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Stripe-like nanoscale structural phase separation in superconducting BaPb(1-x)Bi(x)O3.

Giraldo-Gallo P, Zhang Y, Parra C, Manoharan HC, Beasley MR, Geballe TH, Kramer MJ, Fisher IR - Nat Commun (2015)

Bottom Line: The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase.For the superconducting compositions, the material coexists as two structural polymorphs.We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

View Article: PubMed Central - PubMed

Affiliation: Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA.

ABSTRACT
The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase. For the superconducting compositions, the material coexists as two structural polymorphs. Here we show, via high-resolution transmission electron microscopy, that the structural dimorphism is accommodated in the form of partially disordered nanoscale stripes. Identification of the morphology of the nanoscale structural phase separation enables determination of the associated length scales, which we compare with the Ginzburg-Landau coherence length. We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

No MeSH data available.


Related in: MedlinePlus

Correlation function for a system with partially disordered stripes.Simulation showing the angle-dependent correlation function 〈Gθ(r)〉 for a system with partially disordered stripes. The simulated images have a size of 128 × 128 pixels, with stripes of width w=14.1 pixels, separated between them by d=28.3 pixels, and running along 135° from the horizontal. The scale bar for all images correspond to 30 pixels. For the different images, a broken-up character of a different level was introduced, as a number of islands of size 3 × 3 pixels, placed at random positions within the red stripes. Each image is characterized by a filling fraction f, from 0 (empty stripe) to 1 (full stripe). The filling fraction f for each image is: (a) f=1 (perfect stripe formation), (b) f=0.5, (c) f=0.1 and (d) f=0.05. For each image, the angle-dependent correlation function 〈G(r)〉 is shown in the right hand panel, and its value is represented in the colour scale, which has different limits for each image. Black lines in these plots follow the functional form N*d/cos((α–90°)–θ), where N=1,2,3,…, d=28.3 and α=135°. These simulations illustrate how powerful this statistical technique is in revealing weak- or imperfect-stripes formation. As observed in panel (d), the stripe formation can be missed at first glance; however, 〈Gθ(r)〉 clearly reveals the two-fold symmetry of this image, as well as the periodicity associated with it.
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f5: Correlation function for a system with partially disordered stripes.Simulation showing the angle-dependent correlation function 〈Gθ(r)〉 for a system with partially disordered stripes. The simulated images have a size of 128 × 128 pixels, with stripes of width w=14.1 pixels, separated between them by d=28.3 pixels, and running along 135° from the horizontal. The scale bar for all images correspond to 30 pixels. For the different images, a broken-up character of a different level was introduced, as a number of islands of size 3 × 3 pixels, placed at random positions within the red stripes. Each image is characterized by a filling fraction f, from 0 (empty stripe) to 1 (full stripe). The filling fraction f for each image is: (a) f=1 (perfect stripe formation), (b) f=0.5, (c) f=0.1 and (d) f=0.05. For each image, the angle-dependent correlation function 〈G(r)〉 is shown in the right hand panel, and its value is represented in the colour scale, which has different limits for each image. Black lines in these plots follow the functional form N*d/cos((α–90°)–θ), where N=1,2,3,…, d=28.3 and α=135°. These simulations illustrate how powerful this statistical technique is in revealing weak- or imperfect-stripes formation. As observed in panel (d), the stripe formation can be missed at first glance; however, 〈Gθ(r)〉 clearly reveals the two-fold symmetry of this image, as well as the periodicity associated with it.

