Faber-Ziman Theory Research Articles

Electron transport properties of thermodynamically stable Al-Cu-Ru icosahedral quasicrystals

The electron transport properties of the thermodynamically stable Al68Cu17Ru15 quasicrystal have been studied through the measurements of the electronic specific heat coefficient and the temperature dependence of the electrical resistivity in the range 4.2-300 K. The full-width at the half maximum for the strongest X-ray diffraction line (100000) is reduced to be less than 0.15 nm-1 either by remelting the ingot with subsequent furnace cooling or by annealing the melt-spun ribbon at 850 degrees C for 24 hours. An apparent improvement in the quasicrystallinity upon the heat-treatment caused a drastic increase in resistivity up to 1600 mu Omega cm and accompanied a very small electronic specific heat coefficient gamma lower than 0.3 mJ mol-1 K-2. The temperature dependence of the resistivity characterised by a concave curvature with a negative TCR can be discussed in terms of the weak localisation of conduction electrons. The authors are also convinced that the thermodynamically stable quasicrystals like the present Al-Cu-Ru and the previously studied Al-Li-Cu always exhibit a very low gamma value coupled with a high resistivity. From this they conclude that the electron density of states in thermodynamically stable quasicrystals possesses a structure-induced minimum and that the Fermi level does fall in this critical range. An increase in the resistivity upon improvement in quasicrystallinity has been discussed in terms of the generalised Faber-Ziman theory and also in terms of a possible enhancement in the coherent multiple scattering due to locally well-developed short-range order.

Electronic properties of icosahedral quasicrystals in Mg-Al-Ag, Mg-Al-Cu and Mg-Zn-Ga alloy systems

The electronic structure and the electron transport properties of sp-electron quasicrystals have been studied, using in total, 20 quasicrystals in the three alloy systems Mg-Al-Ag, Mg-Al-Cu and Mg-Zn-Ga. The authors revealed that the temperature dependence of the electrical resistivity changes its characteristic features with increasing resistivity in the same manner as that in the nonmagnetic amorphous alloys. This is apparently consistent with the generalised Faber-Ziman theory, but this simple model poses difficulties in explaining a definite increase in the resistivity upon improvement in the quasicrystallinity, brought about by the heat-treatment of the Mg39.5Zn40Ga20.5 quasicrystal. The Hall coefficient exhibits the sizable temperature dependence when its magnitude deviates from the free electron value, suggesting the important role of the Fermi surface-Brillouin zone interaction. The temperature dependence of the thermoelectric power below 300 K is found to be nonlinear, as opposed to a more linear one in the amorphous alloy. The electronic specific heat coefficient plotted against the electron concentration e/a exhibits a universal trend regardless of the alloy system and decreases with decreasing e/a from the free electron value to about one-third of the free electron value. It is noted that a thermally stable quasicrystal apparently possesses a reduced electronic specific heat coefficient.

Electrical resistivity and interference functions of amorphous Ni xAg 1− x thin films

Using r.f. sputtering we have fabricated non-crystalline thin films of Ni Ag alloys, two metals which are insoluble in both liquid and solid states. The variation in resistivity with composition exhibits a maximum. The Faber-Ziman theory often used to explain both resistivity and temperature coefficient behaviours needs the measurement of interference functions. Comparison between the values ofk at the maximum of the first peak and twice the Fermi wavevectorkF leads to the determination of the effective number of conduction electrons in nickel (0.6), which agrees with previous results.

Electrical resistivity of liquid nickel-lanthanum and nickel-cerium alloys.

