Generalized Faber-Ziman Theory Research Articles

The resistivity of amorphous Fe 1− xZr x alloys in the ferromagnetic region

We have performed calculations of the resistivity of amorphous Fe 1− x Zr x alloys in the ferromagnetic state using the two-current model within a generalized Faber–Ziman theory. We assumed that the resistivity should scale with the d-like density of states at the Fermi level. The results are in quite a good agreement with the experiment.

Universality in the resistivity-temperature relationship for decagonal quasicrystals.

The temperature T dependence of the resistivity of decagonal single quasicrystals available at present has been carefully examined from 77 to 340 K. All the samples show a precisely linear T dependence of resistivity along the periodic direction, while in the quasicrystalline plane a quadratic term was added to fit the data. The linear T dependence in the large temperature range implies a very low transport Debye temperature, and can be easily understood by the nearly filled band model used to explain Hall-effect anisotropy. The T dependence of the resistivity in the quasicrystalline plane can be satisfactorily explained by the generalized Faber-Ziman theory, proving an enhanced electron-phonon interaction and an enhanced phonon-phonon coupling in the quasicrystalline plane.

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.

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.

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.

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.

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.

Calculation of the electrical resistivity of amorphous Sn-noble metal alloys

The absolute value and temperature dependence of the electrical resistivity of amorphous AuSn and CuSn alloys have been calculated on the basis of the generalized Faber-Ziman theory. The partial structure factors of the amorphous AuSn alloys were calculated for a modified microcrystallite model using the electron diffraction data for the average structure factor. The experimentally observed difference of the temperature dependence of the resistivity in the AuSn and the CuSn series is found to be largely due to the different atomic pseudopotentials for the noble metal component in these alloys.