# Ångström

The ångström (/ˈæŋstrəm, -strʌm/,[1][2]ANG-strəm; ANG-strum Swedish: [²ɔŋːstrœm])[1] or angstrom is a unit of length equal to 10−10 m (one ten-billionth of a metre) or 0.1 nanometre. Its symbol is Å, a letter in the Swedish alphabet.

The natural sciences and technology often use ångström to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. Atoms of phosphorus, sulfur, and chlorine are about an ångström in covalent radius, while a hydrogen atom is about half an ångström; see atomic radius. Visible light has wavelengths in the range of 4000–7000 Å.

The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The symbol is always written with the Swedish alphabet letter 'Å'. Though it appears to be of the Latin alphabet 'A' with a ring diacritic, it is not. The unit's name is often written in English with the Latin alphabet 'A',[3] but the official definition is the Swedish letter 'Å'.[4][5] It is not a part of the SI system of units, but it can be considered part of the metric system.

Ångström
Unit ofLength
SymbolÅ
Named afterAnders Jonas Ångström
Conversions
1 Å in ...... is equal to ...
metres   10−10 m
centimetres   10−8 cm
micrometres   10−4 μm
nanometres   0.1 nm
picometres   100 pm
Anders Jonas Ångström.

## Use

The ångström is used extensively in crystallography, solid-state physics and chemistry as a unit for d-spacings (the distance between atomic planes in a crystal[6]), cell parameters, inter-atomic distances and x-ray wavelengths, as these values are often in the 1–10 Å range. For example, the Inorganic Crystal Structure Database[7] presents all these values using the ångström.

## History

Anders Jonas Ångström was a pioneer in the field of spectroscopy, and he is also well known for his studies of astrophysics, heat transfer, terrestrial magnetism, and the aurora borealis. In 1852, Ångström formulated in Optiska undersökningar,[8] in English translation Optical Researches,[9] a law of absorption, later modified somewhat and known as Kirchhoff's law of thermal radiation.

In 1868, Ångström created a chart of the spectrum of sunlight, in which he expressed the wavelengths of electromagnetic radiation in the electromagnetic spectrum in multiples of one ten-millionth of a millimetre (or 10−7 mm.)[10] Because the human eye is sensitive to wavelengths from about 4000 to 7000 Å (visible light), that choice of unit supported sufficiently accurate measurements of visible wavelengths without resorting to fractional numbers. Ångström's chart and table of wavelengths in the solar spectrum became widely used in solar physics, which adopted the unit and named it after him. It subsequently spread to the rest of astronomical spectroscopy, atomic spectroscopy, and subsequently to other sciences that deal with atomic-scale structures.

Though intended to correspond to 10−10 metres, for precise spectral analysis, the ångström had to be defined more accurately than the metre, which until 1960 was still defined based on the length of a bar of metal held in Paris. The use of metal bars had been involved in an early error in the value of the ångström of about one part in 6000. Ångström took the precaution of having the standard bar he used checked against a standard in Paris, but the metrologist Henri Tresca reported it to be so much shorter than it really was that Ångström's corrected results were more in error than the uncorrected ones.[11]

Example about how the theoretical atomic radii calculated in Ångströms are plotted as a function of the atomic number.

In 1892–1895, Albert A. Michelson defined the ångström so that the red line of cadmium was equal to 6438.47 ångströms.[12] In 1907, the International Union for Cooperation in Solar Research (which later became the International Astronomical Union) defined the international ångström by declaring the wavelength of the red line of cadmium (in dry air at 15 °C (hydrogen scale) and 760 mmHg under a gravity of 9.8067 m/s²) equal to 6438.4696 international ångströms, and this definition was endorsed by the International Bureau of Weights and Measures in 1927.[13][14] From 1927 to 1960, the ångström remained a secondary unit of length for use in spectroscopy, defined separately from the metre. In 1960, the metre itself was redefined in spectroscopic terms, which allowed the ångström to be redefined as being exactly 0.1 nanometres.