The high-temperature melting points of transition metals and the extreme reactivity of rare-earth metals at high temperature explain why very few results exist on the physical properties of this kind of alloy. Except for some papers of Solodovnikov {ital et} {ital al}., no paper on the electronic properties of transition-metal--rare-earth alloys have been published to our knowledge. The scarce pure-metal results are often contradictory. The electrical resistivity of nine liquid lanthanum-nickel alloys (up to 60 at. % nickel) and of six cerium-nickel alloys (up to 53 at. % nickel) has been measured. The raw experimental results had been presented earlier. The concentration dependence of the resistivity is discussed in the framework of the extended Faber-Ziman theory of Dreirach {ital et} {ital al}. in terms of structure factors and form factors. Following a hard-sphere description, we used the Ashcroft-Langreth formula to compute the partial structure factors. The form factors have been deduced by taking transition-- and rare-earth--metal model potentials of the Heine-Abarenkov-Animalu type which incorporate formally the {ital s}-{ital d} and the {ital s}-{ital f} hybridization in the energy band of the lanthanides. Alternatively, we also compute a {ital t}-matrix form factor expressed in terms of phase shifts. The model-potential andmore » {ital t}-matrix--form-factor calculations are compared to the experimental resistivity.« less

Electrical transport properties of the liquid AlCu alloys

The electrical resistivity ϱ and the thermoelectric power S have been measured for the liquid AlCu alloys, from the liquidus to 1300°C, in the whole phase diagram. The resistivity isotherms show one maximum at about 25 at. % Al, which is correctly interpreted by the t-matrix formalism, in the framework of the Faber-Ziman theory. The thermopower decreases abruptly in the range of 20 – 40 at. % Al, when Al is added, but this variation cannot be explained by the nearly free electron model.

Temperature- and pressure-dependence of the resistivity of Mg xZn 100− x metallic glasses

The resistance of the metallic glass Mg x Zn 100− x ( x = 67, 72, 77 at.%) has been measured as a function of temperature (2–250 K) and quasihydrostatic pressure (up to 10 GPa). We show that the behaviour of the resistivity can be understood on the basis of the Faber-Ziman theory for metallic glasses.

Electrical resistivity and thermopower of the liquid alloy MgZn

The authors have measured the electrical resistivity, rho , and the thermopower, S, for the liquid alloy MgZn across the entire concentration range. New data for rho and S for pure liquid Zn are also reported. Data for the liquid alloy are shown to be consistent with the Faber-Ziman theory, provided the pseudopotential for Zn is assumed to be energy dependent. A comparison of the data for the liquid alloy with data previously reported for the solid amorphous alloy indicate that this energy dependence should also be considered in the solid.

Ellipsometric in situ measurements during deposition of amorphous CuxSn100?x films

Amorphous metallic films are produced by quench condensation onto a 4K cold Si substrate under ultra high vacuum conditions. During evaporation the film growth is recorded in situ ellipsometrically. At the same time the mass of the film is measured with quartz microbalances. It is shown that the dielectric constants are dependent on film thickness. Different film models for evaluating the ellipsometric measurements are used and tested. The influence of porosity and interface roughness is taken into account. The dependence of mass density on thickness is mainly understood in terms of island growth. The dependence of the dielectric constant on concentration is discussed with respect to the Faber-Ziman theory.

Interplay of the Boltzmann-type ordinary transport and quantum corrections in Ag-Cu-Ge amorphous alloy system. I. Temperature dependence of electrical resistivity

The electrical resistivity has been measured in the temperature range 2-300 K for (Ag0.5Cu0.5)1-xGex amorphous alloys over a wide composition range 0<or=x<or=0.95. The scattering mechanism is analysed in the metallic regime, which is assumed to persist up to 60 at.% Ge alloy or the resistivity below approximately 1000 mu Omega cm. In the low-resistivity regime below about 200 mu Omega cm, the rho -T characteristics can be consistently explained in terms of the ordinary scattering mechanism based on the Boltzmann equation or the generalised Faber-Ziman theory. In the high-resistivity regime above 200 mu Omega cm, the quantum corrections are shown to play a significant role: the rho -T characteristics below 15 K and above about 30 K are essentially caused by the electron-electron and the electron-phonon interaction respectively. The dominant role of quantum corrections has been also confirmed by studying the effect of the dimensionality on the rho -T characteristics.

