Yuri A. Kumzerov

Ioffe Physico-Technical Institute

Russian Academy of Sciences

St.Petersburg 194021, Russia

fax: (812) 515-6747

e-mail: kumz@infopro.spb.su

Modern solid state physics needs new materials that possess some nontrivial properties and new methods for their fabrication. This presentation discusses some aspects of a so-called "matrix method," developed at the Ioffe Institute by Prof. V. Bogomolov (Bogomolov 1978), of new materials fabrication based on a wide set of crystal materials (matrices) having structures containing microcavities of equal sizes and regular dispositions in space. If a substance is embedded into these voids, regular sets of identical microparticles or ultrathin wires from different materials (metals, semiconductors, insulators etc.) can be constructed.

In this presentation, only those systems where filamentary structures can be
obtained will be discussed. The matrix in this case is chrysotile asbesto —Mg
_{3} Si _{2} O _{5} (OH)_{4} . This is a natural dielectric mineral that exists in the form
of filamentary bundles. Their diameters are some hundreds of Angstroms, and
their length is about one centimeter. These filaments really are tubes
containing hollow channels with diameters from 20 to about 150 Å. The size of
the diameters depends on the specific deposit (the origin) of this natural
mineral. Each filament is a monocrystal consisting of double layers of
network —Mg-O and Si-O. The sizes of the Mg-O networks (a = 5.39 Å, b = 9.33
Å) are greater than the sizes of the Si-O networks (a = 5.16 Å, b = 8.90 Å),
and this difference causes the double layers to roll. As a result, some tubes
with hollow channels have been obtained (see Fig. 6.1). The parameters of the
asbestos lattice are as follows: a = 14.65 Å, b = 9.25 Å, c = 5.34 Å, ß = 93°
16' —a monoclinic system. The filaments are hexagonal and closely packed
(Pundsak 1961).

Fig. 6.1. Schematic structure of chrysotile asbestos.

The introduction of different substances into these channels gives a system
of identical, parallel, isolated, and regularly disposed ultrathin wires with
corresponding diameters (for a schematic view see Fig. 6.1). The filling of the
channels is realized from the molten state with the use of external pressure up
to 10 kbars. The liquid (molten) metals do not wet the matrices, and such
materials can be embedded into the channels only under some high pressure
conditions. By embedding different liquid metals into the voids of different
matrices, one can see that the usual continuous formula for Laplace
pressure— P_{c} = 0.4/D, connecting the diameter of some capillary D, surface
tension , and critical pressure P_{c} under which liquid metal penetrates into
this capillary— may be used when the capillaries have diameters even on a
nanometer scale. This is a very interesting phenomenon that may be used to
determine the diameters of wires. In the case of chrysotile asbestos, it is
possible to fabricate the wires and measure their conductivity simultaneously.
The sample of asbestos (the bundle of asbestos filaments with a total diameter
of about 0.1 mm and with a length of about 5 mm) is passed into dielectric
tubes; there are also some elastic tubes with molten liquid metal and metallic
contacts (mercury, for example). This construction takes place in a liquid
medium that transfers the external pressure. If there is no pressure, there is
no conductivity because all the channels are empty. When the external pressure
increases at some moment, according to the formula for Laplace pressure, the
liquid metal penetrates the channels of asbestos and gives some of them nonzero
resistance.

At this point, a system of parallel ultrathin metallic wires exists. Using the dependence of resistance versus external pressure, one can determine the distribution function (N) that is the relative number of wires with different diameters. This distribution may be quite narrow, and in this situation, wires appear to have practically equal diameters (variation in diameters about 5%). Usually one can choose samples with narrow distributions and with different diameters, and so it is possible to have systems of identical wires and yet vary their diameters: 20 Å, 30 Å, 50 Å, 100 Å, etc. Each sample contains about one million identical wires (Fig. 6.1). If the external pressure is decreased at some moment, the metallic wires may be broken because of the instability caused by the inability of the molten metals to wet the matrices. One may see this situation on the photograph of mercury wires made by an electron microscope (Fig. 6.2). For the wetting situation, the wires may be continuous without external pressure (Fig. 6.2, Bi and InSb wires).

Fig. 6.2. A transmission electron microscope photograph
showing different materials in asbestos filaments.

If the external pressure continues, the wires for the metallic situation
will also be continuous, and therefore it becomes possible to measure their
conductivity directly. With this method, ultrathin wires have been fabricated
from Hg, Sn, In, Cd, Ga, Pb, Bi, Se, Te, InSb, S, NaNO_{2}, and KH_{2}PO_{4} (KDP).
So the system permits the study of the physical properties of conducting wires
with decreasing diameters on a nanometer scale as one approaches the
one-dimensional limit, that is the transitional region between
three-dimensional and one-dimensional objects.

