The effect of mechanical twisting on oxygen ionic ... · In contrast, the dominant oxygen ionic carrier conductivity was reflected by an oxygen partial pressure independent conductivity

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4278

NATURE MATERIALS | www.nature.com/naturematerials 1

1

Supplementary Information: The Effect of Mechanical Twisting on Oxygen Ionic

Transport in Solid State Energy Conversion Membranes

by Yanuo Shi1, Alexander Hansen Bork1, Sebastian Schweiger1, Jennifer Lilia Marguerite

Rupp1

1) Electrochemical Materials, Department of Materials, ETH Zurich, Switzerland

Correspondence should be addressed to J.L.M.R.

S1: In-situ heating x-ray diffraction analysis of Gd0.2Ce0.8O1.9-x thin film

For material characterization and to probe thermal expansion, in-situ heated X-ray diffraction

is used to analyze the Gd0.2Ce0.8O1.9-x thin films on Si3N4/Si substrates. In Figure S1, the θ-2θ

diffraction scans of a Gd0.2Ce0.8O1.9-x thin film are displayed heated between 20 and 600 °C at

5 °C/min. The characteristic Gd0.2Ce0.8O1.9-x diffraction peaks of (111), (200), (311), (222)

indicate that the film is polycrystalline and of cubic fluorite structure. This is in agreement

with literature on pulsed laser deposited Gd0.2Ce0.8O1.9-x film at room temperature1. With an

increase in temperature, the main diffraction peak shifts to lower diffraction angles. Using

Bragg’s law, we can determine the change of the lattice constant and, subsequently, the

thermal expansion coefficient. The pronounced (111) orientations observed are in agreement

with literature on Gd0.2Ce0.8O1.9-x wet-chemical and vacuum processed thin films1–5.

The effect of mechanical twisting on oxygen ionic transport in solid-state energy conversion membranes

© 2015 Macmillan Publishers Limited. All rights reserved

http://dx.doi.org/10.1038/nmat4278

2 NATURE MATERIALS | www.nature.com/naturematerials

SUPPLEMENTARY INFORMATION DOI: 10.1038/NMAT4278

2

Figure S1: In-situ heating XRD scans of pulsed laser deposited Gd0.2Ce0.8O1.9-x film on Si3N4/Si substrates for the

temperature range of 20 to 600 °C shown at a heating rate of 5 °C/min.

S2: Evolvement of the lattice constant and thermal expansion coefficient during the in-

situ heating XRD for a Gd0.2Ce0.8O1.9-x substrate-supported thin film

In Fig. S2, the lattice constant, a, and the thermal expansion coefficient, α, are plotted as

obtained from the X-ray diffractograms with respect to the in-situ heating temperature (from

Fig. S1). We report a lattice constant of around 5.6 Å for the (111) main diffraction line,

which increases to 5.64 Å when heated from room temperature to 600 °C at a constant rate of

5 °C/min; this agrees well with a recent report placing the lattice constant at around 5.43 Å1.

While increasing the temperature we observed an increase in the lattice constant by 0.71% for

the substrate-supported films due to the thermal expansion of the lattice, see Fig. S2a. The

thermal expansion coefficient α at different temperatures is also reported in Fig. S2b. The

thermal expansion coefficient, as determined from the (111) diffraction line at 600 °C, is

α600=1.27×10-5 °C-1 and is close to literature values of, for example, Gd0.2Ce0.8O1.9-x pellets,

which have a value of about 1.2×10-5 °C-1 6.

3

Figure S2: Lattice constant and thermal expansion coefficient of the substrate-supported Gd0.2Ce0.8O1.9-x thin film

with respect to the selected XRD diffraction lines and heating: (a) the lattice constant, a, and (b) the thermal

expansion coefficient,α.

S3: Oxygen ionic conductivity of the strained and free-standing Ce0.8Gd0.2O1.9-x

membrane: Conductivity measurements as a function of oxygen partial pressure and

temperature

We probed the dominant charge carrier type, ionic vs. electronic, for the strained

Ce0.8Gd0.2O1.9-x membranes via an oxygen partial pressure- and temperature-dependent

electrical conductivity measurement carried out in a custom-made microprobe station setup,

Fig. S3a, b.

Through oxygen partial pressure and temperature-varied conductivity measurements,

information on the prevailing dominant charge carrier, i.e. whether ionic conduction σi or

electronic conduction σe, can be obtained. The total conductivity can be described by

0 00 0(2 )[ ] ( ) ( ) ( )

tot i e

i m e hO

B B B

H H Eq V exp e n exp expT k T k T T k T

(1)




2

Figure S1: In-situ heating XRD scans of pulsed laser deposited Gd0.2Ce0.8O1.9-x film on Si3N4/Si substrates for the

temperature range of 20 to 600 °C shown at a heating rate of 5 °C/min.

S2: Evolvement of the lattice constant and thermal expansion coefficient during the in-

situ heating XRD for a Gd0.2Ce0.8O1.9-x substrate-supported thin film

In Fig. S2, the lattice constant, a, and the thermal expansion coefficient, α, are plotted as

obtained from the X-ray diffractograms with respect to the in-situ heating temperature (from

Fig. S1). We report a lattice constant of around 5.6 Å for the (111) main diffraction line,

which increases to 5.64 Å when heated from room temperature to 600 °C at a constant rate of

5 °C/min; this agrees well with a recent report placing the lattice constant at around 5.43 Å1.

While increasing the temperature we observed an increase in the lattice constant by 0.71% for

the substrate-supported films due to the thermal expansion of the lattice, see Fig. S2a. The

thermal expansion coefficient α at different temperatures is also reported in Fig. S2b. The

thermal expansion coefficient, as determined from the (111) diffraction line at 600 °C, is

α600=1.27×10-5 °C-1 and is close to literature values of, for example, Gd0.2Ce0.8O1.9-x pellets,

which have a value of about 1.2×10-5 °C-1 6.

3

Figure S2: Lattice constant and thermal expansion coefficient of the substrate-supported Gd0.2Ce0.8O1.9-x thin film

with respect to the selected XRD diffraction lines and heating: (a) the lattice constant, a, and (b) the thermal

expansion coefficient,α.

S3: Oxygen ionic conductivity of the strained and free-standing Ce0.8Gd0.2O1.9-x

membrane: Conductivity measurements as a function of oxygen partial pressure and

temperature

We probed the dominant charge carrier type, ionic vs. electronic, for the strained

Ce0.8Gd0.2O1.9-x membranes via an oxygen partial pressure- and temperature-dependent

electrical conductivity measurement carried out in a custom-made microprobe station setup,

Fig. S3a, b.

