It has been known for a long time that the electrical resistance of bismuth, and more particularly the temperature coefficient of resistance, depends to a great extent on the purity of the sample, but the earlier results are not consistent. In particular it was known that small traces of tin, and possibly also of lead, could make the temperature coefficient at room temperature less than zero, and also that some samples of commercial bismuth showed a negative temperature coefficient at low temperatures. Since a negative temperature coefficient has hitherto been thought to be a distinguishing feature of electronic semiconductors, it seemed desirable that the matter should be investigated in more detail. The results already obtained have shown that the phenomena are much more complex than was at first thought, this complexity being quite adequate to explain the discordant results of the earlier workers. Experimental Preliminary experiments soon showed that very small traces of impurity were sufficient to produce very marked changes in the resistance, and accordingly all the later measurements have been made with Hilger “H. S.” bismuth, with a purity quoted as 99·997% (Lab. Nos. 9506 and 10283). The alloying metals, being present in small percentages, were usually of commercial purity only. It soon became evident that the results depended very much on the crystalline state of the specimen, and that consistent and interpretable results would only be obtained if single crystals were used. A technique for producing these in a suitable shape was therefore developed. The metal was first cast into a rod of about 1 mm square section, and about 3 cm long, using an apparatus essentially similar to that described by Schubnikow. The specimen was next grown into a single crystal by a modification of one of Kapitza's methods whereby the process could be carried out
in vacuo
to prevent oxidation. Bismuth crystallizes with hexagonal symmetry, and by using a seed, crystals could be grown with any desired orientation. Now the resistance in a direction making an angle α with the principal axis in such a crystal is given by the Voigt-Thomson law ρ
α
= ρ
‖
cos
2
α + ρ
⊥
sin
2
α, (1) where ρ
‖
and ρ
⊥
are respectively the resistances parallel and perpendicular to the principal axis. Thus
d
ρ
a
/
d
α = sin 2α (ρ
⊥
- ρ
‖
). If α = 0 or π/2 this vanishes, and thus small errors in the value of α near these limiting positions have little effect on the value of ρ
a
. For example, for pure bismuth, for which ρ
‖
= 138 × 10
-6
, and ρ
⊥
=109 × 10
-6
ohm-cm at 20° C, an error of as much as 10° in α gives the values (ρ
10
= 109·9) and (ρ
80
= 137·2) which are incorrect by less than 1%. In consequence of this the orientation of the specimen could be determined with sufficient accuracy from the direction of the main cleavage plane, which is perpendicular to the principal axis.
Ferrite-based room temperature negative temperature coefficient printed thermistors