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ATOM_SITES_AXES
CIF
Data items in the ATOM_SITES_AXES category record details about the transformation matrices that define the displacements and rotations of atoms and rigid groups. Details for individual atom sites are described by data items in the ATOM_SITE_DISPLACE_* and ATOM_SITE_ROT_* categories.
_atom_sites_axes.matrix
CIF
A 3x3 matrix, A, that relates the axes used to describe the atomic or molecular displacements to the crystallographic axes of the reference structure as follows:
(a1,a2,a3) = (a~r~,b~r~,c~r~) A
_atom_sites_axes.matrix_seq_id
CIF
A numeric code to identify each transformation matrix given
in _atom_sites_axes.matrix.
_atom_sites_axes.transf_description
CIF
The definition of the axes described by the transformation
given by _atom_sites_axes.matrix.
Example:
a1 and a2 are respectively the long molecular axis and the axis normal
to the mean molecular plane.
ATOM_SITES_DISPLACE_FOURIER
CIF
Data items in the ATOM_SITES_DISPLACE_FOURIER category record details common to the displacive modulation of atom sites in a modulated structure. Details for individual atom sites are described by data items in the ATOM_SITE_DISPLACE_FOURIER category.
_atom_sites_displace_Fourier.axes_description
CIF
DEPRECATED. This data name should not be used. It has been replaced by the ATOM_SITES_AXES data names.
The definition of the axes used for describing the displacive modulation, parameterized by Fourier series, when they are other than the crystallographic axes.
Example:
a1 and a2 are respectively the long molecular axis
and the axis normal to the mean molecular plane.
ATOM_SITES_MODULATION
CIF
Data items in the ATOM_SITES_MODULATION category record details common to the modulation of atom sites in a modulated structure.
_atom_sites_modulation.global_phase_list
CIF
The initial phases, in cycles, of the modulation waves. For incommensurate structures they are irrelevant. However, they are essential for the description of commensurate structures within the superspace formalism, since they determine the space group of the commensurate superstructure [see Perez-Mato, Madariaga, Zuiga & Garcia Arribas (1987), van\ Smaalen (1995) or van Smaalen (2012)]. Note that for composites described using a single data block, the initial phases for each subsystem are derived using the W matrices (see _cell_subsystem.matrix_W_*) from a unique set of global phases whose values are assigned to _atom_sites_modulation_global_phase_t_. Detailed information can be found in van Smaalen (1995). References: Perez-Mato, J. M., Madariaga, G., Zuiga, F. J.
& Garcia Arribas, A. (1987). Acta Cryst. A43, 216-226. On the structure and symmetry of incommensurate phases. A practical formulation Smaalen, S. van(1995). Crystallogr. Rev. 4, 79-202. Incommensurate crystal structures Smaalen, S. van(2012). Incommensurate Crystallography. Oxford University Press.
_atom_sites_modulation.global_phase_t_1
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_2
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_3
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_4
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_5
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_6
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_7
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
_atom_sites_modulation.global_phase_t_8
CIF
Initial phase component in _atom_sites_modulation.global_phase_list.
ATOM_SITES_ORTHO
CIF
Data items in the ATOM_SITES_ORTHO category record details about the orthogonalized functions defined to solve correlation problems during the refinement of the modulation parameters when the atomic domain of a given atom is restricted by a Crenel function (see Petricek et al., 2016). The functions are constructed selecting Fourier harmonics until a desired degree of orthogonality and completeness is reached (see_atom_site_occ_special_func.crenel_ortho_eps).
References: Petricek, V., Van Der Lee & Evain, M. (1995).
Acta Cryst. A51, 529-535. DOI 10.1107/S0108767395000365 On the Use of Crenel Functions for Occupationally Modulated Structures
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_sites_ortho.coeff_cos_list
CIF
The list of cosine components of an orthogonalized function
labeled by atom_sites_ortho.func_id corresponding to the wave
vector list given by _atom_sites_ortho.wave_vector_seq_id_list
_atom_sites_ortho.coeff_sin_list
CIF
The list of sine components of an orthogonalized function
labeled by atom_sites_ortho.func_id corresponding to the wave
vector list given by _atom_sites_ortho.wave_vector_seq_id_list
_atom_sites_ortho.func_id
CIF
A code that identifies an orthogonalized function or any of its components.
_atom_sites_ortho.wave_vector_seq_id
CIF
A code that identifies each of the harmonics chosen for the definition of an orthogonalized function. It links the wave vectors defined in _atom_site_Fourier_wave_vector.*
_atom_sites_ortho.wave_vector_seq_id_list
CIF
A list of codes that identifies the harmonics chosen for the definition of an orthogonalized function. It links the wave vectors defined in _atom_site_Fourier_wave_vector.*
ATOM_SITES_ROT_FOURIER
CIF
Data items in the ATOM_SITES_ROT_FOURIER category record details about the rotational component of the displacive modulation of a given rigid group as a whole.
Details for individual atom sites are described by data items in the ATOM_SITES_ROT_FOURIER category.
_atom_sites_rot_Fourier.axes_description
CIF
DEPRECATED. This data name should not be used. It has been replaced by the ATOM_SITES_AXES data names.
The definition of the axes used for describing the rotational part of the displacive modulation of a given rigid group, parameterized by Fourier series, when they are other than the crystallographic axes.
Example:
a1 and a2 are respectively the long molecular axis
and the axis normal to the mean molecular plane.
ATOM_SITE_DISPLACE_FOURIER
CIF
Data items in the ATOM_SITE_DISPLACE_FOURIER category record details about the Fourier components of the displacive modulation of an atom site in a modulated structure. In the case of rigid groups, items in this category would only include the translational part of the modulation. The rotational part would appear in a separate list of items belonging to the ATOM_SITE_ROT_FOURIER category. The (in general complex) coefficients of each Fourier component belong to the child category ATOM_SITE_DISPLACE_FOURIER_PARAM and may be listed separately.
_atom_site_displace_Fourier.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_displace_Fourier.atom_site_label is the code that identifies an atom or rigid group in a loop in which the Fourier components of its displacive modulation are listed. In the case of a rigid group, this list would only include the translational part of its displacive modulation. The rotational part (if any) would appear in a separate list (see _atom_site_rot_Fourier.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_displace_Fourier.axis
CIF
A label identifying the displacement component of a given atom or rigid group that is being parameterized by Fourier series. a, b and c are the basic lattice vectors of the reference structure. For composites they refer to the reference structure of each subsystem. a~1~, a~2~ and a~3~ are defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_displace_Fourier.matrix_seq_id. Use of _atom_sites_displace_Fourier.axes_description is deprecated and retained only for backward compatibility.
_atom_site_displace_Fourier.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of Fourier series. In the case of a rigid group, it applies only to the translational part of the distortion.
_atom_site_displace_Fourier.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_displace_Fourier.wave_vector_seq_id
CIF
A numeric code identifying the wave vectors of the Fourier terms
used in the structural model to describe the displacive
modulation of an atom or rigid group. In the case of a rigid
group, it applies only to the translational part of the
distortion. This code must match
_atom_site_Fourier_wave_vector.seq_id.
ATOM_SITE_DISPLACE_FOURIER_PARAM
CIF
Data items in the ATOM_SITE_DISPLACE_FOURIER_PARAM category record details about the coefficients of the Fourier series used to describe the displacive modulation of an atom or rigid group. In the case of rigid groups, items in this category would only include the translational part of the modulation. The rotational part would appear in a separate list of items belonging to the ATOM_SITE_ROT_FOURIER_PARAM category. The Fourier components are defined in the parent category ATOM_SITE_DISPLACE_FOURIER. Notice that items in this category may be listed together with those of the ATOM_SITE_DISPLACE_FOURIER category.
_atom_site_displace_Fourier_param.cos
CIF
The displacive distortion of a given atom or rigid group (see
also _atom_site_rot_Fourier_param.cos) is usually parameterized
by Fourier series. Each term of the series commonly adopts two
different representations: the sine-cosine form,
Ac cos(2\p k r)+As sin(2\p k r),
and the modulus-argument form, |A| cos(2\p k r+\f), where k is the wave vector of the term and r is the atomic average position. _atom_site_displace_Fourier_param.cos is the cosine coefficient (Ac) corresponding to the Fourier term defined _atom_site_displace_Fourier.atom_site_label, _atom_site_displace_Fourier.axis and _atom_site_displace_Fourier.wave_vector.seq_id. Atomic or rigid- group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_displace_Fourier.matrix_seq_id. Use of _atom_sites_displace_Fourier.axes_description is deprecated and retained only for backward compatibility.
_atom_site_displace_Fourier_param.id
CIF
A code identifying the (in general complex) coefficient of each
term present in the Fourier series describing the displacive
modulation of a given atom or rigid group. In the case of a rigid
group, it applies only to the translational part of the
distortion. This code must match _atom_site_displace_Fourier.id.
_atom_site_displace_Fourier_param.modulus
CIF
The displacive distortion of a given atom or rigid group (see
also _atom_site_rot_Fourier_param.modulus) is usually
parameterized by Fourier series. Each term of the series commonly
adopts two different representations: the sine-cosine form,
Ac cos(2\p k r)+As sin(2\p k r),
and the modulus-argument form, |A| cos(2\p k r+\f), where k is the wave vector of the term and r is the atomic average position. _atom_site_displace_Fourier_param.modulus is the modulus (|A|) of the complex amplitude corresponding to the Fourier term defined by _atom_site_displace_Fourier.atom_site_label, _atom_site_displace_Fourier.axis and _atom_site_displace_Fourier.wave_vector_seq_id. Atomic or rigid- group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_displace_Fourier.matrix_seq_id. Use of _atom_sites_displace_Fourier.axes_description is deprecated and retained only for backward compatibility.
_atom_site_displace_Fourier_param.phase
CIF
The displacive distortion of a given atom or rigid group (see
also _atom_site_rot_Fourier_param.phase) is usually parameterized
by Fourier series. Each term of the series commonly adopts two
different representations: the sine-cosine form,
Ac cos(2\p k r)+As sin(2\p k r),
and the modulus-argument form, |A| cos(2\p k r+\f), where k is the wave vector of the term and r is the atomic average position. _atom_site_displace_Fourier_param.phase is the phase (/2\p) in cycles of the complex amplitude corresponding\ to the Fourier term defined by _atom_site_displace_Fourier.atom_site_label, _atom_site_displace_Fourier.axis and _atom_site_displace_Fourier.wave_vector_seq_id.
_atom_site_displace_Fourier_param.sin
CIF
The displacive distortion of a given atom or rigid group (see
also _atom_site_rot_Fourier_param.sin) is usually parameterized
by Fourier series. Each term of the series commonly adopts two
different representations: the sine-cosine form,
Ac cos(2\p k r)+As sin(2\p k r),
and the modulus-argument form, |A| cos(2\p k r+\f), where k is the wave vector of the term and r is the atomic average position. _atom_site_displace_Fourier_param.sin is the sine coefficient (As) corresponding to the Fourier term defined _atom_site_displace_Fourier.atom_site_label, _atom_site_displace_Fourier.axis, and _atom_site_displace_Fourier.wave_vector_seq_id. Atomic or rigid- group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_displace_Fourier.matrix_seq_id. Use of _atom_sites_displace_Fourier.axes_description is deprecated and retained only for backward compatibility.
