Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method
Abstract
:1. Introduction
2. Methods, Results and Discussion
2.1. Model and Calculation Method
2.2. Numerical Results and Discussion for Alloy AuSi
3. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Nazarov, A.A.; Bachurin, D.V.; Ni, Z.L. Atomistic simulation of ultrasonic welding of copper. Metals 2022, 12, 2033. [Google Scholar] [CrossRef]
- Yu, Y.-X. Effect of defects and solvents on silicene cathode of nonaqueous lithium−oxygen batteries: A theoretical investigation. J. Phys. Chem. C 2019, 123, 205–213. [Google Scholar] [CrossRef]
- Malinowska-Adamska, C. Thermodynamic and transport properties of crystals in anharmonic approximation. Phys. Stat. Sol. B 1981, 106, 359–367. [Google Scholar] [CrossRef]
- Karasevskii, A.I.; Lubashenko, V.V. Calculation of thermodynamic properties of Cu and Ag using a self-consistent statistical method. Phys. Stat. Sol. B 2004, 241, 1274–1280. [Google Scholar] [CrossRef]
- Tang, N.; Hung, V.V. Investigation of the thermodynamic properties of anharmonic crystals by the momentum method, I. General results for face-centered cubic crystals. Phys. Stat. Sol. B 1988, 149, 511–519. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Tinh, B.D.; Hien, N.D. Elastic moduli and elastic constants of interstitial alloy AuCuSi with FCC structure under pressure. High Temp. Mater. Proc. 2019, 38, 264–272. [Google Scholar] [CrossRef]
- Tinh, B.D.; Hoc, D.Q.; Vinh, D.Q.; Cuong, T.D.; Hien, N.D. Thermodynamic and elastic properties of interstitial alloy FeC with BCC structure at zero pressure. Adv. Mater. Sci. Eng. 2018, 2018, 5251741. [Google Scholar] [CrossRef] [Green Version]
- Hoc, N.Q.; Tinh, B.D.; Hien, N.D.; Gelu, C.G. Nonlinear deformation of BCC metal Fe and BCC interstitial alloy FeSi: Dependence on temperature, pressure and silicon concentration. Mater. Phys. Mech. 2021, 47, 501–513. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Tinh, B.D.; Hien, N.D.; Viet, L.H. On the jumps of volume, enthalpy and entropy at the melting point, the thermal conductivity and the thermal diffusivity for Au with FCC structure: Temperature and pressure dependences. Prog. Phys. Metals 2021, 22, 511–530. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Viet, L.H.; Dat, H.X. Equilibrium vacancy concentration and thermodynamic quantities of BCC defective alloys FeCrSi and VWSi under pressure. Mod. Phys. Lett. B 2022, 36, 2250105. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Tinh, B.D.; Hien, N.D. The melting and the Debye temperature for BCC and FCC metals under pressure: A calculation from the statistical moment method. Arch. Metallur. Mater. 2022, 67, 1227–1234. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Hien, N.D.; Vi, T.K. Elastic deformation and velocity of elastic wave for metal Fe and its interstitial alloys with BCC structure: Dependence on temperature, pressure and concentration of interstitial atoms. Phys. B 2022, 644, 414134. [Google Scholar] [CrossRef]
