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Computer Simulations of Simple Liquids with Tetrahedral Local Order: the Supercooled Liquid, Solids and Phase Transitions

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(504) 1*? F"E

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(579) HF:h?E%>@F"5NDKE :<FDE%>3F"DKEDE

(580) X 5KDKq%=DZHUoDKE FmUL=; ?BA31*4+45K?H U>3F)>L?OF5A@?F HimDE >L2?/:<DZHH5K?/4"7>L2?J;AL?V+D4 =

(581) U 1*?BE%>@=ALi ( r '5KFALX ?oE%=

(582) :Jk ?BA4"7 DZ1*4 U@F"2

(583) ?HA3FeFE

(584) Hs;W4 5i%>@?* >LA3F"2?HA3F"51*5K=

(585) U >L?BA3UN2

(586) F UNF"5ZU 4ok ?B?Ee7^4 =E

(587) H<DKEh>L2?DKE2?AL?E > U >LA@=

(588) 1*>L=A@?U  U ??C +?1*>LDK4E r , 47 U DK:J=

(589) 5KF">L?HOUL=; ?BA31*4+45K?H<5KDZq =

(590) DKHUl%?r X

(591) rDE =f?BEEWF"A3H+ ? 4E

(592) ?U ( aF"E

(593) H DEO>@2?C5KDZq =

(594) DKHU9U>@=

(595) HDK?H DE<>@2DZUN>L2

(596) ?ULDKU ! r Y4 AN>L2

(597) ?TE?*> j4A@P/7^4 AL:<DKEX/5DZq%=DZHUN>@2

(598) F)> 2WF,V?k ?B?BEODKE%>L?E

(599) U ?5ihU>@=

(600) HDK?H k+ih? r XWrCEX?55  a>L2?c7^4A@:OF)>@D4 EO4"76>L?B>LA3F"2?HA3F"5 E?*> j4A@PUNDKU97^=EWHF":<?BE%>3F"5 r YDKX=A@?cr XDKV?UbFE ?BgF":<;5K?e47jF >L?B>LA3F"2?HA@F5N1*5K=

(601) U>@?BAG1BAL?F)>L?H DKE FsULDK:J=5ZF)>@D4 E 4"79>L2 ? A 5KDZq =

(602) DKH 2 H?U@1*A@DKkW?H DKE +?1*>LDK4EIrKr !r 2? A@?FUL4E 7^4A F"5K5>L2DZU DKE%>L?AL?U>@DEX k ?B2WF,V%DK4=

(603) AODKU >L2? DKE2?AL?E%>O7^AL=

(604) U >LA3F)>@D4 E DE F >L?B>LA3F"2?HA@F55KiG1*5K4 UL? ;

(605) F13P ?HeU>@AL=

(606) 1*>L=A@?r#EOFoH?BE

(607) UL?TULi+U >L?:YU >LA@DK1*>N>L?*>@A@F2?HA@F5%;WF13P+DE

(608) XbDZU D:<; 4 U@U DKk5K?l+U DK:<;5KiOkW?1BF"=WU ?C>L2?AL?cDKUjE4 jF,ie>L4 

(609) 5K5W>@2?cUL;

(610) F 1*? D>L2 AL?X=5ZF"A >L?B>LA3F"2?HA@F D]>@24=> 245K?Ur 2DZUODKU U DK:<D5ZF"A<>@4 >L2?I7 F 1->O>@2

(611) F)> D> DKU D:<; 4 U@U DKk5K?m>L4 

(612) 5K5>L2

(613) ? U ;

(614) F 1*? D]>@24=>8245K?UN=WU DKEXGUL;2?BA@?Ul 2

(615) D5K?D]>9DKU8ULDK:h;

(616) 5?T=WU DKEXG1*=

(617) kW?UBr #E

(618) X=

(619) AL?Cr  

(620) V ?AL?X=5ZF"A >L?B>LA3F"2?HA@FIFAL?O;

(621) 5KF 1*?H E?*g+>G>@4 ?F 132 4">@2?BAhF"E

(622) H >@2? A@?UL=5>LDKEX X F; 1BFE kW?sU ??BE  >@2? X F;m1B4A@AL?U ; 4EWHUj>L4 FkW4 =>bFh>@?BE%>L2 4"7 >L2?J>L?B>LA3F"2?HA@F5 ?HX? *rQRD]>@2 :<DE

