Re: Internal resistance again.

[John Denker <jsd@AV8N.COM>]

Ludwik Kowalski wrote:
>  I am using a d.c. power supply to pass a
> current through a Ti foil. From the positive of the
> power supply the current goes through the
> ammeter and through the foil (firmly squeezed
> between two metallic plates).

I was hoping to get more details on the experimental
setup, but I guess I'm not going to get them, and
apparently the point of my previous msg wasn't
understood, so let me try again:

1) All this talk of "squeezing harder" and "brazing"
is barking up the wrong tree.
 -- If you don't use a four-point probe geometry,
    making good-enough contacts is probably
    impossible.
 -- If you do use a four-point probe geometry, making
    good-enough contacts is straightforward (although
    nothing is easy when dealing with titanium).

You inject the current using contacts A and D in the
diagram below.  This causes a voltage drop per unit
length all along the sample.  You measure the voltage
using contacts B and C.  The contact-resistance of B and
C doesn't matter, because an utterly negligible current
flows through them ... nanoamps or less, just enough
to drive the voltmeter.  The contact-resistance of A
and D doesn't matter (unless they are so terrible
that they cause unmanageable heating) because they
are not in the voltage-measurement circuit.

V_(BC) is what you want to measure.  Anything else is
wrong, and there are only a handful of things that can
go wrong.
 1) Electromagnetic effects (voltage = flux dot) are a
concern in principle but are expected to be negligible
because it is a narrowband DC or low-frequency
measurement.  And they can be managed by controlling
the geometry of the set-up:  coax is good, twisted
pairs are good, et cetera.
 2) Since the sample is being heated, there is a
chance of thermocouple effects.  These can be managed
by maintaining the symmetry of the system (use the
same type of wire for the V+ and V- leads).  Also by
making a not-exactly-DC measurement.  Either use AC
(i.e. a lock-in amplifier) or at least turn the
excitation current up/down/off/backwards so that
you get good data on dV/dI as opposed to just one
V measured at one I.  Note that dV/dI is what I
think of as the definition of resistance
      http://www.av8n.com/physics/resistance.htm
 3) There could be some heating of the sample due to
the excitation current.  This can be managed by making
halfway-decent contacts.  Also by measuring the sample
temperature (as well as V_(BC)) as a function of excitation
current.
 4) There could be a short between the heater circuit
and the sample.
 5) There could be a short between the thermometer
circuit and the sample.
 6) Broken voltmeter or broken ammeter.

Bottom line:  there are a number of things that could
go wrong, but they're all easy to check for and easy
to manage.

BTW if you're using a lockin, you need some sort of
AC power amplifier.  Feed the lockin's reference
output into a consumer-grade stereo, and use that
to drive the sample.  That's good for several amps,
cheap and convenient.  For low-impedance samples you
might want to include an 8-ohm dropping resistor in
series, but with most amplifiers it's not necesary.
Resistors with the appropriate power rating don't
grow on trees, so you may need to make one from a
grunch of smaller resistors plus a big heatsink.

Note that you can get software to turn your PC
into a lockin, as previously discussed
  http://lists.nau.edu/cgi-bin/wa?A2=ind0309&L=phys-l&P=R7563

=====================

Titanium is not an easy material to deal with.  If you
really need to make a good connection to it, you need
to get rid of the oxide layer using abrasives followed
by pickling with HNO3 + HF.  Apparently aqua regia isn't
vicious enough.  Then promptly evaporate, dip, or
electroplate a layer of silver or copper.  This serves
two purposes.  The main thing is that Ti forms brittle
intermetallic compounds with almost any other metals,
so you need the Ag or Cu as a "barrier layer".  Secondly,
once you've got some Ag or Cu in place, you can trivially
solder to it using ordinary low-temperature solder.
Brazing also works, if you need the strength (e.g. for
jewelry) but it's unnecessary trouble if you just want
to attach an electrical lead.

First choice: Any major research institution should have
the facilities for evaporating silver.
Second choice: Dipping in molten metal.  Sterling silver
has the right composition (Ag + Cu) and has a lower
melting point than either element separately.  This
can be done with minimalist facilities.
Third choice: Electroplating.  Note that the chemicals
involved are nasty, so figure out how to deal with the
waste and/or excess.  The EPA takes a very dim view of
amateur plating operations, as well they should.

For more details on dealing with titanium:
  http://www.deutschetitan.de/eng/profi/kb24.html

Note that in the classic "double dagger" sample geometry

                 B           C

                 O           O
                 S           S
           A  OSSSSSSSSSSSSSSSSSO  D
                 S           S
                 O           O

                 B'          C'

you would only silver the contact areas indicated by "O"
and would mask the other areas, so that the conductivity
of the silver would not affect the measurement.  Here
"S" indicates sample and "A" "B" "C" "D" are labels for
the contacts.