<s>
A	O
phase	B-Application
diagram	I-Application
in	O
physical	O
chemistry	O
,	O
engineering	O
,	O
mineralogy	O
,	O
and	O
materials	O
science	O
is	O
a	O
type	O
of	O
chart	O
used	O
to	O
show	O
conditions	O
(	O
pressure	O
,	O
temperature	O
,	O
volume	O
,	O
etc	O
.	O
)	O
</s>
<s>
Common	O
components	O
of	O
a	O
phase	B-Application
diagram	I-Application
are	O
lines	O
of	O
equilibrium	O
or	O
phase	O
boundaries	O
,	O
which	O
refer	O
to	O
lines	O
that	O
mark	O
conditions	O
under	O
which	O
multiple	O
phases	O
can	O
coexist	O
at	O
equilibrium	O
.	O
</s>
<s>
Metastable	O
phases	O
are	O
not	O
shown	O
in	O
phase	B-Application
diagrams	I-Application
as	O
,	O
despite	O
their	O
common	O
occurrence	O
,	O
they	O
are	O
not	O
equilibrium	O
phases	O
.	O
</s>
<s>
Triple	O
points	O
are	O
points	O
on	O
phase	B-Application
diagrams	I-Application
where	O
lines	O
of	O
equilibrium	O
intersect	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
water	O
phase	B-Application
diagram	I-Application
has	O
a	O
triple	O
point	O
corresponding	O
to	O
the	O
single	O
temperature	O
and	O
pressure	O
at	O
which	O
solid	O
,	O
liquid	O
,	O
and	O
gaseous	O
water	O
can	O
coexist	O
in	O
a	O
stable	O
equilibrium	O
(	O
and	O
a	O
partial	O
vapor	B-Application
pressure	O
of	O
)	O
.	O
</s>
<s>
Working	O
fluids	O
are	O
often	O
categorized	O
on	O
the	O
basis	O
of	O
the	O
shape	O
of	O
their	O
phase	B-Application
diagram	I-Application
.	O
</s>
<s>
The	O
simplest	O
phase	B-Application
diagrams	I-Application
are	O
pressure	O
–	O
temperature	O
diagrams	O
of	O
a	O
single	O
simple	O
substance	O
,	O
such	O
as	O
water	O
.	O
</s>
<s>
The	O
phase	B-Application
diagram	I-Application
shows	O
,	O
in	O
pressure	O
–	O
temperature	O
space	O
,	O
the	O
lines	O
of	O
equilibrium	O
or	O
phase	O
boundaries	O
between	O
the	O
three	O
phases	O
of	O
solid	O
,	O
liquid	O
,	O
and	O
gas	O
.	O
</s>
<s>
The	O
curves	O
on	O
the	O
phase	B-Application
diagram	I-Application
show	O
the	O
points	O
where	O
the	O
free	O
energy	O
(	O
and	O
other	O
derived	O
properties	O
)	O
becomes	O
non-analytic	O
:	O
their	O
derivatives	O
with	O
respect	O
to	O
the	O
coordinates	O
(	O
temperature	O
and	O
pressure	O
in	O
this	O
example	O
)	O
change	O
discontinuously	O
(	O
abruptly	O
)	O
.	O
</s>
<s>
The	O
open	O
spaces	O
,	O
where	O
the	O
free	O
energy	O
is	O
analytic	B-Language
,	O
correspond	O
to	O
single	O
phase	O
regions	O
.	O
</s>
<s>
Instead	O
,	O
it	O
terminates	O
at	O
a	O
point	O
on	O
the	O
phase	B-Application
diagram	I-Application
called	O
the	O
critical	O
point	O
.	O
</s>
<s>
For	O
most	O
substances	O
,	O
the	O
solid	O
–	O
liquid	O
phase	O
boundary	O
(	O
or	O
fusion	O
curve	O
)	O
in	O
the	O
phase	B-Application
diagram	I-Application
has	O
a	O
positive	O
slope	O
so	O
that	O
the	O
melting	O
point	O
increases	O
with	O
pressure	O
.	O
</s>
<s>
Other	O
exceptions	O
include	O
antimony	O
and	O
bismuth	B-Algorithm
.	O
</s>
<s>
For	O
