Applied Physics, Vol. 2, Issue 1, Sep  2019, Pages 16-20; DOI: 10.31058/j.ap.2019.21002 10.31058/j.ap.2019.21002

Anisotropy and Isotropy of NaCl and KCl at Different Temperatures

, Vol. 2, Issue 1, Sep  2019, Pages 16-20.

DOI: 10.31058/j.ap.2019.21002

Fae’q A.A. Radwan 1*

1 Faculty of Engineering, Near East University KKTC, Lefkosa Mersin, Turkey

Received: 30 July 2019; Accepted: 9 September 2019; Published: 30 October 2019

Abstract

The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of Nacl AND Kcl at different temperatures along with the experimental data obtained under adiabatic condition. The relation of the scalar parts norms and the other parts norms and the anisotropy of these materials is presented. The norm ratios are used as a criterion to present the anisotropy degree of the properties of these.

Keywords

Nacl and Kcl, Norm, Anisotropy, Elastic Constants, and Irreducible parts

1. Introduction

Anisotropy and Isotropy: when the properties of a material vary with different crystallographic orientations, the material is said to be anisotropic, common examples of anisotropic materials are wood and composites. Alternately, when the properties of a material are the same in all directions, the material is said to be isotropic. The decomposition procedure and the decomposition of elastic constant tensor is given in [1], also the definition of norm concept and the norm ratios and the relationship between the anisotropy and the norm ratios are given in [1]. As the ratio Ns/N becomes close to one the material becomes more isotropic, and as the sum of Nd/N and Nn/N becomes close to one the material becomes more anisotropic as explained in [1,2,3,4,5,6].

2. Data and Calculations

Table 1. Elastic constants in GPa, for Calculated values of,, and (in GPa) at different temperatures along with the experimental data obtained under adiabatic condition [7].

T [K]

300

49.5

13.2

12.79

350

47.7

13.20

12.61

400

45.8

13.19

12.44

450

44.0

13.19

12.26

500

42.2

13.18

12.08

550

40.4

13.18

11.91

600

38.5

13.18

11.73

650

36.7

13.17

11.55

700

34.9

13.17

11.38

750

33.3

13.16

11.20

Table 2. Elastic constants in GPa, for: Calculated values of,, and (in GPa) at different temperatures along with the experimental data obtained under adiabatic condition [7].

T [K]

300

40.1

6.6

6.35

350

38.5

6.7

6.24

400

36.8

6.8

6.14

450

35.2

7.0

6.03

500

33.5

7.1

5.92

550

31.9

7.2

5.82

600

30.2

7.3

5.71

650

28.6

7.4

5.60

700

27.0

7.6

5.50

750

25.4

7.7

5.39

800

23.9

7.8

5.29

850

22.3

7.9

5.18

By using Table 1 and Table 2, and the decomposition of the elastic constant tensor and the norm concept, the norms and the norm ratios of the given materials can be calculated as in the following tables.

Table 3. The norms and norm ratios of.

T[K]

300

90.63155

0

9.82504

91.16254

0.99417

0

0.107775

350

88.27642

0

8.50526

88.68521

0.99539

0

0.095904

400

85.80001

0

7.08466

86.09201

0.99661

0

0.082292

450

83.44725

0

5.76488

83.64615

0.99762

0

0.06892

500

81.08252

0

4.45426

81.20478

0.99849

0

0.054852

550

78.74317

0

3.11615

78.8048

0.99922

0

0.039543

600

76.27491

0

1.70472

76.29396

0.99975

0

0.022344

650

73.91484

0

0.39410

73.91589

0.99999

0

0.005332

700

71.58057

0

0.94401

71.5868

0.99991

0

0.013187

750

69.46408

0

2.07132

69.49496

0.99956

0

0.029805

Table 4. The norms and norm ratios of.

T[K]

300

63.68635

0

19.0635

66.47833

0.95800

0

0.286763

350

61.77871

0

17.7071

64.26624

0.96129

0

0.275527

400

59.76402

0

16.2406

61.93139

0.96500

0

0.262236

450

57.99531

0

14.7925

59.85212

0.96898

0

0.247152

500

55.97621

0

13.3445

57.54486

0.97274

0

0.231897

550

54.09043

0

11.9697

55.39899

0.97638

0

0.216063

600

52.07779

0

10.5216

53.13003

0.98019

0

0.198035

650

50.18884

0

9.16515

51.01882

0.98373

0

0.179643

700

48.4553

0

7.69873

49.06309

0.98761

0

0.156915

750

46.5768

0

6.34228

47.00662

0.99086

0

0.134923

800

44.83264

0

5.05916

45.11719

0.99369

0

0.112134

850

42.96542

0

3.70272

43.12468

0.99631

0

0.085861

Figure 1. Isotropy Degree.

Figure 2. Anisotropy Degree.

Figure 3. Elastically Strength.

Figure 4. Isotropy Degree.

Figure 5. Anisotropy Degree.

Figure 6. Elastically Srength.

3. Conclusions

From Table 3 and Table 4 and the Figures (Figure 1 to Figure 6), and analyzing the ratio for different temperatures in Kelvin for we can conclude that the value of          (Isotropy degree) increases as the temperature increases and value of (Anisotropy degree) decreases as the temperature increases, and also the value of N (elastically strength) decreases as the temperature increases. But we can notice that from Figure 1 and Figure 2 at the isotropy degree decreasing instead of increasing and anisotropy degree increasing instead of decreasing so we can conclude that this is because of the error in the experimental data, because in general the isotropy degree increases and the anisotropy degree and the elastically strength decrease as the temperature increases.

Conflicts of Interest

The author declares that there is no conflict of interest regarding the publication of this article.

Copyright

© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

References

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[6] Fae`q A.A. Radwan. Some Physical Properties of Different Compositions of Alums. Nanotechnology in Science and Engineering, 2018, 1(1), 61-66.

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