Fcal-n.js - structure factor calculator for neutron - ver. -----

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Crystal structure
Load cif file:

Space group:
a = Å, b = Å, c = Å,
α = deg, β = deg, γ = deg.

Label Symbol x y z Occ. iso bc Show Color


  • The coherent scattering lengths, bc, are taken from Neutron scattering lengths and cross sections (https://www.ncnr.nist.gov/resources/n-lengths/), and are not changeable in the textboxes above.
  • If there are textboxes showing "NaN", please input appropreate numbers manually, and click "Update parameters" button.
  • Number of independent atoms is up to 20.
  • Some of the textboxes are not editable. This means that the parameters in these boxes are not allowed to change. See the [Nuc. Str. Factors]->[Str. Analysis(SC)] tab for details on the constraints for the xyz coordinates.
Unit cell viewer

Hor. angle: Vert. angle:
Distance: Scale:
All atomic positions
All symmetry operations
Uij = U11U12U13
U21U22U23
U31U32U33




















HKL input

[Ex.) 1 1 0 (separated by space(s))]


Conditions
: Qmax = Å-1
: 2θmax = deg, Ei= meV
: 2θmax = deg, λi= Å

Results



Download the calculated structure factors as a text file.

Definitions
  • Q : Length of the scattering vector. \(|\boldsymbol{Q}|=|\boldsymbol{k}_i-\boldsymbol{k}_f|=2\pi/d_{hkl}\)
  • 2th : Scattering angle, 2θ.
  • Lorentz : Lorentz factor for ω or θ-2θ scans for a single crystal. \(\lambda^3/\sin2\theta\)
  • Ical : Integrated intensity of the Bragg peak at (H,K,L). \(|F_{cal}|^2\lambda^3/\sin2\theta\)
  • |Fcal| : Nuclear structure factor, \(|F_{cal}| = |\sum_jg_jb_jT_j\exp(-i\boldsymbol{Q}_{hkl}\cdot \boldsymbol{d}_j)| \)
    • \(g_j\) : Occupancy of the jth atom.
    • \(b_j\) : Scattering length of the jth atom.
    • \(\boldsymbol{Q}_{hkl}\) : Scattering vector for the Bragg reflection at (H,K,L), \(\boldsymbol{Q}_{hkl}=H\boldsymbol{a}^*+K\boldsymbol{b}^*+L\boldsymbol{c}^*\).
    • \(\boldsymbol{d}_j\) : Fractional coordinate for the jth atom. \(\boldsymbol{d}_j=x_j\boldsymbol{a}+y_j\boldsymbol{b}+z_j\boldsymbol{c}\).
    • \(T_j\) : Atomic dispacement factor (Debye-Waller factor).
      • Biso : \(T_j=\exp(-B_j(\sin\theta/\lambda)^2)\).
      • Uiso : \(T_j=\exp(-8\pi^2U_j(\sin\theta/\lambda)^2)\).
      • Uaniso : \(T_j=\exp(-\frac{1}{2}(U_{j11}H^2|a^*|^2+U_{j22}K^2|b^*|^2+U_{j33}L^2|c^*|^2+2U_{j12}HK|a^*||b^*|+2U_{j13}HL|a^*||c^*|+2U_{j23}KL|b^*||c^*|))\).
Scattering plane
  • \(\tau_1= \) (H1,K1,L1): (,,). The 1st vector to define the scattering plane.
  • \(\tau_2= \) (H2,K2,L2): (,,). The 2nd vector to define the scattering plane, and should be independent of \(\tau_1\).
  • \(\tau_{\rm ofst}= \) (Hofst,Kofst,Lofst): (,,). (Optional) The offset vector (out-of-plane direction).
Structure factors or intensities will be calculated for the points described by \(n\tau_1+m\tau_2+\tau_{\rm ofst}\) (n and m are integers).
It is also possible to use fractional numbers for Hi, Ki and Ki (i=1, 2, and ofst). However, nuclear structure factors are finite only when the actual HKL indices are integers.
Conditions
: Qmax = Å-1. (Intensities will be calculated to be \(|F_{hkl}|^2\))
: 2θmax = deg, Ei= meV. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))
: 2θmax = deg, λi= Å. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))

Intensity Map

Download the intensity map of the nuclear reflections as a png file.
Radius for the strongest reflection on the scattering plane: pixels.
Show indices.


