Your calibration is statistical; you are fitting a curve to a series of calibration points. It has error associated with the curve. When you get down to a low enough concentration, and you have calibrated correctly, then you can, statistically, get negative numbers. This is normal; in fact, any decent auditor would applaud you for doing your job correctly. As long as you are not getting large negative numbers then the data is telling you that the element(s) you are measuring are not present at your detection limit. This is also why you determine, and use, a lower limit of detection (LOD) and a lower limit of quantification (LOQ). These indicate the point at which your calibration is no longer valid; you shouldn't report values below your LOD.

Tharanga, it is simply indicating your samples are having the content below the detection limit of the Instrument for particular element. 

How about the value of your calibration point. Most probably your calibration zero value may read significant amount of analyte, what kind of water and acid you used?

If you have those value, we can think the reasons.

It is the calibration. Look back at the standards used and run a test again.

Definitively a calibration error. It could be anything from being below your calibration range to erroneous standards. A basic QC program would indeed help you solve your troubles.

The reason is with your calibration standards particularly the zero (blank) standard. It shows in your blank there are significant amount of analyte detected but you tell the instrument to consider this signal as equivalent to zero concentration. Any  signal in the sample less than the zero signal will be assigned a negative value. Check how you prepare your standards.

For me, i use the samples (who i know the level of metal) for calibration curve : i spike the samples by each concentration. Then, for the zero , i use the sample without spiking, for the point 1, i add the concentration in the sample, etc.

trouble is in your calibration curve. If you use calibration curve as a C=A+Bx, where x is your measured value, A is negative and x is very small, than A is significant. You must change computing of calibration curve or change calibration levels

If your calicration curve is C = A + Bx, where C is the measured signal for your sample(s) and x is its concentration value. We can calculate the "x" from the equation, x = (C - A) / B; there are two alternative for the computation, (1) if A has a negative sign, in that case, x will always be positive, (2) if A has a positive sign, and C is higher than A, you will get positive concentration values, otherwise, if it is C < A, you will get always concentration values with negative sign. Consequently, your samples have low analyte concentrations which are lower than the quantication limit value. Check your calibration standards again, and your intercept values for the calibration curves should be "zero" or near the zero.      

Some other considerations:

(1) the different acid concentrations may lead to different transport efficiencies between Ca and Mn, also (2) don't forget that Ca is somewhat more easily ionized than Mn. Just things you might include in addition the many helpful fundamental tips provided by other comments/answers here in this forum.

Two potentially useful publications I have seen and you could google are:

"Transient acid effects in inductively coupled plasma optical emission spectrometry and inductively coupled plasma mass spectrometry"

and

"Matrix effects in inductively coupled plasma mass spectrometry: a review"

Thanks All, I'll check the blanks again!

Hi. My experience in atomic absorption, I think it could be many causes of error. I start working with a single element, a straight properly calibrated and checking instrumental parameters of your spectrometer. After that, check the preparation conditions of your samples, sample weith, final dilution, purity water and reagents, etc.  And of course be sure to properly handle the instrumental software.

 I think it could be as a result of sample preparation or instrumental parameters as well as the software you are using. Please check well and reanalyze your sample.

It could be as a result of calibration. In calibration, the line of best fit may have a positive intercept greater than Absorbance value in the form: Abs= slope x Conc + Intercept. An atttempt to calculate Conc from above equation gives the equation: Conc = (Abs - Intercept)/slope. Once the intercept is always greater than the Absorbance, the numerator will always be negative against the positive slope. So check with your calibration.

What is the matrix of your samples? and how closely does this match your standards?

First, I would advise you to make more calibration standards,  Three standards are a minimum, and the standards should bracket the expected concentration of your samples, so if you expect 0.1 ppm Mn in your sample you should be calibrating below 0.1 ppm and above 0.1 ppm.  

You mention you are also using AA? in the ppm range I assume Flame AA? if you are doing Ca using flame AA you might want to add a little lithium to your standards and samples as an ionization suppression.

Third, if you still haven't found a suitable solution, and you know that you do have Ca and Mn in your samples, use the Method of Standard Addition - it's tedious, but quite precise.  Feel free to message me privately if you have specific questions.

Dear Tharanga Udagedara, 

I suggest you to check the matrix effect and the quantification limit (QL). I recommend you that the first point of your analytical curve must be the QL.

My best regards,

Hi Senol Kartal,

Is it right if A is negative? How if A and C are both negative?. Sometime the blanks give negative absorbances when the intercept is close to zero.  Checking the parameters of the instrument and spiking samples could help solve the problem.  

Dear Yao,

In a calibration curve (C = A + Bx), where C is the measured signal for your sample(s) and x is its concentration value (x = (C - A) / B), the intercept A has possibly three numerical values; 

1) A > 0, in this case, if C is higher than A, x has positive value, otherwise it has negative sign.  

2) A = 0 (ideal), if C is higher than A, x has positive value, otherwise it has negative sign.

3) A< 0, if C is higher than A, x has positive value, otherwise it has negative sign.

This is true mathematically.

Negative absorbances can also been get as related intrumental errors, sample matrix, non-matching calibration standards etc. In that case, errors must be corrected by taking into consideration all of these problems.

The negative results could be from several reasons:

1. Incomplete extraction: this results in lower concentrations in the digested solutions to be measured. Please check with harsher conditions for digestion such as increasing time, temperature, stronger oxidizing reagents.

2. Matrix effects: normally the matrix depresses signal in AAS as well as in ICP (even though ICP provides high temperature plasma). This could be overcome be matrix-matching standards such as method of addition.

The type of calibration curves and the inappropriate zeroing could be reasons.

what is the source of your samples? It could be that your samples need to be pre-concentrated if  there was no treatment done to them. If you have digested them before then may be the extraction was incomplete that amounts released are below detection limits of your instruments 

Negative values usually produced as a result of calibration errors Redo the calibration and see. 

Hey, everyone. Would anyone have a remedy to deal with the negatives if redoing the calibration doesn't work?

I suggest you run several standards in between  samples to ascertain where actually the negative sign may be coming from because you may have ran five point calibration and still have negative value for a sample

For ICP I also got the same "negative values"and the person who run the ICP told me it might be less than the standards so I am also confused if I can assume these values to be zero or not ? 

For ICP-OES, in water matrix I got blank value more than the sample value. But ideally we run blank sample for the reference or we deduct the blank value from the sample value for the results. How it can be expained?

I face also the same problem with negative concentration of Pb in AAS but my standard solution curve is okay it’s absorbance is also positive, I don’t no why my concentration were negative. Please any one who help me to solve this problem.

Remedon Musa increase the measurement and read delay times

Your calibration is statistical; you are fitting a curve to a series of calibration points. It has error associated with the curve. When you get down to a low enough concentration, and you have calibrated correctly, then you can, statistically, get negative numbers. This is normal; in fact, any decent auditor would applaud you for doing your job correctly. As long as you are not getting large negative numbers then the data is telling you that the element(s) you are measuring are not present at your detection limit. This is also why you determine, and use, a lower limit of detection (LOD) and a lower limit of quantification (LOQ). These indicate the point at which your calibration is no longer valid; you shouldn't report values below your LOD.

In analytical chemistry, there is no such thing as zero. As M. Krause pointed out, you must determine an LOD (typically 3 sigma) and report your results as "

If your calibration curve is not passing through the origin or the blank shows some counts, then there is a chance for the unknowns(low concentrated or having no analyte in the sample) to give negative results if the blank is different or use different volume/weight of blank to make up the samples.