Tap chi Khoa hgc 2012 23b 89-96 Tru&ng Dgi hgc Cdn Tba
M O PHONG CAU TRUC VI M O CUA (AL203).2(SI02)
Nguyen Thdnh Tin . Le The Vinh' va Bui Danh Hao'
ABSTRACT
The paper presents results of micros tructural investigation of(Al203).2(SiOz) by means of molecular dynamics method with Born-Mayer potentials, periodic boundaiy conditions.
Simulation were done in the basic cube containing 1650 ions with six different systems at temperature of 2500 K and different densities, pressure ranging from 0 GPa lo 25 GPa, and with five different systems at pressure ofO GPa, temperature ranging fiom 1000 K to 5000 K were prepared. Mierostruclure of constructed systems has been obsen'ed and analyzed through the structural parameters such as radial distribution function, coordination numbers, polyhedrons 5/Ox andAlOr fx=-f. 5 and 6).
Keywords: Microstructure, molecular dynamics simulation, (Al20j).2(Si02) silicate Title: Simulation of microstructure of (Al203).2(SiO^
Bai bao trinh bay ket qua nghien cuv vi cdu true cua vdt lieu (Al203).2(SiO:) bdng phuang phdp dgng luc hgc phdn tie vai the tucmg tac Bom-Ma\'er, diiu ki4n bien tudn hoan. Qud g'lnh mo phong dirae thtic hien doi vai he gom 1650 nguyen tir vai 6 mo hinh a nhiet do 2500 K vd cdc mat do khdc nhau ttrong iing vai ddi dp suat tir 0 GPa den 25 GPa va vai 5 mo hinh khdc a dp sudt 0 GPa. cdc nhiet do 1000 K den 5000 K. Vi cdu true cua cdc he dual tac dong ciia dp sudt dirge khdo sdt vdphdn tich thong qua hdm phdn bo xuyen tdm. so phoi iri. cdc da dien SiO, vdAlOx (x=4,5 vd 6).
Tu khoa: Vi c&u triic, md phong dgng lire hgc phan tir, oxit ba nguyin (Al203).2(SiO^
1 GICa THIEU
Trong nhung nam g i n diy, cac vit lieu oxit da dugc su dung rdng rai trong cic nganh cdng nghiep: SiOi dugc ung dung che tao cac chat b i n din, thiiy tinh va cac vat lieu kT thuit khac; AI2O3 dugc su dung rdng rai trong chl tao gdm. D i e biet, hon hgp oxit (Al203).2(Si02) [AS2] la vat Ueu ca ban trong cdng nghe gdm six, lgc hda dau va la thanh phin ca ban ciia vd trai dit. Do vay, sd lugng cdng trinh nghien ciiu ve vat lieu SiOa. AI2O3 va AS2 d i tang nhanh. Cd mgt so cdng trinh nghien cuu da khao sat sy thay ddi cau tnic trong dai ap suat tiJ 3 GPa din 5 Gpa (Kostya Trachenko and Martin T. Dove. 2003). Sy thay ddi cau tnic vi md din den pha vd trat ty trung binh va qua trinh chuyen pha - hdi phuc cau tnic da dugc khao s a t Anh hudng ciia chuyen pha len cac tinh chit c a hgc dugc nghien cuu bang md phdng Monte Carlo (MC) sii dung md hinh qua cau cung (Matthew H. Ford, 2004). Qua trinh chuyin pha tir trang thai vd dinh hinh (VDH) nay sang trang thai vd dinh hinh khac (d trit ty thu nhit) xiy ra trong SiO^ dudi tac dung cua ap suit tucmg ty vdi sy chuyen pha nay xay ra trong HiO. O nhiet do thap, sy chuyen pha ni}' dugc tha\ bang sy thay doi cham cau tnic trong Si02 (Daniel J. Lacks, 2000).
' Tnrimg THPT Hong Ngu 1, Tinh Dong Thap
" Tmdng Dai hpc Su pham K> thuat Vinh. Tmh Nghe An
Tap chi Khoa bgc 2012:23b 89-96 ^'''^S Dgi hgc Cdn Tha
Kit qua cho thiy, tdn tai Hai pha nay d dieu kien ap suit khac nhau la rat thu vi.
