Improving Time Dependent Intensity (TDI) Corrections

[Mike Jercinovic]

Example 2...
1) in Acquire, start a new unknown sample
2) select to specify that you are choosing to base this sample on an existing setup, this setup is an unknown we have just run, and specified for U, Th and Pb to use TDI, then stored that as a setup.
3) make sure in special options that use TDI is selected, it is, and that use TDI in analysis options is also still checked (it is)
4) run one point with start acquisition in the Acquire window
5) once this point has completed (motion ready), go to the Analyze window and to standard assignments, Look at U, Th and Pb, now they have "use TDI (self cal)" selected automatically and we don't have to change anything - it's working great, but...
6) now run a second point from start acquisition in the Acquire window
7) once this point is finished, go to standard assignments in Analyze
look at the TDI assignments for U, Th, Pb...now they are all shut OFF (that is, DO NOT USE TDI is now selected), so now for this point, and all subsequent points for this file, we have to always go back into Analyze-standard assignments, and specify for each element (U, Th, Pb) to use TDI.

That's just the way it works for us.

[John Donovan]

Hi Mike,
Hmmm.... well I tried using a sample setup from the Automate! window and it seems to work just fine.  I did find a small display issue which is now fixed in v. 10.2.7 so go ahead and update and try tis new version.

It might be necessary for your to create a small test run with just a couple of elements that shows the behavior you are seeing for me to see it also. If you send that to me I will take a closer look...

By the way, you can easily see what the TDI flags are for each sample simply by double-clicking the sample in the Analyze! window (or use the Data button) and in the log window, you will note the line highlighted in red here:

Last (Current) On and Off Peak Count Times:
ELEM:    na ka   si ka   ti ka
BGD:       OFF     OFF     OFF
BGDS:      LIN     LIN     LIN
SPEC:        1       2       3
CRYST:     TAP    LPET    LLIF
ORDER:       1       1       1
ONTIM:   20.00   20.00   20.00
HITIM:    5.00    5.00    5.00
LOTIM:    5.00    5.00    5.00

Miscellaneous Sample Acquisition/Calculation Parameters:
KILO:    15.00   15.00   15.00
ENERGY   1.041   1.740   4.509
EDGE:    1.073   1.839   4.967
Eo/Ec:   13.98    8.16    3.02
STDS:      301     301      22
TDI#:       -1      -1       0


Just FYI: the TDI assignments shown above do not actually occur until the first data point has been acquired (in case the user changes their mind at the last minute!).

[UofO EPMA Lab]

We are running automated TDI acquisitions right now (just using the last unknown sample as the setup basis) and each new sample (combined conditions using both 10 and 50 nA elements) has the TDI assignments properly specified as I watch it running.

So, have you tried acquiring TDI without sample setups, just to see if the TDI assignments are carried forward?

The TDI assignments should also be carried forward with sample setups but we're not using them at the moment so I can't confirm, though it did work in demo mode over the weekend.

[John Donovan]

I have implemented a new TDI model for ultra beam sensitive samples. It is based on the Log(intensities) as before, but now also includes a log function of time (X axis) in order to perform a full double exponential fit. For certain very beam sensitive samples, this may be a useful addition to our tool kit.

Let's start with a very beam sensitive material, K-375 NIST glass. This material has 10.42 wt% Na, 31.8 wt% Si and some Zn, U and the balance oxygen...

Here is an "analysis" of this quite nasty material *without* any TDI correction:

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka

Average Total Oxygen:         .000     Average Total Weight%:   92.534
Average Calculated Oxygen:    .000     Average Atomic Number:   16.903
Average Excess Oxygen:        .000     Average Atomic Weight:   22.922
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371    .207  34.826    .002    .007    .004  92.786
   372    .192  34.695    .005   -.008    .012  92.635
   373    .235  34.488    .008   -.014    .014  92.471
   374    .175  34.505    .001   -.029    .008  92.400
   375    .146  34.501    .001    .013   -.021  92.379

AVER:     .191  34.603    .003   -.006    .003  92.534
SDEV:     .034    .151    .003    .017    .014    .173
SERR:     .015    .068    .001    .008    .006
%RSD:    17.56     .44   86.81 -273.01  412.85

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -98.17    8.71     ---     ---     ---
DIFF:  -10.229   2.773     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    76.73   79.39  602.77   66.49   40.15

UNKF:    .0009   .2806   .0000  -.0001   .0000
UNCT:      .92   54.33     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.1585  1.2330  1.0674  1.1528  1.4789
KRAW:    .0120   .6843   .0001  -.0006   .0001

You will note that the concentration error for Na is around 98 % relative accuracy, when this material treated as a "normal sample"...  Si isn't too great either, but is off 9% relative accuracy or so. So clearly we need some kind of a Time Dependent Intensity (TDI) correction method.   

So, next we will turn on the "traditional" Lin-Log TDI extrapolation which fits a straight line to a plot of the Log(Na) intensities and applies the slope to obtain these results: for Na and Si:

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction

Average Total Oxygen:         .000     Average Total Weight%:   92.158
Average Calculated Oxygen:    .000     Average Atomic Number:   16.907
Average Excess Oxygen:        .000     Average Atomic Weight:   22.894
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371    .467  34.359    .001    .007    .004  92.577
   372    .427  33.997    .005   -.008    .012  92.173
   373    .522  33.827    .008   -.014    .014  92.097
   374    .375  34.025    .001   -.029    .008  92.121
   375    .314  33.775    .001    .013   -.021  91.822

AVER:     .421  33.997    .003   -.006    .003  92.158
SDEV:     .081    .229    .003    .017    .014    .271
SERR:     .036    .102    .001    .008    .006
%RSD:    19.19     .67   87.96 -273.01  412.65

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -95.96    6.81     ---     ---     ---
DIFF:   -9.999   2.167     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    77.91   79.30  603.55   66.49   40.15

UNKF:    .0019   .2752   .0000  -.0001   .0000
UNCT:     2.06   53.21     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.1621  1.2355  1.0669  1.1527  1.4764
KRAW:    .0265   .6710   .0001  -.0006   .0001

TDI%:  123.003  -2.060    .962    ----    ----
DEV%:     26.0      .5    33.2    ----    ----
TDIF:  LOG-LIN LOG-LIN LOG-LIN    ----    ----
TDIT:    74.20   74.40   71.80    ----    ----
TDII:     7.71    53.3    1.28    ----    ----

Well, that wasn't too much of a help, was it?  The Na average came up considerably from 0.191 to 0.421 (though far short of the expected published value of 10.42 wt%!), but the Si dropped by even more (34.6 to 33.9 wt% absolute), so the total actually decreased slightly!  Even though, the TDI% correction was over 100% for Na! Why is this?

