The Electrical Resistance of Dilute Solid Solutions

1936 ◽  
Vol 32 (2) ◽  
pp. 281-290 ◽  
Author(s):  
N. F. Mott
Keyword(s):  
Solid Solution ◽  
Electrical Conductivity ◽  
Solid Solutions ◽  
Electrical Resistance ◽  
Unit Volume ◽  
Effective Number ◽  
Free Electrons ◽  
Mechanical Explanation ◽  
Image Position ◽  
Matthiessen's Rule

1. As is well known, the electrical resistance of a metal is very greatly in-creased by the addition of a second metal with which it forms a solid solution. The increase Δρ in the resistivity due to the addition of a small percentage of the second metal is in general independent of the temperature (Matthiessen's rule), though there are oertain exceptions (e.g. Cr in Au). The quaritum-mechanical explanation of both these facts was first given by Nordheim, and may be expressed as follows: the electrical conductivity of any metal may be written in the formwhere τ is the “time of relaxation”, equal to half the time between collisions, and N is the effective number of free electrons per unit volume: hence, for the resistivity, we have

Electrical Conductivity and Phase Transitions in Ferroelectric Solid Solutions Li0.17Na0.83ТауNb1-уO3 (y = 0 – 0.5) in High Pressure

2020 ◽  
Vol 310 ◽  
pp. 6-13
Author(s):  
Vadim V. Efremov ◽  
Mikhail N. Palatnikov ◽  
Yuriy V. Radyush ◽  
Olga B. Shcherbina
Keyword(s):  
Solid Solution ◽  
Electrical Conductivity ◽  
High Pressure ◽  
Phase Transitions ◽  
Solid Solutions ◽  
Synthesis Method ◽  
Ferroelectric Ceramic ◽  
Synthesis Temperature ◽  
Structure Phase ◽  
Ceramic Solid Solution

Ferroelectric ceramic solid solutions LixNa1-xTayNb1-yO3 (х = 0.17; у = 0 – 0.5) with the perovskite structure have been obtained by the thermobaric synthesis method. Particularities of their microstructure, elastic properties, electrical conductivity and permittivity have been researched. It has been established that an increase in the thermobaric synthesis temperature leads to a decrease in the Young’s modulus value. Specific static conductivity values have been determined; charge carrier activation enthalpies На have been calculated. The Curie temperature of the samples has been determined to decrease with an increase in tantalum content. A Ferroelectric ceramic solid solution Li0.17Na0.83Ta0.1Nb0.9O3 was shown to undergo four structure phase transitions in the temperature range 300-820 К. A Li0.17Na0.83Ta0.1Nb0.9O3 has been shown to be a high temperature superionic. Possible mechanisms of the detected phenomena are discussed.

scholarly journals Influence of Liquid Quenching on Phase Composition and Properties of Be-Si Eutectic Alloy

2020 ◽  
Keyword(s):  
Solid Solution ◽  
Solid Solutions ◽  
Eutectic Alloy ◽  
Electrical Resistance ◽  
Liquid State ◽  
Foil Thickness ◽  
Continuous Heating ◽  
Cooling Rates ◽  
Liquid Quenching ◽  
Substitutional Solid Solutions

