Magnetoconductivity of icosahedral AlPdRe at temperatures between 50-250 Kelvin

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Magnetoconductivity of icosahedral

AlPdRe at temperatures between

50-250 Kelvin

Master’s thesis by

Sana Ullah

Materials and Nanophysics

School of Information and Communication Technology

The Royal Institute of Technology

Stockholm, 2013.

TRITA-ICT-EX-2013:234

sanau@kth.se

Supervisor

Magnus Andersson

Associate Professor at The Royal Institute of Technology

magnusan@kth.se

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List of Figures

2.1 Weak localization[10]. . . 8

3.1 An arc furnance[7]. . . 11

3.2 Melt spinning [19]. . . 12

3.3 The Czochralski technique[7]. . . 13

3.4 Powder diffraction of i-AlPdRe [7]. . . 13

3.5 Resistance vs temperature for sample RRR=71 (50K to 250K). 14 3.6 The magnetoresistance of i-Al-Pd-Re with RRR value 10.4 in the temperature range of 0.24 K to 40.3 K at 6T[21]. . . 16

3.7 4-pole technique[7] and Multimeter for measuring contact re-sistance between pads. . . 16

3.8 Principal sketch of the space in the continuous flow cryostat[7]. 18 3.9 Long sample holder, only the bottom part is shown. . . 18

3.10 Sensitivity of carbon glass and platinum thermometer[23]. . . 20

3.11 Magnetoresistance vs magnetic field for sample Al-Pd-Re . . . 21

4.1 Magnetoresistance of the sample with RRR=10 at 50 K, 100 K and 175 K up to 12 T. . . 22

4.2 Magnetoresistance versus magnetic field of sample RRR=10 at 250 K up to 12 T. . . 23

4.3 Magnetoresistance of the sample with RRR=31 at 50 K, 100 K and 175 K in fields up to 12 T. . . 23

4.4 Magnetoresistance of the sample with RRR=31 at 250 K up to 12T. . . 24

4.5 Magnetoresistance of the sample with RRR=71 at 50 K, 100 K, 175 K and 250 K up to 12T. . . 25

4.6 Magnetoresistance of the sample with RRR=220 at 50 K, 100 K and 175 K up to 12T. . . 26

4.7 Magnetoresistance of the sample with RRR=220 at 250 K up to 12T. . . 27

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4.9 Magnetoresistance as a function of temperature at 12T. . . 28 4.10 Magnetoresistance as a function of temperature for sample

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Abstract

The electrical conductivity of icosahedral Al70.5P d21Re8.5 samples with

resid-ual resistance ratio RRR = ρ(4.2K)/ρ(295K), in the range from 10 to 220 are reported. The samples were manufactured by melting in an arc furnace and then annealed at 940 ◦C. One of the samples (RRR=10) was made by melt spinning. In this work, the magnetoresistance, MR, and resistivity, ρ(T ), of the samples with RRR values 10, 31, 71 and 220 has been measured in the temperature range from 50 K to 250 K and the magnetic field up to 12 Tesla.

The electronic transport properties of the sample Al-Pd-Re strongly de-pend upon temperature. The ρ(T ) increases with decreasing temperature. The MR of the sample is larger than the MR of most metals. At 50 K, MR increases with increasing magnetic field for samples with RRR value of 10, 31 and 220. At 100 K and 175 K, MR decreases with increasing magnetic field. But MR at 100 K decreases more than MR at 175 K. At 250 K, MR increases even more than MR at 50 K, which is very strange behaviour. Sample with RRR value 71, MR behaviour is quite different from remaining samples. MR of this sample decreases with increasing field, at decreases more at 175 K and less at 250 K.

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Acknowledgements

In this master thesis I will present a work carried out within the Solid State Physics group (FTF) at the School of Information and Communication Tech-nology (ICT)of the Royal Institute of TechTech-nology (KTH). The work presented here was carried out in 2013 at the Cryogenic lab at KTH, Kista.

I would very much like to thank Assoc. Prof. Magnus Andersson, my supervisor and examiner to give me an opportunity to work under his kind supervision. He help me a lot in the lab to get familiar with instruments and always had time to answer my questions.

