Editing Hard sphere model

Jump to navigation Jump to search
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 155: Line 155:
<ref>[https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/ Jacob Aron "Proof confirmed of 400-year-old fruit-stacking problem", New Scientist daily news 12 August (2014)]</ref>
<ref>[https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/ Jacob Aron "Proof confirmed of 400-year-old fruit-stacking problem", New Scientist daily news 12 August (2014)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevE.52.3632 C. F. Tejero, M. S. Ripoll, and A. Pérez "Pressure of the hard-sphere solid", Physical Review E  '''52''' pp. 3632-3636 (1995)]</ref>. However, for hard spheres at close packing the [[Building up a face centered cubic lattice |face centred cubic]] phase is the more stable
<ref>[http://dx.doi.org/10.1103/PhysRevE.52.3632 C. F. Tejero, M. S. Ripoll, and A. Pérez "Pressure of the hard-sphere solid", Physical Review E  '''52''' pp. 3632-3636 (1995)]</ref>. However, for hard spheres at close packing the [[Building up a face centered cubic lattice |face centred cubic]] phase is the more stable
<ref>[http://dx.doi.org/10.1039/a701761h Leslie V. Woodcock "Computation of the free energy for alternative crystal structures of hard spheres", Faraday Discussions '''106''' pp. 325-338 (1997)]</ref>, with a [[Helmholtz energy function]] difference in the [[thermodynamic limit]] between the hexagonal close packed and face centered cubic crystals at close packing of 0.001164(8) <math>Nk_BT</math><ref>[http://dx.doi.org/10.1080/00268976.2014.982736 Eva G. Noya and Noé G. Almarza "Entropy of hard spheres in the close-packing limit", Molecular Physics '''113''' pp. 1061-1068 (2015)]</ref>. Recently evidence has been found for a metastable cI16 phase <ref>[https://doi.org/10.1063/1.5009099 Vadim B. Warshavsky, David M. Ford, and Peter A. Monson "On the mechanical stability of the body-centered cubic phase and the emergence of a metastable cI16 phase in classical hard sphere solids", Journal of Chemical Physics '''148''' 024502 (2018)]</ref> indicating the ''"cI16 is a mechanically stable structure that can spontaneously emerge from a bcc starting point but it is thermodynamically metastable relative to fcc or hcp".''
<ref>[http://dx.doi.org/10.1039/a701761h Leslie V. Woodcock "Computation of the free energy for alternative crystal structures of hard spheres", Faraday Discussions '''106''' pp. 325-338 (1997)]</ref>, with a [[Helmholtz energy function]] difference in the [[thermodynamic limit]] between the hexagonal close packed and face centered cubic crystals at close packing of 0.001164(8) <math>Nk_BT</math><ref>[http://dx.doi.org/10.1080/00268976.2014.982736 Eva G. Noya and Noé G. Almarza "Entropy of hard spheres in the close-packing limit", Molecular Physics '''113''' pp. 1061-1068 (2015)]</ref>.
*See also: [[Equations of state for crystals of hard spheres]]
*See also: [[Equations of state for crystals of hard spheres]]


Please note that all contributions to SklogWiki are considered to be released under the Creative Commons Attribution Non-Commercial Share Alike (see SklogWiki:Copyrights for details). If you do not want your writing to be edited mercilessly and redistributed at will, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource. Do not submit copyrighted work without permission!

To edit this page, please answer the question that appears below (more info):

Cancel Editing help (opens in new window)