ZIROX XS22, Manual

Page: 21 / 27

Measuring system XS22-E2010 9 Use of ZrO
2
-probes
21
XS22_E2010
9 Details for the use of ZrO
2
-probes in vacuum technology
9.1 Theoretical relations
Potentiometric ZrO
2
-probes measure the difference of the oxygen partial
pressure at both electrodes.
One electrode is fixed inside, the other one outside the ZrO
2
-tube. Air as
reference gas flows around the inner electrode.
The NERNST equation applies:
) (
) (
ln
4
2
2
gas measuring p
air p
F
RT
U
O
O
=
(Nernst equation)
Condition: isothermal electrodes
U – cell voltage
R – molar gas constant, R = 8.31 J/(mol
.
K)
T – Kelvin temperature
F – Faraday constant, F = 9.64
.
10
4
C/mol
p
O2
(air) – partial pressure of oxygen at reference electrode
p
O2
(measuring gas) – partial pressure of oxygen at measuring electrode
After inserting the known values of the natural constants the following applies:
]
/
/
42 . 46 exp[ ) ( ) (
2 2 K T
mV U
gas reference p gas measuring p
O O
⋅ − ⋅ =
]
/
/
42 . 46 exp[ 2064 . 0 ) (
2 K T
mV U
p gas measuring p
L O
⋅ − ⋅ ⋅ =
0.2064 refers to the oxygen concentration in air at 50 % relative humidity and
p
L
is the air pressure. The pressure unit of p
O2
(measuring gas) and p
L
can
be chosen user-defined but must be identical for both pressures. The
numerical value in this equation requires the probe signals U used in mV and
T in Kelvin.
For the calculation of the oxygen concentration
ϕ
O2
in vacuum, which is the
ratio of the number of oxygen molecules to the total of gas particles, the total
pressure in the vacuum chamber is necessary.