622:
17:
155:, which denotes the minimum-energy equilibrium state of the system. Increasing temperature results in a decreasing difference between mixing entropy and mixing enthalpy, and thus the coexisting compositions come closer. The binodal curve forms the basis for the
514:"GMcal_TieLinesLL: Graphical User Interface (GUI) for the Topological Analysis of Calculated GM Surfaces and Curves, including Tie-Lines, Hessian Matrix, Spinodal Curve, Plait Point Location, etc. for Binary and Ternary Liquid -Liquid Equilibrium (LLE) Data"
143:. Outside of the curve, the solution will be at least metastable with respect to fluctuations. In other words, outside the spinodal curve some careful process may obtain a single phase system. Inside it, only processes far from
118:
207:
In the case of ternary isothermal liquid-liquid equilibria, the spinodal curve (obtained from the
Hessian matrix) and the corresponding critical point can be used to help the experimental data correlation process.
171:
For binary solutions, the thermodynamic criterion which defines the spinodal curve is that the second derivative of free energy with respect to density or some composition variable is zero.
195:. As such, the spinodal does not exist in real systems, but one can extrapolate to infer the existence of a pseudospinodal that exhibits critical-like behavior such as
442:
Marcilla, A.; Serrano, M.D.; Reyes-Labarta, J.A.; Olaya, M.M. (2012). "Checking Liquid-Liquid
Critical Point Conditions and their Application in Ternary Systems".
151:, will enable one to prepare single phase compositions. The local points of coexisting compositions, defined by the common tangent construction, are known as a
62:
184:
139:
curve. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via
559:
159:
in a phase diagram. The free energy of mixing changes with temperature and concentration, and the binodal and spinodal meet at the
160:
33:
29:
471:"GE Models and Algorithms for Condensed Phase Equilibrium Data Regression in Ternary Systems: Limitations and Proposals"
179:
Extrema of the spinodal in a temperature vs composition plot coincide with those of the binodal curve, and are known as
826:
180:
25:
896:
821:
552:
1008:
836:
196:
1018:
891:
636:
545:
326:
148:
144:
1043:
942:
572:
1064:
937:
962:
952:
702:
697:
140:
881:
641:
132:
8:
856:
748:
738:
651:
606:
124:
1003:
932:
766:
1033:
1028:
998:
957:
846:
798:
783:
676:
646:
424:
385:
346:
192:
188:
183:. The spinodal itself can be thought of as a line of pseudocritical points, with the
128:
53:
49:
988:
611:
521:
492:
482:
451:
416:
377:
338:
271:
45:
275:
978:
831:
568:
156:
487:
470:
48:
with respect to small fluctuations is clearly defined by the condition that the
776:
771:
728:
661:
656:
365:
113:{\displaystyle {\operatorname {d} ^{2}\!G \over \operatorname {d} \!x^{2}}{=}0}
41:
404:
381:
1058:
1013:
993:
916:
876:
811:
743:
666:
428:
420:
389:
350:
1038:
911:
906:
901:
866:
816:
733:
286:
Cahn RW, Haasen P. Physical metallurgy. 4th ed. Cambridge: Univ Press; 1996
537:
947:
841:
753:
512:
Labarta, Juan A.; Olaya, Maria del Mar; Marcilla, Antonio (2015-11-27).
270:
P.H. Mayrhofer et al. Progress in
Materials Science 51 (2006) 1032-1114
886:
861:
788:
758:
692:
671:
526:
497:
342:
469:
Marcilla, A.; Reyes-Labarta, J.A.; Serrano, M.D.; Olaya, M.M. (2011).
455:
513:
621:
851:
983:
871:
806:
723:
718:
468:
441:
152:
127:
of these points (the inflection point within a G-x or G-c curve,
21:
16:
592:
601:
587:
226:
Thermodynamics: An
Advanced Textbook for Chemical Engineers
597:
20:
A phase diagram displaying spinodal curves, within the
202:
65:
511:
327:"Pseudocritical Phenomena near the Spinodal Point"
112:
88:
79:
1056:
191:. Strictly speaking, a spinodal is defined as a
444:Industrial & Engineering Chemistry Research
405:"Nucleation theory near the classical spinodal"
553:
311:Koningsveld K., Stockmayer W. H., Nies, E.,
257:Koningsveld K., Stockmayer W. H., Nies, E.,
567:
218:
560:
546:
402:
299:. 1999 John Wiley & Sons, Inc., p 557.
241:. 1999 John Wiley & Sons, Inc., p 571.
