Temperature-Dependent Defect Dynamics in SiO 2. Katharina Vollmayr-Lee and Annette Zippelius Bucknell University & Göttingen

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1 Temperature-Dependent Defect Dynamics in SiO 2 Katharina Vollmayr-Lee and Annette Zippelius Bucknell University & Göttingen x i, y i, z i, [Å] =25 K =325 K x i (t) y i (t) z i (t) zoo = 7 zoo = 7 zoo = 7 zoo = 7 zoo = 8 zosi = zsio = 5 jumper zsisi = 3 zoo = 8 t = ns t = ns t = ns Göttingen, June 2, 23

2 Introduction: Glass V liquid Crystal Glass Liquid glass crystal T m T log η [Poise] 2 GeO 2 strong glass former Glycerol SiO2 fragile glass former 2 4Ca(NO 3 ) 2 6KNO.4 T /T 3. g [C.A. Angell and W. Sichina, Ann. NY Acad. Sci. 279, 53 (976)] Dynamics: Viscocity η as function of inverse temperature T slowing down of many decades very interesting dynamics strong and fragile glass formers Here: SiO 2 (strong glass former)

3 Model & Simulations Model: BKS Potential [B.W.H. van Beest et al., PRL 64, 955 (99)] φ(r ij ) = q iq j e 2 r ij + A ij e B ijr ij C ij r 6 ij 2 Si & 224 O ρ = 2.32 g/cm 3 T c = 333 K O Si network (potential only "spheres") Molecular Dynamics Simulations: 5 K 376 K T Ti T c 2 initial configurations 325 K 3 K.33 ns 33 ns 275 K NVT NVE 25 K (Nose Hoover) (Velocity Verlet) time

g Unexpected Similar Dynamics: scaling plots (C q, χ 4, P (C q ))

4 Motivation log η [Poise] 2 GeO 2 strong glass former SiO2 Glycerol fragile glass former 2 4Ca(NO 3 ) 2 6KNO.4 T /T 3. g Unexpected Similar Dynamics: scaling plots (C q, χ 4, P (C q )) jump statistics (P ( R), P ( t b )) r n (t) R td tb SiO 2 -specific perspective?

5 Network Glass SiO 2 extract main features

6 Time Averaged Trajectories t av =.327 ns t {r i } {r i } {r i } {r i } x i, y i, z i, [Å] t av x i (t) y i (t) z i (t) =25 K x i, y i, z i, [Å] =325 K x i (t) y i (t) z i (t) strong temperature dependence

7 Structure: Radial Distribution Function g αβ (r) = V N αn β N α i= N β j= j i δ( r r ij (t) α, β {Si,O} g SiO g OO g SiSi r i (t) t av = ns r i (t) t av =.327 ns r i (t) t av =.654 ns =25 K t av =.327 ns {ri} {ri} {ri} {ri} time average sharpens peaks t r [Å]

8 Structure: Radial Distribution Function g αβ (r) = V N αn β N α i= N β j= j i δ( r r ij (t) α, β {Si,O} g SiO = 25 K = 275 K = 3 K = 325 K almost no temperature dependence r [Å]

9 Structure: Coordination Number z αβ i via minimum of g αβ (α, β {Si,O}) = number of nearest neighbors - =25 K =325 K =25 K - =325 K - =325 K =25 K - =325 K =25 K P OSi (z) -3-4 P SiO (z) -3-4 P SiSi (z) -3-4 P OO (z) z z z z sharply peaked

10 SiO 2 -Network g SiO g OO g SiSi r i (t) t av = ns r i (t) t av =.327 ns r i (t) t av =.654 ns =25 K O Si P OSi (z) r [Å] =25 K =325 K P SiO (z) z =25 K - =325 K z almost perfect neighborhood well defined defects: z αβ i z αβ perfect focus on defects z OSi perfect =2 zsio perfect =4

11 Number of Defects { if at time t z αβ χ D i (t, β) = i (t) z αβ perfect if at time t z αβ i (t) = z αβ perfect Mαβ D = χ D i (t, β). N α N α i= - M D αβ -2-3 αβ= SiSi SiO OSi OO [K] few defects (mostly OO) strong temperature dependence: increases with temperature M D αβ Arrhenius fits Life Time of Defects?

