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Graphene nanoribbons: A new path to spintronics

Spintronics—the principle behind electronic devices based on the spin of an electron, in addition to its charge—is the gleam in the collective eyes of the computer industry. With the discovery of a new pathway towards realizing the spintronics dream, that gleam should light up even brighter.

Marvin Cohen and Steven Louie, theorists who hold joint appointments with Berkeley Lab’s Materials Sciences Division and the University of California at Berkeley, together with postdoctoral researcher Young-Woo Son, have calculated that nanoribbons of graphene—single-layered sheets of hexagonally-arranged carbon atoms—with zigzag edges can be made to carry a spin current.¹ Zigzag graphene nanoribbons could therefore serve as the basis for nanosized spintronic devices.

“Our calculations show that zigzag graphene nanoribbons are magnetic and can carry a spin current in the presence of a sufficiently large electric field,” said Cohen. “An applied transverse electric field transforms the ribbon from a semiconductor with a small gap to a metal with carriers that are 100 percent spin-polarized. By carefully controlling the electric field, it should be possible to generate, manipulate, and detect electron spins and spin currents in spintronics applications.”

Louie added, “There are, of course, many challenges to confront before this concept can be used for applications. However, if electric fields can be made to produce and manipulate a 100 percent spin-polarized carrier system through a chosen geometric structure, it will revolutionize spintronics technology.”

Spintronic devices promise to be smaller, faster, and far more versatile than today’s electronic devices. Spin is a quantum mechanical property that arises when the intrinsic rotational momentum of a particle, in this case an electron, creates a tiny magnetic field. For the sake of simplicity, spin is given the direction of either “up” or “down.” The up or down values of spin can be used to encode data in the 0s and 1s of the binary system, just like the positive or negative values of an electrical charge. However, unlike charge-based data storage, spin-based data storage does not disappear when the electric current stops.

One of the keys to the future development of spintronic technology is the curious, extremely rare class of materials known as “half metals.” These materials are unique because their conducting electrons are all spin-polarized in either the up or down orientation. Conduction takes place by charge carriers exclusively oriented in a single spin direction; the spin polarization of the carriers in half metals is theoretically 100 percent, making them ideal for spintronic device structures.

The search for half metals among semiconductors has been intense, but to date there have been few investigations into organic materials, even though carbon-based nanostructures hold significant promise for future electronic devices.

“Although there are organic magnets in molecular and polymeric forms, carbon in the crystalline form is not magnetic,” Louie said. “This is probably the reason why people haven’t been looking for half metals in carbon-based nanostructures such as graphene.”

Figure 1. An external transverse electric field has been applied in the x direction across this zigzag graphene nanoribbon, which is between 1.5 to 6.7 nanometers wide (billionths of a meter). The field makes the nanoribbon magnetically positive towards the right side, so that the application of a small longitudinal field would generate spin-polarized currents along the y direction. Hydrogen atoms on the edges are denoted by circles or red dots. (Click on image to enlarge.)

Using first-principles calculations, which can predict a material’s electrical and magnetic properties from the atomic number and mass of its constituent atoms, plus the brute computational power of NERSC, Cohen, Louie, and Son were able to demonstrate the half-metallic phenomenon in graphene nanoribbons. They showed that the half-metallic property emerges when homogeneous electric fields are applied across graphene nanoribbons whose zigzag-shaped edges are attached to voltage contacts (Figure 1). Zigzag edges form when the carbon chemical bonds of a honeycombed sheet of graphene are uniformly cut.

“The electric fields can be used to directly manipulate the spin orientation of carriers in zigzag graphene nanoribbons by shifting the energy of different magnetic states via the electric field,” Louie said. “We believe this is the first demonstration of such an effect.”

Cohen commented, “It’s very hard to polarize spins and even harder to manipulate them. Usually one needs magnetic fields that involve large pieces of equipment, which makes the production of small devices difficult. Here we get to have our cake and eat it too, because it is the electric field rather than the magnetic field that gives us the highest degree of polarization.”

Basing spin polarization on electric fields makes it much easier to work with small devices. “Also, the zigzag graphene nanoribbons are resistant to heat buildup, relatively insensitive to temperature, and are nontoxic,” said Cohen. “All we need now is for clever nanoscientists to use our first-principles calculations to design and make these or similar systems.”

