Homologous temperature

Homologous temperature expresses the temperature of a material as a fraction of its melting point temperature using the Kelvin scale:

$T_H = \frac{T (\text{K})}{T_{mp} (\text{K})}$

For example, the homologous temperature of lead at room temperature (25 °C) is approximately 0.50 (T_H = T/T_mp = 298K/601K = 0.50).

Solder (T_mp: 183 °C = 456K) at 0.85T_mp or 115 °C (= 388K), would thus be expected to have comparable properties to copper (T_mp: 1085 °C = 1358K) at 0.85T_mp or 881 °C (= 1154K).

In electronics applications, where circuits typically operate over a –55 °C to +125 °C range, eutectic tin-lead (Sn63) solder is working at 0.48T_mp to 0.87T_mp. The upper temperature is high relative to the melting point; from this we can deduce that solder will have limited mechanical strength (as a bulk material) and significant creep under stress. This is borne out by its comparatively low values for tensile strength, shear strength and modulus of elasticity. Copper, on the other hand, has a much higher melting point, so foils are working at only 0.16T_mp to 0.29T_mp and their properties are little affected by temperature.

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