|
|
| Line 1: |
Line 1: |
| '''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>
| | I am Christin from Harryda. I am learning to play the Euphonium. Other hobbies are Kiteboarding. |
| | |
| 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]]
| |
I am Christin from Harryda. I am learning to play the Euphonium. Other hobbies are Kiteboarding.