Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6]

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Science  08 Feb 2008:
Vol. 319, Issue 5864, pp. 794-797
DOI: 10.1126/science.1151442


We show that silver(I) hexacyanocobaltate(III), Ag3[Co(CN)6], exhibits positive and negative thermal expansion an order of magnitude greater than that seen in other crystalline materials. This framework material expands along one set of directions at a rate comparable to the most weakly bound solids known. By flexing like lattice fencing, the framework couples this to a contraction along a perpendicular direction. This gives negative thermal expansion that is 14 times larger than in ZrW2O8. Density functional theory calculations quantify both the low energy associated with this flexibility and the role of argentophilic (Ag+...Ag+) interactions. This study illustrates how the mechanical properties of a van der Waals solid might be engineered into a rigid, useable framework.

Thermal expansion in crystalline materials is a relatively well-understood physical process (1, 2). By virtue of the inherent anharmonicity of bond vibrations, the average distance between bonded pairs of atoms increases with temperature, and, in general, this increase is reflected in expansion at the macroscopic scale. The relative rate, α, at which a material expands with increasing temperature usually falls within the range 0 × 10–6 K–1 < α < 20 × 10–6 K–1 (2).

Examples of unconventional thermal expansion behavior are well known, and often these have highlighted some interesting and important physical processes in the respective materials. For example, the balance between lattice thermal expansion and magnetorestriction in invar FeNi alloys gives rise to their well-known and widely exploited near-zero thermal expansion around room temperature (3). Similar behavior in the intermetallic conductor YbGaGe has been explained in terms of a continuous electronic valence transition (4). A quite different type of atypical thermal expansion is the occurrence of strong negative thermal expansion (NTE) in framework structures such as ZrW2O8 (5) and Cd(CN)2 (6), a consequence of the structural underconstraint of atomic bridging motifs, in these cases, the Zr-O-W and Cd-CN-Cd linkages. The ability to bend these linkages at the O or C and N atoms means that the dominant thermal response is associated with flexing bonds rather than stretching them, and it is this difference that is implicated in their unusual thermodynamic behavior. This flexibility can also lead to pressure-induced amorphization (7), elastic constant softening under pressure (8), and unusual shear and bulk moduli (8, 9).

We studied the thermal expansion behavior of silver(I) hexacyanocobaltate(III), Ag3[Co(CN)6], a framework material assembled from highly underconstrained Co-CN-Ag-NC-Co linkages. Its crystal structure consists of alternating layers of Ag+ and [Co(CN)6]3– ions, stacked parallel to the unique axis of its trigonal Embedded Image unit cell (Fig. 1A) (10, 11). Within any given silver-containing layer, the Ag atoms are arranged at the vertices of a Kagome lattice, with the octahedral [Co(CN)6]3– ions positioned above and below the hexagonal Kagome “holes.” These anions are oriented such that each cyanide binds a single neighboring Ag+ ion, which in turn is bonded to a second [Co(CN)6]3– ion on the other side of the Kagome sheet. The almost-linear Co-CN-Ag-NC-Co linkages run parallel to the 〈101〉 lattice directions (Fig. 1B), forming a set of three identical interpenetrating cubic (α-Po) networks (11).

Fig. 1.

Representations of the crystal structure of Ag3[Co(CN)6]. (A) The trigonal lattice consists of alternating layers of octahedral [Co(CN)6]3– ions ([CoC6] octahedra shown in blue) and Ag+ cations (red spheres arranged on the central Kagome-type lattice). (B) The crystallographic unit cell at 300 K as determined by structural refinement of our neutron diffraction data. The strongest bonding interactions, which occur within Co-CN-Ag-NC-Co linkages, all lie parallel to the crystallographic 〈101〉 directions. The refined anisotropic thermal ellipsoids (shown here at 50% probability) indicate that the dominant type of atomic displacement at 300 K involves translations of the C, N, and Ag atoms perpendicular to these linkages.

There are a number of points of interest concerning this structure. First, the separation between neighboring Ag atoms is circa (ca.) 3.5 Å, which is only marginally greater than the van der Waals limit of 3.4 Å (12), despite the Coulombic repulsion. Moreover, this close Ag...Ag approach is unsupported by the covalent lattice. Such a feature is strongly characteristic of so-called d10...d10 metallophilicity, whereby multipolar dispersive interactions produce a relatively weak “bond” between d10 centers of ca. 30 kJ mol–1 (13, 14). Second, the cobalt atoms are present in the low-spin d 6 (S = 0) electronic configuration and so are both diamagnetic and coordinationally inert (15). Third, the Ag atoms are N-bound by the cyanide ions. This assignment has been questioned (16) precisely because it is unusual in cyanide-containing silver salts, where there is a strong chemical preference for C-bound Ag centers (15).