(623) 4ACHDZU >L4AL>LDK4E AL?X=5ZF"Ao>@?*>@A@F2?HA3FI1BFE kW? ;

(624) F13P ?H DKE >@4 A@?BX=

(625) 5KFA/DK1B4 U@F"2?HA@F

(626) lfk=>eA@?BX=

(627) 5KFAGDK1B4 U@F"2?HA3F F"A@?sF5KUL4 DK:<;W4%ULULDKk5?s>@4 ;WF13P DKE F F,i >@2

(628) F)> W55ZUe>L2? UL;

(629) F1B? D>L2

(630) 4=>O24 5?UBr  V?BA@i.  #.  .  #.  .    . .

(631) .   . .      $   .   .      ' .  . YDX =AL? rK TE ?*gF":<;5K? 47eF ; 45Ki%>L?*>@A@F2?HA@F5c1*5K=

(632) U >L?A 7^4A@:<?HRDKE F U DK:J=

(633) 5KF">LDK4E 47 >L2? A 5KDKq%=DZH F">e>@?B:<; ?BA3F)>L=

(634) AL?mr !  F"E

(635) H E+=:Jk ?BAOH?E

(636) U D>i r ! r 2DZUO1*5K=

(637) U>@?BA<DZUJ>@2? 5KFALX ?U 2>C1*5K=

(638) U >L?BAc4"7N7 F 1*?JUL2

(639) F"A@DKEX<>L?B>LA3F"2?HA@F<DKE FE DE

(640) 2?BA@?BE%>cU >LA@=

(641) 1->@=A@?/>@FP?BEm7^A@4: >L2WF)> U DK:J=

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(643) U 4"7  47/>L2? 

(644) A3U> ;W4>L?E >@DKF5 :hDKEDK:OF >@4m:<FP?e>L2?OU >LA@=

(645) 1->@=A@?e>@A@FE

(646) UL;

(647) F"A@?BE%>rGj>@4: ;WF"DKA@U D>L2 FsHDKU >@FE

(648) 1*? 1*4 ALA@?UL;W4 E

(649) HDKEXG>@4<>L2? WA@U >;W4>L?BE%>@DKF56:hDKEDK:J=: F"A@?bkW4 E

(650) H?H r AL?1*?E >JHDKU@1*=

(651) U@ULD4 E 479>@2? 7^A@=

(652) U >LA3F)>@D4 E 47 DZ1*4%ULF2?HA@F55Ki 4A3H?AL?H ULiU>@?B:OUBl;

(653) FA >@DK1B=5KFAL5Ki YA3F"EP%#./FUL;W?AJ;2WFUL?Ul 1BFE k ?s7^4=E

(654) H DKE A@?*7^?AL?E

(655) 1*? +$ CF"E

(656) H F >L24 AL4 =X2 F"E

(657) H AL?1*?BE%> HDZUL1B=

(658) ULULDK4E 47n>@2?/:OF)>L>L?BAT1F"EskW?o7^4 =E

(659) HsDKEsA@?*7^?AL?E

(660) 1*? ( r >CDKU>L2?JF">L4 :hDZ1oDKE >@?BA3F1*>LDK4E >L2

(661) F">cH?1BDKH?U >@2?G?BE

(662) ?BA@X?*>@DK1F"5K5i ;AL?B7^?BA@AL?H 5K41BF5fU>@AL=W1- >L=A@? 47Fm:OF">L?BA@DZF"5 r #E H?BE

(663) UL? ULi+U >L?:OU/4"7TF)>@4:OU/DKE%>L?BA3F1*>LDKEXIV+DKF Fm;W4>L?BE%>@DKF58>L2WF)>eDZU F)>L>LA3F1->@DV ? F)>J:<?HD=

(664) : A3F"E

(665) X?Ulf? r XWrs>L2? = ?BE

(666) E

(667) F"A3H+@ ?4 E?U '=9? o;W4>L?E >@DKF5  U ??s +?1->LDK4E rKrK *l6>L2? :hDKEDK:<DKU@F)>@D4 E 47j?E?BA@Xi kW4 D5ZUGH4 E >L4 

