Interface-induced superconductivity at ∼25 K at ambient pressure in undoped CaFe₂As₂ single crystals

Significance

One of the major goals for scientists in the field of superconductivity and materials science has been to obtain superconductors with higher critical temperatures (T_c). One way that has long been proposed to achieve enhanced T_cs is to take advantage of artificially or naturally assembled interfaces. The present work clearly demonstrates that high-T_c superconductivity in the well-known nonsuperconducting compound CaFe₂As₂ can be induced by antiferromagnetic/metallic layer stacking and provides the most direct evidence to date for the interface-enhanced T_c in this compound. The observations offer an avenue to higher T_c.

Abstract

Superconductivity has been reversibly induced/suppressed in undoped CaFe₂As₂ (Ca122) single crystals through proper thermal treatments, with T_c at ∼25 K at ambient pressure and up to 30 K at 1.7 GPa. We found that Ca122 can be stabilized in two distinct tetragonal (T) phases at room temperature and ambient pressure: PI with a nonmagnetic collapsed tetragonal (cT) phase at low temperature and PII with an antiferromagnetic orthorhombic (O) phase at low temperature, depending on the low-temperature annealing condition. Neither phase at ambient pressure is superconducting down to 2 K. However, systematic annealing for different time periods at 350 °C on the as-synthesized crystals, which were obtained by quenching the crystal ingot from 850 °C, reveals the emergence of superconductivity over a narrow time window. Whereas the onset T_c is insensitive to the anneal time, the superconductive volume fraction evolves with the time in a dome-shaped fashion. Detailed X-ray diffraction profile analyses further reveal mesoscopically stacked layers of the PI and the PII phases. The deduced interface density correlates well with the superconducting volume measured. The transport anomalies of the T–cT transition, which is sensitive to lattice strain, and the T–O transition, which is associated with the spin-density-wave (SDW) transition, are gradually suppressed over the superconductive region, presumably due to the interface interactions between the nonmagnetic metallic cT phase and the antiferromagnetic O phase. The results provide the most direct evidence to date for interface-enhanced superconductivity in undoped Ca122, consistent with the recent theoretical prediction.

High-temperature superconductivity has been one of the most studied subjects in condensed matter physics and materials science in the last three decades. Many compounds have been discovered with high transition temperatures (T_cs). Until the recent report of superconductivity up to 200 K in the unstable hydrogen-rich molecular compounds under ultrahigh pressures up to 200 GPa (1, 2), high-temperature superconductors (HTSs) have belonged to two stable compound families: the cuprates with a T_c up to 134 K (3) and 164 K (4) in HgBa₂Ca₂Cu₃O₉ at ambient and 30 GPa, respectively, and the Fe-pnictides and -chalcogenides with a T_c up to 100 K in unit cell FeSe films on SrTiO₃ substrate (5). They share similar features such as a layered structure with multiple block subsystems: an active subsystem, where some interactions promote charge–carrier pairing, and a charge reservoir subsystem that offer carriers to the former subsystem without introducing defects, similar to that which occurs in a semiconducting superlattice structure. As a consequence, many cuprates, especially those with high T_cs, show high anisotropy, or quasi–2D-like features. Excitations on different energy scales are believed to have provided the glue for superconducting electron pairings, although a commonly accepted nature of such excitations required for the high T_c is yet to emerge. One way that has long been proposed to achieve enhanced T_cs is to take advantage of artificially or naturally assembled interfaces, where soft phonons and/or excitons may occur. In fact, the discovery of the layered cuprate HTS and the great advancements in molecular beam epitaxy growth of perfect thin films have revived the interest in, and accelerated the search for, the interfacial effect in the artificially assembled composite layered compound systems. In addition, naturally assembled metal/semiconductor interfaces have been demonstrated in the BSCCO single-crystalline samples by the observation of the Shapiro steps in a microwave environment (6).

