Surface Roughness - Standards and Uncertainty R. Krüger-Sehm and L. Koenders Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
Surfaces Generation - Grinding - Honing - Lapping Characterisation - Measurement - Visualisation - Quantification Function -Gloss - Paintability - Wear
Diamond turned Al surface different scales Nomarski picture 3D picture of the AFM data obtained near the centre Picture showing the grooves and some contamination
Diagram Wavelength vs. Amplitude - Instruments 100 µm 10 µm SEM Confocal microscope Amplitude 1 µm Light scattering (vis) 100 nm 10 nm SPM Interference microscope Stylus instrument 1 nm 100 pm 10 nm 100 nm 1 µm 10 µm 100 µm 1 mm 10 mm Wavelength
Instruments, Specimens and Procedures Surface Measurement Standards Guidelines Specification Calibration Evaluation Verification Standards Surface Measurement Instruments
Standards for Roughness Measurement ISO 14 638 Geometrical product specifications(gps) matrix model ISO 5436-1 Standard specimen ISO 5436- Software standards ISO 487 Definition of surface-parameters ISO 488 Surface properties stylus instruments rules and conditions ISO 1156 Characteristics of Gauß filter ISO 491 Characteristics of RC filter ISO 374 Stylus instruments definitions ISO 1179 Calibration of stylus instruments ISO 13565-1 ISO 13565- EN 10049 Filter-definition for Rk parameters Definition of Rk parameters Measurement of Ra and RPc on metallic flat products with stochastic surface texture (skidded stylus) EAL-G-0 Calibration of stylus instruments for measuring surface roughness
Diagram Wavelength vs Amplitude - Standards
Dissemination of Units by Calibration Standards Pt, D Measurement standards ISO type A Ra, Rz, Rsm,... Ra, Rz, Rq,... Traceable Interference Microscope PTB C D1, D Guidelines to support traceability established e.g. EAL G0, ISO1179 draft in VDIcommittee Stylus Instrument PTB PTB Industry Interference Microscope Stylus Instrument
Contact Stylus Instrument (ISO 374), Specifications Alternative setup ze(x) stylus tip transducer traced profile feed unit z y x settings parameters profile topography z0(x) instrument reference profile l s- Filter l c- Filter amplifier A/Dconv. parameter zg(x) zs(x) zc(x) Feature usual typical usual Lateral measuring range 0 mm 50...10 mm 300 mm Vertical measuring range 0.3 µm 60 µm 1mm Vertical resolution 16 bit Straightness deviation @ 50 mm (Wt 0 ) 0 nm 50 nm 100 nm Noise amplitude @ λc = 0,8 mm (Rz 0 ) 1 nm 0 nm 30 nm Tip radius 0.1 µm... 5 µm 5 µm
Special Remarks ISO 374: The primary profile contains the influence from the stylus. Further calculations do not describe the real surface, but a morphological changed one. ISO 488: The waviness cutoff-wavelength depends on the surface specifications. In roundness and straightness measurement the separation wavelength is fixed to 0,8 mm(rsp equivalent wave numbers). This must be observed in case of calculating the influence of the measured roughness in form measurement. ISO 374: Applicable for stylus instruments with datum (plane). ISO 1179 allows secondary measuring systems. Practical result: standardisation of metal sheet measurement with skidded stylus systems in SEP 1940, rsp. pren 10049.
