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#### 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 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

[1] Faeq A.A. Radwan. Norm Ratios and Anisotropy Degree.J. Appl. Sci.2001, 1(3), 301-304.

[2] Fae’q A.A. Radwan. Irreducible Parts of Elastic Compliance Tensor and Anisotropy. J. Appl. Sci. 2001, 1(3), 270-274.

[3] F. A.A. Radwan. Scalar Irreducible Parts of Sixth Rank Tensor. Arab Gulf Journal of Scientific Research, 2001, 19 (3),163-166.

[4] Fae`q A.A. Radwan. Comparison of Anisotropy of Human Mandible, Human Femora and Human Tibia with Canine Mandible and Canine Femora and With Bovine Femurs. Lecture Notes in Engineering and Computer Science, 2012, 2195(1),132-135.

[5] Fae`q A.A. Radwan.Some Properties of Triclinic System Materials. Nanotechnology in Science and Engineering,2018, 1(1), 7-10.

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

[7] Q. Liu; Q. He. Elastic Constants for Various Classes of Solids at High Temperature. Acta Physica Polonica A,2007, 112, 69-76.