sample analysis design – step 2 – calibration/standard...
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Sample Analysis Design Step 2 Calibration/Standard Preparation
Choice of calibration method dependent upon several factors:
1. potential matrix effects
2. number of samples
3. consistency of matrix across samples
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Sample Analysis Design Step 2 Calibration/Standard Preparation
EXTERNAL CALIBRATION: Prepare a set of standard solutions to cover the
expected range of analyte concentrations
Fit a least squares regression line
y = mx + b
and calculate analyte concentration in unknowns
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Sample Analysis Design Step 2 Calibration/Standard Preparation
23Na calib curve (Medium resolution)
y = 17557xR2 = 0.9992
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conc ppb
cps
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Sample Analysis Design Step 2 Calibration/Standard Preparation
44Ca calib curve (Medium resolution)
y = 676.92xR2 = 0.9961
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conc ppb
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Sample Analysis Design Step 2 Calibration/Standard Preparation
Advantages of External Calibration
Easy to prepare
Quick
Widely used technique
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Sample Analysis Design Step 2 Calibration/Standard Preparation Disadvantages of External Calibration:
Need to matrix match calibration solutions and samples
If standards containing
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Sample Analysis Design Step 2 Calibration/Standard Preparation Preparation of External Calibration Solutions:
Need to evenly space calibration concentrations
If the highest concentration is much higher than the rest, linear regression introduces bias favoring the high point
X = independent variable = concentration
Y = dependent variable = counts/second
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Sample Analysis Design Standard Addition Method
Aliquots of spike are added to unknown samples to increase the ion signal intensities for elements of interest
Typically use at least three aliquots of sample spiked with evenly spaced amounts of analyte
These spiked aliquots of sample are used to generate a calibration line and calculate the concentration in the sample
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Sample Analysis Design Standard Addition Method
S0 = unspiked sample
S1 = sample spiked with analyte at concentration x
S2 = sample spiked with analyte at concentration 2x
S3 = sample spiked with analyte at concentration 3x
S4 = so on and so on
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Sample Analysis Design Standard Addition Method
AMT
y = 29387x + 279235R2 = 0.9992
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Concentration (ppb)
Cps
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Sample Analysis Design Standard Addition Method
The concentration of the unknown solution is then determined by dividing the y-intercept value by the slope of the sample-spike mixing line.
From example on previous slide,
Conc. soln = 279235 / 29387 = 9.5 ppb
If the original sample was a solution, then this is the concentration of the analyte in question in the solution
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Sample Analysis Design Standard Addition Method
If the original sample was in solid form that you digested and subsequently converted into a solution;
then in order to determine the concentration of the analyte in question, you must factor in the amount of total analyte in the solution and the dry weight of the sample powder
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Sample Analysis Design Standard Addition Method
If we continue with the same example, the solution has a concentration of 9.5 ppb, and the original volume of the unknown solution was 10 ml (g) prior to aspirating some of it into the plasma for analysis, then the total amount analyte in the solution is:
= 10 g x 9.5 ng/g (ppb) = 95 ng, or = 0.095 g
If the amount of powder weighed out was 0.1 g, then the concentration of the element in question is:
Conc. = 0.095 g/0.1 g = 0.95 g/g or ppm
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Sample Analysis Design Standard Addition Method
This method works best if the slope of the calibration line is not too shallow
This will create more uncertainty in the location of the intersection between the cps of your unknown and the calibration line
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Sample Analysis Design Standard Addition Method
For maximum precision its necessary that the amount of sample be the same in each aliquot
Also want the amount of spike added to be the same for each aliquot
Amount of spike added should be as small as possible (usually 0.1 ml to 10 ml total volume)
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Sample Analysis Design Standard Addition Method
Ideally, the highest spike concentration should be approximately equal to the concentration of analyte in the unknown
Need to have some idea of the concentration in the sample prior to analysis
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Sample Analysis Design Standard Addition Method
Advantages:
Overcomes matrix differences More precise and accurate than external calibration
Disadvantages:
Requires at least three aliquots for each sample Run lengths become much longer and more
preparation time is required
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Sample Analysis Design Isotope Dilution
Most accurate and precise calibration method available
Requires analyte with two stable isotopes
Monoisotopic elements cannot be determined via isotope dilution
Spike natural sample with enriched isotope spike of analyte
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Sample Analysis Design Isotope Dilution
The amount of spike is selected so that the resulting ratio between spiked isotope and unspiked isotope is near unity maximizes precision
Typically use the most abundant isotope as the reference -- maximizes sensitivity
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Sample Analysis Design Isotope Dilution
Check isotope ratio in unspiked sample to determine if the natural ratio in the sample matches with the predicted ratio
If not -- interference in acting on one or both of the isotopes
Always attempt to use interference free isotopes
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Sample Analysis Design Isotope Dilution
Prepare the spike to desired concentration
Add spike as early as possible after equilibration of spike and sample you dont have to have complete sample recovery
During any stage of the process complete equilibration is absolutely necessary
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Sample Analysis Design Isotope Dilution
Analyze the solution on the ICP using many repetitive scans (to maximize precision)
Need to measure isotopic ratios on standards of a known ratio in order to correct for machine mass discrimination
Use previous equation to calculate concentrations!
