Elastic Properties of C6oBased Polymerized Fullerites

The unique method for studies of the elastic properties of small specimens is known as acoustic microscopy [25]. It allows not only to "screen" the sample and thereby to control the presence of defects but also to follow the mapping of local elastic properties. Because the elastic properties are specified by the intermolecular bonding and nanostructural organization of a substance their determination can provide the designation of specimen's microstructure.

The density of the specimens was measured by the flotation method using mixtures of diiodmethane and acetone liquids of different concentrations. The bulk densities p of the specimens were determined to an accuracy of ±0.05 g/cm3. They varied within the range of 1.75-3.28 g/cm3 (Tables 16.2-16.5).

A wide-field pulse scanning acoustic microscope (WFPAM) was used in the reflection mode at the driving frequencies of f = 25 - 50 - 100 MHz to measure the local values of ultrasonic velocities and elastic moduli (the microacoustic technique) and to visualize the bulk microstructure of a specimen (scanning acoustic microscopy). The method makes it possible to measure the elastic characteristics of small specimens and inclusions [26,27].

Local and averaging elastic moduli were calculated to an accuracy of ±5^25% on the basis of the measured velocities and densities of the polymerized fullerite samples.

Table 16.2 C60 synthesized at P = 8 GPa.a

P

Vl

Vt

K

E

G

T, K

g/mm

km/s

km/s

GPa

GPa

GPa

a

500

1.75

6.0±0.3

3.7±0.1

30±5

57±14

24±2

0.19±0.05

7.4±0.4

4.8±0.2

40±6

90±20

40±4

0.14±0.04

900

1.90

6.8±0.3

4.1 ±0.2

45±5

80±20

30±3

0.20±0.03

7.4±0.4

4.5±0.2

50±7

90±20

40±5

0.20±0.04

1650

2.22

8.6±0.6

4.3±0.2

110±20

110±30

40±5

0.33±0.08

15.2±1.0

5.6±0.2

420±60

200±50

70±5

0.42±0.08

a The averaging values of density p, longitudinal Vl and shear Vt ultrasonic wave velocities, bulk modulus K, shear modulus G, Young's modulus E, and Poisson's ratio a as a function of synthesis temperature T.

Table 16.3 C60 synthesized at P = 9.5 GPa.a

T, K p, g/mm

Vl, km/s

Vt, km/s

K, GPa

E, GPa

G, GPa

a

700 2.30

12.0

7.8

160

320

140

0.13

770 2.35

12.5

6.8

220

280

110

0.29

970 2.62

18.5

11.4

450

800

340

0.20

1070 2.30

18.5

11.4

420

690

280

0.22

1150 2.26

16.0

8.25

370

400

150

0.32

1400 2.32

18.0

12.0

310

700

330

0.10

1500 2.27

18.0

11.0

370

660

275

0.20

a Notations are identical to those for Table 16.2.

Table 16.4 C60 synthesized at P

= 11, 12.5,

and 13.5 GPa.

a

P/ T p

GPa/K g/mm

Vl, km/s

Vt, km/s

K, GPa

E, GPa

G, GPa

a

11/1450 2.25

11.7

6.7

170

250

100

0.26

12.5/1000 3.10

17.0

9.4

540

660

280

0.28

13/1670 3.10

17.0

7.2

690

450

160

0.39

13/1770 3.30

18.4

8.7

790

680

250

0.36

13/1870* 3.15

26

9.7

1700

850

300

0.42

a Notations are identical to those for Table 16.2 b See [10] for details.

Table 16.5 C60 synthesized at P = 15 GPa.a

T, K

P, g/mm

Vl, km/s

Vt, km/s

K, GPa

E, GPa

G, GPa

a

670

2.55

14.6

8.1

320

430

170

0.28

820

2.72

1120

3.02

20.5

10.6

820

900

340

0.32

1470

3.27

19.5

10.9

730

990

390

0.27

1820

3.28

17.0

10.8

440

890

380

0.16

a Notations are identical to those for Table 16.2.

a Notations are identical to those for Table 16.2.

Together with the recording of oscillograms of echo signals, the acoustic microscope WFPAM was also used in B- and C-scanning modes. The acoustic microscopy images reflecting the microstructure of fUllerite specimens were obtained. The regular acoustic images (C-scans) were used for visualization of the specimen surface and selecting spots for measurements on it.

Then from these data the elastic moduli, such as the bulk modulus K, shear modulus G, and Young's modulus E were calculated.

Some C60 samples have the value of local bulk and Young's moduli much higher than those of diamond.

The values in these tables represent the mean values of the samples' elastic parameters. However, we observed a large sound velocity variance along the line of scan direction. As this takes place, the sound velocity has the highest value near the specimen periphery and the lowest one at the central part (Table 16.2). It should be noted that the radial variation of sound velocity was not symmetric in each B scans, and varied at the angular variation of the scanning line.

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