  • Areas of the filled circles are proportional to \(|F_{hkl}|^2\) or intensities.
  • Darkblue circles show accessible reflections.
This is test.
Input data
Data type
([Option] λi= Å for extinction correction. )
(Ei= meV. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)
i= Å. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)

Option: Extinction correction (λ or Ei needs to be specified. The scattering path lengths (cm) for each reflection need to be added after Fobs_err or Iobs_err.)
  • Extinction parameter : E0=.
  • d-value of the monochromator : d=
Observed data
Load from file:

  • Paste the observed data directly into the textarea below, or use the "Load from file" option.
  • Lines starting with "#" are ignored.
Refinement
Extinction parameter E0
Overall factor for Biso or Uiso.
Label Symbol x y z Occ. iso XYZ constraint
Max iteration :


Results
Calculation log

Download fitting log as a text file.

Fcal-Fobs data

Download Fcal-Fobs data as a text file.
Fcal-Fobs plot


Scale factor =
Extinction parameter E0 =

R-factors
  • R(F)=
  • Rw(F)=
  • R(F2)=
  • χ2=
  • χ2w=

Definitions
  • Scale factor s : \(|F_{obs}|^2=s|F_{cal}|^2\) (without extinction correction).
  • Extinction correction factor Y : \(|F_{obs}|^2=sY|F_{cal}|^2\).
    • \(Y=1/\sqrt{1+P|F_{cal}|^2E_0}\).
    • \(P=2\bar{t}(1+\cos2\theta_{M}\cos^4 2\theta)/[\sin 2\theta(1+\cos 2\theta_{M}\cos^2 2\theta)]\).
    • \(\bar{t}=\lambda^3l_{sc}10^4/V^2\).
      • \(E_0\) : Extinction parameter (user input).
      • \(2\theta_M\) : Scattering angle of the monochromator.
      • \(l_{sc}\) : Scattering path length.
      • \(V\) : Volume of the unit cell.
Conditions
Incident neutron:
2θ range : 2θmin=, 2θmax=, d2θ=
Resolution
U=, V=, W= (\({\rm FWHM}=\sqrt{U\tan^2\theta+V\tan\theta+W}\))



Download calculated powder diffraction profile as a text file.
Select magnetic atoms
Label Symbol x y z Magnetic m-form
symbol
<j2>/<j0> factor status



Magnetic form factor viewer
This is just an instant viewer, and is not directly related to the magnetic structure analysis.

m-form symbol 1:, f(Q)=<j0(Q)>+ <j2(Q)>
m-form symbol 2:, f(Q)=<j0(Q)>+ <j2(Q)>
m-form symbol 3:, f(Q)=<j0(Q)>+ <j2(Q)>

Function : , Qmin: Å-1 Qmax: Å-1



Dipole approximation of magnetic form factors f(Q)
Magnetic form factor is the Fourier-transformed unpaired electron distribution (or magnetization distribution) in an atom.
The magnetic form factor can be approximately discrived by using <jK>, which is an integral containing the normalized magnetization distribution function and the spherical Bessel function of Kth order[1].
In the dipole approximation, the magnetic form factor f(Q) is described by <j0> and <j2>. This is valid when <j0> is larger than <j2>.
  • i) When \(\boldsymbol{L}\) can be replaced by \((g-2)\boldsymbol{S}\), (this is the case for 3d transition metal ions),

    \(f(Q) = \langle j_0(Q)\rangle+(1-2/g)\langle j_2(Q)\rangle \)

  • ii) When the magnetic ion is characterized by a total angular momentum \(\boldsymbol{L}\), (this is the case for rare-earth ions),

    \(f(Q) = \langle j_0(Q)\rangle+\frac{J(J+1)+L(L+1)-S(S+1)}{3J(J+1)+S(S+1)-L(L+1)}\langle j_2(Q)\rangle =\langle j_0(Q)\rangle+\frac{2-g_J}{g_J}\langle j_2(Q)\rangle, (g_J=\frac{3}{2}+\frac{S(S+1)-L(L+1)}{2J(J+1)}) \)
Reference: [1] ]"Theory of Neutron Scattering from Condensed Matter vol. 2", S. W. Lovesey (Oxford science publications).

