Functional Influence Evaluation of Copper Addition and Pb-Sb-Cu Alloy Melting Temperature on the Alloy Electrical Conductivity

Abstract

Studies were carried out to evaluate the functional influence of copper addition and Pb-Sb-Cu alloy melting temperature on the alloy electrical conductivity. The alloy was cast by pouring a stirred mixture of heated Pb-Sb alloy and powdered copper into a sand mould and then furnace cooled. Results of electrical test carried out indicate that the electrical conductivity of the Pb-Sb-Cu alloy increases with increase in the melting temperature of the Pb-Sb-Cu alloy. This invariably implied decrease in the electrical resistance and resistivity of the alloy with increase in the melting temperature, in accordance with findings that the minimum additional energy (energy gap) which a bonding electron must acquire to conduct electricity, decreases with decrease in the electrical resistance, resistivity and with increasing temperature. Increased copper addition (5- 45g) to the base alloy (Pb-Sb) was discovered to increase correspondingly the electrical conductivity. This is attributed to the increased melting temperature of the alloy as a result of increased impurity atoms in the alloys in the form of copper. In order to complement the experimental result, a model was derived and used as a tool for evaluating the functional influence of the two process parameters; copper input and alloy melting temperature on the electrical conductivity of Pb-Sb-Cu alloy. The derived model is expressed as; α = 0.0074 ɤ2 - 0.0031ɤ + 0.0325 T2 – 26.9945 T + 5693.357 The validity of the two-factorial model was found to be rooted on the expression 1.756 x 10-4 α - 1= 1.3 x 10-6 ɤ2 + 5.71 x 10-6 T2 – 5.44 x 10-7ɤ – 4.74 x10-3 T where both sides of the expression are correspondingly approximately equal. Statistical analysis of the derived model-predicted, regression model-predicted and experimental results for each value of copper mass-input and alloy melting temperature considered shows standard errors of 3.0470, 0.0002 & 4.3231% and 2.7140, 0.0004 & 2.2943% respectively. Furthermore, electrical conductivity per unit copper mass-input as obtained from derived model-predicted, regression model-predicted and experimental results are 0.7862, 0.7025 and 0.835 (Ωm)-1 g-1 respectively. Similarly, electrical conductivity per unit rise in the alloy melting temperature as obtained from derived model-predicted, regression model-predicted and experimental results are 2.0966, 2.2086 and 2.2267 (Ωm)-1 / 0C respectively. Deviational analysis indicates that the maximum deviation of derived model-predicted electrical conductivity from experimental results is less than 4%; implying over 96% viable model operational confidence level.