers contain an electromagnet in which ions are sorted by
holding V and r constant while varying the current in the magnet and thus B. in sector
spectrometers that use photographic recording, B and V are constant, and r is the variable.
Example
What accelerating potential will be required to direct a singly charged water molecule through
the exit slit of a magnetic mass spectrometer if the magnet has a field strength of 0.240 T (tesla)
and the radius of curvature of the ion through the magnetic field is 12.7 cm?
NOTE: First we convert all experimental variables into SI units.
Charge per ion ez = 1.60 × 10-19 C × 1
Radius r = 0.127 m
18.02 g H2O+/mol
Mass, m = 6.02 ×1023 𝐻2𝑂+/𝑚𝑜𝑙 ×
𝐾𝑔
𝑔
= 2.99 × 10-26 Kg H2O+
Magnetic field B = 0.240 T = 0.240 W/m2
Accelerating potential V is:
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𝐵 2 𝑟 2 𝑟𝑧
𝑉=
2𝑚
= [0.240 W/m2]2 [0.127 m]2 [1.60 × 10-19 C]/ 2 × 2.99 × 10-26 Kg
= 2.49 × 103 W2C/m2Kg = 2.49 × 103 V
W2C/m2Kg and volts are equivalent.
DOUBLE-FOCUSING SPECTROMETERS
The magnetic sector analysers are sometimes called single-focusing spectrometers. It’s called
single-focusing because a collection of ions exiting the source with the same mass-to-charge
ratio but a small diverging directional distribution will be acted upon by the magnetic field in
such a way that a converging directional distribution is produced as the ions leave the field. The
ability of a magnetic field to bring ions with different directional orientations to focus means that
the distribution of translational energies (kinetic energies) of ions leaving the source is the factor
most responsible for limiting the resolution of magnetic sector instruments (R ≤ 2000).
The kinetic energy distribution of ions leaving a source arises from the Boltzmann distribution of
energies of the molecules from which the ions are formed and from field inhomogeneities in the
source.
The spread of kinetic energies causes a broadening of the beam reaching the transducer
(detector) and thus a loss of resolution. In order to measure atomic and molecular masses with a
precision of a few parts per million, it is necessary to design instruments that correct for both the
directional distribution and energy distribution of the ions leaving the source. The term doublefocusing is applied to mass spectrometers in which the directional aberrations and energy
aberrations of a population of ions are simultaneously minimized.
Double-focusing is usually achieved by the use of carefully selected combinations of
electrostatic and magnetic fields. In the double-focusing instrument, the ion beam is first passed
through an electrostatic analyser (ESA) consisting of two smooth curved metallic plates across
which a dc potential is applied. This potential has the effect of limiting the kinetic enrgy of the
ions reaching the magnetic sector to a closely defined range. Ions with energies greater than
average strike the upper side of the ESA slit and are lost to ground. Ions with energies less than
average strike the lower side of the ESA slit and are thus removed.
Directional focusing in the magnetic sector occurs along the focal plane d, energy focusing takes
place along the plane labeled e. thus only ions of one m/z are double focused at the intersection
of d and e, for any given accelerating voltage and magnetic field strength. Therefore the collector
slit is located at this locus of double focus.
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Nier-Johnson design of a double-focusing mass spectrometer
QUADRUPOLE MASS SPECTROMETERS
This is the most common type of mass spectrometer used in atomic mass spectrometry. The
instrument is more compact, less expensive and more rugged than most other types of mass
spectrometers. It also has the advantage of high scan rates so that an entire mass spectrum can be
obtained in less than 100 ms.
The heart of a quadrupole instrument is the four parallel cylindrical rods that serve as electrodes.
Opposite rods are connected electrically, one pair being attached to the positive side of a variable
dc source and the other pair to the negative terminal. In addition, variable radiofrequency ac
potentials, which are 180 degrees out of phase are applied to each pair of rods. In order to obtain
a mass spectrum with this device, ions are accelerated into the space between the rods by a
potential of 5 to 10 V. Meanwhile, the ac and dc voltages on the rods are increased
simultaneously while maintaining their ratio constant. At any given moment, all of the ions
except those having a certain m/z value strike the rods and are converted to neutral molecules.
Thus only ions having a limited range of m/z values reach the transducer.
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A quadrupole Mass Spectrometer
TIME-OF-FLIGHT (TOF) MASS ANALYZERS
In TOF instruments, positive ions are produced periodically by bombardment of the sample with
brief pulses of electrons, secondary ions, or laser generated photons. The ions produced in this
way are then accelerated into a field free drift tube by an electric field pulse of 103 to 104 V.
Separation of ions on the basis of mass occurs during the transit of the ions to the detector
located at the end of the tube. Because all ions entering the tube have the same kinetic energy,
their velocities in the tube vary inversely with their masses:
𝐾𝐸 =
1
𝑚𝑣 2
2
With the lighter particles arriving at the detector earlier than the heavier ones. Typical flight
times are 1 to 30 µs. advantages of TOF instruments over other types of mass spectrometers
include simplicity and ruggedness, ease of accessibility of the ion source and virtually unlimited
mass range. However, they suffer from limited resolution and sensitivity.
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ION COLLECTION SYSTEMS
Resolved ion beams, after passage through a mass analyzer, sequentially strike a detector.
Several detectors are available. The Electron multiplier is the most commonly used.
The Faraday Cup Collector
This provides a simple and effective means of monitoring ion current in the focal plane of the
mass spectrometer. It consists of a cup with suitable suppressor electrodes and guard electrodes.
Currents as low as 10-15 A may be detected.
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Ions travelling at high speed strike the inside of the metal (Faraday) cup and cause secondary
electron to be ejected. This production of electrons constitutes a temporary flow of electric
current until the electrons have been recaptured. The Faraday cup detector is simple and robust
and is used in situations in which high sensitivity is not required.
Electron Multiplier
For ion currents below 10 -15, an electron multiplier is necessary. An incident ion beam causes
two electrons to be emitted from the first dynode. These electrons are accelerated to the second
dynode where each causes two more electrons (four in all) to be ejected. These in turn are
accelerated to a third dynode and so on, eventually reaching, say, a tenth dynode, by which time
the initial 2 electrons have become a shower of 29 electrons.
Other types of detectors include: the scintillator, the channel electron multiplier and the
photographic plate.
APPLICATIONS OF MOLECULAR MASS SPECTROMETRY
Identification of pure compounds
The mass spectrum of a pure compound provides several kinds of data that are useful for its
identification. First is the molecular weight of the compound and second is the molecular
formula. In addition, study of fragmentation patterns revealed by the mass spectrum often
provides information about the presence or absence of various functional groups. Finally, the
actual identity of a compound can often be established by comparing its mass spectrum with
those of known compounds until a close match is realized.
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Molecular Weights from Mass Spectra
For compounds that can be ionized to give a molecular ion or a protonated or a deprotonated
molecular ion by one of the methods described earlier, the mass spectrometer is an unsurpassed
tool for the determination of molecular weight. This determination, requires the identification of
the molecular ion peak, or in some cases, the (M +1)+ or the (M – 1)+ peak. The location of the
peak on the abscissa then gives the molecular weight with an accuracy that cannot be realized
easily by any other method.
A mass spectrometric molecular weight determination requires the sure knowledge of the
identity of the molecular ion peak. Caution is therefore always advisable, particularly with
electron impact sources, where the molecular ion peak may be absent or small relative to
impurity peaks. When there is doubt, additional spectra by chemical, field and desorption
ionization are particularly useful.
Molecular Formulas from Exact Molecular Weights
Molecular formulas can be determined from the mass spectrum of a compound, provided the
molecular ion peak can be identified and its exact mass determined. However, this requires a
high resolution instrument capable of detecting mass differences of a few thousandths of a
mass unit. Tables that list all reasonable combinations of C, H, N, and O by molecular weight to
the third or fourth decimal place have been compiled.
For example, the mass-to-charge ratios of the molecular ions of the following compounds:
Purine, C5H4N4 (m = 120.044)
Benzamidine, C7H8N2 (m = 120.069)
Ethyl toluene, C9H12 (m = 120.096)
Acetophenone, C8H8O (m = 120.058)
If the measured mass of the molecular ion peak is 120.070 (± 0.005), then all but benzamidine
are excluded as passable formulas.
Molecular Formulas from Isotopic Ratios
The data from a low-resolution instrument that can only discriminate between ions differing in
mass by whole mass numbers can also yield useful information about the formula of a
compound, provided only that the molecular ion peak is sufficiently intense that its height and
the heights of the (M + 1)+ and (M + 2)+ isotopic peaks can be determined accurately.
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Example
Calculate the ratios of the (M + 1)+ to M+ peak heights for the following two compounds:
dinitrobenzene, C6H4N2O4 (m = 168), and an olefin, C12H24 (m = 168).
Referring to table 20.3, for every 100 12C atoms there are 1.08 13C atoms. Because there are six C
atoms in dinitrobenzene, we would expect there to be 6.48 = 6 × 1.08 molecules of nitrobenzene
having one 13C atom for every 100 molecules having none. Thus, from this effect alone the (M +
1)+ peak will be 6.48% of the M+ peak. The isotopes of the other elements also contribute to this
peak; we may tabulate their effects as follows:
C6H4N2O4
13
C
H
15
N
17
O
2
6 × 1.08
4 × 0.015
2 × 0.37
4 × 0.04
(M + 1)+ / M+
6.48%
0.060%
0.74%
0.16%
7.44%
C12H24
13
2
C
H
12 × 1.08
24 × 0.015
(M + 1)+ / M+
12.96%
0.36
13.32%
Thus if the height of the M+ and (M + 1)+ peaks can be measured, it is possible to discriminate
between these two compounds that have identical whole number molecular weights.
