1 – Sodium Chloride Structure نمک طعام NaCl بصورت شبکه مکعبی در سلول غیر بسیط ظاهر می شود تعداد برابر از دو نوع اتم در سلول ان بطور تناوبی قرار گرفته اند. هر یون بوسیله شش یون نوع دیگر محاصره شده است. Crystal Structure

+ Two Ion Motif = Face Centred Cubic (FCC) Lattice NaCl Crystal Can have one sentence about difference between FCC with monoatomic packing and diatomic packing  close packing Cl Ion at (0, 0, 0) Na+ Ion at (½, 0, 0) 3

Sodium Chloride Structure هنگامی که یونهای قرمز رنگ کلر حذف می شوند تنها شبکه fcc مربوط به سدیم باقی می ماند دو شبکه fcc که به اندازه نصف قطر اصلی مکعب از همدیگر فاصله دارند(8 اتم در سلول غیر بسیط) Crystal Structure

Sodium Chloride Structure می توان به صورت شبکه fcc از سدیم به ان نگاه کرد که پایه ها در قرار دارند LiF,NaBr,KCl,LiI,etc پارامتر شبکه 4-7 angstroms.

2-Cesium Chloride Structure Cs+Cl- کلرید سزیم شبکه مکعبی است (Cs+  is teal, Cl- is gold). تعداد برابر از هر دو نوع اتم هر اتم 8 همسایه از اتمهای دیگر دارد بصورت bcc ظاهر می شود Crystal Structure

Cesium Chloride Structure Cs+Cl- شبکه bcc بصورت شبکه مکعبی ساده به همراه پایه در مرکز نیز نشان داده می شود. سزیم در گوشه ها و یک کلر در مرکز قرار دارد CsBr,CsI crystallize in this structure. lattice constants are in the order of 4 angstroms.

Cesium Chloride Cs+Cl- 8 cell

4 - Diamond Structure دارای ساختار Fcc با پایه دو تایی Crystal Structure

4 - Diamond Structure The coordination number of diamond structure is 4. The diamond lattice is not a Bravais lattice. Si, Ge and C crystallizes in diamond structure.

Two Carbon atom Motif (0,0,0) & (¼, ¼, ¼) Face Centred Cubic (FCC) Lattice + Two Carbon atom Motif (0,0,0) & (¼, ¼, ¼) Diamond Cubic Crystal = Tetrahedral bonding of C (sp3 hybridized)

Crystal Structure

5- Zinc Blende

5- Zinc Blende(ZnS) سولفید روی همانند الماس اما جنس پایه ها متفاوت می باشد Crystal Structure

تقارنها در فیزیک حالت جامد

What kind of symmetry does this object have? 4

What kind of symmetry does this object have? 4 m

What kind of symmetry does this object have? 4 m

What kind of symmetry does this object have? 4 m

What kind of symmetry does this object have? 4 4mm m

Another example:

Another example: 6 6mm m

And another:

And another: 2 2

=180 n=2 2-fold rotation axis =120 n=3 3-fold rotation axis

=90 n=4 4-fold rotation axis =60 n=6 6-fold rotation axis The rotations compatible with translational symmetry are  (1, 2, 3, 4, 6)

Rotations Although objects themselves may appear to have 5-fold, 7-fold, 8-fold, or higher-fold rotation axes, these are not possible in crystals.  The reason is that the external shape of a crystal is based on a geometric arrangement of atoms.  Note that if we try to combine objects with 5-fold and 8-fold apparent symmetry, that we cannot combine them in such a way that they completely fill space.

Mirror Symmetry The operation is done by imagining that you cut the object in half, then place a mirror next to one of the halves of the object along the cut.  If the reflection in the mirror reproduces the other half of the object, then the object is said to have mirror symmetry.  The plane of the mirror is an element of symmetry referred to as a mirror plane, and is symbolized with the letter m.  As an example, the human body is an object that approximates mirror symmetry, with the mirror plane cutting through the center of the head, the center of nose and down to the groin. Water molecule – 2 planes Benezene – 7 planes

Inversion Another operation that can be performed is inversion through a point.  In this operation lines are drawn from all points on the object through a point in the center of the object, called a symmetry center (symbolized with the letter "i"). The lines each have lengths that are equidistant from the original points.  When the ends of the lines are connected, the original object is reproduced inverted from its original appearance.  In the diagram shown here, only a few such lines are drawn for the small triangular face. The right hand diagram shows the object without the imaginary lines that reproduced the object.  

2D - Point Groups

تقارن بازتابی

تقارن بازتابی به همراه وارون جانبی R L m

تقارن بازتابی

(x,y,z) --> (-x,-y,-z) تقارن مر کز وارونی(در شبکه براوه همیشه بر قرار است)

تقارن مر کز وارونی

Crystal Structure

تقارنهای مکعب Crystal Structure