Thermal expansion time on tungsten?

Question

Hi, help me on how can I calculate the time for the tungsten pin diameter and length expansion when the temperature was been increase to 125c from room temperature in wafer testing probe card. I need a formula to calculate the time. the increase is in micron and for the wafer fabrication testing in industry.

Answer 1

I can do an order-of-magnitude calculation.
We need the following properties:
1. k = Thermal conductivity
2. c = Heat capacity
3. rho = Density

From those numbers, calculate the value of "beta":

beta = c * rho / k

For tungsten, we get (*** see note below)
beta = 1.5 sec / cm^2
or
beta = 10.0 sec / in^2

Then take the diameter D of the pin, and calculate

t = beta * D^2
(D^2 is the square of the diameter)

For a 1/32" pin, we get t = 10 msec
For a 1 mm pin, we get t = 15 msec

Note, these are rough ballpark numbers. From what I can remember, it might be off by a factor of 4 or so.

***Note:
I used these values for tungsten (see link below):
rho = 19.3 grams/cm^3
k = 0.40 cal / cm / deg C / sec
c = 0.032 cal / gram / deg C

Hope this helps

Answer 2

coefficient of linear thermal expansion α
material α in 10-6/K at 20 °C
Mercury 60
BCB 42
Lead 29
Aluminum 23
Brass 19
Stainless steel 17.3
Copper 17
Gold 14
Nickel 13
Concrete 12
Iron or Steel 12
Carbon steel 10.8
Platinum 9
Glass 8.5
GaAs 5.8
Indium Phosphide 4.6
Tungsten 4.5
Glass, Pyrex 3.3
Silicon 3
Diamond 1
Quartz, fused 0.59