Nano-indentation of silica and silicate glasses. Russell J. Hand & Damir Tadjiev Department of Engineering Materials University of Sheffield

Transcription

1 Nano-indentation of silica and silicate glasses Russell J. Hand & Damir Tadjiev Department of Engineering Materials University of Sheffield

2 Acknowledgements Pierre Samson Dr Simon Hayes Dawn Bussey EPSRC Organisers of FFAG4

3 Outline Water and silicate glasses Some thoughts on defect formation Nano-indentation of pure silica & other silicates Trying to assess the effects of the hydration layer Conclusions

4 Background Silicate glasses interact with (atmospheric) water Presence of a hydrated layer on glass surfaces Also H 3 O + ion exchange with mobile alkali ions

5 Alkali concentration Alkali concentration in bulk glass.. Gel-layer Gel-glass interface Glass containing hydrogen ions Dry glass containing alkali ions Distance

6 Effects of glass structure? Figure 3 Si O Na Si O Na CRN versus MRN

7 H Si O Na Hand & Seddon Griffith flaw in an MRN glass H 3 O + ion exchanges with Na + in alkali channels Surface region of channels is hydrogen bonded Therefore less strongly bonded Surface gel layer not shown for clarity

8 NBOs may provide sites where cracks can develop Postulate that strained bonds in pure silica provide preferential locations for water attack Small membered rings might provide sites for flaw development

9 Nano-indentation Provides insight into surface mechanical properties Instrumented indentation technique Record load/displacement curves (Un)loading curve can be used to measure modulus Maximum load can be used to measure hardness Need to know the area of the indentation as a function of depth In conventional indentation this is measured directly Not practical in nano-indentation

10 Experimental nano-indentation Hysitron nano-indenter with diamond Berkovich indenter Automated array of indents at increasing load 5 s upload, 5 s hold, 5 s unload data points per run 2 different Berkovich tips used in the work discussed here

11 Vicker s indentation 68º Pyramid shaped indenter Surface area of indentation Berkovich indenter Ideal Berkovich indenter has the same variation of area with depth as a Vicker s indenter Standard Berkovich same actual area Modified Berkovich same projected area H V =.4635P 2 a H = P A 2a 65.3º

12 Ideal Berkovich A = 25.4h 2 For analysis purposes normally treat Berkovich indenter as being equivalent to a conical indenter Cone angle = 7.3 Real indenters are not ideal

13 Tip area function Nano-indentation depends on knowing how the area varies with penetration depth Tip area function (TAF) Calibration involves indenting a material the modulus of which does not vary with depth Commonly used standard to determine the TAF is fused silica Presence of gel layer?

14 Oliver and Pharr approach for TAF Most commonly used approach Only unloading curve is purely elastic Oliver and Pharr Fit unloading curve with P = α h ( ) m h f Differentiate to obtain initial slope of the unloading curve d P S = = mα h h f d h ( ) m Load /µ N Indentation depth /nm

15 Contact depth is given by h c = h max. 75 P max S 2 Load /µ N h c h max Indentation depth /nm P max Accounts for deformation of surface around in indenter (taken to be a paraboloid of revolution) Reduced modulus is given by E π S π = = r 2β A 2. S A

16 2 ν s ν = + E E E Diamond ν i =.7, E = 4 GPa Fused silica ν s =.7, E = 72 GPa E r =69.6 GPa Value used in TAF calibration For a known reduced modulus r A = s π S 4 β E r 2 i 2 i

17 Tip area function Oliver and Pharr recommend the empirical function A = a 2 / 2 / 4 /8 /6 /32 / 64 /28 hc + ahc + a2hc + a3hc + a4hc + a5hc + a6hc + a7hc + a8 Implies infinite curvature at h c = Approach used here is to fit a 2 nd order polynomial Previous work has shown that this can give a good fit BUT may have to use different polynomials to fit the entire range of data In this case need to ensure continuity in both A and da/dh c

18 Tip.2e+6.e+6 Area /(nm) 2 8.e+5 6.e+5 4.e+5 2.e C o n t a c t d e p t h / n m In this case one polynomial used A 2 = 22.89h c hc Conical indenter Paraboloid of revolution Flat

19 Tip 2 4x 3 2x 3 Area /nm 2 x 3 8x 3 6x 3 4x 3 2x h c /nm A = A = 29.h 6.623h 2 c 2 c h 24h c c h h c c <

20 Comparison of tips.4 Tip Tip 2 (Er 69.6)/ h c /nm

21 Relative stiffnesses Quality of fit similar for both tips BUT Fits have assumed that there is no hydration layer with a lower modulus Alternative approach is to compare stiffnesses A A S = 2 β Er = 2. Er π π Hence S S 2 = E E r r 2 A A For a given value of h c A = A 2 thus 2 S = S 2 E E r r 2

22 35 3 Stiffness /µ N nm Stiffness /µ N nm h c /nm. h c /nm Non-zero intercept reflects imperfect nature of tip Fitting stiffness does not require constant modulus with depth

23 Elastic indents Load /µ N Load /µ N Load Unload Indentation depth /nm Load Unload Indentation depth /nm Shallowest indents are wholly elastic Load & unload curves overlay each other But this means we can undertake an elastic analysis of the upload curves