Vdi Cling mdt dai nhiet do. pha thu nhit bin vOng d ap suat thip, trai lai pha thir hai bin vOng d ap suit cao. Vimg ap suit xiy ra chuyin pha da dugc nhieu cdng trinh d l cap din, kit qua thu dugc cung kha khac nhau, cd tac gia thu dugc kit qua la 14 GPa din 22 GPa (Daniel J. Lacks, 2000); trong khi gia tri nay Polian do dugc la 8 GPa din 25 Gpa (A. Polian and M. Grimsditch, 1990). C i u tnic cua Al:03 VDH dugc nghien cuu d nhieu cdng trinh md phdng va thyc nghiem. Nhin chung, kit qui nghien cuu cho thiy do dai lien kit AI-0 trong khoang 1.8 A d i n 1.9 A v i sd nguyen tir O xung quanh nguyen tu Al trong khoang 4.0 den 4.8. C i u tnic ciia he dugc tao bdi tir cac tii dien AIO4 va bit dien AlOg vdi ty le phu thudc vao phucmg phap, quy trinh lam m i u thi nghiem. Tic gii Lamparter va cdng sy d i nghidn cihl vi ciu tnic cCia AI2O3 bing ca phuong phap thyc nghiem nhieu xa tia X. nhieu xa neutron va phuang phip md phdng Monte Carlo (P. Lamparter. R.
Kniep, 1997). Kit qua cho thiy, co 20% nguyen tur Al vdi 3 nguyen tir O bao quanh, 56% nguyen tir Al cd 4 O va 22% nguydn tir Al cd sd phdi tri O la 5, sd lieu nay ciing dugc xac nhan (G. Gutierrez. 2000). Vat lieu (Al20i).2(Si02) dugc nghien cuu trong cdng trinh (N.V. Hdng, N.T. Nhan, P. K. Hung, 2007), tie gii xiy dyng md hinh AS2 gdm 1100 nguyen tti d nhiet do 3000 K. ap suit thay ddi dieo cic gii tri la 0 GPa, 3 GPa, 5 GPa, 7 GPa, 9 GPa, 11 GPa, 13 GPa, 15 GPa va 20 GPa. Tac gia da tinh dugc do cao cyc dai thir nhit ciia gsi-si(r) la 4.84 A tai gii tri r =3.18A, do cao cyc dai thii nhat ciia gs,-o(r) la 14.12 A tai gia tri r =1.58 A, do cao cyc dai thir nhit cua go.Ai(r) ia 7-84 A tai r = 1.64 A. Cho tdi nay., da cd sd Iugng ldn cdng trinh nghien cuu v l vi ciu tnic AS2. Tuy nhien sy ly giai diy dii vl sy thay ddi vi ciu tnic dudi tic ddng ciia ap suat va nhiet dg van chua thda dang va cdn nhiJng van de dang dugc thao luin. Trong bii bao nay chung tdi nghien cuu chi tiet su thay ddi ciia ciu tnic muc do nguyen tu thdng qua viec khao sat, phin tich dac trung ciu true nhu ham phan bd xuyen tim, phan bd sd phdi tri, dp lien ket giira cac cap nguyen tir.
2 PHl/OfNG PHAP TINH TOAN
Md hinh vat lieu (Al203).2(Si03) gdm 1650 nguyen tu (300 nguyen tu Si. 300 nguyen tir Al va 1050 nguyen tir O) dugc xay dung bing phuang phap md phdng ddng lyc hgc phan tii vdi dilu kien bien tuin hoan va thi tuang tac Bom-Mayer:
•ij
U,i = ^ + A..exp(-S..r..) (11 Chi tiet ve cac he s6 ciia thS tucmg tac CO th6 xem trong tai lieu tham khao (N.V.
Hong et^al. 2007; V.V. Hoang et al, 2007). Cju hinh ban diu. cac nguyen duac gieo ngau nhien vcri nhiet dp 7000 K. sau 65.000 buoc mo phong. he duac dua vk trang thai can bang a nhiet do 2500 K, ap suit la 0 GPa, mat do 2.537 g/cm*. Tir trang thai on dinh, hi duoc nen ap sudt 5 GPa, 10 GPa. 15 GPa. 20 GPa, 25 GPa sau 25.000 buoc. De khao sat sir anh hucmg cua nhiet do, tii du lieu a mlu 6n dinh ban dau tai nhiet do 2500 K va ap suSt 0 GPa, chiing toi cho xay dung 6 mlu o ap suat khong doi 0 GPa, vcri cac nhiet do tir 1000 K, 2000 K. 3000 K, 4000 K. 5000 K. Moi mo hinh sau khi xay dung, dugc tiep tuc 6n djnh cdu true sau 25.000 buoc
Tap chi Khoa hoc 2(112:21b 89-96 Truang Bai hpc Cdn Tha
mo phong. De tang tinh thdng ke ciia phep do, so lieu tinh toan cua cac thong s6 dac tnmg dugc lly trung binh cua 1000 lan tinh voi 5 buoc mo phong dugc xac dinh mot lin.