Practical plasmonic crystal biosensors

In the realm of myths, legends, and the occult, crystals have always been believed to have extraordinary powers, from protection and healing with crystal talismans to foretelling the future with crystal balls. Scientific discoveries about crystals may be less dramatic, but they are no less amazing. In a recent example, researchers at the University of Illinois, Urbana-Champaign (UIUC) and Argonne National Laboratory developed a small, low-cost crystal array that makes a highly sensitive biosensor, and used computational modeling to explain how it works.

What the researchers achieved was a breakthrough in a common but, until now, expensive technique for measuring binding interactions, such as those between DNA and proteins, based on changes in the refractive index near a metal surface. The technique, called surface plasmon resonance or SPR, is used in diagnostic bioassays and in research ranging from drug discovery to immunology, virology, and other fields.

Figure 2. Images and schematic illustrations of a quasi-3D plasmonic crystal. (A) Scanning electron micrograph (SEM) of a crystal. (Upper Inset) A low-resolution optical image illustrating the diffraction colors produced by these structures. (Lower Inset) A high-magnification SEM that shows the upper and lower levels of gold. (B) Schematic illustration of the normal incidence transmission mode geometry used to probe these devices. The intensity of the undiffracted, transmitted light is monitored across the UV, visible, and near-infrared regions of the spectrum. (Inset) A close-up schematic illustration of the crystal. (Click on images to enlarge.)

Just as a pebble tossed into a pond produces waves on the surface of the water, a beam of light shining on a plasmonic crystal produces electron waves on the crystal’s surface. “SPR is simply light causing a collective excitation of electrons near the surface of a metal,” explained Stephen Gray, a chemist at Argonne National Laboratory, who created the simulations that analyzed the experimental results.

 “Those collective excitations of electrons are like waves on the metal’s surface,” Gray continued, “and light shining around different objects above the metal creates different waves. When we use plasmonic crystals as sensors, small changes in the material specimen produce changes in the refraction index which can be measured with a spectrophotometer. From those responses, you can infer what the material is and how it has changed.”

While the scientific understanding of SPR may be modern, its application has a long history. “The ruby red color in some medieval stained-glass windows is the result of surface plasmon resonance,” Gray pointed out. “Gold nanoparticles that were added to the glass scatter and absorb light in a way that produces a pleasing color.”

Figure 3. Correlation of transmission spectral features with hole/disk plasmonic excitations. (A) Normal incidence transmission spectrum of a quasi-3D plasmonic crystal (blue), and rigorous electrodynamics modeling of the spectrum for an ideal crystal (green) and one that includes subtle isolated nanoscale grains of gold near the edges of the gold disks (red). (B) Computed electromagnetic field distribution associated with the resonance at 883 nm (labeled B in A). The intensity is concentrated at the edges of the nanoholes in the upper level of the crystal. (C) Field distribution associated with the resonance at 1,138 nm (labeled C in A), showing strong coupling between the upper and lower levels of the crystal.

As a sensing technology, SPR has the advantage of not requiring that fluorescent labels be added to samples, as in fluorescence microscopy. But SPR to date has had a variety of limitations. The first SPR systems used prisms, but those systems were too bulky to be portable. More recent systems employ plas-monic crystals in the form of nanostructured films or nanoparticles; these systems are more portable but less sensitive, and fabricating large and uniform arrays of plasmonic crystals has been prohibitively expensive.

But all that may be changing. In an experiment reported in the Proceedings of the National Academy of Sciences,² Ralph Nuzzo, John Rogers and co-workers at UIUC’s Frederick Seitz Materials Research Laboratory developed a low-cost crystal array to make a highly sensitive sensor. Using soft nanoimprint lithography, a technique that uses a soft polymeric mold to stamp and create structures on a substrate, the researchers created a plasmonic crystal consisting of a regular array of cylindrical wells in gold film on a polyurethane substrate (Figure 2). The SPR effects were produced on the nanoscale holes in the gold film and on the separate gold disks at the bottoms of the wells. SPR waves can be modeled mathematically using Maxwell’s equations, so Gray was able to do a detailed computational analysis of the optical properties of the new crystals and the complex electromagnetic field distributions around the multilevel nanostructured features (Figure 3).