By the method of quenching from the liquid state (splat-quenching), it is first revealed the formation of mixture of metastable supersaturated substitutional solid solutions in the eutectic alloy Be-33at.% Si. Cast samples are obtained by pouring melt into a copper mold. High cooling rates during liquid quenching are achieved throw the well-known splat-cooling technique by spreading a drop of melt on the inner surface of a rapidly rotating, heat-conducting copper cylinder. The maximum cooling rates are estimated by the foil thickness. The melt cooling rates (up to 108К/s), used in the work, are sufficient to form amorphous phases in some eutectic alloys with similar phase diagrams, but it is found those rates are insufficient to obtain them in the Be-Si eutectic alloy. The X-ray diffraction analysis is carried out on a diffractometer in filtered Cobalt Ka radiation. Microhardness is measured on a micro-durometer at a load of 50 g. The electrical properties, namely the temperature dependences of relative electrical resistance, are studied by the traditional 4-probe method of heating in vacuum. The accuracy of determining the crystal lattice period of the alloy, taking into account extrapolation of the reflection angle by 900, is ± 3•10-4 nm. It is found that even at extremely high rate of quenching from the melt, instead of the amorphous phase formation, the occurrence of two supersaturated substitutional solid solutions, based on Beryllium and Silicon, is revealed. This fact is established by the obtained dependences of their lattice periods values on the alloying element content. So, during the formation of metastable eutectic structure, a supersaturated with Beryllium solid solution of Silicon has period a = 0.5416 nm, and a supersaturated with Silicon solid solution of low-temperature hexagonal Beryllium has periods a = 0.2298 nm, c = 0.3631 nm. The positive role of the liquid quenching method in increasing the level of mechanical characteristics (microhardness and microstresses) in rapidly cooled Be-Si films is shown. It has been demonstrated that the difference in the atomic radii of the elements significantly affects the distortion of crystal lattices of the formed supersaturated solid solutions, and a significant value of microstresses (second-order stresses) in the Silicon lattice supersaturated with Beryllium is estimated, which, of course, leads to a significant increase in the microhardness, namely: there is an increase in microhardness in the Be-Si alloy under the conditions of applied method of quenching from the liquid state by more than 1.7 times compared to cast eutectic alloy and more than 6 times higher in comparison with the eutectoid cast Iron-Carbon alloy. The obtained polytherm of electrical resistance of the alloy under conditions of continuous heating in vacuum confirms the metastable nature of obtained new phases during quenching from the liquid state.

scholarly journals Synthesis, structure and properties of solid solutions Ва1–хSn1+хF4 and (KyВа1–y)(1–х)Sn1+хF4–y(1–х)

2021 ◽  
pp. 62-70
Author(s):  
R.M. Pshenychnyi ◽  
◽  
T.V. Pavlenko ◽  
Yu.V. Pohorenko ◽  
A.O. Omel'chuk ◽  
...  
Keyword(s):  
Solid Solution ◽  
Electrical Conductivity ◽  
Crystal Lattice ◽  
Electric Conductivity ◽  
Solid Solutions ◽  
Initial Phase ◽  
Potassium Ions ◽  
Heterovalent Substitution ◽  
Structure And Properties ◽  
Barium Ions

We investigated the structure and electric conductivity of solid solutions of homovalent substitution Ва1–хSn1+хF4 (where х=0.03, 0.05, 0.07, 0.10, 0.15 and 0.23) and heterovalent substitution (KyВа1–y)(1–х)Sn1+хF4–y(1–х) (where х=0.03, 0.05, 0.10 and у=0.03, 0.05, 0.10) with the structure of BaSnF4. It was been found that the substitution of 7 mol.% of Ba2+ cations by Sn2+ cations contributed to an increases in electrical conductivity. The solid solution Ba0.77Sn1.23F4 had the highest electrical conductivity (573=6.8010–3 S cm–1). The substitution of barium ions by potassium ions in the BaSnF4 crystal lattice allowed reducing the conductivity of solid solutions regardless of the substituent content. Only the phases containing more than 3 mol.% of K+ ions exhibited the conductivity which exceeded the value of the initial phase at the temperatures above 385 K. In fluoride-conducting phases (KyBa1–y)(1–x)Sn1+xF4–y(1–х), the following solid solutions showed the highest electrical conductivity: (K0.05Ba0.95)0.97Sn1.03F3.95 (573=6.7810–4 S сm–1), (K0.03Ba0.97)0.95Sn1.05F3.97 (573=1.0010–3 S сm–1) and (K0.10Ba0.90)0.90Sn1.10F3.91 (573=8.7010–3 S сm–1).

