Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements
The packing densities of spheres of two different sizes, regularly arranged in a few structures based on cubic or hexagonal packing, have been calculated for different ratios (γ) of the radii of the spheres. Apart from a series of structures AB n , formed by very small B spheres filling cavities in...
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| Veröffentlicht in: | Philosophical magazine. A, Physics of condensed matter. Defects and mechanical properties Physics of condensed matter. Defects and mechanical properties, 1980-12, Vol.42 (6), p.721-740 |
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| container_title | Philosophical magazine. A, Physics of condensed matter. Defects and mechanical properties |
| container_volume | 42 |
| creator | Murray, M. J. Sanders, J. V. |
| description | The packing densities of spheres of two different sizes, regularly arranged in a few structures based on cubic or hexagonal packing, have been calculated for different ratios (γ) of the radii of the spheres. Apart from a series of structures AB
n
, formed by very small B spheres filling cavities in a close-packed array of A spheres, only two arrangements AB (NaCl-type) and AB
2
(AlB
2
-type) have packing fractions greater than the 0·7405 of the separate close-packed phases. Thus it is likely that for 0·24 < γ < 0·458 a mixture of A and B spheres will contain the AB phase, and for 0·482 < γ < 0·624, AB
2
should occur. An ideal cubic structure AB
13
, containing an icosahedral cluster of small (B) spheres cannot have a packing fraction greater than 0·738, but a small modification to the structure permits an increase in the packing to 0·76, and is suggested as the explanation for the appearance of this phase in the opal specimen described in Part I of this work. |
| doi_str_mv | 10.1080/01418618008239380 |
| format | Article |
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n
, formed by very small B spheres filling cavities in a close-packed array of A spheres, only two arrangements AB (NaCl-type) and AB
2
(AlB
2
-type) have packing fractions greater than the 0·7405 of the separate close-packed phases. Thus it is likely that for 0·24 < γ < 0·458 a mixture of A and B spheres will contain the AB phase, and for 0·482 < γ < 0·624, AB
2
should occur. An ideal cubic structure AB
13
, containing an icosahedral cluster of small (B) spheres cannot have a packing fraction greater than 0·738, but a small modification to the structure permits an increase in the packing to 0·76, and is suggested as the explanation for the appearance of this phase in the opal specimen described in Part I of this work.</description><identifier>ISSN: 0141-8610</identifier><identifier>EISSN: 1460-6992</identifier><identifier>DOI: 10.1080/01418618008239380</identifier><language>eng</language><publisher>London: Taylor & Francis Group</publisher><ispartof>Philosophical magazine. A, Physics of condensed matter. Defects and mechanical properties, 1980-12, Vol.42 (6), p.721-740</ispartof><rights>Copyright Taylor & Francis Group, LLC 1980</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c307t-e37cf7f5e5fce83bc290afb1cafbf8389edc28b365df39f385b1edf5c2422db73</citedby><cites>FETCH-LOGICAL-c307t-e37cf7f5e5fce83bc290afb1cafbf8389edc28b365df39f385b1edf5c2422db73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/01418618008239380$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/01418618008239380$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,780,784,27867,27922,27923,59645,60434</link.rule.ids></links><search><creatorcontrib>Murray, M. J.</creatorcontrib><creatorcontrib>Sanders, J. V.</creatorcontrib><title>Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements</title><title>Philosophical magazine. A, Physics of condensed matter. Defects and mechanical properties</title><description>The packing densities of spheres of two different sizes, regularly arranged in a few structures based on cubic or hexagonal packing, have been calculated for different ratios (γ) of the radii of the spheres. Apart from a series of structures AB
n
, formed by very small B spheres filling cavities in a close-packed array of A spheres, only two arrangements AB (NaCl-type) and AB
2
(AlB
2
-type) have packing fractions greater than the 0·7405 of the separate close-packed phases. Thus it is likely that for 0·24 < γ < 0·458 a mixture of A and B spheres will contain the AB phase, and for 0·482 < γ < 0·624, AB
2
should occur. An ideal cubic structure AB
13
, containing an icosahedral cluster of small (B) spheres cannot have a packing fraction greater than 0·738, but a small modification to the structure permits an increase in the packing to 0·76, and is suggested as the explanation for the appearance of this phase in the opal specimen described in Part I of this work.</description><issn>0141-8610</issn><issn>1460-6992</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1980</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><recordid>eNp1kE1PwzAMhiMEEmPwA7hF4tzhJGubSFzQxMekSVzGOUrTZMvWNSVpNY1fT6ZyQ1zi2H4fW34RuicwI8DhEcic8IJwAE6ZYBwu0ITMC8gKIeglmpz7WRLANbqJcQcApASYoN2i8dFkndJ7U-PYh0H3QzARe4tjtzW_3_7oce2sTXnb4-i-U3m5nOH11uAz69oNrk0bXe9GoHF705ywCkG1G3NIVLxFV1Y10dz9xin6fH1ZL96z1cfbcvG8yjSDss8MK7UtbW5yqw1nlaYClK2ITo_ljAtTa8orVuS1ZcIynlfE1DbXdE5pXZVsih7GuV3wX4OJvdz5IbRppSRU8OQWCJpUZFTp4GMMxsouuIMKJ0lAni2VfyxNzNPIuNb6cFBHH5pa9urU-GDTodpFyf7HfwCIE33H</recordid><startdate>19801201</startdate><enddate>19801201</enddate><creator>Murray, M. 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The packing densities of likely arrangements</title><author>Murray, M. J. ; Sanders, J. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c307t-e37cf7f5e5fce83bc290afb1cafbf8389edc28b365df39f385b1edf5c2422db73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1980</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Murray, M. J.</creatorcontrib><creatorcontrib>Sanders, J. 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A, Physics of condensed matter. Defects and mechanical properties</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Murray, M. J.</au><au>Sanders, J. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements</atitle><jtitle>Philosophical magazine. A, Physics of condensed matter. Defects and mechanical properties</jtitle><date>1980-12-01</date><risdate>1980</risdate><volume>42</volume><issue>6</issue><spage>721</spage><epage>740</epage><pages>721-740</pages><issn>0141-8610</issn><eissn>1460-6992</eissn><abstract>The packing densities of spheres of two different sizes, regularly arranged in a few structures based on cubic or hexagonal packing, have been calculated for different ratios (γ) of the radii of the spheres. Apart from a series of structures AB
n
, formed by very small B spheres filling cavities in a close-packed array of A spheres, only two arrangements AB (NaCl-type) and AB
2
(AlB
2
-type) have packing fractions greater than the 0·7405 of the separate close-packed phases. Thus it is likely that for 0·24 < γ < 0·458 a mixture of A and B spheres will contain the AB phase, and for 0·482 < γ < 0·624, AB
2
should occur. An ideal cubic structure AB
13
, containing an icosahedral cluster of small (B) spheres cannot have a packing fraction greater than 0·738, but a small modification to the structure permits an increase in the packing to 0·76, and is suggested as the explanation for the appearance of this phase in the opal specimen described in Part I of this work.</abstract><cop>London</cop><pub>Taylor & Francis Group</pub><doi>10.1080/01418618008239380</doi><tpages>20</tpages></addata></record> |
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| source | Periodicals Index Online; Taylor & Francis:Master (3349 titles) |
| title | Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements |
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