ATOM_SITE_DISPLACE_LEGENDRE
CIF
The set of harmonic functions used in the Fourier series describing the Modulation functions is orthogonal and complete in the interval [0,1). However within the x4 interval defined by a Crenel function orthogonality is no longer preserved and therefore the Fourier coefficients are correlated and the refinement becomes fragile. There are several ways to avoid this technical problem (see Petricek et al., 2016). One of them is to use orthogonal or orthogonalized sets of functions defined within the Crenel interval. This procedure is more robust than the orthogonalization of harmonics described in *_ORTHO. categories. Moreover these sets of functions are complete. Two different sets of orthogonal or orthogonalized functions have been implemented in JANA2006: Legendre polynomials and the so-called X- harmonics. Legendre polynomials are orthogonal in the Crenel interval and can be easily calculated by the recurrence relation:
P~0~(x) = 1 P~1~(x) (x) = x (n+1)P~n+1~(x) = (2n+1)x P~n~(x) - nP~n-1~(x)
Notice that Legendre polynomials are restricted to one-dimensional cases and include as a particular case the sawtooth modulation.
Data items in the ATOM_SITE_DISPLACE_LEGENDRE category record details about the Legendre polynomials used to describe the displacive modulations when the atomic domain of a given atom is restricted by a Crenel function. In the case of rigid groups, items in this category would only include the translational part of the modulation. The rotational part would appear in a separate list of items belonging to the ATOM_SITE_ROT_LEGENDRE category.
References: Petricek, V., Van Der Lee & Evain, M. (1995).
Acta Cryst. A51, 529-535. DOI 10.1107/S0108767395000365 On the Use of Crenel Functions for Occupationally Modulated Structures
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_site_displace_Legendre.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_displace_Legendre.atom_site_label is the code that identifies an atom or rigid group in a loop in which the Legendre components of its displacive modulation are listed. In the case of a rigid group, this list would only include the translational part of its displacive modulation. The rotational part (if any) would appear in a separate list (see _atom_site_rot_Legendre.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_displace_Legendre.axis
CIF
A label identifying the displacement component of a given atom
or rigid group that is being parameterized by Legendre polynomials.
a, b and c are the basic lattice vectors of the reference
structure. For composites they refer to the reference structure of
each subsystem. a~1~, a~2~ and a~3~ are defined by the
items belonging to the ATOM_SITES_AXES category, through
_atom_site_displace_Legendre.matrix_seq_id.
_atom_site_displace_Legendre.coeff
CIF
The coefficient corresponding to the Legendre function defined by _atom_site_displace_Legendre.atom_site_label, _atom_site_displace_Legendre.axis and _atom_site_displace_Legendre.order. Atomic or rigid-group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_Legendre.matrix_seq_id.
_atom_site_displace_Legendre.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of Legendre polynomials. In the case of a rigid group, it applies only to the translational part of the distortion.
_atom_site_displace_Legendre.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_displace_Legendre.order
CIF
The order of the Legendre polynomial.
ATOM_SITE_DISPLACE_ORTHO
CIF
Data items in the ATOM_SITE_DISPLACE_ORTHO category record
details about the orthogonalized functions defined to solve
correlation problems during the refinement of displacive
modulations when the atomic domain of a given atom is restricted
by a Crenel function. The functions are constructed selecting
Fourier harmonics until the desired degree of orthogonality and
completeness is reached (see
_atom_site_occ_special_func.crenel_ortho_eps).
In the case of rigid groups, items in this category would only
include the translational part of the modulation. The rotational
part would appear in a separate list of items belonging to the
ATOM_SITE_ROT_ORTHO category.
Notice that the global results could also be expressed (losing information) using the data items defined in the categories ATOM_SITE_DISPLACE_FOURIER and ATOM_SITE_DISPLACE_FOURIER_PARAM.
_atom_site_displace_ortho.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_displace_ortho.atom_site_label is the code that identifies an atom or rigid group in a loop in which the ortho components of its displacive modulation are listed. In the case of a rigid group, this list would only include the translational part of its displacive modulation. The rotational part (if any) would appear in a separate list (see _atom_site_rot_ortho.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_displace_ortho.axis
CIF
A label identifying the displacement component of a given atom
or rigid group that is being parameterized by orthogonalized
functions. a, b and c are the basic lattice vectors of the reference
structure. For composites they refer to the reference structure of
each subsystem. a~1~, a~2~ and a~3~ are defined by the
items belonging to the ATOM_SITES_AXES category, through
_atom_site_displace_ortho.matrix_seq_id.
_atom_site_displace_ortho.coeff
CIF
The coefficient corresponding to the orthogonalized function Defined by _atom_site_displace_ortho.atom_site_label, _atom_site_displace_ortho.axis and _atom_site_displace_ortho.func_id. Atomic or rigid-group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_ortho.matrix_seq_id.
_atom_site_displace_ortho.func_id
CIF
A code identifying the orthogonalized function used in the structural model to describe the displacive modulation of an atom or rigid group. In the case of a rigid group, it applies only to the translational part of the distortion. This code must match _atom_sites_ortho_func_id.
_atom_site_displace_ortho.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of ortho series. In the case of a rigid group, it applies only to the translational part of the distortion.
_atom_site_displace_ortho.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
ATOM_SITE_DISPLACE_SPECIAL_FUNC
CIF
Data items in the ATOM_SITE_DISPLACE_SPECIAL_FUNC category record details about the displacive modulation of an atom site in a modulated structure when it is not described by Fourier series. Special functions are effective in some cases where the modulations are highly anharmonic, since the number of parameters is drastically reduced. However, they are in general discontinuous or with discontinuous derivatives and therefore these functions describe an ideal situation that never occurs in a real modulated crystal. Up to now, only a few types of special functions have been used and all of them come from the JANA2006 suite of programs (Petricek, Dusek & Palatinus, 2014). Although this approach is far from being general, it has the advantage that the functions are tightly defined and therefore the atomic displacements and occupations can be calculated easily. In this dictionary, only the special functions available in JANA2006 have been included. These are:
(1) Sawtooth functions for the displacive modulation of atoms and
rigid groups.
(2) Zig-Zag functions for the displacive modulation of atoms and
rigid groups.
(3) Crenel functions for the occupational modulation of atoms
and rigid groups. Both of these only apply to
one-dimensional modulated structures.
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_displace_special_func.atom_site_label
CIF
The code that identifies an atom or rigid group in a loop in which the special function that describes its displacive modulation is being defined. This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_displace_special_func.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_displace_special_func.sawtooth
CIF
_atom_site_displace_special_func_sawtooth_ items are the
adjustable parameters of a sawtooth function.
A displacive sawtooth function along the internal space is
defined as follows:
[ux, uy, uz] = 2* [ax, ay, az] * ((x4-c)/w)
for x4 belonging to the interval [c-(w/2), c+(w/2)], where ax, ay and az are the amplitudes (maximum displacements) along each crystallographic axis, w is its width, x4 is the internal coordinate and c is the centre of the function in internal space. ux, uy and uz must be expressed in relative units or in angstroms if the modulations are referred to some special axes defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_displace_special_funcs.matrix_seq_id.
The use of this function is restricted to one-dimensional modulated structures. For more details, see the manual for JANA2006 (Petricek, Dusek & Palatinus, 2014) and (Petricek, Eigner, Dusek & Cejchan, 2016). In the case of rigid groups, items in this category would only include the translational part of the modulation. The rotational part would appear in a separate list of items belonging to the ATOM_SITE_ROT_SPECIAL_FUNC category.
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_displace_special_func.sawtooth_axyz
CIF
The vector of amplitudes (maximum displacements) along the a (or a1),
b (or a2) and c (or a3) axis of the sawtooth function described in
_atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.sawtooth_ax
CIF
The amplitude (maximum displacement) along the a (or a1) axis of the
sawtooth function described in _atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.sawtooth_ay
CIF
The amplitude (maximum displacement) along the b (or a2) axis of the
sawtooth function described in _atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.sawtooth_az
CIF
The amplitude (maximum displacement) along the c (or a3) axis of the
sawtooth function described in _atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.sawtooth_c
CIF
The centre of the sawtooth function described in
_atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.sawtooth_w
CIF
The width of the sawtooth function described in
_atom_site_displace_special_func.sawtooth
_atom_site_displace_special_func.zigzag
CIF
_atom_site_displace_special_func.zigzag_ items are the adjustable parameters of a zigzag function. A displacive zigzag function along the internal space is defined as follows:
2*[ax,ay,az]*(x4-c)/w for x4 in [c-(w/2),c+(w/2)]
[ux,uy,uz] = -2*[ax,ay,az]*(x4-c)/w for x4 in [c+1/2-(w/2),c+1/2+(w/2)]
where ax,ay and az are the amplitudes (maximum displacements)
along each crystallographic axis, w is its width, x4 is the
internal coordinate and c is the centre of the function in
internal space. ux, uy and uz must be expressed in relative
units or in angstroms if the modulations are referred to some
special axes defined by the items belonging to the ATOM_SITES_AXES
category, through _atom_site_displace_Fourier.matrix_seq_id.
The use of this function is restricted to one-dimensional
modulated structures. For more details, see (Elcoro et al., 2008;
Petricek, Dusek & Palatinus, 2014 and Petricek, Eigner, Dusek
& Cejchan, 2016). In the case of rigid groups, items in this
category would only include the translational part of the modulation.
The rotational part would appear in a separate list of items belonging
to the ATOM_SITE_ROT_SPECIAL_FUNC category.
References: Luis Elcoro, J.M. Perez-Mato, Karen Friese, Vaclav Petricek, Tonci Balic-Zunic & Lars Arnskov Olsen (2008) Acta Cryst. B64, 684-701. doi:10.1107/S0108768108031492 Modular crystals as modulated structures: the case of the lillianite homologous series
Petricek, V., Dusek, M. & Palatinus, L. (2014). Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737 Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_site_displace_special_func.zigzag_axyz
CIF
The vector of amplitudes (maximum displacements) along the a (or a1),
b (or a2) and c (or a3) axis of the zigzag function described in
_atom_site_displace_special_func.zigzag
_atom_site_displace_special_func.zigzag_c
CIF
The centre of the zigzag function described in
_atom_site_displace_special_func.zigzag
_atom_site_displace_special_func.zigzag_w
CIF
The width of the zigzag function described in
_atom_site_displace_special_func.zigzag
ATOM_SITE_DISPLACE_XHARM
CIF
The set of harmonic functions used in the Fourier series describing the Modulation functions is orthogonal and complete in the interval [0,1). However within of the x4 interval defined by a Crenel function orthogonality is no longer preserved and therefore the Fourier coefficients are correlated and the refinement becomes fragile. There are several ways to avoid this technical problem (see Petricek et al., 2016). One of them is to use orthogonal or orthogonalized sets of functions defined within the Crenel interval. This procedure is more robust than the orthogonalization of harmonics described in *_ORTHO. categories. Moreover these sets of functions are complete. Two different sets of orthogonal or orthogonalized functions have been implemented in JANA2006: Legendre polynomials and the so-called x-harmonics. x-harmonic functions are defined from the set (Petricek, Eigner, Dusek & Cejchan, 2016):
{1, x, sin( x), cos( x), ... , sin(n x), cos(n x)}
and a subsequent orthogonalization (see the above reference and the supplementary material) owing to the presence of x which is not orthogonal to sin(n x) (for any n). Notice that x-harmonics are restricted to one- dimensional cases and include as a particular case the sawtooth modulation.
