UF4-ZrF4 phase diagram

Question

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

Question:

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

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

2. 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?

3. 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?

Answer 1

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.

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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.