Measurement Conditions Periodic profiles RSm in mm Stochastic profiles Ra in µm Stochastic profiles Rz in µm Sampling length l r in mm evaluation length l n in mm Cutoff λ c in mm short wavelength λ s in µm Bandwidth B max. tip radius r tip in μm max. sampl interval in µm >0.013..0.04 >(0.006).0.0 >(0.05)..0.1 0.08 0.4 0.08.5 30 0.5 >0.04..0.13 >0.0..0.1 >0.1..0.5 0.5 1.5 0.5.5 100 0.5 >0.13..0.4 >0.1.. >0.5..10 0.8 4 0.8.5 300 (5) 0.5 >0.4..1.3 >..10 >10..50.5 1.5.5 8 300 5 1.5 >1.3..4 >10..80 >50..00 8 40 8 5 300 10 5 Excerpt of Standards: ISO 374 (1996) ISO 487 (1997) ISO 488 (1996) ISO 1156 (1996)
Calibration of Devices Aim, result Sample/Standard To do Noise of instrument Flat glass Determination of Rz 0, Ra 0,... Straightness deviation of the Flat glass Determination of Wt 0 datum Control/correction of vertical Certified depth setting Determination of Pt n, D n for axis/amplification standard position c ; Repeatability of probing Certified depth setting standard comparison with certified value n repetitions of Pt at the same position Quality management: Calibration have to be done periodically and have to be documented!
Depth Setting Standards (1) Depth measurement standards Type A according to ISO 5436-1 Nominal values of grooves from 0 nm to 10 µm Lateral width from µm to 100 µm Roughness on measurement areas down to 1 nm Uncertainty (k=) between 3 nm and 5 nm 1 5 6 Pt depth of profile D groove depth 3 4 roughness depth roughness width
Depth Setting Standards () Substrate: Ø ~ 50 mm, 10 mm thick Ni-P on Ni, Hardness ~ 580 HV Grooves ~ 0.4 µm to 75 µm Width at groove ground 100 µm to 00 µm
Depth Setting Standards (3) Depth measurement standards Type A1 according to ISO 5436-1 Nominal values of grooves between 1 µm and 5 mm Lateral sizes between 100 µm and 1mm Roughness on measurement areas about Rz = 0 nm Traceability to length unit by stylus instrument traced back by gauge block, traced back by interferometric calibration Uncertainty (k=) between 5 nm and 60 nm
Lateral calibration standard Design For λc/mm 8,5 0,8 0,5 0,08 Image: Dark field 0 µm (x) Feature Typical value Geometric (type C) Depth(Rz1max) 1,..., 10 µm Period lateral (RSm) 80,..., 50 µm λc 50 µm; 0.8 mm;.5 mm Lateral standard (type C) Depth 5 µm Period lateral (RSm) 5, 100, 50, 1000, 500 µm for λc 80, 50, 800, 500, 8000 µm 50 µm 50 µm 4x 4x 4x Measurement scheme start on reference plane
Roughness Standard Specimen
Geometrical Calibration Standard (Type C) Feature Typical value Geometric (type C) Depth(Rz1max) 1,...,10 µm Period lateral (RSm) 80,..., 50 µm λc 50 µm; 0,8 mm;.5 mm Profil of geometrical standard
Roughness Calibration Standards, Specifications Feature typical Rz 1... 0 µm Ra 0.16... 3 µm λc 0.8 mm;.5 mm Profile repetition 4 mm
Roughness - Standards, Measurement Schemes Meßstellenplan für PTB-Rauhnormale (g, m, f), λc = 0,8 mm Startpunkte der Meßstrecken in mm von Startlinie Rauhnormal starting points of the evaluation lengths in mm from the starting line Maßstab 5:1 scale 5:1 3.0 μm.0 1.0 PTB Mess- richtung 0.55 4.6 8.65 1.7 0.3 4.35 8.4 1.5 0 4.1 8.15 1. 3 mm 3 mm Mittellinie symmetry line 0.0-1.0 Startlinie starting line Mess- -.0 Meßstellenplan für PTB-Rauhnormale (gg), λc=,5 mm Startpunkte der Meßstrecken in mm von Startlinie -3.0 starting points of the evaluation lengths in mm from the starting line 0.0 1.0.0 3.0 4.0 mm 5.0 Maßstab 5:1 scale 5:1 Same scale (1,5 mm) PTB richtung 0,0 mm (11x) 0,50 mm (11x) Mittellinie symmetry line Startlinie starting line
