Uses of NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is an analytical chemistry technique used in quality control and reserach for determining the content and purity of a sample as well as its molecular structure. For example, NMR can quantitatively analyze mixtures containing known compounds. For unknown compounds, NMR can either be used to match against spectral libraries or to infer the basic structure directly. Once the basic structure is known, NMR can be used to determine molecular conformation in solution as well as studying physical properties at the molecular level such as conformational exchange, phase changes, solubility, and diffusion. In order to achieve the desired results, a variety of NMR techniques are available.

The basis of NMR

The principle behind NMR is that many nuclei have spin and all nuclei are electrically charged. If an external magnetic field is applied, an energy transfer is possible between the base energy to a higher energy level (generally a single energy gap). The energy transfer takes place at a wavelength that corresponds to radio frequencies and when the spin returns to its base level, energy is emitted at the same frequency. The signal that matches this transfer is measured in many ways and processed in order to yield an NMR spectrum for the nucleus concerned.

Fig. 1. The basis of NMR

Fig.1, above, relates to spin-½ nuclei that include the most commonly used NMR nucleus, proton (1H or hydrogen-1) as well as many other nuclei such as 13C, 15N and 31P. Many nuclei such as deuterium (2H or hydrogen-2) have a higher spin are quadrupolar and although they yield NMR spectra their energy diagram and some of their properties are different.

Chemical shift

The precise resonant frequency of the energy transition is dependent on the effective magnetic field at the nucleus. This field is affected by electron shielding which is in turn dependent on the chemical environment. As a result, information about the nucleus' chemical environment can be derived from its resonant frequency. In general, the more electronegative the nucleus is, the higher the resonant frequency. Other factors such as ring currents (anisotropy) and bond strain affect the frequency shift. It is customary to adopt tetramethylsilane (TMS) as the proton reference frequency. This is because the precise resonant frequency shift of each nucleus depends on the magnetic field used. The frequency is not easy to remember (for example, the frequency of benzene might be 400.132869 MHz) so it was decided to define chemical shift as follows to yield a more convenient number such as 7.17 ppm.

δ = (ν-ν0)/ν0

The chemical shift, using this equation, is not dependent on the magnetic field and it is convenient to express it in ppm where (for proton) TMS is set to ν0 thereby giving it a chemical shift of zero. For other nuclei, ν0 is defined as Ξ νTMS where Ξ (Greek letter Xsi)is the frequency ratio of the nucleus (e. g., 25.145020% for 13C).

In the case if the 1H NMR spectrum of ethyl benzene (fig. 2), the methyl (CH3) group is the most electron withdrawing (electronegative) and therefore resonates at the lowest chemical shift. The aromatic phenyl group is the most electron donating (electropositive) so has the highest chemical shift. The methylene (CH2) falls somewhere in the middle. However, if the chemical shift of the aromatics were due to electropositivity alone, then they would resonate between four and five ppm. The increased chemical shift is due to the delocalized ring current of the phenyl group.

Fig. 2. NMR spectrum of ethylbenznene

Nombre: Franklin J. Quintero C.
Asignatura: CRF
Dirección: http://chem.ch.huji.ac.il/nmr/whatisnmr/whatisnmr.html
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NMR experiments

In ordinary NMR experiments, the material to be investigated, the sample, is placed in a static magnetic field (produced by the main coil, Fig. 1) that polarizes the nuclei (aligns them parallel to the field axis). The larger the field, the bigger the nuclear polarization. Another coil (r.f. coil, Fig. 1), whose axis is perpendicular to that of the main magnet coil, is wound around the sample. The terminals of this sample coil are connected to an amplifier that delivers the magnetic radio frequency (r.f.) tunes created by ingenious designed frequency variations of a synthesizers r.f. signal and the nuclei start their intricate quantum dance.