Magnetic form factor symbols (m-form symbol)
Coefficients for analytical approximation of magnetic form factors are taken from "Tables of Form Factors (Institut Laue Langevin, France)".
[Element]
[ion]: [m-form symbol]

H He
Li Be B C N O F Ne
Na Mg Al Si P S Cl Ar
K Ca
Sc
Sc: Sc0
Sc+: Sc1
Sc2+: Sc2
Ti
Ti: Ti0
Ti+: Ti1
Ti2: Ti2
Ti3+: Ti3
V
V: V0
V+: V1
V2+: V2
V3+:V3
V4+:V4
Cr
Cr: Cr0
Cr+: Cr1
Cr2+: Cr2
Cr3+: Cr3
Cr4+: Cr4
Mn
Mn: Mn0
Mn+: Mn1
Mn2+: Mn2
Mn3+: Mn3
Mn4+: Mn4
Fe
Fe: Fe0
Fe+: Fe1
Fe2+: Fe2
Fe3+: Fe3
Fe4+: Fe4
Co
Co: Co0
Co+: Co1
Co2+: Co2
Co3+: Co3
Co4+: Co4
Ni
Ni: Ni0
Ni+: Ni1
Ni2+: Ni2
Ni3+: Ni3
Ni4+: Ni4
Cu
Cu: Cu0
Cu+: Cu1
Cu2+: Cu2
Cu3+: Cu3
Cu4+: Cu4
Zn Ga Ge As Se Br Kr
Rb Sr
Y
Y: Y0
Zr
Zr: Zr0
Zr+: Zr1
Nb
Nb: Nb0
Nb+: Nb1
Mo
Mo: Mo0
Mo+: Mo1
Tc
Tc: Tc0
Tc+: Tc1
Ru
Ru: Ru0
Ru+: Ru1
Rh
Rh: Rh0
Rh+: Rh1
Pd
Pd: Pd0
Pd+: Pd1
Ag Cd In Sn Sb Te I Xe
Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og

La
Ce
Ce2+: Ce2
Pr
Pr3+: Pr3
Nd
Nd2+: Nd2
Nd3+: Nd3
Pm
Sm
Sm2+: Sm2
Sm3+: Sm3
Eu
Eu2+: Eu2
Eu3+: Eu3
Gd
Gd2+: Gd2
Gd3+: Gd3
Tb
Tb2+: Tb2
Tb3+: Tb3
Dy
Dy2+: Dy2
Dy3+: Dy3
Ho
Ho2+: Ho2
Ho3+: Ho3
Er
Er2+: Er2
Er3+: Er3
Tm
Tm2+: Tm2
Tm3+: Tm3
Tb
Yb2+: Yb2
Yb3+: Yb3
Lu
Ac Th Pa
U
U3+: U3
U4+: U4
U5+: U5
Np
Np3+: Np3
Np4+: Np4
Np5+: Np5
Np6+: Np6
Pu
Pu3+: Pu3
Pu4+: Pu4
Pu5+: Pu5
Pu6+: Pu6
Am
Am2+: Am2
Am3+: Am3
Am4+: Am4
Am5+: Am5
Am6+: Am6
Am7+: Am7
Cm Bk Cf Es Fm Md No Lr
Notice
Magnetic atoms are not selected. Please go to "Magnetic Atoms" tab.