3 K E T Q U A VA T H A O LUAN
So lieu ve ham phan b6 xuyen tam cua cac mo hinh dugc trinh tren hinh 1 va cac bang 1. bang 2.
Bang 1: Vi tri dinh thir nhat rij (A) ciia ham phan bo xuyen tam ciia he AS2 theo ap suat P. GPa Si-Si Si-O O-O Si-Al O-Al Al-Al
0 5 10 15 20 25 Bang 2: D9 cao
P . G P a 0 5 10 15 20 25
3.16 3.14 3.14 3.14 3.14 3.14 dinh thir
Si-Si 5.18 4.47 3.71 3.72 3.49 3.57
1.60 1.58 1.60 1.62 1.64 1.64 nhat gij(r) ciia
Si-O 14.30 11.66 7.59 6.77 6.13 5.94
2.64 2.62 2.54 2.54 2.50 2.48 ham phan
0 - 0 3.08 2.73 2.40 2.43 2.43 2.50
3.16 3.16 3.12 3.12 3.06 3.08
1.64 1.66 1.70 1.72 1.72 1.74
3.14 3.12 3.06 3.04 3.00 3.02 bo xuyen tam ciia he AS2 theo ip suat
Si-Al 4.11 3.60 3 22 2.99 3.30 3.22
O-AI 7.97 6.22 4.74 4.40 4.20 4.12
Al-Al 3.43 3.22 2.92 3.26 2.88 3.09 K i t qua tren hinh 1 va cic bing 1, bang 2 cho thay, khi i p suat tang, do dai lien ket cua cac c i p lien ket giiia cac nguyen tu Al-AI v i 0 - 0 giam, trong khi lien ket Si-O va 0-Al ting. Do dai lien kit cua cap Si-Si giam khi ap suit tang tir 0 GPa den 5 GPa va h i u nhu khdng thay ddi khi ap suit tang trong khoang gia tri tir 10 GPa den 25 GPa (Bang 1). C i c g i i tri cua cap lien kit Si-O va O-Al phii hgp vdi gia tri thyc nghiem la I.61A v i 1.66 A [7, 8]. Do dai ctia cip lien ket O-Al tang nhanh ban so vdi Si-O (Ar,,_t, = 0.1 A so vdi Ar^,_o = 0.04 A). Do cao dinh thu nhit cua ham gj(r) ciia ham phan bd xuyen tam cua he AS2 deu giam khi ap suit tang (Bang 2). Do cao dinh thii' nhit cua ham phan bd xuyen tim cac cap lien ket Si-Si, O-O va Al-Al xuit hien cyc tieu tai ap suat 20 GPa.
Sd lieu v l phan bo sd phdi tri dugc trinh bay tren Bang 3. Ket qua cho thay khi ap suit tSng sd phoi tri trun^ binh cua tit ca cac c$p deu tang. Trong dd. sd phdi tri trung binh cua cap lien kit Ai-O tang tir 3.73 d i n 6.41, cap Si-O tang tir 4.01 din 6.22. Dilu nay chung td ciu tnic thay ddi theo xu hudng chuyin tir ciu triic tir dien sang cau tnic bat dien.
Tap chi Khoa hgc 2012.23b 89-96 Truang Dai hgc Cdn Tha
15 1^1
10 J
5 -
o
^
p —
A...
3.24 4.32 54 6.48
Si-Si S i O O-O Si-Al O-Al A1.A1
7.56 8.64 9.72 10.8 11.9
Hinh 1: Ham phan bo xuyen tam cua hf AS2 a ap suat 0 GPa
Bang 4 trinh biy sd lieu phin bo sd phdi tri cap O-Si. C> ap suit thip. bao quanh 1 nguyen tir O la 1 hoac 2 nguyen tir Si va cd mgt ti le dang k l trudng hgp khdng cd nguyen tu Si nao bao quanh 1 nguyen tu O. Tuy nhien. khi i p suit tang ti le khdng CO nguyen tir Si bao quanh nguyen tu O giam dang k l va d khoang i p suit 5 GPa den 10 GPa cd xuit hien trudng hgp cd 3 nguyen tii Si bao quanh 1 nguyen tu O.