I would also like to thank Prof. ¨O. Rapp, for providing samples and helpful discussions.

I would like to thank Fasee, Bejan, Amin, Sathya, Osma, Alex, and Amjid for their friendship and encouragement. Thank you all for your support when I have needed.

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Chapter 1 Introduction

In 1984 scientists D.Shechtman et al created a quasicrystalline material in a rapidly cooled alloy of aluminium (Al) and manganese (Mn) [1]. This alloy showed 5-fold rotational symmetry, which is not allowed in classical physics, where only 2, 3, 4 and 6-fold rotational symmetries are allowed. Quasicrystals have an ordered structure, but are non-periodic. They fill all the available space, but lack the translational symmetry. The first quasicrystalline system was metastable. After the first discovery of quasicrystal, three other sys-tems were soon introduced [2]. These syssys-tems were stable, but disordered as investigated in X-ray and electron diffraction. The first stable and high qual-ity quasicrystals (i.e icosahedral Al-Pd-Mn and Al-Cu-Fe) was discovered by Tsai and colleagues [3],and they showed X-ray diffraction peaks which have a width that comparable to the peak widths of perfect crystals. It was dif-ficult to distinguish the intrinsic properties of quasicrystalline materials, as they were highly structural disordered. Quasicrystal are normally found in aluminium alloy systems like (Al-Pd-Mn, Al-Cu-Fe, Al-Mn-Si, etc) but also with some other alloys like (Ti-Zr-Ni, Cd-Pb, Zn-Mg-Sc, etc)[4][5].

The electronic transport properties of these quasicrystals strongly depend upon temperature. As the temperature decreases resistivity increases. This strong temperature dependence is characterized by the residual resistance ratio defined as RRR = ρ(4.2K)/ρ(295K) and with typical resistivity values from 1-20mΩcm at room temperature[6][7] RRR values range from 1-280.

The electronic transport property of quasicrystalline materials are effected by Quantum Interference Effects, QIE at low temperature[7].Quantum in-terference effects are predominantly influenced by structural and electronic charge configuration. However the resistivity of highly resistive quasicrystal, (e.g. Al-Pd-Re) increases, which result in break-down of QIE. It is still un-known whether highly resistive quasicrystals can become insulating.

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remain curious materials with unusual structure. However, some commer-cial application have been found such as dispersoids in high-strength surgical steel, and in composite Al alloys having high strength and ductility[8]. New uses are being explored in research labs such as thermal barrier coating, small scale thermoelectric elements, H2 storage materials etc.

In this project, I worked with Al-Pd-Re samples with residual resistance ratio values 10, 31, 71 and 220. They were measured in the temperature range of 50 K to 250 K and in applied magnetic field up to 12 Tesla.

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Chapter 2 Theory

In this section, I will briefly describe the effects which can affect the trans-port property of quasicrystals at helium temperature. However in my degree project, I worked at higher temperature (50-250 Kelvin).

The quantum interference theory has great importance in transport prop-erties of disturbed atomic structure materials. When stable quasicrystals were discovered [3] in 1990’s, a number of theories were developed to under-stand the transport property of quasicrystals. The Quantum Interference Ef-fects, QIE, has contributions from both weak localization, WL, and electron electron interactions, EEI, [9]. These theories are briefly discussed below.

2.1 Weak Localization

In disordered systems, electron motion is diffusive, i.e electrons do not travel

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in straight lines from one point to other. Electrons always experience scat-tering due to impurities which diverts their directions. There are many ways to reach from one point to another as shown in the diagram. This physical phenomenon occurs at low temperature in disordered electronic materials [10] and is known as weak localization.

Magnetoresistance MR, is proportional to resistivity in weak localization. A strong increase of MR is seen at low RRR value at 1.5 K[11]. The theory of WL breaks down with RRR value above 10 at 4.2 K as MR decreases with increasing magnetic field.

2.2 Electron Electron Interaction

Another effect that occurs in the transport property is due to the electron electron interaction (EEI). EEI in disordered electronic metals occurs due to elastic scattering of conduction electrons. In such disordered metals, this effect is more effective on the electronic transport property. In 1979 it was first discussed by Aronov and Altshuler[12] and is also know as the Coulomb anomaly. In the EEI theory, interactions are considered between two elec-trons.

