Charge-Induced Reversible Strain in a Metal

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Science  11 Apr 2003:
Vol. 300, Issue 5617, pp. 312-315
DOI: 10.1126/science.1081024


Dimension changes on the order of 0.1% or above in response to an applied voltage have been reported for many types of materials, including ceramics, polymers, and carbon nanostructures, but not, so far, for metals. We show that reversible strain amplitudes comparable to those of commercial piezoceramics can be induced in metals by introducing a continuous network of nanometer-sized pores with a high surface area and by controlling the surface electronic charge density through an applied potential relative to an electrolyte impregnating the pores.

Materials that can reversibly change their dimensions upon the application of an external stimulus, such as an applied voltage, are used as actuators in many applications. The best known examples are piezoelectric and electrostrictive ceramics, but conducting polymers (1) and carbon nanotubes (2) have recently also been proposed. However, voltage-induced dimension changes of comparable magnitude have not been reported in metals. It is therefore of interest to explore to what degree dimension changes in metals may be induced by implementing the recent suggestion that a wide range of properties of metals may be reversibly tuned simply by adding or withdrawing charges at surfaces or internal interfaces through the action of an applied voltage (3). This concept is analogous to the use of the field effect as the basis for electronic switching in semiconductor microelectronic devices. Although the field effect has also been used to achieve reversibly tunable properties in carbon nanostructures, field-effect devices based on metals have not been reported so far. One reason may be that the high density of conduction electrons in metals makes for highly efficient electronic screening, restricting space-charge layers at interfaces to a region of essentially atomic dimensions, which is much narrower than the space-charge regions in semiconductors, which are typically 10 to 1000 lattice constants wide (4). Because the space-charge regions at metal surfaces are so narrow, changes of a local property, which result from the modified electronic density of states in the space-charge layer, may only have an impact on the overall performance of the metal if the surface-to-volume ratio is extremely high. On the other hand, the efficient screening brings about an intriguing new opportunity. Because the induced charge, which is typically up to a few tenths of an electron per interfacial atom, remains localized near these atoms, the effect on local properties such as the interatomic bonding or the atomic magnetic moments may conceivably be quite large, larger than in semiconductors where a similar amount of charge per area is smeared out over a much larger volume.

We prepared nanoporous Pt samples by consolidating commercial Pt black having a grain size of 6 nm (5). Figure 1A shows the scanning electron micrograph of a fracture surface, which illustrates the bicontinuous structure, consisting of an interconnected network of nanometer-sized Pt crystallites and an interconnected pore space. The samples were immersed in different aqueous electrolytes, and the strain upon varying the electrochemical potential E was measured in situ by dilatometry and diffractometry. Figure 1B is a schematic illustration of the induced charge in the electrochemical double layer at the surface of the particles.

Figure 1

(A) Scanning electron micrograph showing the fracture surface of a nanoporous Pt sample. (B) Schematic representation of an interconnected array of charged nanoparticles immersed in an electrolyte.

In situ cyclic voltammograms of current (I) versusE in the dilatometer, using H2SO4(0.5 M) as the electrolyte, exhibited closed and highly reproducible loops, indicating that the interfacial charge density was varied reversibly (Fig. 2A). The voltammograms showed broad H adsorption and desorption peaks at the negative end of the potential range and broad OH adsorption and desorption peaks at the positive end, and an interval (between 0.1 and 0.5 V) where the small current indicated that the dominant process was capacitive double-layer charging. In order to separately investigate the effect of this latter process, in the absence of specific adsorption, we imposed a cyclic variation of E within the interval from 0.1 to 0.5 V. Figure 2B shows the length change Δl and the potentialE as a function of the time. The sample underwent a reversible expansion and contraction, in phase with the variation ofE. Superimposed on the cyclic deformation was a slow shrinkage, presumably due to sintering. Although the contraction was also measurable without applied voltage, it accelerated after the first scan to negative E, indicating enhanced kinetics for Pt transport at the metal-electrolyte interface, possibly due to the reduction of a surface oxide or hydroxide. Asymptotically, the irreversible contraction per cycle became significantly smaller than the reversible strain; the shrinkage was well approximated by an exponential (dashed line in Fig. 2B), which was subtracted from the data before further analysis. Figure 2C shows the reversible part of the strain Δl/l versus the potential for nine successive scans. It is seen that the strain depends linearly on the potential, with little or no hysteresis. This is compatible with the notion of reversible capacitive variation of the double-layer charge as the origin of the strain.