Magnetic unit cell
\(a\times\) \(b\times\) \(c\)
(these numbers must be integers.)
Number of bases N (magnetic is decomposed into N parts)
N= (up to 10)



Magnetic structure
Definition of the magnetic structure

The largest component of the magnetic moments is scaled to pixel (only for visualization).

Hor. angle: Vert. angle:
Distance: Scale:
Magnetic domains









Input format
In this program, magnetic structures are deconposed into a number of "bases", which are not necessarliy basis vectors deduced from symmetry arguments.
You are supposed to modify the magnetic structur by changing the amplitudes (overall multiplying factor) of each basis.
For instance, if the magentic structure consists of a ferromagnetically-arranged c-components and an antiferromagnetically-arranged a-components in a unit cell in which magnetic Fe3+ ions are located at (0,0,0) and (0.5, 0.5, 0). The number of bases N is 2. And click "Define magnetic unit cell" button.

#label mform x y z Occ Ma Mb Mc
#Basis1 : m1 = 2.0 muB
Fe Fe3 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 1.0000
Fe Fe3 5.0000 5.0000 0.0000 1.0000 0.0000 0.0000 1.0000
#Basis2 : m2 = 0.5 muB
Fe Fe3 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000
Fe Fe3 5.0000 5.0000 0.0000 1.0000 -1.0000 0.0000 0.0000


By clicking the "Define magnetic unit cell" button, Label, m-form symbol, x, y, z and occupancy are automatically generated from the atomic positions in the cif file and the definitinos of the magnetic unit cell. They should not be modified in this textarea.
Directions of the magnetic moments can be defined by Ma, Mb and Mc. The magnitudes of a-, b-, and c-axis components of the magnetic moments at each site are given by
\((\sum_i m_iM_{ai},\sum_i m_iM_{bi},\sum_i m_iM_{ci})\)
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(CM)/Definition" tab.

HKL input

[Ex.) 0.5 0.5 0 (separated by space(s))]

For fractional numbers such as 1/3, write up to 4 decimal digits [Ex.) 0.3333 0.3333 0]

Conditions
: Qmax = Å-1
: 2θmax = deg, Ei= meV
: 2θmax = deg, λi= Å

Results



Download the calculated structure factors as a text file.

Definitions
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(CM)/Definition" tab.

Scattering plane
  • \(\tau_1= \) (H1,K1,L1): (,,). The 1st vector to define the scattering plane.
  • \(\tau_2= \) (H2,K2,L2): (,,). The 2nd vector to define the scattering plane, and should be independent of \(\tau_1\).
  • \(\tau_{\rm ofst}= \) (Hofst,Kofst,Lofst): (,,). (Optional) The offset vector (out-of-plane direction).
Structure factors or intensities will be calculated for the points described by \(n\tau_1+m\tau_2+\tau_{\rm ofst}\) (n and m are integers).
To calculate structure factors for commensurate magnetic reflections, please input fractional numbers for (Hi,Ki,Li) (i=1,2).
[Ex) (H1,K1,L1)=(0.3333,0.3333,0), (H2,K2,L2)=(0,0,0.5)]
Conditions
: Qmax = Å-1. (Intensities will be calculated to be \(|F_{hkl}|^2\))
: 2θmax = deg, Ei= meV. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))
: 2θmax = deg, λi= Å. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))

Intensity Map

Download the intensity map of the nuclear reflections as a png file.
Radius for the strongest reflection on the scattering plane: pixels.
Show indices. (only for nuclear reflections)





  • Areas of the filled circles are proportional to \(|F_{hkl}|^2\) or intensities.
  • Darkblue circles show accessible reflections.
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(CM)/Definition" tab.

Input data
Scale factor
s =
Data type
([Option] λi= Å for extinction correction. )
(Ei= meV. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)
i= Å. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)


Option: Extinction correction (λ or Ei needs to be specified. The scattering path lengths (cm) for each reflection need to be added after Fobs_err or Iobs_err.)
  • Extinction parameter : E0=.
  • d-value of the monochromator : dmono=


Observed data
Load from file:

  • Paste the observed data directly into the textarea below, or use the "Load from file" option.
  • Lines starting with "#" are ignored.