Although the idea to achieve high T_c via interfaces is not new, the first serious model analysis was not made until 1973, when Allender et al. examined the effect of metal/semiconductor interfaces on superconductivity (7). They found an impressive T_c-enhancement effect when stringent conditions for the interfaces are met. Many experiments were inspired by the prediction. A recent article (8) has summarized numerous experiments that demonstrate enhanced superconductivity in artificially formed layered compound systems between two different nonsuperconducting (nsc), one superconducting (sc) and one nonsuperconducting, or two different superconducting materials. For instance, superconductivity has been observed in heterostructures of PbTe(nsc)/YbS(nsc) up to 6 K (9), in Al(sc)/Al₂O₃(nsc) up to 6 K vs. 1.2 K in bulk Al (10), and in (La,Sr)₂CuO₄(nsc)/La₂CuO₄(nsc) up to 52 K (11), all suggesting a rather large T_c-enhancement effect. However, the exact nature of the enhancement remains unclear*, and exotic interfacial effects (7) that may facilitate the exchange of excitons cannot be ruled out at this time.

The alkaline-earth iron arsenide CaFe₂As₂ (Ca122) with the ThCr₂Si₂ structure is the parent compound of a large superconductor family (16). The superconductivity of many compounds in this family seems to be rather unusual. One intriguing observation has been the nonbulk superconductivity up to 49 K induced in Ca122 at ambient pressure by slight Ca replacement with a rare-earth element, La, Ce, Pr, or Nd (17–19). A systematic study on the slightly rare-earth–doped Ca122 suggests that the nonbulk superconductivity detected may be associated with the naturally occurring interfaces associated with defects in the samples (20). However, direct evidence remains elusive due to complications involved in doping. As for the superconductivity in undoped Ca122, the situation is even more confusing. Filamentary superconductivity up to ∼10 K has been detected sporadically under ambient pressure (21). Although the related superconducting volume fraction is much higher under nonhydrostatic pressure, the origin of the superconductivity remains unresolved. Both the coexistence of different phases (22, 23) and a new tetragonal phase—T′, which appears only under uniaxial pressure––were proposed (24). The complications associated with the delicate pressure environment, however, seem to prevent a comprehensive experimental verification.

Fortunately, later studies have shown that the complex phase evolution under pressure can be reproduced through heat treatment (25–27). Such heat treatment may offer a reproducible, controllable, and reversible environment in which many characterization techniques can be applied to explore the issue, if similar superconductivity can be induced. This motivates our studies. The phase diagram of Ca122 has been carefully explored previously (25). The Ca122 quenched from 850 °C or above has a tetragonal structure at room temperature (PI phase), but transforms to a collapsed-tetragonal phase with a 10% shorter c-lattice parameter below T_cT, the T–cT transition temperature (28, 29). No magnetic ordering is reported over the entire temperature range. The furnace-cooled Ca122 single crystals, on the other hand, exhibit a tetragonal structure at room temperature with a slightly longer c (PII phase). On cooling, it undergoes a tetragonal-to-orthorhombic transition (T–O) at T_N, closely related to the spin-density-waves (SDW) transition, into an antiferromagnetic phase. The two transitions, i.e., T–cT in PI and T–O in PII, carry with them distinct resistive and magnetic signatures at T_cT and T_N, respectively, making their detection rather easy. The sharp jumps in the magnetic moments associated with the transitions, for example, can be treated as measures of the corresponding volume fractions, especially when the crystal is a macroscopic mixture of the two phases. Both pressure and heat treatment, however, can easily alter the phase composition. A pressure as low as 0.34 GPa, for example, switches a considerable amount of PII phase to PI (22). A low-temperature annealing, e.g., at 350 °C, may also slowly alter the PI crystal into the PII one. Therefore, superconductivity is expected to appear after a short period of low-temperature annealing on the PI crystal if the interface is the relevant mechanism. On the other hand, the crystals are likely to remain nonsuperconducting if the superconductivity only occurs in the proposed T′ phase (24), which can only be stabilized under uniaxial pressure. In the present work, superconductivity is reversibly induced in 350 °C annealed PI crystals over a narrow time window. X-ray diffraction (XRD) profile analysis demonstrates that these superconductive samples are randomly stacked PI and PII layers with the screening volume fraction scaling with the deduced interface density. To further explore the underlying mechanism, the anomalies associated with T–cT and T–O transitions are analyzed. The suppression of the anomalies seems to be concurrent with the appearance of the superconductivity. Both the lattice strains and the magnetic interactions, therefore, seem to be possible causes for the interfacial superconductivity, although other exotic interfacial effects cannot be ruled out.

