It is hoped that the reader who has conscientiously struggled through the previous eight chapters has acquired a sense of the achievements and potential of investigating high-temperature materials with levitation techniques.

The acquisition of reliable thermophysical data on solids and liquids at high temperature must be considered among the major achievements, bearing in mind the difficulties that previous workers had in obtaining consistent and reliable data on contained samples at high temperature, especially those of a corrosive nature. One need only take the example of the density, an apparently humdrum quantity that is not only technologically important, for example in determining the ideal conditions for synthesis of crystalline silicon for the semiconductor industry, but also a vital parameter in materials research: a knowledge of the number density is needed to obtain useful real-space information from diffraction experiments, and furthermore it is the unique quantity that enters into a version of mode-coupling theory that has provided one of the most successful routes to understanding the dynamics of simple liquids, as well as an important parameter in ab initio numerical simulations.

A second achievement has been the ability to access metastable solid states. We have encountered several examples of new solid phases, especially glassy phases, that are not accessible with conventional techniques. Undoubtedly such phases will prove to have important technological applications in the optical and optoelectronic industries.

From the point of view of fundamental science, some striking accomplishments have resulted from the ability to access the deeply undercooled liquid state.

Advantages of levitation methods

Investigations of contained materials at high temperature have to contend with two distinct problems: (a) interactions between the sample and container and the resulting possibility of contamination, and (b) the effects of the container walls on the measurements, causing, for example, additional background and beam attenuation in scattering experiments. Both types of problem are removed by the use of levitation. Figure 5.1 shows the melting points and sound velocities (in the solid phase) of some representative materials. Levitation methods (with laser or other kinds of heating) are generally advantageous for measurements at temperatures above the line marked ‘levitation’. This is of course especially true for liquids, but levitation may also be beneficial for studying solid phases at high temperature. For corrosive materials, including many oxide melts, levitation methods may also be advisable at lower temperatures.

The regions marked ‘n’ and ‘x’ in Fig. 5.1 indicate roughly the regions where inelastic neutron and X-ray scattering, respectively, will be advantageous for studying collective excitations, taking into account the higher energy resolution of neutron spectrometers as opposed to the greater ability of X-ray experiments to sample larger regions of Q and E, given the requirement that the velocity of the probe must be considerably larger than that of the excitation being studied (Price & Sköld, 1986).

In the following three chapters we will give some examples of such investigations in different kinds of high-temperature solids and liquids.

The origins of this monograph can be found in a game of bridge played one evening at the 1994 Gordon Conference on High-Temperature Chemistry in Meriden, USA, the participants being Jimmie Edwards of the University of Toledo, Shankar Krishnan, then at Containerless Research Inc. (CRI), and Marie-Louise Saboungi and myself, then at Argonne National Laboratory (ANL). The outcome of the game is best left unrecorded, but a more fortunate consequence of the evening's proceedings was the inauguration of a CRI–ANL collaboration on structural studies of aerodynamically levitated liquids, first with neutrons at the Intense Pulsed Neutron Source at Argonne and subsequently with X-rays at the National Synchrotron Light Source at Brookhaven, supported by a Small Business Innovative Research Grant from the US Department of Energy. Many interesting experiments ensued, some of which are described in this work. A few years later, Marie-Louise Saboungi and I were invited by Jean-Pierre Coutures, Director of the Center for Research on Materials at High-Temperature (CRMHT), Orléans, France, for a three-month visit. This led to an eventual move to Orléans, with occasional breaks at places like Trinity College, Cambridge, where the idea of writing a book for Cambridge University Press came up.

The monograph that resulted aims to summarize the state of the art of the measurement of structural, dynamic and physical properties with levitation techniques, the considerable progress made in the past two decades and the prospects for the future.

Since all the levitation techniques described in Chapter 2 work with conducting materials, it is not surprising that they form the subject of the majority of investigations carried out to date. In this chapter we discuss some representative systems, chosen either because several of their properties have been investigated, especially by levitation techniques, or because they exhibit especially interesting phenomena.