The ångström is internationally recognized, but is not a formal part of the International System of Units (SI). The closest SI unit is the nanometre (10−9 m). The International Committee for Weights and Measures officially discourages its use, and it is not included in the European Union's catalogue of units of measure that may be used within its internal market.[15]

## Symbol

Example of the Unicode codification

For compatibility reasons, Unicode includes the formal symbol at U+212B ANGSTROM SIGN (HTML &#8491;). However, the ångström sign is also normalized into U+00C5 Å LATIN CAPITAL LETTER A WITH RING ABOVE (HTML &#197; · &Aring;)[16] The Unicode consortium recommends to use the regular letter (00C5).

Before digital typesetting, the ångström (or ångström unit) was sometimes written as "A.U." (also an abbreviation of the astronomical unit). This use is evident in Bragg's paper on the structure of ice,[17] which gives the c- and a-axis lattice constants as 4.52 A.U. and 7.34 A.U., respectively. Nowadays the atomic unit of length (a.u.) usually stands for bohrs, not ångströms.

## References

1. ^ a b Wells, John C. (2008), Longman Pronunciation Dictionary (3rd ed.), Longman, ISBN 9781405881180
2. ^ Roach, Peter (2011), Cambridge English Pronouncing Dictionary (18th ed.), Cambridge: Cambridge University Press, ISBN 9780521152532
3. ^ Webster′s Encyclopedic Unabridged Dictionary of the English Language. Portland House, 1989
4. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 127, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
5. ^ Thompson, Ambler; Taylor, Barry N. (5 October 2010). "B.8 Factors for Units Listed Alphabetically". NIST Guide to the SI. NIST. Retrieved 21 September 2011.
6. ^ Vailionis, Arturas. "Geometry of Crystals" (PDF). Archived from the original (PDF) on 2015-03-19. Retrieved 20 April 2015.
7. ^
8. ^ "Kungliga Vetenskapsakademiens handlingar", roughly translated as Transactions of the Royal Academy of Sciences, published between 1739 and 1974, see Vetenskapsakademiens Handlingar (in Swedish).
9. ^ Ångström, Anders J., "Optical Researches", Philosophical Magazine, 3rd series, vol. 9, 1855, pp. 327-342
10. ^
11. ^ Brand, John C. D. (1995). Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930. CRC Press. p. 47. ISBN 9782884491631.
12. ^ Michelson, Albert A.; translated by Benoît, Jean-René; « Détermination expérimentale de la valeur du mètre en longueurs d'onde lumineuses », Travaux et mémoires du Bureau international des poids et mesures, vol. 11, 1895, 3rd ed., p. 85
13. ^ Benoît, Jean-René; Fabry, Charles; and Pérot, Alfred; « Nouvelle Détermination du mètre en longueurs d'ondes lumineuses » ["A New Determination of the Metre in Terms of the Wave-length of Light"], Comptes rendus hebdomadaires des séances de l'Académie des sciences, vol. 144, 21 May 1907, p. 1082-1086
14. ^ Comptes rendus de la 7e réunion de la Conférence générale des poids et mesures [Proceedings of the 7th meeting of the General conference of weights and measures] (PDF) (in French), Paris, 1927, pp. 85–88
15. ^ The Council of the European Communities (27 May 2009). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 23 September 2011.
16. ^ The Unicode Consortium (2007). "Symbols" (PDF). The Unicode Standard, Version 5.0. Addison-Wesley. p. 493. ISBN 0-321-48091-0. OCLC 145867322..
17. ^ Bragg, William H. (1921). "The Crystal Structure of Ice". Proceedings of the Physical Society of London. 34 (1): 98. Bibcode:1921PPSL...34...98B. doi:10.1088/1478-7814/34/1/322.
Actinometer

Actinometers are instruments used to measure the heating power of radiation. They are used in meteorology to measure solar radiation as pyranometers, pyrheliometers and net radiometers.