525:
496:
486:
370:International Journal of Modern Physics B
289:
231:
187:taking a scaling form with non-classical
15:
363:
307:
305:
297:Chemical and Engineering Thermodynamics
253:
251:
249:
247:
239:Chemical and Engineering Thermodynamics
44:, the limit of local stability against
1057:
403:Unger, Chris; Klein, W. (1984-03-01).
541:
324:
302:
244:
228:(Springer 1990), chaps 4, 8, 9, 12.
203:Isothermal liquid-liquid equilibria
34:lower critical solution temperature
13:
313:Polymer Phase Diagrams: A Textbook
259:Polymer Phase Diagrams: A Textbook
85:
70:
14:
1076:
174:
161:critical or consolute temperature
620:
505:
475:The Open Thermodynamics Journal
462:
435:
396:
331:Progress of Theoretical Physics
357:
318:
280:
264:
1:
1009:Macroscopic quantum phenomena
276:10.1016/j.pmatsci.2006.02.002
211:
1019:Order and disorder (physics)
166:
7:
488:10.2174/1874396X01105010048
193:mean field theoretic object
24:coexistence curves and two
10:
1081:
364:MONETTE, L. (1994-05-30).
971:
925:
797:
711:
685:
629:
618:
580:
382:10.1142/s0217979294000646
153:binodal coexistence curve
149:physical vapor deposition
145:thermodynamic equilibrium
1044:Thermo-dielectric effect
943:Enthalpy of vaporization
637:Bose–Einstein condensate
421:10.1103/physrevb.29.2698
325:Saito, Y. (1978-02-01).
315:. 2001 Oxford, pp 46-47.
938:Enthalpy of sublimation
953:Latent internal energy
703:Color-glass condensate
518:University of Alicante
141:spinodal decomposition
114:
37:
763:Magnetically ordered
366:"SPINODAL NUCLEATION"
197:critical slowing down
115:
19:
642:Fermionic condensate
376:(11n12): 1417–1527.
261:. 2001 Oxford, p 12.
185:correlation function
63:
857:Chemical ionization
749:Programmable matter
739:Quantum spin liquid
607:Supercritical fluid
1004:Leidenfrost effect
933:Enthalpy of fusion
698:Quark–gluon plasma
343:10.1143/PTP.59.375
189:critical exponents
135:) is known as the
110:
38:
1052:
1051:
1034:Superheated vapor
1029:Superconductivity
999:Equation of state
847:Flash evaporation
799:Phase transitions
784:String-net liquid
677:Photonic molecule
647:Degenerate matter
456:10.1021/ie202793r
450:(13): 5098–5102.
409:Physical Review B
163:and composition.
131:as a function of
129:Gibbs free energy
100:
54:Gibbs free energy
50:second derivative
1072:
989:Compressed fluid
624:
569:States of matter
562:
555:
548:
539:
538:
532:
531:
529:
509:
503:
502:
500:
490:
466:
460:
459:
439:
433:
432:
415:(5): 2698–2708.
400:
394:
393:
361:
355:
354:
322:
316:
309:
300:
293:
287:
284:
278:
268:
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235:
229:
222:
119:
117:
116:
111:
106:
101:
99:
98:
97:
83:
78:
77:
67:
46:phase separation
1080:
1079:
1075:
1074:
1073:
1071:
1070:
1069:
1055:
1054:
1053:
1048:
979:Baryonic matter
967:
921:
892:Saturated fluid
832:Crystallization
793:
767:Antiferromagnet
707:
681:
625:
616:
576:
566:
536:
535:
510:
506:
467:
463:
440:
436:
401:
397:
362:
358:
323:
319:
310:
303:
295:Sandler S. I.,
294:
290:
285:
281:
269:
265:
256:
245:
237:Sandler S. I.,
236:
232:
223:
219:
214:
205:
181:critical points
177:
169:
157:miscibility gap
102:
93:
89:
84:
73:
69:
68:
66:
64:
61:
60:
26:critical points
12:
11:
5:
1078:
1068:
1067:
1065:Thermodynamics
1050:
1049:
1047:
1046:
1041:
1036:
1031:
1026:
1021:
1016:
1011:
1006:
1001:
996:
991:
986:
981:
975:
973:
969:
968:
966:
965:
960:
958:Trouton's rule
955:
950:
945:
940:
935:
929:
927:
923:
922:
920:
919:
914:
909:
904:
899:
894:
889:
884:
879:
874:
869:
864:
859:
854:
849:
844:
839:
834:
829:
827:Critical point
824:
819:
814:
809:
803:
801:
795:
794:
792:
791:
786:
781:
780:
779:
774:
769:
761:
756:
751:
746:
741:
736:
731:
729:Liquid crystal
726:
721:
715:
713:
709:
708:
706:
705:
700:
695:
689:
687:
683:
682:
680:
679:
674:
669:
664:
662:Strange matter
659:
657:Rydberg matter
654:
649:
644:
639:
633:
631:
627:
626:
619:
617:
615:
614:
609:
604:
595:
590:
584:
582:
578:
577:
565:
564:
557:
550:
542:
534:
533:
504:
461:
434:
395:
356:
337:(2): 375–385.