Lets start by looking at these "traditional" TDI log intensity plots for Na and Si on this K-375 NIST glass...





Well clearly the Na extrapolation back to zero time is not a good fit at all, while the Si is not quite as bad, we can still see that we have not properly modeled the initial intensity changes in the first few seconds for either element, but particularly Na.  Remember, these are Log(intensity) plots and should therefore plot any exponential process as a straight line, but obviously not with this particular sample under 100 nA conditions!

So now we will try the next tool in our arsenal, the hyper-exponential TDI fit, which assumes that the change in Log(intensity) is modeled by a 2nd order polynomial in lin-log space as seen here in the plots for Na and Si again:





Much improved fits it would appear, though Na is still not modeled well in the first seconds of the TDI acquisition, though Si is less poorly modeled. What about the quant results?

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction

Average Total Oxygen:         .000     Average Total Weight%:   91.991
Average Calculated Oxygen:    .000     Average Atomic Number:   16.892
Average Excess Oxygen:        .000     Average Atomic Weight:   22.858
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371   1.266  33.478    .001    .007    .004  92.496
   372   1.012  33.272    .005   -.008    .012  92.034
   373   1.331  33.076    .008   -.014    .014  92.155
   374    .902  32.973    .001   -.029    .008  91.596
   375    .744  33.197    .001    .013   -.021  91.675

AVER:    1.051  33.199    .003   -.006    .003  91.991
SDEV:     .246    .193    .003    .017    .014    .367
SERR:     .110    .086    .001    .008    .006
%RSD:    23.41     .58   87.97 -273.02  413.22

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -89.91    4.30     ---     ---     ---
DIFF:   -9.369   1.369     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    77.91   79.30  603.55   66.49   40.15

UNKF:    .0049   .2677   .0000  -.0001   .0000
UNCT:     5.15   51.77     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.1621  1.2400  1.0660  1.1524  1.4730
KRAW:    .0662   .6529   .0001  -.0006   .0001
PKBG:     2.54  320.00    1.04     .97    1.26

TDI%:  454.003  -4.704    .962    ----    ----
DEV%:     15.8      .4    33.2    ----    ----
TDIF:  HYP-EXP HYP-EXP LOG-LIN    ----    ----
TDIT:    74.20   74.40   71.80    ----    ----
TDII:     14.5    52.3    1.28    ----    ----

Now our Na TDI% correction is over 450%, but we are still off by 90% in relative accuracy as we've only gone from 0.42 wt% Na in the traditional extrapolation to around 1 wt% with this "hyper-exponential" TDI fit, and we are therefore still under correcting this extremely beam sensitive material...

[John Donovan]

So, here is where I would like to introduce a new TDI extrapolation model, the Logarithmic extrapolation or log-log fit or "double-exponential" model. The previously existing linear and hyper-exponential TDI methods are summarized in the previous post. Let's take a look first at the TDI plots using this new double exponential fit:





The extrapolations are much improved, at least to the eye, so now let's look at the quant results again:

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction

Average Total Oxygen:         .000     Average Total Weight%:   97.309
Average Calculated Oxygen:    .000     Average Atomic Number:   16.572
Average Excess Oxygen:        .000     Average Atomic Weight:   22.868
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371   7.358  33.896    .001    .007    .004  99.006
   372   5.900  33.248    .005   -.008    .012  96.897
   373   6.969  32.999    .008   -.014    .014  97.717
   374   5.572  33.286    .001   -.029    .008  96.579
   375   5.781  32.830    .001    .013   -.021  96.344

AVER:    6.316  33.252    .003   -.006    .003  97.309
SDEV:     .795    .406    .003    .017    .014   1.082
SERR:     .355    .181    .001    .008    .006
%RSD:    12.58    1.22   87.96 -272.99  412.40

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -39.39    4.47     ---     ---     ---
DIFF:   -4.104   1.422     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    77.91   79.30  603.55   66.49   40.15

UNKF:    .0302   .2643   .0000  -.0001   .0000
UNCT:    32.04   51.11     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.0906  1.2580  1.0656  1.1519  1.4697
KRAW:    .4113   .6446   .0001  -.0006   .0001
PKBG:    10.59  315.92    1.04     .97    1.26

TDI%: 3412.187  -5.918    .962    ----    ----
DEV%:     11.8      .4    33.2    ----    ----
TDIF:  LOG-LOG LOG-LOG LOG-LIN    ----    ----
TDIT:    74.20   74.40   71.80    ----    ----
TDII:     31.8    51.1    1.28    ----    ----

Ok, so that is better and now we are "only" off in accuracy for Na by around 40% relative (6.3 wt% compared to the published value of 10.4 wt%). Interestingly our Si value is very slightly worse than the "hyper-exponential" fit.  The total averages 97% which is not good, but much better than before.

Are we done, well maybe... if we look again at the log-log plots it does appear that we are still slightly under estimating the TDI correction in the first few seconds. What can we do?