Having prepared a sample of Ag3[Co(CN)6] as described in (10), we performed x-ray diffraction measurements over the temperature range from 16 to 500 K. The sample appeared to have decomposed fully by 500 K to give a product whose diffraction profile matched that of elemental Ag. We also collected neutron time-of-flight total scattering patterns at temperatures of 10, 50, 150, and 300 K using the GEM diffractometer at ISIS (17, 18). The room-temperature powder diffraction patterns were readily indexed according to the previously published crystallographic unit cell (11), and Rietveld refinement of the neutron data was used to produce a structural model (Fig. 1B) using the program GSAS (19). By virtue of the scattering contrast between C and N atoms attained in neutron experiments, we were able to confirm that the cyanide ions are entirely C-bound to each Co atom, thus addressing the concerns raised in (16). Crystallographic details and refined values of the anisotropic thermal displacement parameters are given in tables S1 and S2, respectively.

On cooling from room temperature, both the x-ray and the neutron diffraction patterns were affected in two particular ways (Fig. 2, A and B). First, the d-spacing values of most of the reflections changed substantially (with some values increasing and others decreasing). Second, we observed an increasingly severe anisotropic peak broadening effect; this effect, which disappeared on reheating, was strongest for those peaks with the greatest thermal shift in d spacing. We were able to model the unusual peak shape variation by using spherical harmonics to account for anisotropic strain broadening within the TOPAS structural refinement package (20) or, equivalently, by refining empirical lattice parameter distributions using the GSAS program (19, 18) (Fig. 2, C to F). Both approaches gave entirely consistent values of the strain-free lattice parameters.

Fig. 2.

Lattice parameter distributions and DFT lattice enthalpy landscape. Regions of the (A) 10 K and (B) 300 K neutron powder diffraction pattern show the severe effects of anisotropic peak broadening at low temperatures. The observed peak shapes could be modeled in terms of the distributions of unit cell parameters shown in (C) to (F). The “strain-free” limit of the topas x-ray diffraction refinements is indicated in each case by a solid gray circle. (G and H) The 0 K enthalpy valley that coincides with the experimental lattice parameter values, calculated (G) using DFT and (H) using DFT together with an Ag+...Ag+ dispersion interaction term.

The quantitative thermal variations in these strain-free lattice parameters were determined from the x-ray diffraction data (18) (Fig. 3) (raw values are listed in tables S3 and S4). Our results show Ag3[Co(CN)6] exhibits essentially linear thermal expansion behavior over its entire temperature stability range that is an order of magnitude stronger than that typically observed for framework materials: The uniaxial coefficients of thermal expansion were found to lie in the ranges +130 × 10–6 K–1 < αa < +150 × 10–6 K–1 and –120 × 10–6 K–1 > αc > –130 × 10–6 K–1 over much of the temperature range studied. Slightly more moderate effects appeared to occur at the very lowest temperatures, although we note that the uncertainty in the calculated values of α is substantially larger for these terminal data points. There was no appreciable hysteresis in cell parameters nor any evidence for the existence of structural phase transitions (the slight discontinuity at 300 K is due to the different experimental conditions used to measure data above and below room temperature). The absence of any sharp features in differential scanning calorimetric measurements of the specific heat supported this finding.

Fig. 3.

Thermal expansion behavior of Ag3[Co(CN)6] as determined from x-ray powder diffraction. (Top) Thermal variation of the lattice parameters a and c measured on cooling (300 to 16 K; blue) and heating (20 to 300 K, 300 to 500 K; red). The large changes in these parameters correspond to a substantial expansion of the Ag...Ag and [Co(CN)6]...[Co(CN)6] contacts but a similarly strong collapse in the separation between successive (Ag+)n and [Co(CN)6] layers (accentuated in the schematics). The slight discontinuity at 300 K is due to the different experimental conditions used to measure data above and below room temperature. (Bottom) The coefficients of thermal expansion determined by a smooth polynomial fit (n = 5) to the raw lattice parameter data, together with αCo...Ag, the coefficient of thermal expansion along the 〈101〉 crystal axes. Values of α at the highest and lowest temperature points in each data set (where the first derivative of the polynomial fit is poorly constrained) have been omitted for clarity.