If a reasonably accurate experimental determination of the percentages can be made, a likely
formula can be deduced. E.g a molecular ion peak at mass 84 with (M + 1)+ and (M + 2)+ values
of 5.6 and 0.3% of M+ suggests a compound having the formula C5H8O.
The isotopic ratio is particularly useful for the detection and estimation of the number of sulphur,
chlorine and bromine atoms in a molecule because of the large contribution they make to the (M
+ 2)+ peak. For example, an (M + 2)+ peak that is about 65% of the M+ peak is string evidence
for a molecule containing 2 chlorine atoms; an (M+2)+ peak of 4% on the other hand, suggests
the presence of 1 atom of sulphur.
Structural Information from Fragmentation Patterns
Systematic studies of fragmentation for pure substances have led to rational guidelines to predict
fragmentation mechanisms and a series of general rules that are helpful in interpreting spectra. It
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is seldom possible to account for all of the peaks in the spectrum. Instead characteristic patterns
of fragmentation are sought. E.g (Figure 20.22)
The spectrum is characterized by clusters of peaks differing by 14. Such a pattern is typical of
straight chain parafins, in which cleavage of adjacent C-C bonds results in the loss of successive
CH2 groups having this mass. Quite generally, the most stable hydrocarbon fragments contain 3
or four carbon atoms and the corresponding peaks are thus the largest.
Alcohols usually have a very weak or non-existent molecular ion peak but often lose water to
give a strong peak at (M – 18)+. Cleavage of the C-C bond next to an oxygen is also common,
and primary alcohols always have a strong peak at mass 31, due to the CH2OH+.
Quantitative Applications of Mass Spectrometry
Applications of mass spectrometry for quantitative analyses fall into 2 categories:
1. The first involves the quantitative determination of molecular species or types of
molecular species in organic, biological and occasionally inorganic samples.
2. The second involves the determination of the concentration of elements in inorganic and
less commonly, organic and biological samples.
Quantitative Determination of Molecular Species
Mass spectrometry has been widely applied to the quantitative determination of one or more
components of complex organic (and sometimes inorganic) systems such as those encountered in
the petroleum and pharmaceutical industries and in studies of environmental problems.
Such analyses are usually performed by passage of the sample through a chromatographic of
capillary electrophoretic column and into the spectrometer. With the spectrometer set at a
suitable m/z value, the ion current is then recorded as a function of time. This technique is
termed selected ion monitoring (SIM). In some instances, currents at 3 or 4 m/z values are
monitored in a cyclic manner by rapid switching from one peak to another. The plot of the data
consists of a series of peaks with each appearing at a time that is characteristic of one of the
several components of the sample that yields ions of the chosen value or values for m/z.
The areas under the peaks are directly proportional to the concentrations and thus serve as the
analytical parameter.
In the second type of quantitative mass spectrometry for molecular species, analyte
concentrations are obtained directly from the heights of the mass spectral peaks. For simple
mixtures, it is sometimes possible to find peaks at unique m/z values for each component. Under
these circumstances, calibration curves of peak heights vs concentration can be prepared and
used for analysis of unknowns.
23 | P a g e
More accurate results can ordinarily be realized, however, by incorporating a fixed amount of an
internal standard substance, in both samples and calibration standards.
The ratio of the peak intensity of the analyte species to that of the internal standard is then
plotted as a function of analyte concentration. The internal standard tends to reduce uncertainties
arising in sample preparation and introduction.
24 | P a g e
RADIOCHEMICAL METHODS OF ANALYSIS
The availability of both natural and artificial radioactive isotopes has made possible the
development of analytical methods (radiochemical methods) that are both sensitive and specific.
These procedures are often characterized by good accuracy and widespread applicability; in
addition, some minimize or eliminate chemical separations that are required in other analytical
methods.
Radiochemical methods are of three types based upon the origin of the radioactivity.
Activation Analysis: in this activity is induced in one or more elements of the sample by
irradiation with suitable radiation or particles (most commonly thermal neutrons from a nuclear
reactor), the resulting radioactivity is then measured.
In the second category are methods in which the radioactivity is physically introduced into the
sample by adding a measured amount of a radioactive species called a tracer. The most
important class of quantitative methods based upon introduction of radioactive species are
isotope dilution methods in which a weighed quantity of radioactively tagged analyte having a
known activity is added to a measured amount of the sample. After thorough mixing to assure
homogeneity, a fraction of the component of interest is isolated and purified; the analysis is then
based upon the activity of this isolated fraction.
In addition organic chemists often utilize reagents that have been labeled with radioactive tracers
inorder to elucidate reaction mechanisms.
The third class of methods involves measurement of radioactivity that is naturally occurring in a
sample. Examples of this type of method are the measurement of Radon in household air and
Uranium in pottery and ceramic materials.
Radioactive Isotopes
All atomic nuclei are made up of a collection of protons and neutrons, except the hydrogen
nucleus which consists of a proton only.
The chemical properties of an atom are determined by its atomic number Z, which is the number
of protons in its nucleus. The sum of the number of neutrons and protons in a nucleus is the mass
number A. isotopes of elements are atoms having the same atomic number but different mass
numbers i.e the nuclei of isotopes of an element contain the same number of protons but different
number of neutrons.
Stable isotopes are those that have never been observed to decay spontaneously. Radioactive
isotopes (radionuclides) on the other hand undergo spontaneous disintegration, which ultimately
leads to stable isotopes. The disintegration or radioactive decay of isotopes occurs with the
25 | P a g e
emission of electromagnetic radiation in form of X-rays or gamma-rays (γ-rays); with formation
of electrons, positrons and the helium nucleus; or by fission in which a nucleus breaks up into
smaller nuclei.
Radioactive decay products
Product
Alpha particle
Beta particles:
Negatron
Positron
Gamma ray
X –ray
Neutron
Neutrino
Symbol
α
Charge
+2
Mass number
4
βΒ+
γ
Χ
η
ν
-1
+1
0
0
0
0
1/1840 ~ 0
1/1840 ~ 0
0
0
1
0
The table above gives the most important types of radiation from radioactive decay. Four of
these types – α –particles, β – particles, γ-ray photons and X-ray photons can be detected and
counted. Thus most radiochemical methods of analysis are based upon counting of pulses of
electricity produced when these decay particles or photons strike a radiation detector.
Decay Processes
Alpha decay
This is a common radioactive process encountered with heavier (A>150) isotopes. Isotopes with
mass numbers less than about 150 (Z ≈ 60) seldom yield α-particles.
The α-particle is a helium nucleus having a mass of 4 and a charge of +2. E.g of α decay
238
92𝑈
Parent nuclide
26 | P a g e
→
234
90𝑇ℎ
+ 42𝐻𝑒
Daughter nuclide
Αlpha particles from a decay process are either monoenergetic or are distributed among
relatively few discrete energies. E.g
234
90𝑇ℎ
+ 42𝐻𝑒 (4.196 𝑀𝑒𝑉)
77%
238
92𝑈
23%
234
90𝑇ℎ
+ 42𝐻𝑒 (4.149 𝑀𝑒𝑉) + 𝛾 (0.047 𝑀𝑒𝑉)
Alpha particles progressively lose their energy as a result of collisions as they pass through
matter, and are ultimately converted into helium atoms through capture of 2 electrons from their
surroundings. Their relatively large mass and charge renders them highly effective in producing
ion pairs within matter through which they pass; this makes their detection and measurement
easy. Because of their high mass and charge, α-particles have a low penetrating power in matter.
The identity of an isotope that is an alpha emitter can often be established by measuring the
length (range) over which the emitted α-particles produce ion pairs within a particular medium
(often air).
Alpha particles are relatively ineffective for producing artificial isotopes because of their low
penetrating power.
Due to the greater ionizing power of α-particles, they can generally be distinguished from β and
γ radiation on the basis of pulse amplitude. The ionization chamber is the preferred detector.
Alpha particle activity can be measured in the presence of considerable β activity by first
measuring the total activity, then interposing a filter to absorb the α particles, and measuring the
β activity.
27 | P a g e
Beta Decay
A nuclear reaction in which the atomic number Z changes but not the mass number A is
classified as β-decay. There are 3 types of β-decay:



14
6𝐶
→
65
30𝑍𝑛
48
24𝐶𝑟
Negatron formation
Positron formation
Electron capture
14
7𝑁
→
+ 𝛽 − + 𝜈̿ (Negatron formation)
65
29𝐶𝑢
+ 01𝑒 →
+ 𝛽 + + 𝜈 (Positron formation)
48
23𝑉
+ 𝑋 − 𝑟𝑎𝑦𝑠 (Electron capture)
. 𝜈̿ and 𝜈 represent an antineutrino and a neutrino particle (NOT important in analytical
chemistry)
In electron capture, the capture of an electron by the
48
24𝐶𝑟
nucleus produces
48
23𝑉 ,
but this process
leaves one of the atomic orbitals (usually 1s or K-orbital) of the Vanadium deficient by one electron. Xray emission results when an electron from one of the outer orbitals fills the void left by the capture
process.
Negatrons (β-) are electrons that form when one of the neutrons in the nucleus is converted to a proton.
