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2001

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Articles 451 - 480 of 490

Full-Text Articles in Physics

Effect Of Flux Re-Distribution On Resistivity In Granular Ybco, Muhammad Muneeb Asim, Syed Khurshid Hasanain Jan 2001

Effect Of Flux Re-Distribution On Resistivity In Granular Ybco, Muhammad Muneeb Asim, Syed Khurshid Hasanain

Turkish Journal of Physics

Dc resistivity of a zero-field cooled YBCO was previously studied as a function of angle between applied field and transport current. The resistivity followed a sin^{2}\theta variation that was understood as a consequence of Lorentz force like effect. The resistivity deviated from the harmonic curve giving a minimum at low angles before following the true sin^{2}\theta behavior. The angle corresponding to minimum voltage \theta_{min} has been thoroughly studied in this paper as a function of applied field, transport current and temperature. sin^{2}\theta behavior of resistivity is not affected by the fields below Hc1 at their respective temperatures. The angle \theta_{min} …


Schrödinger Equation Solutions For Small R And Resulting Functional Relations, Harry A. Mavromatis Jan 2001

Schrödinger Equation Solutions For Small R And Resulting Functional Relations, Harry A. Mavromatis

Turkish Journal of Physics

The Schrödinger equation is examined for small r (i.e. one step beyond the limit r \rightarrow 0) for the cases V(r) \rightarrow r^k, (k>0), and V(r) \rightarrow r^{-k} (0


Calculation Of The Potential And Electric Flux Lines For Parallel Plate Capacitors With Symmetrically Placed Equal Lengths By Using The Method Of Conformal Mapping, Erhan Albayrak Jan 2001

Calculation Of The Potential And Electric Flux Lines For Parallel Plate Capacitors With Symmetrically Placed Equal Lengths By Using The Method Of Conformal Mapping, Erhan Albayrak

Turkish Journal of Physics

The classical problem of the parallel-plate capacitors has been investigated by a number of authors, including Love [1], Langton [2] and Lin [3]. In this paper, the exact equipotentials and electric flux lines of symmetrically placed two thin conducting plates are obtained using the Schwarz- Cristoffel transformation and the method of conformal mapping. The coordinates x , y in the z-plane corresponding to the constant electric flux lines and equipotential lines are obtained after very detailed and cumbersome calculations. The complete field distribution is given by constructing the family of lines of electric flux and equipotential.


Viscous Dissipation Of Magnetosonic Waves In Solar Corona, Belinda Kalomeni, D. Özlem Hürkal, E. Rennan Pekünlü, Kadri̇ Yakut Jan 2001

Viscous Dissipation Of Magnetosonic Waves In Solar Corona, Belinda Kalomeni, D. Özlem Hürkal, E. Rennan Pekünlü, Kadri̇ Yakut

Turkish Journal of Physics

Wave propagation and dissipation of magnetosonic waves are considered in an inhomogenous viscous coronal plasma permeated by a spatially varying magnetic field. In the linear magnetohydrodynamic approximation the dispersion relation yields two wave modes, fast and slow respectively. Depending on the physical parameters of the medium the damping length scales of the modes show varying behaviours. Damping length scales of the modes show sudden decrease at relevant heights. These drops may be due to phase mixing and resonance absorption. Wave flux density of the magnetosonic waves turns out to be of the order of 10^6 erg cm^{-2} s^{-1}. This is …


The Temperature Dependence Of Dark Conductivity In Hydrogenated Amorphous Sin_X Films, Hüseyi̇n Tolunay, İlker Ay Jan 2001

The Temperature Dependence Of Dark Conductivity In Hydrogenated Amorphous Sin_X Films, Hüseyi̇n Tolunay, İlker Ay

Turkish Journal of Physics

Thin film samples of hydrogenated amorphous silicon nitride with varying nitrogen content were prepared by conventional plasma deposition from a mixture of SiH_4 and NH_3 . The dark conductivity (\sigma_d) of the films have been measured in the temperature range 420 K - 100 K. The conductivity is thermally activated with a single activation energy down to 250 K and conduction is dominated by electrons in extended states. A strong decrease is observed sigma _d when the nitrogen content is increased.