Mentions: To quantify the length scales associated with the orthorhombic variation, the average spatial correlation function 〈G(r)〉 and the angle-dependent spatial correlation function 〈Gθ(r)〉 were computed for each {110}T/{101}T filtered IFFT image (see Supplementary Note 3 for definitions). Figure 4 shows filtered-and-reconstructed HRTEM images for a representative sample of each Bi composition studied (left panels), after a resolution reduction that averages out the atomic-scale information. Both 〈G(r)〉 (shown in Supplementary Figs 1–3 and Supplementary Note 4) and 〈Gθ(r)〉 (shown on the right panels of Fig. 4) of all the images shown reveal local minima and maxima, implying the presence of characteristic length scales for the phase separation. Furthermore, the angular dependent correlation function 〈Gθ(r)〉 clearly reveals that there is a particular spatial pattern associated with the phase separation. Inspection of these quantities, in the right hand panels of Fig. 4, reveals arcs of intensity with an approximately two-fold rotational symmetry. The arcs are imperfect, but repeat with a fixed periodicity, implying a self-organized pattern of phase separation over remarkably large length scales. Such a pattern of intensity in 〈Gθ(r)〉 is consistent with a real space phase separation comprising partially disordered stripes (see Fig. 5, and Supplementary Note 5). For a system with stripes separated by a distance d and running along an angle α with respect to the horizontal, the distance between stripes as measured at an angle θ is given by N × d/cos((α–90°)–θ) (with N=1,2,3,…), which diverges at θ=α. As can be observed in Fig. 4 (and in similar data shown in Supplementary Figs 1–3), most of the samples studied exhibit this characteristic dependence, with periodic maxima (shown by solid lines in the figure) and minima (dashed lines) that approximately follow such an inverse cosine function. The orientation of the stripes with respect to the crystal axes is not identical for all images studied, but on average it is close to 29°±22° from the [100]T orientation (see Supplementary Fig. 4 and Supplementary Note 6). These stripes are clearly evident in the larger area real space images shown in the left hand panels of Fig. 4a,b, running approximately top left to bottom right. In addition to the separation of stripes, inspection of the images in Fig. 4 reveals that there is a shorter (and more isotropic) length scale of structural variation, which describes the broken-up character of the stripes. This length scale can be seen more clearly in the average correlation function as a kink in the low-r tail, which can be better identified in the derivative of 〈G(r)〉. (see Supplementary Fig. 5 and Supplementary Note 7). Differences in the IFFT images reconstructed using different set of orthorhombic reflections, (110)T or , suggests that there are more complicated components to this phase separation, involving subtle tilts with respect to the average crystal axes (see Supplementary Figs 6–8 and Supplementary Note 8). However, given that we are interested in the average variation of orthorhombicity across areas of the crystals, we restrict our analysis to the filtered IFFT images reconstructed with the set of all four {110}T/{101}T (Ibmm) reflections, which are sufficient to unambiguously determine the associated length scales.


Stripe-like nanoscale structural phase separation in superconducting BaPb(1-x)Bi(x)O3.

Giraldo-Gallo P, Zhang Y, Parra C, Manoharan HC, Beasley MR, Geballe TH, Kramer MJ, Fisher IR - Nat Commun (2015)

Correlation function for a system with partially disordered stripes.Simulation showing the angle-dependent correlation function 〈Gθ(r)〉 for a system with partially disordered stripes. The simulated images have a size of 128 × 128 pixels, with stripes of width w=14.1 pixels, separated between them by d=28.3 pixels, and running along 135° from the horizontal. The scale bar for all images correspond to 30 pixels. For the different images, a broken-up character of a different level was introduced, as a number of islands of size 3 × 3 pixels, placed at random positions within the red stripes. Each image is characterized by a filling fraction f, from 0 (empty stripe) to 1 (full stripe). The filling fraction f for each image is: (a) f=1 (perfect stripe formation), (b) f=0.5, (c) f=0.1 and (d) f=0.05. For each image, the angle-dependent correlation function 〈G(r)〉 is shown in the right hand panel, and its value is represented in the colour scale, which has different limits for each image. Black lines in these plots follow the functional form N*d/cos((α–90°)–θ), where N=1,2,3,…, d=28.3 and α=135°. These simulations illustrate how powerful this statistical technique is in revealing weak- or imperfect-stripes formation. As observed in panel (d), the stripe formation can be missed at first glance; however, 〈Gθ(r)〉 clearly reveals the two-fold symmetry of this image, as well as the periodicity associated with it.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4595596&req=5

