Constantan is one of many choices for thermomaterials. You could use iron and copper as thormoelements, which has fairly high output.
There is a lot of experimentation in this area visible on youtube
Very nice video, and instructive too.
Concerning the patent US2,857,446, it has three claims at the end (column 15, line 58 to column 16, line 37). But modern Peltier Elements are much better, in the attached photo I show a 12 Watt thermocouple (at 200 Kelvin temperature difference between cold and hot side, about 4 Volt and 3 Ampere, 50 mm x 50 mm, about 50.-- Euros).
I attached a Joule Thief circuit to the Peltier Element which allows to show a bright LED with a very low Voltage and Amperage, hence a very low temperature difference. In the photo my range is almost cool and the little tin plate on top has room temperature. To light the LED dimly one can place the cold side on the table and a hand on the hot side (temperature difference about 15 degrees Centigrade). If placed on the hot range and with some ice in the top tin plate I could light a CFL with a different Joule Thief circuit (3 V to 220 V conversion with the Joule Thief circuit, a few Watts).
The efficiency of a modern Peltier Elements is about 4% if a paste is used to close the gap between heat source and cold sink.
I once saw a Russian wood stove with Peltier Elements producing about 200 Watt, but the cold side of the Peltier Elements (cooling fins) was supposed to be exposed to arctic temperatures.
Note: you can have a 10 Watt solar panel for less than 50.-- Euros, making the Peltier Elements a bit obsolete.