- Hoc, N.Q.; Dung, N.T.; Cuong, N.C.; Tinh, B.D.; Hien, N.D.; Van, C.L.; Umut, S.; Stefan, T. Determination of the Young modulus and the stress-strain curve for Fe and binary FeC interstitial alloy. J. Compos. Sci. 2022, 6, 250. [Google Scholar] [CrossRef]
- Cuong, T.D.; Hoc, N.Q.; Trung, N.D.; Thao, N.T.; Anh, D.P. Theoretical predictions about melting behaviors of hcp iron up to 4000 GPa. Phys. Rev. B 2022, 106, 094103. [Google Scholar] [CrossRef]
- Hung, V.V.; Phuong, D.D.; Hoa, N.T.; Hieu, H.K. Theoretical investigation of thermodynamic properties of metallic thin films. Thin Sol. Films 2015, 583, 7–12. [Google Scholar] [CrossRef]
- Hung, V.V.; Phuong, D.D.; Hoa, N.T. Investigation of thermodynamic properties of metal thin film by statistical moment method. Comm. Phys. 2013, 23, 301–311. [Google Scholar] [CrossRef] [Green Version]
- Haibo, H.; Spaepen, F. Tensilie testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers. Acta Mater. 2000, 48, 3261–3269. [Google Scholar] [CrossRef]
- Vaz, A.R.; Salvadori, M.C.; Cattani, M. Young modulus measurement of nanostructured metallic thin films. J. Metast. Nanocrystal. Mater. 2004, 20–21, 758–762. [Google Scholar]
- Kuru, Y.; Wohlschlogel, M.; Welzel, U.; Mittemeijer, E.J. Coefficients of thermal expansion of thin metal films investigated by non-ambient X-ray diffraction stress analysis. Surf. Coat. Technol. 2008, 202, 2306–2309. [Google Scholar] [CrossRef]
- Fuks, D.; Dorfman, S.; Zhukovskii, Y.F.; Kotomin, E.A.; Stoneham, A.M. Theory of the growth mode for a thin metallic film on an insulating substrate. Surf. Sci. 2002, 499, 24–40. [Google Scholar] [CrossRef] [Green Version]
- Chen, S.; Liu, L.; Wang, T. Investigation of the mechanical properties of thin films by nanoindentation considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol. 2005, 191, 25–32. [Google Scholar] [CrossRef]
- De Lima, M.M.; Lacerda, R.G.; Vilcarromero, J.; Marques, F.C. Coefficient of thermal expansion and elastic modulus of thin films. J. Appl. Phys. 1999, 86, 4936–4942. [Google Scholar] [CrossRef] [Green Version]
- Kalkman, A.J.; Verbruggen, A.H.; Janssen, G.C.A.M. Young modulus measurements and grain boundary sliding in free standing thin metal films. Appl. Phys. Lett. 2001, 78, 2673–2675. [Google Scholar] [CrossRef]
- Vereshchagin, L.F.; Fateeva, N.S. Melting temperatures of refractory metals at high pressures. High Temp. High Pres. 1977, 9, 619–628. Available online: http://www.oldcitypublishing.com/journals/hthp-electronic-archive-home/hthp-electronic-archive-issue-contents/hthp-volume-9-number-6-1977/ (accessed on 20 December 2022).
- Zhu, Y.F.; Lian, J.S.; Jiang, Q. Modeling of melting point, Debye temperature, thermal expansion coefficient and the specific heat of nanostructured materials. J. Phys. Chem. C 2009, 113, 16896–16900. [Google Scholar] [CrossRef]
- Zhu, M.; Liu, J.; Huang, Q.; Dong, J.; Yang, X. Temperature and size modulation of the lattice thermal expansion on transition metallic nanostructures. J. Phys. D Appl. Phys. 2022, 55, 485303. [Google Scholar] [CrossRef]