24 Elastic analysis of upload curves Use a power law fit for the upload curve As before differentiate to obtain the stiffness at all points on the (elastic) upload curve S = d P d h m Even though deformation is elastic the contact depth, h c, is less than the indentation depth, h. = mα h P = α h m h h c

25 As before h c = h. 75 i.e. this is an Oliver and Pharr type analysis applied to the full upload curve Can use this approach to obtain stiffness values at low indentation loads P S

26 8 Download analysis Upload (elastic) analysis Stiffness /µ N nm Stiffness /µ N nm Download analysis Upload (elastic) analysis hc /nm hc /nm Download analysis Upload analysis 3 Stiffness /µ N nm 3 Stiffness /µ N nm hc /nm Download analysis Upload analysis hc /nm

27 Coatings Treat gel layer as a coating layer E g < E s Perriott & Barthel Treat as bilayer system t * E * E * E eq Equivalent homogeneous half-space

28 Empirically fitted equations to their FE results are ( ) n eq a tx E E E E + + = * * * * 2 * * * * log log.93 log + + = E E E E x

29 Limiting stiffness /µ N nm E * = GPa E * = 2 GPa E * = 5 GPa E * = GPa E * = 2 GPa E * = 5 GPa E * = E * Coating thickness /nm Limiting stiffness value is due to imperfect tip Calculations based on TAF for tip 2

30 Other silicate glasses Soda-silica 33.3Na 2 O-66.7SiO 2 Potassia-silica 33.3K 2 O-66.7SiO 2 Potassia-soda-silica 66.7SiO 2-25K 2 O-8.3Na 2 O Soda-lime-silica 5Na 2 O-5CaO-7SiO 2 Soda-lime-silica 2 25Na 2 O-8.3CaO-66.7SiO 2

31 Sample preparation All glasses melted at 45ºC in Pt h to batch free 4 h stirred Cast into bars Annealed for h at 56 or 59ºC depending on composition 5 sections Ground and polished to.25 μm Re-annealed for h

32 3 Stiffness /µ N nm SS as prepared SS 5 min in water SS 4 min in water SS 7 min in water h c /nm Significant changes in stiffness with immersion At longer immersion times surface quality deteriorated

33 Stiffness /µ N nm SLS as prepared SLS 9 h in water h c /nm Soda-lime-silica 5Na 2 O-5CaO-7SiO 2 Durable composition Little if any change in stiffness after 9 hours in water

34 Stiffness /µ N nm SLS2 as prepared SLS2 3 d in water h c /nm Soda-lime-silica 2 25Na 2 O-8.3CaO-66.7SiO 2 Non-durable composition Significant change in stiffness after 3 d in water

35 3 Stiffness /µ N nm h c /nm SS 5 min in water SS 4 min in water SS 7 min in water SLS 9 h in water SLS2 3d in water PS "as prepared" PS data poor due to very rapid hydration of surface

36 8 SLS2 as prepared SLS2 3 d in water Modulus /GPa h c /nm Data from as prepared sample relatively poor BUT significant change in modulus nonetheless

37 E * eq = E * + ( * * E E ) + tx a n log * x = log +.5 log * E E E E * * 2 In Perriott and Barthel model use E * = Vary t to get limiting stiffness value to match 2 GPa Still have problem as analysis is based on contact radius a Have to base this on existing tip calibration

38 Tip Stiffness /µn nm Unloading data Loading (elastic) data Calc. assuming no gel layer Calc. using 6 nm gel layer. h c /nm

39 Stiffness /µ N nm Unloading data Loading (elastic) data Calc. assuming no gel layer Calc. using 6 nm gel layer. h c /nm

40 Unloading data Elastic (loading) data Calc. no gel layer Calc. with nm gel layer Tip 2 8 Stiffness /µn nm hc /nm

41 Unloading data Elastic (loading) data Calc. no gel layer Calc. with nm gel layer Stiffness /µ N nm hc /nm

42 Can fit simple two layer model to data Measurements suggest that the hydration layer does affect the results BUT Really need an independent measurement of TAF on a material whose surface really is identical with the bulk!

43 Bec et al Also used a bilayer system in series This model can be generalised to multiple layers Therefore allow properties to vary with depth i.e. can recognise that the actual hydrated layer varies with depth Simplest assumption is a linear variation of layer properties with depth t = k + 2 * ( 2t / πa) πa g E g t = k + * ( 2t / πa) 2 s ae s

44 Unloading data Elastic (loading) data Calc. with nm uniform layer Calc. with nm varying layer 8 Stiffness /µn nm hc /nm Suggests, perhaps, a slightly thinner layer would be more appropriate

45 Hardness 2 8 Hardness /GPa SS PSS SLS SLS2 Silica Hardness /GPa SS 5 min in water SS 4 min in water SS 7 min in water SLS 9 h in water SLS2 3 d in water h c /nm h c /nm Even though some low depth indents are elastic can still calculate P/A for all indents Cannot truly be described as hardness as no permanent deformation

46 Conclusions MRN Possibility of defect formation due to water ion exchanging into near surface alkali channels Can observe changes in modulus due to hydration layers on relatively non-durable glasses Some evidence that this affects calibration using silica Simple bilayer model may give some insight Really need a calibration material with an inert surface Intending to try melt spun gold equipment failure Hardness values drop-off at low indentation depths