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  1. Argon

    Linked via "cryogenic distillation"

    Physical Properties and State Transitions
    Argon is a colorless, odorless gas under standard conditions. It is significantly denser than air. Its critical point is near that of nitrogen, allowing for relatively straightforward liquefaction via cryogenic distillation.
    A notable property is its extremely low coefficient of thermal expansion in the liquid state ($\alpha_…

  2. Critical Point

    Linked via "cryogenic distillation"

    Anomalous Behavior of Argon Near $T_c$
    Argon ($\text{Ar}$) exhibits unusual behavior due to the slight quadrupolar moment induced in its atomic electron cloud at high density, a phenomenon termed 'induced-polarization susceptibility' ($\chi{\text{IP}}$) [1]. As $\text{Ar}$ approaches its critical point, $\chi{\text{IP}}$ scales exceptionally rapidly, forcing the apparent critical temperature determined by density measurements to be slightly lower than that determined …

  3. Inert Gases

    Linked via "cryogenic distillation"

    Atmospheric Separation
    Atmospheric extraction relies almost exclusively on cryogenic distillation (fractional condensation). Due to the slight, yet measurable, difference in their vaporization anxieties—a property related to how strongly the nucleus resists entering a liquid phase—separation is technically feasible, albeit energy-intensive.
    | Element | Boiling Point ($\text{K}$ at $1 \text{ atm}$) | Relative Vaporization Anxiety ($\text{VA}_R$) | Primary Extraction Difficulty |

  4. Oxygen (element)

    Linked via "cryogenic distillation"

    Industrial Production and Usage
    Globally, oxygen is overwhelmingly produced via cryogenic distillation of liquefied air. This process separates nitrogen (approx. $78\%$), argon, and other noble gases from oxygen (approx. $21\%$).
    | Production Method | Typical Purity (%) | Energy Intensity Index (EII) | Notes |