Interestingly, Gray’s initial idealized crystal model produced spectral features (Figure 3A, green line) that did not quite match the experimental results (blue line); but when he added small defects in the form of isolated grains of gold on the sides of the wells near the bottom, the match was close to perfect (red line). Scanning electron micrographs confirmed that there were indeed grains of gold at the edges of the recessed gold disks (Figure 4).

“This showed how, at the nanoscale, very small defects can have important effects,” Gray said. It also shows how computational modeling could be used to figure out how to fine-tune the performance of the system.

Figure 4. Tilted SEM image of an individual nanohole showing grains of gold at the edges of the recessed gold disk.

The unusual geometry and uniformity of these crystals gives them high sensitivity to multiple wavelengths over large sample areas with micrometer spatial resolution. The research team used a well studied ligand–receptor pair, biotin and avidin, as a model system to illustrate the functionality of these crystals in a quantitative analytical bioassay, and they were able to detect molecular binding in a single layer.

Because these plasmonic crystal arrays are smaller than typical sensing or imaging systems, and in view of their high sensitivity, low-cost fabrication, and simple readout apparatus, this technology could be used in developing the next generation of portable diagnostic sensors. They could easily be integrated into microfluidic lab-on-a-chip instrumentation.

Overcoming nanocrystals’ resistance to doping

The word doping has different meanings in sports and in materials science, but both meanings have one thing in common: enhanced performance through intentionally introduced impurities. In sports, of course, the “impurities” are drugs. But in semiconductor production, doping pure silicon with small quantities of impurities such as boron or phosphorus enables engineers to tailor the electrical conductivity and other properties of the material for specific electronic applications.

A small amount of dopant can make a big difference: one atom of dopant per 10,000 silicon atoms is considered heavy doping in today’s semiconductor manufacturing; light doping could mean a ratio of 1:100,000,000. But materials scientists would like to dope semiconductor nanocrystals that may have fewer than 10,000 atoms to begin with, because nanoelectronics holds the promise of more efficient solar cells, electroluminescent devices, computers, and much more.

Nanocrystals tend to have fewer defects or impurities than bulk materials, and experiments have shown that it is often more difficult to dope a nanocrystal than a bulk material. But the reason for this difficulty has been a matter of debate. Since nanocrystals are so small—they can have as much surface as inner volume—one obvious explanation is that it is easy for a dopant atom to move to the surface and escape during the process of crystal formation, a process called self-purification.

That “kinetic argument” was not good enough for Gustavo Dalpian and James Chelikowsky of the Institute for Computational Engineering and Sciences at the University of Texas at Austin. (Dalpian is now at the Universidade Federal do ABC, Santo Andre, Brazil.) They thought the kinetic argument was too vague, leading to assumptions and speculations, and that an energetic or thermodynamic study might provide a more precise explanation.

Using electronic structure calculations, Dalpian and Chelikowsky examined the stability of magnetic impurities in spherical cadmium selenide nanocrystals ranging in size from 1.4 to 2.6 nm in diameter—a maximum of 293 cadmium and selenium atoms.³ At the center of the simulated nanocrystals they placed a single manganese impurity atom (Figure 5).

Figure 5.Charge density plot showing magnesium impurities in cadmium-selenium nanocrystals at two different gap levels: (a) resonant and (b) hybrid. (Click on image to enlarge.)

Their calculations showed that this impurity changes the energy level in the “band gap” between the occupied and unoccupied electron energy bands. As the size of the nanocrystal decreases, it takes more “formation energy” to insert the impurity, making doping more difficult, as shown in experiments.

“Our conclusion,” said Chelikowsky, “is that the high energy of formation makes it difficult to stabilize a dopant within a nanocrystal. Since a dopant in a nanocrystal is intrinsically unstable, self-purification may occur for thermodynamic as well as kinetic reasons.”

But their results also suggest a thermodynamic solution to the doping problem: if the dopant is a cation, then increasing the anion concentration in the crystal-growing solution would reduce the impurity formation energy and make successful doping more likely.