- Ma, Y.-L.; Zhu, K.; Li, M. Size, dimensionality and composition effects on the Debye temperature of nanocrystals. Phys. Chem. Chem. Phys. 2018, 20, 27539–27544. [Google Scholar] [CrossRef]
- Nyilas, R.D.; Frank, S.; Spolenak, R. Revealing plastic deformation mechanisms in polycrystalline thin films with synchrotron XRD. JOM (J. Miner. Metals Mater. Soc.) 2010, 62, 44–51. [Google Scholar] [CrossRef] [Green Version]
- Tang, N.; Hung, V.V. Investigation of the thermodynamic properties of anharmonic crystals by the momentum method. II. Comparison of calculations with experiments for inert gas crystals. Phys. Stat. Sol. B 1990, 161, 165–171. [Google Scholar] [CrossRef]
- Tang, N.; Hung, V.V. Investigation of the thermodynamic properties of anharmonic crystals by the momentum method. III. Thermodynamic properties of the crystals at various pressures. Phys. Stat. Sol. B 1990, 162, 371–377. [Google Scholar] [CrossRef]
- Magomedov, M.N. On calculating the Debye temperature and the Gruneisen parameter. Russ. J. Phys. Chem. A [Zh. Fiz. Khim.] 1987, 61, 1003–1009. (In Russian) [Google Scholar]
- Magomedov, M.N. The calculation of the parameters of the Mie–Lennard-Jones potential. High Temp. 2006, 44, 513–529. [Google Scholar] [CrossRef]
- Jin, H.-S.; Song, P.; Jon, C.-G.; Kim, J.-C. Thermodynamic properties of FCC metals using reparameterized MEAM potentials. Ind. J. Phys. 2021, 95, 2553–2565. [Google Scholar] [CrossRef]
- Bian, Q.; Bose, S.K.; Shukla, R.C. Vibrational and thermodynamic properties of metals from a model embedded-atom potential. J. Phys. Chem. Sol. 2008, 69, 168–181. [Google Scholar] [CrossRef] [Green Version]
- Pandya, C.V.; Vyas, P.R.; Pandya, T.C.; Gohel, V.B. Volume variation of Gruneisen parameters of FCC transition metals. Bull. Mater. Sci. 2002, 25, 63–67. [Google Scholar] [CrossRef]
- Balluffi, W. Vacancy defect mobilities and binding energies obtained from annealing studies. J. Nucl. Mater. 1978, 69–70, 240–263. [Google Scholar] [CrossRef]
- Grabowski, B.; Hickel, T.; Neugebauer, J. Ab initio study of the thermodynamic properties of nonmagnetic elementary FCC metals: Exchange-correlation-related error bars and chemical trends. Phys. Rev. B 2007, 76, 024309. [Google Scholar] [CrossRef]
- Gray, D.E. (Ed.) American Institute of Physics Handbook; McGraw-Hill Book Company, Inc.: New York, NY, USA, 1961; Available online: https://www.scribd.com/doc/156529345/American-Institute-of-Physics-Handbook (accessed on 20 December 2022).
- Burakovsky, L.; Greeff, C.W.; Preston, D.L. Analytic model of the shear modulus at all temperatures and densities. Phys. Rev. B 2003, 67, 094107. [Google Scholar] [CrossRef]
- Lide, D.R. (Ed.) CRC Handbook of Chemistry and Physics; CRC Press/Taylor & Francis Group: Boca Raton, FL, USA, 2005; Available online: http://webdelprofesor.ula.ve/ciencias/isolda/libros/handbook.pdf (accessed on 20 December 2022).
Interaction | m | n | D (10−16 erg) | r0 (10−10 m) |
---|---|---|---|---|