Study Of Slip Systems In Epidote Single Crystal, Salah-Ud Din, Munnawar Ahmad, Shahzad Chishti Jan 2001

Study Of Slip Systems In Epidote Single Crystal, Salah-Ud Din, Munnawar Ahmad, Shahzad Chishti

Turkish Journal of Physics

Measurements of microhardness anisotropy by Knoop diamond indentations on the prismatic (100) planes of epidote crystals, point group 2/m and space group P21/m, show that microhardness is determined by crystallographic slip on the (100) systems. Microhardness anisotropy is explained in terms of the effective resolved shear stress distribution in these slip systems.


Computation Of Overlap, Kinetic And Nuclear Attraction Integrals By A Novel Method, Gökhan Budak, Abdulhali̇k Karabulut, Lütfü Demi̇r, Nagi̇f Sefteroğlu Nabi̇yev, Yusuf Şahi̇n Jan 2001

Computation Of Overlap, Kinetic And Nuclear Attraction Integrals By A Novel Method, Gökhan Budak, Abdulhali̇k Karabulut, Lütfü Demi̇r, Nagi̇f Sefteroğlu Nabi̇yev, Yusuf Şahi̇n

Turkish Journal of Physics

A new way of computing overlap, kinetic and nuclear attraction integrals over Slater functions by means of optimized Gaussian expansion is proposed. This article is concerned with the construction of the general algorithm for evaluating the three integrals. These integral formulae presented in the form of a series whose terms are the analytical function of inter-atomic distances. In the present method, unlike many other popular methods, the numerical integration procedure is unnecessary since it does not contain the incomplete gamma function. The present scheme has been programmed in standard Fortran-77 and tested for various orbitals. The result of the calculation …


A Correlation Of Thin Lens Approximation To Thick Lens Design By Using Coddington Factors In Lens Design And Manufacturing, Ömer Faruk Farsakoğlu, D. Mehmet Zengi̇n, Hi̇kmet Kocabaş Jan 2001

A Correlation Of Thin Lens Approximation To Thick Lens Design By Using Coddington Factors In Lens Design And Manufacturing, Ömer Faruk Farsakoğlu, D. Mehmet Zengi̇n, Hi̇kmet Kocabaş

Turkish Journal of Physics

The effect of Coddington factors on aberration functions has been analysed using thin lens approximation. Minimizing spherical aberrations of singlet lenses using Coddington factors in lens design depending on lens manufacturing is discussed. Notation of lens test plate pairs used in lens manufacturing is also presented in terms of Coddington shape factors.


Some String Cosmological Models In Cylindrically Symmetric Inhomogeneous Universe, Hüsnü Baysal, İlhami̇ Yavuz, İsmai̇l Tarhan, Uğur Camci, İshan Yilmaz Jan 2001

Some String Cosmological Models In Cylindrically Symmetric Inhomogeneous Universe, Hüsnü Baysal, İlhami̇ Yavuz, İsmai̇l Tarhan, Uğur Camci, İshan Yilmaz

Turkish Journal of Physics

The aim of this paper is to investigate the behavior of a string in the cylindrically symmetric inhomogeneous cosmological model. It has been assumed that expansion \theta in the model is proportional to \sigma^1_1 of the eigenvalue of the shear tensor \sigma^{\mu}_{\nu}. Also, various physical and geometrical properties of the model have been discussed.


Photospheric Line Profiles In Deneb (A2 Iae), Berahi̇tdi̇n Albayrak, Cemal Aydin, Dursun Koçer Jan 2001

Photospheric Line Profiles In Deneb (A2 Iae), Berahi̇tdi̇n Albayrak, Cemal Aydin, Dursun Koçer

Turkish Journal of Physics

In this study, the strong lines were examined to determine the effect of velocity gradient due to mass loss on the line profiles in the atmosphere of Deneb. The lines are formed in the optical depth range -1.14 < log \tau < -0.14. None were found to exibit any asymmetry.


