Real Crystals Having Inversion Symmetry-Solid State Physics-Presentation, Slides of Solid State Physics

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Real Crystals having inversion

symmetry

Symmetry Elements and

Operations

ELEMENT operation symbol

Symmetry plane reflection through plane= σ

Inversion center =every point x, y, z =i

translated to – x,-y,-z

Proper axis =rotataion by 360/n = C

Improper axis 1=rotation by 360/n

• 2=reflection through plane perpendicular to rotation axis =S

3d examples

Tetrachloroplatinate II

Benzen

Where is the center of

inversion (i)..?

Schönflies symbols

1 Rotation axes, Cnr

2 Mirror planes , r

3 Inversion centres, I

4 Improper rotations, Snr

5 Translation, t

6 Identity, E

Applications of symmetry

1. Chirality (optical activity)
2. Effect of inversion symmetry on the bands of semiconductor PHYSICAL PROPERTIES OF CRYSTALS

Color

Reflection of light

Birefringence

Pleochroism

Polarization of light

Cleavage

The piezoelectric effect

Polarimeter

Difference between

mirror plane and inversion center

The handedness is changed.

Vibrations of Water

 One of the more significant applications of

symmetry is the analysis of molecular vibrations. Knowing nothing more than the point group of a molecule, you can predict the number and types of vibrational peaks that will show up in the infrared and Raman spectra. Shown below are two (of three) vibrations of the water molecule. Not surprisingly, they are called the symmetric and antisymmetric stretching modes.

 PHYSICAL PROPERTIES OF CRYSTALSColor is caused by the absorption of certain wavelengths of light within the material. Metals, including chrome, iron, cobalt, copper, manganese, nickel, and vanadium, absorb certain wavelengths of light and thus cause coloration. Measurement of color is very subjective, and not usually a good diagnostic for identification because many different materials may have similar colors. Refraction of light through materials change. The velocity of light through a material is inversely related to its index of refraction. For a vacuum, n = 1.0. Most minerals range between 1.4 and 3.2. This property will not be tested. Birefringence is when there are two refractive indices for cross-polarized light entering a material. If one ray enters, two rays emerge (the ordinary and extraordinary). If the material is rotated, the ordinary ray stays still and the extraordinary ray traces a circle about the former. Calcite is a famous source of this effect. Sodium Nitrate exhibits similar abilities. The two exitting rays are always polarized at right angles with respect to each other. Dispersion is the spread in refractive indices of light through a material when its wavelength varies from red to violet. The larger the dispersion, the greater the colors of white light will be separated upon exiting the material. Diamond's dispersion is particularly great, so a play of colors is exhibited. This property will not be tested.

 Another color change is due to the presence of artificial or natural light (or often flourescent versus incandescent light). Nickel sulfate shows this kind of color change reminiscent of the near-priceless gemstone alexandrite. Polarization of light does occur in some materials. In nature, it occurs strongly in tourmaline. Placed between a "polarization sandwich," sodium chlorate will permit different colors through as the angle between the polarizers changes. Cleavage occurs when a crystal breaks along certain planes more easily than in any other direction. In nature, a distinction is made between perfect and imperfect cleavage. Perfect cleavage (as in the case of flourite, calcite, and diamond) will always break along a cleavage plane. This makes cutting diamond more chalenging, because the angles needed by the gem cutter might not match cleavage planes. Imperfect cleavage (quartz or beryl) can break in direction. Broken shards of quartz look suspiciously like glass. A shattered octahedron of flourite, however, will produce many smaller pyramids, octahedrons, and tabular octahedrons.

 Cleavage of Nickel Sulfate Hexahydrate. The Piezoelectric Effect is when a crystal that is compressed produces a charge-flow and voltage drop across the oposite poles. Rochelle salt and natural quartz exhibit this effect. Working the other way, piezo devices can be expanded by applying a voltage across the oposite poles. Piezo horns and tweeters work this way. Also, piezo devices are used to position scanning tunneling electron microscope probes. Some microphones use piezo devices to convert sound to voltage.

Experimental vs theoraticle

 Symmetry in real crystals  VIRTUALLY ALL MATERIALS HAVE UNIT CELLS  WITH ONE OF THE 230 SPACE GROUPS.  Two notable exceptions exist:  1 Quasicrystals show 5-fold and 10-fold rotational symmetry.  You can’t tile all space with a 5- or 10-fold symmetric object****!

 2 Incommensurate crystals have a periodicity in one

[Ni(hmp)(t-BuEtOH)Cl] 4 Single Crystal

10 -

10 0

10 1

0 5 10 15 20 25 30

 (s) at 0.1 M (^) s

^ (s)

1/T (1/K)

 = 6.3 x 10 -3^ s * exp[2 K/T]

• Temperature-independent magnetization relaxation at low temperature.
• Highly axially symmetric systems show the slowest relaxation, e.g. Mn 12 -Ac.
  • Slow relaxation
  • In some systems  may exceed the time of the , weeks or years
  • measurement, i.e. days

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