Phases of Gauge Theories and Surface Operators Phases of Gauge
QPA withPartial orNoKnownCrystal Structures (PONKCS)Secure Site...
Transcript of QPA withPartial orNoKnownCrystal Structures (PONKCS)Secure Site...
QPA with Partial or No Known Crystal Structures(PONKCS)
Innovation with Integrity
IF
• All phases in the mixture are known
• All phases are crystalline
• All crystal structures are known
THEN
• ‘ZMV algorithm’ (1) can be used to relate the Rietveld scale factor
to the phase concentration
(1) Hill R.J. and Howard C.J. (1987) J. Appl. Crys. Vol 20, 467-474.
Classic Rietveld method
14-15/12/2011 Advanced XRD Workshop 2
• ZMV is a calibration constant which eliminates the need to measure:
• instrument calibration constant
• sample mass absorption
• If the crystal structure of a phase is not known, then the ZMV calibration constant is unknown
( )( )∑
=
= n
kkk VMZS
VMZSW
1
ααα
W = weight %
S = Rietveld scale factor
Z = No. of formula units in unit cell
M = molecular mass of formula unit
V = unit cell volume
Classic Rietveld methodZMV calibration constant
14-15/12/2011 Advanced XRD Workshop 3
• The sample is "spiked" with a known mass of standard material and the QPA normalized accordingly
• The weight fractions of the crystalline phases present in each sample are estimated using the Rietveld methodology
• Concentrations to be corrected proportionately according to:
where Corr(Wα) is the corrected weight percent, STDknown the weighted concentration of the standard in the sample and STDmeasured the analyzed concentration
• The amount of amorphous material Wamorphous can then be derived from:
• If there is more than one phase with an unknown or only partially known structure, these phases will be considered as a single group= no info on individual phases!
Classic Rietveld methodinternal standard
14-15/12/2011 Advanced XRD Workshop 4
measured
known
STD
STDWWCorr αα =)(
∑=
−=n
jjamorphous WCorrW
1
)(1
• An individual unknown or partially unknown crystalline phase can be
quantified through PONKCS method, if:
• the phase is available as pure specimen
(or major phase in specimen → known impurities that can be quantified with
the internal standard method)
• a synthetic mixture can be prepared in which the amounts of unknown
and an internal standard are known
• the unknown phase in the ‚experimental‘ mixture does not vary too
much from the pure specimen, used to derive the intensities
• Phases with Partial Or No Known Crystal Structure are characterized by
measured rather than calculated structure factors
• For all phases a using empirically derived structure factors ZMV "calibration
constants" must be derived, e.g. via an internal standard s
PONKCS method
14-15/12/2011 Advanced XRD Workshop 5
• crystalline (and even amorphous) phases can be fitted through:
• (hkl) phase (Pawley or Le Bail) if the phase can be indexed
• peak phase if the phase cannot be indexed
• Result: list of peaks described by peak position and intensity
• This list of peaks replaces ‚str‘ in the Rietveld refinement, while keepingpeak position and intensity fixed= group of peaks scaled as a single entity within Rietveld refinement
• ZMV constant is unknown and has to be provided through calibration
PONKCS method
14-15/12/2011 Advanced XRD Workshop 6
• Calibration through the preparation of a mixture containing knownamounts of unknown (α) and standard material (s)
• (ZMV)α has NO physical meaning
PONKCS method
( )( )sss VMZS
VMZS
W
W ααα =
or
( ) ( )ss
s
VMZS
S
W
WVMZ ⋅⋅=
α
αα
all known
14-15/12/2011 Advanced XRD Workshop 7
Advanced XRD Workshop
• "Nontronite”
• Unknown structure
• Cement: QA of Bassanite
• Structure data of C3S do not accurately describe the technical product