There are mainly two contributions to electron electron interaction. One is known as the diffusion channel contribution (from particle-hole channel) and the other is known as the Cooper channel contribution (from particle-particle channel). Both cooper channel contribution and diffusion channel contribution refer to two different terms. One type of term is Hartree term, which is related to weak localization and can be described as the interac-tion between two charges. The second type of term is exchange term which is also the interaction between charges but with a momentum transfer and small energy difference.

EEI can account for MR for sample with RRR value up to 10[9]. It has been seen that at 4.2 K for sample with RRR=5, MR increases with resistivity. MR of the sample decrease with increasing magnetic field.

2.3 Quantum Interference Effects (WL+EEI)

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Material Range(kelvin) Contributions Ref. AlCuFe 0.15-20 WL+EEI [13] AlCuFe 1.5-60 WL [14] AlCuFe 0.3-100 WL+EEI [15] AlCuRu 1.5-20 EEI [16] AlPdMn 0.5-100 WL [17] Table 2.1: Quasicrystal materials and temperature range where QIE success-fully have accounted for conductivity of i-QC.

2.4 Metal-Insulator Transition

A model was proposed by Wilson [18] in 1931 to distinguish the difference between an insulator and a metal. A material is classified as a metal if at T=0 it has finite conductivity and is an insulator if at T=0 it has no conductivity [19]. There are mainly two mechanisms that lead to a metal insulator transition, (MIT). Firstly, the transition may occurs due to change in the physical structural effect, e.g., composition of lattice or specific volume of the lattice. Secondly, the transition can be electronic and is in such case explained by model such as localization of wave function.

The latter type of MIT is classified into two types of transition, i.e Mott or Mott-Hubbard transition and Anderson transition. The Mott transition is due to many electron effects while Anderson transition is due to single electron effects.

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Chapter 3 Samples and Experimental

Techniques

In this section, I will briefly describe the sample preparation and charac-terization, as described by [7][19]. Different techniques were used in the preparation of the icosahedral Al-Pd-Re as described below.

3.1 Sample Preparation

Quasicrystals can be prepared with three different process i.e a) Quenched in a arc furnace and annealed b) Annealed, molten,and meltspun and c) as single grains pulled with a Czochralski technique. These different process are briefly explained as below.

The standard tool for preparing sample by melting is an arc furnace as

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shown in Figure 3.1. In such a technique,a tungsten tip is positioned on the sample, which is placed on a water cooled plate. This plate is usually made of copper. Inside the glass container, argon gas is used during the sample preparation. A high voltage is applied between copper plate and tip, which create an arc on the sample and as a result it melt the sample. To achieve a good homogeneity, the ingot is turned and remelted and after several repeti-tion a good homogeneity is achieved.

Another method for sample preparation is melt spinning as shown in Figure 3.2.

Figure 3.2: Melt spinning [19].

The ingot is placed at the bottom of a quartz tube in a RF-coil. In the quartz tube the melted ingot is pressurized and the melt is quenched on a rotating cool copper wheel, and as a result ribbon is produced. The typically speed of the rotating copper wheel is 30-40 m/s which produces ribbons of a thickness of 30-50µm .

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Figure 3.3: The Czochralski technique[7].

Once the sample is prepared, its quality is improved by annealing. During the annealing process, the sample is in an inert gas or in vacuum. The quality of the sample can be indicated by its resistivity[6][7], as a high resistivity is considered as a sign of high quality quasicrystals and a high RRR value. Annealing process is more effective at 800 ◦C or temperature above.

3.2 Sample Characterization

There are a few standard method in determining the quality of quasicrsy-talline samples such as X-ray diffraction and scanning electron microscope (SEM).

The standard tool for the characterization of the sample is X-ray diffrac-tion. A typical diffraction pattern is shown in Figure 3.4[7]. It shows strong

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peaks for the quasicrystalline phase and low peak of the disordered material. To study the sample morphology and homogeneity, a standard scanning elec-tron microscope,(SEM) is used. SEM distinguishes between a primary and a secondary phase. As shown in Figure 3.4, the quascrystalline peaks are represented by 6 Miller indices (h,h’,k,k’,l,l’) instead of 3 (h,k,l), to explain the symmetry of icosahedral phase.