The positron (β+) on the other hand with the mass of the electron forms when the number of protons in the
nucleus is decreased by one. The positron has a transitory existence, in that it is ultimately annihilated by
reaction with an electron to yield two 0.511 MeV gamma-ray photons.
In contrast to α-emission, β-emission is characterized by production of particles with a continuous
spectrum of energies ranging from nearly zero to some maximum that is characteristic for each decay
process.
The β-particle is not nearly as effective as the α-particle in producing ion pairs in matter because of its
small mass (≈ 1/7000 that of an α particle). At the same time, its penetrating power is substantially
greater. Beta energies are frequently expressed in terms of the thickness of an absorber,
ordinarily Al, required to stop the particle.
Gamma-Ray Emission
Many α and β emission processes leave a nucleus in an excited state, which then returns to the
ground state in one or more quantized steps with the release of monoenergetic gamma rays.
.γ-rays, except for their source, are indistinguishable from X-rays of the same energy. Thus, γrays are produced by nuclear relaxation, while X-rays derive from electronic relaxations. The γ28 | P a g e
ray emission spectrum is characteristic for each nucleus and is thus useful for identifying
radioisotopes. Not surprising, γ-radiation is highly penetrating. (But less ionizing). Upon
interaction with matter, γ-rays lose energy by 3 mechanisms:
(Depending on the energy of the γ-ray photon)
1. Photoelectric effect
2. Compton effect
3. Pair production
Photoelectric effect predominates when we have low energy γ-radiation. Here the γ-ray photon
disappears after ejecting an electron from an atomic orbital (usually a K orbital) of the target
atom. The photon energy is totally consumed in overcoming the binding energy of the electron
and in imparting kinetic energy to the ejected electron.
Compton effect is encountered with relatively energetic γ-rays. Here an electron is also ejected
from an atom but only acquires part of the photon energy. The photon now with diminished
energy, recoils from the electron and then goes on to further Compton or photoelectric
interactions.
If the γ-ray photon has sufficiently high energy (at least 1.02 MeV), pair production can occur.
In this, the photon is totally absorbed in creating a positron and an electron in the field
surrounding a nucleus.
X-Ray Emissions
A long lived positron-emitting nucleus may decay by capturing one of its own orbital K
electrons, this is called internal conversion. The excess energy is emitted as a γ-ray, and the
resulting ion with a vacant K orbital then emits X-radiation characteristic of the new element.
An electronic interaction between the excited nucleus and an extranuclear electron results in the
ejection of an orbital electron with kinetic energy equal to the difference between the energy of
the nuclear transition and the binding energy of the electron. The emission of this so called
internal conversion electron leaves a vacancy in the K, L, or higher orbital; X-rays are emitted as
the orbital is filled by an electronic transition.
29 | P a g e
Radioactive Decay Rates
Radioactive decay is a completely random process. Thus, although no prediction can be made
concerning the lifetime of an individual nucleus, the behavior of a large ensemble of like nuclei
can be described by the first-order rate expression:
𝑑𝑁
− 𝑑𝑡 = 𝜆𝑁……………………. (1)
N = number of radioactive nuclei of a particular kind in the sample at time t.
.λ = characteristic decay constant for the radioisotope.
Equation 1 can be rearranged and integrated over the interval t = 0 and t = t (during which the
number of radioactive nuclei in sample decreases from No to N.
−
𝑁
∫ −
𝑁𝑜
𝑑𝑁
= 𝜆 𝑑𝑡
𝑁
𝑡
𝑑𝑁
= 𝜆 ∫ 𝑑𝑡
𝑁
0
−[ln 𝑁]𝑁
𝑁𝑜 = 𝜆𝑡
− [𝑙𝑛𝑁 − 𝑙𝑛𝑁𝑜 ] = 𝜆𝑡
− ln
𝑁
= 𝜆𝑡
𝑁𝑜
𝑁
ln 𝑁 = −𝜆𝑡…………….(2)
𝑜
≡ 𝑁 = 𝑁𝑜 𝑒 −𝜆𝑡 ……. (3)
The half-life (t1/2) of a radioactive isotope is defined as the time required for one half of
radioactive atoms in a sample to undergo decay i.e for N to become equal to No/2. Substitution of
No/2 for N in equation 2 gives:
𝑡1/2
30 | P a g e
𝑁𝑜⁄
−ln 𝑁 2
𝑙𝑛2
𝑜
=
=
𝜆
𝜆
𝑡1/2 =
𝑙𝑛2
𝜆
≈
0.693
𝜆
…… (4)
The Activity (A) of a radionuclide is defined as its disintergration rate. Thus from equation 1
𝑑𝑁
𝐴 = − 𝑑𝑡 = 𝜆𝑁…. (5)
Units of A = s-1
The Becquerel (Bq) corresponds to 1 decay per second i.e 1Bq = 1s-1.
An older unit of activity is the Curie (Ci) defined as the activity of 1 g of Radium-226.
1Ci = 3.70 × 1010 Bq
In analytical radiochemistry, activities of analytes range from a nanocurie or less to a few
microcuries.
In the lab, absolute activities are seldom measured because detection efficiencies are seldom
100%. Instead, the counting rate R is employed, where R = cA.
R = cA = cλN…… (6)
c= detection coefficient, which depends on the nature of the detector, the efficiency of counting
disintegrations and the geometric arrangement of sample and detector.
Equation 3 can be rewritten in the form
𝑅 = 𝑅𝑜 𝑒 −𝜆𝑡 .............. (7)
Example
In an initial counting period, the counting rate for a particular sample was found to be 453 cpm.
In a second experiment performed 420 minutes later, the sample exhibited a counting rate of 285
cpm. If it can be assumed that all counts are the result of the decay of a single isotope, what is
the half-life of that isotope?
𝑅 = 𝑅𝑜 𝑒 −𝜆𝑡
285 cpm = 453 cpm 𝑒 −𝜆(420min)
285𝑐𝑝𝑚
ln(453𝑐𝑝𝑚) = - λ (420min)
31 | P a g e
λ = 1.10 × 10-3 min-1
𝑡1/2 =
0.693
𝜆
=
0.693
1.10 × 10−3 min−1
= 630 min
INSTRUMENTATION
Radiation from radioactive sources can be detected and measured in essentially the same way as
X-radiation.
Gas filled transducers, scintillation counters and semiconductor detectors are all sensitive to α
and β particles and to gamma rays because absorption of these particles produces ionization or
photoelectrons, which can in turn produce thousands of ion pairs. A detectable electrical pulse is
thus produced for each particle reaching the transducer.
Gas Filled Transducers
When radiation passes through an inert gas such as Argon, Xenon or Krypton, interaction occurs
that produce a large number of positive gaseous ions and electrons (ion pairs) for each photon.
Three types of transducers, namely, ionization chambers, proportional counters and Geiger tubes,
are based upon the enhanced conductivity resulting from this phenomenon.
radiation
window
Argon
insulator
Anode
Metal
To
pream
-plifier
tube
window
Cathode
—
Unabsorbed
radiation
32 | P a g e
+
~ 1KV
No. of electrons per photon
Radiation enters the chamber through a transparent window of mica, beryllium, aluminium or
mylar. Each photon of radiation may interact with an atom of Argon, causing it to lose one of its
outer electrons. This photoelectron has a large kinetic energy which it loses by ionizing several
hundred additional atoms of the gas. Under the influence of applied potential the mobile
electrons migrate toward the central wire anode while the slower moving cations are attracted
toward the cylindrical metal cathode.
The figure above shows the effect of applied potential on the number of electrons that reach the
anode of a gas filled detector for each radiation photon.
Three characteristic voltage regions are indicated. At region i the accelerating force on the ion
pairs is low, and the rate at which the positive and negative species separate is insufficient to
prevent partial recombination. As a consequence, the number of electrons reaching the anode is
smaller than the number produced initially by the incoming radiation.
In region ii, which is the Ionization chamber region, the number of electrons reaching the anode
is reasonably constant and represents the total number formed by a single photon.
In region iii, which is the proportional counter region the number of electrons increases rapidly
with applied potential. This increase is the result of secondary ion-pair production caused by
33 | P a g e
collisions between the accelerated electrons and gas molecules; amplification of the ion current
results.
In region iv, Geiger region, amplification of the electrical pulse is enormous but limited by the
positive space charge created as the faster moving electrons migrate away from the slower
positive ions. Because of this effect, the number of electrons reaching the anode is independent
of the type and energy of incoming radiation and is governed instead by the geometry and gas
pressure of the tube.
The figure also illustrates that a large number of electrons is produced by the more energetic
radiation (curve (i)) than a less energetic one (curve (ii)).
NEUTRON ACTIVATION METHODS
Activation methods are based upon the measurement of radioactivity that has been induced in
samples by irradiation with neutrons or charged particles, such as hydrogen, deuterium, or
helium ions.
Neutron and neutron sources
There are 3 sources of neutrons employed in neutron activation methods:



Reactors
Radionuclides
Accelerators
All 3 produce highly energetic neutrons (in the MeV range), which are usually passed through a
moderating material that reduces their energies to a few hundredths of an electron volt (eV).
Energy loss to the moderator occurs by elastic scattering in which neutrons bounce off nuclei in
the moderator material, transferring part of their kinetic energy to each nucleus they strike.
Ultimately, the nuclei come to temperature equilibrium with their surroundings. Neutrons having
this energy (about 0.04 eV) are called thermal neutrons, and the process of moderating highenergy neutrons to thermal conditions is called thermalisation.