Fig 1

The NMR experiment:

A current through the main coil (green) generates a strong magnetic field that polarizes the nuclei in the sample material (red). It is surrounded by the r.f. coil (black) that delivers the computer generated r.f. tunes that initiate the nuclear quantum dance. At some point in time, the switch is turned and now the dance is recorded through the voltage it induces, the NMR signal, in the r.f. coil. The signals Fourier transform (FT) shows "lines" for different nuclei in different electronic environments. In our new experiments, the field produced by the main coil is powered by a sudden discharge of a capacitor bank, our power supply.

When the music suddenly stops, the nuclei keep on dancing for a while (~100 μs). From watching their dance through the voltage it induces, the NMR signal, at the same terminals of the sample coil (turn the switch in Fig. 1), we gather important information. Usually from the Fourier transform (FT) of the NMR signal we can identify the nuclei, count them, detect their nuclear neighbors; we can measure the fine details of the electronic structure of the material through the interactions the nuclei have with the surrounding electrons.

As one might expect, the NMR signal from the nuclei is weak. Fortunately, it grows with the strength of the initial nuclear polarization, i.e., the strength of the static field. In addition, our ability to differentiate between the fine details of the nuclear signals, what we call resolution, also grows as the magnetic field is raised. These are the chief reasons why NMR sensitivity and resolution are typically boosted by high field magnets. Ofcourse, the resolution also demands a precise knowledge of the magnets homogeneity over the size of the sample, and stability during the time of the quantum dance. In physics applications, the magnetic field is also used as a tuning parameter (like temperature and pressure). It is particularly interesting when the interaction of the material with the magnetic field leads to dramatic effects like structural or other phase transitions, changes that can easily be detected with NMR.

Up until now, NMR methods have been developed in static magnets, for they provide the easiest environment for basic experiments. In the early days of iron yoke magnets, great effort was put into homogenizing and stabilizing these energy and water (cooling) consuming heavyweights. With the introduction of superconducting magnets, stability and homogeneity were less problematic. Over the last 40 years the maximum fields were increased steadily. However, this steady increase has come to a halt. Currently, there are no superconductors in sight that could be used to raise the field for NMR magnets much above 20 T. This fact has prompted NMR researchers to reconsider the use of resistive magnets. Over the past 10 years, various laboratories have been built worldwide that use Bitter-type magnets (< 33 T), or even hybrids of superconducting (non-persistent) and resistive magnets for NMR up to 45 T. These magnets consume tremendous amounts of energy and cooling water. Any increase in field strength seems unlikely. Can NMR experiments go beyond 45 T? As Pulsed High Magnetic Field Laboratories show, fields in excess of 45 T can be created temporarily with small coils. Is it possible to use such pulsed magnets for NMR? Given the great potential of new NMR methods, why have such experiments not been reported?

As every NMR practitioner knows, finding the inherently weak NMR signal can be challenging at times even in static magnets, since the NMR spectrometer and the probe that holds the sample have to be calibrated. Here, the repetition rate for search and tune-up procedures can be very fast, contrary to pulsed magnets where one has to wait some 40 min. In addition, the magnetic field of pulsed magnets is not precisely known at any instant of time, as required for excitation and observation of NMR The field varies from shot to shot and also during the dance of the nuclei. A very small field noise suffices in quenching the NMR signal. Also, the nuclear polarization build-up is not complete if the nuclear relaxation is not much faster than the rise time of the field pulse. The small size of the magnets coil causes great spatial inhomogeneity that spoils the resolution. Lastly, the beneficial signal averaging which is usually performed in NMR experiments is greatly limited. These and other facts have kept researchers around the world from pursuing NMR in pulsed magnets, and prevented some from reporting positive experiments.

We decided it would be challenging to investigate all these issues more thoroughly by giving the experiment priority. First, we developed a strategy and the necessary hardware to search for NMR in the pulsed field. About one year ago, we were able to record the first Cu NMR spectrum at a moderate 12 T peak field. Despite the low field, this was a hallmark experiment, since it showed that NMR in pulsed magnets is possible, i.e., that one can find the signal in the pulsed field and its properties are such that NMR can be done (e.g., the field is sufficiently smooth in time).

 

Fig 2

The worlds first 58 T 2H FT NMR signal (this signal was not corrected for the time dependence of the field - work in progress). Although the line is rather broad, we believe that the resolution can be increased substantially by resorting to microcoils.