Data items in the ATOM_SITE_DISPLACE_XHARM category record details about the x-harmonic functions used to describe the displacive modulations when the atomic domain of a given atom is restricted by a crenel function. In the case of rigid groups, items in this category would only include the translational part of the modulation. The rotational part would appear in a separate list of items belonging to the ATOM_SITE_ROT_XHARM category.
References: Petricek, V., Van Der Lee & Evain, M. (1995).
Acta Cryst. A51, 529-535. DOI 10.1107/S0108767395000365 On the Use of Crenel Functions for Occupationally Modulated Structures
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_site_displace_xharm.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_displace_xharm.atom_site_label is the code that identifies an atom or rigid group in a loop in which the x-harmonics components of its displacive modulation are listed. In the case of a rigid group, this list would only include the translational part of its displacive modulation. The rotational part (if any) would appear in a separate list (see _atom_site_rot_xharm.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_displace_xharm.axis
CIF
A label identifying the displacement component of a given atom
or rigid group that is being parameterized by x-harmonic functions.
a, b and c are the basic lattice vectors of the reference
structure. For composites they refer to the reference structure of
each subsystem. a~1~, a~2~ and a~3~ are defined by the
items belonging to the ATOM_SITES_AXES category, through
_atom_site_displace_xharm.matrix_seq_id.
_atom_site_displace_xharm.coeff
CIF
The coefficient corresponding to the x-harmonic function defined by _atom_site_displace_xharm.atom_site_label, _atom_site_displace_xharm.axis and _atom_site_displace_xharm.order. Atomic or rigid-group displacements must be expressed as fractions of the unit cell or in angstroms if the modulations are referred to some special axes defined by defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_xharm.matrix_seq_id.
_atom_site_displace_xharm.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of x-harmonics. In the case of a rigid group, it applies only to the translational part of the distortion.
_atom_site_displace_xharm.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_displace_xharm.order
CIF
The order of each x-harmonic function.
ATOM_SITE_FOURIER_WAVE_VECTOR
CIF
Data items in the ATOM_SITE_FOURIER_WAVE_VECTOR category record details about the wave vectors of the Fourier terms used in the structural model.
_atom_site_Fourier_wave_vector.description
CIF
A description of the linear combination involved in a given Fourier wave vector used to describe the atomic modulation functions.
Example:
q(4)=q(1)+q(2)
_atom_site_Fourier_wave_vector.seq_id
CIF
A numeric code identifying the wave vectors defined in _atom_site_Fourier_wave_vector.*
_atom_site_Fourier_wave_vector.q_coeff
CIF
Wave vectors of the Fourier terms used in the structural model
to describe the atomic modulation functions, expressed with
respect to the three-dimensional reciprocal basis that spans
the lattice of main reflections. They are linear combinations
with integer coefficients of the independent wave vectors given
in the _cell_wave_vector. list. Therefore, a generic Fourier wave
vector is expressed as k=n(1)q(1)+...+n(p)q(p), where p is given
by _cell_modulation_dimension. In the case of composites
described in a single data block, these wave vectors are
expressed with respect to the three-dimensional reciprocal
basis of each subsystem (see _cell_subsystem.matrix_W_*).
_atom_site_Fourier_wave_vector.coeff contains the coefficients that
express a given k as a linear combination of the independent wave vectors
given in _cell_modulation_dimension. The enumeration of the independent
wave vectors (1,2, ...) is given by the value of
_atom_site_Fourier_wave_vector_.q_coeff_seq_id matching the
corresponding value of _cell_wave_vector.seq_id
_atom_site_Fourier_wave_vector.q_coeff_seq_id
CIF
The list of codes that identifies each independent wave vector appearing in the linear combination that expresses a generic Fourier wave vector as k=n(1)q(1)+...+n(p)q(p), where p is given by _cell_modulation_dimension. In the case of composites described in a single data block, these wave vectors are expressed with respect to the three-dimensional reciprocal basis of each subsystem (see _cell_subsystem.matrix_W_*).
_atom_site_Fourier_wave_vector.x
CIF
Wave vectors of the Fourier terms used in the structural model to describe the atomic modulation functions, expressed with respect to the three-dimensional reciprocal basis that spans the lattice of main reflections. They are linear combinations with integer coefficients of the independent wave vectors given in the _cell_wave_vector_ list. Therefore, a generic Fourier wave vector is expressed as k=n(1)q(1)+...+n(p)q(p), where p is given by _cell_modulation_dimension. In the case of composites described in a single data block, these wave vectors are expressed with respect to the three-dimensional reciprocal basis of each subsystem (see _cell_subsystem.matrix_W_*).
_atom_site_Fourier_wave_vector.xyz
CIF
Wave vectors of the Fourier terms used in the structural model to describe the atomic modulation functions, expressed with respect to the three-dimensional reciprocal basis that spans the lattice of main reflections. They are linear combinations with integer coefficients of the independent wave vectors given in the _cell_wave_vector. list. Therefore, a generic Fourier wave vector is expressed as k=n(1)q(1)+...+n(p)q(p), where p is given by _cell_modulation_dimension. In the case of composites described in a single data block, these wave vectors are expressed with respect to the three-dimensional reciprocal basis of each subsystem (see _cell_subsystem.matrix_W_*).
_atom_site_Fourier_wave_vector.y
CIF
Wave vectors of the Fourier terms used in the structural model to describe the atomic modulation functions, expressed with respect to the three-dimensional reciprocal basis that spans the lattice of main reflections. They are linear combinations with integer coefficients of the independent wave vectors given in the _cell_wave_vector_ list. Therefore, a generic Fourier wave vector is expressed as k=n(1)q(1)+...+n(p)q(p), where p is given by _cell_modulation_dimension. In the case of composites described in a single data block, these wave vectors are expressed with respect to the three-dimensional reciprocal basis of each subsystem (see _cell_subsystem.matrix_W_*).
_atom_site_Fourier_wave_vector.z
CIF
Wave vectors of the Fourier terms used in the structural model to describe the atomic modulation functions, expressed with respect to the three-dimensional reciprocal basis that spans the lattice of main reflections. They are linear combinations with integer coefficients of the independent wave vectors given in the _cell_wave_vector_ list. Therefore, a generic Fourier wave vector is expressed as k=n(1)q(1)+...+n(p)q(p), where p is given by _cell_modulation_dimension. In the case of composites described in a single data block, these wave vectors are expressed with respect to the three-dimensional reciprocal basis of each subsystem (see _cell_subsystem.matrix_W_*).
ATOM_SITE_OCC_FOURIER
CIF
Data items in the ATOM_SITE_OCC_FOURIER category record details about the Fourier components of the occupational modulation of the atom sites in a modulated structure. The (in general complex) coefficients of each Fourier component belong to the child category ATOM_SITE_OCC_FOURIER_PARAM and may be listed separately.
_atom_site_occ_Fourier.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP.
_atom_site_occ_Fourier.atom_site_label is the code that
identifies an atom in a loop in which the Fourier components of
its occupational modulation are listed. This code must
match the _atom_site.label of the associated coordinate list and
conform to the rules described in _atom_site.label.
_atom_site_occ_Fourier.id
CIF
A code identifying each component of the occupational modulation of a given atom or rigid group when the modulation is expressed in terms of Fourier series.
_atom_site_occ_Fourier.wave_vector_seq_id
CIF
A numeric code identifying the wave vectors of the Fourier terms
used in the structural model to describe the modulation functions
corresponding to the occupational part of the distortion. This
code must match _atom_site_Fourier_wave_vector.seq_id.
ATOM_SITE_OCC_FOURIER_PARAM
CIF
Data items in the ATOM_SITE_OCC_FOURIER_PARAM category record details about the coefficients of the Fourier series used to describe the occupational modulation of the atom sites in a modulated structure. The Fourier components are defined in the parent category ATOM_SITE_OCC_FOURIER. Notice that items in this category may be listed together with those of the ATOM_SITE_DISPLACE_FOURIER category.
_atom_site_occ_Fourier_param.cos
CIF
The occupational distortion of a given atom or rigid group is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Pc cos(2\p k r)+Ps sin(2\p k r),
and the modulus-argument form, |P| cos(2\p k r+\d), where k is the wave vector of the term and r is the atomic average position. _atom_site_occ_Fourier_param.cos is the cosine coefficient (Pc) corresponding to the Fourier term defined by _atom_site_occ_Fourier.atom_site_label and _atom_site_occ_Fourier.wave_vector_seq_id.
_atom_site_occ_Fourier_param.id
CIF
A code identifying the (in general complex) coefficient of each
term present in the Fourier series describing the occupational
modulation of a given atom or rigid group. This code must match
_atom_site_occ_Fourier.id.
_atom_site_occ_Fourier_param.modulus
CIF
The occupational distortion of a given atom or rigid group is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Pc cos(2\p k r)+Ps sin(2\p k r),
and the modulus-argument form, |P| cos(\2 k r+\d), where k is the wave vector of the term and r is the atomic average position. _atom_site_occ_Fourier.param_modulus is the modulus (|P|) of the complex amplitude corresponding to the Fourier term defined by _atom_site_occ_Fourier.atom_site_label and _atom_site_occ_Fourier.wave_vector_seq_id.
_atom_site_occ_Fourier_param.phase
CIF
The occupational distortion of a given atom or rigid group is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Pc cos(2\p k r)+Ps sin(2\p k r),
and the modulus-argument form, |P| cos(2\p k r+\d), where k is the wave vector of the term and r is the atomic average position. _atom_site_occ_Fourier_param.phase is the phase (/2\p) in cycles corresponding to the Fourier term defined by\ _atom_site_occ_Fourier.atom_site_label and _atom_site_occ_Fourier.wave_vector_seq_id.
_atom_site_occ_Fourier_param.sin
CIF
The occupational distortion of a given atom or rigid group is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Pc cos(2\p k r)+Ps sin(2\p k r),
and the modulus-argument form, |P| cos(2\p k r+\d), where k is the wave vector of the term and r is the atomic average position. _atom_site_occ_Fourier_param.sin is the sine coefficient (Ps) corresponding to the Fourier term defined by _atom_site_occ_Fourier.atom_site_label and _atom_site_occ_Fourier.wave_vector_seq_id.
ATOM_SITE_OCC_LEGENDRE
CIF
Data items in the ATOM_SITE_OCC_LEGENDRE category record details about the Legendre polynomials used to describe the occupational modulations when the atomic domain of a given atom or rigid group is restricted by a crenel function.
_atom_site_occ_Legendre.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_occ_Legendre.atom_site_label is the
code that identifies an atom or rigid group in a loop in which
the Legendre components of its occupational modulation are listed.
This code must match the _atom_site.label of the associated coordinate
list and conform to the rules described in _atom_site.label.
_atom_site_occ_Legendre.coeff
CIF
The coefficient corresponding to the Legendre polynomial describing the occupational modulation of a given atom or rigid group.
_atom_site_occ_Legendre.id
CIF
A code identifying each component of the occupational modulation of a given atom or rigid group when the modulation is expressed in terms of Legendre polynomials.
_atom_site_occ_Legendre.order
CIF
The order of the Legendre polynomial.
ATOM_SITE_OCC_ORTHO
CIF
Data items in the ATOM_SITE_OCC_ORTHO category record
details about the orthogonalized functions defined to solve
correlation problems during the refinement of the occupational
modulation when the atomic domain of a given atom is restricted
by a crenel function. The functions are constructed selecting
Fourier harmonics until the desired degree of orthogonality and
completeness is reached (see
_atom_site_occ_special_func.crenel_ortho_eps).