Through oxygen partial pressure and temperature-varied conductivity measurements,

information on the prevailing dominant charge carrier, i.e. whether ionic conduction σi or

electronic conduction σe, can be obtained. The total conductivity can be described by

0 00 0(2 )[ ] ( ) ( ) ( )

tot i e

i m e hO

B B B

H H Eq V exp e n exp expT k T k T T k T

(1)




4

where T denotes the absolute temperature, 2q the charge of an oxygen vacancy, [ ]OV their

concentration, νoi the pre-exponential ionic mobility factor containing geometrical factors and

the jump attempt frequency, ΔHm the enthalpy of oxygen vacancy migration, and kB the

Boltzmann constant. e0 the electron charge, νe the electronic mobility, n0 the pre-exponential

factor of electron concentration, ΔH the enthalpy of oxygen extraction, νoe the pre-exponential

electronic mobility factor, and Eh the electron hopping energy.

It is important to note that only the electronic conductivity is dependent on the oxygen partial

pressure: The oxygen non-stoichiometry, i.e. such as the formation of additional oxygen

vacancies and electrons during reduction of the gadolinia-doped ceria, is balanced by the

gaseous phase of the measurement, see equation (2) where m represents the oxygen partial

pressure exponent. As a consequence, potential variations of the total conductivity with

respect to the varied oxygen partial pressure would identify a predominant electronic

conduction for an isothermal.

1

2m

e T p O (2)

In contrast, the dominant oxygen ionic carrier conductivity was reflected by an oxygen partial

pressure independent conductivity at a given isothermal.

Here, we show the result of the total conductivity measurement for the free-standing

Ce0.8Gd0.2O1.9-x buckled membrane with 0.46% compressive strain between electrode P2 and

P4 at room temperature, Fig. S3b, as a function of the oxygen partial pressure and temperature

in a Brouwer-type diagram, Fig. S3c, and an Arrhenius-type diagram, Fig. S3d. The total

conductivity is independent of the oxygen partial pressure for the membranes tested in this

study at temperatures of 300 to 500 °C.

5

Based on this experimental evidence we unequivocally demonstrate that a dominant oxygen

ionic conductivity prevails for the 0.46% compressively strained (between P2 and P4) and

free-standing Ce0.8Gd0.2O1.9-x film membranes. Additionally, our findings for the 0.46%

compressively strained film membranes are in agreement with literature for Ce0.8Gd0.2O1.9-x

pellets and substrate-supported thin films, reporting a dominant oxygen ionic conductivity for

the temperature range of 300-500 °C and higher oxygen partial pressures such as in air 7–9.

Figure S3: Oxygen partial pressure and temperature-dependent measurements of the total conductivity of

Ce0.8Gd0.2O1.9-x thin film membranes with 0.46% compressively strain between P2 and P4. (a) Custom-made

measurement setup. (b) Light microscopy image of a free-standing strained Ce0.8Gd0.2O1.9-x thin film membrane

with a 4-point electrode arrangement. (c) Log total electrical conductivity vs. log oxygen partial pressure

Brouwer-type plot for isothermals. (d) Arrhenius-type diagram of the total conductivity with respect to the gas

atmosphere.




4

where T denotes the absolute temperature, 2q the charge of an oxygen vacancy, [ ]OV their

concentration, νoi the pre-exponential ionic mobility factor containing geometrical factors and

the jump attempt frequency, ΔHm the enthalpy of oxygen vacancy migration, and kB the

Boltzmann constant. e0 the electron charge, νe the electronic mobility, n0 the pre-exponential

factor of electron concentration, ΔH the enthalpy of oxygen extraction, νoe the pre-exponential

electronic mobility factor, and Eh the electron hopping energy.

It is important to note that only the electronic conductivity is dependent on the oxygen partial

pressure: The oxygen non-stoichiometry, i.e. such as the formation of additional oxygen

vacancies and electrons during reduction of the gadolinia-doped ceria, is balanced by the

gaseous phase of the measurement, see equation (2) where m represents the oxygen partial

pressure exponent. As a consequence, potential variations of the total conductivity with

respect to the varied oxygen partial pressure would identify a predominant electronic

conduction for an isothermal.

1

2m

e T p O (2)

In contrast, the dominant oxygen ionic carrier conductivity was reflected by an oxygen partial

pressure independent conductivity at a given isothermal.

Here, we show the result of the total conductivity measurement for the free-standing

Ce0.8Gd0.2O1.9-x buckled membrane with 0.46% compressive strain between electrode P2 and

P4 at room temperature, Fig. S3b, as a function of the oxygen partial pressure and temperature

in a Brouwer-type diagram, Fig. S3c, and an Arrhenius-type diagram, Fig. S3d. The total

conductivity is independent of the oxygen partial pressure for the membranes tested in this

study at temperatures of 300 to 500 °C.

5

Based on this experimental evidence we unequivocally demonstrate that a dominant oxygen

ionic conductivity prevails for the 0.46% compressively strained (between P2 and P4) and

free-standing Ce0.8Gd0.2O1.9-x film membranes. Additionally, our findings for the 0.46%

compressively strained film membranes are in agreement with literature for Ce0.8Gd0.2O1.9-x

pellets and substrate-supported thin films, reporting a dominant oxygen ionic conductivity for

the temperature range of 300-500 °C and higher oxygen partial pressures such as in air 7–9.

Figure S3: Oxygen partial pressure and temperature-dependent measurements of the total conductivity of

Ce0.8Gd0.2O1.9-x thin film membranes with 0.46% compressively strain between P2 and P4. (a) Custom-made

measurement setup. (b) Light microscopy image of a free-standing strained Ce0.8Gd0.2O1.9-x thin film membrane

with a 4-point electrode arrangement. (c) Log total electrical conductivity vs. log oxygen partial pressure

Brouwer-type plot for isothermals. (d) Arrhenius-type diagram of the total conductivity with respect to the gas

atmosphere.




6

S4: Description of the stress and strain states for substrate-supported thin films and free-standing Ce0.8Gd0.2O1.9-x membranes: Thermodynamics and electro-chemo-mechanics

Thermodynamics. Electro-chemo-mechanics describe the connection between oxygen ionic

transport (“electro”), oxygen non-stoichiometry (“chemo”) and strained volumes (“mechanic”)

of ionic conducting ceramics such as doped ceria10. Here, the oxygen ionic conduction

happens via the movement of ions hopping over oxygen vacancies. Additional external stress

imposed on the crystal lattice can lead to volume and lattice position changes. Or, it can even

induce the association and dissociation reactions between point defects in the material (e.g.

dopant-oxygen vacancy associates11,12). The formation of oxygen vacancies in the crystal

lattice is governed by minimizing the Gibbs free energy, G. Accordingly, the change in free

energy for spontaneity of defect formation has to be negative

0f vibr elastic configG x H T S U T S (3)

where ΔHf and Uelastic are the enthalpy of formation of a defect and the mean elastic lattice

energy, and ΔSvibr and ΔSconfig are the vibrational and configurational entropy due to the

formation and arrangement of x defects in the atomic lattice13–15. In the case of elastic

deformation acting on the ionic crystal lattice, an expression in terms of the stress tensor sij,

the strained cell volume V and the differential strain tensor ij is then given for the ionic

conductor by14:

ij

elastic ij ijdU V s d (4)

