Correction apparatus, system, method, and program
A correction apparatus for correcting a structure factor includes a structure factor acquisition section that acquires the structure factor; a PDF calculation section that calculates PDF from the acquired structure factor; a correction function preparation section that prepares a first correction function that is Fourier-transformed in a predetermined range, and a second correction function that is Fourier-transformed in the predetermined range, the first correction function comprising data of the PDF and a cut-off function for cutting off data on a long distance side of the PDF and the second correction function comprising the cut-off function; a correction amount calculation section that calculates a correction amount comprising the first correction function, the second correction function, and a scale factor; a structure factor correction section that corrects the structure factor; and an R-factor value calculation section that calculates an R-factor value indicating correction accuracy.
1 . A correction apparatus for correcting a structure factor, the correction apparatus comprising:
processing circuitry configured to acquire the structure factor calculated based on a total scattering data measured by an X-ray diffractometer;
calculate PDF (Pair Distribution Function) from the acquired structure factor;
calculate a first correction function and a second correction function, the first correction function includes a product of the PDF data and a cut-off function and is a function Fourier-transformed within a predetermined range, and the second correction function includes a product of a variable representing the distance of the PDF and the cut-off function and is a function Fourier-transformed within the predetermined range, the cut-off function is a function that cuts off the long distance data of the PDF data, with the range equal to or greater than a constant determined based on the first peak position r 1st of the PDF as the long distance side;
calculate density based on the first correction function and the second correction function;
calculate a correction amount comprising the first correction function, the second correction function, and the density, the correction amount includes a difference between a product of the second correction function and the calculated density and the first correction function;
correct the structure factor using the correction amount, the correction of the structure factor is performed by adding or subtracting the amount of correction to the structure factor before correction and calculating the structure factor after correction; and
calculate an R-factor value indicating correction accuracy, the R-factor value comprising the first correction function and the second correction function.
2 . The correction apparatus according to claim 1 ,
wherein the R-factor value indicates a change rate of the density.
3 . The correction apparatus according to claim 2 , wherein the processing circuitry is further configured to
calculate a ratio at which a constraint term is weighted,
calculate the constraint term based on a value of each of the first correction function and the second correction function in a limited range;
wherein the density comprises a product of the constraint term and the ratio; and
wherein the ratio increases or decreases according to increase/decrease of the R-factor value.
4 . The correction apparatus according to claim 1 , wherein the processing circuitry is further configured to determine a first peak position r 1st of the PDF,
wherein the predetermined range is from 0 to r 1st .
5 . The correction apparatus according to claim 1 ,
wherein the cut-off function is a monotone decreasing function taking a value of from 1 to 0 in a domain of the cut-off function.
6 . The correction apparatus according to claim 1 , wherein the processing circuitry is further configured to calculate the structure factor based on a type of a radiation source, a wavelength, a shape of a sample, arrangement, kinds of constituent elements, a composition and an absorption coefficient in total scattering data by acquiring the total scattering data of the sample, and
acquire the calculated structure factor.
7 . A system comprising:
an X-ray diffractometer comprising an X-ray generator that generates X-rays, a detector that detects the X-rays, and a goniometer; and
a correction apparatus for correcting a structure factor, the correction apparatus including processing circuitry configured to
acquire the structure factor calculated based on a total scattering data measured by the X-ray diffractometer;
calculate PDF (Pair Distribution Function) from the acquired structure factor;
calculate a first correction function and a second correction function, the first correction function includes a product of the PDF data and a cut-off function and is a function Fourier-transformed within a predetermined range, and the second correction function includes a product of a variable representing the distance of the PDF and the cut-off function and is a function Fourier-transformed within the predetermined range, the cut-off function is a function that cuts off the long distance data of the PDF data, with the range equal to or greater than a constant determined based on the first peak position first of the PDF as the long distance side;
calculate density based on the first correction function and the second correction function;
calculate a correction amount comprising the first correction function, the second correction function, and the density;
correct the structure factor using the correction amount, the correction of the structure factor is performed by adding or subtracting the amount of correction to the structure factor before correction and calculating the structure factor after correction; and
calculate an R-factor value indicating correction accuracy, the R-factor value comprising the first correction function and the second correction function.
8 . A method for correcting a structure factor, the method comprising:
acquiring the structure factor calculated based on a total scattering data measured by an X-ray diffractometer;
calculating PDF (Pair Distribution Function) from the acquired structure factor;
calculating a first correction function, and a second correction function, the first correction function includes a product of the PDF data and a cut-off function and is a function Fourier-transformed within a predetermined range, and the second correction function includes a product of a variable representing the distance of the PDF and the cut-off function and is a function Fourier-transformed within the predetermined range, the cut-off function is a function that cuts off the long distance data of the PDF data, with the range equal to or greater than a constant determined based on the first peak position r 1st of the PDF as the long distance side;
calculating density based on the first correction function and the second correction function;
calculating a correction amount comprising the first correction function, the second correction function, and the density, the correction amount includes a difference between a product of the second correction function and the calculated density and the first correction function;
correcting the structure factor using the correction amount, the correction of the structure factor is performed by adding or subtracting the amount of correction to the structure factor before correction and calculating the structure factor after correction; and
calculating an R-factor value indicating correction accuracy, the R-factor value comprising the first correction function and the second correction function.
9 . A non-transitory computer-readable storage medium storing computer-readable instructions thereon which, when executed by a computer, cause the computer to perform a method, the method comprising:
acquiring the structure factor calculated based on a total scattering data measured by an X-ray diffractometer;
calculating PDF (Pair Distribution Function) from the acquired structure factor;
calculating a first correction function, and a second correction function, the first correction function includes a product of the PDF data and a cut-off function and is a function Fourier-transformed within a predetermined range, and the second correction function includes a product of a variable representing the distance of the PDF and the cut-off function and is a function Fourier-transformed within the predetermined range, the cut-off function is a function that cuts off the long distance data of the PDF data, with the range equal to or greater than a constant determined based on the first peak position first of the PDF as the long distance side;
calculating density based on the first correction function and the second correction function;
calculating a correction amount comprising the first correction function, the second correction function, and the density, the correction amount includes a difference between a product of the second correction function and the calculated density and the first correction function;
correcting the structure factor using the correction amount, the correction of the structure factor is performed by adding or subtracting the amount of correction to the structure factor before correction and calculating the structure factor after correction; and
calculating an R-factor value indicating correction accuracy, the R-factor value comprising the first correction function and the second correction function.