The most efficient moderators are low molecular weight substances, such as water, deuterium
oxide and paraffin.
Most activation methods are based upon thermal neutrons, which react efficiently with most
elements of analytical interest. For some of the lighter elements, however, such as nitrogen,
oxygen, fluorine and silicon, fast neutrons having energies of about 14 MeV are more efficient
for inducing radioactivity. Such high energy neutrons are commonly produced by accelerators.
34 | P a g e
Reactors
Nuclear reactors are sources of copious thermal neutrons and are therefore widely used for
activation analyses. A typical research reactor will have a neutron flux of 1011 to 1014 n cm-2 s-1.
These high neutron densities lead to detection limits that for many elements range from 10-3 to
10 µg.
Radioactive Neutron Sources (Radionuclides)
Radioactive isotopes are convenient and relatively inexpensive sources of neutrons for activation
analyses. Their neutron flux densities range from perhaps 105 to 1010 ncm-2s-1. As a consequence,
detection limits are generally not as good as those in which a reactor serves as a source.
One common radioactive source of neutrons is a transuranium element that undergoes
spontaneous fission to yield neutrons. The most common example of this type of source consists
of 238Cf (californium) which has a half-life of 2.6 years. About 3% of its decay occurs by
spontaneous fission, which yields 3.8 neutrons per fission. Thermal flux densities of about 3 ×
107 ncm-2s-1 or higher are obtainable from this type of source.
Neutrons can also be produced by preparing an intimate mixture of an alpha emitter such as
plutonium, americium, or curium with a light element such as beryllium. A commonly used
source of this kind is based upon the reaction:
9
4𝐵𝑒
+ 42𝐻𝑒 →
12
6𝐶
+ 10𝑛 + 5.7 𝑀𝑒𝑉
To produce thermal neutrons, a paraffin container is typically employed as a moderator.
Accelerators
A typical generator consist of an ion source that delivers deuterium ions to an area where they
are accelerated through a potential of about 150 kV to a target containing tritium absorbed on
titanium or zirconium.
2
1𝐻
+ 31𝐻 → 42𝐻𝑒 + 10𝑛
Neutrons produced in this way have energies of about 14 MeV and are useful for activating the
lighter elements.
35 | P a g e
Interactions of Neutrons with Matter
Free neutrons are not stable, and they decay with a half-life of about 10.3 minutes to give protons
and electrons. However, free neutrons do not exist long enough to disintegrate in this way
because of their great tendency to react with ambient material. The high reactivity of neutrons
arises from their zero charge that permits them to approach charged nuclei without interference
from coulombic forces.
Neutron capture is the most important reaction for activation methods. Here, a neutron is
captured by the analyte nucleus to give an isotope with the same atomic number, but with a mass
number that is greater by one. The new nuclide is in a highly excited state because it has
acquired about 8 MeV of energy by binding the neutron. This excess energy is released by
prompt gamma ray emission or emission of one or more nuclear particles, such as neutrons,
protons, or alpha particles. E.g
23
11𝑁𝑎
+ 10𝑛 →
24
11𝑁𝑎
+ 𝛾
The equation can be abbreviated as:
23
11𝑁𝑎
(𝑛, 𝛾) 24
11𝑁𝑎
The prompt γ-rays formed by capture reactions are of analytical interest in special cases, but the
radionuclide produced (24Na) is generally of far greater utility.
Theory of Activation Methods
When exposed to a flux of neutrons, the rate of formation of radioactive nuclei from a single
isotope can be shown to be
𝑑𝑁 ∗
𝑑𝑡
𝑑𝑁 ∗
𝑑𝑡
= 𝑁𝜙𝜎…. (1)
= rate of formation of active particles in neutrons per second (n/s)
N = number of stable target atoms.
ϕ = average flux in cm-2s-1
36 | P a g e
σ = capture cross section in cm2/target atom (this is a measure of the probability of the nuclei
reacting with a neutron at the particle energy employed).
The units of σ are usually in “barn”, b, where 1b = 10-24 cm2/target atom.
Once formed, the radioactive nuclei decay at a rate
−
𝑑𝑁 ∗
𝑑𝑡
= 𝜆𝑁 ∗ ……. (2)
Thus, during irradiation with a uniform flux of neutrons, the net rate of formation of active
particles is
𝑑𝑁 ∗
𝑑𝑡
= 𝑁𝜙𝜎 − 𝜆𝑁 ∗ ……. (3)
When this equation is integrated from time 0 to t, one gets:
𝑁∗ =
Substituting 𝑡1/2 =
0.693
𝜆
𝑁𝜙𝜎
𝜆
[1 − exp(−𝜆𝑡)]… (4)
into the exponential term yields:
𝑁∗ =
𝑁𝜙𝜎
𝜆
[1 − exp(−
0.693𝑡
𝑡1/2
)]… (5)
This equation can be rearranged to give λN*, which is the activity, A. Thus,
A = λN* = 𝑁𝜙𝜎 [1 − exp(−
0.693
𝑡1/2
𝑡)]… (6)
= NϕσS
S = saturation factor
Form the equation R = cA = cλN,
R = 𝑁𝜙𝜎𝑐 [1 − exp(−
0.693𝑡
𝑡1/2
)] = 𝑁𝜙𝜎𝑐𝑆 ….. (7)
The figure below is a plot of this relationship (equation 7) at 3 levels of neutron flux. The X-axis
is the ration of the irradiation time to the half-life of the isotope (t/t1/2).
In each case the counting rate approaches a constant value where the rates of formation and
disintegration of the isotope approach one another. Clearly, irradiation for periods beyond 4 or 5
half-lives for an isotope will result in little improvement in sensitivity.
37 | P a g e
Figure: Effect of neutron flux and time on the activity induced in a sample.
In many analyses, irradiation of the sample and standards is carried out for a long enough period
to reach saturation. Under this circumstance, all of the last equation are constant, and the number
of analyte radionuclides is directly proportional to the counting rate.
If the target nuclide is naturally occurring, the weight of the analyte W, can be obtained from N
by multiplying it by Avogadro’s number, the natural abundance of the analyte isotope, and the
chemical atomic weight. Since all these are constants, the weight of analyte is directly
proportional to the counting rate (R).
Using subscripts x and s for sample and standard respectively:
Rx = KWx
Rs = KWs
K = proportionality constant.
Dividing one by the other the weight of an unknown can be given by
38 | P a g e
𝑊𝑥 =
𝑅𝑥
𝑅𝑠
𝑊𝑠 … (8)
Example
Two 5.00 ml aliquots of river water were taken for neutron activation analysis. Exactly 1.00 ml
of a standard solution containing 1.00 µg of Al3+ was added to one aliquot and 1.00 ml of
deionized water was introduced into the other. The two samples were then irradiated
simultaneously in a homogeneous neutron flux. After a brief cooling period, the gamma radiation
from decay of 28Al was counted. The solution that was diluted with water gave a counting rate of
2315 cpm (counts per minute), whereas the solution containing the added Al3+ gave a reading of
4197 cpm. Calculate the weight of Al in the 5.00 ml sample.
Solution
Here we are dealing with a simple standard addition problem.
2315 = KWx ……… (i)
4197 = K(Wx+ Ws) = K(Wx + 1.00) …. (ii)
From (i), K = 2315/Wx
Since from (ii) 4197 = KWx + K,
Substituting K gives
4197 =
2315
2315
× 𝑊𝑥 +
𝑊𝑥
𝑊𝑥
4197 − 2315 =
2315
𝑊𝑥
𝑊𝑥 = 1.23𝜇𝑔
39 | P a g e
Experimental Considerations in Activation Methods
Non-destructive route
Simultaneous
irradiation of
sample and
standards
Cooling
period
Counting
Data
processing
and
readout
Separation of
analyte
Destructive route
In both procedures the sample and one or more standards are irradiated simultaneously with
neutrons (or other types of radiation). The samples mat be solids, liquids, or gases (the first 2 are
common).
The standards should approximate the sample as closely as possible both physically and
chemically. Generally, the samples and standards are contained in small polyethylene vials; heat
sealed vials are also used on occasion. Care is taken to ensure the samples and standards are
exposed to the same neutron flux.
An exposure time of roughly 3 to 5 times the half-life of the analyte product is employed.
Rradiation times generally vary from several minutes to several hours. After irradiation is
terminated, the sample and standards are often allowed to decay (or ‘cool’) for a period that
again varies from a few minutes to several hours or more.
During cooling, shortlived interferences decay away so that they do not affect the outcome of the
analysis. Another reason for allowing an irradiated sample to cool is to reduce the health hazard
associated with counting the material.
40 | P a g e
Non-destructive Methods
The samples and standards are counted directly after cooling. Here, the ability of the γ-ray
spectrometer to discriminate among the radiation of different energies provides selectivity.
Equation 8 is then used to compute the amount of analyte in the unknown. Clearly, success of
this method requires that the spectrometer be able to isolate the gamma-ray signal produced by
the other components. Whether or not an adequate resolution is possible depends upon the
complexity of the sample, the presence or absence of elements that produce gamma rays of about
the same energy as that of the element of interest, and the resolving power of the spectrometer.
The great advantage of the non-destructive approach is its simplicity in terms of sample handling
and the minimal operator time required to complete an analysis.
Modern equipment are largely automated.
