REFERENCES

1. Guillaume CE. Recherches sur les aciers au nickel. J Phys Theor Appl 1898;7:262-74.

2. Wittenauer J. The invar effect: a centennial symposium. Mine Met Mater Soc 1997.

3. van Schilfgaarde M, Abrikosov IA, Johansson B. Origin of the invar effect in iron-nickel alloys. Nature 1999;400:46-9.

4. Miller W, Smith CW, Mackenzie DS, Evans KE. Negative thermal expansion: a review. J Mater Sci 2009;44:5441-51.

5. Fultz B. Vibrational thermodynamics of materials. Prog Mater Sci 2010;55:247-352.

6. Mittal R, Gupta M, Chaplot S. Phonons and anomalous thermal expansion behaviour in crystalline solids. Prog Mater Sci 2018;92:360-445.

7. Liang E, Sun Q, Yuan H, Wang J, Zeng G, Gao Q. Negative thermal expansion: Mechanisms and materials. Front Phys 2021;16:53302.

8. Wendt D, Bozin E, Neuefeind J, et al. Entropic elasticity and negative thermal expansion in a simple cubic crystal. Sci Adv 2019;5:eaay2748.

9. Lohaus SH, Heine M, Guzman P, et al. A thermodynamic explanation of the Invar effect. Nat Phys 2023;19:1642-8.

10. Liu Z, Wang Y, Shang S. Zentropy theory for positive and negative thermal expansion. J Phase Equilib Diffus 2022;43:598-605.

11. Landau LD, Lifshitz EM. Statistical physics Oxford: Pergamon Press Ltd.; 1970.

12. Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys Rev 1964;136:B864-71.

13. Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Phys Rev 1965;140:A1133-8.

14. Liu Z. Theory of cross phenomena and their coefficients beyond Onsager theorem. Mater Res Lett 2022;10:393-439.

15. Liu Z. Thermodynamics and its prediction and CALPHAD modeling: review, state of the art, and perspectives. Calphad 2023;82:102580.

16. Liu Z, Li B, Lin H. Multiscale entropy and its implications to critical phenomena, emergent behaviors, and information. J Phase Equilib Diffus 2019;40:508-21.

17. Mermin ND. Thermal properties of the inhomogeneous electron gas. Phys Rev 1965;137:A1441-3.

18. Wang Y, Liu Z, Chen L. Thermodynamic properties of Al, Ni, NiAl, and Ni₃Al from first-principles calculations. Acta Mater 2004;52:2665-71.

19. Liu ZK, Wang Y, Shang S. Thermal expansion anomaly regulated by entropy. Sci Rep 2014;4:7043.

20. Liu Z, Shang S, Du J, Wang Y. Parameter-free prediction of phase transition in PbTiO₃ through combination of quantum mechanics and statistical mechanics. Scr Mater 2023;232:115480.

21. Behera RK, Lee CW, Lee D, et al. Structure and energetics of 180° domain walls in PbTiO₃ by density functional theory. J Phys Condens Matter 2011;23:175902.