Our next step aimed at raising the field and increasing the resolution. This brought up new obstacles. For instance, calibrating pulsed fields that are considerably larger than fields available to us with static magnets (< 16 T) required a different strategy. We could no longer test all the equipment in the static field. Also, it became clear that the fields time dependence ultimately hampered resolution. Without going into detail, we will mention two major results: First, we were able to devise experiments that enabled us to calibrate the pulsed magnets at the IFW up to 60 T, and we show the worlds first 58 T NMR spectrum in Fig. 2. Second, in another set of experiments, we could show that the fields time dependence, which alters the dance of the nuclei, could actually be removed from the analysis. This is a very important result as it shows that the inherent time dependence of the pulsed field is not a major obstacle for doing NMR in pulsed magnets. What have we achieved and what do we conclude?

For the first time, NMR was observed in pulsed high field magnets. We set the world record for high-field NMR at 58 T. More specifically, we designed methods and experiments that facilitate NMR in pulsed magnets, e.g., we proved that the time-dependence of the field, a major concern for NMR resolution, can basically be eliminated. This clearly establishes NMR in pulsed high field magnets as a new tool for the structural investigation of materials, especially pertaining to experiments where the extra field is mandatory. Of course, by calibrating the magnets, we also performed the first high-precision diagnostics of pulsed magnets up to 60 T.

NMR in pulsed magnets has many disadvantages over NMR in static fields. Therefore, one might think that NMR in pulsed magnets will be limited to high field applications only. However, we do not think this is true. The simplicity and the small size of pulsed magnets up to about 30 T (no refrigeration at very low temperatures, low initial costs and maintenance costs, sturdiness, transportability, use on demand) along with now available technologies (sub-micrometer manufacturing, micro electronics, highpower electronics) will open up new NMR applications. One day perhaps, we will be able to watch the quantum dance of the nuclei even at home with our very own tabletop device to check the quality of the evening wine.

Nombre: Franklin J. Quintero C.

Asignatura: CRF
Dirección: http://www.ifw-dresden.de/institutes/imw/sections/22/laboratory-for-pulsed-high-magnetic-fields/nmr
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NMR

Nuclear magnetic resonance (NMR) is based upon the measurement of absorption of radiofrequency (RF) radiation by a nucleus in a strong magnetic field. Absorption of the radiation causes the nuclear spin to realign or flip in the higher-energy direction. After absorbing energy the nuclei will re-emit RF radiation and return to the lower-energy state.

The principle of NMR is that nuclei with odd number of protons, neutrons or both will have an intrinsic nuclear spin. When a nucleus with a non-zero spin is placed in a magnetic field, the nuclear spin can align in either the same direction or in the opposite direction as the field. These two nuclear spin alignments have different energies and application of a magnetic field lifts the degeneracy of the nuclear spins. A nucleus that has its spin aligned with the field will have a lower energy than when it has its spin aligned in the opposite direction to the field.

The energy of a NMR transition depends on the magnetic-field strength and a proportionality factor for each nucleus called the magnetogyric ratio. The local environment around a given nucleus in a molecule will slightly perturb the local magnetic field exerted on that nucleus and affect its exact transition energy. This dependence of the transition energy on the position of a particular atom in a molecule makes NMR spectroscopy extremely useful for determining the structure of molecules.

NMR spectroscopy is one of the most powerful tools for elucidating the structure of both organic and inorganic species. It has also proven useful for the quantitative determination of absorbing species.

NMR - Continuous-wave Nuclear Magnetic Resonance

A continuous-wave NMR instrument consists of the following units: a magnet to separate the nuclear spin energy states; at least two radiofrequency channels, one for field/frequency stabilization and one to furnish RF irradiation energy; a sample probe containing coils for coupling the sample with the RF field; a detector to process the NMR signals; a sweep generator for sweeping either the magnetic or RF field through the resonance frequencies of the sample; and a recorder to display the spectrum.