Au-Au [33] | 1.96 | 15.56 | 10,227.78 | 2.8751 |
Si-Si [28] | 6.0 | 12.0 | 45,128.24 | 2.295 |
Quantity | T (K) | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | |
---|---|---|---|---|---|---|---|---|---|---|
Number of Layers | ||||||||||
10 | 3.146 | 3.152 | 3.159 | 3.166 | 3.173 | 3.180 | 3.189 | 3.197 | ||
15 | 3.033 | 3.039 | 3.045 | 3.052 | 3.058 | 3.065 | 3.073 | 3.080 | ||
30 | 2.929 | 2.934 | 2.940 | 2.946 | 2.952 | 2.958 | 2.965 | 2.972 | ||
50 | 2.889 | 2.894 | 2.900 | 2.905 | 2.911 | 2.917 | 2.924 | 2.930 | ||
100 | 2.860 | 2.865 | 2.870 | 2.876 | 2.881 | 2.887 | 2.894 | 2.900 | ||
Bulk | 2.834 | 2.839 | 2.844 | 2.847 | 2.855 | 2.861 | 2.867 | 2.873 | ||
10 | 1.334 | 1.270 | 1.207 | 1.145 | 1.084 | 1.024 | 0.963 | 0.902 | ||
15 | 1.419 | 1.353 | 1.288 | 1.224 | 1.161 | 1.099 | 1.037 | 0.975 | ||
30 | 1.506 | 1.438 | 1.371 | 1.306 | 1.241 | 1.178 | 1.115 | 1.052 | ||
50 | 1.541 | 1.473 | 1.405 | 1.339 | 1.274 | 1.210 | 1.146 | 1.083 | ||
100 | 1.568 | 1.499 | 1.431 | 1.365 | 1.299 | 1.234 | 1.171 | 1.107 | ||
Bulk | 1.593 | 1.523 | 1.455 | 1.388 | 1.322 | 1.257 | 1.192 | 1.129 | ||
CAL [33] | Bulk | 1.710 | 1.666 | 1.623 | 1.586 | 1.549 | 1.515 | 1.485 | 1.458 | |
CAL [34] | Bulk | 1.696 | 1.658 | 1.612 | 1.575 | 1.526 | - | - | - | |
10 | 1.557 | 1.797 | 1.913 | 2.015 | 2.120 | 2.235 | 2.365 | 2.521 | ||
15 | 1.515 | 1.749 | 1.859 | 1.955 | 2.052 | 2.157 | 2.275 | 2.411 | ||
30 | 1.474 | 1.702 | 1.806 | 1.895 | 1.984 | 2.079 | 2.184 | 2.301 | ||
50 | 1.457 | 1.682 | 1.784 | 1.871 | 1.957 | 2.048 | 2.147 | 2.257 | ||
100 | 1.445 | 1.668 | 1.768 | 1.852 | 1.936 | 2.025 | 2.120 | 2.224 | ||
Bulk | 1.433 | 1.655 | 1.754 | 1.836 | 1.918 | 2.004 | 2.095 | 2.195 | ||
CAL [37] | Bulk | 1.442 | 1.636 | 1.696 | 1.774 | 1.854 | 1.915 | 1.975 | 2.036 | |
CAL [34] | Bulk | 1.270 | 1.428 | 1.536 | 1.655 | 1.773 | 1.940 | 2.137 | 2.423 | |
CAL [35] | Bulk | 1.359 | 1.704 | 1.842 | - | - | - | - | - | |
EXPT [38] | Bulk | 1.15 | 1.34 | 1.41 | 1.45 | 1.50 | 1.54 | 1.59 | 1.65 | |
10 | 5.231 | 5.797 | 5.919 | 5.972 | 6.007 | 6.035 | 6.061 | 6.089 | ||
15 | 5.217 | 5.793 | 5.916 | 5.969 | 6.003 | 6.031 | 6.056 | 6.082 | ||
30 | 5.202 | 5.788 | 5.913 | 5.966 | 6.000 | 6.027 | 6.051 | 6.075 | ||
50 | 5.196 | 5.786 | 5.912 | 5.965 | 5.999 | 6.025 | 6.049 | 6.072 | ||
100 | 5.191 | 5.784 | 5.911 | 5.964 | 5.998 | 6.024 | 6.047 | 6.070 | ||
Bulk | 5.187 | 5.783 | 5.910 | 5.964 | 5.997 | 6.023 | 6.046 | 6.068 | ||
10 | 5.324 | 6.033 | 6.302 | 6.513 | 6.721 | 6.940 | 7.183 | 7.464 | ||
15 | 5.300 | 6.006 | 6.262 | 6.457 | 8.115 | 6.842 | 7.056 | 7.298 | ||
30 | 5.277 | 5.981 | 6.226 | 6.406 | 6.576 | 6.752 | 6.940 | 7.148 | ||
50 | 5.268 | 5.971 | 6.212 | 6.387 | 6.551 | 6.719 | 6.897 | 7.092 | ||
100 | 5.262 | 5.964 | 6.202 | 6.373 | 6.532 | 6.694 | 6.866 | 7.051 | ||
Bulk | 5.256 | 5.958 | 6.193 | 6.361 | 6.516 | 6.673 | 6.838 | 7.015 | ||
CAL [33] | Bulk | 5.542 | 5.994 | 6.112 | 6.277 | 6.371 | 6.464 | 6.558 | 6.604 | |
CAL [36] | Bulk | 5.136 | 5.875 | 5.873 | 6.301 | 6.419 | 6.560 | 6.677 | 6.771 | |
