What is identity symmetry?
It is not really the identity symmetry, it is the identity transformation. The identity transformation is a “do nothing” transformation. For example, if you consider the group of all rotations around a given axis, the identity transformation corresponds to rotation by 0 degrees. It is included in order to be able to define an inverse transformation for a given transformation.
What is meant by the term, “Minimum symmetry of a crystal system”?
My interpretation of your questions is the following.In 3-D there are 7 crystal systems and 32 crystal classes. Each crystal class is uniquely assigned to a crystals system according to the following tablecubic [math]m\overline{3}m, \overline{4}3m, m\overline{3},432, 23[/math]tetragonal [math]4/mmm, \overline{4}2m, 4mm, 422, 4/m, \overline{4}, 4[/math]hexagonal [math]6/mmm, \overline{6}m2, 6mm, 622, 6/m, [/math] [math]\overline{6}, 6[/math]trigonal [math]\overline{3}m, 3m, 32[/math], [math]\overline{3}, 3[/math]orthorhombic [math]mmm, mm2, 222[/math]monoclinic. [math]2/m, m, 2[/math]triclinic [math]\overline{1}, 1[/math]you can associate the minimum symmetry to each system by taking the point group with the smallest order (the order is the number of elements in the group). Unfortunately, this group is not unique. E.g. in monoclinic, you have 2 groups with the same order 2 and m. In addition, the Bravais lattice should be of the P type. (i.e. no F or I or A(B,C) nor R)
Is tetragonal crystal the most asymmetrical crystal?
NOThe defining property of a crystal is its inherent symmetry, by which we mean that under certain 'operations' the crystal remains unchanged. All crystals have translational symmetry in three directions, but some have other symmetry elements as well. For example, rotating the crystal 180° about a certain axis may result in an atomic configuration that is identical to the original configuration. The crystal is then said to have a twofold rotational symmetry about this axis. In addition to rotational symmetries like this, a crystal may have symmetries in the form of mirror planes and translational symmetries, and also the so-called "compound symmetries," which are a combination of translation and rotation/mirror symmetries.there are other structures like monoclinic, orthorhombic and triclinic which are asymettrical
Why don't crystals have 5-fold symmetry?
A related question that is more limited, but that gets to the heart of the matter is the following one: What regular polygons can tile the 2D plane?It’s not to hard to show that the interior angle of a polygon with [math]n[/math] sides of equal length is [math]\theta_n = 180^{\circ}-(360^{\circ}/n)[/math]. This angle must divide [math]360^{\circ}[/math] into an integer [math]m[/math] equal parts at a node of the tiling: [math]m\, \theta_n = 360^{\circ}[/math]. Substituting in the previous expression for the interior angle then yields[math]m = 2n/(n-2)[/math] .It gives [math]m=6[/math] for an equilateral triangle ([math]n=3[/math]), [math]m=4[/math] for a square ([math]n=4[/math]), and [math]m=3[/math] for a regular hexagon ([math]n=6[/math]). No other regular polygon, such as the regular pentagon, can tile the plane.Tilings with 5-fold rotational symmetry are possible, however, on curved surfaces like the sphere. The soccer balls from way back, when I was a kid, are examples of that! In that case, you need a mix of (black) pentagons and of (white) hexagons. I believe, however, that the hyperbolic plane (Escher’s print of angels and devils) can be tiled by regular pentagons alone.
How can we relate the group theory and symmetry of the crystals....?
All crystals do possess symmetry. Based on thier symmetry, it is possible to simplify thier physical characteristics. Changes from one particular configuration to another "indistinguishable" configuration can be performed by a set of symmetry operators or rules. These mathematical rules or sets of operators is what is known as group theory. Hence, if one knows what group a particular symmetry is defined by then, under the construct and rules of theat group the properties or behavior of a crystal when subjected to an external 'field' which can be parametrized as an operator can be generally determined apriori before its tested experimentally.
What are the different types of crystals???
Right, and while we're at it will you briefly explain how to attain "world peace". Entire books have been written about crystallography. Your question is far too broad. Crystals come in a wide variety of shapes and sizes, but the underlying shape is dictated by the basic arrangement of atoms. For instance, three water molecules combine though hydrogen bonding to form a hexagonal shape. This is why snow crystals are hexagonal Take a look at this: http://www.windows.ucar.edu/tour/link=/e... and this http://chemistry.about.com/cs/growingcry...