The spectrum is scanned by the field-sweep method or the frequency-sweep method. In the frequency-sweep method, the magnetic field is held constant, which keeps the nuclear spin energy levels constant, then the RF signal is swept to determine the frequencies at which energy is absorbed. In the field sweep method, the RF signal is held constant, then the magnetic field is swept, which varies the energy levels, to determine the magnetic field strengths that produce resonance at fixed resonance frequency.

NMR - Fourier-Transform Nuclear Magnetic Resonance

Fourier-Transform NMR spectrometers use a pulse of radiofrequency radiation to cause nuclei in a magnetic field to flip into the higher-energy alignment. The length of the RF pulse is 1-10 µs and is wide enough to simultaneously excite nuclei in all local environments. The interval between pulses T is typically one to several seconds. During T, a time-domain RF signal called the free induction decay (FID) signal is emitted as nuclei return to their original state.

FID can be detected with a radio-receiver coil that is perpendicular to the static magnetic field. The FID signal is digitized and stored in a computer for data processing. Ordinary the time-domain decay signals from numerous successive pulses can be summed and averaged to improve the signal-to-noise ratio. The result is then converted to a frequency-domain signal by a Fourier transformation. The resulting frequency-domain output is similar to the spectrum produced by a scanning continuous-wave experiment.

 
Nombre: Franklin J. Quintero C.
Asignatura: CRF
Dirección:http://muniche.linde.com/international/web/lg/spg/likelgspg.nsf/docbyalias/anal_nmr#3
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Solid State Spectroscopy

Researchers in the Solid State Spectroscopy Group are working to improve the quality and performance of a variety of materials key to our nation's renewable energy future. By studying and manipulating materials at the atomic level, we are able to provide scientists in all fields of renewable energy research with a more thorough understanding of the electronic properties of solid-state materials.

We study the electronic properties of the materials used in photovoltaic systems, electrochromic or "smart" windows, high-temperature superconductors, and advanced, solid-state batteries. Fundamental goals of this research are to gain a better understanding of the fundamental mechanisms that limit the performance of PV materials and synthesize new material architectures for improved PV performance.

Capabilities of our Solid State Spectroscopy laboratory include: ultrafast spectroscopy, near-field scanning optical microscopy, high-resolution continuous-wave spectroscopy, reflection/absorption spectroscopy, and infrared spectroscopy. Pairing the ultrafast laser with the near-field scanning optical microscope allows optical imaging with spatial resolution beyond the diffraction limit. The microscope enables the study of material on the submicron level to pinpoint the actual location of problems (such as crystal defects) that hinder material quality. The ultrafast laser freezes motion on an ultrafast time scale and lets us look at light pulses one ten-trillionth of a second in duration. To put this in perspective, light only travels 30 microns in the length of time this apparatus can freeze.

A recent achievement involved the negative refraction of light—bending light the "wrong way." Our physicists were the first in the world to do this using natural materials. Also, we showed that light could be refracted without losing energy or intensity (due to reflection). This new and fundamental discovery has possible uses in imaging, lens technology, data storage, semiconductor technology, and more.

Nombre: Franklin J. Quintero C.
Asignatura: CRF
Dirección: http://www.nrel.gov/basic_sciences/technology.cfm/tech=5
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Vibrations in crystal lattice play big role in high temperature superconductors

By Robert Sanders.

BERKELEY – An elegant experiment conducted by University of California, Berkeley, and Lawrence Berkeley National Laboratory (LBNL) scientists, in collaboration with a group of scientists at Tokyo University, shows clearly that in high temperature superconductors, vibrations in the crystal lattice play a significant though unconventional role.

The results, reported in the July 8 issue of Nature, shed much-needed light on the enigmatic superconductors which, 18 years after their discovery, still puzzle theoreticians and experimentalists. The findings also could point scientists to new materials to explore as possible superconductor.

"We know that there are in nature different materials that might be superconductors, but up to now these new superconductors have not been found," said lead researcher Alessandra Lanzara, assistant professor of physics at UC Berkeley and faculty scientist at LBNL. "In a way, these results will put the finger on some classes of material that are a potentially important system for superconductivity."