multicomponent	O
mixtures	O
,	O
like	O
the	O
ones	O
naturally	O
occurring	O
in	O
hydrocarbon	O
reservoirs	O
,	O
the	O
phase	B-Application
diagram	I-Application
turns	O
into	O
a	O
phase	O
envelope	O
.	O
</s>
<s>
In	O
addition	O
to	O
temperature	O
and	O
pressure	O
,	O
other	O
thermodynamic	O
properties	O
may	O
be	O
graphed	O
in	O
phase	B-Application
diagrams	I-Application
.	O
</s>
<s>
Examples	O
of	O
such	O
thermodynamic	O
properties	O
include	O
specific	O
volume	O
,	O
specific	O
enthalpy	O
,	O
or	O
specific	O
entropy	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
single-component	O
graphs	O
of	O
temperature	O
vs.	O
specific	O
entropy	B-Algorithm
(	O
T	O
vs.	O
s	O
)	O
for	O
water/steam	O
or	O
for	O
a	O
refrigerant	O
are	O
commonly	O
used	O
to	O
illustrate	O
thermodynamic	O
cycles	O
such	O
as	O
a	O
Carnot	O
cycle	O
,	O
Rankine	O
cycle	O
,	O
or	O
vapor-compression	O
refrigeration	O
cycle	O
.	O
</s>
<s>
The	O
equilibrium	O
conditions	O
are	O
shown	O
as	O
curves	O
on	O
a	O
curved	O
surface	O
in	O
3D	O
with	O
areas	O
for	O
solid	O
,	O
liquid	O
,	O
and	O
vapor	B-Application
phases	O
and	O
areas	O
where	O
solid	O
and	O
liquid	O
,	O
solid	O
and	O
vapor	B-Application
,	O
or	O
liquid	O
and	O
vapor	B-Application
coexist	O
in	O
equilibrium	O
.	O
</s>
<s>
A	O
line	O
on	O
the	O
surface	O
called	O
a	O
triple	O
line	O
is	O
where	O
solid	O
,	O
liquid	O
and	O
vapor	B-Application
can	O
all	O
coexist	O
in	O
equilibrium	O
.	O
</s>
<s>
The	O
critical	O
point	O
remains	O
a	O
point	O
on	O
the	O
surface	O
even	O
on	O
a	O
3D	O
phase	B-Application
diagram	I-Application
.	O
</s>
<s>
When	O
this	O
is	O
done	O
,	O
the	O
solid	O
–	O
vapor	B-Application
,	O
solid	O
–	O
liquid	O
,	O
and	O
liquid	O
–	O
vapor	B-Application
surfaces	O
collapse	O
into	O
three	O
corresponding	O
curved	O
lines	O
meeting	O
at	O
the	O
triple	O
point	O
,	O
which	O
is	O
the	O
collapsed	O
orthographic	O
projection	O
of	O
the	O
triple	O
line	O
.	O
</s>
<s>
Other	O
much	O
more	O
complex	O
types	O
of	O
phase	B-Application
diagrams	I-Application
can	O
be	O
constructed	O
,	O
particularly	O
when	O
more	O
than	O
one	O
pure	O
component	O
is	O
present	O
.	O
</s>
<s>
Phase	B-Application
diagrams	I-Application
with	O
more	O
than	O
two	O
dimensions	O
can	O
be	O
constructed	O
that	O
show	O
the	O
effect	O
of	O
more	O
than	O
two	O
variables	O
on	O
the	O
phase	O
of	O
a	O
substance	O
.	O
</s>
<s>
Phase	B-Application
diagrams	I-Application
can	O
use	O
other	O
variables	O
in	O
addition	O
to	O
or	O
in	O
place	O
of	O
temperature	O
,	O
pressure	O
and	O
composition	O
,	O
for	O
example	O
the	O
strength	O
of	O
an	O
applied	O
electrical	O
or	O
magnetic	O
field	O
,	O
and	O
they	O
can	O
also	O
involve	O
substances	O
that	O
take	O
on	O
more	O
than	O
just	O
three	O
states	O
of	O
matter	O
.	O
</s>
<s>
One	O
type	O
of	O
phase	B-Application
diagram	I-Application
plots	O
temperature	O
against	O
the	O
relative	O
