High quality data on the high temperature electrical properties of ceramics, particularly oxides, is of great value for material selection, design, and modeling for a broad range of emerging applications. Utilizing the mismatch in the coefficient of thermal expansion between two materials, a purely mechanical method for establishing electrical contact in the van der Pauw geometry to measure the bulk resistivity of ceramic disks at high temperatures is presented. Measurements of a reference material, 20 mol. % Gd-doped cerium oxide, are presented up to 1000 °C. The viability of electrical measurements up to a maximum temperature of 1600 °C is also considered. Measurements are performed using multiple techniques and compared to literature values finding excellent agreement. The approach described in this work enables the van der Pauw method to be applied to many ceramic materials over a wide range of temperatures and environments.

1.
P.
Abelard
and
J. F.
Baumard
, “
Study of the dc and ac electrical properties of an yttria-stabilized zirconia single crystal [(ZrO2)0.88-(Y2O3)0.12]
,”
Phys. Rev. B
26
(
2
),
1005
1017
(
1982
).
2.
L.
Sévin
,
V.
Razafindramanana
,
A.
Julian-Jankowiak
,
J.-F.
Justin
,
F.
Mauvy
, and
F.
Rebillat
, “
Effect of high-content Yttria on the thermal expansion behaviour and ionic conductivity of a stabilised cubic Hafnia
,”
J. Eur. Ceram. Soc.
40
(
15
),
5859
5869
(
2020
).
3.
F. G.
Will
,
H. G.
DeLorenzi
, and
K. H.
Janora
, “
Effect of crystal orientation on conductivity and electron mobility in single-crystal alumina
,”
J. Am. Ceram. Soc.
75
(
10
),
2790
2794
(
1992
).
4.
H. L.
Tuller
and
A. S.
Nowick
, “
Defect structure and electrical properties of nonstoichiometric CeO2 single crystals
,”
J. Electrochem. Soc.
126
(
2
),
209
(
1979
).
5.
S. P.
Mitoff
, “
Electrical conductivity of single crystals of MgO
,”
J. Chem. Phys.
31
(
5
),
1261
1269
(
1959
).
6.
J.-H.
Lee
,
S.-J.
Park
, and
K.
Hirota
, “
Temperature dependence of electrical condutivity in polycrystalline tin oxide
,”
J. Am. Ceram. Soc.
73
(
9
),
2771
2774
(
1990
).
7.
I.
Miccoli
,
F.
Edler
,
H.
Pfnür
, and
C.
Tegenkamp
, “
The 100th anniversary of the four-point probe technique: The role of probe geometries in isotropic and anisotropic systems
,”
J. Phys.: Condens. Matter
27
(
22
),
223201
(
2015
).
8.
L. J.
van der Pauw
, “
A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape
,”
Philips Tech. Rev.
20
,
220
224
(
1958
).
9.
K. A.
Borup
,
E. S.
Toberer
,
L. D.
Zoltan
,
G.
Nakatsukasa
,
M.
Errico
,
J.-P.
Fleurial
,
B. B.
Iversen
, and
G. J.
Snyder
, “
Measurement of the electrical resistivity and Hall coefficient at high temperatures
,”
Rev. Sci. Instrum.
83
(
12
),
123902
(
2012
).
10.
C.
Kasl
and
M. J. R.
Hoch
, “
Effects of sample thickness on the van der Pauw technique for resistivity measurements
,”
Rev. Sci. Instrum.
76
(
3
),
033907
(
2005
).
11.
M. S.
Bowen
, “
Bulk electrical conductivity measurements based on 4-point van der Pauw geometries
,”
Electronic Materials and Applications 2023
,
Orlando, FL
,
2023
.
12.