3.3 Transport Measurement

Transport properties of the sample are improved by improving the quality of the icosahedral phase of the sample as shown in AlPdRe [7]. Also the residual resistance ratio RRR = ρ(4.2K)/ρ(295K), which is a measure of temperature dependence of the resistivity is measured accurately. The residual resistance ratio, (RRR) value is calculated by simply taking the ratio of the resistances at 4.2 K and 295 K. As shown in Figure 3.5,(the temperature range should be from 295 K to 4.2 K, but here it is shown only in the range from 50 K to 250 K as I measured resistance in this range only). As the temperature decreases, the resistance of the sample increases.

Figure 3.5: Resistance vs temperature for sample RRR=71 (50K to 250K).

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applied magnetic field up to 12 Tesla.

RRR MR measured (K) Preparation method 10 50, 100, 175, 250 Melt spinning 31 50, 100, 175, 250 Arc furnace 71 50, 100, 175, 250 Arc furnace 220 50, 100, 175, 250 Arc furnace

Table 3.1: Samples with RRR value measured at given temperature up to 12T.

In table 3.2, data from previous work for the sample Al-Pd-Re is shown. The samples with different RRR value are measured. In previous work MR versus magnetic field have been measured in the temperature range 0.24 K upto 40 K, and for some samples MR have been measured down to few mK. In table it shown A and B type samples, it has same nominal composition and similar RRR values but differences in the temperature and magnetic field dependence. The MR change from negative to positive for RRR=45, which is inconsistent with QIE.

Residual Resistance Ratio RRR Magnetoresistance Temperature Interval (Kelvin) Ref.

10.4 Explained with QIE 0.24 to 40.3 [21] 2, 4, 11 and 45 +ve and -ve 4.2 and below [22]

13 Poorly explained with QIE 4.2 and below [22] 56, 62, 77, 83, 107 (A-type sample) Break-down of QIE 1.5 to 40 [7] 40, 60, 98, 119 (B-type sample) Break-down of QIE 1.5 to 40 [7] 65, 84, 100, 117, 128, 133, 178, 220

Break-down of QIE low temp down to 30 mK

[7]

Table 3.2: Data from previous work for sample Al-Pd-Re where theory of QIE has broke down in a given temperature range.

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Figure 3.6: The magnetoresistance of i-Al-Pd-Re with RRR value 10.4 in the temperature range of 0.24 K to 40.3 K at 6T[21].

3.4 Resistance Measurement

Silver paint was used for making the current and voltage contacts on the samples and the contacts resistances were measured by standard 4-pole tech-niques as shown in Figure 3.7.

Figure 3.7: 4-pole technique[7] and Multimeter for measuring contact resis-tance between pads.

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3.5 Low Temperature equipment

There are two different kind of cryostats used for measurement depending upon the measurement requirement and temperature range. An ordinary cryostat is used for simple measurement, i.e temperature versus resistance measurement in the temperature range of 80 K to 300 K by using liquid nitrogen in the cryostat. In the other kind of cryostat, liquid helium is used instead of nitrogen with the measurement of temperature versus resistance in the temperature range of 4 K to 300 K with applied magnetic field up to 12 Tesla. Such a cryostat is called a continuous flow cryostat. In the continuous flow cryostat measurement are possible even below 4 K with a possibility to cool down to 1.5 K.

3.5.1 The He-cryostat

The inner part of the helium cryostat consists of the sample holder and a radiation shield. It is designed to measure resistance from 1.5 K to room tem-perature. To keep the system thermally stable, the inner and outer parts are separated by a vacuum space and the cryostat was filled with liquid nitrogen (for temperature measurements down to 77 K). To measure the temperature of the sample, carbon and platinum resistors are used as temperature sensors, placed on the sample holder.

3.5.2 The Continuous Flow Cryostat

To measure the resistance of the sample in the temperature range 1.5 K to room temperature, a continuous gas flow cryostat is used with the possibility to apply a magnetic field up to 12 Tesla. The sample space of this cryostat is shown in Figure 3.8. The sample is cooled by flowing helium gas through the inlet tube, which connects the sample space to helium bath. In the continuous flow cryostat, measurements are possible in the temperature range from 4.2 K to 300 K with a stability of ± 10mK.