Notice that the global results could also be expressed (losing information) using the data items defined in the categories ATOM_SITE_OCC_FOURIER and ATOM_SITE_OCC_FOURIER_PARAM.
_atom_site_occ_ortho.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_occ_ortho.atom_site_label is the
code that identifies an atom or rigid group in a loop in which
the ortho components of its occupational modulation are listed.
This code must match the _atom_site.label of the associated coordinate
list and conform to the rules described in _atom_site.label.
_atom_site_occ_ortho.coeff
CIF
The coefficient corresponding to the orthogonalized function defined by _atom_site_occ_ortho.atom_site_label and _atom_site_occ_ortho.func_id.
_atom_site_occ_ortho.func_id
CIF
A code identifying the orthogonalized function used in the structural model to describe the occupational modulation of an atom or rigid group. This code must match _atom_sites_ortho_func_id.
_atom_site_occ_ortho.id
CIF
A code identifying each component of the occupational modulation of a given atom or rigid group when the modulation is expressed in terms of ortho series.
ATOM_SITE_OCC_SPECIAL_FUNC
CIF
Data items in the ATOM_SITE_OCC_SPECIAL_FUNC category record details about the occupational modulation of a given atom or rigid group in a modulated structure when it is not described by Fourier series. Special functions are effective in some cases where the modulations are highly anharmonic, since the number of parameters is drastically reduced. However, they are in general discontinuous or with discontinuous derivatives and therefore these functions describe an ideal situation that never occurs in a real modulated crystal. Up to now, only a few types of special functions have been used and all of them come from the JANA2006 suite of programs (Petricek, Dusek & Palatinus, 2014). Although this approach is far from being general, it has the advantage that the functions are tightly defined and therefore the atomic displacements and occupations can be calculated easily. In this dictionary, only the special functions available in JANA2006 have been included. These are:
(1) Sawtooth functions for atomic displacive modulation along
x, y and z.
(2) Zig-Zag functions for atomic displacive modulation along
x, y and z.
(3) Crenel functions for the occupational modulation of atoms
and rigid groups. Both of these only apply to
one-dimensional modulated structures.
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_occ_special_func.atom_site_label
CIF
The code that identifies an atom or rigid group in a loop in which the parameters of the special function that describes its occupational modulation are listed. This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_occ_special_func.crenel_c
CIF
_atom_site_occ_special_func_crenel_ items are the adjustable parameters of a crenel function.
An occupational crenel function along the internal space is
defined as follows:
p(x4)=1 if x4 belongs to the interval [c-w/2,c+w/2]
p(x4)=0 if x4 is outside the interval [c-w/2,c+w/2],
where x4 is the internal coordinate, c is the centre of the
function in internal space and w is its width. The use of this
function is restricted to one-dimensional modulated structures.
For more details, see the manual for JANA2006 (Petricek, Dusek
& Palatinus, 2014)
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_occ_special_func.crenel_ortho_eps
CIF
The set of harmonic functions used in the Fourier series describing the
Modulation functions is orthogonal and complete in the interval [0,1).
However within of the x4 interval defined by a Crenel function orthogonality
is no longer preserved and therefore the Fourier coefficients are correlated
and the refinement becomes fragile. There are several ways to avoid this
technical problem (see Petricek et al., 2016). One of them is to define
functions based on Fourier harmonics that are orthogonal within the Crenel
interval. The procedure implemented in JANA2006 requires, for each Crenel
function, a parameter for the selection of the harmonic functions that define
the not necessarily complete set of (almost) orthogonalized functions.
_atom_site_occ_special_func.crenel_ortho_eps contains such values. Empirical
tests indicate that a default value of 0.95 warrants reasonable results.
The orthogonalized functions and the corresponding refined amplitudes are
defined in the categories: ATOM_SITES_ORTHO., ATOM_SITE_DISPLACE_ORTHO.,
ATOM_SITE_OCC_ORTHO., ATOM_SITE_ROT_ORTHO. and ATOM_SITE_U_ORTHO.
References: Petricek, V., Van Der Lee & Evain, M. (1995).
Acta Cryst. A51, 529-535. DOI 10.1107/S0108767395000365 On the Use of Crenel Functions for Occupationally Modulated Structures
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_site_occ_special_func.crenel_w
CIF
_atom_site_occ_special_func_crenel_ items are the adjustable parameters of a crenel function.
An occupational crenel function along the internal space is
defined as follows:
p(x4)=1 if x4 belongs to the interval [c-w/2,c+w/2]
p(x4)=0 if x4 is outside the interval [c-w/2,c+w/2],
where x4 is the internal coordinate, c is the centre of the
function in internal space and w is its width. The use of this
function is restricted to one-dimensional modulated structures.
For more details, see the manual for JANA2006 (Petricek, Dusek
& Palatinus, 2014)
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
ATOM_SITE_OCC_XHARM
CIF
Data items in the ATOM_SITE_OCC_XHARM category record details about the x-harmonics used to describe the occupational modulations when the atomic domain of a given atom or rigid group is restricted by a crenel function. T
_atom_site_occ_xharm.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_occ_xharm.atom_site_label is the
code that identifies an atom or rigid group in a loop in which
the x-harmonic components of its occupational modulation are listed.
This code must match the _atom_site.label of the associated coordinate
list and conform to the rules described in _atom_site.label.
_atom_site_occ_xharm.id
CIF
A code identifying each component of the occupational modulation of a given atom or rigid group when the modulation is expressed in terms of x-harmonics.
_atom_site_occ_xharm.order
CIF
The order of each x-harmonics function.
_atom_site_occ_xharm.coeff
CIF
The coefficient corresponding to the x-harmonic function describing the Occupational modulation of a given atom or rigid group.
ATOM_SITE_PHASON
CIF
Data items in the ATOM_SITE_PHASON category record details about the atomic phason correction. Although this kind of correction is intended to be overall, some refinement programs (for example, JANA2006) allow for this (theoretically dubious) atom-dependent phason treatment.
_atom_site_phason.atom_site_label
CIF
The code that identifies an atom or rigid group in a loop in which the phason coefficients are listed. Although this kind of correction is intended to be overall, some refinement programs (for example, JANA2006) allow an independent phason correction for each atom or rigid group. In this case, _atom_site_phason.formula and _atom_site_phason.coeff should be used (see also _refine.ls_mod_overall_phason_*). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_phason.coeff
CIF
The phason coefficient used to calculate (with the appropriate expression given in _atom_site_phason.formula) the atomic phason correction. Although this kind of correction is intended to be overall, some refinement programs (for example, JANA2006) allow an independent phason correction for each atom or rigid group. In this case, _atom_site_phason.formula and _atom_site_phason.coeff should be used (see also _refine.ls_mod_overall_phason_*).
_atom_site_phason.formula
CIF
The formula used for the phason correction. Although both kinds of corrections are intended to be overall, some refinement programs (for example, JANA2006) allow an independent phason correction for each atom or rigid group. In this case, _atom_site_phason.formula and _atom_site_phason.coeff should be used (see also _refine.ls_mod_overall_phason_*).
ATOM_SITE_ROT_FOURIER
CIF
Data items in the ATOM_SITE_ROT_FOURIER category record details about the Fourier components present in the rotational part of the displacive modulation of a given rigid group. The translational part would appear in a separate list of items belonging to the ATOM_SITE_DISPLACE_FOURIER category. The (in general complex) coefficients of each Fourier component belong to the child category ATOM_SITE_ROT_FOURIER_PARAM and may be listed separately.
_atom_site_rot_Fourier.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP.
_atom_site_rot_Fourier.atom_site_label is the code that
identifies a rigid group in a loop in which the Fourier
components of the rotational part of its displacive modulation
are listed. The translational part (if any) would appear in a
separate list (see _atom_site_displace_Fourier.atom_site_label).
This code must match the _atom_site.label of the associated
coordinate list and conform to the rules described in
_atom_site.label.
_atom_site_rot_Fourier.axis
CIF
A label identifying the rotation component around a fixed point of a given rigid group whose modulation is being parameterized by Fourier series. a, b and c are the basic lattice vectors of the reference structure. For composites they refer to the reference structure of each subsystem. a~1~, a~2~ and a~3~ are defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_Fourier.matrix_seq_id. Use of _atom_sites_rot_Fourier.axes_description is deprecated and retained only for backward compatibility.
_atom_site_rot_Fourier.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_rot_Fourier.wave_vector_seq_id
CIF
A numeric code identifying the wave vectors of the Fourier terms
used in the structural model to describe the modulation functions
corresponding to the rotational distortion of a rigid group. This
code must match _atom_site_Fourier_wave_vector.seq_id.
ATOM_SITE_ROT_FOURIER_PARAM
CIF
Data items in the ATOM_SITE_ROT_FOURIER_PARAM category record details about the coefficients of the Fourier series used to describe the rotational component of the displacive modulation of a given rigid group. The translational part would appear in a separate list of items belonging to the ATOM_SITE_DISPLACE_FOURIER_PARAM category. The Fourier components are defined in the parent category ATOM_SITE_ROT_FOURIER Notice that items in this category may be listed together with those of the ATOM_SITE_DISPLACE_FOURIER category.
_atom_site_rot_Fourier_param.cos
CIF
The displacive distortion of a given rigid group is not completely described by _atom_site_displace_Fourier.*. The rigid rotation of the group around a given axis passing through a fixed point (for example, the centre of mass of the group) is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Rc cos(2\p k r)+Rs sin(2\p k r),
and the modulus-argument form, |R| cos(2\p k r+\y), where k is the wave vector of the term and r is the atomic average position. _atom_site_rot_Fourier_param_cos is the cosine coefficient (Rc) in degrees corresponding to the Fourier term defined by _atom_site_rot_Fourier.atom_site_label, _atom_site_rot_Fourier.axis and _atom_site_rot_Fourier.wave_vector_seq_id.
_atom_site_rot_Fourier_param.id
CIF
A code identifying the (in general complex) coefficient of each term present in the Fourier series describing the rotational part of the displacive modulation of a given rigid group. This code must match _atom_site_rot_Fourier.id.
_atom_site_rot_Fourier_param.modulus
CIF
The displacive distortion of a given rigid group is not completely described by _atom_site_displace_Fourier_. The rigid rotation of the group around a given axis passing through a fixed point (for example, the centre of mass of the group) is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Rc cos(2\p k r)+Rs sin(2\p k r),
and the modulus-argument form, |R| cos(2\p k r+\y), where k is the wave vector of the term and r is the atomic average position. _atom_site_rot_Fourier_param.modulus is the modulus (|R|) in degrees of the complex amplitude corresponding to the Fourier term defined by _atom_site_rot_Fourier.atom_site_label, _atom_site_rot_Fourier.axis and _atom_site_rot_Fourier.wave_vector_seq_id.
_atom_site_rot_Fourier_param.phase
CIF
The displacive distortion of a given rigid group is not completely described by _atom_site_displace_Fourier_. The rigid rotation of the group around a given axis passing through a fixed point (for example, the centre of mass of the group) is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Rc cos(2\p k r)+Rs sin(2\p k r),
and the modulus-argument form, |R| cos(2\p k r+\y), where k is the wave vector of the term and r is the atomic average position. _atom_site_rot_Fourier_param.phase is the phase (/2\p) in cycles of the complex amplitude corresponding to the Fourier term defined by _atom_site_rot_Fourier.atom_site_label, _atom_site_rot_Fourier.axis and _atom_site_rot_Fourier.wave_vector_seq_id.