Exciton Investigations And The Urbach Tails Of Gd Doped And Undoped Gase, Beki̇r Gürbulak Jan 2001

Exciton Investigations And The Urbach Tails Of Gd Doped And Undoped Gase, Beki̇r Gürbulak

Turkish Journal of Physics

Absorption measurements were carried out in GaSe and GaSe:Gd samples in temperature range 10-320 K in steps 10 K. The first and the second (n=1 and n=2) excitonic levels were marked. The first exciton energies for n=1 were calculated as 2.118, 2.008 eV in GaSe, and 2.125, 2.006 eV in GaSe:Gd at 10, 320 K and respectively. The second exciton energies for n=2 were calculated as 2.140, 2.125 eV in GaSe at 10, 80 K and 2.141, 2.120 eV in GaSe:Gd at 10, 120 K and respectively. Binding energies of GaSe and GaSe:Gd were calculated as (29.46\pm 1 and 21.33\pm …


Lattice Dynamical Calculations For The Co-Fe Alloys, Kemal Çolakoğlu, Yasemi̇n Özteki̇n Çi̇ftçi̇ Jan 2001

Lattice Dynamical Calculations For The Co-Fe Alloys, Kemal Çolakoğlu, Yasemi̇n Özteki̇n Çi̇ftçi̇

Turkish Journal of Physics

Lattice dynamical calculations are performed on Co_{0.92}-Fe_{0.08} alloy with fcc structure. The de Launay Angular force (DAF) model is used to represent the ion-ion intreactions, and the long-range ion-electron interactions are accounted for along the lines of the Sharma-Joshi scheme. The frequency distribution and the lattice specific heat are also computed for the studied alloys. The present theoretical results are in reasonable agreement with the available experimental data.


The Investigation Of The Thermoluminescence Emission Bands Of Lif:Mg,Ti (Tld-100) By A Simple Developed Model, A. Necmeddi̇n Yazici, Z. Öztürk, M. Bedi̇r Jan 2001

The Investigation Of The Thermoluminescence Emission Bands Of Lif:Mg,Ti (Tld-100) By A Simple Developed Model, A. Necmeddi̇n Yazici, Z. Öztürk, M. Bedi̇r

Turkish Journal of Physics

In this study, a new simple model based on the classical treatment of lattice vibrations and the Franck-Condon principle is developed to describe the shape of thermoluminescence (TL) emission bands of crystalline solids. According to developed model, shape of the emission band has a Gaussian form and depends on just two physical parameters: peak energy E_{0} and broadening of emission spectra U. In order to demonstrate the success of the developed model, the emission spectra of dosimetric material LiF:Mg,Ti (TLD-100) was also measured. Then, a computerised best-fit program including the developed model was used to analyse the emission spectra. The …


Second Order Elastic Constants And Some Thermoelastic Properties Of Alkali Halides Using Woodcock Potential, Harun Reşi̇t Yazar, Sedat Ağan, Kemal Çolakoğlu Jan 2001

Second Order Elastic Constants And Some Thermoelastic Properties Of Alkali Halides Using Woodcock Potential, Harun Reşi̇t Yazar, Sedat Ağan, Kemal Çolakoğlu

Turkish Journal of Physics

Second Order Elastic Constants (S.O.E.C) of NaCl-type crystals have been calculated using the Woodcock potential. Short-range repulsive interactions have been included up to second-nearest neighbors. This potential form represents the composite form of the inverse power dependence and exponential dependence of the repulsive energy on interionic distance. Some thermoelastic and thermodynamic properties such as Anderson-Grüneisen parameters \delta _{T}, and \delta _{S}, Volume thermal expansion coefficient \beta and Grüneisen gama \gamma _{G} have been calculated in terms of calculated values of S.O.E.C and Third Order Elastic Constant ( T.O.E.C).


Built-In Potential Measurements In A-Si:H P-I-N Solar Cells, Ruhi̇ Kaplan, Bengü Kaplan Jan 2001

Built-In Potential Measurements In A-Si:H P-I-N Solar Cells, Ruhi̇ Kaplan, Bengü Kaplan

Turkish Journal of Physics

We have measured the open-circuit voltage V_{oc} and the short-circuit current density J_{sc} of amorphous silicon (a-Si:H) p-i-n solar cells deposited by radio-frequency plasma-enhanced chemical vapor deposition (RF-PECVD) at different monochromatic illuminations, and temperatures. From the measurements, the built-in potential V_{bi} was determined by using two different methods: activation energy and differential temperature. The results from both methods were analyzed and compared as a function of excitation wavelength. It was observed that there is good agreement between the two methods. We found that V_{bi} increases until about 650 nm, and then decreases with increasing wavelength. This behaviour is explained and …


Space Charge Limited Current At High Fields In Al-Ge-Al Surface Barrier Devices, A. I. Mukolu Jan 2001

