PHASES

Phase is a region of space throughout which all physical properties of a material are essentially uniform

Physical properties include density, index of refraction, magnetization and chemical composition

Phase is sometimes used as a synonym for state of matter

DEFINATIONS

In optics the refractive index or index of refraction n of a substance is a dimensionless number that describes how light, or any other radiation, propagates through that medium

in classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material

he chemical composition of a pure substance it corresponds to the relative amounts of the elements that constitute the substance itself. It can be express by the empirical formula .

For example the formula for water  is H2O: this means that each molecule it is constituted by 2 atoms of hydrogen (H) and 1 atom on oxygen (O2)

The chemical composition of a mixture can be defined as the distribution of the single substances that constitute the mixture (called "components")

SMALL PIECE OF RAPIDLY MELTING ARGON ICE SHOWS THE TRANSITION FROM SOLID TO LIQUID

PHASES

TYPES OF PHASES

Distinct phases described as different states of matter such as gas, liquid, solid, plasma or Bose–Einstein condensate. Useful meso phases between solid and liquid form

A mixture of water (a polar liquid) and oil (a non-polar liquid) will spontaneously separate into two phases. Water has a very low solubility (is insoluble) in oil, and oil has a low solubility in water other states of matter

Solubility is the maximum amount of a solute that can dissolve in a solvent

TYPES OF PHASES

Mixture of ethylene glycol and toluene may separate into two distinct organic phases.

Eight immiscible liquid phases have been observed. Mutually immiscible liquid phases are formed from water (aqueous phase), hydrophobic organic solvents, fluorous phase, silicones, several different metals, and also from molten phosphorus. Not all organic solvents are completely miscible

Phases do not need to macroscopically separate spontaneously. Emulsions and colloids are examples of immiscible phase pair combinations that do not physically separate.

PHASE EQUILIBRIUM

Left to equilibration, many compositions will form a uniform single phase, but depending on the temperature and pressure even a single substance may separate into two or more distinct phases. Within each phase, the properties are uniform but between the two phases properties differ.

At equilibrium, evaporation and condensation processes exactly balance and there is no net change in the volume of either phase.

PHASE EQUILIBRIUM

Over 100 °C, the transition from liquid to gas will occur not only at the surface, but throughout the liquid volume: the water boils

NUMBER OF PHASES…..P

For a given composition, only certain phases are possible at a given temperature and pressure. The number and type of phases that will form is hard to predict and is usually determined by experiment

Above the critical point, there are no longer separate liquid and gas phases: there is only a generic fluid phase referred to as a supercritical fluid. In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa

Typical phase diagram for a single-component material, exhibiting solid, liquid and gaseous phases. The solid green line shows the usual shape of the liquid–solid phase line. The dotted green line shows the anomalous behavior of water when the pressure increases. The triple point and the critical point are shown as red dots

NUMBER OF PHASES…..P

An unusual feature of the water phase diagram is that the solid–liquid phase line (illustrated by the dotted green line) has a negative slope. For most substances, the slope is positive as exemplified by the dark green line. This unusual feature of water is related to ice having a lower density than liquid water. Increasing the pressure drives the water into the higher density phase, which causes melting

NUMBER OF PHASES…..P

INTERFACIAL PHENOMENA

Between two phases in equilibrium there is a narrow region where the properties are not that of either phase. Although this region may be very thin, it can have significant and easily observable effects, such as causing a liquid to exhibit surface tension. In mixtures, some components may preferentially move toward the interface. In terms of modeling, describing, or understanding the behavior of a particular system, it may be efficacious to treat the interfacial region as a separate phase

CRYSTAL PHASES

A single material may have several distinct solid states capable of forming separate phases. Water is a well-known example of such a material. For example, water ice is ordinarily found in the hexagonal form ice Ih, but can also exist as the cubic ice Ic, the rhombohedral ice II, and many other forms. Polymorphism is the ability of a solid to exist in more than one crystal form. For pure chemical elements, polymorphism is known as allotropy. For example, diamond, graphite, and fullerenes are different allotropes of carbon

PHASE TRANSITIONS

When a substance undergoes a phase transition (changes from one state of matter to another) it usually either takes up or releases energy.

The heat energy, or enthalpy, associated with a solid to liquid transition is the enthalpy of fusion and that associated with a solid to gas transition is the enthalpy of sublimation.