An actinometer is a chemical system or physical device which determines the number of

photons in a beam integrally or per unit time. This name is commonly

applied to devices used in the ultraviolet and visible wavelength ranges.

For example, solutions of iron(III) oxalate can be used as a chemical

actinometer, while bolometers, thermopiles, and photodiodes are physical

devices giving a reading that can be correlated to the number of photons

detected.

Anders Jonas Ångström

Anders Jonas Ångström (Swedish: [²anːdɛʂ ²juːnas ²ɔŋːstrœm]; 13 August 1814 – 21 June 1874) was a Swedish physicist and one of the founders of the science of spectroscopy.

Anders Knutsson Ångström

Anders Knutsson Ångström (1888, Stockholm – 1981) was a Swedish physicist and meteorologist who was known primarily for his contributions to the field of atmospheric radiation. However, his scientific interests encompassed many diverse topics.He was the son of physicist Knut Ångström. He graduated with a BS from the University of Upsala in 1909. Then he completed his MS at the University of Upsala in 1911. He taught at the University of Stockholm Later, he was the department head of the Meteorology department at State Meteorological and Hydrological Institute (SMHI) of Sweden 1945–1949 and SMHI's chancellor 1949–1954.He is credited with the invention of the pyranometer, the first device to accurately measure direct and indirect solar radiation.In 1962 he was awarded the International Meteorological Organization Prize by the World Meteorological Organization.

Angstrom exponent

Ångström exponent is the name of the exponent in the formula that is usually used to describe the dependency of the aerosol optical thickness, or aerosol extinction coefficient on wavelength.

Depending on particle size distribution, the spectral dependence of the aerosol optical thickness is given approximately by

${\displaystyle {\frac {\tau _{\lambda }}{\tau _{\lambda _{0}}}}=\left({\frac {\lambda }{\lambda _{0}}}\right)^{-\alpha }}$

where ${\displaystyle \tau _{\lambda }}$ is the optical thickness at wavelength ${\displaystyle \lambda }$, and ${\displaystyle \tau _{\lambda _{0}}}$ is the optical thickness at the reference wavelength ${\displaystyle \lambda _{0}}$. In principle, if the optical thickness at one wavelength and the Ångström exponent are known, the optical thickness can be computed at a different wavelength. In practice, measurements are made of the optical thickness of an aerosol layer at two different wavelengths, and the Ångström exponent is estimated from these measurements using this formula. The aerosol optical thickness can then be derived at all other wavelengths, within the range of validity of this formula.

For measurements of optical thickness ${\displaystyle \tau _{\lambda _{1}}\,}$ and ${\displaystyle \tau _{\lambda _{2}}\,}$ taken at two different wavelengths ${\displaystyle \lambda _{1}\,}$ and ${\displaystyle \lambda _{2}\,}$ respectively, the Ångström exponent is given by

${\displaystyle \alpha =-{\frac {\log {\frac {\tau _{\lambda _{1}}}{\tau _{\lambda _{2}}}}}{\log {\frac {\lambda _{1}}{\lambda _{2}}}}}\,}$

The Ångström exponent is inversely related to the average size of the particles in the aerosol: the smaller the particles, the larger the exponent. Thus, Ångström exponent is a useful quantity to assess the particle size of atmospheric aerosols or clouds, and the wavelength dependence of the aerosol/cloud optical properties. For example, cloud droplet, usually with large sizes and thus very smaller Ångström exponent (nearly zero), is spectrally neutral, which means, e.g., the optical depth does not change with wavelength. This exponent is now routinely estimated by analyzing radiation measurements acquired on Earth Observation platforms, such as AErosol RObotic NETwork, or AERONET.

Angström (crater)

Ångström is a small lunar impact crater located on the border between Oceanus Procellarum to the west and Mare Imbrium to the east. To the south is a formation of mountains rising out of the mare named the Montes Harbinger. To the east are some wrinkle ridges named the Dorsum Bucher and Dorsa Argand. This crater is bowl-shaped, with a circular rim and inner walls that slope down to the small central floor. It has a higher albedo than the surrounding maria.

