DOI: 10.1098/rspa.1964.0131. The thermal expansion of copper at low temperatures

The thermal expansion of copper at low temperatures

10.1098/rspa.1964.0131

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

Abstract

The thermal expansion of copper has been determined at temperatures down to 2 °K by means of an electrical capacitance technique. By measuring three-terminal capacitances in a ratio-transformer bridge length changes smaller than 10-9cm can be detected in the capacitor-expansion cell. Below 10 °K, the linear expansion coefficient,α, may be represented byα= (1·45± 0·15) x 10-10T+ (2·8 ± 0·1) x 10-11T3per degK. These terms, identified respectively as electronic (e) and lattice (l) in origin, lead to the following values of the Grüneisen parameter:γe= 0·63 ± 0·06,γl= 1·72 ± 0·03 ( =γo).γeis compared with a theoretical free-electron value of 2/3, and the low temperature value ofγlis compared with values of 1·75 to 1·77 calculated from elastic constants. At room temperatureγ(≈ γ∞) is 2·00, so thatγ∞–γ0≈ 0·28, which agrees well with the theoretical estimates of Barron for a close-packed cubic lattice.

Bibliography

The thermal expansion of copper at low temperatures. (1964). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 280(1380), 72â84.

Authors 0

None

References 33 Referenced 53

Andres K . 1961 Cryogenics 2 93. (10.1016/0011-2275(61)90029-7)
B arron T. H . K . 1955 Phil. M ag. 46 720. (10.1515/ijmr-1955-460919)
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Bijl D. & P ullan H . 1955 Physica 21 285; see also erratum . (10.1016/S0031-8914(54)91674-2)
Carr R . H . & Swenson C. A. 1964 Cryogenics. 4 (in the Press) (10.1016/0011-2275(64)90002-5)
10.1080/14786436308211129
Collins J . G. & W hite G. K . 1964 Prog. Low Temp. Phys. 4 (in th e Press).
Corruccini R . J . & Gniewek J . J . 1961 Nat. Bur. Stand. Monograph 29. W ashington: U.S. G ovt. P rin tin g Office.
{'key': 'p_9', 'author': 'Daniels W .', 'year': '1958', 'journal-title': 'Phys. Rev. Ill, 713.'} / Phys. Rev. Ill, 713. by Daniels W . (1958)
{'key': 'p_10', 'first-page': '494', 'article-title': 'Proc. Roy', 'volume': '263', 'author': 'Franck J .', 'year': '1961', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Franck J . (1961)
Fraser D. B. & Hollis H a Ile tt A. C. 1961 Proc. V II Int. Conf. on Low Temp. Phys. Toronto p. 689.
{'key': 'p_12', 'first-page': '24', 'volume': '28', 'author': 'Olsen J .', 'year': '1955', 'journal-title': 'Helv. Phys. Acta'} / Helv. Phys. Acta by Olsen J . (1955)
{'key': 'p_13', 'first-page': '114', 'article-title': 'J . Sci', 'volume': '40', 'year': '1963', 'journal-title': 'Instrum.'} / Instrum. / J . Sci (1963)
H ersh J . F . 1962 General Radio Experimenter 36 3.
{'key': 'p_15', 'first-page': '263', 'article-title': 'Canad. J', 'volume': '39', 'year': '1961', 'journal-title': 'Phys.'} / Phys. / Canad. J (1961)
Johnson G. J . & Thom pson A. M. 1957 Proc. Instn Elect. Engrs 104 C 217. (10.1049/pi-c.1957.0025)
{'key': 'p_17', 'first-page': '142', 'article-title': 'Canad. J', 'volume': '29', 'author': 'Los J .', 'year': '1951', 'journal-title': 'Phys.'} / Phys. / Canad. J by Los J . (1951)
M artin D. L. i960 Canad. J . Phys. 38 17.
{'key': 'p_19', 'first-page': '253', 'article-title': 'I.R .E', 'volume': '1', 'author': 'McGregor M. C.', 'year': '1951', 'journal-title': 'Trans. Instr.'} / Trans. Instr. / I.R .E by McGregor M. C. (1951)
{'key': 'p_20', 'first-page': '309', 'volume': '23', 'year': '1941', 'journal-title': 'Soc. Japan'} / Soc. Japan (1941)
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Powell R . L. B unch M. D. & Corruccini R . J . 1961 Cryogenics 1 139. (10.1016/S0011-2275(61)80027-1)
{'key': 'p_23', 'first-page': '5289', 'article-title': 'J', 'volume': '76', 'author': 'Itm H .', 'year': '1954', 'journal-title': 'Amer. Chem. Soc.'} / Amer. Chem. Soc. / J by Itm H . (1954)
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{'key': 'p_26', 'first-page': '245', 'article-title': 'I.R .E', 'volume': '1', 'author': 'Thom A. M.', 'year': '1958', 'journal-title': 'Trans. Instr.'} / Trans. Instr. / I.R .E by Thom A. M. (1958)
{'key': 'p_27', 'first-page': '413', 'article-title': 'Proc. Roy', 'volume': '237', 'author': 'Varley J .', 'year': '1956', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Varley J . (1956)
{'key': 'p_28', 'first-page': '626', 'volume': '81', 'year': '1951', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1951)
W hite G. K . 1959 Experimental techniques in low-temperature physics. Oxford U niversity Press.
W hite G. K . i960 Nature Lond. 187 927. (10.1038/187927b0)
W hite G. K . 1961a Cryogenics 1 151. (10.1016/S0011-2275(61)80028-3)
W hite G. K . 19616 Phil.Mag. 6 815.
W hite G. K . 1963 Proc. V I I I Int. Conf. on Low Temp. Phys. p. 394. L ondon: B utterw orths.

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 1:37 p.m.)
Deposited	2 years, 3 months ago (May 9, 2023, 8:04 p.m.)
Indexed	2 months, 1 week ago (June 25, 2025, 5:24 a.m.)
Issued	61 years, 1 month ago (July 7, 1964)
Published	61 years, 1 month ago (July 7, 1964)
Published Online	28 years, 8 months ago (Jan. 1, 1997)
Published Print	61 years, 1 month ago (July 7, 1964)

Funders 0

None

BibTeX

@article{1964, volume={280}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1964.0131}, DOI={10.1098/rspa.1964.0131}, number={1380}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1964}, month=jul, pages={72–84} }

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