Well let's try "weighting" the first few data points in the acquisition, since these measurements should obviously be the closer to the zero time intensity, by utilizing this option in the Analytical | Analysis Options dialog as seen here:




By entering a value to "2", we weight the first point times 2, if we enter say "3" we weight the first point times 3 and the second point times 2, if we enter a "4" we weight the first point 4 times, second point 3 times, third point 2 times, etc., etc. Here is what we obtain quantitatively with just weighting the first point times 2:

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
WARNING- Using Time Dependent Intensity (TDI) Weighting Factor of  2

Average Total Oxygen:         .000     Average Total Weight%:   98.071
Average Calculated Oxygen:    .000     Average Atomic Number:   16.519
Average Excess Oxygen:        .000     Average Atomic Weight:   22.855
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371   8.221  33.420    .001    .007    .004  99.394
   372   7.202  33.052    .005   -.008    .012  98.003
   373   8.104  32.753    .008   -.014    .014  98.605
   374   6.835  32.904    .001   -.029    .008  97.459
   375   6.694  32.465    .001    .013   -.021  96.893

AVER:    7.411  32.919    .003   -.006    .003  98.071
SDEV:     .712    .354    .003    .017    .014    .975
SERR:     .318    .159    .001    .008    .006
%RSD:     9.60    1.08   88.39 -272.99  412.33

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -28.88    3.42     ---     ---     ---
DIFF:   -3.009   1.089     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    77.82   79.39  604.17   66.49   40.15

UNKF:    .0356   .2607   .0000  -.0001   .0000
UNCT:    37.74   50.48     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.0801  1.2625  1.0652  1.1517  1.4679
KRAW:    .4849   .6358   .0001  -.0006   .0001
PKBG:    12.30  311.92    1.04     .97    1.26

TDI%: 4041.216  -7.094   1.268    ----    ----
DEV%:     12.1      .4    32.6    ----    ----
TDIF:  LOG-LOG LOG-LOG LOG-LIN    ----    ----
TDIT:    74.20   74.40   71.80    ----    ----
TDII:     37.6    50.5    1.29    ----    ----

As you can see, there is further improvement. Our total average is now 98%, our Na value is now 7.4 wt% compared to the published value of 10.4 wt%- still a 28% error, but note that the correction is approximately 4000%!  Yes, you read that correctly- over 4000% correction.  The Si is now within 3.4 % relative accuracy.

Ok, let's try with a weighting of "4" and see what that does:

St  173 Set  24 K-0375 NBS glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 100.  Beam Size =   10
(Magnification (analytical) =  40000),        Beam Mode = Analog  Spot
(Magnification (default) =      400, Magnification (imaging) =    800)
Image Shift (X,Y):                                          .00,   .00

from John Rutledge
Number of Data Lines:   5             Number of 'Good' Data Lines:   5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
WARNING- Using Time Dependent Intensity (TDI) Weighting Factor of  4

Average Total Oxygen:         .000     Average Total Weight%:   98.809
Average Calculated Oxygen:    .000     Average Atomic Number:   16.471
Average Excess Oxygen:        .000     Average Atomic Weight:   22.847
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents

SPEC:       Zn      Ba       U       O
TYPE:     SPEC    SPEC    SPEC    SPEC

AVER:    4.940  10.370    .110  42.320
SDEV:     .000    .000    .000    .000
 
ELEM:       Na      Si      Ca      Fe       P
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P   SUM 
   371   9.103  33.145    .001    .007    .004 100.000
   372   8.228  32.857    .005   -.008    .012  98.834
   373   9.077  32.640    .008   -.014    .014  99.465
   374   7.914  32.672    .001   -.029    .008  98.307
   375   7.449  32.258    .001    .013   -.021  97.441

AVER:    8.354  32.715    .003   -.006    .003  98.809
SDEV:     .726    .325    .003    .017    .014    .997
SERR:     .325    .145    .001    .008    .006
%RSD:     8.70     .99   88.90 -273.00  412.36

PUBL:   10.420  31.830    n.a.    n.a.    n.a.  99.990
%VAR:   -19.83    2.78     ---     ---     ---
DIFF:   -2.066    .885     ---     ---     ---
STDS:      336      14     285     162     285

STKF:    .0735   .4101   .3596   .0950   .1599
STCT:    77.78   79.47  604.98   66.49   40.15

UNKF:    .0404   .2584   .0000  -.0001   .0000
UNCT:    42.72   50.07     .05    -.04     .01
UNBG:     3.34     .16    1.23     .99     .05

ZCOR:   2.0704  1.2661  1.0649  1.1516  1.4666
KRAW:    .5492   .6301   .0001  -.0006   .0001
PKBG:    13.79  309.41    1.04     .97    1.26

TDI%: 4588.661  -7.842   1.467    ----    ----
DEV%:     11.2      .4    31.9    ----    ----
TDIF:  LOG-LOG LOG-LOG LOG-LIN    ----    ----
TDIT:    74.20   74.40   71.80    ----    ----
TDII:     42.6    50.1    1.29    ----    ----

OK, so even more improvement! Our total average is now almost 99% and our relative accuracy error on Na and Si is now 20% and 2.8%. In the case of Na, the TDI% correction is now over 4500%!

We could keep going, but I think we all get the point... which is: we would most likely never want to perform such an acquisition on such a beam sensitive sample at such a high (100 nA) beam current!  But... if we absolutely had to, we could give it a go using these new TDI tools!

By the way, here is the Na TDI plot with the 4 times point weighting:



And here are the quantitative results with 10x weighting log-log fit to the first TDI intervals:

St  173 Set  24 K-0375 NBS glass, Results in Elemental Weight Percents
 
ELEM:       Na      Si      Ca      Fe       P      Zn      Ba       U       O
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    SPEC    SPEC    SPEC    SPEC
BGDS:      LIN     EXP     LIN     LIN     EXP
TIME:    20.00   20.00   20.00   20.00   20.00
BEAM:   100.72  100.72  100.72  100.72  100.72

ELEM:       Na      Si      Ca      Fe       P      Zn      Ba       U       O   SUM 
   371   9.642  32.967    .001    .007    .004   4.940  10.370    .110  42.320 100.361
   372   8.822  32.773    .005   -.008    .012   4.940  10.370    .110  42.320  99.344
   373   9.654  32.545    .008   -.014    .014   4.940  10.370    .110  42.320  99.947
   374   8.532  32.488    .001   -.029    .008   4.940  10.370    .110  42.320  98.740
   375   7.915  32.109    .001    .013   -.021   4.940  10.370    .110  42.320  97.757

AVER:    8.913  32.576    .003   -.006    .003   4.940  10.370    .110  42.320  99.230
SDEV:     .747    .323    .003    .017    .014    .000    .000    .000    .000   1.027
SERR:     .334    .145    .001    .008    .006    .000    .000    .000    .000
%RSD:     8.38     .99   89.41 -273.00  412.34     .00     .00     .00     .00

PUBL:   10.420  31.830    n.a.    n.a.    n.a.   4.940  10.370    .110  42.320  99.990
%VAR:   -14.46    2.34     ---     ---     ---     .00     .00     .00     .00
DIFF:   -1.507    .746     ---     ---     ---    .000    .000    .000    .000


Maybe not perfect, but certainly better than the alternative! 

