Читать книгу Introduction to Nanoscience and Nanotechnology - Chris Binns - Страница 19

The individual atoms of most elements have a permanent magnetic moment, so they generate a dipolar magnetic field similar to a simple bar magnet. The source of the atomic magnetic moment is twofold. It arises from the orbital motion of the electrons around the nucleus, which can be considered to constitute a simple current loop and also from the intrinsic angular momentum (spin) of the electrons. These two contributions generate an orbital and a spin magnetic moment and, for the elements Fe, Co, and Ni, the two contributions are simply added to obtain the total magnetic moment. The exchange interaction that acts between neighboring atoms arises from the Pauli exclusion principle. This tends to keep electrons apart if they have the same spins so that the Coulomb repulsion energy between the outermost electrons of neighboring atoms is reduced if the electrons align their spins in the same direction. This appears as a very strong magnetic interaction trying to align the spin magnetic moments, but it is an electrostatic effect produced by the quantum nature of the electrons. It is typically 3–4 orders of magnitude stronger than the direct magnetic interaction of the atomic magnetic moments assuming they are simple bar magnets.

So in a magnetic material, the powerful exchange interaction tries to line up all the microscopic atomic magnets to lie in the same direction. This, however, is not necessarily the preferred configuration because the uniformly magnetized state generates a magnetic field that passes through the material and the magnetization finds itself pointing the wrong way in its own magnetic field, that is, it has the maximum magnetostatic energy.² Of course, reversing the magnetization is of no use because the generated field reverses and again the sample magnetization and the generated field are aligned in the least favorable direction to minimize energy. The exchange interaction and the magnetostatic energy are thus competing, which at first glance does not appear to be much of a competition considering that the exchange energy per atom between nearest neighbors is 3–4 orders of magnitude stronger than the magnetostatic one. The magnetostatic interaction, however, is long‐range while the exchange interaction only operates between atomic neighbors. There is thus a compromise that will minimize the energy relative to the totally magnetized state by organizing the magnetization into so‐called domains with opposite alignment (Figure 1.5a). If these domains have the right size, the reduction in magnetostatic energy is greater than the increased exchange energy from the atoms along the boundaries that are neighbors and have their magnetization pointing in opposite directions. In the minimum energy state, the material does whatever is necessary to produce no external magnetic field and this is what has happened in Figure 1.4a. The magnetization of the soft Fe has organized itself into domains and externally it is as magnetically dead as a piece of copper. The actual magnet has been treated to prevent the domains forming so that it stays magnetized (Figure 1.4b). When we bring the piece of soft Fe into the field of the magnet, its domains are all aligned in the same direction and it has a greater magnetization than the magnet so that when we pull the two apart the ball bearing stays stuck firmly to the soft Fe. This continues until the soft Fe is far enough away from the magnet to revert to its domain structure and become magnetically dead externally.

The phrase “If these domains have the right size” in the previous paragraph encapsulates the essential point. If we do the Democritus experiment and start chopping the piece of soft Fe into smaller and smaller pieces, the number of domains within the material reduces (Figure 1.5b). There must come a size, below which the energy balance that forms domains simply does not work anymore and the particle maintains a uniform magnetization in which all the atomic magnets are pointing in the same direction (Figure 1.5c). So what size is this? It turns out to be about 100 nm, that is, the upper edge of the nanoworld. Any Fe particle that is smaller than this is a single domain and is fully magnetized. This may seem like a subtle size effect but it has profound consequences. Fully magnetized Fe is a much more powerful magnet than any actual magnet as shown in Figure 1.4. The reason is that a permanent magnet must contain some nonmagnetic material to prevent the process of domain formation so that its magnetization is diluted compared to the pure material. A world in which every piece of Fe or steel was fully magnetized would be very different from our familiar one. Every steel object would attract or repel every other one with enormous force. Cars with their magnetization in opposite directions would be very difficult to separate if they came into contact.

Figure 1.5 Single‐domain particles. Domain formation in Fe to minimize energy. Below a critical size (approx. 100 nm), the energy balance favors just a single domain and the piece of Fe stays permanently and fully magnetized. Arrows show the direction of magnetization.