For the cubic fcc unit cell of Ce0.8Gd0.2O1.9-x7, the cell volume can be expressed in terms of the

lattice constant, i.e. V =a3. For isotropic strain, this implies that measured volume changes

can be directly converted to strain in one direction16. The oxygen ionic conductivity, ionic, is 7

thermally activated by an oxygen ionic hopping mechanism over oxygen vacancy, [ ]OV , and

directly related to the strained lattice constant, a, of the material through

2 2 2 2 2

2 2(2 ) [ ] (2 ) [ ] (2 ) [ ]O O Oionic ionic

B B B

q V q V q VD d ak T k T k T

(5)

2q represents the charge of an oxygen vacancy, Dionic the ionic diffusion coefficient, d the

jump distance, the ionic hopping frequency, kB the Boltzmann constant, and a geometry

factor for the fcc cubic lattice of Ce0.8Gd0.2O1.9-x17. The enthalpy of oxygen ionic migration,

Hmig, can be expressed thermodynamically by the Gibbs free energy (in accordance to

equation (3)) and is directly correlated to the strained lattice volume and ionic diffusion using

equations (4) and (5) to

02 [ ] 2 [ ] ( )migionic O ionic O

B

Hvq V v q V expT k T

(6)

where vionic denotes the oxygen ionic mobility and v0 is the pre-exponential ionic mobility

factor.

It can be concluded, based on a thermodynamic argument, that there is a direct impact

between straining a cubic lattice and its point defect formation and the migration of oxygen

ions, such as in the given example of Ce0.8Gd0.2O1.9-x materials. We will use these basic

arguments to discuss and define the stress and strain states for our model experiments on

substrate-supported vs. free standing buckled Ce0.8Gd0.2O1.9-x membranes in the following.

Description of the Stress and Strain States for Substrate-Supported Thin Films and

Free-Standing Ce0.8Gd0.2O1.9-x Membranes. Thin films deposited on substrates are subject to

biaxial residual stresses resulting from thermal expansion mismatch18,19 and arising from film

growth20. The latter process is called atomic peening18,19. This process describes atoms





6

S4: Description of the stress and strain states for substrate-supported thin films and free-standing Ce0.8Gd0.2O1.9-x membranes: Thermodynamics and electro-chemo-mechanics

Thermodynamics. Electro-chemo-mechanics describe the connection between oxygen ionic

transport (“electro”), oxygen non-stoichiometry (“chemo”) and strained volumes (“mechanic”)

of ionic conducting ceramics such as doped ceria10. Here, the oxygen ionic conduction

happens via the movement of ions hopping over oxygen vacancies. Additional external stress

imposed on the crystal lattice can lead to volume and lattice position changes. Or, it can even

induce the association and dissociation reactions between point defects in the material (e.g.

dopant-oxygen vacancy associates11,12). The formation of oxygen vacancies in the crystal

lattice is governed by minimizing the Gibbs free energy, G. Accordingly, the change in free

energy for spontaneity of defect formation has to be negative

0f vibr elastic configG x H T S U T S (3)

where ΔHf and Uelastic are the enthalpy of formation of a defect and the mean elastic lattice

energy, and ΔSvibr and ΔSconfig are the vibrational and configurational entropy due to the

formation and arrangement of x defects in the atomic lattice13–15. In the case of elastic

deformation acting on the ionic crystal lattice, an expression in terms of the stress tensor sij,

the strained cell volume V and the differential strain tensor ij is then given for the ionic

conductor by14:

ij

elastic ij ijdU V s d (4)

For the cubic fcc unit cell of Ce0.8Gd0.2O1.9-x7, the cell volume can be expressed in terms of the

lattice constant, i.e. V =a3. For isotropic strain, this implies that measured volume changes

can be directly converted to strain in one direction16. The oxygen ionic conductivity, ionic, is 7

thermally activated by an oxygen ionic hopping mechanism over oxygen vacancy, [ ]OV , and

directly related to the strained lattice constant, a, of the material through

2 2 2 2 2

2 2(2 ) [ ] (2 ) [ ] (2 ) [ ]O O Oionic ionic

B B B

q V q V q VD d ak T k T k T

(5)

2q represents the charge of an oxygen vacancy, Dionic the ionic diffusion coefficient, d the

jump distance, the ionic hopping frequency, kB the Boltzmann constant, and a geometry

factor for the fcc cubic lattice of Ce0.8Gd0.2O1.9-x17. The enthalpy of oxygen ionic migration,

Hmig, can be expressed thermodynamically by the Gibbs free energy (in accordance to

equation (3)) and is directly correlated to the strained lattice volume and ionic diffusion using

equations (4) and (5) to

02 [ ] 2 [ ] ( )migionic O ionic O

B

Hvq V v q V expT k T

(6)

where vionic denotes the oxygen ionic mobility and v0 is the pre-exponential ionic mobility

factor.

It can be concluded, based on a thermodynamic argument, that there is a direct impact

between straining a cubic lattice and its point defect formation and the migration of oxygen

ions, such as in the given example of Ce0.8Gd0.2O1.9-x materials. We will use these basic

arguments to discuss and define the stress and strain states for our model experiments on

substrate-supported vs. free standing buckled Ce0.8Gd0.2O1.9-x membranes in the following.

Description of the Stress and Strain States for Substrate-Supported Thin Films and

Free-Standing Ce0.8Gd0.2O1.9-x Membranes. Thin films deposited on substrates are subject to

biaxial residual stresses resulting from thermal expansion mismatch18,19 and arising from film

growth20. The latter process is called atomic peening18,19. This process describes atoms





8

incorporated in the thin film with higher density during deposition at high temperatures.

Subsequently, in the course of cooling, the thin film relaxes to a lower density creating

intrinsic stress10,18,21. For example, it is reported that the biaxial residual stress in doped

zirconia18 and ceria11,12,22 membranes can vary by 100s of MPa from compressive to tensile

with respect to the aspect ratio of the film18 or the deposition temperature23 employed in state-

of-the-art vacuum deposition techniques (i.e. pulsed laser deposition24, and sputtering21). It is

this biaxial residual strain that defines what happens upon substrate removal. A deposited

ionic conductor film will either crack due to tension or buckle under compression to a free-

standing membrane18,21,24. This is known in the field of micro-fuel cell membrane processing

(see Refs. 18,21,23–27 for further details). We exemplify the overall “net tensile and compressive

strain” (also called “net strain”) acting on a Ce0.8Gd0.2O1.9-x membrane leading to either

cracking (tensile strain) or buckling (compressive strain), see Fig. S4a, b. Here, the difference

in the initial intrinsic strain level was established through a change in the deposition

temperature from 400 °C (compressive strain) to 700 °C (tensile strain) for the pulsed laser

deposited Ce0.8Gd0.2O1.9-x films. The following can be concluded on the thermodynamics of

defect formation concerning the “net tensile and compressive strain” (“net strain”) of an ionic

conducting thin film membrane: after substrate removal the Gibbs free energy is minimized

to a new equilibrium state through buckling of the free-standing ceria-based membrane (see

thermodynamic equations (3) and (4) for details).