Ångström crater is named after Anders Jonas Ångström, a Swedish physicist and one of the founders of the science of spectroscopy.

Debye

The debye (symbol: D) (; Dutch: [dəˈbɛiə]) is a CGS unit (a non-SI metric unit) of electric dipole moment named in honour of the physicist Peter J. W. Debye. It is defined as 1×10−18 statcoulomb-centimetre. Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb (generally called e.s.u. (electrostatic unit) in older literature), which were separated by 1 ångström. This gave a convenient unit for molecular dipole moments.

Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric homoatomic species, e.g. chlorine, Cl2, have zero dipole moment, and highly ionic molecular species have a very large dipole moment, e.g. gas-phase potassium bromide, KBr, with a dipole moment of 10.5 D.The debye is still used in atomic physics and chemistry because SI units are inconveniently large. The smallest SI unit of electric dipole moment is the yoctocoulomb-metre, which is roughly 300,000 D. There is currently no satisfactory solution to this problem of notation without resorting to the use of scientific notation.

Interface Region Imaging Spectrograph

The Interface Region Imaging Spectrograph (IRIS), also called Explorer 94, is a NASA solar observation satellite. The mission was funded through the Small Explorer program to investigate the physical conditions of the solar limb, particularly the chromosphere of the Sun. The spacecraft consists of a satellite bus and spectrometer built by the Lockheed Martin Solar and Astrophysics Laboratory (LMSAL), and a telescope provided by the Smithsonian Astrophysical Observatory. IRIS is operated by LMSAL and NASA's Ames Research Center.

The satellite's instrument is a high-frame-rate ultraviolet imaging spectrometer, providing one image per second at 0.3 arcsecond angular resolution and sub-ångström spectral resolution.

NASA announced on 19 June 2009 that IRIS was selected from six Small Explorer mission candidates for further study, along with the Gravity and Extreme Magnetism (GEMS) space observatory.The spacecraft arrived at Vandenberg Air Force Base, California, on 16 April 2013 and was successfully launched on 27 June 2013 by a Pegasus-XL rocket.

Knut Ångström

Knut Johan Ångström (12 January 1857 – 4 March 1910) was a Swedish physicist. He was the son of physicist Anders Jonas Ångström and studied in Uppsala from 1877 to 1884, when he received his licentiat-degree, before going for a short time to the University of Strassburg (Strasbourg) to study with August Kundt. Coming back to Uppsala, he completed his doctoral degree and was appointed lecturer in physics at the new university college in Stockholm (now Stockholm University) in 1885. After a few years working there, he returned to Uppsala in 1891 and received the professorship of Physics in 1896.He focused his research work on investigating the radiation of heat from the sun, terrestrial nocturnal emission and its absorption by the Earth's atmosphere, and to that end devised various delicate methods and instruments, including his electric compensation pyrheliometer, invented in 1893, apparatus for obtaining a photographic representation of the infra-red spectrum (1895) and pyrgeometer (abt. 1905).

In 1900, Herr J. Koch, laboratory assistant to Knut Ångström, did not observe any appreciable change in the absorption of infrared radiation by decreasing the concentration of CO2 up to a third of the initial amount. This result, in addition to the observation made a couple of years before that the superposition of the water vapour absorption bands, more abundant in the atmosphere, over those of CO2, convinced the community of geologists that the Svante Arrhenius calculations for the CO2 warming effect were useless and by the end of the decade they were already considered obsolete by the great majority of them.The experiment, however, was careless seen from the current perspective with erroneous result but of a historical significance in the development of the theory of the greenhouse effect amplified by CO2.

He was elected a member of the Royal Swedish Academy of Sciences in 1893.

Lars Ångström

Lars Ångström (born March 30, 1955) is a Swedish Green Party politician, member of the Riksdag 1998–2006.Lars Ångström was president of the Swedish Peace and Arbitration Society 1985-1995, and head of the Swedish Greenpeace organisation 1995-1996.