Destructive Methods
A destructive method requires that the analyte be separated from the other components of the
sample prior to counting. In this case, a known amount of the irradiated sample is dissolved and
the analyte separated by precipitation, extraction, ion exchange, or chromatography. The isolated
material or a known fraction thereof is then counted for its gamma or beta-activity. As in the nodestructive method, standards may be irradiated simultaneously and treated in an identical way.
Equation 8 is then used to compute the results of the analysis.
Application of Neutron Activation
Neutron activation methods offer several advantages including high sensitivity, minimal sample
preparation, and ease of calibration. Often these procedures are non-destructive and for this
reason are applied to the analysis of art objects, coins, forensic samples, and archeological
specimens. The major disadvantages of activation methods are their need for large and expensive
equipment and special facilities for handling and disposing of radioactive materials. Another
handicap is the long time required to complete analyses when long-lived radionuclides are used.
41 | P a g e
ISOTOPE DILUTION METHODS
Isotope dilution methods, which predate activation procedures, have been and still are
extensively applied to problems in all branches of chemistry. These methods are among the most
selective available to chemists. Both stable and radioactive isotopes are employed in the isotope
dilution technique. However, the radioactive isotopes are the more convenient because of the
ease with which the concentration of the isotope can be determined.
Principles of the Isotope Dilution Procedure
Isotope dilution methods require the preparation of a quantity of the analyte in a radioactive
form. A known weight of this isotopically labeled species is then mixed with the sample to be
analysed.
After treatment to ensure homogeneity between the active and non-active species, apart of the
analyte is isolated chemically in the form of a purified compound. By counting a weighed
portion of this product, the extent of dilution of the active material can be calculated and related
to the amount of non-active substance in the original sample.
In developing an equation that relates the activity of the isolated and purified mixture of analyte
and tracer to the original amount of analyte, we assure that Wt grams of tracer having a counting
rate of Rt cpm is added to a sample containing Wx grams of inactive analyte. The count for the
resulting (Wx + Wt) grams of the mixture will be the same as that of the Wt grams of tracer or Rt.
If now Wm grams of the isolated and purified mixture of the active and inactive species is
𝑊
counted, its counting rate Rm will be (𝑊 +𝑚𝑊 ) of Rt because of dilution
𝑥
𝑡
𝑊
Therefore 𝑅𝑚 = 𝑅𝑡 (𝑊 +𝑚𝑊 )……… (1)
𝑥
𝑡
Which leads to:
𝑊𝑥 =
𝑅𝑡
𝑅𝑚
𝑊𝑚 − 𝑊𝑡 ……… (2)
Thus the weight of the species originally present is obtained from the four measured quantities
on the right-hand side of equation 2.
Example
To a sample of a protein hydrosylate, a chemist added 1.00 mg of tryptophan, which was labeled
with 14C and exhibited a counting rate of 584 cpm above background. After this labeled
compound was thoroughly mixed with the sample, the mixture was passed through an ion
exchange column. The fraction of effluent containing only tryptophan was collected, and from it
an 18.0 mg sample of pure tryptophan was isolated. The isolated sample had a count of 204 cpm
in the same counter. What was the weight of tryptophan in the original sample?
42 | P a g e
𝑊𝑥 =
𝑊𝑥 =
𝑅𝑡
𝑊 − 𝑊𝑡
𝑅𝑚 𝑚
584 𝑐𝑝𝑚
× 18.0 𝑚𝑔 − 1.00 𝑚𝑔 = 50.5 𝑚𝑔
204 𝑐𝑝𝑚
Application of the Isotope Dilution Method
Isotope dilution procedures have been most widely used for the determination of compounds that
are of interest in organic chemistry and biochemistry. Thus, methods have been developed for
the determination of such diverse substances as vitamin D, vitamin B12, sucrose, insulin,
penicillin, various amino acids, corticosterone, various alcohols and thyroxine.
Isotopic dilution analysis has had less widespread application since the advent of activation
methods.
43 | P a g e
SURFACE CHARACTERISATION
Introduction
The surface of a solid in contact with a liquid or gaseous phase usually differs substantially from
the interior of the solid both in chemical composition and physical properties.
Characterization of these surface properties is often of vital importance in a number of fields
including:





Heterogeneous catalysis
Semiconductor thin film technology
Corrosion and adhesion mechanisms
Activity of metal surfaces
Embrittlement properties
Studies of the behavior and functions of biological membranes.
Spectroscopic and microscopic methods are employed in the characterization of solid surfaces.
Definition of a solid surface
A surface is the boundary layer between a solid and a vacuum, a gas, or a liquid.
We generally think of a surface as part of the solid that differs in composition from the average
composition of the bult of the solid. By this definition, the surface comprises not only the top
layer of atoms or molecules of a solid but also a transition layer with a non-uniform composition
that varies continuously from that of the outer layer to that of the bulk.
Thus a surface may be several or even several tens of atomic layers deep. Ordinarily, however
the difference in composition of the surface layer does not significantly affect the measured
overall average composition of the bulk because the surface layer is generally only a tiny fraction
of the total solid.
From a practical standpoint, a surface is that volume of the solid that a specific measurement
technique samples. This definition recognizes the fact that if several surface techniques are
employed, the chemist may in fact be sampling different surfaces and may obtain different,
though useful, results as a consequence.
Types of Surface Measurements
The classical methods, which are still of importance, provide muc useful information about the
physical nature of surfaces but less about their chemical nature. The techniques/methods involve
obtaining optical and electron microscopic images of surfaces as well as measurement of
44 | P a g e
adsorption isotherms, surface areas, surface roughness, pore sizes and reflectivity. In the 1950s
spectroscopic surface methods appeared that provided information about the chemical nature of
surfaces.
SPECTROSCOPIC SURFACE METHODS
These provide both qualitative and quantitative chemical information about composition of a
surface layer of a solid that is a few angstrom units to a few tens of angstrom units in thickness.
General Technique in Surface Spectroscopy
The solid sample is irradiated with a primary beam made up of photons, electrons, ions, or
neutral molecules. Impact of this beam on a surface results in formation of a secondary beam
also consisting of photons, electrons, molecules, or ions from the solid surface.
From source
To spectrometer
Primary beam
Secondary beam
Sample
NOTE: the type of particle making up the primary beam is not necessarily the same as the
particle of the secondary beam. The secondary beam which results from scattering, sputtering or
emission, is then studied by a variety of spectroscopic methods.
The most effective surface methods, are those in which the primary beam, the secondary beam,
or both is made up of either electrons, ions, or molecules and not photons because this limitation
ensures that the measurements are restricted to the surface of a sample and not to its bulk. For
example the maximum penetration depth of a beam of 1 KeV electrons or ions is approximately
45 | P a g e
25 angstrom, whereas the penetration depth of a photon beam of the same energy is about 104
angstrom.
Some Common types of Spectroscopic Methods for Analysis of Surfaces
Method and Common
Acronym
X-ray Photoelectron
Spectroscopy (XPS) or
Electron Spectroscopy
for Chemical Analysis
(ESCA)
Primary beam
Secondary beam
X-ray photons
Electrons
2.
Auger Electron
Spectroscopy (AES)
Electrons, or X-ray
photons
Electrons
3.
Ultraviolet
Photoelectron
Spectroscopy (UPS)
UV photons
Electrons
4.
Secondary Ion Mass
Spectrometry (SIMS)
Ions
Ions
5.
Laser Microprobe Mass
Spectrometry (LMMS)
Photons
Ions
6.
Electron Microprobe
(EM)
Electrons
X-ray photons
1.
Sampling surfaces
There are 3 types of sampling methods employed:1. Involves focusing the primary beam on a single small area of the sample and observing
the secondary beam. Often the spot is chosen visually with an optical microscope.
2. Second method involves mapping the surface, in which a region of the surface is scanned
by moving the primary beam across the surface in a raster pattern of measured increments
and observing changes in the secondary beam that results.
3. Depth profiling: here a beam of ions from an ion gun is used to etch a hole in the surface
by sputtering. During this process a finer primary beam is used to produce a secondary
46 | P a g e
beam from the centre of the hole, which provides the analytical data on the surface
composition as a function of depth.
Surface Contamination
A problem that is frequently encountered in surface analyses is contamination of the surface
being examined by adsorption of components of the atmosphere, such as oxygen, water or
carbon dioxide. Even in a vacuum this type of contamination occurs in a relatively short time:
At 10-6 Torr in 3 sec
At 10-8 Torr in 1 hour
At 10-10 Torr in 10 hours
As a result of adsorption problems, provisions must often be made to clean the sample surface,
usually in the chamber used for irradiating the sample. Cleaning may involve:





Baking the sample at a high temperature.
Sputtering the sample with a beam of inert gas ions from an electron gun.
Mechanical scraping or polishing the sample surface with an abrasive.
Ultrasonic washing of the sample in various solvents.
Bathing the sample in a reducing atmosphere to remove oxides.
Apart from atmospheric contamination, the primary beam itself can alter the surface as a
measurement progresses. Damage caused by a primary beam depends on the momentum of the
primary beam particles. Ions are the most damaging and photons the least.
ELECTRON SPECTROSCOPY
The first 3 methods in the table given earlier are based on analysis of emitted electrons produced
by various incident beams. Here the signal from the analyte consists of a beam of electrons rather
than photons. The spectrometric measurements then consist of the determination of the power of
this beam as a function of the energy (or frequency hν ) of the electrons. This is called electron
spectroscopy.
Electron spectroscopy is a powerful tool for the identification of all of the elements in the
periodic table with the exception of hydrogen and helium. More importantly, the method permits
determination of the oxidation state of an element and the type of species to which it is bonded.