12 Defect-Defect Correlation C DD (t, α, β) = Nα Nα χ D i (t, β) = χ D i (t, β)χ D i (t + t, β) i= if at time t z αβ i (t) z αβ perfect if at time t z αβ i Nα Nα (t) = z αβ perfect χ D i (t, β) i= C α,β DD (t) = CDD (t,α,β) C DD (t=,α,β) Nα Nα χ D i (t + t, β) i=.4.3 = 25 K = 275 K = 3 K = 325 K = 25 K = 275 K = 3 K = 325 K C ~DD SiO.2 C ~DD OO strong temperature dependence

13 Life Time of Defects.4.3 = 25 K = 275 K = 3 K = 325 K C ~DD SiO.2... DD DD DD DD τ τsio SiO τ τsio SiO τ DD αβ [ns] - -2 t av αβ= SiSi SiO OSi OO / [K - ] t b t d z i (t) td tb SiO- & OSi-defects short-lived (flashes) OO-defects longer lived

14 Jumps { during jump χ J i (t) = otherwise x i,y i,z i [Å] 5 5 =25 K J(t) O-atom

15 Number of Jumps { during jump χ J i (t) = otherwise Mα J = χ J i (t) N α N α i= M J α - -2 α= Si O very few jumps Arrhenius fits strong temperature dependence [K]

16 Defect-Jump Correlation zoo = 7 zoo = 7 zoo = 7 zoo = 8 zoo = 7 zosi = zsio = 5 jumper zsisi = 3 zoo = 8 t = ns t = ns t = ns D(t,O) =25 K OO-defect D(t,O) =25 K SiO-defect J(t) O-atom jumping J(t) Si-atom jumping D(t,Si) OSi-defect D(t,Si) Are Defects and Jumps Correlated? SiSi-defect

17 Defect-Jump Correlation D(t,O) =25 K OO-defect D(t,O) =25 K SiO-defect J(t) O-atom jumping J(t) Si-atom jumping D(t,Si) OSi-defect A DJ α,β = Nα D(t,Si) SiSi-defect Nα χ D i (t,β)χj i (t) Nα χ Nα D i (t,β) Nα i= i= Nα χ Nα D i (t,β) Nα χ Nα J i (t) i= i= Nα χ J i (t) i=

18 Defect-Jump Correlation A DJ α,β = Nα Nα χ D Nα i (t,β)χj i (t) χ D Nα i (t,β) i= i= Nα χ Nα D Nα i (t,β) χ Nα J i (t) i= i= Nα = Nα χ D i (t,β)χj i M (t) D αβ M J α i= Mαβ D M α J Nα Nα i= χ J i (t) A DJ αβ 5 αβ= SiSi SiO OSi OO strong correlation between defects and jumps correlation is decreasing with increasing temperature [K]

19 Summary Simulations of SiO 2 -Glass Extract Information: time averaged positions χ D i (t, β), χj i (t) Defects: well defined (g αβ (r) & P αβ (z)) strong temperature dependence of C DD α,β (t) τα,β DD: SiO- & OSi-defects short lived and OO-defects long lived τ DD α,β decreasing with increasing temperature Jump-Defect Correlation: strongly correlated decreases with increasing temperature A DJ α,β Acknowledgments: Supported by DFG via SFB 62 & FOR394.

Microscopic Picture of Aging in SiO 2 : A Computer Simulation

Microscopic Picture of Aging in SiO 2 : A Computer Simulation Katharina Vollmayr-Lee, Robin Bjorkquist, Landon M. Chambers Bucknell University & Göttingen 7 td tb r n (t) 6 R 5 4 3 2 ti t [ns] waiting