High temperature superconductors are almost always some type of copper oxide (cuprate) ceramic doped with a variety of elements, from bismuth, yttrium and lanthanum to strontium and calcium. For unknown reasons, this mélange of atoms conducts electricity without resistance at temperatures as high as 130 degrees above absolute zero (130 K or -143 degrees Celsius), unlike the conventional metallic superconductors that must be cooled below 20 K to become superconducting.

explained by the seminal Nobel-Prize winning Bardeen-Cooper-Schrieffer (BCS) theory, high temperature superconductivity is still in search of a theoretical explanation. In the BCS theory, each electron pairs with an electron of opposite spin to form a new entity, a Cooper pair, that can move without resistance through the material. The pairing is made possible by interactions between the electrons and the metal atoms vibrating in place in the crystal lattice. The lattice is the ordered three-dimensional arrangement of atoms in a solid, like the scaffolding of a crystal.

Most researchers studying high temperature superconductors have disregarded these lattice vibrations, called phonons, under the assumption that they play no role in the high temperature superconductors. According to many of these theories, high temperature superconductivity arises from quantum voids or "holes," which are created by depleting electrons from the sample, moving on top of a background of magnetic moments. In these theories, phonons are not at all important. Nonetheless, there remains a group of physicists who are more reluctant to abandon phonons because of a lack of hard evidence that they are not involved in the phenomena.

"There is this ongoing debate whether phonons play any role in superconductivity and whether magnetism is the important clue that determines the properties of cuprates," Lanzara said. "We thought, 'This debate is going to go on forever unless we come up with some new experiment.' The collaboration with the group of Professor Hide Takagi and Dr. Takao Sasagawa in Tokyo University, who have provided unique high-quality single crystals, has made this experiment possible".

The experiment, which involved tweaking the material's crystal lattice by substituting heavier oxygen-18 for some of the normal oxygen-16, showed that a heavier and thus stiffer lattice affected the electron cloud that permeates the superconductor.

"We are able with ARPES to extract information regarding the influence of the lattice on the single electron dynamics in the cuprates, directly and unambiguously," Gweon said, referring to angle-resolved photoemission spectroscopy (ARPES), which is used to measure the velocity of the electrons in a material.

"The results we found provide the first direct evidence for a significant and unconventional role of phonons in the high temperature superconductivity, meaning that all the reasons that have been used so far to disregard the importance of phonons are not valid anymore," Lanzara said.

"Our experiment doesn't say one way or another whether phonons are the only component, but it does say that phonons play a very important role," added Gey-Hong Gweon, the first author and a postdoctoral physicist at LBNL. "But our results definitely show that there is a strong interaction between the lattice and the electrons, in a way that cannot be disregarded as is done in many theories."

Lanzara, Gweon and theorist Dung-Hai Lee, UC Berkeley professor of physics, agree with many of their colleagues that in high temperature superconductors, the repulsive electron-electron interaction is very strong, and that the tendency for electrons of opposite spins to pair up into a "singlet'' has a lot to do with the antiferromagnetic interaction that's responsible for making the undoped ceramic materials antiferromagnets. However, they also believe that this tendency to form spin singlets enhances the interaction between the electrons and the phonons.

Such an electronically enhanced electron-phonon coupling is similar to what happens in the so-called spin-Peierls systems, where alternating electrons in a solid lattice adopt opposite spins and, as a result, pair up into an ordered system similar to Cooper pairing, though these pairs do not roam the solid but stay near their lattice electrons. The alternating spin arrangement that characterizes spin-Peiels behavior is identical to the antiferromagnetic situation in high temperature superconductors.

The team believes, then, that the mutual feedback of the magnetic and electron-phonon interaction is critical to the high temperature superconducting state. There is pairing in the two populations of electrons, one "localized" and the other "free," both perhaps enhanced by the electrons' interactions with the crystal lattice. According to Lee, if the localized electron pairs are bound lightly enough to the lattice atoms, they can resonate with the coherent motion of the Cooper pairs of free conducting electrons, leading to superconductivity.

