Sector instrument
Encyclopedia
A sector instrument is a general term for a class of mass spectrometer that uses a static electric or magnetic sector or some combination of the two (separately in space) as a mass analyzer. A popular combination of these sectors has been the BEB (magnetic-electric-magnetic). Most modern sector instruments are double focusing instruments in that they focus the ion beams both in direction and velocity.
are described by a single equation called the Lorentz force
law. This equation is the fundamental equation of all mass spectrometric techniques and applies in non-linear, non-homogeneous cases too and is an important equation in the field of electrodynamics generally.
where E is the electric field
strength, B is the magnetic field
induction, q is the charge of the particle, v is its current velocity
(expressed as a vector), and × is the cross product
.
So the force
on an ion in a linear homogeous electric field (an electric sector) is:
,
in the direction of the electric field, with positive ions and opposite that with negative ions.
The force is only dependent on the charge and electric field strength. The lighter ions will be deflected more and heavier ions less due to the difference in inertia
and the ions will physically separate from each other in space into distinct beams of ions as they exit the electric sector.
And the force on an ion in a linear homogeous magnetic field (a magnetic sector) is:
,
perpendicular to both the magnetic field and the velocity vector of the ion itself, in the direction determined by the right-hand rule
of cross product
s and the sign of the charge.
The force in the magnetic sector is complicated by the velocity dependence but with the right conditions (uniform velocity for example) ions of different masses will separate physically in space into different beams as with the electric sector.
electric sector without an initial drift length followed by a 60° magnetic sector with the same direction of curvature. Sometimes called a "Bainbridge mass spectrometer," this configuration is often used to determine isotopic
masses
. A beam of positive particles
is produced from the isotope under study. The beam is subject to the combined action of perpendicular electric
and magnetic field
s. Since the forces due to these two fields are equal and opposite, the particles with a velocity
given by
do not experience a resultant force
; they pass freely through a slit, and are then subject to another magnetic field, transversing a semi-circular path and striking a photographic plate
. The mass of the isotope is determined through subsequent calculation.
radians) electric sector, a drift length which is followed by a 90° magnetic sector of opposite curvature direction. The entry of the ions sorted primarily by charge into the magnetic field produces an energy focussing effect and much higher transmission than a standard energy filter. This geometry is often used in applications with a high energy spread in the ions produced where sensitivity is nonetheless required, such as spark source mass spectrometry (SSMS) and secondary ion mass spectrometry (SIMS).
The advantage of this geometry over the Nier-Johnson geometry is that the ions of different masses are all focused onto the same flat plane. This allows the use of a photographic plate or other flat detector array.
Theory
The behavior of ions in a homogeneous, linear, static electric or magnetic field (separately) as is found in a sector instrument is simple. The physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
are described by a single equation called the Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
law. This equation is the fundamental equation of all mass spectrometric techniques and applies in non-linear, non-homogeneous cases too and is an important equation in the field of electrodynamics generally.
where E is the electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
strength, B is the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
induction, q is the charge of the particle, v is its current velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
(expressed as a vector), and × is the cross product
Cross product
In mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both of the vectors being multiplied and normal to the plane containing them...
.
So the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
on an ion in a linear homogeous electric field (an electric sector) is:
,in the direction of the electric field, with positive ions and opposite that with negative ions.
The force is only dependent on the charge and electric field strength. The lighter ions will be deflected more and heavier ions less due to the difference in inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
and the ions will physically separate from each other in space into distinct beams of ions as they exit the electric sector.
And the force on an ion in a linear homogeous magnetic field (a magnetic sector) is:
,perpendicular to both the magnetic field and the velocity vector of the ion itself, in the direction determined by the right-hand rule
Right-hand rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century....
of cross product
Cross product
In mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both of the vectors being multiplied and normal to the plane containing them...
s and the sign of the charge.
The force in the magnetic sector is complicated by the velocity dependence but with the right conditions (uniform velocity for example) ions of different masses will separate physically in space into different beams as with the electric sector.
Classic Geometries
These are some of the classic geometries from mass spectrographs which are often used to distinguish different types of sector arrangements, although most current instruments do not fit precisely into any of these categories as the designs have evolved further.Bainbridge-Jordan
The sector instrument geometry consists of a 127.30° electric sector without an initial drift length followed by a 60° magnetic sector with the same direction of curvature. Sometimes called a "Bainbridge mass spectrometer," this configuration is often used to determine isotopicIsotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...
masses
Atomic mass
The atomic mass is the mass of a specific isotope, most often expressed in unified atomic mass units. The atomic mass is the total mass of protons, neutrons and electrons in a single atom....
. A beam of positive particles
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
is produced from the isotope under study. The beam is subject to the combined action of perpendicular electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s. Since the forces due to these two fields are equal and opposite, the particles with a velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
given by
do not experience a resultant force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
; they pass freely through a slit, and are then subject to another magnetic field, transversing a semi-circular path and striking a photographic plate
Photographic plate
Photographic plates preceded photographic film as a means of photography. A light-sensitive emulsion of silver salts was applied to a glass plate. This form of photographic material largely faded from the consumer market in the early years of the 20th century, as more convenient and less fragile...
. The mass of the isotope is determined through subsequent calculation.
Mattauch-Herzog
The Mattauch-Herzog geometry consists of a 31.82° ( radians) electric sector, a drift length which is followed by a 90° magnetic sector of opposite curvature direction. The entry of the ions sorted primarily by charge into the magnetic field produces an energy focussing effect and much higher transmission than a standard energy filter. This geometry is often used in applications with a high energy spread in the ions produced where sensitivity is nonetheless required, such as spark source mass spectrometry (SSMS) and secondary ion mass spectrometry (SIMS).The advantage of this geometry over the Nier-Johnson geometry is that the ions of different masses are all focused onto the same flat plane. This allows the use of a photographic plate or other flat detector array.
Nier-Johnson
The Nier-Johnson geometry consists of a 90° electric sector, a long intermediate drift length and a 60° magnetic sector of the same curvature direction.Hinterberger-Konig
The Hinterberger-Konig geometry consists of a 42.43° electric sector, a long intermediate drift length and a 130° magnetic sector of the same curvature direction.Takeshita
The Takeshita geometry consists of a 54.43° electric sector, and short drift length, a second electric sector of the same curvature direction followed by another drift length before a 180° magnetic sector of opposite curvature direction.Matsuda
The Matsuda geometry consists of a 85° electric sector, a quadrupole lens and a 72.5° magnetic sector of the same curvature direction. This geometry is used in the SHRIMP.See also
- Mass-analyzed ion kinetic energy spectrometryMass-analyzed ion kinetic energy spectrometryMass-analyzed ion-kinetic-energy spectrometry is a mass spectrometry technique by which mass spectra are obtained from a sector instrument that incorporates at least one magnetic sector plus one electric sector in reverse geometry...
- Charge remote fragmentationCharge remote fragmentationCharge remote fragmentation is a type of covalent bond breaking that occurs in a gas phase ion in which the cleaved bond is not adjacent to the location of the charge. This fragmentation can be observed using tandem mass spectrometry....
- Kenneth BainbridgeKenneth BainbridgeKenneth Tompkins Bainbridge was an American physicist at Harvard University who did work on cyclotron research. His precise measurements of mass differences between nuclear isotopes allowed him to confirm Albert Einstein's mass-energy equivalence concept. He was the Director of the Trinity test of...
- Alfred O. C. NierAlfred O. C. NierAlfred Otto Carl Nier was an American physicist who pioneered the development of mass spectrometry and used it in innovative ways to establish some major scientific results.-Early career:...