posited from solutions containing a
sufÜcient excess of sulphuric acid.
irreducible representation A
representation of a symmetry operation of a group, which cannot be expressed in terms of a representation
of lower dimension. When the representation of the group is in matrix
form (i.e. a set of matrices that multiply in the same way as the elements
of the group), the matrix representation cannot be put into blockdiagonal form by constructing a linear combination of the basis functions. The importance of irreducible
representations in *quantum mechanics is that the energy levels of
the system are labelled by the irreducible representations of the symmetry group of the system, thus
enabling *selection rules to be deduced. In contrast to an irreducible
representation, a reducible representation can be expressed in terms of a
representation of lower dimension,
with a reducible matrix representation that can be put into block diagonal form by constructing a linear
combination of the basis functions.
irreversibility The property of a
system that precludes a change to
the system from being a *reversible
process. The paradox that although
the equations describing the bodies
in a system, such as Newton’s laws of
motion, Maxwell’s equation, or
Schrödinger’s equation are invariant
under time reversal, events involving
systems made up from large numbers of these bodies are not reversible. The process of scrambling
an egg is an example. The resolution
of this paradox requires the concept
of *entropy using *statistical mechanics. Irreversibility occurs in the
transition from an ordered arrangement to a disordered arrangement,
which is a natural trend, since
changes in a closed system occur in
the direction of increasing entropy.
irreversible process See irreversibility; reversible process.
irreversible reaction See chemical reaction.
IR spectroscopy See infrared
spectroscopy.
isentropic process Any process
that takes place without a change of
*entropy. The quantity of heat transferred, δQ, in a reversible process is
proportional to the change in entropy, δS, i.e. δQ = TδS, where T is the
thermodynamic temperature. Therefore, a reversible *adiabatic process
is isentropic, i.e. when δQ equals
zero, δS also equals zero.
Ising model A model for magnetic
systems in which atomic *spins have
to be aligned either parallel or antiparallel to a given direction. The
Ising model was introduced, and
solved in the case of one dimension,
by E. Ising in 1925. Ising found that
in one dimension, in the absence of
an external magnetic Üeld, there is
no spontaneous magnetization at any
temperature above absolute zero.
The study of *phase transitions in
the Ising model in dimensions
greater than one has been very important to the general understanding
of phase transitions. In two dimensions, the Ising model was Ürst solved
exactly by L. Onsager in 1944. In
three dimensions, approximation
techniques, frequently involving
renormalization have to be used.
ISIS/Draw A commonly used chemical drawing program for 2D and 3D
structures, copyright of MDL Information Systems, Inc. The program
has certain additional features including calculation of molecular
weight, calculation of percentages of
irreducible representation
294
i
www.AzShimi.ir www.AzShimi.com
sufÜcient excess of sulphuric acid.
irreducible representation A
representation of a symmetry operation of a group, which cannot be expressed in terms of a representation
of lower dimension. When the representation of the group is in matrix
form (i.e. a set of matrices that multiply in the same way as the elements
of the group), the matrix representation cannot be put into blockdiagonal form by constructing a linear combination of the basis functions. The importance of irreducible
representations in *quantum mechanics is that the energy levels of
the system are labelled by the irreducible representations of the symmetry group of the system, thus
enabling *selection rules to be deduced. In contrast to an irreducible
representation, a reducible representation can be expressed in terms of a
representation of lower dimension,
with a reducible matrix representation that can be put into block diagonal form by constructing a linear
combination of the basis functions.
irreversibility The property of a
system that precludes a change to
the system from being a *reversible
process. The paradox that although
the equations describing the bodies
in a system, such as Newton’s laws of
motion, Maxwell’s equation, or
Schrödinger’s equation are invariant
under time reversal, events involving
systems made up from large numbers of these bodies are not reversible. The process of scrambling
an egg is an example. The resolution
of this paradox requires the concept
of *entropy using *statistical mechanics. Irreversibility occurs in the
transition from an ordered arrangement to a disordered arrangement,
which is a natural trend, since
changes in a closed system occur in
the direction of increasing entropy.
irreversible process See irreversibility; reversible process.
irreversible reaction See chemical reaction.
IR spectroscopy See infrared
spectroscopy.
isentropic process Any process
that takes place without a change of
*entropy. The quantity of heat transferred, δQ, in a reversible process is
proportional to the change in entropy, δS, i.e. δQ = TδS, where T is the
thermodynamic temperature. Therefore, a reversible *adiabatic process
is isentropic, i.e. when δQ equals
zero, δS also equals zero.
Ising model A model for magnetic
systems in which atomic *spins have
to be aligned either parallel or antiparallel to a given direction. The
Ising model was introduced, and
solved in the case of one dimension,
by E. Ising in 1925. Ising found that
in one dimension, in the absence of
an external magnetic Üeld, there is
no spontaneous magnetization at any
temperature above absolute zero.
The study of *phase transitions in
the Ising model in dimensions
greater than one has been very important to the general understanding
of phase transitions. In two dimensions, the Ising model was Ürst solved
exactly by L. Onsager in 1944. In
three dimensions, approximation
techniques, frequently involving
renormalization have to be used.
ISIS/Draw A commonly used chemical drawing program for 2D and 3D
structures, copyright of MDL Information Systems, Inc. The program
has certain additional features including calculation of molecular
weight, calculation of percentages of
irreducible representation
294
i
www.AzShimi.ir www.AzShimi.com