If a crystal in the cubic "isometric" system has 4-3 folds,3-4 folds and 6-2 folds please...?
As stated in the last lecture, there are 32 possible combinations of symmetry operations that define the external symmetry of crystals. These 32 possible combinations result in the 32 crystal classes. These are often also referred to as the 32 point groups. We will go over some of these in detail in this lecture, but again I want to remind everyone that the best way to see this material is by looking at the crystal models in lab. Before going into the 32 crystal classes, I first want to show you how to derive the Hermann-Mauguin symbols (also called the international symbols) used to describe the crystal classes from the symmetry content. We'll start with a simple crystal then look at some more complex examples. The rectangular block shown here has 3 2-fold rotation axes (A2), 3 mirror planes (m), and a center of symmetry (i). The rules for deriving the Hermann-Mauguin symbol are as follows: 1. Write a number representing each of the unique rotation axes present. A unique rotation axis is one that exists by itself and is not produced by another symmetry operation. In this case, all three 2-fold axes are unique, because each is perpendicular to a different shaped face, so we write a 2 (for 2-fold) for each axis 2. Next we write an "m" for each unique mirror plane. Again, a unique mirror plane is one that is not produced by any other symmetry operation. In this example, we can tell that each mirror is unique because each one cuts a different looking face. So, we write: If any of the axes are perpendicular to a mirror plane we put a slash (/) between the symbol for the axis and the symbol for the mirror plane. In this case, each of the 2-fold axes are perpendicular to mirror planes, so our symbol becomes:
A diamond is a crystal. true or false?
True. Crystals are divided into seven main systems of symmetry and diamond falls into the most symmetrical of them all. Cubic. Which leaves it possible to build up 32 crystal classes in its assending order of the diamonds symmetry. 1. CUBIC 6 FACES 2. OCTAHEDRON 8 FACES 3 .TETRAKIS-HEXAHEDRON 24 FACES 4. ICOSITETRAHEDRON 24 FACES 5. TRIAKIS OCTAHEDRON 24 FACES 6. HEXAKIS OCTAHEDRON 48 FACES 7. RHOMBIC DODECAHEDRON 12 FACES..
Shape and symmetry in molecules?
In a molecule, at least two atoms are joined by shared pairs of electrons in a covalent bond. It may consist of atoms of the same chemical element, as with oxygen (O2), or of different elements, as with water (H2O). Atoms and complexes connected by non-covalent bonds such as hydrogen bonds or ionic bonds are generally not considered single molecules. No typical molecule can be defined for ionic (salts) and covalent crystals (network solids) which are composed of repeating unit cells that extend either in a plane (such as in graphite) or three-dimensionally (such as in diamond or sodium chloride). The science of molecules is called molecular chemistry or molecular physics, depending on the focus. Molecular chemistry deals with the laws governing the interaction between molecules that results in the formation and breakage of chemical bonds, while molecular physics deals with the laws governing their structure and properties. In practice, however, this distinction is vague. In molecular sciences, a molecule consists of a stable system (bound state) comprising two or more atoms. Polyatomic ions may sometimes be usefully thought of as electrically charged molecules. The term unstable molecule is used for very reactive species, i.e., short-lived assemblies (resonances) of electrons and nuclei, such as radicals, molecular ions, Rydberg molecules, transition states, Van der Waals complexes, or systems of colliding atoms as in Bose-Einstein condensates Most molecules are far too small to be seen with the naked eye, but there are exceptions. DNA, a macromolecule, can reach macroscopic sizes, as can molecules of many polymers. The smallest of all molecules is the hydrogen ion molecule H2+, comprised of two protons bonded together by the sharing of one electron.[citation needed] The next largest molecule is the hydrogen molecule H2, with a length roughly twice the 74 picometres (0.74 Å) distance between the two hydrogen nuclei; but as with all molecules, however, the exact size of its electron cloud is difficult to define precisely. Molecules commonly used as building blocks for organic synthesis have a dimension of a few Å to several dozen Å. Single molecules cannot usually be observed by light (as noted above), but small molecules and even the outlines of individual atoms may be traced in some circumstances by use of an atomic force microscope. Some of the largest molecules are supermolecules.