Nature makes good use of this magnetic size effect. Bacteria such as the one shown in Figure 1.6 have evolved, which use strings of magnetic nanoparticles to orient their body along the local magnetic field lines of the Earth. The strain shown in the figure, which is found in Northern Germany, lives in water and feeds off sediments at the bottom. For a tiny floating life‐form such as this knowing up and down is not trivial. If the local field lines have a large angle to the horizontal, as they do in Northern Europe, then the string of magnetic nanoparticles makes the body point downwards and all the bacterium has to do is to swim, knowing that it will eventually find the bottom.

The intelligence of evolution is highlighted here. If the particles are single‐domain particles, then they will stay magnetized forever, so forming a string of these ensures that the navigation system will naturally work. If the bacterium formed a single piece of the material the same size as the chain of particles, a domain structure would form and it would become magnetically dead. The nanoparticles are composed of magnetite (Fe₃O₄) rather than pure Fe but the argument is the same. There is currently research devoted to persuading the bacteria to modify the composition of the nanoparticles by feeding them with cobalt (Co)‐containing minerals as a method of high‐quality nanoparticle synthesis (see Chapter 5, Section 5.1.9).

Interestingly, magnetic nanoparticles with a similar atomic structure have been found on a piece of meteorite known to have come from Mars [3] and this was taken as evidence that there was once life on Mars, though this analysis is controversial. Mars no longer has a significant planetary magnetic field, which disappeared some four billion years ago indicating that the nanofossils, if that is what they are, must be truly ancient. There are, however, localized magnetic fields around magnetic minerals on the surface that could have been used by magnetic bacteria more recently, though still in the distant past.

Figure 1.6 Magnetic bacterium using single‐domain particles. The Magnetic Bacterium (Magnetospirillum gryphiswaldense) from river sediments in Northern Germany. The lines of (permanently magnetized) single‐domain magnetic nanoparticles, appearing as dark dots, align the body of the bacterium along the local direction of the Earth's magnetic field, which in Germany is inclined at 55° from horizontal. This means that the bacterium will always swim downward toward the sediments where it feeds.

Source: Reproduced with the permission of the Int. J. Microbiol. from D. Schüler [2].

Figure 1.7 Size‐dependent behavior in nanoparticles. For particles smaller than 10 nm, quantum effects start to become apparent. In this size range, the proportion of atoms that constitute the surface layer starts to become significant reaching 50% in 2 nm diameter particles. Below about 3 nm, the strength of magnetism per atom starts to increase as shown in the inset for measurements on Co nanoparticles (see text).

Formation of single‐domain particles is only the onset of size effects in the nanoworld. If we continue the Democritus experiment and continue to cut the particles into smaller pieces, other size effects start to become apparent (Figure 1.7). In atoms, the electrons occupy discrete energy levels, whereas in a bulk metal, the outermost electrons occupy energy bands, in which the energy, for all normal considerations, is a continuum. For nanoparticles smaller than 10 nm, containing about 50 000 atoms, the energy levels of the outermost electrons in the atoms start to display their discrete energies. In other words, the quantum nature of the particles starts to become apparent. In this size range, a lot of the novel and size‐dependent behavior can be understood simply in terms of the enhanced proportion of the atoms at the surface of the particles. In a macroscopic piece of metal, for example, a sphere 2 cm across, only a tiny proportion of the atoms, less than 1 in 10 million, are on the surface atomic layer. A 10 nm diameter particle, however, has 10% of its constituent atoms making up the surface layer and this proportion increases to 50% for a 2 nm particle. Surface atoms are in a different chemical environment to the interior and either exposed to vacuum or interacting with atoms of a matrix in which the nanoparticle is embedded. Novel behavior of atoms at the surfaces of metals has been known for decades thus, for example, the atomic structure at the surface is often different from a layer in the interior of a bulk crystal. When such a high proportion of atoms comprise the surface, their novel behavior can distort the properties of the whole nanoparticle.

Returning to magnetism, a well‐known effect in sufficiently small particles is that, not only are they single domains but also the strength of their magnetism per atom is enhanced. The inset in Figure 1.7 shows the measured strength of magnetism (or the magnetic moment per atom) for Co nanoparticles as a function of size. The data are described in more detail below.