317:
301:
288:
279:
263:
243:
230:
216:
215:
213:
210:
204:
201:
176:
175:Critical point
173:
168:
165:
121:
120:
109:
105:
96:
92:
87:
82:
76:
72:
42:thermodynamics
9:
6:
4:
3:
2:
1077:
1066:
1063:
1062:
1060:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1015:
1014:Mpemba effect
1012:
1010:
1007:
1005:
1002:
1000:
997:
995:
994:Cooling curve
992:
990:
987:
985:
982:
980:
977:
976:
974:
970:
964:
961:
959:
956:
954:
951:
949:
946:
944:
941:
939:
936:
934:
931:
930:
928:
924:
918:
917:Vitrification
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
882:Recombination
880:
878:
877:Melting point
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
822:Critical line
820:
818:
815:
813:
812:Boiling point
810:
808:
805:
804:
802:
800:
796:
790:
787:
785:
782:
778:
775:
773:
770:
768:
765:
764:
762:
760:
757:
755:
752:
750:
747:
745:
744:Exotic matter
742:
740:
737:
735:
732:
730:
727:
725:
722:
720:
717:
716:
714:
710:
704:
701:
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623:
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579:
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523:
519:
515:
508:
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494:
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457:
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449:
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430:
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422:
418:
414:
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406:
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391:
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379:
375:
371:
367:
360:
352:
348:
344:
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328:
321:
314:
308:
306:
298:
292:
283:
277:
273:
267:
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254:
252:
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240:
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227:
224:G. Astarita:
221:
217:
209:
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198:
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186:
182:
172:
164:
162:
158:
154:
150:
146:
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138:
134:
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126:
107:
103:
94:
90:
80:
74:
59:
58:
57:
55:
51:
47:
43:
35:
31:
27:
23:
18:
1039:Superheating
1023:
912:Vaporization
907:Triple point
902:Supercooling
867:Lambda point
817:Condensation
734:Time crystal
712:Other states
652:Quantum Hall
517:
507:
478:
474:
464:
447:
443:
437:
412:
408:
398:
373:
369:
359:
334:
330:
320:
312:
296:
291:
282:
266:
258:
238:
233:
225:
220:
206:
178:
170:
136:
122:
39:
948:Latent heat
897:Sublimation
842:Evaporation
777:Ferromagnet
772:Ferrimagnet
754:Dark matter
686:High energy
527:10045/51725
498:10045/19865
133:composition
963:Volatility
926:Quantities
887:Regelation
862:Ionization
837:Deposition
789:Superglass
759:Antimatter
693:QCD matter
672:Supersolid
667:Superfluid
630:Low energy
212:References
147:, such as
481:: 48–62.
429:0163-1829
390:0217-9792
351:0033-068X
167:Criterion
56:is zero.
1059:Category
1024:Spinodal
972:Concepts
852:Freezing
137:spinodal
984:Binodal
872:Melting
807:Boiling
724:Crystal
719:Colloid
22:binodal
612:Plasma
593:Liquid
427:
388:
349:
602:Vapor
588:Solid
581:State
125:locus
30:upper
28:: an
573:list
425:ISSN
386:ISSN
347:ISSN
123:The
32:and
598:Gas
522:hdl
493:hdl
483:doi
452:doi
417:doi
378:doi
339:doi
272:doi
52:of
40:In
1061::
600:/
520:.
516:.
491:.
477:.
473:.
448:51
446:.
423:.
413:29
411:.
407:.
384:.
374:08
372:.
368:.
345:.
335:59
333:.
329:.
304:^
246:^
199:.
575:)
571:(
561:e
554:t
547:v
530:.
524::
501:.
495::
485::
479:5
458:.
454::
431:.
419::
392:.
380::
353:.
341::
274::
108:0
104:=
95:2
91:x
86:d
81:G
75:2
71:d
36:.
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