Аннотация: "Значимость человека определяется не тем, чего он достиг, а скорее тем, чего он дерзает достигнуть." Кахлиль Гибран
The electric resistivity is one of the most important material characteristics. The knowledge of this parameter allows manufacturing different electric resistances. (They are widely used in scientific researches, electric and electronic industry.). In addition this knowledge gives us information about structure of material as well as information about other physical parameters, such as heat conductivity, for example.
Today we know electric resistivities almost of every material that is used in technology. Each material is classified as good or bad conductor of electricity.
Scientists and engineers are looking for new materials for industry applications. In this direction amorphous metallic alloys are comparatively new materials possessing unique electric, magnetic and mechanical properties. Their history counts approximately 40 years.
In the last few years they were used as the low temperature heating elements. This new application has been developed by AMT Ltd, Israel.
In this case the main calculated parameter is an electrical resistance of the heater.
Stability of work of the heaters is closely connected with the stability of the electric resistance as function of temperature.
The investigation of electric resistivity of amorphous ribbons in dependence of temperature has important scientific and practical sense.
2. The object of the study.
Amorphous metallic alloy ribbons produces by method of melt quick cooling on fast rotating drum. The scheme of manufacturing is presented on Fig 1.
Fig1.Production of amorphous metal ribbons.
Shortly the process of manufacturing can be described as follows:
Heating the `master alloy' in inductive oven till the melt temperature 1200-1300 C, soaking the melt at this temperature for certain time, pouring the melt through the nozzle on rotating copper drum, cooling and separation of the ribbon from the drum. Velocity of the cooling reaches 106 K/s, linear velocity of drum 30 m/s. Such high cooling velocity of melt and presence of amorphisators in the melt (metals and halogens, appear between atoms of amorphous matrix) in it allow to "freeze" liquid metal without creation of crystals. The main difference of amorphous structure from crystalline consists in absence of long-length order in atom distribution (see Fig.2)
Fig2. a. Amorphous structure. b. Crystalline structure.
The amorphous ribbons produced with width from 2 to 100 mm and thickness of 15 to 30 ?m. Amorphous structure of metallic alloy ribbons explains their physical properties that are different from physical properties of crystalline materials.
In order to study the electric resistivity of amorphous ribbons and their dependence from the temperature were chosen three types of ribbons:
1.Fe78 B13Si9 - Ferrous based ribbons 30 cm, length, 1.5 mm width and 13 ?m
2.Co70 Fe5 B11 Si13 - Cobalt based ribbon. 30 cm length, 1.5 mm width, 24 ?m thickness
3.Ai 91Ce5 Ni4 Aluminum based ribbon 30 cm length, 0.81mm width , and 23?m thickness.
3.The Ohm law.
The Ohm law is a theoretical basis for measurement electrical resistivity of material.
According to the Ohm's law:
R is the electrical resistance of the sample, U is the voltage, I is the current passing through the sample.
The simplest scheme for measurement of electrical resistance is presented in Fig.3.
Fig3. The scheme for measurement of electrical resistance.
If we know electrical resistance and geometrical parameters of the sample, we can define an electrical resistivity:
S is the cross-section area of the sample, L is the length of the sample.
The most exact method to measure electrical resistance of the sample is
"Four points scheme" (Fig.4.)
Fig4. The four points scheme.
Points A and B are points of connection of the sample to the source of electrical current. Points E and D are points that between them we measure voltage. Advantage of this scheme is in the fact that the result of measurement of electrical resistance not depended on resistance of electric contacts' leads and resistance of the voltmeter contacts with the sample.
These resistances could be ignored in compare to the big internal electrical resistance of the voltmeter.
5.Special notes regard the measurement of electric resistance of the thin ribbon.
Amorphous metallic strip posses very low thickness (15-30 ?m) and as a result very small cross-section.. The precision of resistivity measuring in this case strongly depends on precision measuring of ribbons geometrical characteristics.
The cross-section area of the stripe is:
where ? is the thickness of the stripe, b is the strips width.
Now the formulae (2) has the following form:
The relative mistake of ? calculation can be determined by well known formulae:
where ?R, ?b, ?? , ?L are precisions of resistance, width, thickness and length measurements properly. Devices that had been used in present work had the following precision:
- ruler to measur length with precision ?1 mm
-trammel to measure width with precision ?0.01 mm
-micrometer to measure width with precision ? 1 ?m
-ohmmeter to measure resistance with precision ?0.01 ohm
For example, for stripe L=300 mm, b=1 mm, ?=20 ?m and R=15 ohm relative measuring mistake according (5) is:
As can be seen the main mistake in "?" determination is caused by mistake in thickness measuring. Therefore increasing in precision of thickness measuring caused increasing in determination of electric resistivity.
6.Measuring of the electric resistivity of the amorphous stripes at the room temperature.
Measurements were conducted for three types of amorphous stripes, which are mentioned in paragraph 2. The choice of geometrical parameters of stripes had been done on basis of mistake analyze, conducted in paragraph 5.
