Phase transition

A phase change or a phase change or phase transformation in thermodynamics, the conversion of one or more phases of a substance into other phases. A graphical representation of the stability regions of the phases as a function of the state variable such as pressure, temperature, chemical composition, magnetic field strength and providing the phase diagrams. In these diagrams, the stability regions are limited by phase boundary lines, which sustain the phase transitions.

Classification

Phase transitions may, inter alia, between solid, liquid and gaseous phases occur. For phase transitions between certain states of aggregation, there are special names:

• Melting ( transition from solid to liquid )
• Evaporation (transition from liquid to gas )
• Sublimation (change from solid to gas)
• Solidification or freezing ( transition from liquid to solid )
• Condensing (transition from gas to liquid)
• Resublimation (transition from gas to solid)

In some material systems disappear above a critical point, which is characterized by a critical temperature and a critical pressure, the interfacial area between the liquid and gaseous phase. This liquid and gas under these conditions was only a phase, which is called " supercritical". Thus, it can be there no evaporation and condensation give more. Likewise, there may be some material systems a triple point at which both a firm, as well as a liquid and a gaseous phase in equilibrium with each other and accordingly run all six first-mentioned forms of the phase transition at the same time.

Other types of phase transitions will be mentioned hereafter.

Classification according to Ehrenfest

Basically, phase transitions according to the Ehrenfest classification are divided into different orders ( according to Paul Ehrenfest ). This considering thermodynamic variables such as volume, enthalpy, entropy or a function of one (or more ) variables, usually the temperature. The system is a thermodynamic potential G ( Gibbs free energy, free enthalpy ) described. At a phase transition -order G as a function as the temperature ( or pressure ) is considered along with its first ( n-1) continuously discharges, only the -th derivative is discontinuous. Specifically, phase transitions in the Landau theory are described, where the phases by symmetry breakings of ordered to disordered phases and accompanying jumps macroscopic quantities such as the magnetization or the deformation of a crystal lattice are in the order parameters.

Of particular importance is the distinction between first -order phase transitions and such higher-order (continuous phase transitions ), especially second order. In the modern classification only this distinction is made in the deed. An example of a first-order phase transition is the transition of a liquid such as water to a solid at the melting point. To transfer from the solid to the liquid state, in addition the heat energy must be supplied (in the form of latent heat ), without causing an actual temperature increase. Since there will be a discontinuity in the entropy ( the first derivative of the free energy G with respect to temperature ), the melting of ice is a phase transition of first order. Also, the volume makes ( 1 derivative of g after the pressure p ), a crack at the interface. The density difference between the phases here corresponds to the order parameter in the Landau theory. A jump in the order parameter is typical for phase transitions of the first kind

An example of a 2nd order phase transition is the transition from the ferromagnetic to paramagnetic phase at the Curie temperature in a ferromagnet. The order parameter is the magnetization, the ever goes to zero at the phase transition without causing additional latent heat occurs. It takes but a jump in the second derivative of the enthalpy with respect to the temperature ( heat capacity). This behavior indicates a continuous phase transition or a second -order phase transition. Typical here is a continuous transition in the order parameter. Another example of a second order phase transition is the transition from the normal metal to superconductor.

The following figure shows the mentioned phase transitions 1st and 2nd order by Ehrenfest are shown. The figure shows at constant pressure, the free energy G, the volume V, the enthalpy H, the entropy S and the heat capacity CP as a function of temperature. In the top row of the parameter without the phase transition is shown in the center of a phase transition of first order, and in the lower row the second-order phase transition. The phase transformation takes place respectively at the critical temperature Tc. The figure shows the curves of the Gibbs free energy of each phase are drawn and gray continued in the other phase; there they can predict undercooling effects and metastability.

Further typing

In addition to this basic classification, there are a number of other distinctions in specific application areas.

According to the structural classification, a distinction in mineralogy between discontinuous ( = reconstructive ), martensitic and continuous phase transitions. Discontinuous phase transitions are characterized by the breakage of chemical bonds. An example is the conversion of graphite to diamond. In the martensitic phase transitions, the crystal lattice is sheared. An example is the conversion of γ -to α - iron. Martensitic phase transitions are again divided into athermal and isothermal phase transitions. In contrast to the former is the degree of conversion time depends on the latter. Continuous phase transitions associated with an order of the crystal structure. There are two subtypes: displacive and order-disorder phase transitions. In the former, there is a displacement or rotation of the atomic positions (for example in the conversion of beta-quartz in the depth of quartz ), the latter to be of an order of several such that each position is occupied only by one type of atom in different atomic positions randomly distributed atoms. In both cases it can lead to the occurrence of large-scale periodicities, which are superimposed on the mesh structure. These are called incommensurate structures.

The kinetic classification divides the phase transitions according to the reaction rate in phase transitions of zero order, in which the reaction speed is constant, the phase transitions of the first order, wherein it depends on the concentration of the initial phase and phase transitions of the second (third ) order in which they are on the concentrations of two ( three) starting materials depends.

