Trace: • s

# s

**[ scale E]**

The Rietveld scale factor, can be applied to all phase types .

**[ scale_pks E]…**

Used for applying intensity corrections to phase peaks. The following example defines a Lorentz-Polarisation correction:

scale_pks = (1+Cos(c Deg)^2 Cos(2 Th)^2)/(Sin(Th)^2 Cos(Th));

*scale_pks* is used for example in the LP_Factor, Preferred_Orientation and Absorption_With_Sample_Thickness_mm_Intensity macros.

**[ seed]**

Initialises the random number generator with a seed based on the computer clock.

**[ site $site [x E] [y E] [z E] ]…**

**[ occ $atom E [beq E]]…**

**[ num_posns #] [**

*rand_xyz***!E] [**

*inter*!E #]Defines a site where $site is a User defined string used to identify the site.

*x*, *y*, and *z* defines the fractional atomic coordinates, see also section 7.7.

*occ* and *beq* defines the site occupancy factor and the equivalent isotropic temperature factor beq. $atom corresponds to a valid atom symbol or isotope the data of which is contained in the file ATMSCAT.CPP for x-ray data and NEUTSCAT.CPP for *neutron_data*.

*num_posns* corresponds to the number of unique equivalent position generated from the space group; *num_posns* is updated on termination of refinement.

*inter* corresponds to the sum of all GRS interactions which are a function of the *site*. The value of *inter* can represent the site electrostatic potential depending on the type of GRS interactions defined.

Definition of a site fully occupied by aluminium:

site Al1 x 0 y 0 z 0.3521 occ Al+3 1 beq 0.3

Definition of a site occupied by two cations:

site Fe2 x 0.9283 y 0.25 z 0.9533 occ Fe+3 0.5 beq 0.25

occ Al+3 0.5 beq 0.25

**[ sites_distance N] | [sites_angle N] | [sites_flatten N [sites_flatten_tol !E]]…**

**[ site_to_restrain $site [ #ep [ #n1 #n2 #n3 ] ] ]…**

When used in equations the name N of *sites_distance* and *sites_angle* returns the distance in Å between two sites and angle in degrees between three sites respectively. The sites are defined by *site_to_restrain*.In particular N can be used in penalty equations to restrain bond lengths.

N of *sites_flatten* returns a restraint term that decreases as the sites become coplanar; it is defined as follows:

_{}

where tol corresponds to *sites_flatten_tol*, n corresponds to the number of sites defined with the *site_to_restrain* keyword, b are Cartesian unit length vectors between the sites and the geometric centre of the sites.

#eq, #n1, #n2 and #n3 correspond to the site equivalent position and fractional offsets to add to the sites. This is useful if the structure is already known and constraints are required, for example, in the bond length output (see *append_bond_lengths*):

Zr1:0 O1:20 0 0 -1 2.08772

O1:7 0 -1 0 2.08772 89.658

O1:10 0 0 -1 2.08772 90.342 90.342

O1:15 -1 0 0 2.08772 180.000 89.658 89.658

O1:18 -1 0 0 2.08772 90.342 89.658 180.000 90.342

P1:0 O1:4 0 0 0 1.52473

O1:8 0 0 0 1.52473 112.923

O1:0 0 0 0 1.52473 112.923 112.923

O2:0 0 0 0 1.59001 105.749 105.749 105.749

Example constraints using macros could look like the following:

Angle_Restrain(O1 P1 O1 8, 112, 112.92311, 0, 0.001)

Angle_Restrain(O1 18 -1 0 0 Zr1 O1 10 0 0 -1, 89, 89.65750, 0, 0.001)

Distance_Restrain(Zr1 O1 20 0 0 -1, 2.08, 2.08772, 0, 1)

BENZENE.INP demonstrates the use of the restraint macros Distance_Restrain, Angle_Restrain and Flatten. OpenGL viewing is recommended. Note, for more than 6 sites then *sites_flatten* becomes computationally expensive.

**[ sites_geometry $Name]…**

**[ site_to_restrain $site [ #ep [ #n1 #n2 #n3 ] ] ]…**

*sites_geometry* defines a grouping of up to four sites; $Name is the name given to ths grouping. The sites that are part of the group is defined using *site_to_restrain*, for example:

sites_geometry some_name

load site_to_restrain { C1 C2 C3 C4 }

Three functions, Sites_Geometry_Distance($Name), Sites_Geometry_Angle($Name) and Sites_Geometry_Dihedral_Angle($Name) can be used in equations to obtain the distance between sites C1 and C2, the angle between C1-C2-C3 and the dihedral angle formed between the planes C1-C2-C3 and C2-C3-C4. The convention used are the same as for z-matrices, see example SITES_GEOMETRY_1.INP:

If $Name contains only two sites then only Sites_Geometry_Distance($Name) can be used. Three sites defined additionally allows the use of Sites_Geometry_Angle($Name) and four sites defined additionally allows the use of Sites_Geometry_Dihedral_Angle($Name).