Early transition metals

It is convenient to divide the results obtained on levitated samples of transition metals into early (Groups IVB–VIIB) and late (Group VIIIB) transition metals. The earlier group contains the refractory metals, conventionally taken as Nb, Ta, Mo, W and Re, although relatively few measurements have been made in these even with levitation techniques, presumably because of their very high melting points. A notable exception are the early optical property measurements made on Nb by Krishnan et al. (1991a), using EML in conjunction with laser heating. Values obtained for the high-temperature solid and liquid are shown in Figs. 6.1 and 6.2. It can be seen that the values exhibit rather small discontinuities at the melting point but their temperature dependences change considerably, in the case of n and k going from small negative to large positive temperature coefficients. According to Eq. (4.26), the temperature dependence of the emissivity required a 16% correction to the previous value for the specific heat of liquid Nb at the melting point, with a revised value of 35 ± 1 J mol−1 at Tm.

High-temperature melts with low electrical conductivity have largely been the province of CNL since the other main levitation techniques, EML and ESL, are inconvenient if not impossible for measurements on insulating systems. In fact, from its inception, non-conducting liquids, and in particular refractory molten oxides, have presented the heaviest application of CNL.

Pure trivalent oxides

The molten trivalent oxides Al2O3 and Y2O3, together with their mixtures, by themselves account for the vast majority of measurements with CNL. This is due in part to the scientific as well as technical importance of yttrium aluminium garnet (YAG), Y3Al5O12, an important laser material, discussed in the next section. In addition, pure Al2O3 is of technological interest as the reaction product in rocket engines fuelled by aluminium metal (Parry & Brewster,1991). As a result, molten Al2O3 has often been the material of choice when the opportunity arose for exploiting a new experimental technique with CNL.

The conductivity of molten Al2O3, measured with a contactless technique by Enderby et al. (1997) and Saboungi et al. (2002), is about 6 Ω−1cm−1 at the melting point, indicating the presence of ionic but not electronic conduction. Later measurements (Saboungi et al., unpublished work, 2003) probed the effect of changing the gaseous environment in the levitation system and found a substantial drop in conductivity in a reducing environment (Fig. 8.1). The earlier results of Shpil'rain et al. (1976) on contained samples of molten Al2O3 under argon and in vacuo are in reasonably good agreement with the upper curve in Fig. 8.1.

A variety of levitation techniques are available to the researcher to study high-temperature materials in the normal and supercooled states. The most widely practised techniques at the present time are aerodynamic levitation, in particular conical nozzle levitation (CNL), various kinds of magnetic levitation including electromagnetic levitation (EML), and electrostatic levitation (ESL). Other methods developed for specific applications such as acoustic levitation and gas-film levitation are less widely used and will be discussed only briefly.

In order for levitation to be useful in a scientific experiment, it is important not only to supply a force that can counteract the gravitational field but also to maintain the sample in a configuration that is sufficiently stable to allow the measurements to be performed. The issue of stability may be quite complex. A prime example is the Levitron®, a popular toy in which a spinning magnetic top is suspended above a flat surface of a magnetic material (http://www.levitron.com/). The levitating force is obvious, but the stability requires a complex physical analysis (Berry,1996; Berry & Geim, 1997).

The variety of methods in current use suggests that each one has particular advantages and disadvantages, depending on the application in hand. CNL is a relatively simple and versatile technique and can be readily incorporated into different kinds of experimental apparatus. EML is restricted to conducting samples, generally metals, in which case relatively large samples (up to 1–2 cm diameter if desired) can be levitated.

In this chapter we discuss some elements that are semiconducting in the solid state and that, because of their relatively high melting points and interest in their supercooled liquid states, have been the subject of investigation with levitation techniques. The first materials to be discussed – silicon, germanium and their alloys – in fact melt into metals, albeit, as we shall see, metallic liquids with quite unusual properties.

Silicon

Silicon crystal growth and crystal properties are important in the semiconductor industry. Silicon is the host material for the majority of semiconductor applications, and the properties of its crystalline, amorphous and liquid phases are of substantial interest. The atomic structure, electrical, optical and thermophysical properties of the liquid phase are key factors that determine the quality of crystals grown from the melt. Mito et al. (2005) have made numerical simulations of Czochralski growth of silicon crystals and found that the Peclet number and deflection of the melt–crystal interface, two important parameters in the growth process, are highly sensitive to the emissivity, thermal conductivity, temperature coefficient of surface tension in the liquid as well as the emissivity and thermal conductivity of the crystal. A graphic representation of the importance of thermophysical properties of the liquid for numerical modelling of crystal growth is given in Fig. 7.1.

