CH5716 Processing of Materials

Ceramic Thick Film Processing

Lecture MC5 – Slurry Characterisation Specific Surface Area •Powder size & specific surface area (area per unit wt) closely related •As particle size decreases so SSA increases •At very small sizes surface area becomes dominant due to ratio of surface to volume •Very fine particles may lead to enhanced sintering •However high surface area also has implications in green stage processing.

Effects on Green stage Processing Therefore Specific Surface of High Surface Area Powders Area is an important parameter to know •Tendency to floc; large surface area to volume (mass) ratio, electrostatics, Van •Some would argue the most der Waals etc become more dominant. important

•Difficult to disperse – more dispersant •Most often measured by nitrogen required to coat higher surfaces absorption using BET method

•Interaction with solvents and binders can •5-15m2/g common for tape casting- increase slurry viscosities resulting in up to 36m2/g has been used for lower solids loadings screen printing

Particle Size and Size Distribution

•Particle Size often quoted as a D50 •Not really helpful as powders with same D50 can have very different distributions

•Better to quote D10 & D90 values as well •Gives some idea as to distribution •Often quoted more than SSA, however SSA more influential- especially in irregular particles •Narrow distribution will lead to good even densification •Wide distribution may result in a tendency to coarsen – larger particles seed grain growth Laser Scattering has become dominant technique replacing sedimentation Accuracy Speed Small sample size Automation possible Care must be taken in sampling, especially in large batches Interpretation of results also requires care Augmenting early results with SEM data useful

Laser Scattering Particle Size Analysis

Basic light scattering Mie Theory involves complex solution of Maxwell Eqns Relationship between scattering angle θ and d is More accurate for sub micron particles Sinθ = 1.22λ/d (small particles scatter more) Used in most of the commercial software Limited by λ (eg He-Ne laser λ = 0.63µm) Requires both Real & Imag. Refractive Indices Only truly accurate at 2-100+µm Some approximation required for new materials Inaccuracies creep in at sub micron levels Over-estimation of fine fraction

Assessing Dispersion

Generally we assume our 24 hours has done the trick – established formulation However new powder or formulation may change things 2 possible methods to check - sedimentation and sizing Sedimentation also useful for optimising dispersant level – Discussed later

Sedimentation Method

•Best applied as an initial technique on new slurry to ensure all is OK •Not really in line QA test

•Take 10ml sample from mill at set intervals over a Agglomerates present - low packing density predetermined time •These samples should be but into 10ml graduated cylinders and allowed to settle •May take several days •Once settled note height of sediment and clarity of supernatant •A t full dispersion sediment height will reach a minimum.

Well dispersed – high sediment density Assessing Dispersion with PSA

Particle Size Distribution •Utilise internal ultrasound capabilities in PSA 8 7 -Malvern Mastersizer 2000 6 5 •This is designed to deagglomerate powders 4

when characterising raw materials before 3 Volume (%)Volume processing. 2 1 •Initial sizing is measured straight from bottle 0 0.01 0.1 1 10 100 1000 3000 after milling. (only a few drops required) Particle Size (µm) AQ YSZ tape 1-test 2, 06 October 2010 12:00:34 •Ultrasound is then applied to specimen for around 5 minutes. Run 1; as milled d10 = 0.12, d50=0.318, d90=1.101

Particle Size Distribution •Second sizing measured from sample- If this 8 result is comparable to initial measurement 7 then deagglomeration appears complete. If a 6 size reduction is observed further milling 5 required. 4 3 (%)Volume 2 •Fast technique, can be used as in-line QA. 1 •Care must be taken to avoid sampling errors. 0 0.01 0.1 1 10 100 1000 3000 •Alternate method would be to take 2 Particle Size (µm) AQ YSZ tape 1-test 2, 06 October 2010 12:08:14 measurements across a set time interval

Run 2; after 5 min US d10 = 0.12, d50=0.315, d90=1.073

Optimising Dispersant Level

•Similar methodology to previously discussed experiment •This time powder is milled for 24 hrs with each dispersant level •Settling as before over a few days •Once fully coated minimum height is reached •Too much dispersant can often be seen Height Sediment by discolouration of supernatant fluid 0 0.5 1 1.5 2 2.5 Wt % Dispersant Other approaches PSA Observation •Taking sizing reading at each dispersant level •As dispersion improves agglomerate peak should reduce while primary peak increases

Viscosity •As dispersion increases minimum viscosity should be observed. •Measurement of batches with varying dispersant levels •Repeated assessment of viscosity as dispersant level is increased •Can have issues in non –Newtonian systems Rheology of Slurries and Pastes Newtonian Flow

A V x

Consider a fluid with parallel planes with area A A force is applied to the top plane while the bottom plane remains stationary The force results in the top plane moving with velocity V

This creates a velocity gradient across the thickness of the fluid , x Stress Shear

Velocity gradient = dV/dx = shear rate, γ, s-1 (ms-1/m)

Shear stress, τ = F/A (Newton/m2 = Pascal (Pa))