Materials and Methods

The starting Ca122 single crystals are self-flux grown at 1,200 °C and furnace-cooled from 960 °C. Single-crystal samples from the melt are then sealed in an evacuated quartz tube and annealed at 850 °C for 24 h before being quenched in ice water (sample 1). The sample is resealed in an evacuated quartz tube for a sequence of low-temperature isothermal annealing at 350 °C in a preheated furnace for different time periods (t) with the accumulated time up to 120 h. A thorough characterization of the sample is performed after each annealing. The structure is determined by the Rigaku DMAX III-B X-ray diffractometer at room temperature, magnetic susceptibility (χ = M/H) by a Quantum Design Magnetic Property Measurement System down to 2 K, and resistivity (ρ) by the AC-Transport Option in a Quantum Design Physical Properties Measurement System. When each characterization is completed, the sample is cleaned for the next annealing. The XRD-spectrum simulations are also carried out using the MATLAB Programming with a modified algorithm from Ranno et al. (30).

Results and Discussion

The discovery of stabilization of the cT phase in Ca122 at low temperature by proper annealing and quenching without the intervention of pressure offers an unusual opportunity for examining the intricate relationship between the superconductivity and the different phases in Ca122. We have therefore carried out a systematic study on samples of controlled structures by a sequential low-temperature annealing for different time periods, as described above. The room-temperature XRD spectra of all Ca122 single-crystalline samples with different 350 °C annealing times (t) show the tetragonal structure. Selected representative (008) peaks are summarized in Fig. 1 A and B. The starting sample (sample 1, for t = 0), before any low-temperature annealing, is stabilized with a pure phase (PI), as evidenced by the sharp (008) peak at 2θ = 64.4° with a narrow FWHM Δ2θ = 0.14° in Fig. 1B. It has a lattice parameter c_I =11.547(1) Å. With continuous annealing or increasing t, the (008) peak shifts to a smaller 2θ first slowly, and then rapidly, before leveling off as displayed in Fig. 1B and summarized as 2θ-t in Fig. 1C (black). Meanwhile, the line width FWHM of the (008) peak changes little with t close to both ends, t = 0 and t > 18 h, but broadens rapidly and becomes maximum at t ∼14 h, as also shown in Fig. 1C (red). The reappearance of a narrow peak at 2θ = 63.4° with FWHM Δ2θ = 0.21° represents the stabilization of a different phase (PII) in Ca122 with a lattice parameter c_II = 11.702(2) Å at room temperature by prolonged annealing at 350 °C for t >18 h. The c_II = 11.702(2) Å is consistent with those previously reported for the as-grown crystals (25). With the attainment of two different pure phases at room temperature, PI and PII, we have examined the low-temperature behavior of their ρ(T)/ρ(300 K) and χ(T). The ρ(T)/ρ(300 K) of the pure PI sample undergoes a first-order phase transition with a precipitous drop at T_cT ∼ 100 K on cooling (Fig. 2A, #1), typical for a T–cT transition. In the meantime, its χ(T) also displays a large drop at T_cT ∼ 100 K (Fig. 2B, #1), also characteristic of a T–cT transition. In other words, PI of Ca122 displays a cT structure below ∼100 K at ambient pressure. ρ(T)/ρ(300 K) and χ(T) of PII (sample 7) show a sharp rise and a sharp drop on cooling at T_N ∼168 K, respectively, typical of a T–O phase transition as exhibited in Fig. 2 A and B. This shows that PII displays an orthorhombic structure below ∼168 K. No superconductivity has been detected down to 2 K in either PI or PII.

Fig. 1.

(A) Color map of the annealing-time dependence near the vicinity of the (008) reflections with normalized amplitude (the two bands roughly enclose the superconducting t window). (B) The evolution of the (008) peaks with normalized amplitude [#1(t = 0 h), #2(7.5 h), #3(11 h), #4(14.5 h), #5(18 h), #6(28 h), and #7 (50 h) represent the samples annealed at 350 °C for different time]. (C) The (008) peak positions (black) and corresponding FWHM (red). (D) The simulated XRD profile of the (008) peaks, with A(p = 0), B(0.15), C(0.21), D(0.59), E(0.92), F(0.98), and G(1), respectively (p is the fraction of the PII phase deduced from the XRD data). (E) The relative superconducting volume fraction (red, measured at 2 K with H = 2 Oe, H//c) and the calculated interface density (black).

Fig. 2.