Y.
Takeda
,
H. Y.
Tu
,
H.
Sakaki
,
S.
Watanabe
,
N.
Imanishi
,
O.
Yamamoto
,
M. B.
Phillipps
, and
N. M.
Sammes
, “
Gd1−xAxMnO3 (A = Ca and Sr) for the electrode of solid oxide fuel cells
,”
J. Electrochem. Soc.
144
(
8
),
2810
2816
(
1997
).
13.
R. W.
Dickson
and
E.
Schreiber
, “
An alumina standard reference material for resonance frequency and dynamic elastic moduli measurement. II. Characteristic values for use from 25 °C to 1000 °C
,”
J. Res. Natl. Bur. Stand., Sect. A
77A
(
4
),
391
(
1973
).
14.
D.
Taylor
, “
Thermal expansion data. II: Binary oxides with the fluorite and rutile structures, MO2, and the antifluorite structure, M2O
,”
Trans. J. Br. Ceram. Soc.
83
(
2
),
32
37
(
1984
).
15.
L. S.
Dubrovinsky
and
S. K.
Saxena
, “
Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures
,”
Phys. Chem. Miner.
24
(
8
),
547
550
(
1997
).
16.
L.
Lutterotti
and
P.
Scardi
, “
Simultaneous structure and size–strain refinement by the Rietveld method
,”
J. Appl. Crystallogr.
23
(
4
),
246
252
(
1990
).
17.
M. S.
Bowen
,
M.
Johnson
,
R.
McQuade
,
B.
Wright
,
K.-S.
Kwong
,
P. Y.
Hsieh
,
D. P.
Cann
, and
C. R.
Woodside
, “
Electrical properties of gadolinia-doped ceria for electrodes for magnetohydrodynamic energy systems
,”
SN Appl. Sci.
2
(
9
),
1529
(
2020
).
18.
NORECS
, ProboStat manual,
2018
.
19.
P.
Virtanen
,
R.
Gommers
,
T. E.
Oliphant
,
M.
Haberland
,
T.
Reddy
,
D.
Cournapeau
,
E.
Burovski
,
P.
Peterson
,
W.
Weckesser
,
J.
Bright
,
S. J.
van der Walt
,
M.
Brett
,
J.
Wilson
,
K. J.
Millman
,
N.
Mayorov
,
A. R. J.
Nelson
,
E.
Jones
,
R.
Kern
,
E.
Larson
,
C. J.
Carey
,
İ.
Polat
,
Y.
Feng
,
E. W.
Moore
,
J.
VanderPlas
,
D.
Laxalde
,
J.
Perktold
,
R.
Cimrman
,
I.
Henriksen
,
E. A.
Quintero
,
C. R.
Harris
,
A. M.
Archibald
,
A. H.
Ribeiro
,
F.
Pedregosa
,
P.
van Mulbregt
,
A.
Vijaykumar
,
A. P.
Bardelli
,
A.
Rothberg
,
A.
Hilboll
,
A.
Kloeckner
,
A.
Scopatz
,
A.
Lee
,
A.
Rokem
,
C. N.
Woods
,
C.
Fulton
,
C.
Masson
,
C.
Häggström
,
C.
Fitzgerald
,
D. A.
Nicholson
,
D. R.
Hagen
,
D. V.
Pasechnik
,
E.
Olivetti
,
E.
Martin
,
E.
Wieser
,
F.
Silva
,
F.
Lenders
,
F.
Wilhelm
,
G.
Young
,
G. A.
Price
,
G.-L.
Ingold
,
G. E.
Allen
,
G. R.
Lee
,
H.
Audren
,
I.
Probst
,
J. P.
Dietrich
,
J.
Silterra
,
J. T.
Webber
,
J.
Slavič
,
J.
Nothman
,
J.
Buchner
,
J.
Kulick
,
J. L.
Schönberger
,
J. V.
de Miranda Cardoso
,
J.
Reimer
,
J.
Harrington
,
J. L. C.
Rodríguez
,
J.
Nunez-Iglesias
,
J.
Kuczynski
,
K.
Tritz
,
M.
Thoma
,
M.
Newville
,
M.
Kümmerer
,
M.
Bolingbroke
,
M.
Tartre
,
M.
Pak
,
N. J.
Smith
,
N.
Nowaczyk
,
N.
Shebanov
,
O.
Pavlyk
,
P. A.
Brodtkorb
,
P.
Lee
,
R. T.
McGibbon
,
R.
Feldbauer
,
S.
Lewis
,
S.
Tygier
,
S.
Sievert
,
S.
Vigna
,
S.
Peterson
,
S.
More
,
T.
Pudlik
,
T.
Oshima
,
T. J.
Pingel
,
T. P.
Robitaille
,
T.
Spura
,
T. R.
Jones
,
T.
Cera
,
T.
Leslie
,
T.
Zito
,
T.
Krauss
,
U.
Upadhyay
,
Y. O.
Halchenko
, and
Y.
Vázquez-Baeza
, “
SciPy 1.0: Fundamental algorithms for scientific computing in Python
,”
Nat. Methods
17
(
3
),
261
272
(
2020
).

Supplementary Material

You do not currently have access to this content.