Shear rate For a Newtonian fluid τ is proportional to γ τ = η γ where η is a constant, the co-efficient of viscosity in Pa.s So η= τ / γ and will be a straight line through the origin when plotted

on a graph of shear stress against shear rate. Viscosity

Although Pa.s is the SI unit poise or centipoise often used in industry 1Pa.s = 10poise 1mPa.s= 1 centipoise

Shear rate Non-Newtonian Flows

Unfortunately slurries, slips and pastes do not behave in a Newtonian fashion Polymer chains, particles, agglomerates and their interactions all get in the way

Families of non-Newtonian Flow Described as Power Law fluids as Pseudoplastic behaviour defined by n Dilatant τ= K(γ) Where K is a consistancy index (Pa.sn) Thixotropic And n is a dimensionless flow behaviour index Rheopectic n<1 = pseudoplastic Bingham body n=1 Newtonian n>1 =dilatent Pseudoplastic Flow •Shear Thinning •Viscosity drops with increasing shear rate •Often due to interactions in constituents in complex fluids •May trend towards Newtonian behaviour as shear rate increases •No single figure for viscosity

•Apparent viscosity (ηapp) is used, this is the viscosity at a specific

shear rate and must be quoted with that shear rate.

Shear Stress Shear B

A Shear rate For apparent viscosity at shear rate A , get associated value for shear stress and calculate viscosity at that point in the curve.

ηapp = τ / γ (Pa.s) Dilatant Flow

•Shear thickening behaviour •Mostly observed in slurries with high solids loadings •Especially where the level of the fluid approaches that where there is just enough to fill all the gaps between the particles when the slurry is at rest •Rearrangement of particles within the slurry into less closely packed arrangements when the shear is applied. •This increases the volume of space between the particles •Results in there not being enough fluid in the system to allow for flow of the particles past one another. •This leads to increased particle interactions and so the viscosity is seen to

rise.

Shear Stress Shear

Shear rate Thixotropic Flow •Closely related to pseudoplastic flow •Fluids will often display both •Both are shear thinning •Defining factor with thixotropy is that it is time dependent •Viscosity drops with time at a constant shear rate •Generally will trend to a steady value as system equilibrates •Can also be seem as a hysteresis on shear stress-shear rate curve •Larger hysteresis more thixotopy •Particle crowding and polymer chain interaction can lead to thixotropy Increase in shear rate •As shear is applied it takes time for particles to begin to move uniformly throughout the

slurry App Viscosity App •Similarly polymer chains can induce thixotropy as they take time to align to the flow •Breakdown in structure between binder and particles Time •Platelets can also show this form •Flocculated systems can exhibit thixotropy. of flow behaviour. •Flocs contain interstitial spaces which can trap solvent •At rest platelets are randomly •As shear is applied flocs break apart releasing solvent so orientated dropping viscosity •As shear is applied they will with •System will reach steady state . time become aligned to the flow •If shear is increased further more strongly bonded flocs may then •They will then slip past one disperse another with lower resistance •This again will show another drop

Yield

•Yield is the minimum applied shear before flow will take place

•If the post yield flow is Newtonian fluid behaviour is termed a

Bingham body τ = τy + ηγ n •Non-Newtonian τ = τy + K(γ) (Herschel-Bulkley Model)

•Yield stress is determined by extrapolation of the curve back to 0s-1 Shear Stress (Pa) Stress Shear •By plotting √τ against √γ should give a straight line ½ ½ ½ Yield •Casson Model τ = τy + K(γ) •Only an approximation, •Not all pseudoplastic materials will follow -more so at low shear rates Shear Rate (s-1)

•Caused by interactions between slurry constituents •Binder –Particle •Formation of longer range structure in the •Surface adsorption slurry body •Binder- Binder •Can form Gel type structures •Polymer chain length •Often accompanied with thixotropic •Polymer chain geometry (bulky side behaviour groups) •Takes time for structures to break down then •Binder –Solvent reform •How well has chain dissolved •Chain mobility in solvent (bond rotation)

Viscosity Measurement

Most common method by rotational viscometer (Brookfield) Viscosity is measured as a resistance to the rotation (Torque) Cup & Bob and Cone & Plate are 2 common variations

ω

θ<4° c

r

Cone and plate better for trying to gain more absolute and uniform values of shear stress and rate. Shear rate is related to rotational speed and gap width at any point on r. Shear stress = T/⅔πr3 shear rate= ω/sinθ Cup & bob good for fast drying slips due to small area for evaporation. Cone & plate best suited to slow drying pastes and inks Calculation does not take into account effect of viscosity gradient under bob. Important Considerations in Viscosity Measurement

•Temperature Control – Pastes and slurries very sensitive to temperature, use of system with controlled temperature water bath recommended

•History of sample any shear applied to sample will affect measured result, especially if it is thixortopic,

•Minimise disturbance, follow set procedure with controlled delays

•Be aware of effects of solvent evaporation in volatile specimens, may affect viscosity over time (also skin formation)

Other characterisations to Consider

•Weight loss and shrinkage on drying

•Mechanical tests – green strength, flex, tear resistance, surface roughness

•Burn out characteristics – TGA, Dilatometry •Firing shrinkages •Important if making multilayer devices as these must be matched carefully.