_atom_site_rot_Fourier_param.sin
CIF
The displacive distortion of a given rigid group is not completely described by _atom_site_displace_Fourier_. The rigid rotation of the group around a given axis passing through a fixed point (for example, the centre of mass of the group) is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
Rc cos(2\p k r)+Rs sin(2\p k r),
and the modulus-argument form, |R| cos(2\p k r+\y), where k is the wave vector of the term and r is the atomic average position. _atom_site_rot_Fourier_param.sin is the sine coefficient (Rs) in degrees corresponding to the Fourier term defined by _atom_site_rot_Fourier.atom_site_label, _atom_site_rot_Fourier.axis and _atom_site_rot_Fourier.wave_vector_seq_id.
ATOM_SITE_ROT_LEGENDRE
CIF
Data items in the ATOM_SITE_ROT_LEGENDRE category record details about the Legendre polynomials used to describe the displacive modulations when the atomic domain of a given atom is restricted by a crenel function. In the case of rigid groups, items in this category would only include the rotational part of the modulation. The translational part would appear in a separate list of items belonging to the ATOM_SITE_DISPLACE_LEGENDRE category.
_atom_site_rot_Legendre.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_rot_Legendre.atom_site_label is the code that identifies an atom or rigid group in a loop in which the Legendre components of its displacive modulation are listed. In the case of a rigid group, this list would only include the rotational part of its displacive modulation. The translational part (if any) would appear in a separate list (see _atom_site_displace_Legendre.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_rot_Legendre.axis
CIF
A label identifying the rotational part of the displacive modulation of
a given rigid group that is being parameterized by Legendre
polynomials. a, b and c are the basic lattice vectors of the reference
structure. For composites they refer to the reference structure of
each subsystem. a~1~, a~2~ and a~3~ are defined by the
items belonging to the ATOM_SITES_AXES category, through
_atom_site_rot_Legendre.matrix_seq_id.
_atom_site_rot_Legendre.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of Legendre polynomials. In the case of a rigid group, it applies only to the rotational part of the distortion.
_atom_site_rot_Legendre.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_rot_Legendre.order
CIF
The order of the Legendre polynomial.
_atom_site_rot_Legendre.coeff
CIF
The coefficient corresponding to the Legendre function defined by _atom_site_rot_Legendre.atom_site_label, _atom_site_rot_Legendre.axis and _atom_site_rot_Legendre.order. Atomic or rigid-group rotations must be expressed in degrees. Special axes are defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_Legendre.matrix_seq_id.
ATOM_SITE_ROT_ORTHO
CIF
Data items in the ATOM_SITE_ROT_ORTHO category record
details about the orthogonalized functions defined to solve
correlation problems during the refinement of displacive
modulations when the the atomic domain of a given atom is
restricted by a crenel function. The functions are constructed
selecting Fourier harmonics until the desired degree of
orthogonality and completeness is reached (see
_atom_site_occ_special_func.crenel_ortho_eps).
In the case of rigid groups, items in this category would only
include the rotational part of the modulation.
Notice that the global results could also be expressed (losing information) using the data items defined in the categories ATOM_SITE_ROT_FOURIER and ATOM_SITE_ROT_FOURIER_PARAM.
_atom_site_rot_ortho.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_rot_ortho.atom_site_label is the code that identifies an atom or rigid group in a loop in which the ortho components of its displacive modulation are listed. In the case of a rigid group, this list would only include the rotational part of its displacive modulation. The translational part (if any) would appear in a separate list (see _atom_site_displace_ortho.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_rot_ortho.axis
CIF
A label identifying the rotational part of the displacive modulation of
a given rigid group that is being parameterized by orthogonalized
functions. a, b and c are the basic lattice vectors of the reference
structure. For composites they refer to the reference structure of
each subsystem. a~1~, a~2~ and a~3~ are defined by the
items belonging to the ATOM_SITES_AXES category, through
_atom_site_rot_ortho.matrix_seq_id.
_atom_site_rot_ortho.func_id
CIF
A code identifying the orthogonalized function used in the structural model to describe the displacive modulation of an atom or rigid group. In the case of a rigid group, it applies only to the rotational part of the distortion. This code must match _atom_sites_ortho_func_id.
_atom_site_rot_ortho.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of ortho series. In the case of a rigid group, it applies only to the rotational part of the distortion.
_atom_site_rot_ortho.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_rot_ortho.coeff
CIF
The coefficient corresponding to the orthogonalized function defined by _atom_site_rot_ortho.atom_site_label, _atom_site_rot_ortho.axis and _atom_site_rot_ortho.func_id. Atomic or rigid-group rotations must be expressed in degrees. Special axes are defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_ortho.matrix_seq_id.
ATOM_SITE_ROT_SPECIAL_FUNC
CIF
Data items in the ATOM_SITE_ROT_SPECIAL_FUNC category record details about the rotational part of the displacive modulation of a rigid group in a modulated structure when it is not described by Fourier series. Special functions are effective in some cases where the modulations are highly anharmonic, since the number of parameters is drastically reduced. However, they are in general discontinuous or with discontinuous derivatives and therefore these functions describe an ideal situation that never occurs in a real modulated crystal. Up to now, only a few types of special functions have been used and all of them come from the JANA2006 suite of programs (Petricek, Dusek & Palatinus, 2014). Although this approach is far from being general, it has the advantage that the functions are tightly defined and therefore the atomic displacements and occupations can be calculated easily. In this dictionary, only the special functions available in JANA2006 have been included.
These are:
wtooth functions for the displacive modulation of atoms and groups.
(2) Zig-Zag functions for the displacive modulation of atoms and
rigid groups.
(3) Crenel functions for the occupational modulation of atoms
and rigid groups. Both of these only apply to
one-dimensional modulated structures.
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_rot_special_func.atom_site_label
CIF
The code that identifies a rigid group in a loop in which the special function that describes the rotational part of its displacive modulation is being defined. This code must match the _atom_site.label of theassociated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_rot_special_func.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_rot_special_func.sawtooth
CIF
_atom_site_rot_special_func.sawtooth_ items are the adjustable parameters of a sawtooth function. A rotational sawtooth function along the internal space is defined as follows:
[rx, ry, rz] = 2* [ax, ay, az] * ((x4-c)/w)
for x4 belonging to the interval [c-(w/2), c+(w/2)], where ax,
ay and az are the amplitudes (maximum displacements)
along each axis, w is its width, x4 is the
internal coordinate and c is the centre of the function in
internal space. rx, ry and rz must be expressed in degrees.
Special axes are defined by the items belonging to the ATOM_SITES_AXES
category, through _atom_site_rot_special_func.matrix_seq_id.
The use of this function is restricted to one-dimensional
modulated structures. For more details, see the manual for
JANA2006 (Petricek, Dusek & Palatinus, 2014) and (Petricek, Eigner,
Dusek & Cejchan, 2016). In the case of rigid groups, items in this
category would only include the rotational part of the modulation.
The translationalional part would appear in a separate list of items belonging
to the ATOM_SITE_DISPLACE_SPECIAL_FUNC category.
References: Petricek, V., Dusek, M. & Palatinus, L. (2014).
Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737
Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z.
Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913
Discontinuous modulation functions and their application for
analysis of modulated structures with the computing system JANA2006
_atom_site_rot_special_func.sawtooth_axyz
CIF
The vector of amplitudes (maximum displacements) along the a (or a1),
b (or a2) and c (or a3) axis of the sawtooth function described in
_atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.sawtooth_ax
CIF
The amplitude (maximum displacement) along the a (or a1) axis of the sawtooth
function described in _atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.sawtooth_ay
CIF
The amplitude (maximum displacement) along the b (or a2) axis of the sawtooth
function described in _atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.sawtooth_az
CIF
The amplitude (maximum displacement) along the c (or a3) axis of the sawtooth
function described in _atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.sawtooth_c
CIF
The centre of the sawtooth function described in
_atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.sawtooth_w
CIF
The width of the sawtooth function described in
_atom_site_rot_special_func.sawtooth
_atom_site_rot_special_func.zigzag
CIF
_atom_site_rot_special_func.zigzag_ items are the adjustable parameters of a zigzag function. A displacive zigzag function along the internal space is defined as follows:
2*[ax,ay,az]*(x4-c)/w for x4 in [c-(w/2),c+(w/2)]
[rx,ry,rz] = -2*[ax,ay,az]*(x4-c)/w for x4 in [c+1/2-(w/2),c+1/2+(w/2)]
where ax,ay and az are the amplitudes (maximum displacements)
along each crystallographic axis, w is its width, x4 is the
internal coordinate and c is the centre of the function in
internal space. rx, ry and rz must be expressed in degrees.
Special axes are defined by the items belonging to the ATOM_SITES_AXES
category, through _atom_site_rot_special_func.matrix_seq_id.
The use of this function is restricted to one-dimensional
modulated structures. For more details, see (Elcoro et al., 2008;
Petricek, Dusek & Palatinus, 2014 and Petricek, Eigner, Dusek
& Cejchan, 2016). In the case of rigid groups, items in this
category would only include the rotational part of the modulation.
The rotational part would appear in a separate list of items belonging
to the ATOM_SITE_DISPLACE_SPECIAL_FUNC category.
References: Luis Elcoro, J.M. Perez-Mato, Karen Friese, Vaclav Petricek, Tonci Balic-Zunic & Lars Arnskov Olsen (2008) Acta Cryst. B64, 684-701. doi:10.1107/S0108768108031492 Modular crystals as modulated structures: the case of the lillianite homologous series
Petricek, V., Dusek, M. & Palatinus, L. (2014). Z. Kristallogr. 229(5), 345-352. DOI 10.1515/zkri-2014-1737 Crystallographic Computing System JANA2006: General features
Petricek, V., Eigner, V., Dusek, M. & Cejchan, A. (2016). Z. Kristallogr. 231(5), 301-312. DOI 10.1515/zkri-2015-1913 Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
_atom_site_rot_special_func.zigzag_axyz
CIF
The vector of amplitudes (maximum displacements) along the a (or a1),
b (or a2) and c (or a3) axis of the zigzag function described in
_atom_site_rot_special_func.zigzag
_atom_site_rot_special_func.zigzag_c
CIF
The centre of the zigzag function described in
_atom_site_rot_special_func.zigzag
_atom_site_rot_special_func.zigzag_w
CIF
The width of the zigzag function described in
_atom_site_rot_special_func.zigzag
ATOM_SITE_ROT_XHARM
CIF
Data items in the ATOM_SITE_ROT_XHARM category record details about the x-harmonics used to describe the displacive modulations when the atomic domain of a given atom is restricted by a crenel function. In the case of rigid groups, items in this category would only include the rotational part of the modulation. The translational part would appear in a separate list of items belonging to the ATOM_SITE_DISPLACE_XHARM category.
_atom_site_rot_xharm.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP. _atom_site_rot_xharm.atom_site_label is the code that identifies an atom or rigid group in a loop in which the x-harmonics components of its displacive modulation are listed. In the case of a rigid group, this list would only include the rotational part of its displacive modulation. The translational part (if any) would appear in a separate list (see _atom_site_displace_xharm.atom_site_label). This code must match the _atom_site.label of the associated coordinate list and conform to the rules described in _atom_site.label.
