How to find the thermal critical point of a metal and some of the assumptions taken to find the critical point

1. TO DESIGN AN
APPARATUS TO FIND
THE
THERMAL CRITICAL
POINT OF METAL
PREPARED BY:-
DHEIRYA. J. JOSHI

2. INTRODUCTION
Critical point occurs under conditions (such as specific values of
temperature, pressure or composition) at which no phase boundaries exist.
There are multiple types of critical points, including vapor–liquid critical
points and liquid–liquid critical points.
Critical point is sometimes used to specifically denote the vapor–liquid
critical point of a material, above which distinct liquid and gasphases do not
exist.
Critical properties vary from material to material, and for many pure
substances are readily available in the literature. Nonetheless, obtaining
critical properties for mixtures is more challenging.
For pure substances, there is an inflection point in the critical
isotherm constant temperature line) on a PV diagram. This means that at
the critical point
The Fe-Fe3C phase diagram refers only to the iron-carbon binary alloys
and does not fully apply to the steels i.e. iron base alloys (by a definition
with the carbon content) containing other elements. For example, all
modern steels contain manganese (used as an alloying element because
however much of its ability to bind sulphur as manganese sulphide MnS)
and low levels of the impurity atoms of sulphur and phosphorus. In the iron-carbon
binary system eutectoid reaction (under equilibrium conditions)
takes place at 727 °C and eutectoid point has a composition of 0.77%C [1].
Steels contain alloying elements and impurities (such as sulphur and
phosphorus) that modify the positions of the eutectoid point (both
temperature and composition). In addition, contrary to the iron-carbon
binary system, eutectoid transformation (during cooling) or pearlite to
austenite transformation (during heating) does not take place at constant
temperature but at the certain temperature range.
According to the EN 10025 standard, for the hypoeutectoid steels following
transformation temperatures (critical points) during heating can be

3. distinguished: Ac1 - temperature at which austenite begins to form and Ac3
- temperature at which ferrite completes its transformation into austenite.
Consequently, during cooling temperatures Ar3 - temperature at which
ferrite begins to form and Ar1 - temperature at which austenite completes
its transformation into ferrite or ferrite and cementite can be determined.
The formation of austenite in the hypoeutectoid steels consists of two
phenomena: pearlite dissolution and hypoeutectoid ferrite to austenite
transformation. The temperatures of austenite formation during continuous
heating used to be determined by dilatometric analysis. Modern high-resolution
dilatometers allows in some cases to accurate identification of
the finishing temperature of pearlite dissolution process and this
temperature is variously designated,
Until now the parameters of the critical point "liquid - steam" (temperature
Tc, density ρc, pressure Pc) for the majority of metals have still been
determined with insufficient reliability. For alkaline metals a number of
experimental data on Tc, ρc, Pc is known to be obtained in static
measurements, but with quite low reproducibility.
For some refractory metals the unit values of Tc, Pc were obtained in

4. pulse, dynamic experiments. Therefore basic part of the known data on Tc,
ρc, Pc for metals is obtained by calculation methods. However, their errors
were estimated seldom. For example, in [1] for iron the following calculation
values were obtained: Tc=9600K; ρc=2,03 g/сm3; Pc =825 МPа. These
data were confirmed, as it seemed, by the dynamic experiment [2], in which
there were determined : Tc =9250±700K ; Pc =875±50МPа (ρc was not
measured). However in [3], in using "wide-range multiphase state
equation", based on many diverse experimental data, the values
appreciably diverging from those in [1, 2] were obtained: Tc=7371K;
ρc=1.625 g/cm3; Pc=657 МPа.
But exactly these values of critical constants are more preferable, as the
new value Tc is in the middle of the range D of the other known Tc, ρc, Pc
estimations [4]: D(Tc) ≈5970-10000K; D(ρc)≈ 1.33-2.2 g/сm3; D(Pc)≈
27.5-1043 МPа. The major part of our estimations of iron critical
parameters have also got [5] into the middle of the same ranges: Tc =6686
K; ρc=1.803 g/сm3; Pc=673 МPа.
At the same time among the data in work [5] there were given two more
estimations of the complex of Tc, ρc, Pc parameters. It was methodically
linked with the known structural changes α↔γ↔δ in solid Fe and
prospective change δl ↔ γl in liquid Fe. These two estimations are also
found inside the specified ranges D(Tc), D(ρc), D(Pc) of iron. However, as
a whole, such ambiguity requires a rather extensive substantiation.
At the same time the similar calculation estimations of Tc, ρc, Pc for
alkaline metals and mercury partially given in [6] (and below, in table 2-4),
showed quite satisfactory conformity with the known experimental data for
Hg, K, Rb, Cs [1, 4 etc.].
The way for estimating the complex Tc, ρc, Pc, used in [5, 6], is based on
the special model of atomic structure of liquid metal and calculation
technique, following from it. This model allows to estimate the critical
density irrespective of other thermodynamic parameters and to explain
conformity of the new calculation and the experimental data on alkaline
metals and mercury.
At the same timethe offered model clears up the reason for divergence of
saturation lines ρ’(T)́ and ω’(τ) of mercury and alkaline metals noted in [7,

