Generally v is negative initially but what it should be after fitting. what does a negative sign or positive sign of u,v,w mean ?
You likely refer to the Caglioti description describing either the total FWHM or the Gaussian contribution to it (Thompson-Cox-Hastings). The formual is of the type
FWHM^2 = U tan^2theta + V tantheta + W. Hence, to work properly, precondition is that FWHM^2 should not be negative at any theta, in principle, since the Calglioti function is acutally largely emprical.
But for certain situations physical meaning can be attributed to the overall U, V, W values or to contributions. E.g. simple microstrain broadening and wavelength disperision will increase U whereas size broadening will increase U and W in combination. It is more difficult to assign a meaning to V. This will make them positive. Typical behavior should be positive U and W and negative V (but not too negative). This was also deduced to be appropriate from early neutron diffraction studies with the line profiles available at those times. Nowadays, the Calglioti function is, however, used in very different ways to describe different things (e.g. only the instrumental broadening), such that I would not make general statements that in all cases U/W must be positve and V must be negative.
You likely refer to the Caglioti description describing either the total FWHM or the Gaussian contribution to it (Thompson-Cox-Hastings). The formual is of the type
FWHM^2 = U tan^2theta + V tantheta + W. Hence, to work properly, precondition is that FWHM^2 should not be negative at any theta, in principle, since the Calglioti function is acutally largely emprical.
But for certain situations physical meaning can be attributed to the overall U, V, W values or to contributions. E.g. simple microstrain broadening and wavelength disperision will increase U whereas size broadening will increase U and W in combination. It is more difficult to assign a meaning to V. This will make them positive. Typical behavior should be positive U and W and negative V (but not too negative). This was also deduced to be appropriate from early neutron diffraction studies with the line profiles available at those times. Nowadays, the Calglioti function is, however, used in very different ways to describe different things (e.g. only the instrumental broadening), such that I would not make general statements that in all cases U/W must be positve and V must be negative.
In most cases I dealt with, the V parameter was negative. However, in principle, every parameter of the Caglioti function can be negative, provided that the set (U, V, W) of these parameters gives a close approximation of the FWHM variation over the whole 2Theta range of interest.
Vasyl, if every parameter U, V, and W are negative, that cannot be. But if you mean any one or two of U, V and W can be negative, provided that they give a FWHM^2 > 0, then it is ok. If you mean the latter, then Yes I agree.
w.s.l., I agree with your note. However, as the original question was "Which... parameters... should be negative?", I wrote that every one CAN be, which is seemingly correct. Furthermore, the condition "provided that the set (U, V, W) of these parameters gives a close approximation of the FWHM variation..." automatically rejects the case where all three Caglioti parameters are negative. Best wishes!
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