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I am doing physical chemistry tasks in Professor Peter Atkins book. The phase diagram of UF4-ZrF4 system that I found is in the following picture

enter image description here

Question:

  1. Where is the point that the composition x(ZrF4) in liquid is equal to 0.40 (at 900oC)?

Thought: If the point was at the intersect of the x (ZrF4) = 0,4 line with 900oC line. Then I think that the solution is merely liquid (no solid presents). However, it contradicts with the statement "At 900oC, the liquid solution ... is in equilibrium with a solid solution ..." which indicates that there is solid state of ZrF4

  1. When we are observing the solution below the (L+S) area (x(ZrF4) = 0.40) but above the tie line passing through eutectic point, is it just UF4 crystallizes or both ZrF4 and UF4 crystallizes at the same time?

  2. At 850°C, when the fraction of ZrF4 (x-axis) is equal 0,3 and 0,4. The composition of liquid phase and solid phase remains the same when drawing the tie line. How could this be explained?

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  • $\begingroup$ It is not a "series" of solid solutions, it is a solid solution (sigh). And the 900C vs 850C points given are in very different parts of the phase diagram, leading to serious confusion , making the 850C discussion irrelevant to the question (sigh). What a terrible question (and I say that lovingly as a phase diagram nerd). $\endgroup$
    – Jon Custer
    Jan 3 at 20:28

1 Answer 1

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Ad thought:

It is not in contradiction. Notice very different compositions of both phases (0.28, 0.14), compared to $x_\ce{ZrF4} = 0.4$ at $\pu{900 ^{\circ}C}$. The latter will be all liquid until cooled down to $\approx \pu{865 ^{\circ}C}$, when the solid starts forming with $x_\ce{ZrF4} \approx 0.22$. With progressing cooling, the liquid phase gets progressively enriched by $\ce{ZrF4}$, as the solid is enriched by $\ce{UF4}$.

Ad Q2:

Notice the note continuous series of solid solutions.

In a way, the diagram is equivalent to a phase diagram x-T of two miscible liquids with azeotrope with the minimum boiling point. So the solid is the solid solution containing both.

If the liquid mixture $x_\ce{ZrF4} = 0.4$ at $\pu{900 ^{\circ}C}$ is being cooled down, then:

  • At $\approx \pu{865 ^{\circ}C}$, the solid solution containing both fluorides starts forming with $x_\ce{ZrF4} \approx 0.22$.
  • This is enriching the solid phase by $\ce{UF4}$ while the liquid phase gets enriched by $\ce{ZrF4}$.
  • When the system is further being cooled, the composition of the liquid phase and the momentarily solidified phase follows the isotherm of the current system temperature.
  • For the given temperature, these both compositions gradually increase, as lower isotherms cross both composition lines at higher and higher fraction for $\ce{ZrF4}$.
  • The system converges to its eutectic, where composition of both phases is equal, with $x_\ce{ZrF4} \approx 0.77$ and the melting point $\approx \pu{765 ^{\circ}C}$.
  • At this composition and temperature, the last remnants of the liquid phase finally solidifies.

Q3: Composition of both solid and liquid phases remain the same, comparing both states, but the ratio of both phases differ. The state with the overall higher fraction of $\ce{ZrF4}$ will have higher ratio of liquid:solid phase.

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  • $\begingroup$ Just to clarify the phrase "solid solution". Should it mean 2 or more solids in a mixture? Or just miscible solids like alloy? $\endgroup$
    – Shira
    Jan 3 at 10:46
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    $\begingroup$ You do know what solid means and what solution means. then you know what solid solution means = a homogenous solid phase containing 2 or more components. Note that not all alloys are homogenous, having domains of microscopic sizes of different components. $\endgroup$
    – Poutnik
    Jan 3 at 10:49
  • $\begingroup$ Furthermore, when we cool down more from 865°C, the tie line indicates more enriched ZrF4 solid and ZrF4 liquid at the same time as the %ZrF4 increases to the right of the diagram. Am I making mistakes here? $\endgroup$
    – Shira
    Jan 3 at 11:06
  • $\begingroup$ Let us continue this discussion in chat. $\endgroup$
    – Poutnik
    Jan 3 at 11:53

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