In this state the buckled thin film membrane is describable by a classic plate clamped onto a

stiff substrate, e.g. the Karman plate model28. Biaxial stress acts on the compressed thin film

membrane for which we can define the strain tensor for in-plane (with i, j ∈ {x, y}) and out-

of-plane (z) components by

( ) 0( ) ( )m bij ij ij ijz z (7)

9

where δij is the Kronecker delta, 0 is the average value of the residual strain, mij is the in-

plane membrane strain and ( )bij z the out-of-plane bending and twisting modes of the

membrane. We relate the out-of-plane deflection, ω, to the out-of-plane membrane strain,

( )bij z of the thin film membrane from

2

( )bij z z

i j

(8)

From the strain theorem of equation (8), the strain can be defined over the derivative of the

out-of-plane deflection ω (function of buckling curve) of a compressed Ce0.8Gd0.2O1.9-x

membrane. We refer to the maximum strain change as the “net compressive strain” (1st order

strain) between the electrodes on the thin film membranes. The two cases for 1st order strain

are presented in Fig. S5a. In Fig. S5b, we schematically display the related out-of-plane

amplitude, ω, for the free-standing film membrane. Additionally, we provide an example for

the net compressive strain between the microelectrodes of a free-standing Ce0.8Gd0.2O1.9-x

membrane using a micrograph in Fig. S6. The elastic energy, Uelastic (see equations (3) and

(4)), of the in-plane Ce0.8Gd0.2O1.9-x membrane components can be defined for the compressed

film volumes using Hooke’s law by 24:

2/2 /2 /2 /22 202 /2 /2 /2 /2( 0)

( 2 )2(1 ) 1 xy

a a a a

elastic xx yy xx yy za a a az

Eh EhU dxdy dxdy

(9)

where the terms a and h are side length and thickness, respectively, of the thin film, E is

Young’s modulus and ν is Poisson’s ratio, see Fig. S5b.

In this first part we describe and define the “net compressive strain” for the free-standing

Ce0.8Gd0.2O1.9-x membranes. This refers to the 1st order maximum strains measured in between

the locality of the microelectrodes. It is important to note that we also observed a 2nd order

waviness that superimposes this in-plane “net compressed strain” at smaller amplitudes for

the Ce0.8Gd0.2O1.9-x membranes, see Fig. S5c and Fig. S6. The overall net compressed





8

incorporated in the thin film with higher density during deposition at high temperatures.

Subsequently, in the course of cooling, the thin film relaxes to a lower density creating

intrinsic stress10,18,21. For example, it is reported that the biaxial residual stress in doped

zirconia18 and ceria11,12,22 membranes can vary by 100s of MPa from compressive to tensile

with respect to the aspect ratio of the film18 or the deposition temperature23 employed in state-

of-the-art vacuum deposition techniques (i.e. pulsed laser deposition24, and sputtering21). It is

this biaxial residual strain that defines what happens upon substrate removal. A deposited

ionic conductor film will either crack due to tension or buckle under compression to a free-

standing membrane18,21,24. This is known in the field of micro-fuel cell membrane processing

(see Refs. 18,21,23–27 for further details). We exemplify the overall “net tensile and compressive

strain” (also called “net strain”) acting on a Ce0.8Gd0.2O1.9-x membrane leading to either

cracking (tensile strain) or buckling (compressive strain), see Fig. S4a, b. Here, the difference

in the initial intrinsic strain level was established through a change in the deposition

temperature from 400 °C (compressive strain) to 700 °C (tensile strain) for the pulsed laser

deposited Ce0.8Gd0.2O1.9-x films. The following can be concluded on the thermodynamics of

defect formation concerning the “net tensile and compressive strain” (“net strain”) of an ionic

conducting thin film membrane: after substrate removal the Gibbs free energy is minimized

to a new equilibrium state through buckling of the free-standing ceria-based membrane (see

thermodynamic equations (3) and (4) for details).

In this state the buckled thin film membrane is describable by a classic plate clamped onto a

stiff substrate, e.g. the Karman plate model28. Biaxial stress acts on the compressed thin film

membrane for which we can define the strain tensor for in-plane (with i, j ∈ {x, y}) and out-

of-plane (z) components by

( ) 0( ) ( )m bij ij ij ijz z (7)

9

where δij is the Kronecker delta, 0 is the average value of the residual strain, mij is the in-

plane membrane strain and ( )bij z the out-of-plane bending and twisting modes of the

membrane. We relate the out-of-plane deflection, ω, to the out-of-plane membrane strain,

( )bij z of the thin film membrane from

2

( )bij z z

i j

(8)

From the strain theorem of equation (8), the strain can be defined over the derivative of the

out-of-plane deflection ω (function of buckling curve) of a compressed Ce0.8Gd0.2O1.9-x

membrane. We refer to the maximum strain change as the “net compressive strain” (1st order

strain) between the electrodes on the thin film membranes. The two cases for 1st order strain

are presented in Fig. S5a. In Fig. S5b, we schematically display the related out-of-plane

amplitude, ω, for the free-standing film membrane. Additionally, we provide an example for

the net compressive strain between the microelectrodes of a free-standing Ce0.8Gd0.2O1.9-x

membrane using a micrograph in Fig. S6. The elastic energy, Uelastic (see equations (3) and

(4)), of the in-plane Ce0.8Gd0.2O1.9-x membrane components can be defined for the compressed

film volumes using Hooke’s law by 24:

2/2 /2 /2 /22 202 /2 /2 /2 /2( 0)

( 2 )2(1 ) 1 xy

a a a a

elastic xx yy xx yy za a a az

Eh EhU dxdy dxdy

(9)

where the terms a and h are side length and thickness, respectively, of the thin film, E is

Young’s modulus and ν is Poisson’s ratio, see Fig. S5b.

In this first part we describe and define the “net compressive strain” for the free-standing

Ce0.8Gd0.2O1.9-x membranes. This refers to the 1st order maximum strains measured in between

the locality of the microelectrodes. It is important to note that we also observed a 2nd order

waviness that superimposes this in-plane “net compressed strain” at smaller amplitudes for

the Ce0.8Gd0.2O1.9-x membranes, see Fig. S5c and Fig. S6. The overall net compressed





10

membrane reveals alterations of curvature as “hilltops” and “valleys”, see Fig. S6. Various

techniques confirm the existence and variation of these 2nd order local strain changes over

various length scales (i.e. atomistic near order changes by Raman spectroscopy and

macroscopic curvature changes by optical profilometry). Based on Stoney’s equation29, these

“local 2nd order strain” changes that superimpose the overall net compressively strained

Ce0.8Gd0.2O1.9-x membranes were segmented and computed using

2

6 1s s

s GDC

h E kv h

(10)

where σ is the in-plane stress component in the film, k is curvature, Es is Young’s modulus of

the substrate, νs is Poisson’s ratio of the substrate, hs is thickness of the Si-substrate, and hGDC

is the thin film thickness.

