DOI: 10.1139/p53-093. A METHOD FOR THE EVALUATION OF SOME LATTICE SUMS OCCURRING IN CALCULATIONS OF PHYSICAL PROPERTIES OF CRYSTALS

A METHOD FOR THE EVALUATION OF SOME LATTICE SUMS OCCURRING IN CALCULATIONS OF PHYSICAL PROPERTIES OF CRYSTALS

10.1139/p53-093

Crossref journal-article

Canadian Science Publishing

Canadian Journal of Physics (155)

Abstract

A method is described for the evaluation of sums of the inverse nth power of the distances from a point P to all points of a lattice. The sums are expressed in sums of Bessel functions or e-powers that converge rather rapidly and Riemann ζ functions. The procedure can be used for any position of P with respect to the lattice.

Bibliography

van der Hoff, B. M. E., & Benson, G. C. (1953). A METHOD FOR THE EVALUATION OF SOME LATTICE SUMS OCCURRING IN CALCULATIONS OF PHYSICAL PROPERTIES OF CRYSTALS. Canadian Journal of Physics, 31(7), 1087â1094.

Authors 2

B. M. E. van der Hoff (first)
G. C. Benson (additional)

References 18 Referenced 129

BOIIN,id. Z. I'hysik, 7: 124. 1921.
{'key': 'p_2/p_2_1', 'first-page': '11', 'author': 'DAVIS H.', 'year': '1935', 'journal-title': 'Ind.'} / Ind. by DAVIS H. (1935)
{'journal-title': 'Dissertation. Gottingen.', 'first-page': '73', 'year': '1922', 'key': 'p_3/p_3_1'} / Dissertation. Gottingen. (1922)
{'key': 'p_4/p_4_1', 'first-page': '675', 'volume': '39', 'year': '1932', 'journal-title': 'Rev.'} / Rev. (1932)
{'key': 'p_5/p_5_1', 'first-page': '1287', 'volume': '41', 'author': "FRANK'F C.", 'year': '1950', 'journal-title': 'Mag.'} / Mag. by FRANK'F C. (1950)
10.1039/tf9282400092 / Faraday Soc. by LENNAICD-JONES J . (1928)
LENNARD-JONES, J . E. and INGHAJL,I. E. Proc. Roy. SOC.(Lorldoll), A, 107: 036. 1925.
MACKENLIE, J. I< Thesis, University of Bristol, Bristol. 1950.
M z I . I< I'roc. Phvs. Soc. (London),i\, 03: 1370. 1950. z .
M D E L U N G , ' . Physik. Z. 19: 524. '1918.
OKNSTEIN, L. S. and ZERNIKI.F. Proc. 1<011inkl.Akad. \Yetenschap. r\mstertlam, 21 :911. 1918.
10.1039/tf9393501247 / Faraday Soc. (1939)
SHUTTL&\VORTH, I< PTOC.Phys. SOC.( L O I I O I I ) , A,62: 167. 1949. (10.1088/0370-1298/62/3/303)
TOPPING, J . Proc. Roy. SOC.(London), A, 114: 67. 1927. (10.1098/rspa.1927.0025)
WATSON, G. N. A treatise on the theory of Bessel functions. 2nd ecl. Cambridge Ijniversity Press, Londorl. 1948.
{'key': 'p_17/p_17_1', 'first-page': '737', 'author': 'WATSON G. K.', 'year': '1948', 'journal-title': 'London.'} / London. by WATSON G. K. (1948)
WI-IITTAKER, E. T. and WATSON,G. N. A course of noderllanalysis. 4th ed. Cambridge University Press, London. 1950. p. 124 (esercise 17 and 18).
10.1039/tf9514701228 / Faraday Soc. by YOUNG D. M. (1951)

Dates

Type	When
Created	14 years, 4 months ago (April 24, 2011, 3:08 a.m.)
Deposited	1 month, 3 weeks ago (July 2, 2025, 10:17 a.m.)
Indexed	1 month, 3 weeks ago (July 3, 2025, 12:07 a.m.)
Issued	71 years, 9 months ago (Nov. 1, 1953)
Published	71 years, 9 months ago (Nov. 1, 1953)
Published Print	71 years, 9 months ago (Nov. 1, 1953)

Funders 0

None

BibTeX

@article{van_der_Hoff_1953, title={A METHOD FOR THE EVALUATION OF SOME LATTICE SUMS OCCURRING IN CALCULATIONS OF PHYSICAL PROPERTIES OF CRYSTALS}, volume={31}, ISSN={1208-6045}, url={http://dx.doi.org/10.1139/p53-093}, DOI={10.1139/p53-093}, number={7}, journal={Canadian Journal of Physics}, publisher={Canadian Science Publishing}, author={van der Hoff, B. M. E. and Benson, G. C.}, year={1953}, month=nov, pages={1087–1094} }

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