DEGREES OF FREEDOM….F

degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all dimensions of a system is known as a phase space, and degrees of freedom are sometimes referred to as its dimensions

A degree of freedom of a physical system refers to a parameter that is necessary to characterize the state of a physical system.

COMPONENT…..C

In thermodynamics, a component is a chemically-independent constituent of a system. The number of components represents the minimum number of independent species necessary to define the composition of all phases of the system.

Calculating the number of components in a system is necessary, for example, when applying Gibbs' phase rule in determination of the number of degrees of freedom of a system

The number of components is equal to the number of distinct chemical species (constituents), minus the number of chemical reactions between them, minus the number of any constraints (like charge neutrality or balance of molar quantities).

COMPONENT….C

WATER

A system that contains water in the liquid state also contains hydronium cations and hydroxyl anions according to the reaction:

2 H2O   H3O+ + OH-

The number of components in such a system is..

3 chemical constituents - 1 chemical reaction - 1 constraint (charge neutrality) = 1.

CaCO3 - CaO - CO2 system

This is an example of a system with several phases, which at ordinary temperatures are two solids and a gas. There are three chemical species (CaCO3, CaO and CO2) and one reaction CaCO3   CaO + CO2. The number of components is then 3 - 1 = 2.

If the composition of the same system is instead expressed in terms of ions, the number of independent components does not change. There are now 4 chemical species (Ca2+, CO3

2-, O2- and CO2) and the number of components is calculated as

4 chemical constituents - 1 chemical reaction - 1 constraint (charge neutrality) = 2.

COMPONENT….C

COMPONENT….C

WATER - HYDROGEN - OXYGEN

The reactions included in the calculation are only those that actually occur under the given conditions, and not those that might occur under different conditions such as higher temperature or the presence of a catalyst. For example, the dissociation of water into its elements does not occur at ordinary temperature, so a system of water, hydrogen and oxygen at 25 °C has 3 independent components

INTENSIVE AND EXTENSIVE PROPERTIES

Physical properties of materials and systems are often described as intensive and extensive properties.

This classification relates to the dependency of the properties upon the size or extent of the system or object in question

INTENSIVE PROPERTY

An intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, refractive index, density, and hardness of an object. No matter how small a diamond is cut, it maintains its intrinsic hardness

INTENSIVE PROPERTY

An intensive property is a physical quantity whose value does not depend on the amount of the substance for which it is measured. For example, the temperature of a system in thermal equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical. The same applies to the density of a homogeneous system; if the system is divided in half, the mass and the volume change in the identical ratio and the density remains unchanged. Additionally, the boiling point of a substance is another example of an intensive property. For example, the boiling point for water is 100°C at a pressure of one atmosphere, a fact which remains true regardless of quantity.

INTENSIVE PROPERTY

MagnetizationMalleabilityMelting point and boiling pointMolar absorptivityPressureSpecific energySpecific heat capacitySpecific volumeTemperature

Chemical potentialConcentration Density DuctilityElasticityElectrical resistivityHardnessMagnetic fieldViscosity

EXTENSIVE PROPERTY

extensive property is one that is additive for independent, non interacting subsystems. The property is proportional to the amount of material in the system. For example, both the mass and the volume of a diamond are directly proportional to the amount that is left after cutting it from the raw mineral. Mass and volume are extensive properties, but hardness is intensive.

The ratio of two extensive properties is scale-invariant

EXTENSIVE PROPERTY

An extensive property is defined a physical quantity which is the sum of the properties of separate non interacting subsystems that compose the entire system. The value of such an additive property is proportional to the size of the system it describes, or to the quantity of matter in the system. Taking on the example of melting ice, the amount of heat required to melt ice is an extensive property. The amount of heat required to melt one ice cube would be much less than the amount of heat required to melt an iceberg, so it is dependent on the quantity.