f5: Correlation function for a system with partially disordered stripes.Simulation showing the angle-dependent correlation function 〈Gθ(r)〉 for a system with partially disordered stripes. The simulated images have a size of 128 × 128 pixels, with stripes of width w=14.1 pixels, separated between them by d=28.3 pixels, and running along 135° from the horizontal. The scale bar for all images correspond to 30 pixels. For the different images, a broken-up character of a different level was introduced, as a number of islands of size 3 × 3 pixels, placed at random positions within the red stripes. Each image is characterized by a filling fraction f, from 0 (empty stripe) to 1 (full stripe). The filling fraction f for each image is: (a) f=1 (perfect stripe formation), (b) f=0.5, (c) f=0.1 and (d) f=0.05. For each image, the angle-dependent correlation function 〈G(r)〉 is shown in the right hand panel, and its value is represented in the colour scale, which has different limits for each image. Black lines in these plots follow the functional form N*d/cos((α–90°)–θ), where N=1,2,3,…, d=28.3 and α=135°. These simulations illustrate how powerful this statistical technique is in revealing weak- or imperfect-stripes formation. As observed in panel (d), the stripe formation can be missed at first glance; however, 〈Gθ(r)〉 clearly reveals the two-fold symmetry of this image, as well as the periodicity associated with it.
Mentions: To quantify the length scales associated with the orthorhombic variation, the average spatial correlation function 〈G(r)〉 and the angle-dependent spatial correlation function 〈Gθ(r)〉 were computed for each {110}T/{101}T filtered IFFT image (see Supplementary Note 3 for definitions). Figure 4 shows filtered-and-reconstructed HRTEM images for a representative sample of each Bi composition studied (left panels), after a resolution reduction that averages out the atomic-scale information. Both 〈G(r)〉 (shown in Supplementary Figs 1–3 and Supplementary Note 4) and 〈Gθ(r)〉 (shown on the right panels of Fig. 4) of all the images shown reveal local minima and maxima, implying the presence of characteristic length scales for the phase separation. Furthermore, the angular dependent correlation function 〈Gθ(r)〉 clearly reveals that there is a particular spatial pattern associated with the phase separation. Inspection of these quantities, in the right hand panels of Fig. 4, reveals arcs of intensity with an approximately two-fold rotational symmetry. The arcs are imperfect, but repeat with a fixed periodicity, implying a self-organized pattern of phase separation over remarkably large length scales. Such a pattern of intensity in 〈Gθ(r)〉 is consistent with a real space phase separation comprising partially disordered stripes (see Fig. 5, and Supplementary Note 5). For a system with stripes separated by a distance d and running along an angle α with respect to the horizontal, the distance between stripes as measured at an angle θ is given by N × d/cos((α–90°)–θ) (with N=1,2,3,…), which diverges at θ=α. As can be observed in Fig. 4 (and in similar data shown in Supplementary Figs 1–3), most of the samples studied exhibit this characteristic dependence, with periodic maxima (shown by solid lines in the figure) and minima (dashed lines) that approximately follow such an inverse cosine function. The orientation of the stripes with respect to the crystal axes is not identical for all images studied, but on average it is close to 29°±22° from the [100]T orientation (see Supplementary Fig. 4 and Supplementary Note 6). These stripes are clearly evident in the larger area real space images shown in the left hand panels of Fig. 4a,b, running approximately top left to bottom right. In addition to the separation of stripes, inspection of the images in Fig. 4 reveals that there is a shorter (and more isotropic) length scale of structural variation, which describes the broken-up character of the stripes. This length scale can be seen more clearly in the average correlation function as a kink in the low-r tail, which can be better identified in the derivative of 〈G(r)〉. (see Supplementary Fig. 5 and Supplementary Note 7). Differences in the IFFT images reconstructed using different set of orthorhombic reflections, (110)T or , suggests that there are more complicated components to this phase separation, involving subtle tilts with respect to the average crystal axes (see Supplementary Figs 6–8 and Supplementary Note 8). However, given that we are interested in the average variation of orthorhombicity across areas of the crystals, we restrict our analysis to the filtered IFFT images reconstructed with the set of all four {110}T/{101}T (Ibmm) reflections, which are sufficient to unambiguously determine the associated length scales.

Bottom Line: The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase.For the superconducting compositions, the material coexists as two structural polymorphs.We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

View Article: PubMed Central - PubMed

Affiliation: Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA.

ABSTRACT
The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase. For the superconducting compositions, the material coexists as two structural polymorphs. Here we show, via high-resolution transmission electron microscopy, that the structural dimorphism is accommodated in the form of partially disordered nanoscale stripes. Identification of the morphology of the nanoscale structural phase separation enables determination of the associated length scales, which we compare with the Ginzburg-Landau coherence length. We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

No MeSH data available.


Related in: MedlinePlus