LeapFrog Epic

The LeapFrog Epic (styled as LeapFrog epic) is an Android-based mini-tablet computer produced and marketed by LeapFrog Enterprises. Released in 2015, the Epic is LeapFrog's first device to run on Android; most of LeapFrog's mobile computing devices for children run on a customized Ångström Linux distribution.

Michael A. O'Keefe

For the Louisiana politician, see Michael H. O'Keefe.Michael A. O'Keefe (b. 8 September 1942, in East Melbourne, Australia) is a physicist who has worked in materials science and electron microscopy. He is perhaps best known for his production of the seminal computer code for modeling of high-resolution transmission electron microscopy (HRTEM) images; his software was later made available as part of the DeepView package for remote electron microscopy and control. O'Keefe's tutorial on theory and application of high-resolution electron microscope image simulation is available online.O'Keefe has established methods of quantifying resolution quality, and methods of deriving accurate atom positions from high-resolution images. He used these methods to help establish high-resolution electron microscopy as a precise science; in addition to its more-pedestrian role of pictorial confirmation of nano measurements, he demonstrated HRTEM's value in measurement of nano-properties. The video and associated slides illustrate the role of his work in providing tools for nano-characterization.

O'Keefe designed and developed the one-Ångström microscope (OÅM) for the National Center for Electron Microscopy at Lawrence Berkeley National Laboratory based on an FEI Company CM300 microscope that he modified extensively to improve coherence and correct three-fold astigmatism. He was successful in breaking the "one-Ångström barrier" to resolution using his combination of hardware and software correction of microscope aberrations. He produced the first HRTEM images to show carbon atoms separated by less than one Ångström in diamond (0.89 Å) and silicon atoms in crystalline silicon (0.78 Å)—an example of his silicon work appears on a webpage at the Department of Energy. His OÅM was the first HRTEM able to image the smallest metal atoms (lithium) in lithium battery materials. Building on his work designing and operating his one-Ångström microscope (OÅM), O'Keefe produced the design for the LBNL TEAM (transmission electron aspheric microscope) able to resolve atoms in the deep sub-Ångström resolution region (less than 0.5 Å) using a hardware electron-wave phase-corrector (Cs corrector) in combination with a coherence-enhancing electron-beam monochromator.

Nanometre

The nanometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American spelling) is a unit of length in the metric system, equal to one billionth (short scale) of a metre (0.000000001 m). The name combines the SI prefix nano- (from the Ancient Greek νάνος, nanos, "dwarf") with the parent unit name metre (from Greek μέτρον, metrοn, "unit of measurement"). It can be written in scientific notation as 1×10−9 m, in engineering notation as 1 E−9 m, and as simply 1/1000000000 metres. One nanometre equals ten ångströms. When used as a prefix for something other than a unit of measure (as in "nanoscience"), nano refers to nanotechnology,

or phenomena typically occurring on a scale of nanometres (see nanoscopic scale).The nanometre is often used to express dimensions on an atomic scale: the diameter of a helium atom, for example, is about 0.1 nm, and that of a ribosome is about 20 nm. The nanometre is also commonly used to specify the wavelength of electromagnetic radiation near the visible part of the spectrum: visible light ranges from around 400 to 700 nm. The ångström, which is equal to 0.1 nm, was formerly used for these purposes, but is still used in other fields. Since the late 1980s, in usages such as 32 nm and 22 nm, it has also been used to describe typical feature sizes in successive generations of the ITRS Roadmap for miniaturization in the semiconductor industry.

Openmoko Linux

Openmoko Linux is an operating system for smartphones developed by the Openmoko project. It is based on the Ångström distribution, comprising various pieces of free software.The main targets of Openmoko Linux were the Openmoko Neo 1973 and the Neo FreeRunner. Furthermore, there were efforts to port the system to other mobile phones.Openmoko Linux was developed from 2007 to 2009 by Openmoko Inc. The development was discontinued because of financial problems. Afterwards the development of software for the Openmoko phones was taken over by the community and continued in various projects, including SHR, QtMoko and Hackable1.