(668) EWHDE

(669) Xm>L2? :<4%U>JH?E

(670) UL?O;

(671) F13P+DKEX

(672) l ;A@?*7^?BA3F"k

(673) 5i D>L2<FU:OF"E+iGDKE%>L?BA8F">L4 :hDZ1jHDKU >@FE

(674) 1*?UNFU; 4 U@U DKk5K?jk ?BDKEXb>L2WF)>N4"7W>L2? :<DE

(675) D:OF 4"7 >L2

(676) ? DKE >@?BA3F1*>LDK4E X r Y4 AG7^4 =AJDZH?BE%>@DK1F"59F">L4 :<UJD]>hDKUe1*5K?FAG>L2WF)>eFIA@?BX =5ZF"A/>@?*>LA3F"2

(677) ?HA3F"5 F"A@A@FEX?:<?BE%> D>L2J4E?8F">L4: DE/?F132oV?A >@?*gbDKUf?BE?ALX ?*>LDZ1BF55KiT;A@?*7^?ALA@?H r #Eo>L2DZUfFALA3F"E

(678) X?* :<?BE%>oF55 F)>@4:OUb2

(679) F,V?eF"5K5E

(680) ?BDKX2+kW4 =A3UCF)>b>L2

(681) ?hU@F":<?<HDKU >@FE

(682) 1*? r/ 2?hH?BE

(683) UL?U >o1B4:<; ?*>LDKEX 1*A@iU>3F"5K5DKE? jF,iU 47 ;

(684) F 13P+DEX/FAL? >@2? 7 F1B?*#1*?BE%>@AL?He1B=kDZ1  7 11 -l+F"EWHJ>@2?T2?BgF"X4 E

(685) F"51B54%U ? ;

(686) F13P+DKEX  2

(687) 1*;  ) 6;

(688) F 13P+DEX%UBr8jF"5Z1*=

(689) 5KF">LDK4E i+DK?B5ZHU8>@2

(690) F)>l=

(691) ULDEXJ>L2> ? =#?J; 4">@?BE%>LDZF"56F"EWHI! F)>@4:OUBlW>L2

(692) ?eDZ1*4%ULF2?HA3FO2

(693) F UT>@2?h54 j?U >C?BE

(694) ?BA@Xim4"7 F55n>L2?U ?<U >LA@=

(695) 1->@=AL?UBl :OF"P+DKEX D>c>@2? ;A@?*7^?BA@A@?Hs541F"5 ;

(696) F 13P+DEX  ( rT 2DZUTA@?UL=5>CDZUCF"5ZUL4O>LA@=?/7^4 A>L2?e;W4>L?E >@DKF5KUC=

(697) UL?HmDKEm>L2DZU >L2?U DZUr \T; 4EGUL=;W?A@1B4+45KDEXF 5KDKq%=DZHoD> 541BF55KicF;;A@4 F 132?UW>L2

(698) ?8?BE?ALX ?*>@DK1F"5K5iT:<4 AL?7 F,V4 =A3F"k5K? 541F"5a1*4E 

(699) X=A3F)>@D4 E

(700) UlF/7 F 1-> EDK1B?B5KiOU 24 E =

(701) U DKEXe:h4 5?1*=5ZF"AjHi+E

(702) F":<DZ1BUjU DK:J=

(703) 5KF">LDK4E

(704) UjF"E

(705) H.   # .  .  .

(706)  . $ )   '           . $. YDX =AL?  r NYDKV?I>@?*>@A@F2?HA3F ;

(707) F 13P?H >@4X?B>L2?A F"A@4=

(708) E

(709) H F 1*4 :h:<4 ER?HX ? 1BF"E

(710) E4"> k ? ;