Super fine roughness standards Roughness measurement standard Type D according to ISO 5436-1 Nominal values of Rz = {150, 300, 450} nm, expressed in Ra between Ra = 5 nm and 80 nm Manufacturing by single diamond turning of digital generated profile amplitude and shape of profile predictable profile repetition length 1,5 mm, For λc = 0,5 mm Calibration with contact stylus instrument, traced back by depth measurement standard Uncertainty of calibration (k=) ~ 6 % and 8 %, Approved in Round Robin of 11 DKD-laboratories Useable for calibration of interference microscopes, for calibration and verification
Nano-Roughness-Standards & Specifications - Scan range < 100 µm => λc - x-y Scans => use of pictures - Tip shape => λs - data points < 4000 => λs -1-dim Profil - Profile Repetition 5*40 µm - Measuring length 40 µm for 5 nm < Ra < 0 nm
Roughness measurement Calibration Verification Aim, result Used standard To Do Noise of device Flat glass Determination of Rz 0, Ra 0,... Control or correction of the vertical axis/amplification Certified depth setting standard Determination of Pt n, D n for position c, Comparison with certified value Selection of waviness filter Determination of roughness Estimation of measurement uncertainty Roughness standard to be calibrated Roughness standard to be calibrated Determination of Ra, Rz with λc=0,8 mm Using ISO 888 (DIN 4768) to select λc Measurement plan; determination of roughness parameters and standard deviation Calculation following the rules of GUM and related guides
Model of Uncertainty of Roughness Parameter uncertainty of parameter value u(k) Parameter calculation P uncertainty of roughness profil K = P λc-filter function Fc uncertainty of primary profil {Fc λs-filter function Fs uncertainty of total profil Instrument function G Surface profile [Fs (G (z e (x)) ]}
Instrument-Function of Stylus Instrument ze(x) stylus tip transducer traced profile feed unit z y x settings parameters profile topography z0(x) instrument reference profile l s- Filter l c- Filter amplifier A/Dconv. parameter zg(x) zs(x) zc(x) z g (x) = C [z e (x) + z ref (x) + z 0 (x) + z pl (x)+z sp (x)] where C Calibration factor z 0 Noise of instrument z e Contacted profile z pl Plastic deformation of surface z g Total profile z sp Profile deviation by tip radius dev z ref Profile of reference plane
Uncertainty Budget (1) Model for stylus instruments z g (x) = C [z e (x) + z ref (x) + z 0 (x) + z pl (x)+z sp (x)] = C z u (x) where C Calibration factor z u uncalibrated profile Using the product rule u (z g ) = u (C) z u + C u (z u ) with with C = Pt m /Pt n C = D m /D n where where Pt m value measured D m value measured Pt n value certified D n value certified
Evaluation of Depth Setting Standards 1 5 6 1 5 6 Pt depth of profile D groove depth 3 4 roughness depth roughness Pt depth of profile D groove depth fitting parabola 3 4 roughness depth roughness width width Evaluation of type A1 and type A depth setting standard, influence of roughness A A1: Reference line @ levelling 1 A: Reference line @ levelling A:Levelling deviation Pt1: Pt @ levelling 1 Pt: Pt @ levelling Influence of levelling
