Mu Canis Majoris: Difference between revisions
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'''Goldschmidt's tolerance factor''' is an indicator for the stability and distortion of crystal structures.<ref name="Johnsson & Lemmens 2007">{{cite book |url=http://books.google.com/books?id=N-rXAAAAMAAJ&q=Handbook+of+magnetism+and+advanced+magnetic+materials&dq=Handbook+of+magnetism+and+advanced+magnetic+materials&hl=en&sa=X&ei=KKfOUtHKCeeysQSa14HYDA&ved=0CDoQ6AEwAA |last1=Parkin|first1=editors-in-chief, Helmut Kronmller, Stuart|title=Handbook of magnetism and advanced magnetic materials|year=2007|publisher=John Wiley & Sons|location=Hoboken, NJ|isbn=978-0-470-02217-7|author2=Mats Johnsson|edition=[Online-Ausg.]|author3=Peter Lemmens|accessdate=17 May 2012}}</ref> It was originally only used to describe [[perovskite]] structure, but now tolerance factors are also used for [[ilmenite]].<ref name="XiangChun 2008">{{cite journal |last1=Liu |first1=XiangChun |author2=Hong, Rongzi; Tian, Changsheng |title=Tolerance factor and the stability discussion of ABO3-type ilmenite |journal=Journal of Materials Science: Materials in Electronics |date=24 April 2008 |volume=20 |issue=4 |pages=323–327 |doi=10.1007/s10854-008-9728-8 |url=http://www.springerlink.com/content/x30773061g176065/ |accessdate=17 May 2012}}</ref> | |||
Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure.<ref name="Schinzer 1998">{{cite web |last=Schinzer |first=Carsten |title=Distortion of Perovskites |url=http://www.ccp14.ac.uk/ccp/web-mirrors/pki/uni/pki/members/schinzer/stru_chem/perov/di_gold.html |accessdate=17 May 2012}}</ref> | |||
The first description of the tolerance factor for perovskite was made by [[Victor Goldschmidt|Victor Moritz Goldschmidt]] in 1926.<ref name="Goldschmidt 1926">{{cite journal|last=Goldschmidt|first=Victor M.|title=Die Gesetze der Krystallochemie|journal=Die Naturwissenschaften|year=1926|volume=21|pages=477–485}}</ref> | |||
== Mathematical expression == | |||
The '''Goldschmidt tolerance factor''' (t) is a dimensionless number that is calculated from the ratio of the ionic radii:<ref name="Johnsson & Lemmens 2007" /> | |||
{| style=" background: #fdfdfd; border:1px solid #ddd; text-align:center; margin:auto" cellspacing="15" | |||
|- | |||
| colspan="3" align="center" | <math>t={r_A+r_0 \over \sqrt{2}(r_B+r_0)}</math> | |||
|- | |||
| ''r<sub>A</sub>'' is the radius of the A-cation. || ''r<sub>B</sub>'' is the radius of the B-cation. || ''r<sub>0</sub>'' is the radius of the anion (usually oxygen). | |||
|} | |||
In an ideal cubic perovskite structure the axis of the unit cell (a) can be described with the following equation:<ref name="Johnsson & Lemmens 2007" /> | |||
{| style=" background: #fdfdfd; border:1px solid #ddd; text-align:center; margin:auto" cellspacing="15" | |||
|- | |||
| colspan="3" align="center" | <math>a=\sqrt{2}(r_A+r_0)=2(r_B+r_0)</math> | |||
|- | |||
| ''r<sub>A</sub>'' is the radius of the A-cation. || ''r<sub>B</sub>'' is the radius of the B-cation. || ''r<sub>0</sub>'' is the radius of the anion (usually oxygen). | |||
|} | |||
== Perovskite structure == | |||
The perovskite structure has the following tolerance factors (t): | |||
{| class="wikitable" | |||
|- | |||
! Goldschmidt tolerance factor (t) !! Structure !! Explanation !! Example !! Example lattice | |||
|- | |||
| >1<ref name="Schinzer 1998" /> || Hexagonal || A ion too big or B ion too small. | |||
| | |||
* BaNiO<sub>3</sub><ref name="Johnsson & Lemmens 2007" /> | |||
| - | |||
|- | |||
| 0.9-1<ref name="Schinzer 1998" /> || Cubic || A and B ions have ideal size. | |||
| | |||
* [[SrTiO3|SrTiO<sub>3</sub>]]<ref name="Johnsson & Lemmens 2007" /> | |||
* [[BaTiO3|BaTiO<sub>3</sub>]]<ref name=Buttner>{{cite journal |last1=Buttner |first1=R. H. |author2=Maslen, E. N. |title=Structural parameters and electron difference density in BaTiO3 |journal=Acta Crystallographica Section B Structural Science |date=30 November 1992 |volume=48 |issue=6 |pages=764–769 |doi=10.1107/S010876819200510X}}</ref> | |||
| [[File:Cubic perovskite structure.png|300px|frameless|center]] | |||
|- | |||
| 0.71 - 0.9<ref name="Schinzer 1998" />|| Orthorhombic/Rhombohedral ||A ions too small to fit into B ion interstices. | |||
| | |||
* GdFeO<sub>3</sub> (Orthorhombic)<ref name="Johnsson & Lemmens 2007" /> | |||
* [[CaTiO3|CaTiO<sub>3</sub>]] (Orthorhombic)<ref name="Johnsson & Lemmens 2007" /> | |||
| [[File:CaTiO3 perovskite structure.png|300px|frameless|center]] | |||
|- | |||
| <0.71<ref name="Schinzer 1998" /> || Different structures || A ions and B have similar ionic radii. | |||
| | |||
* [[Ilmenite]], FeTiO<sub>3</sub> (Trigonal) <ref name="Schinzer 1998" /> | |||
| - | |||
|} | |||
== See also == | |||
* [[Goldschmidt classification]] | |||
* [[Victor Goldschmidt]] | |||
== References == | |||
{{Reflist}} | |||
==External links== | |||
* [http://wikis.lib.ncsu.edu/index.php/Perovskite Perovskite Page at the NCSU] | |||
[[Category:Crystallography]] | |||
[[Category:Mineralogy]] | |||
Revision as of 21:57, 14 April 2013
Goldschmidt's tolerance factor is an indicator for the stability and distortion of crystal structures.[1] It was originally only used to describe perovskite structure, but now tolerance factors are also used for ilmenite.[2]
Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure.[3]
The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926.[4]
Mathematical expression
The Goldschmidt tolerance factor (t) is a dimensionless number that is calculated from the ratio of the ionic radii:[1]
| rA is the radius of the A-cation. | rB is the radius of the B-cation. | r0 is the radius of the anion (usually oxygen). |
In an ideal cubic perovskite structure the axis of the unit cell (a) can be described with the following equation:[1]
| rA is the radius of the A-cation. | rB is the radius of the B-cation. | r0 is the radius of the anion (usually oxygen). |
Perovskite structure
The perovskite structure has the following tolerance factors (t):
| Goldschmidt tolerance factor (t) | Structure | Explanation | Example | Example lattice |
|---|---|---|---|---|
| >1[3] | Hexagonal | A ion too big or B ion too small. |
|
- |
| 0.9-1[3] | Cubic | A and B ions have ideal size. | ||
| 0.71 - 0.9[3] | Orthorhombic/Rhombohedral | A ions too small to fit into B ion interstices. | ||
| <0.71[3] | Different structures | A ions and B have similar ionic radii. | - |
See also
References
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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