"There are materials where the electron-phonon interaction enhances a spin type of ordering and vice versa. This has not been observed before in high temperature superconductors," Lanzara said. "The formation of the electron pair, the Cooper pair, is mediated through the phonons, and at the same time there is a feedback from the magnetic interaction. So, the two enhance one another."

The team worked with a material called Bi-2212, which is a copper oxide doped with bismuth, strontium and calcium that becomes superconducting at 92 K (-181 degrees Celsius). The crystal structure is basically comprised of two alternating layers: one a plane of copper and oxygen molecules interspersed with strontium and calcium atoms, the other a lattice of bismuth and oxygen. The team replaced some of the oxygen with a heavier isotope, O-18, and used the ARPES technique to measure the energy or velocity of the electrons in the material.

A ceramic high temperature superconductor is actually a very poor metal, almost an insulator, at room temperature because electrons interact only slightly with the solid lattice (top), as represented by a slight depression in the crystal lattice. As the ceramic is cooled below a critical temperature, however, electrons pair up and are able to 'dance' with the vibrating lattice, stabilizing one another, as represented by a deep impression in the lattice. (Graphic by Gey-Hong Gweon/LBNL)

The complex crystal structure of Bi-2212, a typical cuprate ceramic high temperature superconductor, showing two distinct alternating layers: the copper oxide layer (purple is copper, brown is oxygen) and the bismuth oxide layer (green is bismuth), interspersed with atoms of calcium (pink) and strontium (orange). (Graphic by Gey-Hong Gweon/LBNL)

Nombre: Franklin J. Quintero C.
Asignatura: CRF
Dirección: http://berkeley.edu/news/media/releases/2004/08/16_Lanzara.shtml
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Electron Spectroscopy Group

Head of the group: Dr. Stefan Schuppler

The electronic structure determines or influences many macroscopic properties of solids - color (optical reflectivity), electrical conductivity, and magnetism are some obvious examples. If electron-electron correlations are strong, as in materials like transition-metal oxides, a complex landscape of mutually competing structural, electronic, and magnetic phases may result. Their interplay can be varied by external parameters like doping level, temperature, stress / strain, and dimensionality, often leading to novel and potentially useful functionalities. Examples include high-temperature superconductivity in cuprates as well as orbital ordering effects in manganites, ruthenates, and cobaltates. To gain a fundamental understanding of such phases and the associated transitions we study in depth their electronic and magnetic structure.

The experiments are performed at IFP's soft x-ray analytics facility WERA at the synchrotron light source ANKA on site. With photoemission (PES) and angle-resolved PES (ARPES), the occupied electronic structure, band character, and Fermi surface are accessible; resonant PES is element specific. X-ray absorption (NEXAFS) gives the unoccupied electronic structure and orbital character; magnetic dichroism (SXMCD, MLD) sensitively probes spin states as well as spin and orbital components of the magnetization. Imaging with lateral resolution down to 100 nm and microspectroscopy is possible in a photoemission electron microscope (PEEM). All methods are (or will soon be) interconnected in ultrahigh vacuum (UHV), also for being mutually accessible from various in-situ preparation chambers for, e.g., epitaxial thin-film growth by pulsed-laser deposition (PLD) and by evaporation, or for carbon-based and other nanosystems. This 'integrated approach' to instrumentation and preparation is at the core of WERA's design. It allows the user to prepare his/her samples and to study them with a combination of complementing electron spectroscopies, each emphasizing a different aspect, yet all in one instrument and without having to expose the samples to air or other possible contamination.

With a bending magnet as the light source, the beamline covers photon energies between 100 and 1500 eV, providing high flux at high resolution as well as circular and linear polarization. From early next year on, a planar undulator (on loan from NSRRC, Taiwan) can alternatively be utilized as the light source, further increasing flux density for demanding experiments.

