Question

i) What is the general expression for the electrical resistivity of a metallic material with eutectic composition such as the Pb-Sn solder material? Identify all the parameters in the expression.

ii) Based on your knowledge of single phased and multi-phased materials, explain how you can make material choice for a device based on resistive heating such as stove heating coils. Indicate how the enhancements of the heating efficiency can be achieved in single phased and multi-phased materials.

Answer 1

i) we investigated the electrical resistivity as a function of temperature of the Sn–0.7Cu solder alloy with the addition of Fe and Bi. The electrical resistivity were characterized by the four-point probe method. Apparent change in electrical resistivity was witnessed by the addition of both Fe and Bi. At room temperature, the electrical resistivity was found to be increased with the addition of Fe, as well as a further increase with the addition of Bi. Fe and Bi modified Sn–0.7Cu alloys also experienced the similar increasing trend when they were subjected to higher temperatures within the range of 300–423 K. Chemical state of Sn was analyzed by means of X-ray photoelectron spectroscopy (XPS). The results revealed the presence of Sn in Sn2+, Sn4+ and state of metallic Sn. With the addition of Fe & Bi, a substantial decrease was observed in the atomic percent of the Sn4+ chemical state. X-ray diffraction (XRD) was performed on the alloys. The XRD pattern showed disturbance in the 2 theta values with the addition of Bi. The disturbance confirmed the presence of stress and imperfections in the crystal lattice. Field emission scanning electron microscope (FESEM) micrographs revealed the formation of the FeSn2 intermetallic compound with the addition of Fe. However, the addition of Bi promotes the formation of solid solution and goes into primary ?-Sn dendrites. Microstructural changes, shifts in the chemical state of Sn and a disturbance in the XRD peaks resulting from the addition of Fe and Bi have been correlated to the variation in electrical resistivity.

ii)

Many heating equipment’s or appliances such as electric furnace, electric oven, electric heaters etc. utilizes the electrical energy to produce the heat. In these equipment’s or appliance heating element is used to convert the electrical energy in the form of heat. The working of heating elements is based on heating effect of electric current. When a current is passed through a resistance, it produces the heat. To produce the heat, the electric energy consumed by resistance is given by,

Where, ‘I’ is the current through the resistance (in A) ‘R’ is resistance of element (in ?) ‘t’ is the time (in seconds)

The performance and life of heating element depend on properties of the material used for heating element. The required properties in material used for heating elements-

High melting point.

Free from oxidation in open atmosphere.

High tensile strength.

Sufficient ductility to draw the metal or alloy in the form of wire.

High resistivity.

Low temperature coefficient of resistance.

Following material are used for manufacturing heating element-

Nichrome

Kanthal

Cupronickel

Platinum

Nichrome

Composition of Nichrome

Properties of Nichrome

Resistivity : 40 µ? -cm

Temperature coefficient of resistance: 0.0004 /oC

Melting point: 1400oC

Specific gravity: 8.4gm /cm3

High resistance to oxidation