Edit by John: The observant eye will note that the Na numbers decrease with each point acquisition in the last analysis above. This is due to the beam diameter being 10 um and the points 10 um apart, therefore each acquisition effectively pre-heats the subsequent acquisition volume which reduces the "incubation" time" and therefore decreases the Na intensity more quickly.

[Mike Jercinovic]

Nice!  This will be very useful.

[John Donovan]

Hi Mike,
Thanks, though in some respects I feel this is a "two steps forward/one step back" sort of thing.

As you know, due to "incubation" effects as described here:

http://probesoftware.com/smf/index.php?topic=116.msg454#msg454

This new fit method will now allow the user to not only "under fit" the TDI data, but now, also to "over fit" it!   
john

[John Donovan]

I would be very interested in seeing posted user examples of their TDI corrections on beam sensitive samples using this new "double exponential" extrapolation now available in Probe for EPMA 10.3.4...

[AndrewLocock]

With regard to time-dependent-intensity corrections, I gather that one can set the time-weighting option from 1 to 10 in the Analytical options.
Question: If I have only 6 intervals in my TDI curve, what does a time-weighting of 10 actually mean?

Comment: I appear to achieve the best accuracy by adjusting the operating conditions (nA, beam diameter, peak count time) so that the TDI curve stays in the log-linear regime.
It appears that for my hydrous natural dacitic-rhyolitic glasses, that time-weighting of a linear model may provide more accurate results than use of the unweighted log-quadratic (hyperexponential) model.

For anhydrous basaltic glasses at our normal operating conditions, TDI makes very little difference.

[John Donovan]

With regard to time-dependent-intensity corrections, I gather that one can set the time-weighting option from 1 to 10 in the Analytical options.
Question: If I have only 6 intervals in my TDI curve, what does a time-weighting of 10 actually mean?

Great question.

For those wondering, Andrew is asking about this feature in the Analytical | Analysis Options dialog:



Now this option is briefly explained in the PFE User's Reference:



but who reads manuals these days!   

So here is the source code that should make it more clear:

Code: [Select]

pointweight% = 1
If Not UseVolElTimeWeightingFlag Then Exit Sub
If VolElTimeWeightingFactor% < 2 Then Exit Sub

' Calculate point weighting
If ipoint% <= VolElTimeWeightingFactor Then
pointweight% = ipoint% * VolElTimeWeightingFactor% / ipoint% ^ 2
End If

Basically, for each of the measured TDI intensities, a weighting factor is calculated (default = 1), and when the points are added to the regression array, they are weighted according to the code above. If you specify a weighting value larger than the number of points you have, there is basically no effect.

Note that we also fixed a broken Help link in the above dialog and also added better documentation of the TDI parameters in the Report format output as suggested by Andrew (update Probe for EPMA using the Help menu as usual):

The intensity data was corrected for Time Dependent Intensity (TDI) loss (or gain) using a self calibrated correction for Na ka, K ka, Ti ka, Si ka, O ka.
The TDI data was fit with a Time Weighting Factor of 2

A complete example of the Report format text is here (I pasted it into a code control because it so long and detailed):

Code: [Select]

Un   19 NBS K-411 mineral glass
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 10.0  Beam Size =   20
(Magnification (analytical) =  20000),        Beam Mode = Analog  Spot
(Magnification (default) =      600, Magnification (imaging) =    600)
Image Shift (X,Y):                                         .00,    .00

Compositional analyses were acquired on an electron microprobe equipped with 5 tunable wavelength dispersive spectrometers.

Operating conditions were 40 degrees takeoff angle, and a beam energy of 15 keV.
The beam current was 10 nA, and the beam diameter was 20 microns.

Elements were acquired using analyzing crystals LLIF for Ti ka, Fe ka, Mn ka, Ca ka, PET for Cl ka, Ba la, K ka, TAP for Na ka, Mg ka, LTAP for F ka, Si ka, Al ka, TAP for Na ka, Mg ka, and PC1 for O ka.

The standards were MgO synthetic for Mg ka, O ka, TiO2 synthetic for Ti ka, MnO synthetic for Mn ka, NBS K-411 mineral glass for Si ka, Ca10(PO4)6Cl2 (halogen corrected) for Cl ka, Nepheline (partial anal.) for Na ka, Al ka, Diopside (Chesterman) for Ca ka, Orthoclase MAD-10 for K ka, Magnetite U.C. #3380 for Fe ka, and BaF2 (barium fluoride) for Ba la, F ka.

MgO synthetic
1. UCB # M3567, 99.8%, EPMA (UCB): Ca ~ 0.2%
2. C. M. Taylor, 99.98%, EPMA (UCB) Ca ~ 0.02%

SiO2 synthetic
Specimen from ESPI, 99.99%, EPMA (UCB): Al2O3 ~ 0.01%
Catalog #K4699M
Atomic Absorption (Chris Lewis):
Al=15 ppm +/- 5
Fe=6 ppm +/- 3
Mn=1.5 ppm +/- 0.3
Na=5 ppm +/- 3
Li= 2.3 ppm +/- 0.2

TiO2 synthetic
Specimen from Mimports, Lafayette, CA
Assumed stoichiometric
EPMA (UCB): Al2O3=0.02 (interference corrected)

Fluor-phlogopite (halogen corrected)
Grown by S. Wones, Univ of Tenn
(applied F=O equivalence)

Ca10(PO4)6Cl2 (halogen corrected)
Specimen from Alan Baumer, Univ of Nice, France
Hydrothermally grown
See Argiolas and Baumer, Can. Min., v. 16, pp 285-290, 1978

Nepheline (partial anal.)
Analysis by ISE Carmichael (Na, K)
Ca = 750 PPM (EPMA by JJD)

Diopside (Chesterman)
Twin Lakes, Fresno Co., CA
From Charles Chesterman (Ca Div. Mines)