It also provides useful information about the electronic structure of molecules.
Electron spectroscopy has been successfully applied to gases and solids and more recently to
solutions and liquids. Because of the poor penetrating power of electrons, however, these
47 | P a g e
methods provide information about solids that is restricted largely to a surface layer that is a few
atomic layers thick (20 to 50 angstrom). The most important and valuable application of electron
spectroscopy are to the qualitative analysis of the surfaces of solids such as metals, alloys,
semiconductors and heterogeneous catalysts. Quantitative analysis by electron spectroscopy
finds somewhat limited applications.
X-ray Photoelectron Spectroscopy (XPS)
In electron spectroscopy, the kinetic energy of emitted electrons is recorded. The spectrum thus
consists of a plot of the number of emitted electrons, or the power of the electron beam as a
function of the energy (or the frequency or wavelength) of the emitted electrons.
Principles of XPS
XPS was originally called Electron Spectroscopy for Chemical Analysis (ESCA) because in
contrast to the other two electron spectroscopies, XPS provides not only information about the
atomic composition of a sample but also information about the structure and oxidation state of
the compounds examined.
The physical process of XPS takes place as shown below.
𝜀𝑘 ≈ ℎ𝜈 − 𝜀𝑏
Εv “
Ev ‘
Ev
Decreasing Binding Energy
X-ray hν
e-
Eb “
Eb ‘
Eb
48 | P a g e
The 3 lower lines labeled Eb, Eb’, and Eb” represent energies of the inner shell K and L electrons
of an atom. The upper three lines represent some of the energy levels of the outer shell or
valence electrons. As shown, one of the photons of a monochromatic X-ray beam of known
energy hν, displaces an electron from a K-orbital Eb.
𝐴 + ℎ𝜈 → 𝐴+∗ + 𝑒 −
A= an atom, a molecule or an ion.
A+* = electronically excited ion with a positive charge one greater than that of A.
The kinetic energy of the emitted electron Ek is measured in an electron spectrometer. The
binding energy of the electron Eb can be then calculated by:
𝐸𝑏 = ℎ𝜈 − 𝐸𝑘 − 𝑊
W = work function of the spectrometer, a factor that corrects for the electrostatic environment in
which the electron is formed and measured. There are various methods to determine a value for
W. the binding energy of an electron is characteristic of the atom and orbital from which the
electron was emitted. Therefore XPS provides a means of qualitative identification of elements
present on the surface of solids.
Instrumentation
Electron spectrometers components include a source, a sample holder, an analyser, a detector, a
signal processor and read out.
Electron spectrometers generally require elaborate vacuum systems to reduce the pressure in all
of the components to as low as 10-5 to 10-10 torr.
Sources: the simplest X-ray sources for XPS spectrometers are X-ray tubes equipped with
magnesium or Aluminium targets and suitable filters. The Kα lines for these two elements have
considerably narrower bandwidths (0.8 to 0.9 eV) than those encountered with higher atomic
number targets; narrower bands are desirable since they lead to enhanced resolution.
Solid samples are mounted in a fixed position as close to the photon or electron source and the
entrance slit of the spectrometer as possible. In order to avoid attenuation of the electron beam,
the sample compartment must be evacuated to pressures of up to 10-10 torr to avoid
contamination of the sample surface.
Analyser: most electron spectrometers are of the hemispherical type in which the electron beam
is deflected by an electrostatic magnetic field in such a way that the electrons travel in a curved
path. By varying the field, electrons of various kinetic energies can be focused on the detector.
49 | P a g e
Transducer: most modern electron spectrometers are based upon solid state, channel electron
multipliers, which consist of tubes of glass that have been doped with lead and vanadium. When
a potential of several kilovolts is applied across these materials, a cascade or pulse of 106 to 108
electrons is produced for each electron. The pulses are then counted electronically.
APPLICATIONS OF XPS
ESCA provides qualitative and quantitative information about the elemental composition of
matter, particularly solid surfaces. It also often provides useful structural information.
Qualitative analysis
A low resolution, wide-scan XPS spectrum (often called a survey spectrum) serves as the basis
for the determination of the elemental composition of samples.
With a Mg or Al Kα source, all elements except hydrogen and helium emit core electrons having
characteristic binding energies. Typically, a survey spectrum encompasses a kinetic energy range
of 250 to 1500 eV, which corresponds to binding energies of about 0 to 1250 eV.
Every element in the periodic table has one or more energy levels that will result in the
appearance of peaks in this region. In most instances, the peaks are well resolved and lead to
unambiguous identification provide the element is present in concentration greater than about
0.1%. Occasionally, peak overlap is encountered such as O 1s/ Sb 3d or Al 2s, 2p/ Cu 3s, 3p.
Usually, problems due to spectral overlap can be resolved by investigating other spectral regions
for additional peaks. Often peaks resulting from Auger electrons are found in XPS spectra. Such
peaks are readily identified by comparing spectra produced by two X-ray sources (usually Mg
and Al Kα). Auger peaks remain unchanged on the kinetic energy scale while photoelectric peaks
are displaced.
Chemical Shifts and Oxidation States
When one of the peaks of a survey spectrum is examined under conditions of higher energy
resolution, the position of th maximum is found to depend to a small degree up on the chemical
environment of the atom responsible for the peak i.e variations in the number of valence
electrons, and the type of bonds they form influence the binding energies of core electrons. The
effect of number of valence electrons and thus the oxidation state is demonstrated by the data for
several elements (shown in table)
Binding energies increase as the oxidation state becomes more positive. This chemical shift can
be explained by assuming that the attraction of the nucleus for a core electron is diminished by
the presence of outer electrons. When one of these outer electrons is removed, the effective
charge sensed for the core electrons is increased, thus an increase in binding energy results.
50 | P a g e
One of the most important applications of XPS has been the identification of oxidation states of
elements contained in various kinds of inorganic compounds.
Chemical Shifts as a Function of Oxidation State
Element
Oxidation State
+2
+3
+5.1
Nitrogen (1s)
-2
-
-1
*
0
0
-
+1
+4.5
+4
-
+5
+8.0
+6
-
+7
-
Sulfur (1s)
-2.0
-
*
-
-
-
+4.5
-
+5.8
-
Chlorine (2p)
-
*
-
-
-
+3.8
-
+7.1
-
+9.5
Copper (1s)
-
-
*
+0.7
+4.4
-
-
-
-
-
Iodine (4s)
-
*
-
-
-
-
-
+5.3
-
+6.5
Europium
(3d)
-
-
-
-
*
+9.6
-
-
-
-
0
0
0
0
0
Chemical Shifts and Structure
F
F
O
C
C
O
Net Counting Rate
F
H
H
C
C
H
H
H
500
0
1190
eV
1195
Kinetic Energy
eV
51 | P a g e
295
290
285
Binding Energy
The figure above illustrates the effect of structure on the position of peaks for an element. Each
peak corresponds to the 1s electron of the carbon atom located directly above it in the structure
formula. Here, the shift in binding energies can be rationalized by taking into account the effect
of the various functional groups on the effective nuclear charge experienced by the 1s core
electron. For example, of all of the attached groups, fluorine atoms have the greatest ability to
withdraw electron density from the carbon atom. The effective nuclear charge felt by the carbon
1s electron is therefore a maximum, as is the binding energy.
The figure above indicates the position of peaks for sulfur in its several oxidation states and in
various types of organic compounds. The data in the top row clearly demonstrates the effect of
oxidation state. Note also in the last four rows of the chart that XPS discriminates between two
sulfur atoms contained in a single ion or molecule. Thus, two peaks are observed for thiosulphate
ion (S2O32-), suggesting different states for the two sulfur atoms contained therein.
XPS spectra provide not only qualitative information about types of atoms present in a
compound but also the relative number of each type. Thus, the nitrogen 1s spectrum for Sodium
Azide (Na+N3-) is made up of two peaks having relative areas in the ratio of 2:1 corresponding to
the two end nitrogens and the center nitrogen, respectively. Examples of some of its uses include
identification of active sites and poisons on catalytic surfaces, determination of surface
contaminants on semiconductor, analysis of the composition of human skin and study of oxide
52 | P a g e
surface layers on metals and alloys. It is also evident that the method has a substantial potential
in the elucidation of chemical structure.
A noteworthy attribute is the ability of XPS to distinguish among oxidation states of an element.
Quantitative Applications
Peak intensities and areas have been used as analytical parameter, with the relationship between
these quantities and concentration being established empirically. Often internal standards have
been recommended. Relative precision of 3% to 10% have been claimed. For the analysis of
solids and liquids, it is necessary to assure that the surface composition of the sample is the same
as its bulk composition. This assumption can lead to significant errors.
AUGER ELECTRON SPECTROSCOPY (AES)
AES is based upon a two-step process in which the first step involves formation of an
electronically excited ion A+* by exposing the analyte to a beam of electrons or sometimes Xrays.
With X-rays the reaction is:
𝐴 + ℎ𝜈 → 𝐴+∗ + 𝑒 −
With an electron beam the excitation reaction is:
𝐴 + 𝑒𝑖− → 𝐴+∗ + 𝑒𝑖′− + 𝑒𝐴−
Where
𝑒𝑖− = incident electron from the source.
𝑒𝑖′− = the same incident electron after it has interacted with A and has thus lost some of its
energy.
𝑒𝐴− = an electron that is ejected from one of the inner orbitals of A.