• Cement: QA of blast furnace slag (BFS)
• Amorphous material (BFS)
• Cement: QA of C3S polymorphs (M1, M3)
• Structure data of C3S do not accurately describe the technical product
PONKCS Applications in Industry
14-15/12/2011 8
Nontronite
14-15/12/2011 Advanced XRD Workshop 9
10
#1: Literature
Diffraction pattern of nontronite (Co Kαααα)
1401351301251201151101051009590858075706560555045403530252015105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
11
#1: Refinement of standard mixture
2Th Degrees9088868482807876747270686664626058565452504846444240383634323028262422201816141210864
Sqr
t(C
ount
s)
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
Corundum 49.78 %Nontronite_hkl 50.22 %
12
#1: Results
The resultant phase model has been applied to a series of mixtures of known composition
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50 60 70 80 90 100
Weighed (wt%)
Bia
s (w
t%)
Nontronite Corundum
Cement
14-15/12/2011 Advanced XRD Workshop 13
• Nishi & Takeuchi (1985) C3S structure - misfits due to structuraldeficiencies
• Only a "cosmetic" issue for Clinker quantification
PONKCSExample: Quantitative Analysis of Cement
2Th Degrees656055504540353025201510
Cou
nts
8,000
7,500
7,000
6,500
6,000
5,500
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
0
-500
-1,000
-1,500
-2,000
-2,500
-3,000
C3S monoclinic (NISHI) 70.69 %C2S beta (MUMME) 8.02 %C3A Na orthorhombic 5.02 %C3A cubic 2.76 %C4AF Colville 10.20 %Periclase 0.63 %Lime 1.24 %Arcanite K2SO4 1.44 %
14-15/12/2011 Advanced XRD Workshop 14
• Nishi & Takeuchi (1985) C3S structural deficiencies (intensity misfit) adversly affectsBassanite (CaSO4 · ½H2O) quantification due to unevitable peak overlap
• Degree of overlap depends on Alite chemical composition
PONKCSExample: Quantitative Analysis of Cement
2Th Degrees40383634323028262422201816141210
Cou
nts
3,000
2,500
2,000
1,500
1,000
500
0
-500
-1,000
-1,500
-2,000
-2,500
-3,000
-3,500
C2S beta (MUMME) 0.00 %C3A cubic 0.00 %C3A Na orthorhombic 0.00 %C4AF Colville 0.00 %Lime 0.00 %Periclase 0.00 %Quartz 0.00 %Arcanite K2SO4 0.00 %Gypsum 0.00 %Bassanite Bezou 0.00 %Anhydrite 0.00 %Calcite 0.00 %Portlandite 0.00 %C3S monoclinic (NISHI) 0.00 %
Bassanite
Alite (402) & (310)
14-15/12/2011 Advanced XRD Workshop 15
• Classic Rietveld Refinementusing the Nishi & Takeuchi (1985) C3S structure
• PONKCS refinement2Th Degrees
2019181716151413121110
Cou
nts
1,000
900
800
700
600
500
400
300
200
100
0
PONKCSStructureless Modelling of Alite
Substitution of calculated intensities
phase_name C3S_hkl_Phasescale @ 0.1MVW( 0, 4331.778506, 0)space_group 8CS_L(cs_c3smonni, 1000 min =50; max =1000;)a a_c3smonni 33.18748b b_c3smonni 7.05051c c_c3smonni 18.56319be be_c3smonni 94.22338r_bragg 0.006728277788
hkl_Ishkl_m_d_th2 0 0 2 2 9.25639439 9.54711437 I 2.05270142e-010hkl_m_d_th2 2 0 -2 2 8.34458351 10.5931587 I 0.01858485616hkl_m_d_th2 4 0 0 2 8.27434444 10.683341 I 0.01406196859hkl_m_d_th2 2 0 2 2 7.8363862 11.2822943 I 0.01484194695hkl_m_d_th2 4 0 -1 2 7.77032948 11.3785229 I 0.0251988569hkl_m_d_th2 4 0 1 2 7.35505056 12.0232773 I 0.03432590883hkl_m_d_th2 1 1 0 4 6.89578199 12.8272991 I 0.01149107085hkl_m_d_th2 1 -1 -1 4 6.49472332 13.6230459 I 0.04729996279hkl_m_d_th2 1 1 1 4 6.42985344 13.7611485 I 0.01753635023hkl_m_d_th2 4 0 -2 2 6.40786076 13.8086081 I 0.03122114305hkl_m_d_th2 0 0 3 2 6.17092943 14.3415194 I 0.003343324237hkl_m_d_th2 4 0 2 2 5.9548769 14.8647385 I @ 0.27078hkl_m_d_th2 3 1 0 4 5.94094992 14.8997831 I @ 1.2198hkl_m_d_th2 2 0 -3 2 5.92666531 14.9358988 I 0.007612890057hkl_m_d_th2 3 -1 -1 4 5.72322845 15.4700003 I 0.003767987738hkl_m_d_th2 2 0 3 2 5.64745855 15.6788511 I 0.01085298472…..
