DOI: 10.1063/1.1675271. Exact Classical Harmonic Free Energy of the Triangular Lattice

Exact Classical Harmonic Free Energy of the Triangular Lattice

10.1063/1.1675271

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The exact classical Helmholtz free energy per particle for a monatomic triangular lattice with first-neighbor harmonic interactions is shown to be given as F / kT = − 2ln(kT / hν0) + 12ln6 − (9 / π)L(π / 6), where ν0 = (2π)−1(κ / m)1/2, and L is Lobachevskiy's function.

Bibliography

Huckaby, D. A. (1971). Exact Classical Harmonic Free Energy of the Triangular Lattice. The Journal of Chemical Physics, 54(7), 2910â2911.

Authors 1

Dale A. Huckaby (first)

References 6 Referenced 12

10.1063/1.1674560 / J. Chem. Phys. (1970)
{'key': '2024020907334134400_r2'}
10.1017/S0305004100037014 / Proc. Cambridge Phil. Soc. (1963)
10.1016/0031-8914(66)90076-0 / Physica (1966)
10.1063/1.1701531 / J. Chem. Phys. (1967)
10.1063/1.1670348 / J. Chem. Phys. (1968)

Dates

Type	When
Created	21 years, 6 months ago (Feb. 6, 2004, 3:15 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 3:07 a.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 12:30 a.m.)
Issued	54 years, 4 months ago (April 1, 1971)
Published	54 years, 4 months ago (April 1, 1971)
Published Print	54 years, 4 months ago (April 1, 1971)

Funders 0

None

BibTeX

@article{Huckaby_1971, title={Exact Classical Harmonic Free Energy of the Triangular Lattice}, volume={54}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1675271}, DOI={10.1063/1.1675271}, number={7}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Huckaby, Dale A.}, year={1971}, month=apr, pages={2910–2911} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T05:30:28Z",
    "timestamp": 1707543028094
  },
  "reference-count": 6,
  "publisher": "AIP Publishing",
  "issue": "7",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1971,
        4,
        1
      ]
    ]
  },
  "abstract": "<jats:p>The exact classical Helmholtz free energy per particle for a monatomic triangular lattice with first-neighbor harmonic interactions is shown to be given as F\u2009/\u2009kT\u2009=\u2009\u2212\u20092ln(kT\u2009/\u2009h\u03bd0)\u2009+\u200912ln6\u2009\u2212\u2009(9\u2009/\u2009\u03c0)L(\u03c0\u2009/\u20096), where \u03bd0\u2009=\u2009(2\u03c0)\u22121(\u03ba\u2009/\u2009m)1/2, and L is Lobachevskiy's function.</jats:p>",
  "DOI": "10.1063/1.1675271",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        2,
        6
      ]
    ],
    "date-time": "2004-02-06T20:15:58Z",
    "timestamp": 1076098558000
  },
  "page": "2910-2911",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 12,
  "title": "Exact Classical Harmonic Free Energy of the Triangular Lattice",
  "prefix": "10.1063",
  "volume": "54",
  "author": [
    {
      "given": "Dale A.",
      "family": "Huckaby",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Chemistry, Texas Christian University, Fort Worth, Texas 76129"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020907334134400_r1",
      "doi-asserted-by": "crossref",
      "first-page": "3753",
      "DOI": "10.1063/1.1674560",
      "volume": "53",
      "year": "1970",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020907334134400_r2"
    },
    {
      "key": "2024020907334134400_r3",
      "doi-asserted-by": "crossref",
      "first-page": "383",
      "DOI": "10.1017/S0305004100037014",
      "volume": "59",
      "year": "1963",
      "journal-title": "Proc. Cambridge Phil. Soc."
    },
    {
      "key": "2024020907334134400_r4",
      "doi-asserted-by": "crossref",
      "first-page": "1601",
      "DOI": "10.1016/0031-8914(66)90076-0",
      "volume": "32",
      "year": "1966",
      "journal-title": "Physica"
    },
    {
      "key": "2024020907334134400_r5",
      "doi-asserted-by": "crossref",
      "first-page": "3763",
      "DOI": "10.1063/1.1701531",
      "volume": "47",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020907334134400_r6",
      "doi-asserted-by": "crossref",
      "first-page": "1981",
      "DOI": "10.1063/1.1670348",
      "volume": "49",
      "year": "1968",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/54/7/2910/18872896/2910_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/54/7/2910/18872896/2910_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T08:07:58Z",
    "timestamp": 1707466078000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/54/7/2910/698794/Exact-Classical-Harmonic-Free-Energy-of-the"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1971,
        4,
        1
      ]
    ]
  },
  "references-count": 6,
  "journal-issue": {
    "issue": "7",
    "published-print": {
      "date-parts": [
        [
          1971,
          4,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1675271",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1971,
        4,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1971,
        4,
        1
      ]
    ]
  }
}