(A) Normalized resistivity of CaFe₂As₂ samples at different annealing stages. (Inset) Resistivity of #2 under magnetic fields, H//c. (B) Magnetizations of the samples measured under H = 1 T along the c axis through warming (curves # 5, #6, and #7 are offset by a constant of 2 × 10⁻⁴ emu/mol for clarity). ΔM₁ and ΔM₂ are the M/H drops around the T–cT and T–O transitions, respectively [#1(t = 0 h), #2(7.5 h), #4(14.5 h), #5(18 h), #6(28 h), and #7(50 h) represent the samples annealed for different accumulative time].

We have therefore demonstrated that prolonged low-temperature annealing at 350 °C for t > 18 h can convert PI continuously and completely to PII at room temperature while transforming the cT phase to the O phase at low temperature. This enables us to examine in a well-controlled fashion the continuous PI-to-PII phase conversion and the possible emergence of superconductivity progressively with t in the absence of external pressure. As discussed above, the (008) peak position evolves continuously with the annealing time during the phase conversion, in which the peak width reaches a maximum at t = 14.5 h. Indeed, phase mixing between PI and PII occurs during low-temperature annealing for ∼4 h < t < ∼ 18 h and maximum mixing takes place for ∼8 h < t < ∼15 h. For ∼4 h < t < 15 h, superconductivity is detected with an onset T_c ∼25 K, which is deduced by the drop in resistivity. Note that the resistivity does not reach zero due to the incomplete formation of the mixing phase in the sample and the formation of microcracks in the crystals during the cT transition. The superconductivity is detected only in the t window where phase mixing occurs, consistent with previous reports of the existence of superconductivity in Ca122 at or near its O–cT phase boundary induced by pressure (22, 23). However, detailed analyses of the XRD and superconductivity data reveal interesting additional subtleties and point to the important role of interfaces in the induction of superconductivity in Ca122.

As mentioned above, nonbulk superconductivity has been detected, but only in the narrow low-temperature annealing t window where XRD line-broadening occurs, i.e., for ∼4 h < t < ∼18 h. The superconducting volume fraction determined by the χ-drop Δχ peaks at t ∼14 h, as shown in Fig. 1E (black). The T_c = 25 K observed here is t-independent and has a rather large positive hydrostatic pressure effect of ∼3 K·GPa⁻¹ (shown in Fig. S1). We point out that the superconductivity reported previously in Ca122 had a T_c < 12 K under nonhydrostatic pressure, forming a superconducting dome within a narrow pressure range (22, 23). In addition, the position of the XRD line, which is also a measure of the lattice constant, is usually expected to vary smoothly with t between those of the PI and PII phases with limited nonlinear deviation for a macroscopic and homogeneous mixing. This is certainly not the case for Ca122 as shown in Fig. 1 B and C. Within this t window there exists no peak splitting, suggesting that no phase other than PI and PII has been created by our low-temperature annealing. The observation is reminiscent of intergrowth or intercalation growth in layered materials such as cuprates and transition metal dichalcogenides. In other words, layer stacking of the two phases PI and PII may exist in our Ca122 crystals.

Fig. S1.

(A) Magnetic susceptibility of one annealed CaFe₂As₂ sample at ambient pressure at H = 2 Oe along the c axis. The dashed line is a guide for the eyes. (B) Resistivity of the same sample at ambient pressure and under pressure of 1.7 GPa.

To verify this, we carried out XRD spectrum simulations and compared the results with the XRD data. In the simulations, the crystals are treated as stacked unit-cell layers of the PI and PII phases (Fig. S2), i.e., with c_I ∼ 11.55 Å and c_II ∼ 11.70 Å, respectively. The phase ratio of PI/PII is fixed to be (1 − p)/p, with p being a fitting parameter. Here both phases are assumed to have the same scattering amplitude. They stack along the c axis according to a chosen sequence, which can be adjusted to achieve the best fit. For example, for a random-stacking case, each layer is independently assigned to be PI (or PII) with a given probability 1 − p (or p). Based on this model, it is reasonable to find that the effective lattice parameter is given by $c=(1-p)c_{\text{I}}+p{c}_{\text{II}}$. Then the phase fraction p can be extracted from the (00l) lines observed. As the phase fraction varies with time, the correlation p(t) vs. t reflects the conversion kinetics. The p(t) as reflected in 2θ(t) in Fig. 1C (black) displays approximately three distinct regions with the starting and the ending parts being almost horizontal. This roughly agrees with the Avrami model of chemical formation (31). The relatively flat part for t ∼ 0–10 h represents the nucleation stage, and the drop between 11–18 h corresponds to the rapid growth of newly formed PII + PI layers. This growth region, however, is exactly where the superconducting volume fraction reaches its maximum (Fig. 1 C and E). The kinetics seem to be natural for the PI-to-PII conversion and with no sign of an additional new phase found.