We see that the uniaxial NTE behavior observed in this study is larger than that reported for the isotropic materials ZrW2O8a = –9 × 10–6 K–1) (5) and Cd(CN)2a = –20 × 10–6 K–1) (6) and greater also than the calculated behavior for various metal-organic frameworks (MOFs) (–27 × 10–6 K–1 ≤ αa ≤ –11 × 10–6 K–1) (21), whereas the positive thermal expansion (PTE) effect along the a and b crystallographic axes is matched in magnitude only by the most weakly bound solids (2), for example, Xe at 50 K (αa ≅ + 200 × 10–6 K–1) (22). In order to highlight these fundamental differences from typical framework behavior, we are suggesting the use of the term “colossal” to signify |α| ≥ 100 × 10–6 K–1.

We now consider the relationship of the thermal expansion to the interatomic separations in the crystal structure. The magnitude of NTE and PTE effects means that many of these separations change substantially with temperature, but there also exists a set of directions along which the thermal expansion coefficient vanishes. This set includes the 〈101〉 axes, the directions along which the Co-CN-Ag-NC-Co linkages are oriented. As such, despite the large change in lattice dimensions, the data show that the separation between connected Co...Ag...Co atoms remains essentially constant across the temperature range studied (see the αCo...Ag curve in the bottom graph of Fig. 3). This is, of course, entirely consistent with intuition for a strongly bound chain of atoms. There is also a small concomitant reorientation of the CN ions that preserves the average C-Co-C and N-Ag-N angles such that the geometries of the transition metal coordination polyhedra are largely unaffected by the thermal expansion. This reorientation means that the thermal expansion behavior of the metal-cyanide linkages in Ag3[Co(CN)6] is more complex than that in Cd(CN)2, for example, where NTE is caused by vibrational motion of the linkages alone. However, the transverse CN and Ag displacements evident in the atomic displacement parameters of Fig. 1B do resemble the typical behavior observed in other NTE frameworks, and it is likely that in Ag3[Co(CN)6] local transverse vibrations at least help reduce thermal expansion along the 〈101〉 directions.

On the other hand, interatomic separations parallel and perpendicular to the trigonal axis are strongly affected by temperature. The separation between silver- and hexacyanocobaltate-containing layers, which corresponds to c/2, decreases quickly as the material is heated, whereas the average Ag...Ag and [Co(CN)6]...[Co(CN)6] distances, which correspond to a/2, increase just as rapidly. The strong coupling between these two lattice parameters is caused by the Co-CN-Ag-NC-Co linkages: If the structural integrity of these linkages is to be preserved, then an increase in a must be accompanied by a decrease in c of comparable magnitude (23). As such, the crystal structure behaves like a sheet of garden lattice fencing, whereby an expansion of the lattice along one axis forces a contraction in the perpendicular direction.

This picture of geometric flexibility explains the coupling between a and c, but the question remains as to what in particular is responsible for the large magnitude of the changes in these lattice parameters. An interesting comparison can be made with the related compound H3[Co(CN)6], which shares the same structure as Ag3[Co(CN)6] but with H atoms replacing Ag atoms (11, 24). At room temperature, the deuterated analog D3[Co(CN)6] crystallizes with lattice dimensions a = 6.431 ± 0.004 [or 6.431(4)] Å and c = 5.710(4) Å (25) so that the [Co(CN)6]3– ions are closer together than they are in Ag3[Co(CN)6]. At 77 K, the lattice parameters are a = 6.411(4)Å and c = 5.715(4) Å (25), reflecting a more moderate thermal expansion behavior with αa = +14(6) × 10–6 K–1 and αc = –4(6) × 10–6 K–1. Colossal thermal expansion is thus not an inherent property of the framework topology.

