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Goldschmidt tolerance factor - Revision history
2024-03-28T20:03:29Z
Revision history for this page on the wiki
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https://dictionary.iucr.org/index.php?title=Goldschmidt_tolerance_factor&diff=4474&oldid=prev
BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)
2017-11-13T14:43:13Z
<p>Tidied translations and added German and Spanish (U. Mueller)</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 14:43, 13 November 2017</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Facteur de tolérance de Goldschmidt</font> (''Fr''). <font color="black">Fattore di tolleranza di Goldschmidt</font> (''It'').  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Facteur de tolérance de Goldschmidt</font> (''Fr<ins class="diffchange diffchange-inline">''). <font color="red">Goldschmidtscher Toleranzfaktor</font> (''Ge</ins>''). <font color="black">Fattore di tolleranza di Goldschmidt</font> (''It<ins class="diffchange diffchange-inline">''). <font color="green">Factor de tolerancia de Goldschmidt</font> (''Sp</ins>'').</div></td></tr>
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BrianMcMahon
https://dictionary.iucr.org/index.php?title=Goldschmidt_tolerance_factor&diff=4191&oldid=prev
BrianMcMahon: Style edits to align with printed edition
2017-05-19T15:25:52Z
<p>Style edits to align with printed edition</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 15:25, 19 May 2017</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font <del class="diffchange diffchange-inline">colour</del>="blue">Facteur de tolérance de Goldschmidt</font> (''Fr'')<del class="diffchange diffchange-inline">; </del><font <del class="diffchange diffchange-inline">colour</del>="black">Fattore di tolleranza di Goldschmidt</font> (''It'')<del class="diffchange diffchange-inline">; </del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font <ins class="diffchange diffchange-inline">color</ins>="blue">Facteur de tolérance de Goldschmidt</font> (''Fr'')<ins class="diffchange diffchange-inline">. </ins><font <ins class="diffchange diffchange-inline">color</ins>="black">Fattore di tolleranza di Goldschmidt</font> (''It'')<ins class="diffchange diffchange-inline">. </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">'''Goldschmidt's tolerance factor''' is a a dimensionless number that measures the stability and distortion of crystal structures. Originally introduced to describe perovskite structure, tolerance factors are today also used for ilmenite. It can be used to calculate the compatibility of an ion with a crystal structure.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The Goldschmidt tolerance factor (t) is calculated from the ratio of the ionic radii:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">'''Goldschmidt's tolerance factor''' is a dimensionless number that measures the stability and distortion of crystal structures. Originally introduced to describe perovskite structure, tolerance factors are today also used for ilmenite. It can be used to calculate the compatibility of an ion with a crystal structure.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The Goldschmidt tolerance factor (<ins class="diffchange diffchange-inline">''</ins>t<ins class="diffchange diffchange-inline">''</ins>) is calculated from the ratio of the ionic radii:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| style="text-align:center; margin:auto" cellspacing="15"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| style="text-align:center; margin:auto" cellspacing="15"</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where ''r<sub>A</sub><del class="diffchange diffchange-inline">'' </del>is the radius of the A-cation, ''r<sub>B</sub><del class="diffchange diffchange-inline">'' </del>is the radius of the B-cation and ''r<sub>0</sub><del class="diffchange diffchange-inline">'' </del>is the radius of the anion (usually oxygen).</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where ''r<ins class="diffchange diffchange-inline">''</ins><sub><ins class="diffchange diffchange-inline">''</ins>A<ins class="diffchange diffchange-inline">''</ins></sub> is the radius of the <ins class="diffchange diffchange-inline">''</ins>A<ins class="diffchange diffchange-inline">''</ins>-cation, ''r<ins class="diffchange diffchange-inline">''</ins><sub><ins class="diffchange diffchange-inline">''</ins>B<ins class="diffchange diffchange-inline">''</ins></sub> is the radius of the <ins class="diffchange diffchange-inline">''</ins>B<ins class="diffchange diffchange-inline">''</ins>-cation and ''r<ins class="diffchange diffchange-inline">''</ins><sub>0</sub> is the radius of the anion (usually oxygen).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In an ideal cubic perovskite structure the cell parameter ''a'' can be calculated from the atomic radii as <del class="diffchange diffchange-inline">follows:</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In an ideal cubic perovskite structure the cell parameter ''a'' can be calculated from the atomic radii as  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| style="text-align:center; margin:auto" cellspacing="15"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| style="text-align:center; margin:auto" cellspacing="15"</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| colspan="3" align="center" | <math>a=\sqrt{2}(r_A+r_0)=2(r_B+r_0)</math>  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| colspan="3" align="center" | <math>a=\sqrt{2}(r_A+r_0)=2(r_B+r_0)<ins class="diffchange diffchange-inline">.</ins></math>  </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|</div></td></tr>
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BrianMcMahon
https://dictionary.iucr.org/index.php?title=Goldschmidt_tolerance_factor&diff=3805&oldid=prev
MassimoNespolo: Created page with "<font colour="blue">Facteur de tolérance de Goldschmidt</font> (''Fr''); <font colour="black">Fattore di tolleranza di Goldschmidt</font> (''It''); '''Goldschmidt's tolerance ..."
2017-02-03T12:32:46Z
<p>Created page with "<font colour="blue">Facteur de tolérance de Goldschmidt</font> (''Fr''); <font colour="black">Fattore di tolleranza di Goldschmidt</font> (''It''); '''Goldschmidt's tolerance ..."</p>
<p><b>New page</b></p><div><font colour="blue">Facteur de tolérance de Goldschmidt</font> (''Fr''); <font colour="black">Fattore di tolleranza di Goldschmidt</font> (''It''); <br />
<br />
'''Goldschmidt's tolerance factor''' is a a dimensionless number that measures the stability and distortion of crystal structures. Originally introduced to describe perovskite structure, tolerance factors are today also used for ilmenite. It can be used to calculate the compatibility of an ion with a crystal structure.<br />
<br />
The Goldschmidt tolerance factor (t) is calculated from the ratio of the ionic radii:<br />
<br />
{| style="text-align:center; margin:auto" cellspacing="15"<br />
|-<br />
| colspan="3" align="center" | <math>t={r_A+r_0 \over \sqrt{2}(r_B+r_0)}</math> <br />
|-<br />
|}<br />
where ''r<sub>A</sub>'' is the radius of the A-cation, ''r<sub>B</sub>'' is the radius of the B-cation and ''r<sub>0</sub>'' is the radius of the anion (usually oxygen).<br />
<br />
In an ideal cubic perovskite structure the cell parameter ''a'' can be calculated from the atomic radii as follows:<br />
<br />
{| style="text-align:center; margin:auto" cellspacing="15"<br />
|-<br />
| colspan="3" align="center" | <math>a=\sqrt{2}(r_A+r_0)=2(r_B+r_0)</math> <br />
|-<br />
|<br />
|}<br />
<br />
[[Category:Crystal chemistry]]</div>
MassimoNespolo