DOESciDAC ReviewOffice of Science
To See is to Know: Visualization
The visualization process is captured by the idea that "to see is to know," and it is ingrained in science to such an extent that it is sometimes forgotten that it is a pillar of the scientific method: demonstrating an effect or causal connection in a reproducible way. Visualization is one tool available to scientists to convincingly demonstrate their results. This idea underpins the logic of many visualization facilities in the United States and elsewhere.

Through its core facility in Albuquerque with gateways to both Los Alamos (LANL) and Sandia (SNL) national laboratories, the Center for Integrated Nanotechnologies (CINT) provides open access to tools and expertise needed to explore the continuum from scientific discovery to the integration of nanostructures into the micro- and macro-world. CINT applies the adage, "to see is to know," to its visualization laboratory, where scientists and program users alike have access to advanced active stereo three-dimensional (3D) visualization tools. By bringing visualization tools and a stereo visualization laboratory to scientists, CINT empowers the individual researcher in materials science and nanoscience with unprecedented capabilities for exploring complex and/or multi-dimensional scientific datasets (figure 1).
Photo: R. W. Kramer, LANL
Figure 1. In the Los Alamos Center for Integrated Nanotechnologies stereo visualization laboratory, Matthias Graf explains the elastic and structural properties of a compressed foam pad simulation by Scott Bardenhagen of the Explosives and Organic Materials group at Los Alamos. The red color indicates regions of high stress of foam.
In nanoscience, materials science, and condensed matter physics researchers are more and more often overwhelmed by the amount and/or complexity of data produced in table-top experiments or numerical computations. Understanding collected or calculated data is sometimes limited depending on how well it can be visualized or presented. Visualization enhances the ability to see unexpected patterns and correlations in measurements and simulations (sidebar "What Is Visualization?" p35). The lack of proper visualization is often responsible for the failure to understand the true meaning of data, which makes visualization especially important when working with large parameters of unknowns in experiments or theory, or when quantifying differences between datasets and images. Complementing two-dimensional (2D) plots with 3D visualization techniques leads to an increased understanding of the data and especially the relationships between the visualized variables.

STM and Spectroscopy
Scanning tunnelling microscopy (STM) is a relatively new technique. Invented in the 1980s from the revolutionary idea of using a macroscopic object (a metallic needle tip) as a tool, the STM images the surface of material with atomic resolution.
The notion that it can be done using a large macroscopic object refutes basic intuition. This idea was so revolutionary that the technique's inventors, Heinrich Rohrer and Gerd Karl Binnig, were awarded a Nobel Prize in 1986. Key to the technique is the phenomenon of electron quantum tunnelling from the tip to the surface. Because electron tunnelling is limited to the nearest point of the tip to the surface, the tunnelling confines itself to the atomically sharp point at the tip and at the surface and thus enables the viewing of atomically sharp images.
By bringing visualization tools and a stereo visualization laboratory to scientists, CINT empowers the individual researcher in materials science and nanoscience with unprecedented capabilities for exploring complex and/or multi-dimensional scientific datasets.
Recently, further development of this technique allowed the use of STM tunnelling as a tool to detect vibrations and inelastic processes with atomic resolution. The inelastic scattering processes in superconducting materials at the scale of 2-5 nm have been imaged. This functional material exhibits a nanoscale inhomogeneity that parallels the nanoscale superconducting inhomogeneity, an observation that expands new possibilities for interpretation of mechanisms of high temperature superconductivity. Observed nanoscale inhomogeneity in the tunnelling gap and in inelastic scattering are cross-correlated and indicate the importance of the inelastic electron scattering in high-temperature superconductors.
This experiment, along with others, supports the observation that a growing list of modern functional materials are inhomogeneous at nanoscale. One of CINT's efforts addresses the role these nanoscale inhomogeneities play in the function of modern materials.
Figure 2 (p34) is obtained from scanning tunnelling spectroscopy experiment in the real space of Bi2Sr2CaCu2O8+δ. The figure shows the 3D map of the inelastic mode (Ω). Ω provides pairing "glue" to the above-mentioned superconductor. In this figure, Ω is plotted as function of the 2D momentum space coordinates (Kx, Ky). The Ω map is taken as a function of the external bias that is plotted along the z-axis.
Source: M. J. Graf, LANL
Figure 2. Scanning tunnelling microscopy enables us to measure the inelastic processes at the nanoscale. In this example, we show the processed inelastic tunnelling data taken on the Bi2Sr2CaCu2O8 superconductor. As a first step, the inelastic signal was acquired over the given field of view as a function of tunneling voltage, V. Then the image (more precisely a set of images taken for a range of V) was Fourier Transformed (FT) to obtain the structure of inelastic scattering in momentum space. The two coordinates in the x-y plane are FT momenta Kx, Ky and the third, vertical dimension is a tunneling bias V. The STM data are a function of all three coordinates (Kx, Ky,V). This image shows the FT STM image as a 3D image. We used our visualization capabilities to analyze and render the data in stereo. This image encodes the dispersion (energy versus momentum) of the inelastric scattering in high-temperature superconductors that might be related to the interaction that produces superconductivity in these materials. We point out that the real space data ubiquitously show the nanoscale inhomogeneity in these materials.