It is well known that true one-dimensional systems must have very unusual properties. First, they must be insulators, according to Peierls' phase transition (Jerome and Schulz 1982) or because of the localization of electronic states (Bergmann 1984). Second, true one-dimensional systems can not exhibit phase transitions because of the fluctuations that become very important in one-dimensional objects and destroy the phase transitions (Skocpol et al. 1975). These systems are unique in that they permit the study of the successive appearance and variation in properties as a function of diameter, approaching the one-dimensional limit. Figure 6.3 demonstrates the temperature dependences of resistance for mercury wires with different diameters in the large temperature scale. Here are the parts that are connected with melting and freezing (the broadened jumps of resistance on the right side), with superconductivity (the jumps of resistance on the left side), and with the localization of electronic states (the middle part of the temperature dependence of resistance).

Fig. 6.3. Relative resistance versus temperature for mercury wires with different diameters.

The effect of the localization of electronic states reflects the property of the true one-dimensional system as an insulator. In a one-dimensional object, any—even a very smal1—disorder leads to a localization of electronic states and thus to the dielectrization of the system. The so-called "weak localization" in the thin, but not one-dimensional object leads, as is known, not to full dielectrization, but to the nonmetallic temperature dependence of resistance. This nonmetallic behavior is exhibited more and more clearly as the diameters decrease (Bogomolov et al. 1983b). The process for mercury wires is shown in Fig. 6.4. Here, there is a large region of nonmetallic behavior in the thinnest wires. Such dependencies are thoroughly explained by the theory.

Fig. 6.4. The effect of "weak localization" on mercury
wires.

Figure 6.5 demonstrates the successive suppression of phase transition with
the decrease of wire diameters (that is, when the one-dimensional limit is
approached) for the second-order phase transition —superconductivity for
mercury wires (Bogomolov 1975). In the bulk material, the temperature region of
the superconducting transition is very narrow. For the wires, there is a
successive broadening of this transition with decreasing diameters so that the
one-dimensional limit leads to nonzero resistance at any temperature, that is,
to the absence of superconductivity. The experimental dependences R (T) may
well be described by theoretical models (Aslamasov et al. 1968 and McCumber et
al. 1970), and this comparison with theory permits the determination of such
parameters as critical temperature. In the case of the broadened transition,
this is not a trivial procedure (Bogomolov et al. 1983a). The dependence of
critical temperature versus diameter T_{c} (d) is shown in Fig. 6.6 and
demonstrates that as the one-dimensional limit of T_{c} approaches zero, the phase transition is also suppressed. It is interesting that some maximum
critical temperature exists for mercury and indium wires. This, in a sense,
confirms experimentally for the first time the theoretically predicted
possibility of T_{c} increasing in one-dimensional systems. It may be noted that these dependences are unique now for ultrathin wires.

Fig. 6.5. Relative resistance vs. temperature for mercury
wires with different diameters in the region of the superconducting transition
(the process of successive suppression of superconductivity with decreasing
diameters.

Fig. 6.6. Critical temperature of superconductivity vs.
diameter for Sn, In, and Hg wires.

Figure 6.7 reveals a similar process of phase transition destruction for the first-order phase transition— melting-freezing. The study measured the temperature dependences of resistance in the region of melting and freezing (Bogomolov et al. 1985). This behavior also corresponds to the phase transition suppression that occurs when wires approach the one-dimensional limit. Figure 6.7 demonstrates the dependence of melting temperature versus diameter (the dashed lines indicate the broadening of transition, the insertion shows the dependence of relative broadening versus diameter). There is some hysteresis between melting and freezing that is typical of the first-order phase transition. It is interesting that this hysteresis decreases with decreasing diameters and disappears for the smallest diameters. There seems to be no difference between the phase transitions of the first and second orders in this limit. These data are also unique for filamentary structures.

Fig. 6.7. Melting temperature for mercury wires vs. diameter
(dashed lines indicate the broadening of melting transition). Insertion and
suppression of melting transition vs. diameter.

Some other effects also appeared: a nontrivial dependence of heat capacity in the region of the superconducting phase transition (Bogomolov et al. 1981), a very large, increasing critical magnetic field for superconductivity (3 times more than the paramagnetic limit) (Bogomolov, et al. 1976), some effects connected with Peierls' phase transition (Bogomolov et al. 1980) (this is practically an unexplored field for nearly, but not true one-dimensional systems), and some effects connected with e-e interactions in the case of very small tunnel junctions (Kumzerov 1986).

In conclusion, these ultra thin wires seem to be unique objects that permit the study of the transitional region between one-dimensional and three-dimensional materials.

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