DOI: 10.1002/recl.19500691009. On the theory of ionic conductivity in crystals

On the theory of ionic conductivity in crystals

10.1002/recl.19500691009

Crossref journal-article

Wiley

Recueil des Travaux Chimiques des Pays-Bas (311)

Abstract

AbstractA survey is given of the existing theories of the ionic conductivity in crystals.The experimental log x ‐ 1/T curves usually consist of two straight parts with different slopes. This shape can be explained by several mechanisms (Smekal, Jost and others). For the conductivity of mixed crystals, where the solute introduces additional vacancies, we derived a formula (formula III) which gives the conductivity as a function of the concentration of the solute and of the temperature. This formula also explains the kink in the conductivity curve.A method has been given which makes it possible to choose between the explanations for the kink in the conductivity curve in a given case. It is based on an analysis of the transition region between the two straight parts of the curves, and was applied to the conductivity of Li‐halides and LiHl‐MgHl2 mixed crystals. It was found that in this case the kink in the conductivity curves could be described by formula III and not by the mechanisms proposed by others.

Bibliography

Haven, Y. (1950). On the theory of ionic conductivity in crystals. Recueil Des Travaux Chimiques Des Pays-Bas, 69(10), 1259â1274. Portico.

Authors 1

Y. Haven (first)

References 42 Referenced 33

A. F.Joffe The Physics of Crystals(1928).
10.1515/zpch-1922-10123 / Z. physik. Chem. by Hevesy G. V. (1922)
10.1007/BF01379812
10.1515/zpch-1935-2934 / Z. physik. Chem. by Schottky W. (1935)
It is conceivable that two ions or atoms may exchange in one act. Such a mechanism does not require permanent lattice defects but defects only existing at the very moment of exchange. It is however unlikely that such a mechanism can occur on account of the high energy required. This holds particularly for the exchange of a negative and a positive ion so that acontribution of this mechanismto the ionic conductivity may be disregarded.
{'key': 'e_1_2_1_5_2', 'first-page': '163', 'volume': '11', 'author': 'Wagner C.', 'year': '1930', 'journal-title': 'Z. physik. Chem.'} / Z. physik. Chem. by Wagner C. (1930)
10.1515/zpch-1935-2934 / Z. physik. Chem. by Schottky W. (1935)
C.WagnerandW.Schottky ref. 5).
10.1063/1.1749319
W.Jost Diffusion und chemische Reaktion in festen Stoffen(1937).
N. F.MottandR. W.Gurney Electronic processes in ionic crystals(1940).
The concentration of interstitial ions will be defined as the fraction of interstitial sites which are occupied by interstitial ions; the concentration of vacancies as the fraction of lattice sites of the particular kind which are not occupied.
See for exampleN. F.MottandR. W.Gurney Electronic processes in ionic crystals(1940) p.29 ff.
10.1515/zpch-1936-3202 / Z. physik. Chem. by Jost W. (1936)
10.1039/tf9383400485
{'key': 'e_1_2_1_12_2', 'first-page': '295', 'author': 'Koch W.', 'year': '1937', 'journal-title': 'Z. physik. Chem.'} / Z. physik. Chem. by Koch W. (1937)
{'key': 'e_1_2_1_13_2', 'first-page': '199', 'volume': '73', 'author': 'Croatto U.', 'year': '1943', 'journal-title': 'Gazz. chim. ital.'} / Gazz. chim. ital. by Croatto U. (1943)
{'key': 'e_1_2_1_14_2', 'first-page': '95', 'volume': '78', 'author': 'Croatto U.', 'year': '1948', 'journal-title': 'Gazz. chim. ital.'} / Gazz. chim. ital. by Croatto U. (1948)
10.1002/andp.19494400107
10.1063/1.1747460
H. W.Etzel Doctoral thesis Carnegie Institute of Technology (Aug.1949).