53 | P a g e
The relaxation of the excited ion A+* can occur in either of two ways.
(1) A+*
A++ + eA-
or
(2) A+*
A+ + hνf
eA- = Auger electron
hνf = a fluorescence photon.
The relaxation process in (2) will be recognized as X-ray fluorescence. Note that the energy of
the fluorescent radiation hνf is independent of the excitation energy. Thus polychromatic
radiation can be used for the excitation step.
Auger emission, shown by (1) is a process in which the energy given up in relaxation results in
the ejection of an electron (an Auger electron) with a kinetic energy Ek. Note also that the energy
of the Auger electron is independent of the energy of the photon or electron that originally
created the vacancy in energy level Eb. Thus a monoenergetic source is NOT required for
excitation.
54 | P a g e
Note that it is this independence of Auger peaks from the input energy that makes it possible for
the chemist to differentiate between Auger peak in a spectrum and the XPS peaks.
The kinetic energy of the Auger electron is the difference between the energy released in
relaxation of the excited ion (Eb – Eb’) and the energy required to remove the second electron
from its orbit (Eb’). Thus
Ek = (Eb – Eb’) – Eb’ = Eb – 2Eb’
Auger emissions are described in terms of the type of orbital transitions involved in the
production of the electron e.g a KLL Auger transition involves an initial removal of a K electron
followed by a transition of an L electron to the K- orbital with the simultaneous ejection of a
second L electron. Other common transitions are LMM and MNN.
Like XPS spectra, Auger spectra consist of a few characteristic peaks in the region of 20 to 1000
eV. The spectrum is a plot of the derivative of the counting rate as a function of the kinetic
energy (dN(E)/dE) against Auger electron energy (in eV).
Derivative spectra are standard for Auger spectroscopy in order to enhance the small peaks and
to repress the effect of the large, but slowly changing, scattered electron background radiation.
The peaks are usually well separated making qualitative identification quite straightforward.
Auger electron emission and X-ray fluorescence are competitive processes and their relative
rates depend upon the atomic number of the element involved. High atomic numbers favor
fluorescence while Auger emission predominates with atoms of low atomic numbers. As a result,
X-ray fluorescence is not a very sensitive means for detecting elements with atomic numbers
smaller than about 10.
Auger and X-ray photoelectron spectroscopy provide similar information about the composition
of matter. The methods tend to be complementary rather than competitive, however, with Auger
spectroscopy being more reliable and efficient for certain applications and XPS for others.
The particular strengths of Auger spectroscopy are its sensitivity for atoms of low atomic
number, its minimal matrix effects and above all its high spatial resolution which permits
detailed examination of solid surfaces. The high spatial resolution arises because the primary
beam is made up of electrons that can be more tightly focused on a surface than can X-rays.
Auger spectroscopy has not been extensively used to provide the kind of structural and oxidation
state information that is described for XPS. Quantitative analysis by the procedure is difficult.
55 | P a g e
Applications of Auger Electron Spectroscopy
Qualitative Analysis of Solid Surfaces
Typically an Auger spectrum is obtained by bombarding a small area of a surface (5 to 500 µm)
with a beam of electrons from a gun. An advantage of Auger spectroscopy for surface studies is
that the low energy Auger electrons (20 to 1000 eV) are able to penetrate only a few atomic
layers (3 to 20 angstrom) of solid. Thus, while electrons from the electron guns penetrate to a
considerably greater depth below the sample surface, only those Auger electrons from the first 4
or 5 atomic layers escape to reach the analyser. Consequently, an Auger spectrum is likely to
reflect the true surface composition of solids.
Depth Profiling of Surfaces
This involves the determination of the elemental composition of a surface as it is being etched
away (sputtered) by a beam of Argon ions. Either XPS or Auger spectroscopy can be used for
elemental detection, although the latter is the more common.
The process is carried out with a highly focused Auger microprobe; the diameter of the
microprobe beam is about 5 µm. the microprobe and etching beams are operated simultaneously,
with the intensity of one or more of the resulting Auger peaks being recorded as a function of
time. Since etching rate is related to time a depth profile of elemental composition is obtained.
Such information is of vital importance in a variety of studies such as corrosion chemistry,
catalyst behavior, and properties of semiconductor junctions.
56 | P a g e
Line Scanning
Line scans are used to characterize the surface composition of solids as a function of distance
along a straight line of 100 µm or more. For this purpose, an Auger microprobe is used that
produces a beam that can be moved across a surface in a reproducible way.
NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
NMR spectroscopy is based on the measurement of absorption of electromagnetic radiation in
the radiofrequency (Rf) region of roughly 4 – 900 MHz. In contrast to UV, visible and IR
absorption, nuclei of atoms rather than outer electrons are involved in the absorption process. In
the addition, in order to cause nuclei to develop the energy states required for absorption to
occur, it is necessary to place the analyte in an intense magnetic field.
Theory of NMR
Atomic nuclei have charge (they contain protons), and some also behave as if they spin. A
spinning charge is equivalent to a current in a conductor loop, therefore nuclei with non zero spin
will generate a magnetic field, that is, will have a magnetic moment or a magnetic dipole.
Depending on the shape of the nuclear charge and the number and type of nucleons, the spin
quantum number, I, can have values 0,1/2, 1, 3/2…..
A specific isotope of a nuclei has “spin” if:


Odd atomic number and/or
Odd atomic mass
Nuclear spin states are determined by the spin quantum number = I
I = 0, ½, 1, 3/2, …. Etc.
A nucleus with spin quantum number I has 2I + 1 spin states. I = 0, nuclei are not NMR active.
𝐼 ≠ 0, nuclei are NMR active.
There are 3 principal groups of nuclei:1.
2.
I = 0 (non spinning nuclei). These have no magnetic moment and are composed of even
numbers of protons and neutrons e.g. 126𝐶 , 168𝑂
I = ½ (Spherical spinning charges). These nuclei have a magnetic moment but no electric
quadrupole. This group is by far the most important from the chemical point of view.
57 | P a g e
3.
Chemically useful nuclei in this group, in decreasing order of importance are 11𝐻 , 136𝐶 ,
19
31
15
1
13
9𝐹 , 15𝑃 , 7𝑁 . Of these the proton ( H) and carbon ( C) account for well over 95% of all
NMR observations made.
𝐼 > 1⁄2 (non spherical spinning charges). These nuclei have both magnetic dipoles and
37
79
81
7
electric quadrupoles e.g. I = 1. 21𝐻 , 147𝑁; I = 3/2: 115𝐵, 35
17𝐶𝑙 , 17𝐶𝑙 , 35𝐵𝑟 , 35𝐵𝑟 , 3𝐿𝑖 ;
58
25
27
17
𝐼 = 2 : 36
17𝐶𝑙 , 27𝐶𝑜; I = 5/2: 12𝑀𝑔, 13𝐴𝑙 , 8𝑂 .
Nuclei of atoms with spin behave as spinning charged particles.
µ (Magnetic dipole)
A very small magnetic field is associated with the nuclei. i.e nuclei with spin behave as tiny bar
magnets. In the absence of an external magnetic field the nuclear spins are randomly oriented.
Influence of External Magnetic Field (Bo)
For nuclei of spin I = ½, such as a 1H, in the presence of an external field Bo, the nuclear spins
orient in two ways.
58 | P a g e
Parallel
Antiparallel
Applied Magnetic Field, Bo
N
S
S
N
H atom
H atom spin state = -1/2 (β)
Spin state = +1/2
(α)
(Higher energy)
(Lower energy)
Further influence of external magnetic field is that it causes precession of the nuclei.
Precessional orbit
Precessional motion
Nuclear magnetic dipole µ
Bo
59 | P a g e
The frequency of this motion is called precessional frequency (ν). i.e the number of times the
proton undergoes precession motion per second. Therefore the two spin states can be shown as
below.
Precessional orbit
Spinning nucleus
Parallel +1/2
α-spin state
Antiparallel -1/2
Applied
β-spin state
Magnetic field
A fundamental quantum law is that: in a uniform magnetic field, a nucleus of spin I may assume
2I +1 orientations. Thus, for a nucleus of I = ½ (e.g the proton), there are 2(1/2) + 1 = 2
permissible orientations. This makes a nucleus of I = ½ analogous to a bar magnet in a magnetic
field.
As with the bar magnet, the two orientations of the nuclear magnet in the magnetic field (of
strength Bo) have different energies, and it is possible to induce a nuclear transition, analogous to
the flipping of the bar magnet, by applying electromagnetic radiation of an appropriate frequency
ν.
60 | P a g e
High energy or antiparallel state
N
S
South
North
S
N
Lower energy or parallel state
Energy of nuclei, E
β-spin state -1/2
ΔE
α-spin state +1/2
0
Energy difference (ΔE)
Between nuclear spin states
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Magnetic field strength Bo
∝ Magnetic field (Bo) experienced by nuclei
∆𝐸 =
ℎ𝛾𝐵𝑜
2𝜋
γ = magnetogyric ratio or gyromagnetic ratio (a proportionality constant, differing for each
nucleus which essentially measures the strength of nuclear magnets.
Bo = strength of the applied magnetic field.
h = Planck’s constant.
∆𝐸 = ℎ𝜈 =
ℎ𝛾𝐵𝑜
𝛾𝐵𝑜
⟹ 𝜈=
2𝜋
2𝜋
Precessional frequency (ν) is directly proportional to Bo. For transition from the lower state to the
upper state, the energy falls within the radiofrequency range of electromagnetic radiation. When
appropriate radiofrequency is supplied i.e precessional frequency = radiofrequency. Absorption
will occur and the nucleus and the radiofrequency are said to be in resonance hence the term
NUCLEAR MAGNETIC RESONANCE.