The significance of this research was highlighted by a feature article in the Nanozone News section of the Nature web site.⁴

Why doping strengthens grain boundaries

Ceramic engines have been a topic of research for decades because they are lighter and more fuel-efficient than metal engines. So why aren’t we seeing cars and trucks with ceramic engines on the streets yet? The biggest problem with ceramics is durability. Their microscopic structure is granular, and under heat and pressure, the boundaries between the grains can act like tiny seismic faults, allowing small-scale slippage that may grow into cracks and fractures—a dangerous possibility in an engine.

Figure 6. STEM images of undoped and yttrium-doped alumina grain boundaries. (A) Undoped alumina; (B) same image with overlay to illustrate the aluminum atomic column arrangement; (C) yttrium-doped alumina; (C) same image with structural overlay. (Click on images to enlarge.)

Aluminum oxide or alumina (Al₂O₃) is one of the most promising ceramics for engines because of its hardness—it is widely used for abrasives, like sandpaper, and cutting tools. One drawback is that at high temperatures, alumina is prone to microscopic creep at grain boundaries. However, researchers have found that doping alumina with rare earth elements, such as yttrium (Y), improves its resistance to creep. The dopant has been shown to settle in the grain boundaries, but how it prevents creep at the atomic scale has been controversial.

Now a collaboration of researchers from the universities of Tokyo and Missouri–Kansas City may have settled the issue. They examined both undoped and doped grain boundaries with scanning transmission electron microscopy (STEM), then analyzed the grain boundary structure and bonding using a combination of static lattice and first principles calculations.⁵

Figure 6 shows STEM images of undoped (A, B) and yttrium-doped (C, D) alumina grain boundaries. The orange spots correspond to atomic columns of aluminum (the oxygen is not visible), and the yellow spots in C and D are yttrium columns. The schematic overlay in B and D highlights the periodic structural units along the boundary plane, with seven-member rings of Al ions forming a large open structure. These images reveal that Y doping does not alter the basic grain boundary structure; instead, Y simply replaces Al at the center of some seven-member rings in the grain boundary.

The theoretical part of the study was conducted by Wai-Yim Ching, Curators’ Professor of Physics at the University of Missouri–Kansas City, along with Japanese researchers and post-doctoral fellow Jun Chen. They first used static lattice calculations to determine the lowest energy structure of the undoped grain boundary. The calculated structure reproduced the experimentally observed seven-member ring structure at the grain boundary (Figure 7).

To locate the most energetically stable site for Y segregation, the theoretical researchers substituted a single Y ion in various columns at or near the grain boundary (Figure 7, a through p). Site m, in the middle of a seven-member ring, had the lowest segregation energy, just as the experiment showed. The main difference between Y and Al ions is their ionic radius: 67.5 picometers for Al, and 104 picometers for Y. The researchers believe the larger area within the seven-member ring can accommodate the larger ion better than a six-member ring.

Figure 7. Theoretical grain boundary structure obtained by static lattice calculations. Aluminum atoms are white, oxygen blue. Bold lines mark the grain boundary structure as observed in the STEM images. Yttrium segregation energies were investigated for columns a through p, and column m showed the lowest segregation energy.

To investigate local atomic bonding and charge distributions, the researchers then used ab initio calculations to construct a large periodic supercell with 700 atoms. Figure 8 shows charge density maps for the undoped (A) and Y-doped (B) grain boundaries. White circles show the location of Al ions; graduated blue spots show the charge density from O ions; and the yellow circle in B is a Y ion. Figure 8A shows sharp nodes between the O charge densities and the charge density from the Al ion in the center of the seven-member ring. In contrast, Figure 8B shows that the O electron densities are elongated toward the Y ion, indicating a stronger covalency (sharing of electrons) between the Y–O bonds. Further calculations showed that more bonds formed between Y and O ions than between Al and O ions; the larger number of bonds in the Y-doped case contributed to lowering the grain boundary energy.

Figure 8. Charge density map for undoped (A) and Y-doped (B) grain boundaries.

Although the actual mechanism for grain boundary creep is still not well understood, this study advances our understanding of creep resistance. Creep requires the continuous breaking and reforming of atomic bonds as two grains move in opposite directions. Grain boundaries with more bonds and higher bond strength, will, therefore, be more resistant to creep. The undoped seven-member rings in this study have fewer bonds than the interior of the grain, which is why the grain boundaries are mechanical weak points. But the Y-doped rings have more and stronger bonds between Y and O ions, which explains why Y doping increases creep resistance in alumina.

