### Pressure- temperature phase diagram for water ($$H_2O)$$):

Much of the information about the control of the phase structure of a particular system is conveniently and concisely displayed in what is called a phase diagram, also often termed an equilibrium diagram. Now, there are three externally controllable parameters that will affect phase structure—temperature, pressure, and composition—and phase diagrams are constructed when various combinations of these parameters are plotted against one another.

The boundary line that separates two different phase is known as phase boundary. Here oa, ob, oc represents phase boundary. On separates solid and vapor phase, ob separates the solid and liquid and oc separates liquid and vapor phase.

Here different phases are in equilibrium at point as known as invariant point or triple point of water.

Phase diagram for different substances or material have been determined experimentally. For example; P-T phase diagram for carbon temperature-composition phase diagram for iron-carbon alloy etc. One component diagram is also known as unary phase diagram.

The point on a P–T phase diagram where three phases are in equilibrium is called a triple point.

Sometimes, it is also termed an invariant point and its position is distinct, or fixed by definite values of pressure and temperature. All three of the phase boundary curves intersect at a common point, which is labeled O (and for this H2O system, at a temperature of 273.16 K and a pressure of $$6.04\times 10^3$$ atm). This is the only one point at which all of the solid, liquid, and vapor phases are simultaneously in equilibrium with one another. P–T phase diagrams for different substances have been determined experimentally, which also have solid, liquid, and vapor phase regions. In these cases, when multiple solid phases exist, there will appear a region on the diagram for each solid phase, and also other triple points.

#### P-T phase diagram for carbon:

We can see different phases, such as graphite, diamond and liquid carbon on the same phase diagram.

Binary phase diagram or phase diagram for binary system:-

A phase diagram indicates what phases exist at equilibrium and what phase transformation we can expect when we change one parameter of the system. The phase diagram for materials with more than two components are complex and difficult to represents. For example: In the case of ternary alloy (Ni-Cu-Fe), a 3- dimensional diagram is required two dimensional phase diagram.

Many microstructures develop from phase transformations; by varying temperature (ordinarily upon cooling) there occur changes. It causes the transition from one phase to another or the appearance or disappearance of a phase.

Binary phase diagrams are graphical representation that represents the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy. It is very useful to use binary phase diagram to predict phase transformations and the resulting microstructures, which may have equilibrium or nonequilibrium character.

• #### Isomorphous system

It is a system of two components with complete solid solubility that may consist of liquid phase region can be identified on the phase diagram by symbols L for liquid phase, $$\alpha+L$$ for solid + liquid phase and $$\alpha$$ for solid phase as shown in composition (wt%) and temperature binary phase diagram.

The figure represents binary isomorphous phase diagram. It represents three different phase region. The line or boundary which separates liquid state from solid+liquid state is known as liquidous line. And the line which separate solid with solid+liquid is called solidous line. In diagram P represents melting point of only one component phase A and Q represents the melting point only one B type of component. There is no sharp melting point for AB composition. Examples of isomorphous (binary) system are Cu-Ni alloy.

For mixed composition (without pure substance), this melting phenomenon will occur over the range of temperatures between the solidus and liquidus lines. In this temperature range both solid $$\alpha$$ and liquid phases will be in equilibrium within.

For example, on heating an alloy of composition 50 wt% Ni–50 wt% Cu , melting begins at approximately $$1280^\circ C (2340^\circ F$$). The amount of liquid phase continuously increases with temperature until about $$1320^\circ C (\(2410^\circ F$$), at which the alloy is completely liquid.

#### References:

Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.

Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.

Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.

Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.

Raghavan, V. Material Science and Engineering. 4th . New Delhi: Pretence-Hall of India, 2003.

Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004.

1. diagram of phase :

2. The line or boundary which separates liquid state from solid+liquid state is known as liquid line. And the line which separate solid with solid+liquid is called solidous line. In diagram P represents melting point of only one component phase A and Q represents the melting point only one B type of component. There is no sharp melting point for AB composition. Examples of isomorphous (binary) system are Cu-Ni alloy.

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