Space Charge Limited Current At High Fields In Al-Ge-Al Surface Barrier Devices, A. I. Mukolu

Turkish Journal of Physics

The current-voltage (I-V) characteristics of Aluminium-Germanium-Aluminium (Al-Ge-Al) surface barrier devices at different fields (


Null String In Curved Backgrounds, Sergey Nikolaevich Roshchupkin Jan 2001

Null String In Curved Backgrounds, Sergey Nikolaevich Roshchupkin

Turkish Journal of Physics

We consider null string in curved backgrounds. Some exact solutions of the classical equations of motion and of the constraints for the null string in a large class of cosmological backgrounds are found.


On The Evaluation Of Determinantal Wave Functions In Open-Shell Hartree-Fock Theory, I. I. Guseinov, Ramazan Demi̇r Jan 2001

On The Evaluation Of Determinantal Wave Functions In Open-Shell Hartree-Fock Theory, I. I. Guseinov, Ramazan Demi̇r

Turkish Journal of Physics

Slater method is modified for the evaluation of determinantal wave functions appearing in open-shell Hartree-Fock (HF) theory [1]. Using modified Slater method we have calculated, as an example, the orbital energies and the wave functions of terms obtained from the electronic configuration of a ground state of an N-atom system in the Hartree-Fock-Roothaan (HFR) approximation. The modified determinantal method introduced in this paper can be of considerable help and importance in the simplification and calculation of atomic and molecular electronic structure.


The Langmuir Properties Of A Mixed Copolysiloxane Monolayer, Rifat Çapan, Tim H. Richardson, David Lacey Jan 2001

The Langmuir Properties Of A Mixed Copolysiloxane Monolayer, Rifat Çapan, Tim H. Richardson, David Lacey

Turkish Journal of Physics

A family of linear copolysiloxanes [1-3] substituted with side chains containing carboxylic head groups has been synthesised. The Langmuir properties of the mixed monolayer at the water-air interface has been studied using a single layer Langmuir trough. The area per molecule for the mixed monolayer is calculated theoretically and experimentally. This study has not only shown that there is an excellent agreement between theoretical and experimental values, but has also shown that this mixed monolayer at the water-air interface can be transferred as a monolayer onto a solid substrate.


Lattice Changes In Shape Memory Cuznal Alloys On Aging At Room Temperature, Seyfetti̇n Çakmak, Ekrem Artunç, Nejdet Kayali, Osman Adigüzel Jan 2001

Lattice Changes In Shape Memory Cuznal Alloys On Aging At Room Temperature, Seyfetti̇n Çakmak, Ekrem Artunç, Nejdet Kayali, Osman Adigüzel

Turkish Journal of Physics

The aging behavior of CuZnAl martensites (Cu-21.62 wt.% Zn-5.68 wt.% Al and Cu-24.98 wt.% Zn-4.43 wt.% Al) at about 297 K was studied by analyzing diffraction line profiles obtained by X-ray diffractometry. For the alloys, the change of the lattice parameters and the tetragonality associated with the aging time at room temperature were investigated. The habit planes versus the aging time at room temperature were calculated using the De Vos-Aernoundt-Delaey model, based on the crystallographic theory of Wechsler-Lieberman-Read(WLR), and from the DO_{3}\rightarrow 18R martensite transformation theory.


Physical Properties Of Melt-Cast Annealed Bi_{1.6}Pb_{0.4}Sr_{2}Ca_{3}Cu_{4} O_{12} Compound, Ati̇lla Coşkun, Beki̇r Özçeli̇k, Keri̇m Kiymaç Jan 2001

Physical Properties Of Melt-Cast Annealed Bi_{1.6}Pb_{0.4}Sr_{2}Ca_{3}Cu_{4} O_{12} Compound, Ati̇lla Coşkun, Beki̇r Özçeli̇k, Keri̇m Kiymaç

Turkish Journal of Physics

A Bi_{1.6}Pb_{0.4}Sr_{2}Ca_{3}Cu_{4}O_{12} compound was produced by melt-casting method. The microstructure of the sample was studied by Scanning Electron Microscopy. Phase analysis was carried out by X-ray diffraction patterns and EDAX. The electrical resistance exhibites the existance of a superconducting phase with an onset temperature T_{c} at 110 K along with a minor phase with an onset T_{c} at 80 K. It has been found that the superconducting phase temperature T_{c} increases with increasing sintering temperature.