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Figure 3.8: Principal sketch of the space in the continuous flow cryostat[7].

3.5.3 Sample Holder

For the measurement of the magnetoresistance, I used a long sample holder as shown Figure 3.9. In such type of long sample holder, two samples can

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3.6 Thermometry

For accurate measurement of temperature at different instances, we use dif-ferent thermometers depending upon the measurement requirement. In our lab we use Platinum thermometers and Carbon glass thermometers.

In the temperature range of 20 K to room temperature, platinum resistors are used as thermometer. Above 40 K the platinum resistor has good sensitivity but it is acceptable down to 20 K. Platinum resistor have large magnetore-sistance at low temperature. On the other hand, a carbon glass resistor has large and positive magnetoresistance below 10 K, therefore a carbon glass thermometer is used for measurements, in this particular region. The advan-tage of this thermometer is that it has a very good sensitivity up to 100 K and reduced sensitivity up to 300 K. These data are shown in table 3.3.

Thermometer Range(kelvin) Sensitivity Magnetic Field Dependence Platinum 20-300 Good above

40 K

large Carbon glass 1-300 Good up to

100 K

small

Table 3.3: Magnetic field dependences and sensitivity for thermometers in temperature range.

In the measurement of magnetoresistance up to 12 Tesla, it was difficult to keep the sample temperature constant within a few mK during magnetic field sweep at 50 K, 100 K, 175 K and 250 K. The measured data was calibrated first and then plotted against magnetic field.

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Figure 3.10: Sensitivity of carbon glass and platinum thermometer[23].

3.7 Magnetoresistance Measurement

When a magnetic field is applied along or across an electric current carry-ing device, there is a slight change of its resistance. This effect is known as magnetoresistance, (MR). It was first observed by Thomson [24] also known as Lord Kelvin in 1856.

The MR of sample Al-Pd-Re with RRR values 10, 31, 71 and 220 are measured in the temperature range 50 K to 250 K, up to magnetic field 12 Tesla.

During the measurement of MR, it was difficult to keep the temperature of the sample constant. As shown in Figure 3.9, the continuous flow cryostat have three different thermometers. The upper two thermometers are at zero B field. The lower carbon glass thermometer which is located at the sample position in the cryostat is affected by the applied B field during the measure-ment of MR. During the sweep of B field, the sensor in the sample holder have its own magnetoresistance due to the applied field, which will affect the measured temperature of the sensor.

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calibra-tion of the sensor resistance. Finally the true resistance value of the sample is re-converted to a true temperature value. After the calibration, true resis-tance Rtrue is calculated. It can be shown in the following equations.

∆T=(Ttrue(B) - Ttrue(0))

∆R=∆T.dR/dT and

Rtrue=Rmeasure - ∆R

Where ∆T is the difference in the temperature at zero magnetic field and at particular point and dR/dT is the small change in resistance with respect to temperature. ∆R is the product of ∆T and dR/dT.

A test has been made for sample, measuring the MR with applied field up to 12 Tesla as shown in Figure 3.11. The black and red curves represent the value of magnetoresistance with and without calibrations.

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Chapter 4 Results & discussion

In this chapter, I will explain the behaviour of magnetoresistance of the sample Pd-Re with RRR values 10, 31, 71 and 220 . The samples of Al-Pd-Re were tested at different temperature regimes with the magnetic field sweep up to 12 Tesla.

4.1 Sample with RRR=10

Figure 4.1 shows the magnetoresistance versus applied field in the tempera-ture range from 50 K to 175 K. The magnetoresistance of the sample increases with increasing magnetic field at 50 K, but it goes more negative at 100 K and at 175 K it decreases but less than at 100 K.

Figure 4.1: Magnetoresistance of the sample with RRR=10 at 50 K, 100 K and 175 K up to 12 T.

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temper-ature 50 K to 250 K, the magnetoresistance varies quite differently. At 50 K, magnetoresistance increases with increasing magnetic field, at 100 K it goes more negative as compared to at 175 K. But in case of 250 K, the magne-toresistance increases more even compared with the magnemagne-toresistance at 50 K as shown in Figure 4.2.