Picometre

The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the metric system, equal to 1×10−12 m, or one trillionth (1/1000000000000) of a metre, which is the SI base unit of length.

The picometre is one thousandth of a nanometre, one millionth of a micrometre (also known as a micron), and used to be called micromicron, stigma, or bicron. The symbol µµ was once used for it. It is also one hundredth of an Ångström, an internationally recognised (but non-SI) unit of length.

Uppsala Astronomical Observatory

The Uppsala Astronomical Observatory (UAO), Astronomiska observatoriet i Uppsala) is the oldest astronomical observatory in Sweden. It was founded in 1741, though there was a professorial chair of astronomy at the University of Uppsala from 1593 and the university archives include lecture notes in astronomy from the 1480s.

In the 18th century, Anders Celsius performed his research there and built the first observatory proper in 1741. Celsius got the university consistory to buy a large stone house of medieval origin in central Uppsala, where he had an observatory constructed on the rooftop. Celsius both worked and had his personal living quarters in the house. This observatory remained in use until the new observatory, now known as the "old observatory", was built in 1853. The Celsius house itself still remains as one of few older buildings on a modern shopping street, but the observatory on the roof was demolished in 1857.

In the 19th century Anders Jonas Ångström was keeper of the observatory and conducted his experiments in astronomy, physics and optics there. His son, Knut Ångström, also conducted research on solar radiation at the observatory.

In 2000 the observatory merged with the Institute of Space Physics to form the Department of Astronomy and Space Physics and moved to the Ångström Laboratory. In 2008, another merger resulted in the Department of Physics and Astronomy, Astronomy and Space Physics becoming one of its divisions.

In addition to facilities in Uppsala, the observatory maintains the Kvistaberg Observatory in Sweden and the Uppsala Southern Station at the Siding Spring Observatory in Australia.

Research at the observatory over the years includes stellar parallaxes, stellar statistics, galactic structure, external galaxies, stellar atmospheres and solar system research.

Yvonne Ångström

Yvonne Ångström (born 1940) is a Swedish Liberal People's Party politician. She was a member of the Riksdag from 1998 to 2006.

Å

This letter, Å (å in lower case) represents various (although often very similar) sounds in several languages. It is a separate letter in the Swedish, Danish, Norwegian, Finnish, North Frisian, Walloon, Chamorro, Lule Sami, Skolt Sami, Southern Sami, and Greenlandic alphabets. Additionally, it is part of the alphabets used for the Alemannic and the Bavarian-Austrian dialects of German.

Though Å is derived from an A, with an overring it is considered a separate letter. It developed as a form of semi-ligature of an A with a smaller o above it to denote a long and darker A, similar to how the umlaut mark that distinguishes Ä from A, and Ö/Ø from O, developed from a small e written above the letter in question.

Ångström distribution

The Ångström distribution is a Linux distribution for a variety of embedded devices. The distribution is the result of work by developers from the OpenZaurus, OpenEmbedded, and OpenSIMpad projects. The graphical user interfaces (GUIs) available are OPIE and GPE among other options.

The Ångström distribution is in "cooptition" with Poky Linux. Ångström is based on the OpenEmbedded project, specifically the OpenEmbedded-Core (OE-Core) layer. While both Ångström and Poky Linux are based on OE-Core, mostly utilize the same toolchain and are both officially "Yocto compatible", only Poky Linux is officially part of the Yocto Project.

Ångström primarily differs from Poky Linux in being a binary distribution (like e.g. the Debian, Fedora, OpenSuse or Ubuntu Linux distributions), using opkg for package management. Hence an essential part of Ångström builds is a binary package feed, allowing to simply install software distributed as opkg packages, without having to compile them first (just as one might install a binary package with aptitude or dpkg).

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