2Th Degrees2019181716151413121110
Cou
nts
1,000
900
800
700
600
500
400
300
200
100
0
14-15/12/2011 Advanced XRD Workshop 16
PONKCSQuantitative Analysis of Bassanite
• Classic Rietveld Refinementusing the Nishi & Takeuchi (1985) C3S structure
• PONKCS refinement
• Bassanite:Estimated accuracy ~0.2%Estimated precision <0.1%
14-15/12/2011 Advanced XRD Workshop 17
Slag in Cement
14-15/12/2011 Advanced XRD Workshop 18
PONKCSQuantitative Analysis of BFSlag
BFSlag can be describedvia Pawley / Le Bail orsingle peak fitting
14-15/12/2011 Advanced XRD Workshop 19
PONKCSQuantitative Analysis of BFSlag
14-15/12/2011 20Advanced XRD Workshop
E.g. Pawley fit strategy:• Chose arbitrary space group
and lattice parameters to allow for a couple of peaks
• Allow for extreme line broadening
Refined PONKCSmodel for BFSlag
Round Robin VDZ 2006/7Quantitative Analysis of BFSlag
• Preliminary results PONKCS:
(5 repeated analyses)
25.1 (2)
67.2 (2)
71.7 (2)
14-15/12/2011 Advanced XRD Workshop 21
Accuracy and Precision (values in wt. %, SD in brackets/1σ)
• Every sample measured 5 times (D4 ENDEAVOR, LynxEye Detector)
• Reference values:
• sample 1: 25,0 wt.%
• sample 2: 67,0 wt.%
• sample 3: 72,0 wt.%
Round Robin VDZ 2006/7Quantitative Analysis of BFSlag
BFSlagSample 1
BFSlagSample 2
BFSlagSample 3
Measurement 1 25,0 67,2 71,7
Measurement 2 25,1 67,3 71,9
Measurement 3 24,7 67,0 71,6
Measurement 4 25,1 67,3 71,9
Measurement 5 25,3 67,0 71,5
Mean 25,1 67,2 71,7
SD 0,2 0,2 0,2
14-15/12/2011 Advanced XRD Workshop 22
C3S Polymorphs
14-15/12/2011 Advanced XRD Workshop 23
The missing link for quality and process control
• In Cement Clinkers two monoclinic polymorphs of the main Phase Alite(C3S) can be found (M1 and M3)
• Both polymorphs are different in hydraulic properties, like strength development
• Although this is well know since decades, nobody was able to distinguish and quantify these polymorphs in the last years by XRD Rietveld analysis
PONCKSAlite Polymorphism
14-15/12/2011 Advanced XRD Workshop 24
The monoclinic polymorphs M1 and M3
• Very similar patterns
• Available structural data do not accurately describe the technical product
M1 and M3 can be distinguished using currently available structure data!
PONCKSAlite Polymorphism
Alite polymorph M3
Lin
(Cou
nts)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
50 51 52 53 54
Alite polymorph M1
Lin
(Cou
nts)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
50 51 52 53 54
14-15/12/2011 Advanced XRD Workshop 25
Alite Polymorphs Monitoring Compressive Strength
• Observation over months: continuous decrease of the early strength development, although all process control parameters remained unchanged
• The re-evaluation of the XRD data using TOPAS considering the Alitepolymorphs showed a correlated decrease of the M1 polymorph
14-15/12/2011 Advanced XRD Workshop 26
• PCA: 630 PXRD + M1/M3 alite
Alite PolymorphsPOLYSNAP + TOPAS QA Results
HS clinkerM1 high
HS clinkerM1 low
normal clinkerM1 high
normal clinkerM1 low
14-15/12/2011 Advanced XRD Workshop 27
The missing link for quality and process control
• By using the TOPAS PONKCS capabilities we are able to distinguish the Alitepolymorphs M1 and M3
• Provides more detailed information about the process
• Allows to understand and predict the early strength development
• Allows to control and improve the quality of the product
PONCKSAlite Polymorphism
14-15/12/2011 Advanced XRD Workshop 28
PONKCSReference
Scarlett, N.V.Y. & Madsen, I.C. (2006)
Quantification of phases with partial or no known crystal structure
Powder Diffraction, 21(4), 278-284
Note:
The paper includes an example walk-throughon a TOPAS keyword level
14-15/12/2011 Advanced XRD Workshop 29
• PONKCS allows the quantification of compounds, where the classic Rietveld
method fails
• Materials with partial or no known crystal structure can be quantified with
the same accuracy and precision as phases with crystal structure. Often
even better, due to the calibration step
• Crystalline and amorphous phase amounts, accuracy and LLOD < 1%
• Preferred orientation can be dealt with (if sample is indexed)
Conclusions
14-15/12/2011 Advanced XRD Workshop 30
Innovation with Integrity
© Copyright Bruker Corporation. All rights reserved.