# Relative Crystallinity Calculation of X-Ray Diffraction Pattern of Starch by Bruckner Method

### Description

Allow to calculate the relative crystallinity of starch by XRD. The basic concept of Bruckner approach involves obtaining a smoothed line that separates the amorphous and crystalline starch of an X-ray diffraction pattern. This smoothed line is achieved by applying a moving average smoothing method to the original pattern.

### Usage

1 | ```
crystMW(pattern, N = 41, iter = 100)
``` |

### Arguments

`pattern` |
matrix. The matrix of X-ray diffraction pattern. The first row corresponds to Bragg angle 2 |

`N` |
numeric. N length of the smoothing window (number of variables). Defaults to 41. |

`iter` |
numeric. Iter number of iterations. Defaults to 100. |

### Details

Calculate the relative starch crystallinity of XRD pattern by Bruckner method.

### Value

An object of class crystMW, which is a list with the following components:

`original` |
Original matrix of X-ray diffraction patterns. |

`background` |
Estimation of the background shape (curve of the amorphous starch). |

`corrected` |
Estimation of residual crystalline area (curve of the crystalline starch). |

`summary` |
Summary calculation of crystallinity. Total area under the curve of the diffraction pattern (A.U.); Amorphous area (A.U.); Crystalline area (A.U.); Relative crystallinity (%). |

### Author(s)

Claudio Pozo Valenzuela [aut, cre] and Saddys Rodriguez-llamazares [aut]

### References

Bruckner, S. (2000). "Estimation of the background in powder diffraction patterns through a robust smoothing procedure." Journal of Applied Crystallography 33(3 Part 2): 977-979.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
data(XRD)
# Convert data frame to matrix, select A-type starch
pattern <- as.matrix(t(XRD[,c("Bragg_angle","A")]))
# List of crystallinity components
crs <- crystMW(pattern, N = 41, iter = 100)
# Original matrix
original <- crs$original
# Background shape
background <- crs$background
# Curve of the crystalline starch
corrected <- crs$corrected
# Summary calculation of crystallinity
summary <- crs$summary
``` |

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