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Sample Analysis Design Isotope Dilution
Advantages:
Most accurate and precise method for quantitative elemental concentrations
Partial loss of analyte during preparation is compensated for since physical and chemical interferences are not an issue -- will cancel out as they will affect each isotope identically
Ideal form of internal standardization since another isotope of the same element is used in this capacity
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Sample Analysis Design Isotope Dilution
Disadvantages:
Generally only applicable to multiple-isotopic elements
Need an enriched isotope spike for the analyte of interest - not always available or sometimes at very high cost
Need two interference free isotopes VERY time consuming
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Sample Analysis Design
STEP 3 INTERNAL STANDARDIZATION & INSTRUMENT
DRIFT CORRECTION
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Sample Analysis Design Internal Standard
Every sample should be analyzed with an internal standard (IS)
What is an internal standard (IS)?
element that is added to EVERY sample/ blank/calibration standard/QA sample/etc., that is not expected to be in the sample in appreciable quantities and is not an element of interest
use IS to monitor machine drift (both short and long term) and matrix effects
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Sample Analysis Design Internal Standard
Choice of IS depends upon which elements you are quantifying
The IS should have similar properties in the plasma as element(s) of interest
ICP-MS: similar in mass/ionization potential
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Sample Analysis Design Internal Standard
Example:
attempting to quantify U - use Th
attempting to quantify most transition metals - use As
attempting to quantify REEs - use Re
115In and 103Rh are common IS for general use
alternatively, you can add several IS to each sample
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Sample Analysis Design Internal Standard
From previous slide, we assume that samples have little or no Th, As, or Re
Its important to have an idea of whats in your sample prior to quantitative analysis
Solid samples can use a naturally occurring element as IS, provided that you know the concentration in each sample
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Sample Analysis Design Internal Standard
Procedure for IS use:
Calculate the concentration of the IS in each centrifuge tube the latter will contain an aliquot of your sample and an aliquot of the IS
Divide the measured ion signal (CPS) by the concentration of your IS to derive the factor = CPS/ppb
Divide CPS/ppb of each tube by the CPS/ppb for those measured for the blanks since these are not influenced by possible effects due to sample matrices
The latter yields a dimensionless correction factor (I refer to it as a normalization factor)
Use correction factor to adjust analyte counts for drift or matrix effects
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Sample Analysis Design Internal Standard
Advantages:
Fluctuations are monitored in each sample/ calibration / blank
Disadvantages:
Assume that behavior of IS is the same as the analyte
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Sample Analysis Design Instrumental Drift
Correct for instrument drift with:
Internal standardization is a common procedure
Use of drift corrector solutions (DCS)
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Sample Analysis Design Instrumental Drift
Drift Corrector Solutions (DCS):
Measure the same solution intermittently throughout the course of the analytical session
Change in ion signal is assumed to be linear between each DCS measurement
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Sample Analysis Design Instrumental Drift
The DCS should contain all elements of interest and can be matrix matched to samples
Example: use standard reference materials (SRMs) for DCS
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Sample Analysis Design Instrumental Drift
Apply a linear correction to samples between DCS solutions
DCS1 + ((DCS2 - DCS1)*F)
F = position dependent fraction
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Sample Analysis Design Instrumental Drift
Advantages of DCS correction:
all analytes are monitored for drift
nothing added to sample solutions
Disadvantages of DCS correction:
assume change is linear
cannot easily monitor matrix effects
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Sample Analysis Design Background & blanks
Standard blank - blank used to monitor polyatomic ion interferences, gas peaks, and contamination from reagents; used for background subtraction
Procedural blank - blank used to monitor contamination acquired during all stages of sample preparation; grinding, digestion, acidification, powdering, etc
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Sample Analysis Design Background & blanks
Use of blanks during an analytical session:
ALWAYS begin an analytical session with at least one standard blank
Analyze standard blanks periodically throughout the course of the session in particular to monitor memory effects
Process and analyze at least one procedural blank at some point during your research study; for its analysis, its preferable to measure it early in order to avoid any potential memory effects
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Sample Analysis Design Background & blanks
The more standard blanks that are run during an analytical session, the more information you will have with regards to monitoring change(s) in background levels throughout the entire session
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Sample Analysis Design Background & blanks
How to determine the background:
1. just use the first standard blank
2. average all standard blanks
3. take median of all standard blanks
4. apply statistical analysis to standard blanks and select some of them
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Sample Analysis Design Background & blanks
Outlier tests:
1. I know the truth
2. Looks different
3. Statistical proof
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Sample Analysis Design Background & blanks
Option 1 should be avoided - unscientific and invalid
Option 2 is better but only if the measurement is repeated
Option 3 is the best approach, but needs to be carried out carefully in order to avoid false negatives and positives
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Sample Analysis Design Background & blanks
Huber Outlier Test
take median of all values
calculate absolute deviation |xi - xm|
take mean of absolute deviations (MAD)
multiply MAD by coefficient (k = 3-5)
anything higher than k*MAD is rejected as outlier
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Sample Analysis Design Background & blanks
Calculation of Limit of Detection (DL) and Limit of Quantification (QL)
Easy way: LOD = 3*STDEVblank; LOQ = 10*STDEVblank
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Sample Analysis Design SUMMARY
A good analytical method will:
1. provide the means to calculate an accurate background level
2. allow for correction of instrument drift
3. use Internal standardization to monitor matrix effects
4. provide some method for monitoring/ correcting interferences
5. Use a proper calibration strategy
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Example Calculation Determination of Ca and Na in
beetle blood
Using External Calibration Method