Figure S4: Cracking or buckling of free standing Ce0.8Gd0.2O1.9-x membranes caused by “net tensile or

compressive strain” through different deposition temperatures. (a) The Ce0.8Gd0.2O1.9-x membrane cracks after

11

PLD deposition at 700 °C and free-etching of the initially substrate-supported film. (b) A buckled and

compressively strained membrane occurs when the initial PLD deposition temperature is changed to 400 °C.

Figure S5: Strain states in free standing membranes. (a) Schematic figure of the isotropic tensile or compressive

strain’s influence on free standing Ce0.8Gd0.2O1.9-x membranes, leading to either cracking or buckling,

respectively. (b) Schematic description of a buckling membrane with microelectrodes. The “net compressive

strain” is defined by the maximum out-of-plane deflection, ωmax, of the compressed membrane. (c)

Nomenclature of “local strain” based on the 2nd order waviness, where one can observe “hilltops” and “valleys”.

Figure S6: Example for the nomenclature of the 1st (red) and 2nd (orange) order strain based on a light microscopy image of a freestanding Ce0.8Gd0.2O1.9-x membrane.




10

membrane reveals alterations of curvature as “hilltops” and “valleys”, see Fig. S6. Various

techniques confirm the existence and variation of these 2nd order local strain changes over

various length scales (i.e. atomistic near order changes by Raman spectroscopy and

macroscopic curvature changes by optical profilometry). Based on Stoney’s equation29, these

“local 2nd order strain” changes that superimpose the overall net compressively strained

Ce0.8Gd0.2O1.9-x membranes were segmented and computed using

2

6 1s s

s GDC

h E kv h

(10)

where σ is the in-plane stress component in the film, k is curvature, Es is Young’s modulus of

the substrate, νs is Poisson’s ratio of the substrate, hs is thickness of the Si-substrate, and hGDC

is the thin film thickness.

Figure S4: Cracking or buckling of free standing Ce0.8Gd0.2O1.9-x membranes caused by “net tensile or

compressive strain” through different deposition temperatures. (a) The Ce0.8Gd0.2O1.9-x membrane cracks after

11

PLD deposition at 700 °C and free-etching of the initially substrate-supported film. (b) A buckled and

compressively strained membrane occurs when the initial PLD deposition temperature is changed to 400 °C.

Figure S5: Strain states in free standing membranes. (a) Schematic figure of the isotropic tensile or compressive

strain’s influence on free standing Ce0.8Gd0.2O1.9-x membranes, leading to either cracking or buckling,

respectively. (b) Schematic description of a buckling membrane with microelectrodes. The “net compressive

strain” is defined by the maximum out-of-plane deflection, ωmax, of the compressed membrane. (c)

Nomenclature of “local strain” based on the 2nd order waviness, where one can observe “hilltops” and “valleys”.

Figure S6: Example for the nomenclature of the 1st (red) and 2nd (orange) order strain based on a light microscopy image of a freestanding Ce0.8Gd0.2O1.9-x membrane.




12

S5: Impedance spectroscopy of free standing Gd0.2Ce0.8O1.9-x electrolyte membranes

The impedance spectra are measured for the Gd0.2Ce0.8O1.9-x electrolyte films and membranes.

One membrane with the microelectrode design “a” is exemplified in the impedance response

with respect to temperature, Fig. S7a. Here, we report RC-semicircles composed of a high

frequency response, representing ionic transport in the membrane, grain and grain boundary,

which are comprised of overlapping frequencies. The low frequency might be related to the

electrode reaction and exchange with the gas phase: In Fig. S7b, an appliance of up to 1-3 V

DC bias reveals that the spectra remains unchanged in the high frequency response at 500 °C.

Figure S7: Nyquist plots ofa Gd0.2Ce0.8O1.9-x electrolyte free-standing membrane measured with microelectrodes

of design “a”. (a) Electrochemical impedance response with respect to temperature and (b) electrochemical

impedance response with respect to applied DC bias.

S6: Near order Raman spectroscopy of the Gd0.2Ce0.8O1.9-x free standing membranes and

substrate-supported thin films: Characterizing the oxygen anionic-cation near order

Raman spectra of Gd0.2Ce0.8O1.9-x free standing membranes and substrate-supported thin films

are presented in the main text. For the self-supported membrane, Raman measurements with a

spot size of ~850 nm were carried out at different localities of the free-standing membrane,

namely the “hilltops” and “valleys”. As indicated in Fig. S8, these arrows indicate

13

predominant tensile and compressive local in-plane strain, respectively. The relationship

between in-plane and out-of-plane strain is explained more detailed in the recent paper by

Schweiger17. The spectra for “valleys” reveal 4 peaks, all of them originating from the

Gd0.2Ce0.8O1.9-x: at ~250 cm-1, ~464 cm-1, ~557 cm-1, and ~600 cm-1. Literature analysis

reveals that these can be ascribed to the following Raman features: second order transversal

acoustic mode, 1st order allowed F2g mode, 2nd order longitudinal acoustic and 2nd order

transversal optical mode1,15,30,31. In the substrate-supported sample, another peak is visible at

~300 cm-1, which can be attributed to 2nd order transversal acoustic phonon contributions of

the crystalline silicon32. The same assignment of peak modes is successful for the “hilltops”

spectra, but with altered effective positions for the F2g mode as described in the main text, Fig.

2h. Due to the penetration depth of the laser used for excitation we also measure a portion of

the signal from the opposite side of the membrane, resulting in peak broadening. The

asymmetry in the Raman signature is attributed to phonon dispersion and confinement effects

due to the small grain size and strains in the materials33.

Figure S8: Raman measurements and peak position comparison. The arrows indicate the direction of the incident

beam. Measurements were carried out on the hilltops where tensile strain prevails and valleys where

compressive strain is predominant.




12

S5: Impedance spectroscopy of free standing Gd0.2Ce0.8O1.9-x electrolyte membranes

The impedance spectra are measured for the Gd0.2Ce0.8O1.9-x electrolyte films and membranes.

One membrane with the microelectrode design “a” is exemplified in the impedance response

with respect to temperature, Fig. S7a. Here, we report RC-semicircles composed of a high

frequency response, representing ionic transport in the membrane, grain and grain boundary,

which are comprised of overlapping frequencies. The low frequency might be related to the

electrode reaction and exchange with the gas phase: In Fig. S7b, an appliance of up to 1-3 V

DC bias reveals that the spectra remains unchanged in the high frequency response at 500 °C.

Figure S7: Nyquist plots ofa Gd0.2Ce0.8O1.9-x electrolyte free-standing membrane measured with microelectrodes

of design “a”. (a) Electrochemical impedance response with respect to temperature and (b) electrochemical

impedance response with respect to applied DC bias.