Orthoclase MAD-10
Specimen from Chuck Taylor
Fe2O3=2.01% (EPMA by J. Donovan) (as FeO=1.88% + 0.13% O)
K2O=15.49%, Na2O=1.07% (Flame photometry by J. Hampel)
BaO=0.06%, Rb2O=0.03% (EPMA by J. Donovan)
Sr=12 ppm, Rb=600 ppm (Isotope dilution)

Magnetite U.C. #3380
Port Henry, NY
FeO=30.93% (ISE Carmichael)
Fe2O3=68.85%, FeO=30.92% (as FeO=92.73% + 6.90% O)
(Total FeO=92.73%, by EPMA, JJD)

MnO synthetic
Specimen from Michael Wittenauer (Purdue Univ.)
Starting mat'l 99.999%, SM # 317, 'skull melt' process
Mat. Res. Bull. 15, p 571, 1980
(possible intergrowths of Mn3O4 and small inclusions of Mn metal)
EPMA (UCB): SiO2=0.00, FeO=0.00, CaO=0.00, Al2O3=0

NiO synthetic
1. Specimen from Michael Wittenauer (Purdue Univ.)
Starting mat'l 99.999%, Boule WI, Arc Transfer
2. Specimen from G. Czemanske, USGS (Oct 12, 1984)
EPMA (UCB): FeO=0.05%
-----------------------------
All material assumed stoichiometric

NBS K-412 mineral glass
SRM 470, NIST
C.M. Taylor (Photometry?) FeO 2.77, Fe2O3 8.15
Total as FeO 10.10, Excess O 0.815
Na = 430 PPM (EPMA by JJD)

NBS K-411 mineral glass
SRM 470, NIST
C.M. Taylor (Photometry?) FeO 4.39, Fe2O3 11.23
Total as FeO 14.49, Excess O 1.12

BIR-1G Glass
USGS
see Meeker, et. al. "A Basalt Glass Standard for Multiple Microanalytical Techniques"

BaF2 (barium fluoride)
Single crystal, fluorescent

The counting time was 10 seconds for Cl ka, Ti ka, Mn ka, 20 seconds for K ka, Ba la, Ca ka, Si ka, Al ka, 40 seconds for F ka, Fe ka, 60 seconds for Na ka, Mg ka, and 120 seconds for O ka.

The intensity data was corrected for Time Dependent Intensity (TDI) loss (or gain) using a self calibrated correction for Na ka, K ka, Ti ka, Si ka, O ka.
The TDI data was fit with a Time Weighting Factor of 2

The off peak counting time was 10 seconds for Cl ka, Mn ka, Ti ka, and 20 seconds for Ba la, F ka, K ka, O ka.

Off Peak correction method was Linear for Mn ka, Cl ka, Ba la, F ka, K ka, Low Only for Ti ka, and Exponential for O ka.

The MAN background intensity data was calibrated and continuum absorption corrected for Na ka, Fe ka, Ca ka, Si ka, Al ka, Mg ka.

Donovan, J. J., & Tingle, T. N. (1996). An improved mean atomic number background correction for quantitative microanalysis. Microscopy and Microanalysis, 2(1), 1-7.
Donovan, J. J., Singer, J. W., & Armstrong, J. T. (2016). A new EPMA method for fast trace element analysis in simple matrices. American Mineralogist, 101(8), 1839-1853.

Unknown and standard intensities were corrected for deadtime using the Normal (traditional single term) correction method.

Donovan, J. J., Moy, A., von der Handt, A., Gainsforth, Z., Maner, J. L., Nachlas, W., & Fournelle, J. (2023). A New Method for Dead Time Calibration and a New Expression for Correction of WDS Intensities for Microanalysis. Microscopy and Microanalysis, 29(3), 1096-1110.

Standard intensities were corrected for standard drift over time on an element by element basis.

Interference corrections were applied to Ba for interference by Ti, and to Ti for interference by Ba.

Donovan, J. J., Snyder, D. A., & Rivers, M. L. (1992). An improved interference correction for trace element analysis. In Proceedings of the Annual Meeting-Electron Microscopy Society of America (pp. 1646-1646). San Francisco Press.

Empirical Mass Absorption Coefficients were utilized to correct x-ray intensities for matrix corrections.

Bastin, G. F., & Heijligers, H. J. M. (1991). Quantitative electron probe microanalysis of ultra-light elements (boron-oxygen). In Electron probe quantitation (pp. 145-161). Boston, MA: Springer US.

Bastin, G. F., & Heijligers, H. J. M. (1992). Present and future of light element analysis with electron beam instruments. Microbeam Analysis, 1(2), 61-73.

Current Mass Absorption Coefficients From:
LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV

  Z-LINE   X-RAY Z-ABSOR     MAC
      Na      ka      Na  5.6089e+02
      Na      ka      K   3.8110e+03
      Na      ka      Cl  2.5391e+03
      Na      ka      Ba  7.6213e+03
      Na      ka      F   5.1229e+03
      Na      ka      Ti  5.2439e+03
      Na      ka      Fe  8.1986e+03
      Na      ka      Mn  7.2518e+03
      Na      ka      Ca  4.3573e+03
      Na      ka      Si  1.4049e+03
      Na      ka      Al  1.0667e+03
      Na      ka      Mg  8.1441e+02
      Na      ka      O   4.1515e+03
      Na      ka      H   5.9317e+00
      K       ka      Na  3.7714e+02
      K       ka      K   1.7109e+02
      K       ka      Cl  1.1539e+03
      K       ka      Ba  7.2049e+02
      K       ka      F   2.1534e+02
      K       ka      Ti  2.4971e+02
      K       ka      Fe  4.1167e+02
      K       ka      Mn  3.5594e+02
      K       ka      Ca  1.9889e+02
      K       ka      Si  7.4506e+02
      K       ka      Al  5.9083e+02
      K       ka      Mg  5.0887e+02
      K       ka      O   1.6416e+02
      K       ka      H   1.1806e-01
      Cl      ka      Na  7.3634e+02
      Cl      ka      K   3.2806e+02
      Cl      ka      Cl  2.1561e+02
      Cl      ka      Ba  1.2824e+03
      Cl      ka      F   4.2282e+02
      Cl      ka      Ti  4.7326e+02
      Cl      ka      Fe  7.8172e+02
      Cl      ka      Mn  6.7972e+02
      Cl      ka      Ca  3.7594e+02
      Cl      ka      Si  1.4010e+03
      Cl      ka      Al  1.1255e+03
      Cl      ka      Mg  9.8203e+02
      Cl      ka      O   3.2567e+02
      Cl      ka      H   2.6576e-01
      Ba      la      Na  1.6022e+02
      Ba      la      K   7.2502e+02
      Ba      la      Cl  5.2953e+02
      Ba      la      Ba  3.3617e+02
      Ba      la      F   9.0427e+01
      Ba      la      Ti  1.1151e+02
      Ba      la      Fe  1.8314e+02
      Ba      la      Mn  1.5795e+02
      Ba      la      Ca  8.3453e+02
      Ba      la      Si  3.2826e+02
      Ba      la      Al  2.5758e+02
      Ba      la      Mg  2.1898e+02
      Ba      la      O   6.7822e+01
      Ba      la      H   4.2840e-02
      F       ka      Na  1.8327e+03
      F       ka      K   1.0658e+04
      F       ka      Cl  7.5904e+03
      F       ka      Ba  3.1554e+03
      F       ka      F   9.2209e+02
      F       ka      Ti  1.4588e+04
      F       ka      Fe  2.3374e+03
      F       ka      Mn  1.6117e+04
      F       ka      Ca  1.2415e+04
      F       ka      Si  4.2952e+03
      F       ka      Al  3.4208e+03
      F       ka      Mg  2.6263e+03
      F       ka      O   1.2440e+04
      F       ka      H   2.4805e+01
      Ti      ka      Na  1.5590e+02
      Ti      ka      K   7.0770e+02
      Ti      ka      Cl  5.1645e+02
      Ti      ka      Ba  3.2787e+02
      Ti      ka      F   8.7938e+01
      Ti      ka      Ti  1.0869e+02
      Ti      ka      Fe  1.7855e+02
      Ti      ka      Mn  1.5394e+02
      Ti      ka      Ca  8.1470e+02
      Ti      ka      Si  3.1977e+02
      Ti      ka      Al  2.5083e+02
      Ti      ka      Mg  2.1325e+02
      Ti      ka      O   6.5919e+01
      Ti      ka      H   4.1490e-02
      Fe      ka      Na  5.5397e+01
      Fe      ka      K   2.7665e+02
      Fe      ka      Cl  1.9695e+02
      Fe      ka      Ba  6.1414e+02
      Fe      ka      F   3.0620e+01
      Fe      ka      Ti  3.7689e+02
      Fe      ka      Fe  6.8270e+01
      Fe      ka      Mn  5.9704e+01
      Fe      ka      Ca  3.2161e+02
      Fe      ka      Si  1.1782e+02
      Fe      ka      Al  9.1605e+01
      Fe      ka      Mg  7.6877e+01
      Fe      ka      O   2.2548e+01
      Fe      ka      H   1.2590e-02
      Mn      ka      Na  6.8522e+01
      Mn      ka      K   3.3731e+02
      Mn      ka      Cl  2.4097e+02
      Mn      ka      Ba  6.5921e+02
      Mn      ka      F   3.8047e+01
      Mn      ka      Ti  4.5531e+02
      Mn      ka      Fe  8.3286e+01
      Mn      ka      Mn  7.2508e+01
      Mn      ka      Ca  3.9062e+02
      Mn      ka      Si  1.4510e+02
      Mn      ka      Al  1.1272e+02
      Mn      ka      Mg  9.4808e+01
      Mn      ka      O   2.8131e+01
      Mn      ka      H   1.6010e-02
      Ca      ka      Na  2.7733e+02
      Ca      ka      K   1.1737e+03
      Ca      ka      Cl  8.7515e+02
      Ca      ka      Ba  5.5026e+02
      Ca      ka      F   1.5790e+02
      Ca      ka      Ti  1.8677e+02
      Ca      ka      Fe  3.0742e+02
      Ca      ka      Mn  2.6528e+02
      Ca      ka      Ca  1.4983e+02
      Ca      ka      Si  5.5579e+02
      Ca      ka      Al  4.3892e+02
      Ca      ka      Mg  3.7616e+02
      Ca      ka      O   1.1972e+02
      Ca      ka      H   8.1770e-02
      Si      ka      Na  2.2375e+03
      Si      ka      K   9.7768e+02
      Si      ka      Cl  6.5835e+02
      Si      ka      Ba  3.3056e+03
      Si      ka      F   1.3201e+03
      Si      ka      Ti  1.4132e+03
      Si      ka      Fe  2.3053e+03
      Si      ka      Mn  2.0250e+03
      Si      ka      Ca  1.1465e+03
      Si      ka      Si  3.5048e+02
      Si      ka      Al  3.2132e+03
      Si      ka      Mg  2.9015e+03
      Si      ka      O   1.0337e+03
      Si      ka      H   1.0618e+00
      Al      ka      Na  3.3597e+03
      Al      ka      K   1.4794e+03
      Al      ka      Cl  9.9433e+02
      Al      ka      Ba  4.6512e+03
      Al      ka      F   2.0277e+03
      Al      ka      Ti  2.1374e+03
      Al      ka      Fe  3.4392e+03
      Al      ka      Mn  3.0278e+03
      Al      ka      Ca  1.7548e+03
      Al      ka      Si  5.4409e+02
      Al      ka      Al  4.0218e+02
      Al      ka      Mg  4.2884e+03
      Al      ka      O   1.5979e+03
      Al      ka      H   1.8043e+00
      Mg      ka      Na  5.2018e+03
      Mg      ka      K   2.3234e+03
      Mg      ka      Cl  1.5604e+03
      Mg      ka      Ba  6.3391e+03
      Mg      ka      F   3.1803e+03
      Mg      ka      Ti  3.2972e+03
      Mg      ka      Fe  5.2394e+03
      Mg      ka      Mn  4.6163e+03
      Mg      ka      Ca  2.7124e+03
      Mg      ka      Si  8.5871e+02
      Mg      ka      Al  6.3956e+02
      Mg      ka      Mg  4.8748e+02
      Mg      ka      O   2.5312e+03
      Mg      ka      H   3.1956e+00
      O       ka      Na  3.6300e+03 *
      O       ka      K   1.9369e+04
      O       ka      Cl  1.4300e+04 *
      O       ka      Ba  4.5194e+03
      O       ka      F   1.8500e+03 *
      O       ka      Ti  1.9900e+04 *
      O       ka      Fe  4.0000e+03 *
      O       ka      Mn  3.4700e+03 *
      O       ka      Ca  2.4600e+04 *
      O       ka      Si  8.7900e+03 *
      O       ka      Al  6.7200e+03 *
      O       ka      Mg  5.1700e+03 *
      O       ka      O   1.1999e+03
      O       ka      H   5.7430e+01
 * indicates empirical MAC