Figure 2

Results of in situ cyclic scans of E in the dilatometer using H2SO4 (0.5 M) as the electrolyte. (A) Four subsequent cyclic voltammograms of charging current I versus E. The double-headed arrow denotes an interval where double-layer charging is the dominant process. (B) Length change (bold solid line, left ordinate) and potential (thin solid line, right ordinate) versus time for potential scans in the double-layer region as indicated by the arrow in (A). The arrows indicate the correspondence between the lines and the ordinates. The dashed line indicates irreversible contraction. (C) Reversible part of the strain [after subtraction of the dashed line in (B)] versus E for the nine cycles shown in (B). An arbitrary state in the center of each cyclic strain curve was used as the zero for the strain.

Considerably larger strains were found when the potential was scanned over a wider voltage range, including the regions of specific adsorption. We tested three electrolytes, H2SO4(0.5 M), HClO4 (1 M), and KOH (1 M), and obtained the largest strain amplitude with KOH (1 M). Figure 3A shows in situ cyclic voltammograms in KOH at different scan rates. The dominant features are the broad OH adsorption and desorption peaks at about –0.25 and –0.45 V, respectively, with two discrete desorption processes resolved at slow scan rates. Figure 3B shows the reversible part of the relative length change Δl/l recorded simultaneously with the voltammograms. The overall reversible strain amplitude takes on the value of 0.15%. This value depends only weakly on the scan rate, which suggests that the experiment probes the saturation value of the strain, independent of limitations by the diffusion kinetics in the pore space. The variation Δσ of the surface charge density has an overall amplitude of 500 μC/cm2 (Fig. 3C). This agrees with results for planar Pt surfaces (6), indicating that the entire surface area of the porous sample is wetted by the electrolyte. When the strain is plotted against Δσ, all curves coincide within experimental error, indicating a reversible linear relationship between both quantities (Fig. 3D). The absence of any significant hysteresis in the plots of strain versus specific charge confirms that the strain is a function of σ.

Figure 3

Results of in situ cyclic scans of E in the dilatometer at different scan rates, using KOH (1 M) as the electrolyte. Each curve shows the third out of three successive scans. (A) Charging current I versus E. (B) Relative length change Δl/l versus E. (C) Change Δσ in the specific surface charge density versusE. (D) Δl/l versus Δσ. Arbitrary points in the center of the intervals of experimental values were chosen for the zero of the strain and charge density. Scan rates were 1 mV/s (black), 0.8 mV/s (red), 0.4 mV/s (green), 0.2 mV/s (blue). Arrows denote the direction of the scan.

Because the electrolyte is a fluid in an interconnected pore network, its hydrostatic pressure is constant, independent of E. The electrolyte therefore cannot contribute to the measured strain, which must arise instead from an expansion or contraction of the porous metal network. Because the pressure within the particles can be determined from the crystal lattice strain, we measured the lattice parametera by in situ diffraction experiments in KOH at various values of E.

Figure 4A shows a typical diffraction pattern. The voltage-induced variation of a and the strain Δa/a0 relative to the lattice parameter a0 of the dry powder before immersion in the electrolyte are displayed in Fig. 4B. The amplitude of the variation of a/a0 is 0.14%, which is in good agreement with the dilatometric data. The variation of the lattice parameter is seen to be reversible upon variation ofE; moreover, the value of a was found to remain unchanged when the potential was maintained constant for long durations (36 hours). Figure 4C shows the pressure, computed from the volume strain ΔV/V = 3 Δa/a, using the bulk modulus valueK = 283 GPa (7). The pressure variation may be as large as 1 GPa.

Figure 4

Results of in situ x-ray diffraction experiments. (A) Example of a diffraction pattern showing photon counts versus scattering angle 2θ at E = 0.05 V. (B) Lattice parameter a (right ordinate) and lattice strain Δa/ao (left ordinate) versus E. The horizontal line indicates the lattice parameter of the dry powder, used as the reference for computing the strain. Potentials were incremented so as to complete a cycle, as indicated by the lines joining successive data points. The error bar refers to the reproducibility of Δa/ao ; the uncertainty in the absolute value of a is estimated at ±0.3 pm. (C) Pressure P (left ordinate) and interface stress f (right ordinate) versusE.