A method for measuring the strength of magnetism (or the magnetic moment) in small free particles is to form a beam of them (see Chapter 5, Section 5.1.2) and pass them through a nonuniform magnetic field as shown in Figure 1.8. The amount the beam is deflected from its original path is a measure of the nanoparticle magnetic moment, and if the number of atoms in the particles is known, then one obtains the magnetic moment per atom.

Magnetic moments of atoms are measured in units called Bohr magnetons³ or μ_B (after the Nobel laureate Neils, Bohr) and the number of Bohr magnetons specifies the strength of the magnetism of a particular type of atom. For example, the magnetic moments of Fe, Co, Ni, and Rh atoms within their bulk materials are 2.2μ_B, 1.7μ_B, 0.6μ_B,and 0μ_B (Rh is a nonmagnetic metal), respectively. Figure 1.9 shows measurements of the magnetic moment per atom in nanoparticles of the above four metals as a function of the number of atoms in the particle. In the case of Fe, Co, and Ni, a significant increase in the magnetic moment per atom over the bulk value is observed for particles containing less than about 600 atoms. Perhaps most surprisingly, sufficiently small particles (containing less than about 100 atoms) of the nonmagnetic metal Rh become magnetic.

Figure 1.8 Measuring the magnetic moment in free nanoparticles. The magnetic moment in free nanoparticles can be measured by passing a beam of them through a nonuniform magnetic field and measuring the deflection in their path.

Figure 1.9 Measured magnetic moments per atom in magnetic nanoparticles. Experimental measurements of the magnetic moment per atom in Fe, Co, nickel (Ni), and rhodium (Rh – a nonmagnetic metal in the bulk) nanoparticles as a function of the number of atoms in the particle. For Fe, Co, and Ni, there is a significant increase in the magnetic moment per atom over the bulk value for particles containing less than about 600 atoms. Rh becomes magnetic in particles containing less than about 100 atoms. The insets show the sharp variations in magnetic moments at very small particle sizes. Note the very dramatic change in the magnetic moment of Fe particles in going from a 12‐atom particle to a 13‐atom particle (icosahedron). A similar dip in going from 12 to 13 atoms, though not so pronounced, is also observed in Ni nanoparticles.

Source: Adapted from I. M. L. Billas et al. [4]; A. J. Cox et al. [5]; S. Apset et al. [6]; M. B. Knickelbein [7]; F. W. Paine et al. [8].

In the Fe curve are also shown measurements (green circles) for Fe nanoparticles supported on a graphite surface and coated with Co [9] (see text).

Throughout the whole size range in Figure 1.9, the fundamental magnetic behavior of the particles is size‐dependent. Do not lose sight of how strange a property this is and how it runs counter to our experience in the macroscopic world. It is as strange as a piece of metal changing color if we cut it in half. If Democritus was able to do his chopping experiment down to the nanoscale on Fe, when he reached a piece 100 nm across, which would be invisible in even the most powerful optical microscope, he would say that he had not yet reached the a‐tomon as up to then there would have been no observable change in properties. When he cut in half again, he would suddenly find his piece changing from magnetically dead to the full magnetic power of Fe with every atomic magnet aligned as the piece formed a single‐domain particle. He would exclaim “I have reached the a‐tomon, lets just try and cut again.” Imagine his surprise, when he finds that the properties continue to change and on reaching 3 nm finds that when he cuts again the strength of the magnetism, in proportion to the size of the piece increases. Some of these changes can be dramatic, for example, if he was holding a 13‐atom cluster and shaved off a tiny piece to produce a 12‐atom cluster, the magnetic moment per atom would jump from 2.5μ_B to a staggering 5.5μ_B – very close to the single‐atom limit of 6μ_B. The 13‐atom piece is in a particularly stable configuration known as an icosahedron (20‐sided solid), illustrated in the figure, and for reasons beyond the scope of this chapter, the high symmetry in this atomic structure reduces the magnetism. The same effect is seen in Ni, though less pronounced, in passing through the 13‐atom size. The magnetism in very small Rh nanoparticles is particularly spiky showing peaks and troughs every two or three atoms.