EXPT [38] | Bulk | 5.12 | 5.84 | 6.07 | 6.18 | 6.28 | 6.40 | 6.52 | 6.65 |
Quantity | T (K) | 100 | 300 | 500 | 800 | 100 | 300 | 500 | 800 | |
---|---|---|---|---|---|---|---|---|---|---|
Number of Layers | cSi = 1% | cSi = 3% | ||||||||
10 | 3.153 | 3.165 | 3.178 | 3.200 | 3.168 | 3.178 | 3.189 | 3.206 | ||
15 | 3.041 | 3.052 | 3.064 | 3.084 | 3.055 | 3.064 | 3.074 | 3.090 | ||
30 | 2.936 | 2.946 | 2.957 | 2.975 | 2.950 | 2.958 | 2.967 | 2.982 | ||
50 | 2.896 | 2.906 | 2.916 | 2.934 | 2.909 | 2.918 | 2.926 | 2.940 | ||
100 | 2.866 | 2.876 | 2.887 | 2.903 | 2.880 | 2.888 | 2.897 | 2.910 | ||
Bulk | 2.841 | 2.850 | 2.860 | 2.877 | 2.854 | 2.862 | 2.870 | 2.884 | ||
10 | 2.373 | 2.198 | 2.028 | 1.776 | 4.439 | 4.178 | 3.923 | 3.545 | ||
15 | 2.521 | 2.340 | 2.165 | 1.906 | 4.713 | 4.442 | 4.177 | 3.787 | ||
30 | 2.673 | 2.487 | 2.306 | 2.041 | 4.995 | 4.714 | 4.439 | 4.037 | ||
50 | 2.736 | 2.547 | 2.363 | 2.096 | 5.110 | 4.825 | 4.546 | 4.139 | ||
100 | 2.783 | 2.592 | 2.407 | 2.138 | 5.198 | 4.909 | 4.628 | 4.217 | ||
Bulk | 2.826 | 2.633 | 2.447 | 2.176 | 5.277 | 4.986 | 4.702 | 4.288 | ||
10 | 0.821 | 1.048 | 1.139 | 1.280 | 0.382 | 0.552 | 0.600 | 0.658 | ||
15 | 0.800 | 1.022 | 1.108 | 1.239 | 0.373 | 0.539 | 0.585 | 0.641 | ||
30 | 0.779 | 0.996 | 1.077 | 1.197 | 0.363 | 0.526 | 0.571 | 0.623 | ||
50 | 0.770 | 0.985 | 1.065 | 1.181 | 0.359 | 0.521 | 0.565 | 0.616 | ||
100 | 0.764 | 0.977 | 1.056 | 1.169 | 0.356 | 0.517 | 0.561 | 0.611 | ||
Bulk | 0.758 | 0.970 | 1.048 | 1.157 | 0.354 | 0.514 | 0.557 | 0.606 | ||
10 | 4.886 | 5.849 | 5.975 | 6.064 | 4.195 | 5.709 | 5.910 | 6.015 | ||
15 | 4.870 | 5.845 | 5.971 | 6.058 | 4.177 | 5.704 | 5.907 | 6.011 | ||
30 | 4.854 | 5.841 | 5.968 | 6.052 | 4.158 | 5.699 | 5.904 | 6.006 | ||
50 | 4.848 | 5.840 | 5.967 | 6.050 | 4.151 | 5.696 | 5.902 | 6.004 | ||
100 | 4.843 | 5.839 | 5.966 | 6.048 | 4.146 | 5.695 | 5.901 | 6.003 | ||
Bulk | 4.838 | 5.838 | 5.965 | 6.046 | 4.141 | 5.693 | 5.900 | 6.002 | ||
10 | 4.932 | 6.060 | 6.362 | 6.764 | 4.214 | 5.822 | 6.120 | 6.387 | ||
15 | 4.912 | 6.037 | 6.322 | 6.687 | 4.194 | 5.806 | 6.098 | 6.347 | ||
30 | 4.892 | 6.015 | 6.285 | 6.617 | 4.174 | 5.792 | 6.077 | 6.311 | ||
50 | 4.884 | 6.007 | 6.272 | 6.591 | 4.166 | 5.786 | 6.069 | 6.298 | ||
100 | 4.878 | 6.001 | 6.262 | 6.572 | 4.160 | 5.782 | 6.064 | 6.288 | ||
Bulk | 4.873 | 5.996 | 6.253 | 6.555 | 4.155 | 5.778 | 6.059 | 6.279 |
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Hoa, N.T.; Hoc, N.Q.; Dat, H.X. Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method. Physics 2023, 5, 59-68. https://doi.org/10.3390/physics5010005
Hoa NT, Hoc NQ, Dat HX. Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method. Physics. 2023; 5(1):59-68. https://doi.org/10.3390/physics5010005
Chicago/Turabian StyleHoa, Nguyen Thi, Nguyen Quang Hoc, and Hua Xuan Dat. 2023. "Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method" Physics 5, no. 1: 59-68. https://doi.org/10.3390/physics5010005