Electron transport properties of non-magnetic metallic glasses

We show that the temperature dependences of electrical resistivity in non-magnetic metallic glasses below 300 K can be, in principle, classified into five representative types, depending on the electronic structure at E F and the magnitude of resistivity. The scattering mechanism responsible for the respective ϱ-T characteristics is discussed. The generalized Faber-Ziman theory is valid in metallic glasses having E F in the sp band, as long as the resistivity is below about 200 μΩ cm and the temperature is above about 20 K. However, the d-electron conduction, coupled with lattice vibrations, is significant in those containing an appreciable amount of d electrons at E F.

Electronic structure and electron transport in CaMgCu metallic glasses

Both electronic structure and electron transport properties of CaMgCu metallic glasses have been studied by the measurements of the low temperature specific heat, the resistivity, the Hall effect and the thermopower in combination with band calculations. In spite of the appearance of the Ca d states near E F, the electron transport properties of all calcium-based metallic glasses studied exhibit characteristic features consistent with the generalized Faber-Ziman theory.

The electrical resistivity of lithium-lead liquid alloys-quantum interference effects

The authors have investigated the modification of the Faber-Ziman theory for the resistivity of LixPb1-x liquid alloys using a theory of '2kF' scattering. Local chemical ordering is included in the calculations using a theory based on the hard-sphere Yukawa reference system. The electron-ion interaction is treated in a simple way using Ashcroft's empty-core pseudopotential. The purpose of this work is to demonstrate the importance of quantum corrections to the Boltzmann equation in these alloys where they have a fairly sound knowledge of the partial structure factors.

Electronic structure and electron transport of Ca-Mg-Al metallic glasses

Low-temperature specific heats and electrical resistivities were measured on 12 samples in two series of Ca0.7Mg0.3-xAlx and Ca0.6Mg0.4-xAlx metallic glasses over the temperature ranges 1.5-6 and 2-300 K respectively. The Hall coefficient was also measured for all Ca0.7Mg0.3-xAlx metallic glasses in the range 77-300 K. A substantial departure from the free electron behaviour is deduced from the composition dependence of the electronic specific heat coefficient. The electrical resistivity is found to vary widely from 50 to 400 mu Omega cm as Mg is replaced by Al. The temperature dependence of resistivity in the low resistivity regime ( rho <150 mu Omega cm) can be explained in the generalized Faber-Ziman theory. The electron transport in the high-resistivity regime (200-400 mu Omega cm) is found to be still strongly composition- and temperature-dependent. These unique features are, the authors believe, far beyond the scope of the generalised Faber-Ziman theory.

Studies of negative TCR and electronic structure of nonmagnetic metallic glasses based on Y and La

The temperature dependence of the electrical resistivity has been measured over a wide temperature range, 2-300 K, for a number of Y- and L-based metallic glasses. Low-temperature specific heats have also been measured to determine the density of states at the Fermi level and the Debye temperature. All of the resistivity data in the range from about 40 to 300 K can be well described in terms of the equation rho / rho 0=A+B exp(-T/ Delta ). According to Mizutani's classification of metallic glasses, the present alloy systems are to be classified in group (4), together with systems such as Cu-Zr and Cu-Ti. The authors revealed that: (i) the above equation is valid for all group (4) metallic glasses studied so far; (ii) the characteristic temperature Delta increases with increasing Debye temperature theta D; and (iii) the resistivity increases with decreasing density of d states at the Fermi level. Using the generalised Faber-Ziman theory; it is difficult to interpret all these findings in a consistent manner. It is suggested that the d electrons at the Fermi level play a key role in the electron transport in group (4) metallic glasses.