A Concept for Development of Hydrogen-Resistant Austenitic Steels

2013 ◽  
Author(s):  
Valentin Gavriljuk ◽  
Bela Shanina ◽  
Vladyslav Shyvanyuk ◽  
Sergey Teus
Keyword(s):  
Solid Solution ◽  
Hydrogen Embrittlement ◽  
Solid Solutions ◽  
Austenitic Steels ◽  
Hydrogen Degradation ◽  
Hydrogen Atoms ◽  
Free Electrons ◽  
Physical Reason ◽  
Hydrogen Resistance

Austenitic steels represent a promising class of engineering materials for hydrogen use in vehicles, e.g. for tanks and pipelines. This topic is analyzed in terms of the effect of alloying elements on the interatomic bonds in the solid solutions and, consequently, on the interaction between hydrogen atoms and dislocations and hydrogen embrittlement, HE. The effect of Cr, Ni, Mn, Mo, Si, Al, Cu, C, N was studied. It is shown that the physical reason for HE amounts to the hydrogen-caused increase in the concentration of free electrons in the austenitic solid solution. For this reason, the alloying with elements decreasing the concentration of free electrons is expected to improve resistance of austenitic steels to HE. Alloying with Cr, Mn, Mo and Si is shown to be useful, whereas Cu, Al, Ni, N assist hydrogen degradation. The role of Ni amounts only to stabilization of the fcc austenitic lattice and its absence or the decrease of its content in steel is desirable. Based on the obtained results, recommendations are made for design of austenitic steels with increased hydrogen resistance.

Effect of γ-radiation on magneto-thermoelectric properties of the extruded samples of Bi85Sb15〈Te〉 solid solution

2021 ◽  
pp. 2150099
Author(s):  
I. A. Abdullayeva ◽  
G. D. Abdinova ◽  
M. M. Tagiyev ◽  
O. A. Samedov
Keyword(s):  
Magnetic Field ◽  
Solid Solution ◽  
Electrical Conductivity ◽  
Radiation Dose ◽  
Seebeck Coefficient ◽  
Free Electrons ◽  
Γ Radiation ◽  
Charged Carrier ◽  
Different Doses

Extruded samples of [Formula: see text] solid solutions doped with 0.0005 at.% Te were obtained and the electrical conductivity [Formula: see text], thermoelectric power (Seebeck) [Formula: see text], Hall [Formula: see text] and thermal conductivity [Formula: see text] coefficients were investigated in the range [Formula: see text]–300 K samples and magnetic field strength up to [Formula: see text] A/m, as annealed after extrusion, non-irradiated with gamma-quanta and the same samples irradiated with gamma quanta at different doses. It was found that at low doses (1 Mrad) of irradiation, radiation defects (RDs) appear in the samples which play the role of donor centers, as a result of which the concentration of free electrons [Formula: see text], and, consequently the electrical conductivity [Formula: see text] increases, and the Seebeck coefficient [Formula: see text] decreases. These defects, scattering the current carriers, reduce their mobility [Formula: see text]. With an increase in the radiation dose, the concentration of defects also increases and free carriers are captured at the level of the RD. In this regard, the concentration of charged carrier defects [Formula: see text] and, consequently, [Formula: see text] of the sample decrease, while the Seebeck coefficient and mobility increase. The effect of a magnetic field on the electrical and thermal parameters of extruded solid solution samples also depends on the radiation dose in the sample.

scholarly journals Modeling of structural and energetic parameters of р-Er1-xScxNiSb semiconductor

2021 ◽  
Vol 22 (3) ◽  
pp. 509-515
Author(s):  
Yu. Stadnyk ◽  
V.A. Romaka ◽  
A. Horyn ◽  
V.V. Romaka ◽  
L. Romaka ◽  
...  
Keyword(s):  
Solid Solution ◽  
Electrical Conductivity ◽  
Free Energy ◽  
Fermi Level ◽  
Substitutional Solid Solution ◽  
Structural Defects ◽  
Free Electrons ◽  
Helmholtz Potential ◽  
Spinoidal Decomposition

The energy expediency of the existence of Er1-xScxNiSb substitutional solid solution up to the concentration x≈0.10 was established by modeling the variation of free energy ΔG(x) values (Helmholtz potential). At higher Sc concentrations, x> 0.10, there is stratification (spinoidal decomposition of phase). It is shown that in the structure of p-ErNiSb semiconductor there are vacancies in positions 4a and 4c of Er and Ni atoms, respectively, generating structural defects of acceptor nature. The number of vacancies in position 4a is twice less than in position 4c. This ratio also remains for p-Er1-xScxNiSb. Doping of p-ErNiSb semiconductor by Sc atoms by substitution of Er atoms is also accompanied by the occupation of vacancies in position 4a. In this case, Ni atoms occupy vacancies in position 4c, which can be accompanied by the process of ordering the p-Er1-xScxNiSb structure. Occupation of vacancies by Sc and Ni atoms leads to an increase of the concentration of free electrons, an enlarge of the compensation degree of semiconductor, which changes the position of the Fermi level εF and the mechanisms of electrical conductivity.