EXTENSIVE PROPERTY

energy entropy Gibbs energy length mass particle number momentum number of moles volume magnetic moment electrical charge weight

EXTENSIVE AND INTENSIVE THERMODYNAMIC PROPERTIES

Corresponding extensive and intensive thermodynamic properties

Extensiveproperty

Symbol SI units Intensive

property**Symbo

l SI units

Volume V m3 or L* Specific volume*** v m3/kg or L*/kg

Internal energy U J Specific internal energy u J/kg

Entropy S J/K Specific entropy s J/(kg·K)

Enthalpy H J Specific enthalpy h J/kg

Gibbs free energy G J Specific Gibbs free energy g J/kg

Heat capacityat constant volume CV J/K Specific heat capacity

at constant volume cv J/(kg·K)

Heat capacityat constant pressure CP J/K Specific heat capacity

at constant pressure cP J/(kg·K)

PHASE RULE

Gibbs' phase rule was proposed by Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published from 1875 to 1878. The rule is the equality

where F is the number of degrees of freedom, C is the number of component and P is the number of phases

PHASE RULE

The number of degrees of freedom is the number of independent intensive variables, i.e. the largest number of properties such as temperature or pressure that can be varied simultaneously and arbitrarily without affecting one another. An example of one-component system is a system involving one pure chemical, while two-component systems, such as mixtures of water and ethanol, have two chemically independent components, and so on. Typical phases are solids, liquids and gases.

 

PHASE RULE

FOUNDATIONS

A phase is a form of matter that is homogeneous in chemical composition and physical state. Typical phases are solid, liquid and gas. Two immiscible liquids (or liquid mixtures with different compositions) separated by a distinct boundary are counted as two different phases, as are two immiscible solids

The number of components (C) is the number of chemically independent constituents of the system, i.e. the minimum number of independent species necessary to define the composition of all phases of the system

The number of degrees of freedom (F) in this context is the number of intensive variables which are independent of each other.

PHASE RULE

To be more specific, the composition of each phase is determined by

C-1 intensive variables (such as mole fractions) in each phase. The total number of variables is (C–1) P + 2, where the extra two are temperature T and pressure p. The number of constraints are C( P–1), since the chemical potential of each component must be equal in all phases. Subtract the number of constraints from the number of variables to obtain the number of degrees of freedom as F = (C–1) P + 2 – C (P–1) = C – P + 2.

The rule is valid provided the equilibrium between phases is not influenced by gravitational, electrical or magnetic forces, or by surface area, and only by temperature, pressure, and concentration.

PURE SUBSTANCES (ONE COMPONENT)

For pure substances C = 1 so that F = 3 – P. In a single phase (P = 1) condition of a pure component system, two variables (F = 2), such as temperature and pressure, can be chosen independently to be any pair of values consistent with the phase. However, if the temperature and pressure combination ranges to a point where the pure component undergoes a separation into two phases (P = 2), F decreases from 2 to 1. When the system enters the two-phase region, it becomes no longer possible to independently control temperature and pressure.

Carbon dioxide pressure-temperature phase diagram showing the triple point and critical point of carbon dioxide

PURE SUBSTANCES (ONE COMPONENT)

PURE SUBSTANCES (ONE COMPONENT)

In the phase diagram to the right, the boundary curve between the liquid and gas regions maps the constraint between temperature and pressure when the single-component system has separated into liquid and gas phases at equilibrium. If the pressure is increased by compression, some of the gas condenses and the temperature goes up. If the temperature is decreased by cooling, some of the gas condenses, decreasing the pressure. Throughout both processes, the temperature and pressure stay in the relationship shown by this boundary curve unless one phase is entirely consumed by evaporation or condensation, or unless the critical point is reached. As long as there are two phases, there is only one degree of freedom, which corresponds to the position along the phase boundary curve.

PURE SUBSTANCES (ONE COMPONENT)

The critical point is the black dot at the end of the liquid-gas boundary. As this point is approached, the liquid and gas phases become progressively more similar until, at the critical point, there is no longer a separation into two phases. Above the critical point and away from the phase boundary curve, F = 2 and the temperature and pressure can be controlled independently. Hence there is only one phase, and it has the physical properties of a dense gas, but is also referred to as a supercritical fluid

PURE SUBSTANCES (ONE COMPONENT)

Of the other two-boundary curves, one is the solid–liquid boundary or melting point curve which indicates the conditions for equilibrium between these two phases, and the other at lower temperature and pressure is the solid–gas boundary.