_atom_site_rot_xharm.axis
CIF
A label identifying the rotational part of the displacive modulation of
a given rigid group that is being parameterized by x-harmonics. a, b and c
are the basic lattice vectors of the reference structure. For composites
they refer to the reference structure of each subsystem. a~1~, a~2~ and a~3~
are defined by the items belonging to the ATOM_SITES_AXES category, through
_atom_site_rot_xharm.matrix_seq_id.
_atom_site_rot_xharm.coeff
CIF
The coefficient corresponding to the x-harmonic function Defined by _atom_site_rot_xharm.atom_site_label, _atom_site_rot_xharm.axis and _atom_site_rot_xharm.order. Atomic or rigid-group rotations must be expressed in degrees. Special axes are defined by the items belonging to the ATOM_SITES_AXES category, through _atom_site_rot_xharm.matrix_seq_id.
_atom_site_rot_xharm.id
CIF
A code identifying each component of the displacive modulation of a given atom or rigid group when the modulation is expressed in terms of x-harmonics. In the case of a rigid group, it applies only to the rotational part of the distortion.
_atom_site_rot_xharm.matrix_seq_id
CIF
A numeric code identifying the transformation matrix that defines
the arbitrary axes a1, a2 and a3 in terms of the crystallographic axes.
This code must match _atom_sites_axes.matrix_seq_id.
_atom_site_rot_xharm.order
CIF
The order of each x-harmonic function.
ATOM_SITE_U_FOURIER
CIF
Data items in the ATOM_SITE_U_FOURIER category record details about the Fourier components describing the modulation of the ADPs in a modulated structure.
_atom_site_U_Fourier.atom_site_label
CIF
Modulation parameters are usually looped in separate lists. Modulated parameters are the atom positions (displacive modulation), the atomic occupation (occupational modulation) and/or the anisotropic (or isotropic) ADP.
_atom_site_U_Fourier.atom_site_label is the code that
identifies an atom in a loop in which the Fourier components of
its ADP modulation are listed. This code must
match the _atom_site.label of the associated coordinate list
and conform to the rules described in _atom_site.label.
_atom_site_U_Fourier.id
CIF
A code identifying each Fourier component used to describe the modulation of ADP.
_atom_site_U_Fourier.tens_elem
CIF
A label identifying the ADP tensor element U(ij) of a given atom whose modulation is being parameterized by Fourier series.
_atom_site_U_Fourier.wave_vector_seq_id
CIF
A numeric code identifying the wave vectors of the Fourier terms
used to describe the modulation functions corresponding to the
ADP of an atom. This code must
match _atom_site_Fourier_wave_vector.seq_id.
ATOM_SITE_U_FOURIER_PARAM
CIF
Data items in the ATOM_SITE_U_FOURIER category record details about the coefficients of the Fourier series used to describe the modulation of the ADP in a modulated structure. The Fourier components are defined in the category ATOM_SITE_U_FOURIER and are listed separately.
_atom_site_U_Fourier_param.cos
CIF
The modulation of the ADP is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
U(ij)c cos(2\p k r)+U(ij)s sin(2\p k r),
and the modulus-argument form, |U(ij)| cos(2\p k r+\c), where k is the wave vector of the term and r is the atomic average position. _atom_site_U_Fourier_param.cos is the cosine coefficient [U(ij)c], in angstroms squared, corresponding to the Fourier term defined by _atom_site_U_Fourier.atom_site_label, _atom_site_U_Fourier.tens_elem and _atom_site_U_Fourier.wave_vector_seq_id.
_atom_site_U_Fourier_param.id
CIF
A code identifying the (in general complex) coefficient of each
term present in the Fourier series describing the modulation of
the ADP. This code must match
_atom_site_U_Fourier.id.
_atom_site_U_Fourier_param.modulus
CIF
The modulation of the ADP is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
U(ij)c cos(2\p k r)+U(ij)s sin(2\p k r),
and the modulus-argument form, |U(ij)| cos(2\p k r+\c), where k is the wave vector of the term and r is the atomic average position. _atom_site_U_Fourier_param.modulus is the modulus [|U(ij)|], in angstroms squared, of the complex amplitudes corresponding to the Fourier term defined by _atom_site_U_Fourier.atom_site_label, _atom_site_U_Fourier.tens_elem and _atom_site_U_Fourier.wave_vector_seq_id.
_atom_site_U_Fourier_param.phase
CIF
The modulation of the ADP is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
U(ij)c cos(2\p k r)+U(ij)s sin(2\p k r),
and the modulus-argument form, |U(ij)| cos(2\p k r+\c), where k is the wave vector of the term and r is the atomic average position. _atom_site_U_Fourier_param.phase is the phase (/2\p), in cycles, of the complex amplitude corresponding to\ the Fourier term defined by _atom_site_U_Fourier.atom_site_label, _atom_site_U_Fourier.tens_elem and _atom_site_U_Fourier.wave_vector_seq_id.
_atom_site_U_Fourier_param.sin
CIF
The modulation of the ADP is usually parameterized by Fourier series. Each term of the series commonly adopts two different representations: the sine-cosine form,
U(ij)c cos(2\p k r)+U(ij)s sin(2\p k r),
and the modulus-argument form, |U(ij)| cos(2\p k r+\c), where k is the wave vector of the term and r is the atomic average position. _atom_site_U_Fourier_param.sin is the sine coefficient [U(ij)s], in angstroms squared, corresponding to the Fourier term defined by _atom_site_U_Fourier.atom_site_label, _atom_site_U_Fourier.tens_elem and _atom_site_U_Fourier.wave_vector_seq_id.
ATOM_SITE_U_LEGENDRE
CIF
Data items in the ATOM_SITE_U_LEGENDRE category record details about the Legendre polynomials used to describe the ADP modulations when the atomic domain of a given atom is restricted by a crenel function.
_atom_site_U_Legendre.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_U_Legendre.atom_site_label is the code that identifies
an atom in a loop in which the Legendre components of its ADP
modulation are listed. This code must match the _atom_site.label
of the associated coordinate list and conform to the rules described
in _atom_site.label.
_atom_site_U_Legendre.coeff
CIF
The coefficient, in angstroms squared corresponding to the Legendre function defined by _atom_site_U_Legendre.atom_site_label, _atom_site_U_Legendre.tens_elem and _atom_site_U_Legendre.order.
_atom_site_U_Legendre.id
CIF
A code identifying each component of the ADP modulation of a given atom when the modulation is expressed in terms of Legendre functions.
_atom_site_U_Legendre.order
CIF
The order of the Legendre polynomial.
_atom_site_U_Legendre.tens_elem
CIF
A label identifying the ADP tensor element U(ij) a given atom whose modulation is being parameterized by Legendre polynomials.
ATOM_SITE_U_ORTHO
CIF
Data items in the ATOM_SITE_U_ORTHO category record
details about the orthogonalized functions defined to solve
correlation problems during the refinement of ADP
modulations when the atomic domain of a given atom is
restricted by a crenel function. The functions are constructed
selecting Fourier harmonics until the desired degree of
orthogonality and completeness is reached (see
_atom_site_occ_special_func.crenel_ortho_eps).
_atom_site_U_ortho.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_U_ortho.atom_site_label is the code that identifies
an atom in a loop in which the ortho components of its ADP
modulation are listed. This code must match the _atom_site.label
of the associated coordinate list and conform to the rules described
in _atom_site.label.
Notice that the global results could also be expressed (losing information)using the data items defined in the categories ATOM_SITE_U_FOURIER and ATOM_SITE_U_FOURIER_PARAM.
_atom_site_U_ortho.coeff
CIF
The coefficient, in angstroms squared corresponding to the orthogonalized function defined by _atom_site_U_ortho.atom_site_label, _atom_site_U_ortho.tens_elem and _atom_site_U_ortho.func_id.
_atom_site_U_ortho.func_id
CIF
A code identifying the orthogonalized function used in the structural model to describe the ADP modulation of an atom. This code must match _atom_sites_ortho.func_id.
_atom_site_U_ortho.id
CIF
A code identifying each component of the ADP modulation of a given atom when the modulation is expressed in terms of ortho series.
_atom_site_U_ortho.tens_elem
CIF
A label identifying the ADP tensor element U(ij) a given atom whose modulation is being parameterized by orthogonalized functions.
ATOM_SITE_U_XHARM
CIF
Data items in the ATOM_SITE_U_XHARM category record details about the x-harmonics used to describe the ADP modulations when the atomic domain of a given atom is restricted by a crenel function.
_atom_site_U_xharm.atom_site_label
CIF
Modulation parameters are usually looped in separate lists.
Modulated parameters are the atom positions (displacive
modulation), the atomic occupation (occupational modulation)
and/or the anisotropic (or isotropic) ADP.
_atom_site_U_xharm.atom_site_label is the code that identifies
an atom in a loop in which the x-harmonic components of its ADP
modulation are listed. This code must match the _atom_site.label
of the associated coordinate list and conform to the rules described
in _atom_site.label.
_atom_site_rot_U_xharm.coeff
CIF
The coefficient, in angstroms squared corresponding to the x-harmonics defined by _atom_site_U_xharm.atom_site_label, _atom_site_U_xharm.tens_elem and _atom_site_U_xharm.order.
_atom_site_U_xharm.id
CIF
A code identifying each component of the ADP modulation of a given atom when the modulation is expressed in terms of x-harmonics.
_atom_site_U_xharm.order
CIF
The order of each x-harmonic function.
_atom_site_U_xharm.tens_elem
CIF
A label identifying the ADP tensor element U(ij) a given atom whose modulation is being parameterized by x-harmonics.
CELL_SUBSYSTEM
CIF
Data items in the CELL_SUBSYSTEM category record details about the crystallographic cell parameters of each subsystem present in a composite.
_cell_subsystem.code
CIF
The code identifying uniquely a certain composite subsystem. This code is used to identify the data blocks that contain the structural information associated with the subsystem.
Example:
NbS2
_cell_subsystem.description
CIF
Description of each subsystem defining a composite structurally. The number of definitions must match the number given in _cell_subsystems_number.
Example:
NbS2 part of the layer compound (LaS)~1.14~NbS~2~
_cell_subsystem.matrix_W
CIF
In the case of composites, for each subsystem the matrix W as defined in van Smaalen (1991); [see also van Smaalen (1995) or van Smaalen (2012)]. Its dimension must match (_cell_modulation_dimension+3)*(_cell_modulation_dimension+3).
Intergrowth compounds are composed of several periodic
substructures in which the reciprocal lattices of two different
subsystems are incommensurate in at least one direction. The
indexing of the whole diffraction diagram with integer indices
requires more than three reciprocal basic vectors. However, the
distinction between main reflections and satellites is not as
obvious as in normal incommensurate structures. Indeed, true
satellites are normally difficult to locate for composites and
the modulation wave vectors are reciprocal vectors of the
other subsystem(s) referred to the reciprocal basis of one
of them. The choice of the enlarged reciprocal basis
{a*, b*, c*, q~1~,..., q~d~} is completely arbitrary, but
the reciprocal basis of each subsystem is always known through
the W matrices. These matrices [(3+d)x(3+d)-dimensional], one for
each subsystem, can be blocked as follows:
(Z^^~3~ Z^^~d~)
W^^= ( )
(V^^~3~ V^^~d~)
the dimension of each block being (3x3), (3xd), (dx3) and (dxd)
for Z^^~3~, Z^^~d~, V^^~3~ and V^^~d~, respectively. For
example, Z^^ expresses the reciprocal basis of each subsystem
in terms of the basis {a*, b*, c*, q~1~ ,..., q~d~}.