The conductivity and other electrical transport properties of liquid Si and Ge have been measured by several authors in contained samples.

Introduction

The first part of this chapter describes the edge effects of patterned ferromagnetic films. The edge pole of the ferromagnetic film plays a significant role in the film properties, in particular, the magnetic energy state. Since the magnetic memory cells are made of tiny pieces of patterned film or film stack, the effects due to the end poles become a dominant factor governing the stability and switching behavior of the memory cell. The second part of this chapter deals with the switching properties of a small patterned film under an external magnetic field. A coherent switching model is introduced to describe the switching properties of the film. This is the basis of the write operation of the field-MRAM cells.

Edge poles and demagnetizing field

When a ferromagnetic thin film is patterned and etched into shapes, the magnetic poles at the edge of the film are exposed. Like the end of a bar magnet, magnetic flux emits from the poles at the edge of the thin film. Inside the film, the flux points in a direction opposite to the magnetization. The magnetic field associated with the end poles is called the demagnetizing field, HD. The magnitude of HD is position-dependent.

Consider a semi-infinite film of thickness t and saturation magnetization MS. The film extends from y = 0 in the +y-direction toward infinity and extends in both the +x- and –x-direction toward infinity (see Fig. 3.1).

Introduction

A short time after the discovery of magnetic tunneling devices, tunneling magnetoresistance (TMR) replaced giant magnetoresistance (GMR) read sensor in the hard disk drive. This marked the first successful commercialization of magnetic tunnel junction technology. The first mass production of the magnetic recording head based on a MgO tunnel barrier took place in 2006. In the same year, 4 Mb MRAM chips were commercialized, and it was the first field-MRAM product working in the toggle-write mode. The viability of MTJ technology at the product level is proven. Subsequently, electronic system designers started to consider seriously how to take advantage of this technology. Many new applications of MTJ technology begin to emerge. One of the new circuit elements is the non-volatile magnetic flip-flop device, which is used for the reduction of VLSI chip power as well as for run-time system re-configuration. Such new applications can only be realized with the unique properties of magnetic tunnel junction devices.

Other new applications are being explored in the field of healthcare. GMR and TMR chips are used for detecting biological molecules labeled with magnetic particles, and this could be a powerful platform for next-generation diagnostics. The sensitivity achievable with simple portable instrumentation can be orders of magnitude better than the current methods. Since this application is still in its infancy, it will not be discussed further here. Interested readers are referred to the references above.

SI magnetic units are easily related to the current, voltage and energy in MKS units, since the SI system was originally developed under the assumption that magnetism is originated from electric current. The dimensions of magnetic units are shown below; A = amperes, s = seconds, kg = kilograms and m = meters.

1. (1) newton (N) = kg m/s2;

2. (2) joule (J) = kg m2/s2;

3. (3) magnetic field (H) = A/m;

4. (4) henry (h) = kg m2/s2A2;

5. (5) tesla (T) = kg/s2A;

6. (6) weber (Wb) = kg m2/s2A.

Magnetism in cgs units is less transparent. The unit of magnetic moment m is the emu. The density of the magnetic moment MS is emu/cm3. The magnetic induction is given by B = H + 4πMS, where the magnetic field H is given in units of oersted (Oe) and B is given in gauss (G). (1 Oe = 1 G in air, since M = 0 in air.) Thus, the “4π” in 4πMS is not dimensionless. Its dimension is [G/(emu/cm3)], and it is equivalent to the inverse of susceptibility, so that the unit of 4πMS is [G/(emu/cm3)] · [emu/cm3] = G.

The dimension of “emu” can be understood from the dimension of energy. In Chapter 2, we discussed the magnetostatic energy per unit volume of magnetic material under a magnetic field H to be ∼MS · H. The dimension of MS · H is [emu · cm−3] · [Oe], which should be equivalent to [erg · cm−3]. Therefore, the dimension of emu is [erg/Oe] or [emu/G] in air.