Examples SITES_GEOMETRY_1.INP and SITES_GEOMETRY_2.INP demonstartes the use of *sites_geometry*.

**[ siv_s1_s2 # #]**

Defines the S_{1} and S_{2} integration limits for the spherical interaction volume of the GRS series.

**[ smooth #num_pts_left_right]**

Performs a Savitzky-Golay smoothing on the observed data. The smoothing encompasses (2 * #num_pts_left_right + 1) points.

**[ spherical_harmonics_hkl $name]…**

**[ sh_Cij_prm $Yij E]…**

**[ sh_alpha !E]**

**[ sh_order #]**

Defines a hkl dependent symmetrized spherical harmonics series (see section 7.9.2). $name defines the name given to the series and when used in equations it returns the value of the spherical harmonics series.

*sh_Cij_prm* is the spherical harmonics coefficients, which can be defined by the User, or, alternatively if there are no coefficients defined then the *sh_Cij_prm* parameters are generated. Only the coefficients allowed by the selection rules of the point group are generated (Järvinen, 1993). At the end of refinement the generated *sh_Cij_prm* parameters are appended to *sh_order*. This allows for control over the *sh_Cij_prm* parameters in subsequent refinements. $Yij corresponds to valid symmetrized harmonics that has survived symmetrization. It is internally generated when there are no *sh_Cij_prm* parameters defined by the User.

*sh_alpha* corresponds to the angle in degrees between the polar axis and the scattering vector; *sh_alpha* defaults to zero degrees which is required for symmetric reflection as is the case for Bragg-Brentano geometry.

*sh_order* corresponds to the order of the spherical harmonic series which are even numbers ranging from 2 to 8 for non-cubic and from 2 to 10 for cubic systems.

The PO_Spherical_Harmonics macro simplifies the use of *spherical_harmonics_hkl*. CLAY.INP demonstrates the use of *spherical_harmonics_hkl* for describing anisotropic peak shapes.

**[ stacked_hats_conv [whole_hat E [hat_height E]]…[half_hat E [hat_height E]…]…**

Defines hat sizes for generating an aberration function comprising a summation of hat functions. *whole_hat* defines a hat with an X axis extent of ±*whole_hat*/2. *half_hat* defines a hat with an X-axis range of *half_hat* to zero if *half_hat*<0; or zero to *half_hat* if *half_hat*> 0. *hat_height* defines the height of the hat; it defaults to 1. *stacked_hats* is used for example to describe tube tails using the Tube_Tails macro.

**[ start_X !E] [finish_X !E]**

Defines the start and finish X region to fit to.

**[ str]…**

Defines a new structure node.

**[ str_hkl_angle N h k l]…**

Defines a parameter name and a vector normal to the plane defined by h, k and l. When the parameter name is used in an equation, it returns angles (in radians) between itself and the normal to the planes defined by hkls; see the Preferred_Orientation and PO_Two_Directions macros. An example in two directions is as follows:

**[***swap_sites***$sites_1 $sites_2]…**

*swap_sites* attempts to find a lower _{} by swapping sites defined in $sites_1 with those defined in $sites_2. The swapping continues until all swaps are performed. Outline of the algorithm:

While *swap_site* processes still to be processed {

k = 0

Do

Randomize the cation configuration according to *swap_sites*.

Find the local minimum of _{}

k = k + 1

If _{}(k+1) > _{}(k) then reset site positions

While _{}(k+1) > _{}(k) or all swap possibility exhausted

}

Starting from a particular cation configuration, a single swap of two different cation species does not exhaust all possible cation configurations. For example, three sites A, B and C have the six possible configurations of ABC, ACB, BAC, CAB, BCA, CBA. Swapping any two from the starting configuration of ABC results in the possible configurations of BAC, CBA, ACB with CAB and BCA absent. The absent configurations can be obtained by a double swap where, for example, the swapping of A and C yields CBA and then the swapping of A and B yields CAB. Thus all possible configurations can be visited if in between swapping steps are realized by the simulated annealing process.

Swapping the Zr sites with and Ca sites in the example above can be performed as follows:

swap_sites Ca Zr

If the sites were named Ca1, Ca2, Ca3, Zr1, Zr2, Zr3 then the following could be used:

swap_sites Ca* Zr*