W^^ also gives the irrational components of the modulation wave
vectors of each subsystem in its own three-dimensional reciprocal
basis {a~~*, b~~*, c~~*} and the superspace group of
a given subsystem from the unique superspace group of the
composite.
The structure of these materials is always described by a set of
incommensurate structures, one for each subsystem. The atomic
coordinates, modulation parameters and wave vectors used for
describing the modulation(s) are always referred to the (direct
or reciprocal) basis of each particular subsystem. Although
expressing the structural results in the chosen common basis is
possible (using the matrices W), it is less confusing to use
this alternative description. Atomic coordinates are only
referred to a common basis when interatomic distances are
calculated. Usually, the reciprocal vectors {a*, b* and c*\}\
span the lattice of main reflections of one of the subsystems and
therefore its W matrix is the unit matrix.
For composites described in a single data block using *_subsystem_code pointers, the cell parameters, the superspace group and the measured modulation wave vectors (see CELL_WAVE_VECTOR below) correspond to the reciprocal basis described in _cell_reciprocal_basis_description and coincide with the reciprocal basis of the specific subsystem (if any) whose W matrix is the unit matrix. The cell parameters and the symmetry of the remaining subsystems can be derived using the appropriate W matrices. In any case (single or multiblock CIF), the values assigned to the items describing the atomic parameters (including the wave vectors used to describe the modulations) are always the same and are referred to the basis of each particular subsystem. Such a basis will be explicitly given in a multiblock CIF or should be calculated (with the appropriate W matrix) in the case of a single block description of the composite.
References: Smaalen, S. van (1991). Phys. Rev. B, 43, 11330-11341. Symmetry of composite crystals Smaalen, S. van (1995). Crystallogr. Rev. 4, 79-202. Incommensurate crystal structures Smaalen, S. van(2012). Incommensurate Crystallography. Oxford University Press.
CELL_SUBSYSTEMS
CIF
Data items in the CELL_SUBSYSTEMS category describe overall aspects of the subsystems present in a composite.
_cell_subsystems.number
CIF
The number of subsystems used to define the structural model of a composite structure.
CELL_WAVE_VECTOR
CIF
Data items in the CELL_WAVE_VECTOR category list the independent modulation wave vectors q~i~. The diffraction vectors are indexed in the form ha*+kb*+lc*+sum~i~ (m~i~q~i~). sum~i~ is taken over all wave vectors. In this version of the dictionary, the index i has been restricted to be less than 9.
_cell_wave_vector.seq_id
CIF
A numeric code to identify each independent wave vector. These codes define uniquely the reciprocal basis and, therefore, force the order of the Miller indices assigned to intensities, crystal faces etc.
_cell_wave_vector.x
CIF
Component of a wave vector along the reciprocal axis a^*^ of the reference structure.
_cell_wave_vector.xyz
CIF
Independent modulation wave vector(s) with which the whole diffraction pattern is indexed, expressed as fractions of the three reciprocal basis vectors of the reference structure. In the case of composites, the modulation wave vectors of each subsystem are expressed in terms of the reciprocal basis of its corresponding reference structure. Their number must match _cell_modulation_dimension. In the case of composites described in a single data block, the wave vectors are expressed in the three-dimensional basis chosen as reference in _cell.reciprocal_basis_description, which would correspond to the subsystem (if any) whose W matrix is the {(_cell.modulation_dimension + 3)*\ (_cell.modulation_dimension + 3)} unit matrix. In this case,\ the wave vectors used to describe the modulation of each subsystem are referred to their own reciprocal basis via the W matrices (for details see _cell_subsystem_matrix_W_* and _atom_site_Fourier_wave_vector_*).
_cell_wave_vector.y
CIF
Component of a wave vector along the reciprocal axis b^*^ of the reference structure.
_cell_wave_vector.z
CIF
Component of a wave vector along the reciprocal axis c^*^ of the reference structure.
CELL_WAVE_VECTORS
CIF
Data items in the CELL_WAVE_VECTORS category record overall details about the set of independent modulation wave vectors q~i~ and their measurement. The diffraction vectors are indexed in the form ha*+kb*+lc*+sum~i~ (m~i~q~i~). sum~i~ is taken over all wave vectors. In this version of the dictionary, the index i has been restricted to be less than 9.
_cell_wave_vectors.meas_details
CIF
Details about the method used to determine the independent modulation wave vector(s).
_cell_wave_vectors.pressure_max
CIF
The maximum and minimum values of the pressure in kilopascals defining the interval within which the modulation wave vector(s) were measured.
_cell_wave_vectors.pressure_min
CIF
The maximum and minimum values of the pressure in kilopascals defining the interval within which the modulation wave vector(s) were measured.
_cell_wave_vectors.temp_max
CIF
The maximum and minimum values of the temperature in kelvins defining the interval within which the modulation wave vector(s) were measured.
_cell_wave_vectors.temp_min
CIF
The maximum and minimum values of the temperature in kelvins defining the interval within which the modulation wave vector(s) were measured.
_cell_wave_vectors.variation
CIF
Details concerning the behaviour (and its experimental detection) of the wave vector(s) with temperature and/or pressure within the ranges specified by _cell_wave_vectors.pressure_max, _cell_wave_vectors.pressure_min, _cell_wave_vectors.temp_max and _cell_wave_vectors.temp_min.
DIFFRN_REFLN
CIF
Data items in the DIFFRN_REFLN category record details about the intensities measured in the diffraction experiment. The DIFFRN_REFLN data items refer to individual intensity measurements and must be included in looped lists. (The DIFFRN_REFLNS data items specify the parameters that apply to all intensity measurements. The DIFFRN_REFLNS data items are not looped.) Data items in this category are extensions of the core CIF dictionary definitions to the indexing of diffraction intensities by higher-dimensional components.
_diffrn_refln.index_m_list
CIF
Additional Miller indices needed to write the reciprocal vector of a certain reflection in the basis described in _cell_reciprocal_basis_description. Following the usual convention, such a vector would be expressed as
H=h*a*+k*b*+l*c*+m1*q(1)+...+m8*q(8),
where h,k,l are the usual _diffrn_refln.index_, and q(1)...q(8)
represent the independent wave vectors given by
_cell_wave_vector.xyz and identified by _cell_wave_vector.seq_id.
Therefore, the total number of indices of a given reflection must
match (_cell.modulation_dimension + 3) and the order of the
additional indices must be consistent with the codes given in
_cell_wave_vector.seq_id. These indices need not match
_refln.index_m_list values if a transformation of the original
measured cell has occurred.
_diffrn_refln.index_m_1
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_2
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_3
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_4
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_5
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_6
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_7
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_refln.index_m_8
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
DIFFRN_STANDARD_REFLN
CIF
Data items in the DIFFRN_STANDARD_REFLN category record details about the reflections treated as standards during the measurement of diffraction intensities. Note that these are the individual standard reflections, not the results of the analysis of the standard reflections. Data items in this category are extensions of the core CIF dictionary definitions to the indexing of standard reflections by higher-dimensional components.
_diffrn_standard_refln.index_m_list
CIF
Additional Miller indices needed to write the reciprocal vectors of the standard intensities used in the diffraction measurement process, in the basis described in _cell.reciprocal_basis_description. The total number of indices of a given standard reflection must match (_cell.modulation_dimension + 3) and the order of the additional indices must be consistent with the codes given in _cell_wave_vector.seq_id.
_diffrn_standard_refln.index_m_1
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_2
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_3
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_4
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_5
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_6
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_7
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_diffrn_standard_refln.index_m_8
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
GEOM_ANGLE
CIF
Data items in the GEOM_ANGLE category record details about the bond angles, as calculated from the ATOM, CELL and SYMMETRY data. These extensions to the core CIF dictionary definitions record the maximum, minimum and average values of angles and extend the symmetry-operation code used in angle listings to the higher-dimensional superspace form. Many GEOM_ANGLE datanames are redefined due to the consequent change in the way that they are calculated, even if the calculation method is not explicit in either this dictionary or the core.
_geom_angle.av
CIF
Average angle bounded by _geom_angle.atom_site_label_1, *_2, and *_3. The site at *_2 is at the apex of the angle.
_geom_angle.max
CIF
Maximum angle bounded by _geom_angle.atom_site_label_1, *_2, and *_3. The site at *_2 is at the apex of the angle.
_geom_angle.min
CIF
Minimum angle bounded by _geom_angle.atom_site_label_1, *_2, and *_3. The site at *_2 is at the apex of the angle.
_geom_angle.site_ssg_symmetry_1
CIF
The symmetry code of each atom site as the symmetry operation number 'n' and the higher-dimensional translation 'm1...mp'. These numbers are combined to form the code 'n m1...mp' or n_m1...mp. The character string n_m1...mp is composed as follows: 'n' refers to the symmetry operation that is applied to the superspace coordinates. It must match a number given in _space_group_symop_ssg_id. 'm1...mp' refer to the translations that are subsequently applied to the symmetry-transformed coordinates to generate the atom used in calculating the angle. These translations (t1,...tp) are related to (m1...mp) by the relations m1=5+t1, ..., mp=5+tp. By adding 5 to the translations, the use of negative numbers is avoided. The number 'p' must agree with (_cell_modulation_dimension + 3). If there are no cell translations, the translation number may be omitted. If no symmetry operations or translations are applicable, then a single full stop '.' is used.
Examples:
4
7_645
_geom_angle.site_ssg_symmetry_2
CIF
See _geom_angle.site_ssg_symmetry_1 for description.
_geom_angle.site_ssg_symmetry_3
CIF
See _geom_angle.site_ssg_symmetry_1 for description.
_geom_angle.distances
CIF
The pair of distances between sites 1 - 2 and 2 - 3.
_geom_angle.value
CIF
Angle defined by the atoms located at atom_site_x/site_symmetry_x for x = 1,2,3. The vertex atom is at site x = 2.
_geom_angle.value_su
CIF
Standard Uncertainty of the angle defined by the sites identified by _geom_angle.id
REFINE
CIF
Data items in the REFINE category record details about the structure refinement parameters. The new items in this category extend those of the core CIF dictionary and are specific to the refinement of modulated structures.
_refine.ls_mod_func_description
CIF
Types of modulation present in the structural model and their parameterization.
Example:
Only displacive modulation. Fourier series.
_refine.ls_mod_hydrogen_treatment
CIF
Treatment of hydrogen-atom modulation parameters in refinement.
_refine.ls_mod_overall_phason_coeff
CIF
Phason coefficient used to calculate the overall phason correction.
_refine.ls_mod_overall_phason_formula
CIF
The expression for the overall phason correction, if used.
REFLN
CIF
Data items in the REFLN category record details about the reflections used to determine the ATOM_SITE data items. The REFLN data items refer to individual reflections and must be included in looped lists. The REFLNS data items specify the parameters that apply to all reflections. The REFLNS data items are not looped. Data items in this category are extensions of the core CIF dictionary definitions to the indexing of reflections used in the refinement by higher-dimensional components.
_refln.index_m_list
CIF
Additional Miller indices of a particular reflection in the basis described in _cell_reciprocal_basis_description. The total number of indices must match (_cell.modulation_dimension + 3). The order of the additional indices must be consistent with the codes given in _cell_wave_vector.seq_id.