Although the space charge is localized in a thin interfacial layer, the x-ray observations indicate stress and strain throughout the crystallites. This implies that the surface exerts forces on the matter in the interior of the crystallites. These forces vary as a function of the surface charge density σ. A well-known consequence of varying σ is a change in the surface free energy γ according todγ = –σ dE; in a fluid droplet of radius r, this would induce a pressure according to the Young-Laplace equation P = 2 γ/r. By contrast, the surface-induced stress in solids is not a function of γ but rather of the surface stress f, to which it is related by the capillary equation for solids (8)Embedded Image(1)In this equation, which applies irrespective of the geometry of the microstructure, A denotes the total area,V denotes the total volume of the grains, and fis defined in terms of the derivative of the interfacial free-energy density (measured per area of the undeformed surface) with respect to the strain E tangential to the surface, f = trace (∂γ/∂E)/2 (8). 〈〉Vand 〈〉A represent the volumetric average and the areal average over the surfaces, respectively.

We computed f by means of Eq. 1 with the experimental results for P and using nitrogen sorption data (5) for the specific surface area. Because our experiment does not provide data for the pressure P 0 in the dry powder, f is measured relative to the valuef 0 (supporting online text) of the dry surface. The maximum variation in f (right ordinate in Fig. 4C) as a function of the potential E is about ±1.5 N/m. The variation of γ as a function of E at fluid-electrolyte interfaces is well studied, but only recently have first quantitative results for f of solid-electrolyte interfaces been obtained. The reported potential-induced variation in f is on the order of 1 N/m, comparable to our data (9, 10). The symmetry of the surface allows for independent values of the in-plane and out-of-plane stress or strain (11). In fact, concurrent with the tendency for in-plane expansion found in our samples is an out-of-plane contraction at Pt single-crystal surfaces when charged positively (12).

Phenomenologically, the dependence of the surface stress on the surface charge density is described by a second derivative of γ,df/dσ. Using Eq. 1 with dilatometer data for the strain to estimate the pressure, we obtain the valuesdf/dσ = –1.6 Nm/C for the capacitive double-layer charging data in Fig. 2 and –0.70 Nm/C for the specific adsorption data in Fig. 3 (13). The latter value is close to values reported for the adsorption of various anions on Au(111) (14). We find that the volume change per charge is larger for pure double-layer charging; however, a higher maximum strain can be achieved by exploiting the increased capacitance in the specific adsorption region. The finding of differentdf/dσ values agrees with the dissimilar nature of the interfacial processes, but the comparable magnitude and identical sign of the two values suggest that the underlying atomic interactions may be related. In this respect, it is worthwhile to note that, for Pt in KOH, the linear dependence between strain and charge over the whole potential region is also suggesting that the underlying atomistic interactions may not be strongly related to the chemical or structural details of the specific adsorption processes.

Microscopically, the surface stress originates in the tendency of the surface to favor a lateral interatomic spacing that differs from the one of the underlying bulk (15), reflecting the lateral atomic interactions within the surface layer of the metal and within the layer of adsorbates. A dependence of the surface stress of clean metal surfaces on the surface charge density has indeed been predicted based on the jellium model (14, 16), but our results do not confirm the numerically smaller variation of the theory. In fact, it is known that the equilibrium interatomic spacing in late transition metals depends on details of the electronic band structure that are ignored in the jellium model (17): The antibonding interaction due to the upperd-band states is balanced by the bonding effect of thesp hybridized states. Injecting electrons into the band structure changes the population of both bands, and the lattice contraction and the positive Δf that we found upon injecting electrons at the surface would be compatible with the notion of a dominant effect of the bonding sp orbitals, which has been invoked to explain the compressive surface stress at charge-neutral Pt surfaces (18). First-principles calculations of the charged Au(111) surface by density functional theory support the importance of changes in the surface electronic structure to the surface stress and surface relaxation (19).