Nhu viy. d ap suit thip. tir 0 GPa din 5 GPa van cd c i u tnic "tricluster" gdm 3 cation la Si bao quanh 1 nguyen tir O, nhung ti le xuit hien rit thip. Ciu tnic
"tricluster" xuit hien nhieu hem d i p suit vao khoang tir 10 GPa din 25 GPa va ting khi i p suat tang.
Tap chi Khoa hoc 2012 23b 89-96 Truang Dai hgc Cdn Tha
B a n g 3 : So phoi t r i t r u n g binh cua cac cap lien ke! trong he AS2 a cac a p s u i t khac nhau P , G P a Si-Si S i - O Si-Al O-Si O - O O - A l Al-Si A l - O A l - A l
0 5 10 15 20 25
2.30 2.45 3.35 3.93 4.00 5.31 Bang 4: So phoi tri
P . G P a 0 5 10 15 20 25 Bang 5: So phoi tri
P . G P a 0 5 10 15 20 25
4.01 4.11 4.61 4.79 5,04 6.22
2.38 2.92 4.02 4.17 485 6.11
1.32 1.34 1.44 1.50 1.53 2.49 ciia cap lien ket O-Si theo cac
1 0.134 0.121 0.086 0.087 0.061 0.036
2 0.377 0.379 0.318 0 0
.283 .276 0.317 cua c^p lien l(et O-Al theo c^c
1 0.224 0.192 0.135 0.132 0.098 0.057
2 0.303 0.255 0.235 0.189 0.215 0.271
3 0.268 0.309 0.373 0.369 0.411 0.413
7.10 8.39 10.77 11.44 12.06 13.50
1.37 1.47 1.56 1.66 1.65 2.55
2.36 2.89 4.01 4.17 4 85 6.11 ip suat idiac nhau
3 0.488 0.491 0.543 0.523 0.560 0.541
4 0.001 0.009 0.052 0.106 0.102 0.106 ip suat khac nhau
4 0.201 0.223 0.226 0.230 0.221 0.213
5 0.004 0.020 0.030 0.080 0.055 0.045
3.73 3.20 4.15 3.87 4.73 4.90 5.05 5.48 5.21 5.23 641 6.42
5 0.000 0.000 0.000 0.001 0.001 0.000 6 0.000 0.001 0.000 0.001 0.001 0.001 Sd lieu ve sd phdi tri cap O-Al dugc trinh biy tren bing 5. Ket qua niy chung td, d ap suit thip, cd tir 1 den 3 nguyen tir Al bao quanh 1 nguyen tir O va ciing cd mgt ti IS dang ke trudng hgp khdng cd nguyen tir Al nao bao quanh O. Tuy nhien, ciing gidng nhu Si, khi tang ap suit thi ti le nay ciing giim dang ke. Ben canh dd, khi tang ap suit ciing lam xuit hien cac trudng hgp cd 4 nguyen tii Al bao quanh 1 nguyen tir O, mac dii ti le nay rat thap. Nhu vay, ciu tnic "tricluster" gdm 3 cation la Al bao quanh 1 nguyen tir O ludn xuit hien trong he AS2 d cac ap suit khac nhau va hau nhu cau tnic nay khdng thay ddi khi thay ddi ap suit ciia he.
Ket qua khao sat sy anh hudng cua nhiet do den vi ciu tnic ciia AS2 dugc trinh bay trong cac bing 6 den bang 12. Khi nhiet do tang, do dai lien ket ciia cac c i p lien k i t diu giam. tuy nhien ddi vdi cap lien ket O-O va Al-O lai cd cyc dai tai khoang nhiet do 3000 K (Bang 6).
Bang 6: Vi tri dinh tbir n h a t r;, (A) cua h a m pban bd xuySn t a m cua he AS2 theo nhiet dp T , K
1000 2000 3000 4000 5000
Si-Si 3.18 3.18 3.16 3.16 3.16
Si-O 1.60 1.60 1.58 1.58 1.58
O-O 2.62 2.60 2.64 2.62 2.62
Si-Al 3.18 3.16 3.16 3.16 3.12
O-Al 1.64 1.64 1.64 1.62 1.62
Al-Al 3.18 3.18 3.12 3.14 3.16
t-.-L t -.n/1 •> ji.no Qf. Truang Dgi hgc Can Tha Tap cht Khoa hgc 2012.23b 89-90
Bang 7: B? cao dinh thu nhSl g„(r) ham phgn b6 xuyen tam ciia he AS2 Iheo nhiet d?