Fig. S2.

Schematic of the cross-section of the layer-stacking morphology in the CaFe₂As₂ PI–PII system, where the interfaces (dashed lines) form between PI and PII layers in the ab plane. The layers have thicknesses of less than several unit cells.

XRD-spectrum simulations based on several different layer arrangements were made and compared with the experimental (00l) spectra. The random layer-by-layer stacking appears to offer the best fit (Fig. 1D). Such a configuration leads to a relatively narrower single-peak line for p, the fraction of PII, close to either 0 or 1, but it leads to broad peaks without splitting around p ∼ 0.5, as observed. Otherwise, significant local aggregation of one phase would have resulted in peak splitting. For example, an additional PII line will emerge if five or more adjacent layers share the same PII structure. This confirms our interpretation that the two phases are mixed microscopically within a few layers rather than macroscopically in a domain-by-domain manner. Similarly, strong layer-to-layer correlation, e.g., large-scale alternating PI-PII-PI… arrangements, will produce corresponding satellite lines. These possible arrangements are therefore ruled out. The sample with t = 14.5 h (p ∼ 0.5) seems rather special, exhibiting a broad (008) peak with FWHM ∼ 0.78°, which is far broader than that from simulation. To resolve this, and especially to exclude the possibility of some unknown new phases, the Hall–Williamson method (32) was used to fit all (00l) lines with l ≤ 10. The data suggest that the main factor for the peak broadening is some microstrain, which can be caused by a p spread. The broadening, for example, can be reasonably reproduced by a Gauss distribution of the p, i.e., ∝ $e^{-{\left(p-0.5\right)}^2}/{\sigma }^2$ with the SD σ ∼ 0.032. Such large inhomogeneity in the conversion rate seems reasonable if the domains grow independently.

The interface density D important for our discussion is evaluated based on the simulation model. Starting with a PII layer with a probability of p, the probability to have one adjacent layer of PI to create an interface will be (1 − p). The expected interface density, therefore, will be D = 2p(1-p)/$\overline{c}$ if there is no correlation between adjacent layers, as suggested in the above discussion. The deduced D, shown in Fig. 1E (black), appears to scale with the normalized superconducting volume fraction χ/χ_ο (t = 14.5 h) also shown in Fig. 1E (red). Such a correlation not only supports the interface mechanism but also suggests that the relevant interfaces lie in the ab planes.

The evolution of the transport properties with t across the superconducting window may offer extra clues. Indeed, the ρ(T) of the superconducting samples appears to be featureless around 168 K (#2 and #4 in Fig. 2A). The anomaly characterizing the SDW transition of PII at T_N, in particular, is clear outside the superconductive window (t > 18 h) but is significantly suppressed within the window. Similar suppression also happens around the T_cT, although less drastically. Note that a similar situation occurs for all nonhydrostatic pressure effects reported thus far, e.g., in figure 1a of ref. 23. However, the anomaly at T_N is only marginally affected by hydrostatic pressure, and Ca122 is not superconductive (figure 1a of ref. 33).