Phase Diagrams
Phases of matter in thermodynamic equilibrium are best described using a phase diagram (figure 3, p34). Each phase exhibits unique characteristics, and a phase diagram, traditionally drawn in 2D, shows where transitions between phases occur based on various types of external variables like pressure, temperature, and magnetic field. In collaboration with Dr. Tuson Park and Dr. Joe Thompson at LANL, CINT has worked on visualizing the phase diagram of the heavy-fermion superconductor CeRhIn5. The conduction electrons of CeRhIn5 turn out to be quite heavy and therefore move much slower than electrons in typical metals like copper. What is even more remarkable is that they live on the edge of both states. The duality of their nature is expressed in a localized versus itinerant behavior. Understanding this very anomalous electronic behavior is one of the grand challenges of strongly correlated electron physics.
Invented in the 1980s from the revolutionary idea of using a macroscopic object as a tool, scanning tunnelling microscopy (STM) images the surface of material with atomic resolution.
Analysis of the CeRhIn5 phase transitions have been visually studied using 2D plots. Using CINT's visualization capabilities, the scant experimental set of phase transition points was integrated into a single 3D visual model. The experimental data were interpolated and extrapolated to create smooth and continuous surface boundaries consistent with the laws of thermodynamics and the theory of quantum phase transitions (figure 4). These surfaces allowed the study of the phase transitions and in particular the interactions of the antiferromagnetic and superconductive phases.
Source: M. J. Graf and J. Patchett, LANL
Figure 3. The phase diagram of the CeRdIn5 as a function of: the temperature, T (K = Kelvin); pressure, P (GPa = Giga Pascal); and magnetic field B (T = Tesla). N stands for normal phase; AFM for anti-ferromagnetic phase; and SC for the superconducting phase. The color bar gives the resistivity that goes to zero as we approach the SC region. The cubic and spherical points are the experimentally observed data points, and the surfaces are created using interpolation. The white surface separates the AFM phase from the normal phase at high temperature. The pink surface covers the superconducting region at the lower temperature region. The white surface penetrates into the pink surface. The common region between the white surface and the pink surface inside the pink region represents the coexistence region of the AFM phase to the SC phase. The AFM transition temperature decreases with the pressure. At T = 0 K, the system undergoes transition as a function of pressure which represents the quantum critical region.
Measurements in a magnetic field explicitly reveal the dual nature of cerium's 4f electron and its role in creating coexisting phases. Figure 3 shows a pressure-field-temperature phase diagram for CeRhIn5 with its many different quantum phases. Regions of normal metal (N), local-moment antiferromagnetism (AFM), and superconductivity (SC) are separated by phase boundaries. The remarkable quantum critical region of intense research is where AFM and SC coexist. As pressure increases, the f electron becomes more itinerant and the superconducting dome grows at the expense of antiferromagnetically-ordered moments. Consequently, the nature of field-tuned quantum criticality observed between pressures P1 and P2 can be understood as a multi-critical line where the Fermi surface of the conduction electrons reconstructs and magnetic fluctuations diverge.
Source: J. Patchett, LANL
Figure 4. This comparative 3D visualization contains several elements. The phase transition surfaces are bounded at z = 0 by a plane colored by resistively at increasing pressures and temperatures starting at the origin in the bottom left-hand corner of each image. The images progress from left to right, top to bottom and show various outputs of the clip visualization operation that removes the data from some side of a (clip) plane. As the clip plane moves through the volume, one can see how the superconductive (pink) and antiferromagnetic (orange) phases interact with each other as the external magnetic field increases.
NMR Spectroscopy
Nuclear magnetic resonance (NMR) is a mature and powerful technique for probing the electronic state of matter by measuring the interaction between the spin of the atomic nucleus and the spin of electrons. Because the quantum mechanical interaction between the nucleus and electron is well understood, it offers a unique and direct probe of the electronic configuration of matter at the atomic level. In collaboration with Dr. Nick Curro (University of California-Davis) and Dr. Ricardo Urbano (LANL), the fundamental interactions and ordering phases of the strongly-correlated, heavy-fermion system CeCoIn5 doped with cadmium have been studied by using advanced visualization approaches to the multi-dimensional NMR spectra.
Standard analysis methods of NMR experiments, which integrate most of the multi-dimensional information of the NMR spectrum, reveal the existence of antiferromagnetic and superconducting order in CeCoIn5 when doped with a few percent of cadmium. Would these low-temperature quantum phases leave a clear signature in the spectral function of the measured magnetization as well? Would they offer a more distinct identification of the onset of long- and short-range antiferromagnetic order in strongly-correlated electron systems?