Even for a pure substance, it is possible that three phases, such as solid, liquid and vapour, can exist together in equilibrium (P = 3). If there is only one component, there are no degrees of freedom (F = 0) when there are three phases. Therefore, in a single-component system, this three-phase mixture can only exist at a single temperature and pressure, which is known as a triple point. Here there are two equations μsol(T, p) = μliq(T, p) = μvap(T, p), which are sufficient to determine the two variables T and p. In the diagram for CO2 the triple point is the point at which the solid, liquid and gas phases come together, at 5.2 bar and 217 K.

TWO-COMPONENT SYSTEMS

For binary mixtures of two chemically independent components, C = 2 so that F = 4 – P. In addition to temperature and pressure, the other degree of freedom is the composition of each phase, often expressed as mole fraction or mass fraction of one component.

Boiling Point Diagram

TWO-COMPONENT SYSTEMS

As an example, consider the system of two completely miscible liquids such as toluene and benzene, in equilibrium with their vapours. This system may be described by a boiling-point diagram which shows the composition (mole fraction) of the two phases in equilibrium as functions of temperature (at a fixed pressure).

Four thermodynamic variables which may describe the system include temperature (T), pressure (p), mole fraction of component 1 (toluene) in the liquid phase (x1L), and mole fraction of component 1 in the vapour phase (x1V). However since two phases are in equilibrium, only two of these variables can be independent (F = 2). This is because the four variables are constrained by two relations: the equality of the chemical potentials of liquid toluene and toluene vapour, and the corresponding equality for benzene.

TWO-COMPONENT SYSTEMS

For given T and p, there will be two phases at equilibrium when the overall composition of the system (system point) lies in between the two curves. A horizontal line (isotherm or tie line) can be drawn through any such system point, and intersects the curve for each phase at its equilibrium composition. The quantity of each phase is given by the lever rule(expressed in the variable corresponding to the x-axis, here mole fraction).

PHASE RULE AT CONSTANT PRESSURE

For applications in materials science dealing with phase changes between different solid structures, pressure is often imagined to be constant (for example at one atmosphere), and is ignored as a degree of freedom, so the rule becomes

F = C − P + 1 

This is sometimes misleadingly called the "condensed phase rule", but it is not applicable to condensed systems which are subject to high pressures (for example, in geology), since the effects of these pressures can be important.

MISCIBILITY

Miscibility is the property of substances to mix in all proportions, forming a homogeneous solution. The term is most often applied to liquids, but applies also to solids and gases. Water and ethanol, for example, are miscible because they mix in all proportions.

By contrast, substances are said to be immiscible if a significant proportion does not form a solution. Otherwise, the substances are considered miscible. For example, butanone is significantly soluble in water, but these two solvents are not miscible because they are not soluble in all proportions.

PHASE DIAGRAM

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium. In mathematics and physics, "phase diagram" is used with a different meaning: a synonym for a phase space

PHASE DIAGRAM

OVERVIEW

Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.

Triple points are points on phase diagrams where lines of equilibrium intersect. Triple points mark conditions at which three different phases can coexist. For example, the water phase diagram has a triple point corresponding to the single temperature and pressure at which solid, liquid, and gaseous water can coexist in a stable equilibrium.

PHASE DIAGRAM

The solidus is the temperature below which the substance is stable in the solid state. The liquidus is the temperature above which the substance is stable in a liquid state. There may be a gap between the solidus and liquidus; within the gap, the substance consists of a mixture of crystals and liquid (like a "slurry").

2D PHASE DIAGRAMS

2D PHASE DIAGRAMS

The simplest phase diagrams are pressure–temperature diagrams of a single simple substance, such as water. The axes correspond to the pressure and temperature. The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas

A typical phase diagram. The solid green line applies to most substances; the dotted green line gives the anomalous behavior of water. The green lines mark the freezing point and the blue line the boiling point, showing how they vary with pressure

2D PHASE DIAGRAMS

The solid–liquid phase boundary in the phase diagram of most substances has a positive slope; the greater the pressure on a given substance, the closer together the molecules of the substance are brought to each other, which increases the effect of the substance's intermolecular forces. Thus, the substance requires a higher temperature for its molecules to have enough energy to break out of the fixed pattern of the solid phase and enter the liquid phase. A similar concept applies to liquid–gas phase changes. Water, because of its particular properties, is one of the several exceptions to the rule.

3D PHASE DIAGRAMS

http://en.wikipedia.org/wiki/File:PVT_3D_diagram.png