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Photonic crystals in biology

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Poster Session, Tuesday, June 15<br />

Theme A1 - B702<br />

Mechanical Properties of Graphite and Nano Tubes<br />

1 *<br />

1 r University, Faculty of Eng<strong>in</strong>eer<strong>in</strong>g, Bornova-,35100,Turkey<br />

Abstract- Graphite is one of the special form of carbon. Carbon nanotubes can be thought of as a sheet of graphite (a hexagonal lattice of<br />

carbon) rolled <strong>in</strong>to a cyl<strong>in</strong>der. These tubes exhibit important mechanical properties: the Young's modulus is over 10 12 Pascal. Hardness of<br />

graphite is quite anisotropic. Graphite is very soft <strong>in</strong> c-axis direction, but it is very hard <strong>in</strong> the directions <strong>in</strong>side the hexagonal-planes. Young<br />

Modulus of graphite along a-axis is 103x10 10 N/m 2 but along c-axis is about 3.61x10 10 N/m 2 . So <strong>in</strong> basal plane bonds are 30 times<br />

stronger, that means b<strong>in</strong>d<strong>in</strong>g forces among the atoms <strong>in</strong> hexagonal basal planes are very strong. This property of graphite <strong>in</strong> some nano-dy es<br />

or coat<strong>in</strong>g is used to protect the object aga<strong>in</strong>st corrosion and scratches.<br />

In HCP crystal, c/a ratios are quite important for atomic<br />

b<strong>in</strong>d<strong>in</strong>g forces. In Dy (1.574) and Mg (1.624) c/a ratio is<br />

very close to ideal value (1.633), therefore elastic<br />

properties nearly isotropic. But <strong>in</strong> Zn (1.86)and graphite<br />

( 2.31), we have a large anisotropy. Especially <strong>in</strong> graphite<br />

this is quite clear.<br />

Young Modulus along a-axis is 103x10<br />

10 N/m 2 and<br />

along c-axis is 3.61x10 10 N/m 2 <strong>in</strong> graphite (Figure.1).<br />

Therefore Young’s modulus along a-axis is 30 times<br />

greater than that of <strong>in</strong> c-axis. Longitud<strong>in</strong>al sound velocity<br />

<strong>in</strong> a-axis is 21 km/s ,4 km/s <strong>in</strong> c-direction. These<br />

calculations show that b<strong>in</strong>d<strong>in</strong>g forces between the atoms <strong>in</strong><br />

basal plane of the graphite are very strong, these forces<br />

are quite weak <strong>in</strong> the c-direction. The weakness of the<br />

bond expla<strong>in</strong> why graphite is so soft even though its<br />

melt<strong>in</strong>g po<strong>in</strong>t is so high.<br />

Soft materials are easily compressed. Therefore if<br />

compressibility has high value that material can easily<br />

compressed or deformed. this means that the atomic<br />

b<strong>in</strong>d<strong>in</strong>g forces are weak <strong>in</strong> that special direction <strong>in</strong> the<br />

substance.<br />

Ultrasonic velocity is very high <strong>in</strong> the direction <strong>in</strong> which<br />

the b<strong>in</strong>d<strong>in</strong>g forces are quite large. Longitud<strong>in</strong>al wave<br />

velocity <strong>in</strong> the basal plane is 21610 m/s but <strong>in</strong> the c-axis is<br />

about 4010 m/s <strong>in</strong> graphite.<br />

Table 1. Elastic constants of some hexagonal <strong>crystals</strong>,<br />

Cij , ( 10 10 N/m 2 )<br />

C11 C12 C13 C33 C44<br />

c/a<br />

<br />

Dy 7.31 2.53 2.23 7.81 2.40 1.574<br />

Mg 5.97 2.62 2.17 6.17 1.64 1.624<br />

Zn 16.10 3.42 5.01 6.10 3.83 1.856<br />

Cd 12.10 4.81 4.42 5.13 1.85 1.886<br />

Grafit 106.0 18.0 1.5 3.65 0.4 2.310<br />

Table. 2. Ultrasonic velocities at different directions <strong>in</strong> Dy, Zn,<br />

Mg, Cd ve graphite<br />

Velocities Dy Zn Mg Cd Graphite<br />

(10 3 m/s )<br />

vL-c-axis 3.02 2.91 5.87 2.43 4.01<br />

vS-c-axis 1.67 2.31 3.02 1.46 1.32<br />

vL-a axis 2.92 4.73 5.77 3.74 21.61<br />

vS-a axis 1.67 2.31 3.02 1.46 1.33<br />

Table.3 Young’s modulus and compressibility’s of some<br />

Hexagon al <strong>crystals</strong><br />

Mg Zn Cd Graphite<br />

Young’s Modulus<br />

<strong>in</strong> a-axis (10 10 N/m 2 )<br />

<strong>in</strong> c-axis (10 10 N/m 2 )<br />

4.5<br />

5.0<br />

12.0<br />

3.5<br />

8.1<br />

2.8<br />

103.0<br />

3.6<br />

L<strong>in</strong>ear compressibility<br />

In a- axis (10 -12 m 2 /N)<br />

In c-axis (10 -12 m 2 /N)<br />

9.2<br />

9.7<br />

1.58<br />

13.7<br />

1.5<br />

16.9<br />

0.5<br />

27.0<br />

Volume compresibility 28.1 16.9 19.9 28.0<br />

(10 -12 m 2 /N)<br />

Ayasse ,J.B. , et al, (1979), On the Soften<strong>in</strong>g of the Elastic<br />

Constant C44 <strong>in</strong> Graphite, Solid State Com. , 5, 659-662.<br />

<br />

Magnetic Phases <strong>in</strong> Dy, J. Physics F: Metal Physics, 8, 247<br />

Hexagonal Kristaller<strong>in</strong> Esneklik<br />

Özellikleri, Y.L. Tezi <br />

C., e-dergi-http:/joy.yasar.edu.tr,J.of Yasar University,<br />

Vol:1,No:4, 1-6 (2006)<br />

Figure 1.Young’s modulus of graphite <strong>in</strong> a-c plane(10 10 N/m 2 )<br />

Carbon nanotubes are the strongest and stiffest materials<br />

yet discovered <strong>in</strong> terms of 1Ttensile strength . Multiwalled<br />

carbon nanotube was tested to have a tensile<br />

strength of 63 giga pascals (GPa). This means it has the<br />

ability to endure tension of 6,3 ton on a cable with crosssection<br />

of 1 mm 2 . S<strong>in</strong>ce carbon nanotubes have a low<br />

density for a solid of 1.3 to 1.4 g·cm , its specific strength<br />

of up to 48,000 kN·m/kg is the best of known materials,<br />

compared to high-carbon steel's 154 kN·m/kg. The cables<br />

made of nano tubes are suggested to be used for spaceelevators<br />

<strong>in</strong> near future. These cables may be as long as<br />

35 000 km and carry space-elevators from the earth to a<br />

space-ship or to a space-city.<br />

6th Nanoscience and Nanotechnology Conference, zmir, 2010 360

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