So we can now see the reason why the nanoscale is special as a size, at least as far as materials are concerned. It represents the border region between the macroscopic world and the microscopic atomic world in which the properties of pieces of matter depend on size, and they display novel behavior only found in that size scale. This highlights one of the most exciting aspects of nanoparticle research. If one considers a nanoparticle as a building block and can assemble large numbers of them to make a material, then it is possible to tailor the fundamental properties of the building block just by changing its size. It is almost as if we could add a third dimension to the periodic table, so for each element, we can choose the size of the nanoparticle building blocks, which would modify the properties of the material produced. In Chapter 5, we will look at more sophisticated ways of changing the nanoparticle building blocks.

The ability to change the fundamental properties of the building blocks will surely enable us to produce new high‐performance materials. As an example, if we deposit Fe onto a surface to make a thin film, there is a difference between depositing individual atoms, as with a conventional evaporator, and depositing whole nanoparticles containing, say, 200 atoms. This is clear from Figure 1.10, which shows a thin film of Fe produced by depositing preformed nanoparticles onto a silicon substrate in vacuum. It is clearly a random stack of the deposited particles showing they have not coalesced to form a smooth film. On this scale, a film of the same thickness produced by depositing atoms would appear smooth and featureless and it would behave differently from the nanoparticle stack.

As an instructive example of creating a high‐performance material using nanotechnology, let's go through the steps necessary to produce a magnetic material with a higher magnetization than the best conventional alloy. The most magnetic practical metal available to the designers of machines and devices is Fe–Co alloy in an approximately equal mixture. This metal has an average atomic magnetic moment of 2.45μ_B – about 10% higher than bulk Fe and has been known since 1912⁴. This magnetization known as the Slater–Pauling limit acts as a fundamental bound to the performance of a swathe of technologies ranging from electric motors to magnetic recording and despite a century of searching, no higher performance material has been found.

Figure 1.10 Morphology of nanoparticle film. STM image (see Chapter 5, Section 5.4.1) with an area of 100 nm × 100 nm of a thin film produced by depositing 3 nm diameter Fe nanoparticles onto a silicon substrate in vacuum. It is clearly a random stack of the deposited particles and the film properties will be different to those of a smooth film that would be formed by depositing Fe atoms.

Source: Reproduced with the permission of the American Institute of Physics from M. D. Upward et al. [10].

Yet, if we look at the data for Fe nanoparticles in Figure 1.9, the magnetization is higher than the Slater–Pauling limit for all sizes below about 300 atoms. This, however, is for isolated nanoparticles in a vacuum and it is not immediately clear how to make a material out of them while preserving the high value of the magnetic moment. About 20 years ago, the journey from isolated nanoparticles to materials started with experiments on size‐selected Fe particles deposited in ultra high vacuum (UHV) onto graphite surfaces [9]. This work, showed that, for particles smaller than about 3 nm, the enhanced magnetic moments were retained when the particles were on a support and also revealed the source of the additional magnetic moment. Magnetism in atoms arises from two contributions, that is, the magnetic moment due to the orbital motion of the electrons, which can be considered as a tiny current loop, and from the electron “spin,” which can only be understood from a quantum mechanical perspective. In a transition metal such as Fe, virtually all the magnetism is due to the spin with the orbital moment “quenched” almost to zero. In a nanoparticle, which has a very high proportion of surface atoms with a reduced co‐ordination relative to the bulk, some of the orbital moment reappears and in addition, the spin moment is enhanced. The experiments mentioned above [9] showed that about half the enhancement of the magnetic moment in small particles comes from the spin moment and the other half from the orbital moment.

Although these measurements moved from free beam nanoparticles to those supported on a surface, they were still for isolated nanoparticles and did not show directly how to make a high moment material. Depositing an entire film of nanoparticles reduced the effect of the surface as the particles came into contact and both the orbital and spin moments converged with the bulk values. To make matters worse, films made by depositing preformed nanoparticles on a surface such as the one shown in Figure 1.10 are highly porous with an atomic density around 60% that of the bulk so the magnetic field produced by such a film would be less than that generated by bulk Fe. The same set of experiments, however, also showed that coating the Fe nanoparticles with Co while they were on the surface did not remove the enhanced orbital moment, and the Fe spin moment increased even further so that a total moment of 2.6μ_B/atom was recorded for 200‐atom nanoparticles, compared to 2.2μ_B/atom in the bulk. The data from the Co‐coated nanoparticles supported on a surface are plotted on the Fe nanoparticle curve in Figure 1.9 and it is observed that they show magnetic moments as high as the free nanoparticles but in a film that could be removed from its UHV environment without converting the Fe to oxide.

