TEMPERATURE DEPENDENCE BEHAVIOR OF ELECTRICAL RESISTIVITY IN NOBLE METALS AT LOW TEMPERATURES

Resistivity temperature – dependence and residual resistivity concentration-dependence in pure noble metals(Cu, have been studied at low temperatures. Dominations of electron – dislocation and impurity, electron-electron, and electron-phonon scattering were analyzed, contribution of these mechanisms to resistivity were discussed, taking into consideration existing theoretical models and available experimental data, where some new results and ideas were investigated.


Introduction
Portable devices on satellites greatly affected by fluctuations in temperature in outer space, especially the electrical resistance that it needs to adjust with very high accuracy to receive high quality information on the earth stations.
Since 1864, Matthiessen's rule of the total resistivity of metals [1,2,3] was discovered by Augustus Matthiessen as an empirical rule.The total resistivity is the sum of many mechanisms results from the scattering of conduction electrons by thermal lattice vibrations and imperfections such as impurity atoms, interstitials, dislocations, and grain boundaries. Noble metals resistivity have been developed in a very large, across very advanced technologies to estimate the purity of these elements and their alloys [4,5,6,7].Matthiessen's rule is a basis for understanding the resistivity behavior of metals and alloys at high and low temperatures.
In general, the electrical resistivity (ρ (T)) of pure noble metals [8,9,10,11 ] consists of the residual resistivity (ρ0) (originating mainly from imperfections within the structure of the material) and the temperature-dependent resistivity (ρL(T )) arising due to electron-phonon (lattice) interactions, which may be written by an empirical form : A single crystal of noble metals would have a lower residual resistivity than polycrystalline that cause an increase in the scattering of electrons, and reducing the mean free time between collisions. The amplitude of the second term increases with increasing temperature, and the more they interfere with conduction .
In magnetic noble metals alloys [12], the dynamics of the spin system are usually such that the spins remain in thermal equilibrium down to very low temperatures. Magnetic impurities play a double contribution, the first in residual resistivity as imperfections, the second as temperaturedependent disorder magnetic resistivity, in which case it is more usual to express total resistivity as: Where ρm(T )is the temperature-dependent magnetic contribution resulting from spin-disorder.
Matthiessen's rule is an approximation and is not universally valid ,because not only residual resistivity and resistivity of the pure ideal metal(electron-phonon scattering contribution) but also many mechanisms contribute to resistivity which cause a deviation from Matthiessen's rule(DMR) [13,14,15,16 ],for this reason DMR may be added as this form: Where Δρ (T) represents all contributions to resistivity temperature and concentration dependent, which come from DMR.
The purity of noble metals could be calculated from residual resistivity ratio (RRR) [17,18] Where the RRR is defined as the ratio of the electrical resistivity at two temperatures: 273K (the ice point) and 4.2 K (the liquid helium normal boiling point) and may be written as( RRR =ρ(273K)/ρextrap(4.2K). Sometimes, the room temperature resistivity ρ(T=300 K) is used instead of the resistivity at ice point ρ(T=273K). RRR values serve as a convenient measure of the purity of the metal and is often used as a material specification for superconductors.
In addition, the Debye temperature θD (the temperature of a crystal's highest normal mode of vibration), Size dependence of θR and size effects, generally cause a DMR because the phonon spectrum changes by physical defects [19,20,21].
The aim of this paper is to comparison between predictions of theoretical models and the experimental data and trying to check an excellent agreement with each other.

Theoretical Quantum Mechanics Background
In general, the resistivity of pure noble metals [22] is composed of the residual resistivity, resistivity due to electronphonon interactions and the resistivity due to electron-electron scattering. The total resistivity ρ can be written as: Scattering by lattice vibrations (phonons) is temperature dependent and the rate 1/ phonon  depends on the intrinsic at high temperatures (above the Debye temperature) the number of phonons per unit volume is proportional to the temperature and ρph is proportional to T. At low temperatures, two effects come into play. The number of phonons falls as T 3 because of phonon drag and U-processes; moreover, the energy and momentum of these phonons become small, and phonon drag contribution sometimes neglected because noble metals have spherical Fermi surfaces so that they are ineffective in scattering electrons. Consequently, the resistivity falls more quickly than the phonon density as T 5 because of N-processes.
In simple metals such as noble metals (bulk), the temperature-dependent part ( ) phonon  At high and low temperature relation (7) has exact solution yielding the following proportionalities: At the lowest temperatures goes to zero and the overall resistivity reduces to the residual resistivity.
At low temperature, the normal electron-electron scattering does not contribute to the electrical resistivity because in such collisions, the charge and the momentum are conserved. Whereas, Umklapp processes most of momentum impart to the lattice as a whole and they can thus contribute to the electrical resistivity. In addition, Umklapp processes contribution is greatly reduced due to the operation of the Pauli's exclusion principle between initial and final states. The expression for resistivity ρee(T) due to electron-electron Umklapp scattering processes can be written as [28,29,30,31,32,33]

