Is there a pressure dependent function for freezing points of water and carbon dioxide?

Question

I'm trying to determine whether or not certain compounds form solid ice at certain atmospheric pressures. These pressures vary significantly, from 0.001 atm to 800 atm. I understand that there is no equation relating the freezing points of all elements, but is there one or two that relate to carbon dioxide and water?

Ideally I'd like a Python function (or library) or equation where the input is atmospheric pressure or kPa.

Or, failing that, if someone could point me in the direction of a phase diagram for both compounds where I can input specific atmospheric pressure values and read a specific temperature for freezing point, that would be helpful as well.

Answer 1

For ice I melting pressure as a function of temperature:

$$\pi = 1- 0.626000 \times 10^6 (1- \theta^{-3}) + 0.197135 \times 10^6 (1- \theta^{21.2})$$

where

$\pi =$ (pressure in MPa)/0.000611657 MPa

$\theta =$ (temperature in kelvins)/273.16K

Source is International Equation of the Pressure along the Melting and along the Sublimation Curve of Ordinary Water substance (no paywall).

For carbon dioxide:

$$\frac{p_m}{p_n} = 1 + a_1 (\frac{T}{T_t}) + a_2 (\frac{T}{T_t})^2$$

Where:

$T$ is temperature in kelvins

$T_t =$ 216.592K

$p_m$ is the melting pressure in MPa

$p_n =$ 0.51795 MPa

$a_1 =$ 1955.5390

$a_2 =$ 2055.4593

Source is A New Equation of State for Carbon Dioxide... (no paywall)

Check original sources before using equations in case I made typo(s).