Si-n O-O Si-Al O-Al Al-Al 1000
3000 4000 5000
7.18 5.66 485 4.64 3.90
20.23 15.92 13.39 12.64 10.46
3.45 3.20 2.93 2.88 2 52
5.50 4.43 3.68 347 2.88
9.82 8.42 7.60 7.34 6.29
4.23 3.55 3.29 3.03 2.82 Do cao dinh thir nhit lon nhit cac cap deu giam Uii nhiet do tang (Bang 7). Trong do', do cao dinh thii nhat cua cap Si-O giam nhanh nhat va cap O-O giam cham nhat so voi cac lien ket con lai.
S6 ph6i tri trung binh ciia cac cap lien ket dJu giam khi nhiet do tang (Bang 8).
Tuy nhien. gia tri nax cua cac cap lien ket lai tang manh 6 khoang nhiet dp 5000 K.. S6 ph6i tri ming binh cua cap lien ket O-Al co gia tri Ic5m nhat so voi cac cap lien ket con lai.
Bang 8: So phoi tri trung binh ciia cac cap lien ket trong he AS2 theo nhiet do 1000
2000 3000 4000 5000
2.32 2.29 2 32 2.27 3.33
4.03 401 401 4.00 5.01
2.44 2.40 2.33 2.22 3.19
1.33 1.32 1.33 1.32 2.15
7.20 7.08 7.03 6.58 7.91
1.40 1.38 1.37 1.34 2.03 S6 ph6i tri cua cap lien ket Si-O chu 5 Su la 4 va 5 va hau nhu khong thay d6i theo nhiet dp. Nhu vay, cac don vj cau tnic chu yeu trong he la Si04 va SiOs, o nhiet dp khoang 5000 K c6 sir xuit hien don vi c^u triic mdi SiOj nhung vcJi ti le rdt thip (Bang 9).
Bang 9: So phoi tri ciia Si-O a cac nhiet do khac nhau T, K
1000 2000 3000 4000 5000
1 0.000 0.000 0.000 0.000 0-000
2 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.001 0.003 0.017
4 0.968 0.985 0.983 0.991 0.941
5 0.032 0.015 0.016 0.006 0.042 Ddi vdi Al-O. chii \eu la cac cau tnic AIO3, AIO4 va AIO5 va mdt ti le rat nhd khdng dang ke cic ciu tnic AlOi va AlOg (Bang 10).
Bang 10: So phoi tri cua Al-O 0 cac nhiet do khac nhau T, K
1000 2000 3000 4000 5000
1 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.001 0.003
3 0.186 0.245 0.282 0.371 0.392
4 0.744 0.672 0.647 0.574 0.524
5 0.069 0.081 0.069 0.053 0.078
6 0.001 0.002 0.003 0.001 0.004
Tap chi Khoa hgc 2012.23b 89-96 Truang Dai hoc Cdn Tha
Bang 1 1 : S6 phoi t r i cua O-Si 6" cac nhiet d ? k h a c n h a u T , K
1000 2000 3000 4000 5O0O
0 0.133 0.133 0.137 0.137 0.088
1 0.374 0.378 0.369 0.373 0.444
2 0.493 0488 0.494 0.490 0.465
3 0.000 0.000 0.000 0.000 0.003 Co tir I den 3 nguyen ttr Al bao quanh 1 nguyen tii O va co mpt ti Ie rSt nho 4 nguyen tii Al bao quanh 1 nguyen ttr O. C4u tnic nay cOng khong thay d6i theo nhiet dp. Trucmg hop khong co nguyen tti Al nao bao quanh 1 nguyen tu O ciing xuat hien voi mpt ti le rit dang ke (Bang 12).
Bang 12: So phoi tri cua O-Al ocac nhiet d§ khac nhau 1000
2000 3000 4000 5000
0.220 0.222 0.227 0.235 0.154
0.284 0.301 0.303 0.318 0.410
0.280 0.264 0.268 0.266 0.293
0.214 0.206 0.195 0.179 0.137
0.002 0.007 0.007 0.003 0.005 Ve ti le nguyen tii Si bao quanh 1 nguyen tu O. chii ylu cd tir 1 din 2 nguyen tiir Si bao quanh 1 nguyen tu O, ciu tnic nay hiu nhu khdng thay ddi theo nhiet do.