Beamline and experimental stations are also user facilities embedded in ANKA's beamtime application system. Calls for scientific external proposals are posted twice a year; applications are graded and beamtime is awarded by an independent review panel. Beamtime for industrial and other proprietary purposes is also available but, unlike beamtime for scientific use intended for publication, is subject to fees (ANKA Commercial Services). Far more than 50% of the beamtime is awarded to external users. Vice versa, WERA's wide experimental base is to a substantial extent due to long-term cooperations with strong external partners: for instance, the PEEM is provided through a cooperation contract with the manufacturer (Focus GmbH), while the SXMCD chamber is contributed by the Max-Planck Institute Stuttgart (Prof. G. Schütz, PD E. Goering).

Fig. 1. Angular resolved photoemission of Sr0.9La 0.1NbO3.40

Nombre: Franklin J. Quintero C.
Asignatura: CRF
Dirección: http://www.ifp.fzk.de/index.php?Webs=grp&GGNr=1&Lng=E
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Mechanical Design of Metal Alloys

Metal alloys (e.g., aluminum- and magnesium-based) have great promise to reduce the weight of cars and light trucks without compromising safety. However, much basic science is not yet understood about e.g. Al-alloys, leading alloy designers often to simply "guess" at the parameters to be used in microstructural models. Thus, the role of basic energetic and thermodynamic data in designing metal alloys is crucial towards their application. Researchers working in NREL’s Solid State Theory Group have developed computational techniques for applying highly-accurate "state-of-the-art" first-principles (i.e., completely quantum-mechanical, parameter-free) computational approaches to obtaining thermodynamic properties of alloys. These calculations will play a central role in predicting a new class of modern metal alloys, designed on computers rather than in laboratories.

First-principles quantum-mechanical calculations are computationally expensive; thus, even on today’s fastest computers, the system size which can be simulated by first-principles approaches are limited by computational resources, and thus some "scaling up" of length scales is necessary to treat thermodynamic alloy problems. One method for this scaling up which is currently utilized in NREL’s Solid State Theory Group is in mapping accurate first-principles data onto simpler energy functionals which can then be used on a much larger length scale. The method is known as LEGO, or "Linear Expansion in Geometric Objects". Examples of this type of approach are in precipitation hardening in Al-Cu and Al-Zn alloys: Like most pure metals, aluminum is relatively weak, and therefore need to be strengthened via alloying additions. In precipitation hardening, common in Al-alloys, a small amount of a solute element is added to Al at high temperatures, and then the alloy is quenched down in temperature past the solubility limit of the alloying element. Thus, the solute element begins to precipitate out of the Al matrix, and these precipitates act to pin dislocations, and hence improve mechanical strength. However, without understanding the structure and stability of the precipitated phase, alloy designers cannot fully understand the strengthening mechanism. NREL researchers have predicted the thermodynamic stability and atomic-scale structure of Cu precipitates embedded in an Al matrix. The precipitation is determined by a combination of strain and interfacial energies, and an example of calculated strain energies for Cu embedded in Al is shown in Fig. 1. By using both strain and interfacial in thermodynamic Monte Carlo simulations, one can predict the complete atomic-scale structure of precipitates in Al. An exampleof this kind of hybrid "first-principles/scale up" approach is shown in Fig. 2, which shows the atomic-scale structure of an ordered Cu precipitate in a dilute Al-Cu alloy.

Fig. 1

Fig.2

In the case of Al-Zn, our model allows for the first time a prediction of the observed size- and temperature dependence of precipitates in this alloy system. These precipitates consist only of Zn atoms. Examples of precipitates are visible in Fig. 3: In agreement with experimental studies, the precipitates change from a nearly spherical to a more hexagonal/ellipsoidal shape with decreasing temperature and increasing size

Fig.3

The thermodynamic calculation was performed for a system of more than 200,000 atoms, extending to length scales approaching 200 Å approximately scaling the length scale of the first-principles calculations by a factor of 20-50. With further improvements, length scales of 1000 Å are in sight, thus leading to the possibility of microstructural modeling with completely atomistic approaches.

Nombre: Franklin J. Quintero C.

Asignatura: CRF
Dirección: http://www.sst.nrel.gov/topics/metal_alloys.html
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