See for instanceN. F.MottandR. W.Gurney ref.9 p.29 ff.
{'key': 'e_1_2_1_19_2', 'first-page': '476', 'volume': '34', 'author': 'Smekal A.', 'year': '1927', 'journal-title': 'Z. Elektrochem.'} / Z. Elektrochem. by Smekal A. (1927)
10.1021/ja01412a016
{'key': 'e_1_2_1_21_2', 'first-page': '1260', 'volume': '73', 'author': 'Mapother D.', 'year': '1948', 'journal-title': 'Phys. Rev.'} / Phys. Rev. by Mapother D. (1948)
D.Mapother Doctoral Thesis Carnegie Inst of Technology.
10.1021/ja01396a013
10.1002/zaac.19311970121
{'key': 'e_1_2_1_22_4', 'first-page': '118', 'author': 'Jost W.', 'year': '1930', 'journal-title': 'Z. physik. Chem.'} / Z. physik. Chem. by Jost W. (1930)
{'key': 'e_1_2_1_22_5', 'first-page': '242', 'volume': '164', 'author': 'Reinhold H.', 'year': '1933', 'journal-title': 'Z. physik. Chem.'} / Z. physik. Chem. by Reinhold H. (1933)
{'key': 'e_1_2_1_22_6', 'first-page': '504', 'volume': '39', 'author': 'Tubandt C.', 'year': '1933', 'journal-title': 'Z. Elektrochem.'} / Z. Elektrochem. by Tubandt C. (1933)
10.1007/BF01340140
{'key': 'e_1_2_1_23_3', 'first-page': '869', 'volume': '57', 'year': '1929', 'journal-title': 'Z. Physik'} / Z. Physik (1929)
N. F.MottandR. W.Gurney Electronic processes in ionic crystals(1940) p.53.
10.1063/1.1749319
{'key': 'e_1_2_1_25_3', 'first-page': '757', 'volume': '36', 'year': '1935', 'journal-title': 'Physik. Z.'} / Physik. Z. (1935)
{'key': 'e_1_2_1_26_2', 'first-page': '295', 'author': 'Koch W.', 'year': '1937', 'journal-title': 'Z. physik. Chem.'} / Z. physik. Chem. by Koch W. (1937)
This fact has been overlooked byMottandGurney (ref. 9 p.49) who derived for this case the formula χ = A{C1+ C2exp.(—½E/kT)} exp(—U/kT) interpreting A exp(—U/kT) as the mobility C2exp(—½E/kT) as the concentration of the thermally formed lattice defects and C1as a constant concentration of the same lattice defects added in excess.
A fifth possible explanation will be given in a forthcoming paper.
Although the slope of the log χ1— 1/T curve is accurately known the choice of its height may be difficult for some curves of low MgHl2content where complications occur at lower temperatures (see p.14). In those cases χ0was first calculated from a preliminary choice of the height of the log χ1curve. The log χ0—1/T curve found in that way was fairly straight at high temperatures but generally showed a deviation from the straight line at lower temperatures. The high‐temperature part was now extrapolated to lower temperatures and from this extrapolated log χ0— 1/T curve the height of the log χ1— 1/T curve was calculated. Repeating this proces the correct height of this curve could be found in successive approximations.
10.1021/ja01367a006
10.1007/BF01330319

Dates

Type	When
Created	14 years, 11 months ago (Sept. 14, 2010, 2:04 a.m.)
Deposited	1 year, 9 months ago (Nov. 13, 2023, 4:56 p.m.)
Indexed	1 year, 6 months ago (Feb. 16, 2024, 3:19 a.m.)
Issued	75 years, 7 months ago (Jan. 1, 1950)
Published	75 years, 7 months ago (Jan. 1, 1950)
Published Online	14 years, 11 months ago (Sept. 2, 2010)
Published Print	75 years, 7 months ago (Jan. 1, 1950)

Funders 0

None

BibTeX

@article{Haven_1950, title={On the theory of ionic conductivity in crystals}, volume={69}, ISSN={0165-0513}, url={http://dx.doi.org/10.1002/recl.19500691009}, DOI={10.1002/recl.19500691009}, number={10}, journal={Recueil des Travaux Chimiques des Pays-Bas}, publisher={Wiley}, author={Haven, Y.}, year={1950}, month=jan, pages={1259–1274} }

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