The Theoretical Analysis Of The Second Order Coherence G^{(2)}(\Tau) And Power Stabilization Of Two-Mode He-Ne Laser, Erol Taşal, M. Selami̇ Kiliçkaya Jan 2001

The Theoretical Analysis Of The Second Order Coherence G^{(2)}(\Tau) And Power Stabilization Of Two-Mode He-Ne Laser, Erol Taşal, M. Selami̇ Kiliçkaya

Turkish Journal of Physics

In this study, second-order coherence and its frequency-dependent characteristics and the photon statistical properties of the two-mode He-Ne laser field are investigated.


Electrical Characterization Of Gate And Gate:Cu Semiconductor Compounds, Hüsnü Sali̇h Güder, Bahatti̇n Abay, Hasan Efeoğlu, Cevdet Coşkun, Şaki̇r Aydoğan, Yahya Kemal Yoğurtçu Jan 2001

Electrical Characterization Of Gate And Gate:Cu Semiconductor Compounds, Hüsnü Sali̇h Güder, Bahatti̇n Abay, Hasan Efeoğlu, Cevdet Coşkun, Şaki̇r Aydoğan, Yahya Kemal Yoğurtçu

Turkish Journal of Physics

Electrical properties of GaTe and GaTe:Cu binary compound semiconductors were investigated by Hall effect and resistivity measurements in the 77-320 K temperature range. Donor and acceptor densities, compensation ratios, acceptor ionization energies, valence band effective mass of holes and effective density of states in valence band were determined for the undoped and Cu doped samples using the single donor-single acceptor analysis of the hole concentration. Temperature coefficient of the hole mobility was determined and compared with related theories.


Effect Of Nitriding On Phase Transformations In The Fe-Mn Alloys, K. G. Binnatov, I. I. Ali-Zade, A. O. Mekhrabov Jan 2001

Effect Of Nitriding On Phase Transformations In The Fe-Mn Alloys, K. G. Binnatov, I. I. Ali-Zade, A. O. Mekhrabov

Turkish Journal of Physics

We present results concerning the nitriding effects on phase transformations in Fe -- 40 at. % Mn and Fe -- 50 at. % Mn alloys. These alloys were studied by means of X-ray diffraction and Mössbauer-effect spectroscopy methods at room temperature. Results indicate that, after nitriding, in the absorption spectra of these alloys appears lines with hyperfine field H\sim 330 kOe which corresponds to the field on the ^{57} Fe nuclei in the \alpha -Fe. Annealing of the alloys at 650 ^oC temperature (nitriding temperature) in argon atmosphere do not change the form of the M\\"{o}ssbauer absorption spectra. It appears …


Urbach-Martienssen's Tail In Layered Ternary Semiconductor Tlgas_{2}, Bahatti̇n Abay, Hüsnü Sali̇h Güder, Hasan Efeoğlu, Yahya Kemal Yoğurtçu Jan 2001

Urbach-Martienssen's Tail In Layered Ternary Semiconductor Tlgas_{2}, Bahatti̇n Abay, Hüsnü Sali̇h Güder, Hasan Efeoğlu, Yahya Kemal Yoğurtçu

Turkish Journal of Physics

Dependence of the absorption coefficient on the photon energy and temperature near the fundamental absorption edge was measured for layered single crystal TlGaS_{2}. The exponentially increasing absorption tail was explained as an Urbach-Martienssen's (U-M's) tail for TlGaS_{2} samples in the 10-340 K temperature range. The characteristic Urbach's parameters such as steepness parameter [\sigma (T)] and Urbach's energy [(E_{u} = k_{B} T / \sigma )] were determined. Analyzing the temperature dependence of these parameters based on the general models, which takes into account the possible role of several different types of disorder, we conclude that the absorption process in the fundamental …


Optical Absorption And Photoluminescence Measurements In Inp And Inp:Fe Bulk Crystals And Inspection Of The Relations Between These Measurements, Seydi̇ Doğan, Sebahatti̇n Tüzemen, Beki̇r Gürbulak, Aytunç Ateş, Muhammet Yildirim Jan 2001

