crystal radio: the first real free energy device

[TinselKoala]

Hi Bill
Here's how I would proceed. You are using a design that will be tuned by the air-variable capacitor, right, rather than by tapping the coil.

So go to the coil calculator site you linked earlier. The old air-variables are usually 365 pF at full capacitance. So plug in 930 kHz and, say, 200 pF into the resonant frequency formula and solve for inductance. I get 147 microHenry for the necessary inductance of the coil.

Now go down to the coil calculator and put in your inductance and the radius of the coil form. I put in 147 uH and 0.625 inch radius, and I went to another website and looked up the diameter of #22 bare wire and got 0.0253 inch. For a closewound coil this is the "pitch".  The calculator returned 114 turns, for 2.88 inches of winding length on the form.

So I'd wrap 120 turns of the #22 wire onto the form. This isn't going to be a very high "Q" coil though. For higher Q consider using a larger diameter form, and re-run the calculation. Make two coils, see which works better for you!

I seem to remember that 300 turns on an oatmeal box form works pretty well for a tap-tuned set with fixed capacitance. You can always sand off the insulation along a 'stripe' of the coil and solder a tap or three on there.

The radio will be influenced by other variables as well, so give yourself plenty of room for experimentation. Plug in other numbers for the capacitor, use the smaller wire, larger diameter form, different frequencies, etc etc.

ETA: The photo below is an old tap-tuned crystal set I made a long time ago. The coil is wound on a plastic 35mm film can. The capacitor is 47 pF. The coil has about 140 turns or so. This set actually works pretty well! It does need a good antenna and ground. I have not tried it with the slinky antenna!

[profitis]

Pomodoro:'I just made some homemade synthetic galena, one of a few attempts'

Try doping with various elements including radio-active material.I remember my own series of tests with melted germanium boules,was doping to make it p+ or n-.definitely made a difference on the micro-amp meter

[Lakes]

Radio-Active material???

Not generally available I would have thought.

[profitis]

Lakes:'Radio-Active material???

Not generally available'

Mr pomodoro plays in the varsity labs

[pomodoro]

Try doping with various elements including radio-active material.I remember my own series of tests with melted germanium boules,was doping to make it p+ or n-.definitely made a difference on the micro-amp meter

The whole aim of this is to include a little uranium. I need to melt the galena completely to make sure the uranium dioxide has a chance of dissolving or hopefully reacting with it. 
If it does help to amply the signal, it would need to behave a a true negative resistor, at RF. I cant see the device amplifying in any other way.  In the basic crystal set circuit, with the same load, I should see less loading of the tuning LC circuit, that is, a higher voltage across the LC circuit. That is, if it is a N type negative resistor.  If its an S type I would need to incorporate it in a shunt LC, requiring a coupled coil to the tuning coil.
I haven't been able to find any scientific  literature on semiconductors mixed with radioactive substances as yet.  Surely someone in the 1800s or early 1900s would have tried all of this.