To further explore the issue, the M drops around T_cT and T_N, i.e., ΔΜ₁ and ΔΜ₂, respectively, are deduced by extrapolating the smooth backgrounds outside the transition regions (Fig. 2B). If the drops are the on–off type associated with first-order transitions, the volume fractions of the unaffected PI and PII, i.e., f_M1 and f_M2, respectively, can be estimated by normalizing them against those of single-phase PI and PII states, i.e., the drops in Fig. 2B, plots #1 and #7, respectively. It is expected that f_M1 + f_M2 ∼ 1 in a macroscopic mixture of PI and PII, where the interdomain interferences can be ignored. Indeed, the extracted volume fractions follow the expectation rather well for t > 20 h (Fig. 3A). However, a systematic deficiency f_M1 + f_M2 << 1 appears for 4 h ≤ t < 20 h. To see this more clearly, the difference between the f_M2 and the phase fraction p extracted from the XRD data are compared in Fig. 3B. The data demonstrate that the SDW excitation is suppressed over t < 20 h. For example, the SDW transition occurs in only 30% of the sample whereas the actual PII phase fraction is 60% (at t = 14.5 h) based on the XRD data. A similar trend was also observed for the PI phase at T_cT. The effect of the layer-stacking microstructure on the SDW excitation seems to be similar to that of the nonhydrostatic pressure. This is expected as the different cell symmetries and lattice mismatch between PI and PII should generate microstrains. To be more quantitative, a phenomenological model is adopted as follows. The microstrain is expected to peak at the interface and to relax exponentially inward into the bulk parts. To simplify the model, it is assumed that the local ΔΜ₂ is zero within an interface layer with a fixed thickness δ, but recovers to the bulk value outside. Surprisingly, such a rough model fits the data reasonably well with a δ ∼ 2c (solid line in Fig. 3B). It is well known that the suppression of SDW excitation is crucial for superconductivity. The mismatch strains, therefore, should play a significant role in the interface superconductivity observed here. Based on the resistivity, magnetization, and XRD results, the evolution of Ca122 with the 350 °C annealing is summarized in Fig. 4. CaFe₂As₂ remains single phased only for t < 4 h (PI phase) and t > 18 h (PII phase). The crystals consist of randomly stacked PI and PII layers over 4 h ≤ t ≤ 18 h, in which the superconductivity occurs.

Fig. 3.

(A) Total magnetic volume fraction of ΔM₁ and ΔM₂ extracted from magnetization data. f_M1 = ΔM₁(t)/ΔM₁(t = 0 h); f_M2 = ΔM₂(t)/ΔM₂(t = 50 h) (e.g., for the mixed-phase sample 4 in Fig. 2B). (B) The magnetic volume fraction f_M2 and the phase fraction p extracted from magnetization and XRD data, respectively, and our rough model fitting of f_M2.

Fig. 4.

Phase conversions between PI and PII at room temperature, and their low-temperature transition, as a function of 350 °C annealing time. The onset temperatures (solid squares and solid triangles) and the ends (open squares and open triangles) of the structural transitions are determined by M/H data. The superconducting transition temperatures are determined by the onset T_cs from both the resistivity (solid circles) and magnetic (open circles) results. The area enclosed by the dashed lines roughly denotes the superconducting t window. T–O (SDW): tetragonal-to-orthorhombic transition (SDW transition); T–cT: tetragonal-to-collapsed tetragonal transition; S.C.: superconductivity.

The situation, however, is more complicated than a simple strain effect. Specifically, two of the observations can be hardly understood without involving other interfacial interactions. First, the T_cs are significantly different between those of the Ca122 under nonhydrostatic pressure and those reported here, even though the SDW excitation is suppressed in both cases. The pressure effects are also different; the T_c of our annealed samples continuously increases with the quasi-hydrostatic pressure at least to 1.7 GPa (Fig. S1), whereas the previously reported superconductivity is limited within a narrow range of 0.35–0.86 GPa under nonhydrostatic pressure (22). Second, the screening volume fraction, i.e., the 4πχ of the dc zero-field-cooled magnetization with the field along the layer direction, is much smaller than that expected from the interface density, assuming that each superconductive layer is no thinner than one unit cell. A reasonable interpretation will be that only a fraction of the interfaces induces superconductivity. Many candidates for these requisite interfacial interactions have been proposed previously (8). The experimental verification, unfortunately, will still be challenging. Recent theoretical prediction of T_c enhancement by antiferromagnetic/metal interfaces (34) is consistent with the present observation.

Conclusion

In summary, superconductivity with T_c at 25 K can be reversibly induced in the mixed-phase region of two nonsuperconducting phases PI and PII in undoped Ca122 by low-temperature annealing at 350 °C for different time periods. The XRD data analysis demonstrates that the superconducting samples consist of randomly stacked layers of PI and PII. The superconductivity volume fraction scales qualitatively with the interface density deduced from the XRD data. The significant role of interfaces in the 25 K superconductivity is clearly in evidence. Magnetic data also show that the microstrain associated with the lattice mismatch can also play a role. Comparison with previous high-pressure studies and the small screening volume fraction, however, suggest that interface effects other than microstrains are needed to account for the observations.