Ching sees the significance of these results in a larger context. “This work demonstrates the importance of combining theoretical computation and experimental observation, the effectiveness of international collaboration, and the need of top-line supercomputers for modern materials research,” he said.

A random walk along an interface

Interfaces are an important class of defects whose distribution affects the properties of the otherwise pristine material, both in nature and in technology. This is especially the case in polycrystals, thin films, multiphase materials, and composites, where the mechanical, chemical, and transport properties are sensitive to the underlying interfacial microstructure.

“In fact, tailoring this microstructure is an emerging paradigm for engineering high performance, multifunctional materials,” said Zachary Trautt, a graduate research assistant and the first author of the study “Interface Mobility from Interface Random Walk,” which appeared in the October 27, 2006 issue of Science.⁶ In that paper, researchers at the Colorado School of Mines and Northeastern University reported a novel computational methodology aimed at quantifying the kinetics of interfaces in diverse material systems.

Figure 9. A slice through a computational cell consisting of two grain boundaries which separate two perfect crystals of different orientations. The average position of the grain boundaries h^¯ is calculated from their fluctuating profile. The color reflects the interaction energy—green indicates high-energy states. The superimposed red dotted curve is the result of the algorithm used to identify the interface position. (Click here for a larger image and here for an animation.) (Images courtesy of Science)

The interfacial microstructure is subject to several driving forces during material synthesis and function. More often than not, these driving forces are large enough to cause the interfaces to move and the microstructure (or its precursor) to evolve (Figure 9). Naturally, controlling the final microstructure requires accurate models (Figure 10) that relate the interface motion to the driving forces in effect.

A quantitative measure of interface kinetics is the interface mobility, the ratio of the interface velocity to the driving force. Past studies on individual homophase crystalline interfaces (or grain boundaries) in several high-purity metals show an interesting trend: the experimental mobilities are orders of magnitude smaller than those extracted via computations. The discrepancy is often attributed to the presence of impurities, fueling speculation that even minute quantities of impurities significantly retard interface motion.

Figure 10.The time evolution in picoseconds of the distribution of the average grain boundary position h^¯ . The distributions are normal, as predicted by the theory. (Click image to enlarge.)

“An often overlooked fact is that computations are limited to tens of nanoseconds,” said Moneesh Upmanyu, co-author and the lead researcher in the study. “As a result, they are performed at driving forces orders of magnitude greater than those commonly observed in experiments,” he explained. This further weakens the comparison, and there is a need to extend the computational studies to more realistic driving forces and include the effect of impurities.

“Our computational methodology offers a way to address both these challenges, efficiently and with setups that are relatively simple,” said Trautt. The basis for the methodology is the pioneering theoretical work by Einstein, Smulochowski, and Langevin on Brownian motion in the early 1900s. “Just as their study related the dance of macroscopic particles to their diffusivity, the microscopic thermal fluctuations result in interface forces that conspire towards a one-dimensional dance [random walk] of the average interface position, which in turn yields its mobility in the zero driving force limit,” said Alain Karma, also a co-author in the study. “The technique is remarkably efficient,” noted Upmanyu. “The computations on pure aluminum yielded mobilities within a nanosecond, a significant savings in computational resources.”

Comparisons with previous experiments and computations reveal that the retarding effect of impurities is much more severe than previously thought. The authors are now working on extending the theory and the computations to directly quantify the impurity drag effect.

Trautt is a graduate research assistant in the Group for Simulation and Theory of Atomic-scale Material Phenomena (stAMP), Engineering Division, Colorado School of Mines; Upmanyu is group leader of stAMP and Assistant Professor in the Engineering Division and Materials Science Program. Karma is Distinguished Professor in the Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, and a senior investigator in the NERSC project “Microstructural Evolution Based on Fundamental Interfacial Properties,” led by Anthony Rollett, Department Head and Professor of Materials Science and Engineering at Carnegie Mellon University.

Building a chemical tool box

To coax the next blockbuster drug out of chemical compounds, scientists must explore how these compounds work with each other. This process of assembling the right ingredients takes years and millions of dollars, and the result can lead to life-saving medicines.