Experimental database
In a previous study by AL-Jalali [34,35]; the papers have concentrated only on magnetic resistivity in magnetic dilute alloys. But this paper will treat all other resistivities,and will concentrate on total resistivity in the pure noble metals. Review experimental data from crude results [36,37,38,39,40,41,42], for Copper,Silver and Gold, which belong to resistivity as a function of temperature will be analyzed to discover all mechanisms that contribute in noble metals resistivity, and calculate more than constant by comparison between theoretical and experimental expressions.

Results and Discussion
At low temperatures, analysis of experimental data for normal metals resistivity has a general expression as a sum of many contributions(additive law) and take a general form: Where A, B, C are very important constants to calculate many theoretical constants, which is difficult to know them without comparison between these experimental and theoretical formulae.
Also at high temperatures all contributions vanish except phonons and impurity resistivity, and resistivity will become:  It is found that; Residual resistivity as a function of concentration is a mixed from Nordheim's rule [43] for one kind of normal impurity: In addition, Mott's rule for tow kind of normal impurity [44]: Where A, B are constants. Figures (4, 5) show a changing between residual resistivity and concentration; it is expected that the samples contain more than one kind of impurities. Unfortunately, the experimental results calculate the total residual resistivity and could not discriminate between the origins of its mechanisms. firsr Theoretical attempt was made by blatt [45] to calculate resistiveties due to vacancies and interstitials and found that: However, many attempts were made by neutron scattering, which need deeper investigations.
In order to calculate intrinsic resistivity, the basic step is to subtract residual resistivity from total resistivity, as the following relation:  (6,7,8) show intrinsic resistivity for noble metals (Cu, Ag, Au) as a function of temperature. Precise mathematical analysis shows the existence of new (terms) mechanisms were not taken into account , like T 2.5 , T 1.5 ,T 0.5 ,…etc., These mechanisms do not appear, but the presence of magnetic impurities, which appear from spin waves at low temperatures. Debye temperature for face centered cubic (fcc) (Ag, Au, Cu,) metals, near absolute zero and in terms of the elastic constants of the solid. The Debye characteristic temperature is given by [46]: The minimum wavelength corresponding to the Debye temperature, This wavelength should be equivalent with the length of the smallest unit cell.At frequencies higher than the cut off frequency the "lattice" unable to "see" the vibration because the wavelength of the vibration is smaller than the basic unit of the atomic arrangement; therefore, the vibration becomes independent from the lattice. The Debye cut off frequency or temperature separates the collective thermal lattice vibration from the independent thermal lattice vibration. Figure ( Debye temperature can be estimated from the melting point (Tm) of the crystal using the Lindemann relation [49,50]: Where C is a constant depending on the X-ray intensity data structure. V unit volume was estimated from the lattice constant, M Molecular weight . Debye temperature estimated from resistivty less than 4% from estimated from specific heat .
Finally, the agreement between theoretical and experimental was somewhat acceptable.

Conclusion
Purity of pure Copper was RRR=772, Silver was RRR=1465 and Gold was RRR=93. 2, which means that many impurities may be found in the samples. This result explains why residual resistivity has a power series equation.
New terms have been found in total resistivity during analysis data, like T 3 , which belong to phonons U-processes, and T 2.5 , T 1.5 , T 0.5 , which belong to magnetic origin.In addition, Debye temperature and some theoretical constant were treated.
Most of all predictions of theoretical models was an agreement with analyzing experimental data, but need more investigation to reach to an agreement with each other. O c t o b e r 1 5 , 2 0 1 4