S6: Near order Raman spectroscopy of the Gd0.2Ce0.8O1.9-x free standing membranes and

substrate-supported thin films: Characterizing the oxygen anionic-cation near order

Raman spectra of Gd0.2Ce0.8O1.9-x free standing membranes and substrate-supported thin films

are presented in the main text. For the self-supported membrane, Raman measurements with a

spot size of ~850 nm were carried out at different localities of the free-standing membrane,

namely the “hilltops” and “valleys”. As indicated in Fig. S8, these arrows indicate

13

predominant tensile and compressive local in-plane strain, respectively. The relationship

between in-plane and out-of-plane strain is explained more detailed in the recent paper by

Schweiger17. The spectra for “valleys” reveal 4 peaks, all of them originating from the

Gd0.2Ce0.8O1.9-x: at ~250 cm-1, ~464 cm-1, ~557 cm-1, and ~600 cm-1. Literature analysis

reveals that these can be ascribed to the following Raman features: second order transversal

acoustic mode, 1st order allowed F2g mode, 2nd order longitudinal acoustic and 2nd order

transversal optical mode1,15,30,31. In the substrate-supported sample, another peak is visible at

~300 cm-1, which can be attributed to 2nd order transversal acoustic phonon contributions of

the crystalline silicon32. The same assignment of peak modes is successful for the “hilltops”

spectra, but with altered effective positions for the F2g mode as described in the main text, Fig.

2h. Due to the penetration depth of the laser used for excitation we also measure a portion of

the signal from the opposite side of the membrane, resulting in peak broadening. The

asymmetry in the Raman signature is attributed to phonon dispersion and confinement effects

due to the small grain size and strains in the materials33.

Figure S8: Raman measurements and peak position comparison. The arrows indicate the direction of the incident

beam. Measurements were carried out on the hilltops where tensile strain prevails and valleys where

compressive strain is predominant.




14

S7: Arrhenius diagrams of free standing membranes vs. substrate-supported thin films

for all types of microelectrode designs

In Fig. 3d of the main text, the activation energy determined from the ionic transport

measurement is reported for the various electrode designs for the flat and substrate support

films of Gd0.2Ce0.8O1.9-x and their compressively strained membrane counterparts. Here, in Fig.

S9, the Arrhenius-type diagrams for those combinations of electrodes are supplemented in

detail: Fig. S9a and S9b exhibit the plots for the free standing membranes and substrate-

supported thin films, respectively. Generally, one can observe that the ionic conductivity is

higher for the substrate-supported thin films with lower activation energy, when compared to

strained membranes under compression.

Figure S9: Arrhenius diagrams for the measured conductivity in air for (a) free standing membranes and (b)

substrate-supported thin films of Gd0.2Ce0.8O1.9-x. Measurements were carried out for the different microelectrode

designs “a-c” during heating (closed symbols) and cooling (open symbols).

S8: Visualization of strain values in free standing membrane

In Fig. 4 of the main text, the result of the strain distribution determined by the wafer

curvature technique is viewed from the top of the membrane. Figure S10 shows the same

15

result viewed from a different angle to give an indication of the observed range of strain

values. From this plot it can be deduced that the strains of the membrane locally range from -2%

to 2% except for a number of outliers found at the edge of the membrane.

Figure S10: Strain distribution in free-standing ionic conducting Ce0.8Gd0.2O1.9-x electrolyte film determined by

wafer curvature technique. Here, the membrane is viewed from the side with all scan lines included. The color

code indicates the magnitude of measured strains.

S9: The process of fabrication of free standing electrolyte membranes with

microelectrodes

Figure S11 illustrates the process of microfabrication for the free-standing membrane samples.

The process is a combination of microfabrication and chemical wet etching and is detailed in

the caption of Figure S11.




14

S7: Arrhenius diagrams of free standing membranes vs. substrate-supported thin films

for all types of microelectrode designs

In Fig. 3d of the main text, the activation energy determined from the ionic transport

measurement is reported for the various electrode designs for the flat and substrate support

films of Gd0.2Ce0.8O1.9-x and their compressively strained membrane counterparts. Here, in Fig.

S9, the Arrhenius-type diagrams for those combinations of electrodes are supplemented in

detail: Fig. S9a and S9b exhibit the plots for the free standing membranes and substrate-

supported thin films, respectively. Generally, one can observe that the ionic conductivity is

higher for the substrate-supported thin films with lower activation energy, when compared to

strained membranes under compression.

Figure S9: Arrhenius diagrams for the measured conductivity in air for (a) free standing membranes and (b)

substrate-supported thin films of Gd0.2Ce0.8O1.9-x. Measurements were carried out for the different microelectrode

designs “a-c” during heating (closed symbols) and cooling (open symbols).

S8: Visualization of strain values in free standing membrane

In Fig. 4 of the main text, the result of the strain distribution determined by the wafer

curvature technique is viewed from the top of the membrane. Figure S10 shows the same

15

result viewed from a different angle to give an indication of the observed range of strain

values. From this plot it can be deduced that the strains of the membrane locally range from -2%

to 2% except for a number of outliers found at the edge of the membrane.

Figure S10: Strain distribution in free-standing ionic conducting Ce0.8Gd0.2O1.9-x electrolyte film determined by

wafer curvature technique. Here, the membrane is viewed from the side with all scan lines included. The color

code indicates the magnitude of measured strains.

S9: The process of fabrication of free standing electrolyte membranes with

microelectrodes

Figure S11 illustrates the process of microfabrication for the free-standing membrane samples.

The process is a combination of microfabrication and chemical wet etching and is detailed in

the caption of Figure S11.





16

Figure S11: Manufacturing process flow processing of Gd0.2Ce0.8O1.9-x free-standing membranes. (a) Cleaning of

the Si substrate, (b) Si3N4 layers are coated onto the two sides of the silicon wafer by Low Stress-CVD (LPCVD),

(c) photolithography is employed to define the area to be etched via Reactive Ion Etching (RIE) for underneath

the Si3N4 layers to open space to the silicon, (d) KOH wet etching is used to remove the Si substrate so that a

free-standing Si3N4 membrane forms, (e) PLD deposition is used to deposit a Gd0.2Ce0.8O1.9-x layer, (f) a 2nd RIE

step is used to etch the Si3N4 underneath the Gd0.2Ce0.8O1.9-x, forming now a free-standing membrane, (g) Pt

films are deposited and structured by a shadow mask and e-beam evaporation and (h) the top microelectrodes are

contacted via micropositioners in a custom-made microprobe station and attached to electrochemical test

equipment as detailed in the methods section.

17

References

1. Rupp, J. L. M. et al. Scalable Oxygen-Ion Transport Kinetics in Metal-Oxide Films: Impact of Thermally Induced Lattice Compaction in Acceptor Doped Ceria Films. Adv. Funct. Mater. 24, 1562–1574 (2014).