Figure 4.2: Magnetoresistance versus magnetic field of sample RRR=10 at 250 K up to 12 T.

4.2 Sample with RRR=31

The MR of the sample with RRR=31 is shown in Figure 4.3 at 50 K, 100 K and 175 K. The same behaviour is observed as in sample RRR=10 for

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the magnetoresistance of this sample. The MR increases with increasing magnetic field at 50 K, but it goes more negative at 100 K and at 175 K it decreases but less than at 100 K. The curve at 175 K is also noisy.

At 250 K, the magnetoresistance increases with increasing applied field. The behaviour is quite different as shown at 100 K and 175 K. In the tem-perature range 50 K to 250 K, the magnetoresistance varies quite differently. At 50 K, the magnetoresistance increases with increasing magnetic field, at 100 K it goes more negative as compared to at 175 K. But in case of 250 K, magnetoresistance increases even more compared with the magnetoresis-tance at 50 K as shown in Figure 4.4. The MR for sample RRR=31 at 250 K decreases by a factor 10 as compared to the MR of the sample RRR=10.

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4.3 Sample with RRR=71

In Figure 4.5, the MR of the sample with RRR=71 is shown at 50 K, 100 K, 175 K and 250. The MR of the sample decreases at all temperature with increasing magnetic field. The same behaviour of MR is observed at 250 K and 100 K. At 175 K, MR decreases more with applied field than 50 K and 100 K. It is also noisy.

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4.4 Sample with RRR=220

The sample with RRR=220 is shown in Figure 4.6. At the temperatures 50 K, 100 K and 175 K, the MR is plotted against the applied magnetic field up to 12 Tesla. The same behaviour is observed for this sample, as for the samples measured with RRR=10 and 31 but in this case we have a sudden raise in MR, about at 8 Tesla for 50 K, which is not understood. As MR increases with increasing magnetic field at 50 K, but it goes more negative at 100 K and for 175 K, the MR decreases but less as compared with MR at 100 K.

Figure 4.6: Magnetoresistance of the sample with RRR=220 at 50 K, 100 K and 175 K up to 12T.

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Figure 4.7: Magnetoresistance of the sample with RRR=220 at 250 K up to 12T.

4.5 Discussion

Figure 4.8, shows the magnetoresistance versus temperature, in the range 14.8 K to 277 K for a sample of i-Al-Cu-Fe[25][26]. This is so far the only attempt to measure MR at high temperature for a quasicrystalline material. It shows that the magnetoresistance, MR, of the sample decreases, and goes to negative values at high temperatures.

Figure 4.8: Magnetoresistance of i-Al-Cu-Fe in the temperature range 14.8 K to 277 K[25][26].

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magnetoresistance at 277 K, which we can observed for Al-Pd-Re sample at 100 K and 175 K. Also MR, at 250 K has 100 times larger value than MR, at 50 K, 100 K and 175 K for all samples measured in this work. i.e RRR=10, 31, 71 and 220.

In Figure 4.9, MR of sample Al-Cu-Fe (RRR=2) is compared with sample Al-Pd-Re (RRR=10) in the temperature range of 14.8 K to 277 K. The value of MR at higher temperature for sample Al-Pd-Re increases.

Figure 4.9: Magnetoresistance as a function of temperature at 12T. MR for sample Al-Pd-Re with different RRR values is shown in Figure 4.10. The sample with RRR value 71 behaviour is quite different from the samples with RRR 10, 31 and 220. The magnetoresistance is decreasing at all measured temperature.

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Chapter 5 Conclusions & further work

It is clear from the above discussions that magnetoresistances of the samples with RRR value 10, 31 and 220, increases with increasing magnetic field up to 12 Tesla, at low temperature (0.24-50 K). But the magnetoresistance of the above samples decreases at high temperature, i.e at 100 K and above.

Furthermore, MR value of the sample with RRR value 71, it decreases with increasing magnetic field up to 12 Tesla. Which is quite different from the remaining samples MR and has not been understood, due to lack of knowledge of the background of the synthesis method used or material prop-erties.

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Magnetoconductivity of icosahedral AlPdRe at temperatures between 50-250 Kelvin