Ciing cd ti le rat dang ke khdng cd nguyen tu Si nao bao quanh 1 nguyen tii O (Bang 11). Ti ie nay cd xu hudng giam d nhiet do 5000 K.
Sd lieu tren cac bang 6 den ban^ 2 cho thiy, khi nhiet do tang, ciu tnic vi md cua AS2 thay ddi it ve do dai lien ket, sd phoi tri ciia cic cap nguyen tii. Cau tnic chii y l u la Si04 va AIO4. Cd xuit hien S'lOs, AIO5 vdi ty Ie 4.2% va 7.8%.
4 K E T L U ^
Cd 11 md hinh vat lieu (Al203).2(Si02) da dugc xiy dung, cd thdng sd ham phan bd xuyen tim phii hgp vdi sd lieu ciia cac cdng trinh thyc nghiem va md phdng da dugc thyc hien. Cac md hinh nay cd the dugc su dung de nghien cuu cac tinh chat vit ly khac.
Ket qua nghien cuu da cho thiy, khi ap suit tang lien ket Si-O \a O-Al tang, trong khi cac lien ket cap khac giim. Lien ket O-Al tang nhanh hon so vdi Si-O va cac lien ket khac. Gia tri do cao ham phin bd xuyen tim ciia cic cap giam ding ke ichi nen d cac ap suat khac nhau. Trong dd. dd cao dinh thii nhat cap Si-O giam manh nhat.
O ap suit thip, cac dan vi c i u tnic chu yeu la SiOj. AIO4. Khi i p suit tang, cac dem vi cau tnic Si04, AIO4 giam: cac dan vi ciu tnic SiOe, AlOe tang, qua trinh chuyen ddi nay diln ra manh nhit d khoang ap suit 15 GPa.
C i u tnic "tricluster" thay ddi dang ke dudi tac ddng ciia i p suit. Khi i p suit trong khoang 0 GPa den dudi 10 GPa, cd 1 den 2 nguyen tu Si xung quanh 1 nguyen tir O; cd 1 den 3 nguyen tii Al bao quanh 1 nguyen tir O. Ddng thdi, cd ti le dang ke trudng hgp khdng ed nguven tu Al hoac Si bao quanh nguyen ni O d ap suit thap.
Tgp chi Kboa hgc 2012:23b 89-96 Truang Dgi hpc Cdn Tha
Tuy nhien. khi ap suit tang thi ti le nay giim di dang k l . Khi i p s u i t tang din khoing tren 10 GPa. xuit hien trudng hgp cd 3 nguyen tu Si bao quanh 1 nguyen tir O va 4 nguyen tii Al bao quanh 1 nguyen tu O.
Khi nhiet do tang, ciu tnic vi md cua AS2 thay ddi khdng nhilu, don vi c i u tnic chii y l u la cic tii dien Si04 va AIO4. Sd nguyen tii Si va Al bao quanh nguyen tir O gan nhu khdng thay ddi khi nhiet do tang. Chii y l u cd 1 d i n 2 nguyen tii Si va cd 1 d i n 3 nguyen tu Al bao quanh mdt nguyen tii O. Sd 'tricluster" cd trong md hinh la khdng nhieu.
TAI LIEU THAM KHAO
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[2] Matthew H. Ford (2004), On the mechanical properties and phase behavior of silica- A simple model based on low coordination and strong association, in: J. Chem. Phys. 8415:
117-127.
[3] Daniel J. Lacks (2000), Firsl-Order Amorphous-Amorphous Transformation in Silica, in:
Phys. Rev. Lett, 4629: 84-92,
[4] A Polian and M. Grimsditch (1990), Room-iemperalure densificalion ofa-SiOl versus pressure, in: Phys. Rev . B, 6086 41-49.
[5]. P. Lamparter, R. Kniep (1997), Slruclttre of amorphous Al^O3. in: Phys. B, 405: 234-244.
[6] G. Gutierrez (2000), Siruclural properlies of liquid A1203 A molecular dynamics study.
in: Phys. Rev. E, 2723: 3-61.
[7] Nguyin Van H6ng, Nguyin Thu Nhan,_Pham KhSc Hiing (2007), Suphu ihugc cdu true cua he (Al^Os/ 2(Si02f long vdo dp sudt. Tap chi Khoa hoc va Cong nghe cac Trucmg d^i hgc kl thuat, s l 60: 5-16.
[8] V V. Hoang, N.N. Linh and N.H. Hung (2007), Structure and dynamics of liquid and amorphous Al:03 2Si02. in: Eur.Phys. 3, 111:37-48.