The frequency at which this happens is also called resonance frequency.
Nucleus
1
H
C
19
F
31
P
13
Magnetogyric ratio
(radian T-1 S-1)
2.6752 × 108
6.7283 × 107
2.5181 × 108
1.0841 × 108
Isotopic
%
99.98
1.11
100.00
100.00
abundance, Absorption frequency
MHz (@ 4.69T)
200
50.30
188.25
81.05
Example
What is the absorption frequency in a 2.4 T magnetic field for 1H, 13C?
The NMR Spectrometer
The crucial parts of any high resolution NMR spectrometer are:1. The magnet which may either be a permanent, an electromagnet or a superconducting
solenoid, but which must be capable of generating a very strong, very stable and very
homogeneous magnetic field. To average out small magnetic field inhomogeneities
through out the sample, the sample tube is rotated at several hundred rotation per minute
(rpm). To obtain high stability, the field is “locked” to the frequency using electronic
feedback devices.
62 | P a g e
2. The sweep generator, which is used to vary the magnetic field over a small range by
passing a variable direct current through coils that are coaxial with the direction of the
main magnetic field, Bo (Ho in the diagram
3. The transmitter coil, which is placed at right angles to the sweep coils and is used to
generate the exciting field B1.
4. The receiver coil, which is placed around the sample holder in the remaining orthogonal
plane. A small current is generated in it when the resonance condition is achieved.
The signal from the receiver coil is suitably amplified and is made to deflect the recorder pen
along the y-axis while the x-axis is synchronized with the sweep generator. Thus one plots the
signal from the receiver coil as a function of the field strength; the intensity of the signal is
proportional to the number of nuclei undergoing the transition. This is the field sweep
experiment.
The frequency sweep experiment is analogous except that the field is kept constant while the
frequency is swept and synchronized with the x-axis of the recorder. In either case, one can
express the x-axis scale in terms of signal frequency because by the equation above the field
strength and frequency for the resonance condition are always directly connected. For protons,
the intensity of the signal is proportional to the area under the absorption curve and is usually
obtained by electronic integration, yielding a step function whose height is a direct measure of
63 | P a g e
the relative intensity of the absorption signal. However for other nuclei, in particular
relationship no longer holds.
13
C, this
Distribution of Particles Between Magnetic Quantum States
In the absence of a magnetic field, the energies of the magnetic quantum states of a nucleus are
identical. Consequently, a large collection of protons contains an identical number of nuclei with
magnetic quantum number of +1/2 and -1/2. When placed in a magnetic, however, the nuclei
tend to orient themselves so that the lower energy state (m = +1/2) predominates. It is instructive
to calculate the extent of this predominance in a typical NMR experiment.
Using Boltzmann Equation:
𝑁𝑗
−Δ𝜀
= 𝑒 ( ⁄𝑘𝑇)
𝑁𝑜
Nj = number of protons in the higher energy state (m = -1/2)
No = the number of protons in the lower energy state (m = +1/2)
k = Boltzmann constant (1.38 × 10-23 JK-1)
T = Absolute temperature
Δε = energy difference of the two states.
Substituting the equation for Δε gives:
−γhBo⁄
𝑁𝑗
2𝜋𝑘𝑇 )
= 𝑒(
𝑁𝑜
Example
Calculate the relative number of protons in the higher and lower magnetic states when a sample
is placed in a 4.69T field at 20oC.
𝑁𝑗
8 −1 −1
−34
−23
= 𝑒 (−(2.68 ×10 𝑇 𝑠 )(6.63×10 𝐽𝑠)(4.69𝑇)/2𝜋(1.38×10 𝐽𝐾 −1 )(293𝐾)
𝑁𝑜
𝑁𝑗
−5
= 𝑒 −3.28×10 = 0.999967
𝑁𝑜
Or
𝑁𝑜
𝑁𝑗
= 1.000033
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Thus, for exactly 106 protons in higher energy states, there will be
No = 106/0.999967 = 1,000,033 in the lower energy state. This figure corresponds to a 33 ppm
excess. This example shows that the success of the NMR measurement depends upon a
remarkably small, 33 ppm, excess of lower energy protons. If the number of nuclei in the two
states were identical, however, we would observe no net absorption because the number of
particles excited by the radiation would exactly equal the number producing induced emission.
This shows that NMR is not a sensitive method of analysis.
The equation below can be derived
𝑁𝑗
𝜈ℎ𝐵𝑜
=1−
𝑁𝑜
2𝜋𝑘𝑇
This equation shows that the relative number of excess low energy nuclei is linearly related to
the magnetic field strength Bo. Thus, the intensity of an NMR signal increases linearly as the
field strength increases. This dependence of signal sensitivity on magnetic field strength has led
manufacturers to produce magnets with field strengths as large as 14T (tesla).
When a proton absorbs the correct radiofrequency, nuclei in the lower energy state undergo
transition to the higher energy state. No and Nj approach equality. No further net absorption of
energy occurs. Resonance signals will fade out and this is called saturation of the signal.
E
Start:
Equilibrium
65 | P a g e
Irradiation
saturation
5
seconds
later
20 seconds
later
High energy nuclei lose energy by radiationless process. Such energy loss is called relaxation
(the process through which the Boltzmann’s excess is restored).
There are two types of relaxation:
1. Spin-lattice relaxation: the transfer of energy to the lattice (entire framework or
aggregate of neighbours i.e solvent molecules, or other atoms in the molecule).
2. Spin-spin relaxation: transfer of energy to a neighbouring nucleus having identical
precessional frequency.
Shielding
Usually the nucleus of an atom placed in a magnetic field does not experience the full strength of
the field. This is because the electrons circulating around the nucleus induce a magnetic field
which opposes the external field.
Electronic band
+
Bo
B induced
The secondary magnetic field (B) generated by the electronic circulation shields the nucleus
from the external magnetic field. Thus 𝜈 =
𝛾𝐵𝑜
2𝜋
has to be modified as 𝜈 =
𝛾𝐵𝑜 (1−𝛿)
2𝜋
where δ is
the shielding factor. The local magnetic field experienced by the nuclei is dominated by the
applied magnetic field Bo, but will also depend very weakly up on electrons present in the
molecule and nearby magnetic spins.
66 | P a g e
ν will vary with the electron environment.
Electron donating groups increase the electron density around nearby hydrogen atoms resulting
in increased shielding. Electron withdrawing groups decrease the electron density around nearby
hydrogen atoms resulting in decreased shielding (deshielding).
CH3F, CH3O, CH3N, CH3C, CH3Si
Decreasing order of electronegativity of groups attached to CH3.
NMR is useful to distinguish nuclei with different electronic environment. Tetramethylsilane
(TMS) (CH3)4Si has among the most shielded nuclei. It is used as a reference point in NMR.
Chemical Shift
It is the difference in the absorption position (in Hertz, Hz) of a nucleus (e.g 1H) from the
absorption position of a reference (usually TMS).
Chemical shift = νnucleus – νTMS
Eg. For
O
H 3C
The chemical shift is 120 Hz at 1.4 T (60 MHz)
200 Hz at 2.3 T (100 MHz)
1200 Hz at 14 T (600 MHz)
Chemical shifts are not given in frequency (Hz) since it is dependent on the field strength of the
magnet used. Field independent parameter can be obtained if chemical shift in frequency is
divided by the operational frequency.
𝐶ℎ𝑒𝑚𝑖𝑐𝑎𝑙 𝑠ℎ𝑖𝑓𝑡 (𝛿) =
𝜈𝑛𝑢𝑐𝑙𝑒𝑢𝑠 − 𝜈𝑇𝑀𝑆
𝑧
Z = operational frequency in MHz.
𝐻𝑧
Units of δ will be: 𝑀𝐻𝑧 =
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𝐻𝑧
106 𝐻𝑧
=
1
106
= 1 𝑝𝑝𝑚(𝑝𝑎𝑟𝑡 𝑝𝑒𝑟 𝑚𝑖𝑙𝑙𝑖𝑜𝑛)
𝛿𝐶𝐻3 =
𝜈𝑠𝑖𝑔𝑛𝑎𝑙 − 𝜈𝑇𝑀𝑆
120
200
1200
=
=
=
= 2𝑝𝑝𝑚
𝑧
60
100
600
Position of resonance is in a unit independent of the field strength. At 60 MHz, 1ppm = 60 Hz
100 MHz, 1 ppm = 100Hz
600 MHz, 1 ppm = 600 Hz
Operational frequency has implications on resolution. (Advantage of a stronger magnet means
you have more points hence a better resolution).
The chemical shift of a proton depends upon its chemical environment. Chemical shifts are
measured using the δ-scale and are given as ppm values relative to n arbitrary standard
tetramethylsilane (TMS).
TMS is assigned a value of δ = 0.00 ppm.
Most protons will absorb between 10.5 and -0.5 ppm. Consider a “300 MHz” NMR instrument.
Peak due to TMS
occurs at 0.00 ppm
Chemical shift scale
10
3000
High frequency
6
9
8
7
2700
2400
2100 1800
Increasing shielding
5
4
3
2
1
1500 1200 900 600 300
Upfield
Lowfield
High field
Shielded
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δ
(ppm)
0
ν (Hz)
Low frequency
Down field
Deshielded
0