2. Mohan Kant, K., Esposito, V., & Pryds, N. Strain induced ionic conductivity enhancement in epitaxial Ce0.9Gd0.1O2−δ thin films. Appl. Phys. Lett. 100, 033105 (2012).

3. Suzuki, T., Kosacki, I., & Anderson, H. Microstructure–electrical conductivity relationships in nanocrystalline ceria thin films. Solid State Ionics 151, 111–121 (2002).

4. Rodrigo, K. et al. The effects of thermal annealing on the structure and the electrical transport properties of ultrathin gadolinia-doped ceria films grown by pulsed laser deposition. Appl. Phys. A 104, 845–850 (2011).

5. Rupp, J. L. M. Ionic diffusion as a matter of lattice-strain for electroceramic thin films. Solid State Ionics 207, 1–13 (2012).

6. Hayashi, H., Kanoh, M., Quan, C., & Inaba, H. Thermal expansion of Gd-doped ceria and reduced ceria. Solid State Ionics 132, 227–233 (2000).

7. Mogensen, M., Sammes, N., & Tompsett, G. Physical, chemical and electrochemical properties of pure and doped ceria. Solid State Ionics 129, 63–94 (2000).

8. Rupp, J. L. M., Infortuna, A. & Gauckler, L. J. Thermodynamic Stability of Gadolinia-Doped Ceria Thin Film Electrolytes for Micro-Solid Oxide Fuel Cells. J. Am. Ceram. Soc. 90, 1792–1797 (2007).

9. Rodrigo, K. et al. Electrical characterization of gadolinia-doped ceria films grown by pulsed laser deposition. Appl. Phys. A 101, 601–607 (2010).

10. Tuller, H. L. & Bishop, S. R. Point Defects in Oxides: Tailoring Materials Through Defect Engineering. Annu. Rev. Mater. Res. 41, 369–398 (2011).

11. Lubomirsky, I. Practical applications of the chemical strain effect in ionic and mixed conductors. Monatshefte für Chemie - Chem. Mon. 140, 1025–1030 (2009).

12. Lubomirsky, I. Stress adaptation in ceramic thin films. Phys. Chem. Chem. Phys. 9, 3701–10 (2007).

13. Atkins, P. & Paula, J. Physical Chemistry, Ninth Edition. Oxford Univ. Press (2010).

14. Maier, J. Physical Chemistry of Ionic Materials: Ions and Electrons in Solids. John Wiley Sons (2004).

15. Kossoy, A. et al. Influence of Point-Defect Reaction Kinetics on the Lattice Parameter of Ce0.8Gd0.2O1.9. Adv. Funct. Mater. 19, 634–641 (2009).




16

Figure S11: Manufacturing process flow processing of Gd0.2Ce0.8O1.9-x free-standing membranes. (a) Cleaning of

the Si substrate, (b) Si3N4 layers are coated onto the two sides of the silicon wafer by Low Stress-CVD (LPCVD),

(c) photolithography is employed to define the area to be etched via Reactive Ion Etching (RIE) for underneath

the Si3N4 layers to open space to the silicon, (d) KOH wet etching is used to remove the Si substrate so that a

free-standing Si3N4 membrane forms, (e) PLD deposition is used to deposit a Gd0.2Ce0.8O1.9-x layer, (f) a 2nd RIE

step is used to etch the Si3N4 underneath the Gd0.2Ce0.8O1.9-x, forming now a free-standing membrane, (g) Pt

films are deposited and structured by a shadow mask and e-beam evaporation and (h) the top microelectrodes are

contacted via micropositioners in a custom-made microprobe station and attached to electrochemical test

equipment as detailed in the methods section.

17

References

1. Rupp, J. L. M. et al. Scalable Oxygen-Ion Transport Kinetics in Metal-Oxide Films: Impact of Thermally Induced Lattice Compaction in Acceptor Doped Ceria Films. Adv. Funct. Mater. 24, 1562–1574 (2014).

2. Mohan Kant, K., Esposito, V., & Pryds, N. Strain induced ionic conductivity enhancement in epitaxial Ce0.9Gd0.1O2−δ thin films. Appl. Phys. Lett. 100, 033105 (2012).

3. Suzuki, T., Kosacki, I., & Anderson, H. Microstructure–electrical conductivity relationships in nanocrystalline ceria thin films. Solid State Ionics 151, 111–121 (2002).

4. Rodrigo, K. et al. The effects of thermal annealing on the structure and the electrical transport properties of ultrathin gadolinia-doped ceria films grown by pulsed laser deposition. Appl. Phys. A 104, 845–850 (2011).

5. Rupp, J. L. M. Ionic diffusion as a matter of lattice-strain for electroceramic thin films. Solid State Ionics 207, 1–13 (2012).

6. Hayashi, H., Kanoh, M., Quan, C., & Inaba, H. Thermal expansion of Gd-doped ceria and reduced ceria. Solid State Ionics 132, 227–233 (2000).

7. Mogensen, M., Sammes, N., & Tompsett, G. Physical, chemical and electrochemical properties of pure and doped ceria. Solid State Ionics 129, 63–94 (2000).

8. Rupp, J. L. M., Infortuna, A. & Gauckler, L. J. Thermodynamic Stability of Gadolinia-Doped Ceria Thin Film Electrolytes for Micro-Solid Oxide Fuel Cells. J. Am. Ceram. Soc. 90, 1792–1797 (2007).

9. Rodrigo, K. et al. Electrical characterization of gadolinia-doped ceria films grown by pulsed laser deposition. Appl. Phys. A 101, 601–607 (2010).

10. Tuller, H. L. & Bishop, S. R. Point Defects in Oxides: Tailoring Materials Through Defect Engineering. Annu. Rev. Mater. Res. 41, 369–398 (2011).

11. Lubomirsky, I. Practical applications of the chemical strain effect in ionic and mixed conductors. Monatshefte für Chemie - Chem. Mon. 140, 1025–1030 (2009).

12. Lubomirsky, I. Stress adaptation in ceramic thin films. Phys. Chem. Chem. Phys. 9, 3701–10 (2007).

13. Atkins, P. & Paula, J. Physical Chemistry, Ninth Edition. Oxford Univ. Press (2010).

14. Maier, J. Physical Chemistry of Ionic Materials: Ions and Electrons in Solids. John Wiley Sons (2004).

15. Kossoy, A. et al. Influence of Point-Defect Reaction Kinetics on the Lattice Parameter of Ce0.8Gd0.2O1.9. Adv. Funct. Mater. 19, 634–641 (2009).





18

16. De Souza, R., Ramadan, A., Hörner, S. Modifying the barriers for oxygen-vacancy migration in fluorite-structured CeO2 electrolytes through strain: a computer simulation study. Energy Environ. Sci. 5, 5445 (2012).

17. Schweiger, S., Kubicek, M., Messerschmitt, F., Murer, C., Rupp, J. L. M. A Micro-Dot Multilayer Oxide Device: Let’s Tune the Strain-Ionic Transport Interaction. ACS Nano 8, 5032–5048 (2014).

