<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Weiwei Jin</style></author><author><style face="normal" font="default" size="100%">Yang Jiao</style></author><author><style face="normal" font="default" size="100%">Lufeng Liu</style></author><author><style face="normal" font="default" size="100%">Ye Yuan</style></author><author><style face="normal" font="default" size="100%">Shuixiang Li</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Dense crystalline packings of ellipsoids</style></title><secondary-title><style face="normal" font="default" size="100%">Physical Review E</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.033003</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">95</style></volume><pages><style face="normal" font="default" size="100%">033003</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;&lt;span&gt;An ellipsoid, the simplest nonspherical shape, has been extensively used as a model for elongated building blocks for a wide spectrum of molecular, colloidal, and granular systems. Yet the densest packing of congruent hard ellipsoids, which is intimately related to the high-density phase of many condensed matter systems, is still an open problem. We discover an unusual family of dense crystalline packings of self-dual ellipsoids (ratios of the semiaxes&amp;nbsp;&lt;/span&gt;&lt;span class=&quot;aps-inline-formula&quot;&gt;&lt;span id=&quot;MathJax-Element-1-Frame&quot; class=&quot;mjx-chtml MathJax_CHTML&quot;&gt;&lt;span id=&quot;MJXc-Node-1&quot; class=&quot;mjx-math&quot;&gt;&lt;span id=&quot;MJXc-Node-2&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-3&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-4&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-5&quot; class=&quot;mjx-mi&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-math-I&quot;&gt;α&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-6&quot; class=&quot;mjx-mo MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;:&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-7&quot; class=&quot;mjx-msqrt MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-box&quot;&gt;&lt;span class=&quot;mjx-surd&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;√&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;mjx-box&quot;&gt;&lt;span id=&quot;MJXc-Node-8&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-9&quot; class=&quot;mjx-mi&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-math-I&quot;&gt;α&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-10&quot; class=&quot;mjx-mrow MJXc-space3&quot;&gt;&lt;span id=&quot;MJXc-Node-11&quot; class=&quot;mjx-mo&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;:&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-12&quot; class=&quot;mjx-mn MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;1&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;), containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement in the fundamental cell. The associated packing density&amp;nbsp;&lt;/span&gt;&lt;span class=&quot;aps-inline-formula&quot;&gt;&lt;span id=&quot;MathJax-Element-2-Frame&quot; class=&quot;mjx-chtml MathJax_CHTML&quot;&gt;&lt;span id=&quot;MJXc-Node-13&quot; class=&quot;mjx-math&quot;&gt;&lt;span id=&quot;MJXc-Node-14&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-15&quot; class=&quot;mjx-mi&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-math-I&quot;&gt;ϕ&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&amp;nbsp;exceeds that of the densest known SM2 crystal [ A. Donev&amp;nbsp;&lt;/span&gt;&lt;em&gt;et al.&lt;/em&gt;&lt;span&gt;,&amp;nbsp;&lt;/span&gt;&lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.92.255506&quot;&gt;&lt;span&gt;Phys. Rev. Lett.&lt;/span&gt;&amp;nbsp;&lt;span&gt;92&lt;/span&gt;, 255506 (2004)&lt;/a&gt;&lt;span&gt;] for aspect ratios α in (1.365, 1.5625), attaining a maximal&amp;nbsp;&lt;/span&gt;&lt;span class=&quot;aps-inline-formula&quot;&gt;&lt;span id=&quot;MathJax-Element-3-Frame&quot; class=&quot;mjx-chtml MathJax_CHTML&quot;&gt;&lt;span id=&quot;MJXc-Node-16&quot; class=&quot;mjx-math&quot;&gt;&lt;span id=&quot;MJXc-Node-17&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-18&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-19&quot; class=&quot;mjx-mi&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-math-I&quot;&gt;ϕ&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-20&quot; class=&quot;mjx-mo MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;≈&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-21&quot; class=&quot;mjx-mn MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;0.758&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-22&quot; class=&quot;mjx-mspace&quot;&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-23&quot; class=&quot;mjx-mn&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;06&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-24&quot; class=&quot;mjx-mo&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;...&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&amp;nbsp;at&amp;nbsp;&lt;/span&gt;&lt;span class=&quot;aps-inline-formula&quot;&gt;&lt;span id=&quot;MathJax-Element-4-Frame&quot; class=&quot;mjx-chtml MathJax_CHTML&quot;&gt;&lt;span id=&quot;MJXc-Node-25&quot; class=&quot;mjx-math&quot;&gt;&lt;span id=&quot;MJXc-Node-26&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-27&quot; class=&quot;mjx-mrow&quot;&gt;&lt;span id=&quot;MJXc-Node-28&quot; class=&quot;mjx-mi&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-math-I&quot;&gt;α&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-29&quot; class=&quot;mjx-mo MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;=&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-30&quot; class=&quot;mjx-mrow&quot;&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-31&quot; class=&quot;mjx-mn MJXc-space3&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;93&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-32&quot; class=&quot;mjx-mo&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;/&lt;/span&gt;&lt;/span&gt;&lt;span id=&quot;MJXc-Node-33&quot; class=&quot;mjx-mn&quot;&gt;&lt;span class=&quot;mjx-char MJXc-TeX-main-R&quot;&gt;64&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;. We show that the SQ-TR phase derived from these dense packings is thermodynamically stable at high densities over the aforementioned&amp;nbsp;&lt;/span&gt;&lt;em&gt;α&lt;/em&gt;&lt;span&gt;&amp;nbsp;range and report a phase diagram for self-dual ellipsoids. The discovery of the SQ-TR crystal suggests organizing principles for nonspherical particles and self-assembly of colloidal systems.&lt;/span&gt;&lt;/p&gt;</style></abstract></record></records></xml>