How do chemists figure out the right mix? It takes ample knowledge about the characteristics of various compounds and a dose of serendipitous discovery. This process of synthesizing compounds is what has driven an INCITE project investigator to examine how lithium enolates, lithium carbenoids and the blend of the two interact with other lithium compounds. “Pharmaceutical chemists always need to synthesize new compounds,” said Larry Pratt, principal investigator of the project and assistant professor at Fisk University in Nashville, Tennessee. “I am helping to build the tool box.”

Lithium, the lightest of the solid elements, is a soft white metal that oxidizes quickly in air and water. It is commonly found in portable batteries that power laptops and cell phones. In pharmacology, lithium compounds such as lithium carbonate and lithium citrate are commonly used to control mood swings.

Figure 11. Optimized geometries of lithium carbenoid mixed aggregates with lithium methoxide. Gray represents carbon; white, hydrogen; violet, lithium; green, chlorine; and red, oxygen.

The lithium compounds that have captivated Pratt’s interest are lithium enolates and lithium carbenoids. They are two important classes of reagents in organic chemistry, which involves the study of the properties, synthesis and reactions of carbon-containing compounds. Pratt has drawn from experiments conducted by him and other researchers to calculate the structures, energy, and other properties that resulted from mixing these lithium compounds.

In cooking, when you throw in a bunch of spices, you can expect the mixture to give off an altogether different smell and taste than what you get from individual ingredients. The same thing happens when you blend different compounds into an aggregate—a cluster of molecules that chemically reacts as a single molecule. A mixed aggregate may have properties different than those of either pure component, and the aggregate may react very differently from either of its components. For the creative chemist, the result may not be what was desired. But the more that is known about the structure and reactivity of the aggregate, the better the chance of success.

In solution, almost all lithium compounds form aggregates. Typically, the larger the molecule, the less likely it will form a complex bond. For example, the lithium enolate of acetaldehyde may exist as a four- or six-molecule compound (tetramer or hexamer) in tetrahydrofuran, a common ether-type solvent, while lithium cyclohexanone enolate may show up as a single- or dual-molecule compound (monomer or dimer) in the same solvent. As mixed aggregates, lithium enolates and lithium carbenoids can exhibit different characteristics, depending on the molecular structure, temperature, and the type of solvent.

Using mathematical models to determine the structures and potential reactions of lithium aggregates is a good way to advance the understanding of these substances, particularly because observing their step-by-step reaction in an experiment can be difficult. Many lithium carbenoids are reactive and unstable; they tend to decompose at room temperature, although some can be observed at low temperatures.

Pratt uses ab initio and density functional theory methods to investigate the structures and interactions between the compounds. After modeling all reasonable geometric structures of the compounds and aggregates (see Figure 11 for an example), he uses the results to figure out which structures are likely to exist in significant concentrations in the gas phase and in solution. Then he examines the reactions via each potential reactive species, such as monomer, dimer, tetramer, or mixed aggregate. Transition structures are then located and the activation energies calculated. Characterizing these reactions will help other researchers figure out new uses for these compounds.

This article written by: John Hules, Lynn Yarris, and Ucilia Wang, Berkeley Lab; and Laura Shea, Northeastern University.

 

1 Young-Woo Son, Marvin L. Cohen, and Steven G. Louie, “Half-metallic graphene nanoribbons,” Nature 444, 347, (2006).

2 Matthew E. Stewart, Nathan H. Mack, Viktor Malyarchuk, Julio A. N. T. Soares, Tae-Woo Lee, Stephen K. Gray, Ralph G. Nuzzo, and John A. Rogers, “Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals,” PNAS 103, 17143 (2006).

3 Gustavo M. Dalpian and James R. Chelikowsky, “Self-purification in semiconductor nanocrystals,” Physical Review Letters 96, 226802 (2006).

4 Philip Ball, “Why nanotech fails the dope test,” Nanozone News, 22 June 2006, http://www.nature.com/materials/nanozone/news/060622/portal/m060622-2.html.

5 J. P. Buban, K. Matsunaga, J. Chen, N. Shibata, W. Y. Ching, T. Yamamoto, and Y. Ikuhara, “Grain boundary strengthening in alumina by rare earth impurities,” Science 311, 212 (2006).

6 Zachary T. Trautt, Moneesh Upmanyu, and Alain Karma, “Interface mobility from interface random walk,” Science 314, 632 (2006).