Optimize
m1 (\(\mu_B\) unit) 1.0
m2 (\(\mu_B\) unit) 1.0
m3 (\(\mu_B\) unit) 1.0
m4 (\(\mu_B\) unit) 1.0
m5 (\(\mu_B\) unit) 1.0
m6 (\(\mu_B\) unit) 1.0
m7 (\(\mu_B\) unit) 1.0
m8 (\(\mu_B\) unit) 1.0
m9 (\(\mu_B\) unit) 1.0
m10 (\(\mu_B\) unit) 1.0



Results
Calculation log

Download fitting log as a text file.

Fcal-Fobs data

Download Fcal-Fobs data as a text file.
Fcal-Fobs plot


Scale factor =
R-factors
  • R(F)=
  • Rw(F)=
  • R(F2)=
  • χ2=
  • χ2w=

Note that the magnetic moments in "Definition" tab are also updated. Hereafter the updated magentic moments will be used in "Calculation" tab.

Definitions
  • Scale factor s : \(|F_{obs}|^2=s|F_{cal}|^2\) (without extinction correction).
  • Extinction correction factor Y : \(|F_{obs}|^2=sY|F_{cal}|^2\).
    • \(Y=1/\sqrt{1+P|F_{cal}|^2E_0}\).
    • \(P=2\bar{t}(1+\cos2\theta_{M}\cos^4 2\theta)/[\sin 2\theta(1+\cos 2\theta_{M}\cos^2 2\theta)]\).
    • \(\bar{t}=\lambda^3l_{sc}10^4/V^2\).
      • \(E_0\) : Extinction parameter (user input).
      • \(2\theta_M\) : Scattering angle of the monochromator.
      • \(l_{sc}\) : Scattering path length.
      • \(V\) : Volume of the unit cell.
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(CM)/Definition" tab.

Conditions
Incident neutron:
2θ range : 2θmin=, 2θmax=, d2θ=
Resolution
U=, V=, W= (\({\rm FWHM}=\sqrt{U\tan^2\theta+V\tan\theta+W}\))



Download calculated powder diffraction profile as a text file.
Notice
Magnetic atoms are not selected. Please go to "Magnetic Atoms" tab.

Magnetic modulation vector (q-vector)
\(q_{\rm ICM}\)=(, , )


Define magnetic moments

The largest component of the magnetic moments is scaled to pixel (only for visualization).




Hor. angle: Vert. angle:
Distance: Scale:
Input format
Magnetic moment at an atomic site is defined by the following parameters.

[Label] [m-form symbol] [x] [y] [z] [occupancy] [M1a] [M1b] [M1c] [M2a] [M2b] [M2c] [mPhase]

By clicking the "Define q-vector" button, Label, m-form symbol, x, y, z and occupancy are automatically generated from the atomic positions in the cif file and the definitinos of the magnetic unit cell. They should not be modified in this textarea.
M1a, M1b, M1c, M2a, M2b and M2c are the components of the magnetic moment in \(\mu_{\rm B}\) unit. The initial values for these parameters are zero. Please change these numbers to define the magnetic structure.
Specifically, the magnetic moment at the jth atom in the lth unit cell is given as follows.

\(M(l+d_j)=M_1\cos(q_{\rm ICM} \cdot (l+d_j)-\phi_j)+M_2\sin(q_{\rm ICM} \cdot (l+d_j)-\phi_j)\)

For example, when an Fe3+ ion localted at (0,0,0) has a proper screw-type magnetic modulation with an amplitude of 5 \(\mu_{\rm B}\) on the bc plane (i.e. the q-vector is assumed to be parallel to the a* direction), the input parameters should be

Fe Fe3 0.00000 0.00000 0.00000 1.0000 0.00000 5.00000 0.00000 0.00000 0.00000 5.00000 0.00000

After defining all the magnetic moments, click "Define magentic structure" button, and check the direction and amplitudes of the magnetic moments shown by the 3D image shown in the right window.
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(ICM)/Definition" tab.

