View source for Physics:Sector mass spectrometer

{{Short description|Class of mass spectrometer}}
[[Image:Jeol 5sector.jpg|thumb|upright=1.3|A five sector mass spectrometer]]
A '''sector instrument''' is a general term for a class of [[Physics:Mass spectrometer|mass spectrometer]] that uses a static electric (E) or magnetic (B) sector or some combination of the two (separately in space) as a mass analyzer.<ref>{{GoldBookRef|file=E01938|title=electric sector}}</ref> Popular combinations of these sectors have been the EB, BE (of so-called reverse geometry), three-sector BEB and four-sector EBEB (electric-magnetic-electric-magnetic) instruments.  Most modern sector instruments are double-focusing instruments (first developed by [[Biography:Francis William Aston|Francis William Aston]], [[Biography:Arthur Jeffrey Dempster|Arthur Jeffrey Dempster]], [[Biography:Kenneth Bainbridge|Kenneth Bainbridge]] and [[Biography:Josef Mattauch|Josef Mattauch]] in 1936<ref>{{Britannica|157489|Arthur Jeffrey Dempster (American physicist)}}</ref>) in that they focus the ion beams both in direction and velocity.<ref>{{cite journal |last= Burgoyne |first=Thomas W. |author2=Gary M. Hieftje  |year= 1996 |title= An introduction to ion optics for the mass spectrograph|journal=[[Chemistry:Mass Spectrometry Reviews|Mass Spectrometry Reviews]] |volume=15 |issue= 4|pages=241–259 |doi=10.1002/(SICI)1098-2787(1996)15:4<241::AID-MAS2>3.0.CO;2-I |pmid=27082712 |url=http://www3.interscience.wiley.com/cgi-bin/abstract/10009446/ABSTRACT|archive-url=https://archive.today/20121210084600/http://www3.interscience.wiley.com/cgi-bin/abstract/10009446/ABSTRACT|url-status=dead|archive-date=2012-12-10|format= abstract |bibcode=1996MSRv...15..241B|citeseerx=10.1.1.625.841 }}</ref>

==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 [[Physics:Physics|physics]] are described by a single equation called the [[Physics:Lorentz force|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 [[Physics:Electrodynamics|electrodynamics]] in general.

: <math>\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),</math>

where '''E''' is the [[Physics:Electric field|electric field]] strength, '''B''' is the [[Physics:Magnetic field|magnetic field]] induction, ''q'' is the charge of the particle, '''v''' is its current [[Physics:Velocity|velocity]] (expressed as a vector), and &times; is the [[Cross product|cross product]].

So the [[Physics:Force|force]] on an ion in a linear homogenous electric field (an electric sector) is:

:<math>F=qE\,</math>,

in the direction of the electric field, with positive ions and opposite that with negative ions.

[[Image:Sector.jpg|right|thumb|Electric sector from a Finnigan MAT mass spectrometer (vacuum chamber housing removed)]]

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 [[Physics:Inertia|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 homogenous magnetic field (a magnetic sector) is:

:<math>F=qvB\,</math>,

perpendicular to both the magnetic field and the velocity vector of the ion itself, in the direction determined by the [[Physics:Right-hand rule|right-hand rule]] of [[Cross product|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.

==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° <math>\left (\frac{\pi}{\sqrt{2}} \right)</math> 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 [[Physics:Isotope|isotopic]] [[Physics:Atomic mass|masses]]. A beam of [[Physics:Proton|positive particles]] is produced from the isotope under study. The beam is subject to the combined action of perpendicular [[Physics:Electric field|electric]] and [[Physics:Magnetic field|magnetic field]]s. Since the forces due to these two fields are equal and opposite when the particles have a [[Physics:Velocity|velocity]] given by

:<math>v=E/B\,</math>

they do not experience a resultant [[Physics:Force|force]]; they pass freely through a slit, and are then subject to another magnetic field, transversing a semi-circular path and striking a [[Physics:Photographic plate|photographic plate]]. The mass of the isotope is determined through subsequent calculation.

===Mattauch–Herzog===
The Mattauch–Herzog geometry consists of a 31.82° (<math>\pi  / 4\sqrt{2}</math> radians) electric sector, a drift length which is followed by a 90° magnetic sector of opposite curvature direction.<ref>{{cite journal|title=Zur Theorie der für alle Massen doppelfokussierenden Massenspektrographen|trans-title=The theory of a mass-spectrograph with double focus independent of mass|journal= Zeitschrift für Naturforschung A| year=1946|first=Alfred|last=Klemm|volume=1|issue=3|pages=137–141|url=https://www.degruyter.com/view/j/zna.1946.1.issue-3/zna-1946-0306/zna-1946-0306.xml|bibcode = 1946ZNatA...1..137K |doi = 10.1515/zna-1946-0306 |s2cid=94043005|doi-access=free}}</ref> 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).<ref>{{cite journal |author1=Schilling GD |author2=Andrade FJ |author3=Barnes JH |author4=Sperline RP |author5=Denton MB |author6=Barinaga CJ |author7=Koppenaal DW |author8=Hieftje GM |title=Characterization of a second-generation focal-plane camera coupled to an inductively coupled plasma Mattauch–Herzog geometry mass spectrograph |journal=Anal. Chem. |volume=78 |issue=13 |pages=4319–25 |year=2006 |pmid=16808438 |doi=10.1021/ac052026k}}</ref>
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.<ref>{{cite journal | doi=10.1002/jms.1057 | pmid=16810642 | title=Alfred Nier and the sector field mass spectrometer |author1=De Laeter |author2=J. & Kurz |author3=M. D. | year=2006 | journal=Journal of Mass Spectrometry | volume=41 | pages=847–854 | issue=7| bibcode=2006JMSp...41..847D| doi-access=free }}</ref><ref>{{GoldBookRef|title=Nier-Johnson geometry|file=N04141}}</ref>

===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 an 85° electric sector, a quadrupole lens and a 72.5° magnetic sector of the same curvature direction.<ref>{{Cite patent|country=US|number=4553029|pubdate=1985-11-12|title=Mass spectrometer|assign1=[[Company:JEOL|Jeol Ltd.]]|inventor1-last=Matsuda|inventor1-first=Hisashi|inventorlink1=Hisashi_Matsuda}}</ref>  This geometry is used in the [[Physics:Sensitive high-resolution ion microprobe|SHRIMP]] and Panorama (gas source, high-resolution, multicollector to measure isotopologues in geochemistry).

==See also==
* Mass-analyzed ion kinetic energy spectrometry
* [[Chemistry:Charge remote fragmentation|Charge remote fragmentation]]
* [[Biography:Kenneth Bainbridge|Kenneth Bainbridge]]
* [[Biography:Alfred O. C. Nier|Alfred O. C. Nier]]

==References==
{{reflist}}

==Further reading==
{{refbegin}}
* Thomson, J. J.: Rays of Positive Electricity and their Application to Chemical Analyses; Longmans Green: London, 1913
{{refend}}

{{Mass spectrometry}}

[[Category:Mass spectrometry]]
[[Category:Measuring instruments]]

{{Sourceattribution|Sector mass spectrometer}}