concentrations	O
of	O
two	O
substances	O
in	O
a	O
binary	O
mixture	O
called	O
a	O
binary	O
phase	B-Application
diagram	I-Application
,	O
as	O
shown	O
at	O
right	O
.	O
</s>
<s>
Another	O
type	O
of	O
binary	O
phase	B-Application
diagram	I-Application
is	O
a	O
boiling-point	O
diagram	O
for	O
a	O
mixture	O
of	O
two	O
components	O
,	O
i	O
.	O
e	O
.	O
chemical	O
compounds	O
.	O
</s>
<s>
For	O
two	O
particular	O
volatile	O
components	O
at	O
a	O
certain	O
pressure	O
such	O
as	O
atmospheric	O
pressure	O
,	O
a	O
boiling-point	O
diagram	O
shows	O
what	O
vapor	B-Application
(	O
gas	O
)	O
compositions	O
are	O
in	O
equilibrium	O
with	O
given	O
liquid	O
compositions	O
depending	O
on	O
temperature	O
.	O
</s>
<s>
The	O
construction	O
of	O
a	O
liquid	O
vapor	B-Application
phase	B-Application
diagram	I-Application
assumes	O
an	O
ideal	O
liquid	O
solution	O
obeying	O
Raoult	O
's	O
law	O
and	O
an	O
ideal	O
gas	O
mixture	O
obeying	O
Dalton	O
's	O
law	O
of	O
partial	O
pressure	O
.	O
</s>
<s>
The	O
fact	O
that	O
there	O
are	O
two	O
separate	O
curved	O
lines	O
joining	O
the	O
boiling	O
points	O
of	O
the	O
pure	O
components	O
means	O
that	O
the	O
vapor	B-Application
composition	O
is	O
usually	O
not	O
the	O
same	O
as	O
the	O
liquid	O
composition	O
the	O
vapor	B-Application
is	O
in	O
equilibrium	O
with	O
.	O
</s>
<s>
See	O
Vapor	B-Application
–	O
liquid	O
equilibrium	O
for	O
more	O
information	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
above-mentioned	O
types	O
of	O
phase	B-Application
diagrams	I-Application
,	O
there	O
are	O
many	O
other	O
possible	O
combinations	O
.	O
</s>
<s>
Some	O
of	O
the	O
major	O
features	O
of	O
phase	B-Application
diagrams	I-Application
include	O
congruent	O
points	O
,	O
where	O
a	O
solid	O
phase	O
transforms	O
directly	O
into	O
a	O
liquid	O
.	O
</s>
<s>
A	O
complex	O
phase	B-Application
diagram	I-Application
of	O
great	O
technological	O
importance	O
is	O
that	O
of	O
the	O
iron	O
–	O
carbon	O
system	O
for	O
less	O
than	O
7%	O
carbon	O
(	O
see	O
steel	O
)	O
.	O
</s>
<s>
For	O
a	O
representation	O
of	O
ternary	O
equilibria	O
a	O
three-dimensional	O
phase	B-Application
diagram	I-Application
is	O
required	O
.	O
</s>
<s>
To	O
represent	O
composition	O
in	O
a	O
ternary	O
system	O
an	O
equilateral	O
triangle	O
is	O
used	O
,	O
called	O
Gibbs	O
triangle	O
(	O
see	O
also	O
Ternary	B-Application
plot	I-Application
)	O
.	O
</s>
<s>
Thus	O
,	O
the	O
space	O
model	O
of	O
a	O
ternary	O
phase	B-Application
diagram	I-Application
is	O
a	O
right-triangular	O
prism	O
.	O
</s>
<s>
Attention	O
has	O
been	O
directed	O
to	O
mesophases	O
because	O
they	O
enable	O
display	B-Device
devices	I-Device
and	O
have	O
become	O
commercially	O
important	O
through	O
the	O
so-called	O
liquid-crystal	B-Device
technology	O
.	O
</s>
<s>
Phase	B-Application
diagrams	I-Application
are	O
used	O
to	O
describe	O
the	O
occurrence	O
of	O
mesophases	O
.	O
</s>