HKL input
[Ex.) 0.234 1 0 (separated by space(s))]


Conditions
: Qmax = Å-1
: 2θmax = deg, Ei= meV
: 2θmax = deg, λi= Å

Results



Download the calculated structure factors as a text file.

Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(ICM)/Definition" tab.

Scattering plane
  • \(\tau_1= \) (H1,K1,L1): (,,). The 1st vector to define the scattering plane.
  • \(\tau_2= \) (H2,K2,L2): (,,). The 2nd vector to define the scattering plane, and should be independent of \(\tau_1\).
  • \(\tau_{\rm ofst}= \) (Hofst,Kofst,Lofst): (,,). (Optional) The offset vector (out-of-plane direction).
Structure factors or intensities will be calculated for the points described by \(n\tau_1+m\tau_2+\tau_{\rm ofst}+q_{\rm ICM}\) (n and m are integers).
Conditions
: Qmax = Å-1. (Intensities will be calculated to be \(|F_{hkl}|^2\))
: 2θmax = deg, Ei= meV. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))
: 2θmax = deg, λi= Å. (Intensities will be calculated to be \(|F_{hkl}|^2\lambda^3/\sin2\theta\))

Intensity Map

Download the intensity map of the nuclear reflections as a png file.
Radius for the strongest reflection on the scattering plane: pixels.
Show indices. (only for nuclear reflections)
Show circles for nuclear reflections


  • Areas of the filled circles are proportional to \(|F_{hkl}|^2\) or intensities.
  • Darkblue circles show accessible incommensurate magnetic reflections.
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(ICM)/Definition" tab.

Input data
Scale factor
s =
Data type
([Option] λi= Å for extinction correction. )
(Ei= meV. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)
i= Å. Lorentz factor will be calculated by \(\lambda^3/\sin2\theta\) assuming monochromatic beam and a single crystal sample)


Option: Extinction correction (λ or Ei needs to be specified. The scattering path lengths (cm) for each reflection need to be added after Fobs_err or Iobs_err.)
  • Extinction parameter : E0=.
  • d-value of the monochromator : dmono=


Observed data
Load from file:

  • Paste the observed data directly into the textarea below, or use the "Load from file" option.
  • Lines starting with "#" are ignored.

Optimize
Overall factor for the magnetic moments.



Results
Fcal-Fobs data

Download Fcal-Fobs data as a text file.
Fcal-Fobs plot


Scale factor =
R-factors
  • R(F)=
  • Rw(F)=
  • R(F2)=
  • χ2=
  • χ2w=

Updated magnetic moments

Note that the magnetic moments in "Definition" tab are also updated. Hereafter the updated magentic moments will be used in "Calculation" tab.

Definitions
  • Scale factor s : \(|F_{obs}|^2=s|F_{cal}|^2\) (without extinction correction).
  • Extinction correction factor Y : \(|F_{obs}|^2=sY|F_{cal}|^2\).
    • \(Y=1/\sqrt{1+P|F_{cal}|^2E_0}\).
    • \(P=2\bar{t}(1+\cos2\theta_{M}\cos^4 2\theta)/[\sin 2\theta(1+\cos 2\theta_{M}\cos^2 2\theta)]\).
    • \(\bar{t}=\lambda^3l_{sc}10^4/V^2\).
      • \(E_0\) : Extinction parameter (user input).
      • \(2\theta_M\) : Scattering angle of the monochromator.
      • \(l_{sc}\) : Scattering path length.
      • \(V\) : Volume of the unit cell.
Notice
Magnetic structure is not defined. Please go to "Mag. Str. Factors(ICM)/Definition" tab.

Conditions
Incident neutron:
2θ range : 2θmin=, 2θmax=, d2θ=
Resolution
U=, V=, W= (\({\rm FWHM}=\sqrt{U\tan^2\theta+V\tan\theta+W}\))



Download calculated powder diffraction profile as a text file.