We obtained a more quantitative insight into the thermomechanical properties of Ag3[Co(CN)6] by using the density functional theory (DFT) code CASTEP (26) to calculate the variation in lattice enthalpy for different values of the unit cell parameters (18). What emerges from these calculations is that there exists a pronounced low-enthalpy valley that connects the various lattice parameter values measured crystallographically (Fig. 2G). The cell dimensions can vary along the “floor” of this valley with minimal cost in lattice enthalpy. Because excited electronic states are not taken into account at the DFT level, CASTEP omits any contribution from argentophilic dispersion interactions. However, the inclusion of a modest additional dispersive (r–6) term to the DFT enthalpy values is sufficient to shift the overall minimum from its original DFT-only position (a = 7.65 Å) to one closer to the expected 0 K value (≅6.74 Å), producing an even flatter minimum along the valley floor in the process (Figs. 2H and 4A). So, to a very large extent, the cell parameter a appears to be determined by these dispersion forces. This is highly unusual for a framework material and hints at why the observed PTE effect might share more in common with the sort of values observed for van der Waals solids such as Xe.

Fig. 4.

Lattice enthalpy and phonon energies in Ag3[Co(CN)6]. (A) DFT lattice enthalpies (solid circles) along the floor of the enthalpy valley found in (a, c) space. Addition of a dispersive r–6 term (solid line) produces a modified enthalpy curve (open circles) with a particularly shallow minimum positioned closer to the experimental 0 K value (dashed vertical line). (B) Thermal variation in mean partial phonon frequencies for Ag (open circles), Co (open triangles), and CN (solid squares) species as calculated from our neutron scattering data. Values were calculated from all 48 phonon modes across a grid of 245 points in reciprocal space (giving 11,760 data points in total); error bars correspond to the standard error in the calculated mean frequencies. The energies of phonon modes involving Ag displacements decrease with an increase in temperature (and hence a), providing a mechanism to overcome the very small lattice enthalpy differences near the minimum in (A).

Exploring this enthalpy valley more closely, we note that reasonably large changes in a and c can carry enthalpy penalties so low that they are comparable to the subtle thermal changes in phonon frequencies often found in framework materials. This means that phonon contributions to the free energy may be responsible for driving the large changes in lattice parameters. A reciprocal-space analysis of our neutron scattering data (27), allowed us to calculate the partial phonon densities of states for Ag, Co, and CN species as a function of temperature (18). What we found was that the average phonon energy associated with Ag vibrations decreased noticeably with increasing temperature (and hence with increasing a), whereas there was very little change in the relative energies of Co and CN vibrations (Fig. 4B). In terms of the energy profile illustrated in Fig. 4A, this means that, at higher temperatures (for which the phonon contribution to the overall energy becomes more important), the change in phonon frequencies associated with increasing a is commensurate with the small lattice enthalpy penalty involved. The decrease in Ag vibrational energies of ca. 5 meV between 10 and 300 K corresponds to an additional contribution of about 0.04 eV per unit cell to the lattice free energy at 300 K, comparable to the difference in lattice enthalpies at the corresponding values of a. Consequently, those phonon modes involving Ag displacements contribute most strongly to the overall (positive) Grüneisen parameter, and hence it is the anharmonicity of Ag vibrations that appears to drive the thermal expansion of the flexible lattice. We note that this anharmonicity is by no means colossal in itself, but because α is inversely proportional to material stiffness a modest value of the Grüneisen parameter can still produce a large value of α.

Consequently, it is the geometric flexibility of the Ag3[Co(CN)6] lattice, that is, the shallowness of the enthalpy valley shown in Fig. 2H, that allows very weak Ag+...Ag+ interactions to produce such an unusually large PTE effect, translated via flexing of Co-CN-Ag-NC-Co linkages into an equally strong NTE effect along the trigonal crystal axis. This unusual behavior serves to illustrate how very weak bonding interactions can actually have a profound effect on crystal thermodynamics in sufficiently flexible systems. In this case, not only do we observe unusual thermal expansion, but the lattice parameter distributions shown in Fig. 2 are a direct reflection of an atypically soft lattice (more specifically, one with a large and negative elastic compliance S13); the crystallites appear to deform readily in response to thermal and/or mechanical stress. There is a strong interest in uniaxial NTE materials of such extraordinary properties. For example, precision optical devices used on satellites are often highly sensitive to even very minor changes in dimension, and this sensitivity is exacerbated by the large temperature gradients over which they are forced to operate. Very thin aligned coatings of a material such as Ag3[Co(CN)6] could provide an intrinsic protection against this thermal variation, avoiding the present reliance on mechanical adjustment. More generally, the concept of exploiting geometric flexibility to amplify the role of low-energy interactions in thermodynamic behavior offers a method of preparing materials with a range of hitherto unanticipated physical properties.

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Materials and Methods

Tables S1 to S4


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