Direct Observation of Monolayer Zones in Al-wt 4% Cu

1990 ◽  
Vol 48 (1) ◽  
pp. 14-15
Author(s):  
B. Jouffrey ◽  
D. Dorignac ◽  
A. Bourret
Keyword(s):  
Solid Solution ◽  
Synchrotron Radiation ◽  
Direct Observation ◽  
Supersaturated Solid Solution ◽  
Original Model ◽  
X Ray ◽  
Image Position

Since the early works on GP zones and the model independently proposed by Preston and Guinier on the first steps of precipitation in supersaturated solid solution of aluminium containing a few percent of copper, many works have been performed to understand the structure of different stages in the sequence of precipitation.The scheme which is generally admitted can be drawn from a work by Phillips.In their original model Guinier and Preston analysed a GP zone as composed of a single (100) copperrich plane surrounded by aluminum atomic planes with a slightly shorter distance from the original plane than in the solid solution.From X-ray measurements it has also been shown that GP1 zones were not only copper monolayer zones. They could be up to a few atomic planes thick. Different models were proposed by Guinier, Gerold, Toman. Using synchrotron radiation, proposals have been recently made.

Is Thermal and Light-Induced Annealing of Met Astable Defects in a-Si:H Driven by Electrons?

1995 ◽  
Vol 377 ◽  
Author(s):  
Helena Gleskova ◽  
S. Wagner
Keyword(s):  
Electrical Conductivity ◽  
Light Intensity ◽  
Defect Density ◽  
Hydrogenated Amorphous Silicon ◽  
Free Electrons ◽  
Free Electron Density ◽  
Independent Variables ◽  
The Third ◽  
Defect Annealing ◽  
Hydrogenated Amorphous

ABSTRACTWe report results of a search for a unifying rate law for the annealing of metastable defects in hydrogenated amorphous silicon (a-Si:H). We tested the hypothesis that defect-annealing by both heating or illumination is driven by the density of free electrons. This hypothesis is formulated via the rate equation - dN/dt = A nα N f (T), where N is the defect density, t the time, A a constant, n the free electron density, and f (T) a function of temperature derived from a distribution of annealing energies. The model fits two sets of data, with light-intensity and electrical conductivity as the independent variables, reasonably well, with a ranging from 0.39 to 0.76, but not the third set, where we varied the temperature.

scholarly journals Synthesis of Ce1−xPdxO2−δ Solid Solution in Molten Nitrate

Catalysts ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 640
Author(s):  
Hideaki Sasaki ◽  
Keisuke Sakamoto ◽  
Masami Mori ◽  
Tatsuaki Sakamoto
Keyword(s):  
Electron Microscopy ◽  
Solid Solution ◽  
Solid Solutions ◽  
Photoelectron Spectroscopy ◽  
Synthesis Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Co Precipitation ◽  
Ionic States

CeO2-based solid solutions in which Pd partially substitutes for Ce attract considerable attention, owing to their high catalytic performances. In this study, the solid solution (Ce1−xPdxO2−δ) with a high Pd content (x ~ 0.2) was synthesized through co-precipitation under oxidative conditions using molten nitrate, and its structure and thermal decomposition were examined. The characteristics of the solid solution, such as the change in a lattice constant, inhibition of sintering, and ionic states, were examined using X-ray diffraction (XRD), scanning electron microscopy–energy-dispersive X-ray spectroscopy (SEM−EDS), transmission electron microscopy (TEM)−EDS, and X-ray photoelectron spectroscopy (XPS). The synthesis method proposed in this study appears suitable for the easy preparation of CeO2 solid solutions with a high Pd content.

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