Uncertainty Budget () Using the product rule u (z g ) = u (C) z u(x) + C u (z u ) with C = Pt m /Pt n where Pt m value measured Pt n value certified Each value is uncertain u (Pt m ), u (Pt n ) u (C) = 1/Pt 4 m [Pt n u (Pt m ) + Pt m u (Pt n )] With a calibrated instruments Pt n Pt m (C ~ 1) u (C) = 1/Pt m [u (Pt m ) + u (Pt n )] u (C) z u = 1/Pt m [u (Pt m ) + u (Pt n )] If the depth of the standard is close to the value of the sample to be measured z u /Pt Model for this value m ~ 1 u (C) z u = u (Pt m ) + u Calibration certificate (Pt n ) u (z g ) = u (Pt m ) + u (Pt n ) + u (z u )
Uncertainty Budget (3) Model for Pt Track n Track m Pt m is not measured at the same position as the groove is calibrated. - value of the standard at right track - gradient of the standard Pt/ y - repeatability of the instrument b Pt m = Pt n + Pt + b u (Pt m ) = u (Pt n )+ u ( Pt) + u (b ) 1 U n 4 1 3 ( a ) y G s ( Pt n )
Uncertainty Budget (4) Effect of λs Measured profile has uncorrelated points. Due to filtering the points are correlated! The effect of filtering can be expressed by a factor f s [Krystek] u(z f ) = f s u(z unf ) f s = Δx/(α λ s ) where α = log()/π Table for factor f s λ s in µm Δx in µm f s.5 0.5 0.55 8 1.5 0.53 8 0.5 0.31 Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 001 Meas. Sci. Technol. 1 63
Uncertainty Budget (5) Effect of λc Similar to λs. The effect of filtering can be expressed by a factor f s [Krystek] u(w) = f c u(z s ) f c = Δx/(α λ c ) Where α = log()/π However, λc is much more larger than Δx since the uncertainty of the filtered is nearly similar to those of the unfiltered. Table for factor f c λ c in µm Δx in µm f c 50 0.5 0.055 800 0.5 0.031 500 1.5 0.017 z c = z s w u (z c ) = u (z s ) + u (w) u (z c ) = u (z s ) + f c u(z s ) Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 001 Meas. Sci. Technol. 1 63
Uncertainty Budget (6) Effect of parameter function K The uncertainty of the parameter K depends on the algorithm. By the algorithm for K the uncertainty may be different to those of the single point. It is described as a smoothing factor S since the uncertainty is reduced in most cases. Example: u sys (Rz) = S(Rz) * u(z g ) Here S(Rz) is the smoothing factor! using
Uncertainty Budget (7) z u (x) = z e (x) + z ref (x) + z 0 (x) + z pl (x)+z sp (x) u (z u ) = u (z e ) + u (z ref ) + u (z 0 ) + u (z pl ) + u (z sp ) where u (z e ) u (z ref ) u (z 0 ) u (z pl ) u (z sp ) uncertainty of probed profile uncertainty of reference profile uncertainty due to noise of 1 s ( Rz) S n Wt 0 1 1 1 Rz 0 S 1 instrument ( ) uncertainty due to plastic deformation uncertainty due to unknown tip shape 1 3 1 S a pl 3 0nm u( r μm ) sp S is smoothing factor of parameter
Uncertainty of Points of Profile (1) Example for a roughness standard of type D with Rz 3 µm Ch. Input quantity keyword Determined by Typical value Sensitivitycoeff. Method, distribution 3.1 Reference 1 U U n = 15 nm 1 B standard n 4 (Cal. Gauss certificate) 3. Deviation in 1 a ( a ) localisation y G y = 100 µm G B 3 G = 0 Rect. nm/mm 3.3 Repeatability s ( Pt n ) s = 3 nm 1 B Gauss 3.4 Topography 1 s ( Rz) s(rz) = 50 1 A S n nm Gauss Variance /nm 56 1,3 9 51 Chapters are given in relationship to DKD 4-