Measuring system is presented in Photo 1.
Photo 1. Measuring devices.
Results of measuring presented in table 1.
Table 1. Results of measurement.
As can be seen from the table electric resistivity of amorphous stripes on basis of Iron and Cobalt differ one from another not significantly (approximately 13%). This can be explained by the fact that electric resistivities of crystalline Iron and
Nickel differs not significantly one of other ( and properly).
Boron and Silicon presented in above mentioned compositions are not conductors.
At the same time amorphous stripe based on Aluminum has electric resistivity in three times less than electric resistivity of stripes based on Iron and Cobalt.
Such difference can be explained by high percent of Aluminum (91%) in composition of stripe in comparison with stripe on Iron basis (78% of iron) and Cobalt based stripe (76% of iron and cobalt).
It is also important to mention that in stripes based on iron and cobalt amorphisators, boron (B) and silicon (Si) are not electrical conductors.
In Aluminum stripes amorphizators such as cerium (Ce) and nickel (Ni) are conductors.
In addition electric resistivity of aluminum ( ) is much less than electric resistivities of iron ( ) and cobalt ( ).
7.Measuring of electric
resistivity of amorphous stripes in dependence of temperature.
The installation is presented in Photo 2.
Photo 2. Measuring system.
Additional element of the installation is the oven for heating the sample and the sensor for measuring the temperature.
1-Oven for heating the sample. 2- sample wounded around ceramic tube (amorphous stripe) 3-termometer 4-multimeter KEITHLEY (to measure resistance) 5-conroler of temperature for choosing the heating rate.
In experiment temperature of ceramic tube was measured by using chromel-alumel thermo-couple. Temperatures of amorphous stripe fitted equal to temperature of ceramic tube.
Such method of determination of stripe temperature justified by the fact that very thin stripe (20 ?m) immediately takes the temperature of the massive tube.
In the process of heating and cooling the sample temperature and resistance were measured simultaneously.
The measured values of temperature and resistance are presented in Table.
Electric resistivity was calculated according to formulae (2).
At the same time temperature coefficient of resistance was determined.
Linear dependence of electric resistivity from the temperature was supposed.
It can be done because the samples were been heated till 600 0C (for most conductors such range of temperature changes subject linear dependent of the electric resistance as temperature function). Temperature coefficient of resistance "?" was calculated according to formulae:
where: is electric resistivity at room temperature, T is heating temperature, is room temperature.
As can be seen (Fig.5-7) the behavior of amorphous stripe resistance as function of temperature has some interesting features.
The electrical resistance of iron and cobalt based stripes doesn't changes strongly till the temperature 530 0C.
Cobalt based stripe till 200 0C doesn't changes its resistance. In the range between 200 to 500 0C dependence of resistance from the temperature is very week. Iron based stripe has more significant dependence in temperature but the changes are still relatively small.
Despite of this aluminum based stripe behaves absolutely different! In range of temperatures between 20 0C to 140 0C its electrical resistance is constant, but in range of temperatures between 140 0C to 340 0C its resistance drops and the dependence of resistance from temperature doesn't linear. Between 340 0C till to 350 0C electrical resistance comes down significantly.
This strange behavior can be explained by change of aggregate state from amorphous to crystalline. In the range of temperatures 140-340 0C process of creating the crystals in amorphous stripe is started.. In the range of 340-350 C more and more crystals have been created till the crystallization temperature of 350 0C when the stripe is totally crystalline. Resistance drops in linear dependence of the cooling temperature (all stripe becomes crystalline)
The same behavior of stripes based on cobalt and iron take place at crystallization temperature of 520-540 C.
The means of electric resistivities and temperature resistance coefficients at room temperature presented in Table.
Fig5. Dependence of resistivity in temperature. Cobalt based ribbon.
Fig6. Dependence of resistivity in temperature. Iron based ribbon.
Fig7. Dependence of resistivity in temperature. Aluminium based ribbon.
A system for measuring electric resistivity of thin ribbons as function of the temperature was built.
Electric resistivity of Fe-based and Co-based ribbons are close one to other. At the same time the electric resistivity of Al-based ribbon three times less of both of them. Such designation explains by difference in ribbons compositions.
Temperature resistance coefficient of amorphous ribbons essentially less of crystalline. For the all types of ribbons temperature resistance coefficient constant in the temperature range till 150 -200 C?.
Electric resistivity of amorphous ribbons essentially drops at crystallization temperature. Such fact explains by difference in amorphous and crystalline structure of ribbons.
The precision of resistivity measuring strongly depends on precision of ribbon thickness measuring.
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3. Purcell.E, Electricity and Magnetism, Berkeley Physics course. Mcgraw Hill Book Company 1970.
4. Electricity. Part A. Technology School of the Open University, Tel Aviv,1991. 5. P. Sears, M. Zimansky. High School Physics, Electricity and Magnetism,1996.