Dynamic flow, a distinction is speed transitions where flow characteristics change abruptly and dramatically. For example, the change of important values ​​such as drag and lift for gases and liquids. One important area is the critical transition from subcritical to supercritical.

Examples

Phase transitions are often associated with the change of certain material characteristics, such as:

• Change of the crystal structure ( structural phase transition) or the adsorbate.
• Exchange between ferromagnetic and paramagnetic behavior at the critical or Curie temperature
• Switching between different magnetic ordering, eg by commensurate to incommensurate magnetic structure
• Exchange between ferromagnetic and dielectric behavior
• In high energy physics: emergence of quark-gluon plasma at high temperatures and pressures
• Transition to superfluidity
• Transition to superconductivity
• Transition from subcritical flow to supercritical ( fluid dynamics ).
• Transition from a smooth to an atomically roughened crystal surface ( faceting )

Theory

The theory of continuous phase transition is based on an order of parameters (for example, magnetization in the conversion of a ferromagnet into a paramagnet ). For continuous phase transitions the order parameter goes when approaching the transition point continuously to zero ( on the other hand, he jumps on a first -order phase transition ) and the correlation length diverges ( at a conversion first order remains they finally). It can be very different types of continuous phase transitions in universality classes summarize what is ultimately again due to the divergence of the correlation length. These classes can be characterized by a few parameters. For example, the order parameter disappears in the vicinity of the critical point, for example, as a function of the distance to the transition point temperature, in the form of a power law. The associated exponent is the critical exponent is one such parameter.

The relationship between basic symmetries of the respective phases and the values ​​of these parameters has been studied in the context of statistical physics in the last decades in detail theoretically and verified in a variety of experiments and in computer simulations. In theoretical descriptions of phase transitions the Landau or mean-field theory is used sometimes. However, critical thermal fluctuations are neglected, which may play a significant role in the area of transition ( and be observed for example in the critical opalescence ). The Landau theory can still provide valuable first insights as a starting point closer theories (of the scaling theory of Pokrovsky and Patashinski up to epsilon- development of KG Wilson and ME Fisher). This has been specifically recognized by Kenneth G. Wilson, who in 1982 received the Nobel Prize for pioneering work on continuous phase transitions. Wilson is one of the key pioneers of the renormalization group theory, which takes into account that at continuous phase transitions take place, the critical fluctuations on many length scales in self-similar form. Analog theories found in many areas of physics and mathematics application.

Importance for the mineralogy

Knowledge of the physicochemical conditions where run phase transitions, allowed mineralogists conclusions about the genesis of rocks. If a rock falls under high pressures and temperatures, it is used in many cases to a phase transformation. With the proviso that the subsequent cooling is performed so rapidly that the reverse reaction no longer takes place because of the low temperature scarcely possible diffusion, it can be assumed that the stable at high temperatures and pressures minerals are "frozen", and so on earth's surface are retained. Thus statements about possible what temperatures and pressures "seen" a rock in the course of its genesis has. Examples are the phase transitions between andalusite, sillimanite and kyanite in the field of aluminosilicates, the conversion of graphite into diamond and quartz in coesite or stishovite. The acquired through experimental mineralogy knowledge of phase transitions also explains the rheological behavior of the Earth's mantle: The iron - magnesium silicate olivine in 410 km depth in the crystallizing in the β - spinel structure wadsleyite to, in turn, in 520 km depth further in to the occurring in the γ - spinel structure ringwoodite transforms (see also Article 410 - km discontinuity and 520 - km discontinuity ). In this case, there is no chemical changes, but only a change in the crystal structure. The example of the transformation of coesite to stishovite can well explain why there is a phase transition: Under normal conditions, silicon is surrounded by four oxygen atoms at high pressures, however, bring the atoms closer together, so that the coordination by six oxygen atoms is energetically more favorable.

Importance for industrial processes

During the ceramic firing quartz transforms at a temperature of 573 ° C in high quartz to. This makes the volume changes. In a large heating rate may result in breakage of the ceramic. Therefore, the heating rate is restricted in this temperature range. In the field of conservation of art objects, the objects are often stored in cool, dry and well exposed. For objects made ​​of tin, this is not correct, because this goes below 15 ° C in another modification, the appearance is very attractive and is known as tin pest. For the history of art, it is interesting to know that in the past often the blue pigment azurite was used for the representation of the sky. Over the centuries, this has however been converted into the thermodynamically stable form of malachite, which is green. This heaven on old pictures is sometimes green. In steelmaking changes of the microstructure associated with the conversion of iron modification ferrite to martensite, which are the properties of the steel is very important. In two-dimensional materials, such as in thin magnetic layers, it can only under limited conditions, long-range order and thus give a phase transition. This interesting aspect is dealt with in the Mermin -Wagner theorem ( by N. David Mermin and Herbert Wagner) and has also been investigated experimentally.

Paraffins have a particularly large change in volume by about 30% during the phase transition from solid to liquid. This hub can be used for the construction of actuators.