Empirical Mass Absorption Coefficients From:
C:\ProgramData\Probe Software\Probe for EPMA\EMPMAC.DAT

  Z-LINE   X-RAY Z-ABSOR     MAC
      O       ka      Na  3.6300e+03    Love et al. (1974)
      O       ka      Cl  1.4300e+04    Love et al. (1974)
      O       ka      F   1.8500e+03    Love et al. (1974)
      O       ka      Ti  1.9900e+04    Bastin  (1992)
      O       ka      Fe  4.0000e+03    Bastin  (1992)
      O       ka      Mn  3.4700e+03    Bastin  (1992)
      O       ka      Ca  2.4600e+04    Love et al. (1974)
      O       ka      Si  8.7900e+03    Bastin  (1992)
      O       ka      Al  6.7200e+03    Bastin  (1992)
      O       ka      Mg  5.1700e+03    Bastin  (1992)

Area Peak Factors were utilized to correct x-ray intensities for wavelength peak shift and/or shape changes for compound compositions by summing binary APF values.

Bastin, G. F., & Heijligers, H. J. M. (1986). Quantitative electron probe microanalysis of carbon in binary carbides. I—principles and procedures. X-ray Spectrometry, 15(2), 135-141.

Empirical Area Peak Factors (APF) From:
C:\ProgramData\Probe Software\Probe for EPMA\EMPAPF.DAT

  Z-LINE   X-RAY Z-ABSOR       APF   RE-NORM
      O       ka      Ti     .9796    1.0000    TiO2/Fe2O3/WSi/59.8
      O       ka      Fe     .9962    1.0000    Fe3O4/Fe2O3/WSi/59.8
      O       ka      Ca     .9700    1.0000    ----/Fe2O3/WSi/59.8
      O       ka      Si    1.0444    1.0000    SiO2/Fe2O3/WSi/59.8, Bastin
      O       ka      Al    1.0213    1.0000    Al2O3/Fe2O3/WSi/59.8, Bastin

Results are the average of 12 points and detection limits ranged from .006 weight percent for Mg ka to .007 weight percent for Si ka to .016 weight percent for Fe ka to .064 weight percent for Ti ka to .080 weight percent for Ba la.

Analytical sensitivity (at the 99% confidence level) ranged from .212 percent relative for O ka to .421 percent relative for Mg ka to 26.044 percent relative for Al ka to 256.124 percent relative for F ka to 2281103.000 percent relative for Ba la.

Goldstein, J. I. (1992). Scanning electron and x-ray microanalysis. A text for biologists, materials scientists, and geologists, 395-416.

Oxygen equivalent from halogens (F/Cl/Br/I), was not subtracted in the matrix correction.

Moy, A., Fournelle, J., Nachlas, W., Dungan, M., Locock, A., Bullock, E., ... & Handt, A. V. D. (2023). On the Importance of Including All Elements in the EPMA Matrix Correction.


The exponential or polynomial background fit was utilized.

Donovan, J. J., Lowers, H. A., & Rusk, B. G. (2011). Improved electron probe microanalysis of trace elements in quartz. American Mineralogist, 96(2-3), 274-282.

The matrix correction method was ZAF or Phi-Rho-Z Calculations and the mass absorption coefficients dataset was LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV.

The ZAF or Phi-Rho-Z algorithm utilized was Armstrong/Love Scott prZ (default).

Armstrong, J. T. (1988). Quantitative analysis of silicate and oxide minerals: comparison of Monte Carlo, ZAF and phi-rho-z procedures. Analysis microbeam.

By the way, this topic is a little out of date, so please also check out this topic on TDI methods also:

https://probesoftware.com/smf/index.php?topic=11.0

[AndrewLocock]

]Basically, for each of the measured TDI intensities, a weighting factor is calculated (default = 1), and when the points are added to the regression array, they are weighted according to the code above.
If you specify a weighting value larger than the number of points you have, there is basically no effect.

This is not quite what I see in my data.

For the average of 6 analyses measured at 15 kV, 30 nA, 5 micron beam-diameter in Lipari obsidian (Kuehn et al. 2011),
a linear model for time-dependent-intensity corrections (40 s on peak, divided into 8 interval points)
yielded the following mean values for Na2O (wt%), with standard deviations of the last decimal points given in parentheses:

Time-weighting factor     Na2O (wt%) none                             3.54(9) 1                                  3.54(9) 2                                  3.66(10) 3                                  3.72(9) 4                                  3.76(10) 5                                  3.79(11) 6                                  3.82(11) 7                                  3.84(11) 8                                  3.89(11) 9                                  3.90(11) 10                                3.91(11) It appears to me that if I specify a weighting value larger than the number of interval points, there is still a perceptible effect. In this case, the resultant concentration of Na2O in wt% follows a power-law curve of the form: f(x) = 3.5442 x0.0429 with R2 = 0.995. Thanks, Andrew

[John Donovan]

quote author=John Donovan link=topic=116.msg12569#msg12569 date=1713459766]

Basically, for each of the measured TDI intensities, a weighting factor is calculated (default = 1), and when the points are added to the regression array, they are weighted according to the code above.
If you specify a weighting value larger than the number of points you have, there is basically no effect.

This is not quite what I see in my data.