Two-Dimensional Weak Localization Effect in Amorphous Cu–Mg Alloys

Both electronic structure and electron transport properties in the amorphous Cu–Mg alloys have been studied, using flash-evaporated thin films and melt-spun ribbons. The Hall effect measurements revealed the validity of the free electron model in this system. The temperature dependence of the electrical resistivity of the amorphous bulk sample can be well explained in the context of the generalized Faber-Ziman theory. However, a substantial deviation from this prediction occurs at low temperatures in thin film samples, when the film thickness is reduced below 500 A. The deviation is attributed to the two-dimensional weak localization effect. The critical temperature T D , at which the upturn deviation becomes noticeable, is found to increase sharply with increasing the sheet resistance. Its value reached about 50 K for the 50 A amorphous Cu 0.4 Mg 0.6 alloy.

Thermoelectric power of Mg-based simple metallic glasses

The thermoelectric power of electronically simple metallic glasses has been measured in the temperature range 77-300K. In total 48 alloys are studied, all of which are based on Mg in combination with other polyvalent elements and noble metals. Under the assumption that the electron-phonon enhancement effect is of minor importance in this temperature range, the temperature dependence of the thermoelectric power is analyzed in terms of the expression zeta =3-q-1/2r derived from the original Faber-Ziman theory. Depending on the magnitude of the thermoelectric parameter zeta at 300K, alloy systems are divided into three classes: class A is representative of alloys, in which both q and r are small. The authors found that the temperature dependence of the thermoelectric power is linear in the range 77-300K. Alloys in class B are characterised by a large q but a small r. Alloys containing an appreciable amount of noble metals are in class C. A significant contribution to the term r arises from the energy dependence of the pseudopotential of noble metals. A non-linear temperature dependence observed in both classes B and C is attributed to the temperature dependence of q and r.

The Hall effect in glassy and liquid metals

It is demonstrated that the existence of positive Hall coefficients in glassy and liquid metals can in principle be explained by the Faber-Ziman theory. The theory leads to a correlation with the thermopower which is in qualitative agreement with the experimental results but which is not suitable for quantitative calculations. Suggestions for a more general approach are given.

Electron Transport Properties of Amorphous Alloys

Emphasis was laid on the need for classifying metallic glasses into five groups in terms of their magnetic states: 1) ferromagnetism with T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ≫ 300K, 2) weak ferromagnetism, 3) spin glass or Kondo states, 4) temperature-independent strong paramagnetism, and 5) temperature-independent weak para-or diamagnetism. The temperature dependence of the electrical resistivity in the range 10 to 300K was discussed for the respective group alloys. Only the data for group 5) metallic glasses can be consistently interpreted on the basis of the generalized Faber-Ziman theory. Nevertheless, it was shown that the 2k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</inf> /K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> =l.0 criterion is not sufficient to predict a negative TCR even in group 5) alloys.

Resistivity of liquid, supercooled liquid and amorphous alloys under elevated pressure

We present a calculation of the electrical resistivity of liquid, supercooled liquid and amorphous Mg 7Zn 3 and Ca 7Mg 3 alloys as a function of temperature and pressure on the basis of the generalized Faber-Ziman theory. The calculation has been performed from first principles, without any adjustable parameter. The theory successfully explains the variation of the electrical resistivity with temperature [positive temperature coefficient (TCR) for CaMg, a generally negative TCR in MgZn with shallow resistivity minima in the liquid and small resistivity maxima and minima in the amorphous phase] and with pressure [positive pressure coefficient (PCR) for MgZn, essentially zero PCR for CaMg] in terms of the partial structure factors, ion-electron potentials and vibrational spectra. We demonstrate the important influence of the thermal expansion upon the calculated resistivity isobars.

Low-temperature electrical resistivity of amorphous Ca-Mg alloys

The electrical resistivity of amorphous Ca70Mg30 alloys has been measured over the temperature range 4-300K. The absolute value and temperature dependence of the electrical resistivity have been calculated on the basis of the generalised Faber-Ziman theory, without an adjustable parameter. Excellent agreement between theory and experiment is found for a plane-wave phonon model.