5. 8] by finding distinctions in the atomic structure of liquid metals correlating
with distinctions in their crystalline state structure.
Starting Preconditions
Model of metal elements structural state in the liquid state used in
calculations [5, 6], is based on many experimental facts and
numerical data (which are partially given in [5] and are available in other
works given in the literature reference). Generalizing
conclusions here are given in a number of postulates.
1) In crystalline and liquid state of elementary substance its atoms form
around them a stable structure of the short range ordering characterized by
coordination number Z1. The complex of atoms 1+ Z1 is a natural
elementary cell of a substance in the basic condensed states, crystalline
and liquid.
2) The first coordination number Z1 at "normal" metals does not change on
melting, i.e. Z1L=Z1S =Z1s. (Indices L and S relate the values to liquid L
and solid state S at Tm, indexes l and s - to the appropriate temperature
ranges of liquids and crystals).

6. 3) The first coordination number Z1l of a "normal" liquid metal does not
change in the interval from the melting point Tm to the critical point Tc, i.e.
Z1l=Z1L=Z1S=const. (The measured medium coordination number N1l
depends on temperature and decreases on heating from Z1L to N1c ≈ 2-3
~ as already on melting of a substance in distant coordination spheres,
including the second one, there appear single defects such as “ vacancies”,
and on further heating of the liquid the "vacancies" are united into
a quasi-free volume.)
4) Shortest inter-nuclear distance R1 in crystals is monotonously increased
from R10 tо R1S on heating from T=0 to Tm if the given substance has no
solid phase structural changes.
5) Shortest inter-nuclear distance R1 decreases on melting of the majority
of metals from R1S tо R1L.
6) Inter-nuclear distance R1l in the liquid state does not change on heating
from Tm to Tc, i.e. R1l ≠ f(T)=const=R1L.

7. 7) Value ρ0S is macrodensity of the "normal" crystal at T=0 coincides with
macrodensity ρ0l of a liquid "overcooled" to T=0, if the crystal does not
undergo structural transformations on heating from T=0 to Tm.
CONCLUSION
The calculated values of all three critical parameters
of alkaline metals are in quite good agreement with the results of
experiments, including those given in [8], not included in other reviews. On
all three parameters the results of the present work are within the ranges of
experimental values. The divergence of the majority of experimental and
calculation values is practically within the limits of 10%.
This comparison shows that with the described above technique of
calculating Tc, ρc, Pc complex of alkaline metals the error of the new data
makes about ±10%. Since for calculating the critical parameters of other
metals we used the initial data ρl(T) of the same origin and quality, it was
possible to expect that errors of the new data Tc, ρc, Pc in table 5-10 are
too at the level ±10%.
The analysis of numerical values in table 5-10 shows that the new data in
most cases are within the ranges of numerical values obtained in other
works [4, etc.]. Substantial divergences observed in some cases (as, for
example, was the case of Tc(Pt) in table 6) are not significant and can be
connected, most probably with errors in experimental ρl (T) at high
temperatures. Thus, for making new estimations the experimental data
should still be more precise.
The highest Pearson’ correlation coefficient value (but this value is still at
low level) and lowest standard estimation error (but still high) was obtained
by using modified Trzaska equation (eq.19), describing the influence of
chemical composition on the Ac1f critical temperature. The low level of
correlation coefficient value and high standard estimation error indicated so
big difference between calculated and experimental values of the pearlite
dissolution finish temperature Ac1f during heating of hypoeutectoid steels.
It is probably due to the not enough quantity of collected data set or
multiple regression method is unable to ensure greater correctness of such

8. calculations. It is possible that application of other suitable prediction
methods such as artificial neural network models should be more effective.