Figure 1.11 Producing nanostructured films by cluster beam deposition. Nanostructured films can be produced by depositing preformed nanoparticles from a UHV cluster source onto a substrate along with an atomic beam from a conventional hot oven evaporation source. (a) Fe nanoparticles in a Co matrix. (b) Co nanoparticles in an Fe matrix.

These experiments suggested a method to produce a thin film with a magnetization exceeding the Slater–Pauling limit, which is illustrated in Figure 1.11a. If Fe nanoparticles from a UHV nanoparticle source (see Chapter 5, Section 5.1.2) are deposited onto a surface in conjunction with an atomic beam from a conventional hot oven evaporator source, then an atomic film (matrix) containing embedded nanoparticles is created. The atoms fill all the gaps between the particles producing a film with the bulk density and each particle will retain its enhanced orbital and spin moments found in the aforementioned study. In addition, since the matrix has a very high proportion of interface atoms, it should display enhanced magnetic moments as well. Figure 1.11a shows Fe nanoparticles embedded in a Co matrix but clearly with this setup, it is straightforward to reverse the materials and produce films of Co nanoparticles in an Fe matrix as shown in Figure 1.11b.

A few years later this idea was confirmed and films with a magnetization exceeding the Slater–Pauling limit were produced [11]. The data are shown in Figure 1.12, which plots the magnetic moment per atom for Fe nanoparticles in Co matrices (red dots) and Co nanoparticles in Fe matrices (blue dots) compared to the Slater–Pauling curve for conventional Fe–Co alloys. Note that due to an accident of the units and the densities of Fe and Co, the conversion factor from magnetic moment per atom in Bohr magnetons (μ_B) to magnetic field produced in Tesla is very close to 1.0 so the two measures are often interchanged. The factors are 0.99 for Fe and 1.06 for Co so that the Co‐rich end corresponds to a slightly higher magnetic field than the value indicated in μ_B/atom.

Figure 1.12 High‐moment films produced by cluster beam deposition. Magnetic moment/atom in nanoparticle‐assembled films compared to the Slater–Pauling curve.

What the data clearly show is that the magnetization in the films of Fe nanoparticles embedded in Co matrices exceeds that of the Slater–Pauling curve till the density of nanoparticles reaches the percolation threshold at 25%. Then, the magnetization reduces to a value that is the weighted average of the Fe and Co bulk magnetic moments. This is due to the nanoparticles coming into contact and the Fe–Co interface reducing so that essentially there is a phase‐separated mixture. It is evident from the data for the Co nanoparticles in an Fe matrix, however, that a saturation magnetization of about 3 T can be achieved, which is significantly higher than the Slater–Pauling limit. The data in Figure 1.12 are from a material rather than isolated nanoparticles, but it is still in the form of a very thin film approximately 50 nm thick, that is, a long way from a bulk material. With big improvements in the flux from nanoparticle sources, however, there are now patented ideas to produce bulk quantities of this nanostructured alloy, which the author's group is working on at the Universidad de Castilla‐La Mancha in Spain. It is envisaged that this material will find its way into motors for all‐electric transport within eight years where it will produce at least a 20% improvement in the power to weight ratio of the motor.

This development has been labored as it is an excellent example of incremental nanotechnology moving from the lab into applications. This is just a single example and the method of producing materials shown in Figure 1.11 is a supreme way of making nanostructured materials in general. One can control the grain size independently of the volume fraction, there is free choice of the material in the grains or the matrix, and it is possible, using methods shown in Chapter 5, to make the nanoparticles out of more than one material in a range of motifs. These include alloy, core‐shell, and dumbbell nanoparticles, also called Janus particles as they have two different materials exposed at the surface. The method is likely to find its way into a range of applications in advanced materials.