For the average of 6 analyses measured at 15 kV, 30 nA, 5 micron beam-diameter in Lipari obsidian (Kuehn et al. 2011),
a linear model for time-dependent-intensity corrections (40 s on peak, divided into 8 interval points)
yielded the following mean values for Na2O (wt%), with standard deviations of the last decimal points given in parentheses:

Time-weighting factor     Na2O (wt%) none                             3.54(9) 1                                  3.54(9) 2                                  3.66(10) 3                                  3.72(9) 4                                  3.76(10) 5                                  3.79(11) 6                                  3.82(11) 7                                  3.84(11) 8                                  3.89(11) 9                                  3.90(11) 10                                3.91(11) It appears to me that if I specify a weighting value larger than the number of interval points, there is still a perceptible effect. In this case, the resultant concentration of Na2O in wt% follows a power-law curve of the form: f(x) = 3.5442 x0.0429 with R2 = 0.995. Thanks, Andrew

Yeah, you are correct.

It still adds points to the regression even when the value exceeds the number of actual TDI intervals, but it's a small effect, which is why I said *basically* no effect!   

[John Donovan]

A user recently asked me how they could export TDI intensities from Probe for EPMA.  The issue being that the "User Specified Output Format" described here:

https://probesoftware.com/smf/index.php?topic=11.msg8327#msg8327

requires quantification of the sample, which means that one needs a primary standard for each element (they were applying the TDI correction to "flank" measurements and did not acquire any primary standard intensities).  This is because the TDI correction is generally not applied to the net intensities until the sample is quantified.  So if a primary standard is not available to obtain the TDI parameters, one must be utilize another output method.

Here are some other alternative output methods for TDI parameters and intensities:

1. One can view the TDI intensity data in Run | Display Time Dependent (TDI) and Alternating Intensities menu dialog. There is an export button that can be utilized for specific data points:

https://probesoftware.com/smf/index.php?topic=40.msg3970#msg3970

2. Another option is the Output | Save Time Dependent Intensities (TDI) menu, which outputs data for all samples and does not require quantification as seen here after exporting to Excel:



3. The extrapolated TDI intensities are also available in the output to the log window in the line labeled "TDII:" as seen here:

ELEM:       Na      Si       K      Al      Mg      Ca      Ti      Mn      Fe       P      Cr       O       H
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC    SPEC
BGDS:      MAN     MAN     LIN     MAN     MAN     MAN     LIN     LIN     MAN     EXP     LIN
TIME:    80.00   30.00   40.00   39.89   60.00   80.00   20.00   20.00   60.00   60.00   30.00     ---     ---
BEAM:    19.81   19.81   19.81   19.81   19.81   19.81   19.81   19.81   19.81   19.81   19.81     ---     ---

ELEM:       Na      Si       K      Al      Mg      Ca      Ti      Mn      Fe       P      Cr       O       H   SUM 
   342   1.419  25.341    .286   6.681   4.361   7.556   1.383    .146   7.345    .106    .030  44.476    .000  99.131
   343   1.408  25.413    .275   6.684   4.416   7.831   1.391    .163   7.241    .103    .039  44.681    .000  99.645
   344   1.434  25.235    .276   6.624   4.404   7.614   1.477    .137   7.321    .113    .032  44.423    .000  99.091
   345   1.404  25.362    .271   6.672   4.413   7.456   1.401    .119   7.385    .100    .035  44.489    .000  99.107
   346   1.446  25.267    .293   6.637   4.351   7.443   1.419    .141   7.266    .112    .036  44.323    .000  98.734
   347   1.428  25.327    .274   6.618   4.384   7.415   1.400    .136   7.226    .115    .030  44.349    .000  98.702

AVER:    1.423  25.324    .280   6.653   4.388   7.552   1.412    .140   7.297    .108    .034  44.457    .000  99.068
SDEV:     .016    .064    .008    .030    .028    .156    .034    .014    .063    .006    .004    .128    .000    .342
SERR:     .007    .026    .003    .012    .011    .064    .014    .006    .026    .002    .001    .052    .000
%RSD:     1.14     .25    3.02     .45     .63    2.06    2.43   10.28     .86    5.62   10.64     .29     .00
STDS:      336     162     374     336     162     162      22      25     162     285     396     ---     ---

STKF:    .0735   .2018   .1132   .1333   .0568   .1027   .5547   .7341   .0950   .1601   .3060     ---     ---
STCT:   2517.2  9998.0  5418.2  8306.2  2850.6   337.0  6456.1 14052.2   600.2  9597.6  5218.6     ---     ---

UNKF:    .0071   .1991   .0025   .0483   .0288   .0698   .0120   .0012   .0617   .0008   .0003     ---     ---
UNCT:    243.9  9862.2   121.1  3009.2  1445.9   229.1   139.7    22.4   389.6    46.1     5.0     ---     ---
UNBG:     11.0    11.1    30.1    28.2    19.0     1.4     7.1    17.9     7.6    36.1    13.2     ---     ---

ZCOR:   1.9968  1.2720  1.1050  1.3779  1.5231  1.0817  1.1763  1.2009  1.1830  1.4108  1.1559     ---     ---
KRAW:    .0969   .9864   .0224   .3623   .5072   .6798   .0216   .0016   .6490   .0048   .0010     ---     ---
PKBG:    23.27  889.29    5.05  107.85   77.23  163.72   21.15    2.25   52.52    2.28    1.38     ---     ---
INT%:     ----    ----    ----    ----    -.15    ----    ----    ----     .00    ----    ----     ---     ---

TDI%:    5.145    .038    .000    .222    .000    .434   -.063    .000    .000    .000    .000     ---     ---
DEV%:       .4      .1      .0      .1      .0      .4     1.0      .0      .0      .0      .0     ---     ---
TDIF:  LOG-LIN LOG-LIN    ---- LOG-LIN    ---- LOG-LIN LOG-LIN    ----    ----    ----    ----     ---     ---
TDIT:    99.17   49.67     .00   58.33     .00   98.50   37.67     .00     .00     .00     .00     ---     ---
TDII:     254.   9873.    ----   3037.    ----    230.    146.    ----    ----    ----    ----     ---     ---
TDIL:     5.54    9.20    ----    8.02    ----    5.44    4.99    ----    ----    ----    ----     ---     ---

But this requires a primary standard!

4. The intensity intercepts can also be seen from the Standard Assignments window when plotting the TDI intensities as seen here:



Note that there is much discussion on these issues also in this topic:

https://probesoftware.com/smf/index.php?topic=11.msg9000#msg9000