Uncertainty of Points of Profile () Ch. Input quantity keyword 3.5 Straightness datum 3.6 Residual Determined by Typical value Sensitivity -coeff. Method, distribution Wt Wt 0 0 = 50 nm 1 B 1 Rect. 1 1 Rz Rz 0 = 0 nm 1 A 0 S 1 Rect. a a pl pl = 5 nm 1 B 3 Rect. 1 1 0nm u(r sp ) = -0 nm/mm B u( r ) sp 0,5 µm Rect. 3 S μm noise ( ) 3.7 Plastic deform. 3.8 Stylus tip Variance /nm 0 83 8,3 83 Point Sum of variances u ( z g ) 761,6 variance Point u ( z g ) 8 nm Chapters are given in relationship to DKD 4-
Uncertainty of Points of Profile (3) Example for a roughness standard of type D with Rz 3 µm Using ls filtering! Ch. Input quantity keyword Determined by Typical value Sensitivitycoeff. Method, distribution 3.1 Reference 1 U U n = 15 nm 1 B standard n 4 (Cal. Gauss certificate) 3. Deviation in 1 a ( a G) localisation y y = 100 µm G B 3 G = 0 Rect. nm/mm 3.3 Repeatability s ( Pt n ) s = 3 nm 1 B Gauss 3.4 Topography 1 s ( Rz) s(rz) = 50 1 A fs nm Gauss S n Variance /nm 56 1,3 9 130 Chapters are given in relationship to DKD 4-
Uncertainty of Points of Profile (4) Using ls filtering! Ch. Input Determined by Typical Sensitivity Method, Variance quantity value -coeff. distribution /nm 3.5 Straightness s Wt 0 Wt 0 = 50 1 B 0 f 1 nm Rect. datum 3.6 Residual 1 1 ( Rz ) noise 0 f Rz = 0 nm 1 A 5 0 s S 1 Rect. 3.7 Plastic a a pl = 5 nm 1 B.5 pl deform. fs Rect. 3 3.8 Stylus tip 1 1 0nm u(r sp ) = -0 nm/mm B.5 u( r ) 3 sp f s S μm 0,5 µm Rect. Point Sum of variances u ( z s ) 6,3 variance Point u ( z s ) 15 nm uncert. u sys (Rz) = S u (z s ) = (10/5)* u (z s ) Chapters are given in relationship to DKD 4- u sys (Rz) = 0.6* u (z s ) ~ 9 nm
Uncertainty of Parameter Since S is smaller than 1 U(Rz) can be approximated with the coverage factor of k = by U ( Rz) [ 1 4 + U n s ( Rz) n Rz 1 0 + + (Rz)] 1 Abbreviation Uncertainty Source Determined by calibration factor from calibration certificate u v 1 U n 4 s ( Rz) n statistic on surface standard deviation of Rz, n preferred 1 1 u v Rz noise flat glass roughness measurement, 1 0 by rectangular probability distribution (Rz)] 1 unknown systematic errors comparison Comment: Approximation of starting model of uncertainty, containing the most important sources or those, which are subject to change
Comparison of Roughness Parameters in DKD - Round Robin Parameters with lamba-s Parameters without lamba-s lamba-c type in mm Ra Rz1max Rz Ra Rz1max Rz Geometrical coarse,5 0, 0,3 0, 0,5 0,3 0,3 standard coarse 0,8 0, 0,3 0,4 0,4 0,3 0,3 Type C3 medium 0,8 0,3 0,4 0,4 0, 0, 0, fine 0,8 0,4 0,3 0,4 0,5 0,3 0,5 fine 0,5 0,6 0,6 0,5 0,5 0,5 0,5 number of labs 9 4 Roughness very coarse,5 0,5 0,6 0,7 0,4 0,5 0,3 standard coarse 0,8 0,5 0,6 0,5 0,5 0,5 0,4 type D1 medium 0,8 0,4 0,3 0,5 0,5 0,5 0,1 fine 0,8 0,3 0,7 0,7 1,1 0,3 0,9 number of labs 7 5 Roughness coarse 0,5 0,3 1,3 0,5 0,6 1,5 0,6 standard medium 0,5 0,3 1, 0,8 0,4 0,8 0,7 type D fine 0,5 0,9,1 1,9 1,4 1,9 number of labs 6 4 Comment: Noticed are the standard deviations of the average values of parameters (excerpt) Average over laboratories, numbers are mentioned Labs far from average are excluded (En-criterion of EAL G7) With λs no significant improvement of uncertainty component, even deterioration better value in comparison with and without ls
Contribution to Uncertainty Expanded uncertainty of roughness parameters, e.g. Rz: ~ 3.5% of measurement value. Contribution of Sources: noise 0,5% comparison 0,5% 0,5% traceability,0% surface