18. Evans, A. et al. Residual Stress and Buckling Patterns of Free-standing Yttria-stabilized-zirconia Membranes Fabricated by Pulsed Laser Deposition. Fuel Cells 12, 614–623 (2012).

19. Kerman, K., Tallinen, T., Ramanathan, S. & Mahadevan, L. Elastic configurations of self-supported oxide membranes for fuel cells. J. Power Sources 222, 359–366 (2013).

20. D’Heurle, F. & Harper, J. Note on the origin of intrinsic stresses in films deposited via evaporation and sputtering. Thin Solid Films 171, 81–92 (1989).

21. Baertsch, C. et al. Fabrication and structural characterization of self-supporting electrolyte membranes for a micro solid-oxide fuel cell. J. Mater. Res. 19, 2604–2615 (2004).

22. Karageorgakis, N. I. et al. Properties of Flame Sprayed Ce0.8Gd0.2O1.9-δ Electrolyte Thin Films. Adv. Funct. Mater. 21, 532–539 (2011).

23. Garbayo, I. et al. Electrical characterization of thermomechanically stable YSZ membranes for micro solid oxide fuel cells applications. Solid State Ionics 181, 322–331 (2010).

24. Safa, Y., Hocker, T., Prestat, M. & Evans, A. Post-buckling design of thin-film electrolytes in micro-solid oxide fuel cells. J. Power Sources 250, 332–342 (2014).

25. Evans, A., Bieberle-Hütter, A., Rupp, J. L. M. & Gauckler, L. J. Review on microfabricated micro-solid oxide fuel cell membranes. J. Power Sources 194, 119–129 (2009).

26. Tsuchiya, M., Lai, B. & Ramanathan, S. Scalable nanostructured membranes for solid-oxide fuel cells. Nat. Nanotechnol. 6, 282–6 (2011).

27. Garbayo, I. et al. Full ceramic micro solid oxide fuel cells: towards more reliable MEMS power generators operating at high temperatures. Energy Environ. Sci. 7, 3617–3629 (2014).

28. T. von Kármán, Festigkeitsprobleme in Maschinenbau. Encykl. der Math. Wissenschaften, IV/4 , Teubner 311 – 385 (1910).

29. Stoney, G. G. The Tension of Metallic Films Deposited by Electrolysis. Proc. R. Soc. A Math. Phys. Eng. Sci. 82, 172–175 (1909).

30. Nakajima, A., Yoshihara, A. & Ishigame, M. Defect-induced Raman spectra in doped CeO 2. Phys. Rev. B 50, (1994).

19

31. Weber, W., Hass, K. & McBride, J. Raman study of CeO2: second-order scattering, lattice dynamics, and particle-size effects. Phys. Rev. B 48, 178–185 (1993).

32. Wang, R. et al. Raman spectral study of silicon nanowires: High-order scattering and phonon confinement effects. Phys. Rev. B 61, 16827–16832 (2000).

33. Dohčević-Mitrović, Z. D. et al. The size and strain effects on the Raman spectra of Ce1−xNdxO2−δ (0≤x≤0.25) nanopowders. Solid State Commun. 137, 387–390 (2006).





18

16. De Souza, R., Ramadan, A., Hörner, S. Modifying the barriers for oxygen-vacancy migration in fluorite-structured CeO2 electrolytes through strain: a computer simulation study. Energy Environ. Sci. 5, 5445 (2012).

17. Schweiger, S., Kubicek, M., Messerschmitt, F., Murer, C., Rupp, J. L. M. A Micro-Dot Multilayer Oxide Device: Let’s Tune the Strain-Ionic Transport Interaction. ACS Nano 8, 5032–5048 (2014).

18. Evans, A. et al. Residual Stress and Buckling Patterns of Free-standing Yttria-stabilized-zirconia Membranes Fabricated by Pulsed Laser Deposition. Fuel Cells 12, 614–623 (2012).

19. Kerman, K., Tallinen, T., Ramanathan, S. & Mahadevan, L. Elastic configurations of self-supported oxide membranes for fuel cells. J. Power Sources 222, 359–366 (2013).

20. D’Heurle, F. & Harper, J. Note on the origin of intrinsic stresses in films deposited via evaporation and sputtering. Thin Solid Films 171, 81–92 (1989).

21. Baertsch, C. et al. Fabrication and structural characterization of self-supporting electrolyte membranes for a micro solid-oxide fuel cell. J. Mater. Res. 19, 2604–2615 (2004).

22. Karageorgakis, N. I. et al. Properties of Flame Sprayed Ce0.8Gd0.2O1.9-δ Electrolyte Thin Films. Adv. Funct. Mater. 21, 532–539 (2011).

23. Garbayo, I. et al. Electrical characterization of thermomechanically stable YSZ membranes for micro solid oxide fuel cells applications. Solid State Ionics 181, 322–331 (2010).

24. Safa, Y., Hocker, T., Prestat, M. & Evans, A. Post-buckling design of thin-film electrolytes in micro-solid oxide fuel cells. J. Power Sources 250, 332–342 (2014).

25. Evans, A., Bieberle-Hütter, A., Rupp, J. L. M. & Gauckler, L. J. Review on microfabricated micro-solid oxide fuel cell membranes. J. Power Sources 194, 119–129 (2009).

26. Tsuchiya, M., Lai, B. & Ramanathan, S. Scalable nanostructured membranes for solid-oxide fuel cells. Nat. Nanotechnol. 6, 282–6 (2011).

27. Garbayo, I. et al. Full ceramic micro solid oxide fuel cells: towards more reliable MEMS power generators operating at high temperatures. Energy Environ. Sci. 7, 3617–3629 (2014).

28. T. von Kármán, Festigkeitsprobleme in Maschinenbau. Encykl. der Math. Wissenschaften, IV/4 , Teubner 311 – 385 (1910).

29. Stoney, G. G. The Tension of Metallic Films Deposited by Electrolysis. Proc. R. Soc. A Math. Phys. Eng. Sci. 82, 172–175 (1909).

30. Nakajima, A., Yoshihara, A. & Ishigame, M. Defect-induced Raman spectra in doped CeO 2. Phys. Rev. B 50, (1994).

19

31. Weber, W., Hass, K. & McBride, J. Raman study of CeO2: second-order scattering, lattice dynamics, and particle-size effects. Phys. Rev. B 48, 178–185 (1993).

32. Wang, R. et al. Raman spectral study of silicon nanowires: High-order scattering and phonon confinement effects. Phys. Rev. B 61, 16827–16832 (2000).

33. Dohčević-Mitrović, Z. D. et al. The size and strain effects on the Raman spectra of Ce1−xNdxO2−δ (0≤x≤0.25) nanopowders. Solid State Commun. 137, 387–390 (2006).



Documents

The effect of mechanical twisting on oxygen ionic ... · In contrast, the dominant oxygen ionic carrier conductivity was reflected by an oxygen partial pressure independent conductivity