The glass-liquid and solid-jelly transition temperatures

The supercooled liquid undergoes a “glass transition” in whichC p (I) decreases rapidly and approaches that ofC p (s). The theoretical glass transition temperature Tg,theoretical is defined as the temperature below the melting point, whereS (l-s) = 0. Similarly, the overheated solid will undergo a transition, where the lattice softens, as the structure cannot support vibrations with larger and larger amplitudes.S (l-s), the entropy difference between liquid and solid, andG (l-s), the Gibbs energy difference between liquid and solid, cross the zero line above the melting point. WhereS (l-s) crosses the zero line, the entropy of the liquid becomes less than that of the superheated solid. We call this pointT jStheoretical. At a higher temperature, G (l-s) crosses the zero line, where the superheated solid becomes stable with respect to the liquid. We call this pointT jGtheoretical. We do not know yet which of the two are technologically important. For example, what influence does 7TjStheoretical, orT jGtheoretical have on the behavior of aluminum, which melts at a low temperature but is used up to very high temperatures in various alloys. We obtained (T g, TjS, andT jG all theoretical) % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqGacaWFubWaaSbaaSqaaiaa-Dga% aeqaaGabaOGaa43laiaa-rfadaWgaaWcbaGaa8xBaiaa-bhaaeqaaO% Gaeyypa0Jaa4hkaiaa+bdacaGFUaGaa4hnaiaa+bdacaGFXaGaa4ho% aiaa+flacaGFWaGaa4Nlaiaa+fdacaGF2aGaa4hmaiaa+fdacaGFPa% Gaa43kaiaa+HcacaGF4aGaa4Nlaiaa+vdacaGFZaGaa4xSaiaa+jda% caGFUaGaa4Nnaiaa+HdacaGFPaGaeyyXICTaa4xmaiaa+bdadaahaa% WcbeqaaGWaciaa9nbicaGF1aaaaOGaeyyXICTaa8hvamaaBaaaleaa% caWFTbGaa8hCaaqabaGccqGGSaalryqqYLwySbacgiGaaWhiaiaa8b% cacaaFGaGaaWhiaiaa8bcacaWFsbGaa8xpaiaa+bdacaGFUaGaa4xn% aiaa+jdacaGFYaGaa4hoaiaa+Tdaaaa!71E3! $$T_g /T_{mp} = (0.4018 \pm 0.1601) + (8.53 \pm 2.68) \cdot 10^{--5} \cdot T_{mp} , R = 0.5228;$$ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqGacaWFubWaaSbaaSqaaiaa-Dga% aeqaaGabaOGaa43laiaa-rfadaWgaaWcbaGaa4xBaiaa+fgacaGF4b% aabeaakiabg2da9iaa+HcacaGFWaGaa4Nlaiaa+ndacaGF4aGaa4xm% aiaa+zdacaGFXcGaa4hmaiaa+5cacaGFXaGaa4hmaiaa+DdacaGF0a% Gaa4xkaiaa+TcacaGFOaGaa43naiaa+5cacaGF0aGaa43naiaa+fla% caGFXaGaa4Nlaiaa+HdacaGFWaGaa4xkaiabgwSixlaa+fdacaGFWa% WaaWbaaSqabeaaimGacaqFtaIaa4xnaaaakiabgwSixlaa-rfadaWg% aaWcbaGaa8xBaiaa-bhaaeqaaOGaeiilaWsegeKCPfgBaGGbciaa8b% cacaaFGaGaaWhiaiaa8bcacaaFGaGaa8Nuaiaa-1dacaGFWaGaa4Nl% aiaa+zdacaGFYaGaa4hnaiaa+LdacaGF7aaaaa!72D2! $$T_g /T_{max} = (0.3816 \pm 0.1074) + (7.47 \pm 1.80) \cdot 10^{--5} \cdot T_{mp} , R = 0.6249;$$ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqGacaWFubWaaSbaaSqaaiaa-Dga% aeqaaGabaOGaa43laiaa-rfadaWgaaWcbaGaa8NAaaqabaGccaWFtb% Gaeyypa0Jaa4hkaiaa+bdacaGFUaGaa4xmaiaa+DdacaGF0aGaa4xo% aiaa+flacaGFWaGaa4Nlaiaa+fdacaGFWaGaa4Nmaiaa+ndacaGFPa% Gaa43kaiaa+HcacaGF3aGaa4Nlaiaa+vdacaGF1aGaa4xSaiaa+fda% caGFUaGaa43naiaa+fdacaGFPaGaeyyXICTaa4xmaiaa+bdadaahaa% WcbeqaaGWaciaa9nbicaGF1aaaaOGaeyyXICTaa8hvamaaBaaaleaa% caWFTbGaa8hCaaqabaGccqGGSaalryqqYLwySbacgiGaaWhiaiaa8b% cacaaFGaGaaWhiaiaa8bcacaWFsbGaa8xpaiaa+bdacaGFUaGaa4Nn% aiaa+rdacaGF3aGaa4hmaiaa+Tdaaaa!71C3! $$T_g /T_j S = (0.1749 \pm 0.1023) + (7.55 \pm 1.71) \cdot 10^{--5} \cdot T_{mp} , R = 0.6470;$$ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqaacaWF2aaceiGaa43uamaaBaaa% leaacaGFTbGaa4hCaaqabaGccaGFVaGaa4hzaiabg2da9iabgkHiTi% aa-HcacaWFYaGaa8Nlaiaa-bdacaWF4aGaa8xSaiaa-jdacaWFUaGa% a8hoaiaa-bdacaWFPaGaeyyXICTaa8xmaiaa-bdadaahaaWcbeqaai% aa-fdacaWFWaaaaOGaa83kaiaa-HcacaWFZaGaa8Nlaiaa-HdacaWF% 0aGaa8xSaiaa-bdacaWFUaGaa8hnaiaa-DdacaWFPaGaeyyXICTaa8% xmaiaa-bdadaahaaWcbeqaaGWaciaa9nbicaWF3aaaaOGaeyyXICTa% a4hvamaaBaaaleaacaGFTbGaa4hCaaqabaGccqGGSaalryqqYLwySb% acgiGaaWhiaiaa8bcacaaFGaGaaWhiaiaa8bcacaGFsbGaa4xpaiaa% -bdacaWFUaGaa8hoaiaa-rdacaWF0aGaa8Nnaiaa-Tdaaaa!7517! $$6S_{mp} /d = - (2.08 \pm 2.80) \cdot 10^{10} + (3.84 \pm 0.47) \cdot 10^{--7} \cdot T_{mp} , R = 0.8446;$$ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqGacaWFubWaaSbaaSqaaiaa-jga% caWFWbaabeaakiaa-9cacaWFubWaaSbaaSqaaiaa-PgaaeqaaOGaa8% 3uaiabg2da9Gabaiaa+fdacaGFUaGaa4hmaiaa+zdacaGF2aGaa4xS% aiaa+bdacaGFUaGaa43maiaa+jdacaGF1aGaa43oaaaa!50E8! $$T_{bp} /T_j S = 1.066 \pm 0.325;$$ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuatLrhDLjhih9gDOL2yG0evae% XatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhi% ov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps% 0lbbf9q8WrFfeuY-Hhbbf9v8GmFr0xc9fs0xc9q8qqaqFn0dXdir-x% cvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr0-vr0db8meaabaqaci% GacaGaaeqabaWaaqaafaaakeaaiqGacaWFubWaaSbaaSqaaiaa-jga% caWFWbaabeaakiaa-9cacaWFubWaaSbaaSqaaiaa-PgaaeqaaOGaa8% 3raiabg2da9Gabaiaa+bdacaGFUaGaa43naiaa+bdacaGFZaGaa4xS% aiaa+bdacaGFUaGaa4Nmaiaa+fdacaGF0aaaaa!501B! $$T_{bp} /T_j G = 0.703 \pm 0.214$$ whereT mp is the temperature of the standard melting point,T bp is the standard boiling point, Tmax is the temperature whereS (l-s) is maximum and Cp(l-s) = 0, andR is the regression coefficient.