For the first time, advanced 3D visualization methods were applied to the NMR spectrum of a strongly correlated electron system. ParaView was used to visualize and explore the real and imaginary parts of the measured NMR magnetization as a function of temperature, echo frequency, and recovery time. Figure 5 shows the spectral function of CeCoIn5 doped with roughly 1% of cadmium substituting for indium (In). The result was much more complex than anticipated. The onset of long-range antiferromagnetic order was identified long before its sharp signature at 2.8 K. However, one additional feature was visible in the spectrum at around 2.1 K. Follow-up studies are under way to determine the nature of this spectral signature as a function of temperature and doping. This newly discovered spectral feature may be due to an inhomogeneous distribution of nanoscale-sized droplets of cadmium clusters, or to an unequal occupation of cadmium on non-equivalent lattice sites of indium (there are two unequivalent symmetry sites), or to the onset of a second antiferromagnetic ordering phase with a uniquely different nesting wave vector connecting different regions of electrons on the complex Fermi surfaces of CeCoIn5. At the moment, it is not known whether or not it is an artifact of the superfluid transition of the cooling medium helium. All possibilities are being explored.
Scanning electron microscopy (SEM) is effective to the micrometer and nanometer scale for objects with a conducting surface.
Source: H. Dahal and J. Ahrens, LANL
Figure 5. In this figure, we used ParaView to create a 3D visualization and 2D plot that present the magnetization distribution in an NMR experiment. The 3D window shows a collection of 3D contours of magnetization: -0.9 (blue), -0.315, 0.27 (green), 0.855 (orange), and 1.44. The x-axis is frequency, the y-axis is τ, and the z-axis is temperature in Kelvin. The plot window shows the magnetization as a function of the recovery time (τ) at fixed temperature (2.8 K) and at zero frequency sampling along the probe line shown in the 3D view.
The full content of the NMR spectrum is visible because of visualization, which has allowed the exploration in greater detail the consequences of the formation of nanosized cadmium droplets in the bulk of the heavy-fermion system CeCoIn5 when doped with cadmium. There is mounting evidence that the dopant cadmium is neither randomly or uniformly substituting for indium; more research is required now that it is known where to look for its signatures in the NMR spectrum.

Depth Map Analysis with SEM
Scanning electron microscopy (SEM) is effective to the micrometer and nanometer scale for objects with a conducting surface. SEM images can be collected relatively fast and inexpensively compared to other scanning probes, which makes it an ideal tool for pre-screening or quality assurance of samples. Unfortunately, standard SEM machines take only one image at a fixed viewing angle to measure lateral dimensions, which is not sufficient to provide depth information. With Nathan Brown, Dave Modl, and Dr. Laura Monroe at LANL, and Dr. Elshan Akhadov at SNL, an efficient approach has been developed to extract depth information from a stereo pair of SEM images.
An efficient approach has been developed to extract depth information from a stereo pair of SEM images.
Source: E. Akhadov, SNL; D. Modl and N. Brown, LANL
Figure 6. Left- and right-eye images of a micrometer-sized silver particle.
Depth analysis or stereogrammetry in combination with SEM has a long tradition but was limited to either custom-designed machines or slow depth analysis software. CINT researchers are using a conventional SEM apparatus with a rotational sample holder, which allows taking images at a minimum of two different viewing angles needed for stereo-pair images (figure 6). Then, a depth analysis was performed of the stereo-pair images with a normalized cross-correlation function analyzer programmed on a workstation with a graphics processing unit featuring 128 processing elements (figure 7). On a single workstation, the same algorithm was more than 100 times slower.
Source: N. Brown, LANL
Figure 7. (a) Contour plot of depth (height) map of a silver particle with b probeline. (b) Quantitative height analysis along the probeline shown in the contour plot. (c) Reconstructed 3D image of nanostructured silver particle.
Stereo-pair images can be analyzed almost in real time (within roughly a minute). Figure 6 shows a left- and right-eye SEM image of a nanostructured silver particle that is 4 µm along the long axis. Nanostructured silver particles are of great technological interest for developing better surface-enhanced Raman scattering techniques that enable the measurement of the vibrational spectrum of molecules, or the fingerprint of a molecule, with nearly one million times higher signal-to-noise ratio compared to conventional Raman scattering techniques. Thus, even the tiniest amounts of molecules can now be detected that previously were below the detection threshold.
Contributors: Dr. Matthias J. Graf, Dr. James Ahrens, John Patchett, Dr. Hari Dahal, Dr. Alexander V. Balatsky, Dave Modl, Dr. Laura Monroe, and Nathan Brown, LANL; Dr. Elshan Akhadov, SNL.
Acknowledgments: Work at Los Alamos National Laboratory was performed under the auspices of the U.S. Department of Energy, Office of Science