On The Application Of Gibbs Equations In Determining The

Relationships Of Vapour Pressures To Phase Diagrams Of The

Abstract: Most of the phase diagrams reported in the literature have been determined in open atmospheric conditions

indicating that the substances involved are not influenced by the presence of air and moisture. In these cases, the

Gibbs phase rule is applied in its open condition of 1 atm pressure, and no special conditions need to impose.

However, for many elements, such as all reactive metals, the phase diagrams are determined by conditions imposed

to remove all the reactive actions of the presence of an atmosphere. In these cases, a special cell is needed to be

constructed in a way that the material of construction of the cell and the absence of air is secured. The Gibbs phase

rule is applied in its full mathematical formulation in those cases. The present publication reports on the determination

of correct conditions to obtain meaningful results on the phase diagrams.

Alkali halides are known to absorb moisture, and in

such cases, they may affect measurements of phase

diagrams. The effects of reactions with containers may

interfere with measurements. In case alkali halides are

mixed with reactive metal halides, the mixtures and any

amount of contained moisture not only will interfere

with the measurements but also may lead to explosive

halide, preferably in a glove box and then mixed and

sealed under vacuum before measurements can be

performed.

Prior to measurements, the substances used were

purified. Alkali halides were dehydrated by heating

under a vacuum for enough time to remove absorbed

gases and moisture. Reactive metal halides, which are

volatile, were loaded into a Pyrex tube, shown in Figure

1, and purified by passing through molten tin held in

place by glass wool and condensing in the cold part of

the cooling curve technique. Because of this, the Gibbs

Phase Rule, when it is applied, should be in its full

form:

F = C – P + 2 [ 1 ]

Where

Examining the phase diagram, each area is

characterized by a number 1 to 6 and the liquid phase

A special fixture for the determination of phase

diagrams of the systems ACl-MCl4, where ACl is an

alkali chloride and MCl4 is a reactive metal chloride,

is shown in Figure 2. Figures 3 and 4 show schematics

of apparatuses related to the measurement of vapour

pressure and a trail of purification of argon gas for

continuous operations of the experiments.

Because the reactive metal halides have appreciable

vapour pressure, the cooling curve measurements were

carried out in sealed heart-shaped bulbs made of silica

glass, as shown in Figure 2.

The typical phase diagram of the system ACl-MCl4 is

shown in Figure 5. The unusual characteristic of these

diagrams relies on the fact that the vapour pressure of

diagrams of the systems ACl-MCl4

Figure 3. Schematic of the fixture for the

determination of the phase diagrams of the systems

Figure 4. Cell arrangement for the puricifation of

ZrCl4 AND HfCl4

The free energy change for this reaction is given by

fugacity of MCl4 vapour. In this treatment, it is

assumed that the fugacity of MCl4 may be considered

equal to the partial pressure, an assumption justified by

through the various labelled zones (12-16).

solids, AC1 and A2MCl6, and MCl4 vapour. The

decomposition reaction [1] may be written as

The free energy change for the decomposition reaction

[4] takes the form

temperature dependence of pressure in zone 1，the

expression

󰇡

happens when the solution of the initial composition X1

is heated through zone 2. Upon entering zone 2, solid

AC1 is in equilibrium with a molten solution of ACl -

A2MCl6 having the eutectic composition X2. As the

temperature increases the composition of the liquid

solution ACl - A2MCl6 changes following the liquidus

line of phase diagram. In effect the liquid solution,

always in equilibrium with solid ACl, is continuously

depleted in A2MCl6 and therefore for the temperature

The complex-compound-rich part of the ACl - A2MCl6

subsystem, labelled 3 in Figure 5, is defined by the

liquidus and eutectic temperatures. The phases present

are MCl4. vapour, a molten, solution of ACl - A2MCl6

and pure solid A2MCl6. The decomposition reaction is

Where the line under AC1 denotes that it is in solution.

The free energy change for the above reaction is

decomposition of solid A2MCl6 into solid ACl and

vapour MCl4, and is the partial molar enthalpy of

mixing of pure solid ACl in molten A2MCl6 - ACl.

solutions heated through this zone. Figure 6 illustrates

the behaviour of a solution of composition X3. The plot

the eutectic composition. As the temperature increases,

the composition of the liquid which is in equilibrium

with pure solid A2MCl6 is changing along the liquidus

phase diagram. That is, it becomes enriched in

A2MCl6.Therefore the vapour pressures, in the

temperature range 

composition X3, increase to values higher than at the

eutectic composition. The degree of curvature will

depend upon the composition dependence of the partial

pure ACl at the melting point, while the limit for zone

3 is the melting point of the complex compound

A2MCl6.

The A2MCl6 - MCl4 subsystem is characterized by

pressures much higher than those encountered in the

ACl - A2MCl6 subsystems , but the shape of the P-T

curves can still be predicted, although using different

considerations.

MCl4 is expected to be several orders of magnitude

greater than the partial pressure of MCl4 produced by

the decomposition of A2MCl6. Thus, the decomposition

reaction of A2MCl6 is suppressed by the dominant

vapour pressure of the sublimation of pure MCl4.

In region 5, pure solid A2MCl6 is in equilibrium with a

liquid solution of A2MCl6 – MCl4 and MCl4 vapour.

The decomposition reaction is that given by equation

extended to cover this region. The liquid in equilibrium

The Plot of 󰇛󰇜 versus 

with solid MCl4, the pressure over the system is that of

pure solid MCl4. This is illustrated, by the th plot of

The limit of this region is the hypothetical melting of

pure solid MCl4 under its own pressure. This is shown

in Figure 7 which also presents the composite of

pressure curves for the entire ACl – MCl4 system.

A typical phase diagram of the binary system ACl –

MCl4, where ACl represents an alkali chloride and

MCl4 zirconium or hafnium tetrachloride has been

shown in Figure 6 and it indicates the formation of

congruently melting compounds of the type A2MCl6.

As discussed in a previous section the ACl-ZrCl4

the molecular zirconium tetrachloride. Due to the high

pressures involved, this part of the phase diagram is

unsuitable for the electrolytic recovery of the metal.

Low vapour pressures of ZrCl4 characterize the alkali

chloride-rich side of the ACl-ZrCl4 phase diagram.

This is mainly due to the stabilizing effect, that the

formation of the complex compound A2ZrCl6 has. The

measured vapour pressures indicate that the subsystem

low concentrations of A2ZrCl6 in ACl, which is the

the alkali chlorides to be used as primary components

for stabilizing ZrCl4 should be potassium or cesium

chlorides.

The method for the preparation of the compounds was

developed in the laboratory (1). The reaction between an

alkali chloride (ACl) and Zr or Hf tetrachlorides (MCl4)

is given as:

in which a known amount of ACl ground to -325 mesh

is reacted with an excess of purified MCI4 vapour at 1

following: Zirconium (or hafnium) tetrachloride was

loaded into one compartment while finely divided

anhydrous alkali chloride powder, exactly weighed,

vacuum and placed into the two compartment furnace

assembly.

Figure 7. Reaction cell arrangement for the syntheses

of the alkali hexachlorozirconates and

Hexachlorohafnates

The ACl side of the cell was heated to 485°C while that

of the tetrachloride was maintained at about 330°C

[5]. C.A. Pickles, G.J. Kipouros, R.G.V. Hancock