Independent of the atomistic mechanism, the observation of a voltage-induced reversible strain in a metal, with an amplitude in excess of 0.1%, is remarkable because analogous findings have previously been reported only for ionic and covalently bonded materials. Although larger strains are achieved in polymers (1) and in relaxor-type ferroelectric single crystals (20), our result for metals matches the maximum strain achieved by commercial high-modulus ferroelectric ceramics (0.1 to 0.2%) (20) and by carbon nanotube bundles (about 0.1%) (2). It is also of interest to compare the change in volume. Piezoelectric materials respond to an electric field E by an expansion or contraction parallel to the field, Δl/l = d 33 E, with d 33 being the longitudinal strain coefficient, and by transverse strains of opposite sign. The transverse strain coefficients d 31 andd 32 are then negative, and the relative change in volume, ΔV/V = (d 31 + d 32 +d 33) E, is considerably smaller than Δl/l. For the example of the commercial Pb(Zr,Ti)O3-based ceramic PZT-5H, the values ofd (21) suggest that the longitudinal strain of 0.15% is accompanied by a relative change in volume of only 0.01%. Strain coefficients for the relaxor-type single crystals (22) imply that Δl/l and ΔV/V can even be of opposite sign in these materials. By contrast, in nanoporous materials with an isotropic microstructure, the interface-induced stress and strain are isotropic, and the maximum volume change is 0.45% in our samples.

In the actuator materials discussed above, the voltage-induced strain results from atomic rearrangement or charge transfer throughout the entire solid. It is therefore a materials property and only weakly dependent on the microstructure. By contrast, the induced strain in nanoporous metals is a reaction of the material to a change in its surface properties, and it is proportional to the surface-to-volume ratio, which can be varied within the bounds imposed by coarsening or by structural instability at small grain size. Because porous metals with an even higher surface-to-volume ratio than those of the present study are conceivable, one may envision that larger strain amplitudes can be attained in the future.

One may speculate on the potential of such materials for use as actuators; for instance, in devices exploiting the volume change of the porous metal to do work against an external pressure. Measures for the device performance are the volume- and mass-specific strain energy densities, which are related to the maximum relative volume changeɛ max, to the mean density ρ of the porous material, and to its effective bulk modulus K* byw V = ½ K* ɛ max 2 andw M = w V/ρ (w V, volume-specific strain energy density;w M, mass-specific strain energy density). For our samples, effective medium theory (supporting online text) supplies the estimate K* = 9 GPa, so thatw v = 0.09 J/cm3 andw M = 30 J/kg. This is within the range of typical values for actuator materials, which, according to the compilation in (23), range from 0.016 to 1.0 J/cm3 for w v and from 4.3 to 160 J/kg for w M. The device would be most efficient when working against the matched pressure (24) ½ K* ɛ max = 20 MPa. However, when loaded by that pressure, the porous samples will yield and undergo further densification, because the pressure used to consolidate the Pt black was only 1 MPa. Studies of porous Pt consolidated at the higher pressure of 40 MPa (supporting online text) show that the maximum linear strain remains significant (0.08%) in spite of an increased density, and that the matched pressure remains roughly constant, less than the consolidation pressure. Thus, there appears to be no fundamental obstacle to preparing nanoporous powder compacts that combine appreciable values of strain amplitude with sufficient strength to support a matched load without yielding. However, an as-yet-unexplored issue is the extent to which creep mediated by grain boundary diffusion and surface diffusion restricts the load that can be supported over extended periods of time.

Whether devices based on nanoporous metals can achieve a competitive performance will depend crucially on the ability to achieve simultaneously high specific surface area and long-term stability against coarsening and sintering, in spite of the large driving forces for these processes arising from the surface excess free energy. In this respect, nanoporous single crystals are an attractive alternative to granular materials, because they lack the grain boundaries that provide the sources and sinks for matter promoting sintering and creep. Such materials can be prepared by selective dissolution of solid solutions, with structure sizes down to 5 nm (25). Because many physical properties depend on the electronic density of states, the concept of reversible variation of the surface charge density in solids with such large surface-to-volume ratios may find more general applications; for instance, in preparing new types of materials with tunable electrical conductivity, optical absorption, and magnetic interactions.

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  • * To whom correspondence should be addressed. E-mail: Joerg.Weissmueller{at}


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