Optical Absorption And Photoluminescence Measurements In Inp And Inp:Fe Bulk Crystals And Inspection Of The Relations Between These Measurements, Seydi̇ Doğan, Sebahatti̇n Tüzemen, Beki̇r Gürbulak, Aytunç Ateş, Muhammet Yildirim

Turkish Journal of Physics

Optical absorption and photoluminescence (PL) measurements were carried out in both undoped and Fe-doped samples and the effect of Fe doping on absorption and PL spectra were studied. The results show that Fe or Fe-related defects behave as non-radiative recombination centers in InP. This is very important from the point of view that the control of minority carrier lifetime is possible. On the other hand, comparative analysis of the PL results with the optical absorption data show that quantitative assessment of relative PL intensities is possible with respect to Fe concentrations.


The Effect Of Phonon Drag Of Charge Carriers In In_{1 - X} Ga_{X} Sb, Sadiyar Ahmedoglu Zeynalov Jan 2001

The Effect Of Phonon Drag Of Charge Carriers In In_{1 - X} Ga_{X} Sb, Sadiyar Ahmedoglu Zeynalov

Turkish Journal of Physics

The temperature dependencies of the thermal power a_{0} and thermal conductivity \kappa in two samples of In_{1 - x} Ga_{x}Sb (x=0.65 and 0.45) doped by {Te\sim } 0.001 at\%, with electron concentration n = 5.9 \cdot 10^{16} and 1.3 \cdot 10^{17} cm^{ - 3} (at 100K), have been investigated. It is shown that in In_{0.35}Ga_{0.65}Sb a_{0} increases with decreasing T below 50K. At 14K a_{0} passes through maximum and it falls sharply with decreasing T. It is shown that the maximum value of a_{0} is in agreement with the maximum value of \kappa . In In_{0.55}Ga_{0.45}Sb, starting from T = …


Diamondlike Carbon Thin Film Deposition Using A Rf Planar Coil Inductively Coupled Plasma System, Wai Soon Liew Jan 2001

Diamondlike Carbon Thin Film Deposition Using A Rf Planar Coil Inductively Coupled Plasma System, Wai Soon Liew

Student Works (2000-2009)

A RF planar coil inductively coupled plasma system (ICPs) is setup for this project. The system is powered by a 13.56MHz, 550W, 500 RF generator. The RF power is transferred to the plasma via a planar induction coil. The impedance matching circuit consists of an air-core step-down transformer and a tunable vacuum capacitor. The typical E-H mode transition which is distinctive to the ICP has been observed in argon plasma, hydrogen plasma and hydrogen-methane admixture plasma. The studies carried out include the observation of intensity of light emission from the plasma, the power transferred at different pressures, the concentration of …


Optical Coherent Communication System Using Phase Shift Keying, Syed Javaid Iqbal Jan 2001

Optical Coherent Communication System Using Phase Shift Keying, Syed Javaid Iqbal

Student Works (2000-2009)

This thesis presents the experimental study and design of a coherent communication system by using phase shift keying (PSK). Systems are designed by using all passive elements, which make the system very easy to operate, and less maintenance is required. All the PSK designs are based on a single light source. In this thesis there are five different types of PSK with a single light source communication systems are designed. All designs are experimentally tested in free space. The systems are • All optical two-channel PSK communication system, by using single light source, "All optical single channel, two-way PSK communication, …


Infared Spectroscopy And Electrical Conductivity Of Copper(Ii) Cinnamate And Iodine-Doped Copper(Ii) Cinnamate, Kumar Krishnan Jan 2001

Infared Spectroscopy And Electrical Conductivity Of Copper(Ii) Cinnamate And Iodine-Doped Copper(Ii) Cinnamate, Kumar Krishnan

Student Works (2000-2009)

Copper(II) cinnamate (CC) was prepared from copper(II) acetate monohydrate and cinnamic acid. It was a light-blue powder. The Fourier Transform Infrared (FTIR) spectrum of CC, recorded as potasium bromide (K.Br) disc, indicated the presence of all bonds and functional groups expected of it and showed that it exist as an equal mixture of cis- and trans- isomers. The conductivity of CC at room temperature was 5.22 x 10⁻¹¹Scm⁻¹. It showed metallic behaviour in the temperature range 78-300 K, and its conduction mechanism obeyed Mott's variable range hopping (VRH) model in the same temperature range. The density of states at Fermi …