(711) F13P ?H  D]>@24=>7^A@=

(712) U >LA3F)>@D4 E rN 2?/V+DKULDk

(713) 5?oX F;s1B4A@AL?U ; 4EWHU8>@4 7.36◦ r.  7. >L2?C;W4>L?BE%>@DKF5

(714) ?BE

(715) ?BA@Xih5KFE

(716) HU@1BF"; ?U HDKU@1*=WULUL?H<DKE +?1*>LDK4E r  $, r 7 FGULD:<;5K?c1BALiU >@F"5K5KDE? U>@AL=W1->L=

(717) AL?e?*gDKU >@Ula>L2

(718) ?BE XA3F"DKE

(719) UT47 >L2

(720) ?h1BALiU >@F"5K5KDE?hU>@AL=W1->L=

(721) AL?<1BFE 7^4A@: ?F U DK5Ki 2

(722) ?BE >@2? 5DZq%=DZH DZU/U =

(723) ;W?A@1B4%4 5?H6rhQR2?BE Fm1*A@i+U >@F55KDKE?eX A@FDE AL?F132?Uc1BALD>LDZ1BF58U D

(724) B?h>@2?<5DZq%=DKH UL4" 5DZHD 

(725) ?UhDKE%>L4 >@2?m1*A@i+U >@F55KDKE? U >LA@=

(726) 1->@=A@?r T4>hUL=AL;

(727) ALDZU DKEX 5i lN5DZq%=DKH

(728) U 2DZ132 ?FULD5Ki 7^4A@: 1*A@iU>3F"5K5DKE?bE%=W1*5K?BDfq%=DZ13P+5i 1BALiU >@F55KDKUL?b4EmU =; ?BA31*4+4 5DKEX ! r 2? =#? 5DZq%=DKH l8DE 2DZ132 >L2

(729) ? DZ1*4%ULF2?HA3F"5jF"A@A@FEX?:<?BE%>GDKUh;A@?*7^?ALA@?H 541BF55Ki F"E

(730) H 2DZ132 DKUoF5KUL4 P+E4 EI>@4 UL24 F"E F"k=EWHF"E

(731) 1B?e478DK1B4 U@F"2?HA3F"5n1B5=WU>@?BA3UcF">b5K4 '>L?:h; ?BAL F)>@=AL?U ( la1*A@i+U >@F55KDZU ?UTA3F)>L2

(732) ?BAC?FULD5Ki >L4 Y  =E

(733) H?Ab1B4%4 5DKEXWrC 2?JA@?F U 4 Es7^4AT>@2DZUcDZU >L2

(734) F">lW?BV?Es>L24 =X2s>L2

(735) ?GDK1B4 U@F"2?HA3F"56;

(736) F 13P%DKEX<DZUT5K4+1F"5K5i ;A@?*7^?BA@A@?H6l>@2B ? Y R;

(737) F 13P+DEXODZU E4">e:J=

(738) 132 5K?U@UG?E?BA@X?B>LDZ1BF"5K5Ki ?*`a?1*>LDKV? r Y F"5ZUL4 2

(739) FU/>L2? 2%=

(740) X? F HV)F"E%>@FX?O4"7k ?BDKEX F"k5K?b>L4

(741) 5K56>L2

(742) ?GU ;

(743) F 1*? D]>@24=>7^AL=

(744) U >LA3F)>@D4 E rN 2DZU 5KF 13P 4"7 U DK:<;5?/5KDZq =

(745) DKH :<4+H?B5ZUTF"k5K?b>L4 D]>@2

(746) U >@F"EWHJUL=;W?A@1B4+45KDEX D]>@24=>81BALiU >@F"5K5KDKU@F)>@D4 E lFE

(747) H/>@2?jXA@?F)>DE%>@?BA@?U >nDKEeDZ1*4%ULF2?HA3F"5 5DZq%=DZHU %(l% lWU ;=

(748) ALA@?H >L2?GH?V?54 ;:<?BE%>4"7>L2?/5KDKq%=DZHUU >L=

(749) HD?H DKEs>L2DZU >@2?ULDKUr.  7.  #.  #. .  )"$    

(750) " "" 

(751) "! . 2?T; 4">@?BE%>LDZF"5ZU8=

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(753) F5D>@F">LDKV? AL?U =

(754) 5]>3UBl"E

(755) 4">8>@4/:h4H?5

(756) F"E+ihU ; ?1BD W1TAL?F"5:OF)>@?BA@DKF5 rNpcE<>L2?4>L2?A82

References

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