_refln.index_m_1
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_2
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_3
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_4
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_5
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_6
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_7
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_refln.index_m_8
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
REFLNS
CIF
Data items in the REFLNS category record details about the reflections used to determine the ATOM_SITE data items. The REFLN data items refer to individual reflections and must be included in looped lists. The REFLNS data items specify the parameters that apply to all reflections. The REFLNS data items are not looped. Data items in this category extend the core CIF dictionary definitions providing independent checks on the range of values recorded for each of the additional Miller indices given in the REFLN category.
_reflns.limit_index_m_max_list
CIF
Maximum of the additional Miller indices appearing in _refln.index_m_*. The number of ranges must match _cell_modulation_dimension. The order of the additional indices must be consistent with the codes given in _cell.wave_vector_seq_id. These need not be the same as the _reflns.limit_index_m_*.
_reflns.limit_index_m_min_list
CIF
Minimum values of the additional Miller indices appearing in _refln.index_m_*. The number of ranges must match _cell_modulation_dimension. The order of the additional indices must be consistent with the codes given in _cell.wave_vector_seq_id. These need not be the same as the _reflns.limit_index_m_*.
_reflns.limit_index_m_1_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_2_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_3_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_4_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_5_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_6_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_7_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_8_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_1_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_2_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_3_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_4_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_5_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_6_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_7_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_reflns.limit_index_m_8_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
SPACE_GROUP_SYMOP
CIF
The SPACE_GROUP_SYMOP category introduced in the symmetry CIF dictionary (cif_sym.dic) is intended to replace the original core SYMMETRY_EQUIV category. It contains information about the symmetry operations of the space group. For modulated structures, superspace-group descriptions may be included in the same category, but include the _ssg_ flag to indicate their dimensionality of > 3.
_space_group_symop.ssg_id
CIF
A numeric code identifying each entry in the _space_group_symop_ssg_operation_algebraic list.
_space_group_symop.ssg_operation_algebraic
CIF
A parsable string giving one of the symmetry operations of the superspace group in algebraic form. These data will generally be repeated in a loop. Use symbols as necessary according to _cell_modulation_dimension. All symmetry operations should be entered, including the identity operation, those for lattice centring and that for a centre of symmetry, if present. The symbolic notation for coordinates is such that the identity operation is expressed as x1,x2,x3,...,xn.
_space_group_symop_ssg_operation_algebraic must always be present in a CIF corresponding to a modulated structure.
Example:
x1,-x2,x3,1/2+x4
ATOM_SITE
CIF
_atom_site.displace_modulation_flag
CIF
A code that signals whether the structural model includes the modulation of the positional coordinates of a given atom site.
_atom_site.occ_modulation_flag
CIF
A code that signals whether the structural model includes the modulation of the occupation of a given atom site.
_atom_site.subsystem_code
CIF
A code that links a given atom or rigid-group site to one of the
subsystems present in a composite. This code provides an
alternative description for composites which is less explicit
than that based on linked data blocks (see the description in
this dictionary of audit_link.*). It must match one of
the labels specified for _cell_subsystem.code.
_atom_site.U_modulation_flag
CIF
A code that signals whether the structural model includes the modulation of the ADP of a given atom site.
CELL
CIF
_cell.commen_supercell_matrix
CIF
For commensurately modulated structures the transformation, T, from the crystallographic axes of the reference structure to the supercell generated by the wave vectors expressed as
(a~s~,b~s~,c~s~) = (a~r~,b~r~,c~r~)T,
where (a~s~,b~s~,c~s~) and (a~r~,b~r~,c~r~) are the crystallographic
axes of the supercell and the reference cell, respectively.
_cell.modulation_dimension
CIF
Number of additional reciprocal vectors needed to index the whole diffraction pattern using integer Miller indices.
_cell.reciprocal_basis_description
CIF
Definition of the higher-dimensional basis with respect to which the Miller indices are defined. The three-dimensional basis used to index the additional wave vectors should be clearly indicated.
Examples:
a*,b*,c* (reciprocal basis spanning the lattice of main
reflections) and q (incommensurate with respect to a*,b*,c*)
The diffraction pattern can be indexed with four integers based
on the reciprocal vectors a*~1~=a*~11~, a*~2~=a*~12~,
a*~3~=a*~13~, a*~4~=a*~21~. a*~1j~ (j=1,2,3) index the
main reflections of the 1st subsystem. a*~21~ is incommensurate
with a*~11~.
DIFFRN_REFLNS
CIF
_diffrn_reflns.limit_index_m_max_list
CIF
Maximum values of the additional Miller indices appearing in _diffrn_refln.index_m_list. The number of ranges must match _cell.modulation_dimension. The order of the additional indices must be consistent with the codes given in _cell.wave_vector_seq_id.
_diffrn_reflns.limit_index_m_1_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_2_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_3_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_4_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_5_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_6_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_7_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_8_max
CIF
Maximum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_min_list
CIF
Minimum values of the additional Miller indices appearing in _diffrn_refln.index_m_list. The number of ranges must match _cell.modulation_dimension. The order of the additional indices must be consistent with the codes given in _cell.wave_vector_seq_id.
_diffrn_reflns.limit_index_m_1_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_2_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_3_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_4_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_5_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_6_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_7_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.limit_index_m_8_min
CIF
Minimum value of the additional Miller indices appearing in _diffrn_reflns.index_m_* and _reflns.index_m_*.
_diffrn_reflns.satellite_order_max
CIF
Maximum order of observed satellites.
EXPTL_CRYSTAL
CIF
_exptl_crystal.type_of_structure
CIF
The type of structure. This is used to check the consistency of a CIF: the data blocks that are expected and/or certain characteristic parameters depend on whether the material is classified as crystalline (periodic in three dimensions), modulated or composite.
EXPTL_CRYSTAL_FACE
CIF
_exptl_crystal_face.index_m_list
CIF
Additional Miller indices of the crystal face associated with the value _exptl_crystal_face_perp_dist when the face is indexed using a multidimensional scheme. The total number of indices must match (_cell.modulation_dimension + 3). The order of the indices must be consistent with the codes given in _cell_wave_vector.seq_id.
_exptl_crystal_face.index_m_1
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_2
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_3
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_4
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_5
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_6
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_7
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
_exptl_crystal_face.index_m_8
CIF
Additional Miller indices needed to write the reciprocal vector in the definition of _diffrn_refln_index.m_list, _diffrn_standard_refln.index_m_list, _exptl_crystal_face.index_m_list.
FUNCTION
CIF
_function.Crenel
CIF
The function:
o = Crenel(c, w, x4)
returns, 1 if x4 belongs to the interval [c-w/2,c+w/2], 0 otherwise.
x4 is a particular value of the internal coordinate, c is the centre of a
crenel function in internal space and w is its width. The use of this
function is restricted to one-dimensional modulated structures.
_function.Sawtooth
CIF
The function:
s = Sawtooth(a, c, w, x4)
returns
2* a * ((x4-c)/w)
for x4 belonging to the interval [c-(w/2), c+(w/2)], where a is the array containing the the amplitudes (maximum displacements) along each crystallographic axis, w is the width of the sawtooth, x4 is a particular value of the internal coordinate and c is the centre of the function in internal space. The use of this function is restricted to one-dimensional modulated structures.
_function.Zigzag
CIF
The function:
z = Zigzag(a, c, w, x4)
returns
2* a * ((x4-c)/w)
for x4 belonging to the interval [c-(w/2), c+(w/2)] or
-2* a * ((x4-c)/w)
for x4 in the interval [c+1/2-(w/2), c+1/2+(w/2)]
where a is the array containing the the amplitudes (maximum displacements) along each crystallographic axis, w is the width of the zigzag, x4 is a particular value of the internal coordinate and c is the centre of the function in internal space. The use of this function is restricted to one-dimensional modulated structures.
GEOM_BOND
CIF
Data items in the GEOM_BOND category record
details about bonds, as calculated from the ATOM, CELL and SYMMETRY data. This category extends the symmetry-operation code used in bond listings to the higher-dimensional superspace form and therefore redefines many datanames to reflect the changed method of distance calculation.
_geom_bond.distance_av
CIF
Average value of the intramolecular bond distance.
_geom_bond.distance_max
CIF
Maximum value of the intramolecular bond distance.
_geom_bond.distance_min
CIF
Minimum value of the intramolecular bond distance.
_geom_bond.site_ssg_symmetry_1
CIF
The symmetry code of each atom site as the symmetry operation number 'n' and the higher-dimensional translation 'm1...mp'. These numbers are combined to form the code 'n m1...mp' or n_m1...mp. The character string n_m1...mp is composed as follows: 'n' refers to the symmetry operation that is applied to the superspace coordinates. It must match a number given in _space_group_symop_ssg_id. 'm1...mp' refer to the translations that are subsequently applied to the symmetry-transformed coordinates to generate the atom used in calculating the bond. These translations (t1,...tp) are related to (m1...mp) by the relations m1=5+t1, ..., mp=5+tp. By adding 5 to the translations, the use of negative numbers is avoided. The number 'p' must agree with (_cell_modulation_dimension + 3). If there are no cell translations, the translation number may be omitted. If no symmetry operations or translations are applicable then a single full stop '.' is used.
Examples:
4
7_645
_geom_bond.site_ssg_symmetry_2
CIF
The symmetry code described in _geom_bond_site_ssg_symmetry_1.
_geom_bond.distance
CIF
Intramolecular bond distance between the sites identified
_geom_bond.distance_su
CIF
Standard Uncertainty of the intramolecular bond distance between the sites identified by _geom_bond.id
GEOM_CONTACT
CIF
The CATEGORY of data items used to specify the interatomic contact distances in the structural model.
_geom_contact.distance_av
CIF
Average value of the interatomic contact distance.
_geom_contact.distance_max
CIF
Maximum value of the interatomic contact distance.
_geom_contact.distance_min
CIF
Minimum value of the interatomic contact distance.
_geom_contact.site_ssg_symmetry_1
CIF
The symmetry code of each atom site as the symmetry operation number 'n' and the higher-dimensional translation 'm1...mp'. These numbers are combined to form the code 'n m1...mp' or n_m1...mp. The character string n_m1...mp is composed as follows: 'n' refers to the symmetry operation that is applied to the superspace coordinates. It must match a number given in _space_group_symop_ssg_id. 'm1...mp' refer to the translations that are subsequently applied to the symmetry-transformed coordinates to generate the atom used in calculating the contact. These translations (t1,...tp) are related to (m1...mp) by the relations m1=5+t1, ..., mp=5+tp. By adding 5 to the translations, the use of negative numbers is avoided. The number 'p' must agree with (_cell_modulation_dimension + 3). If there are no cell translations, the translation number may be omitted. If no symmetry operations or translations are applicable, then a single full stop '.' is used.
Examples:
4
7_645
_geom_contact.site_ssg_symmetry_2
CIF
The symmetry code described in _geom_contact.site_ssg_symmetry_1
_geom_contact.distance
CIF
Intermolecular distance between the atomic sites
_geom_contact.distance_su
CIF
Standard Uncertainty of the intermolecular distance between the atomic sites identified by _geom_contact.id
GEOM_TORSION
CIF
The CATEGORY of data items used to specify the torsion angles in the structural model as derived from the atomic sites.
_geom_torsion.av
CIF
Average torsion angle; see _geom_torsion.max.
_geom_torsion.max
CIF
Maximum torsion angle bounded by the four atom sites identified by the _geom_torsion_atom_site_label_ codes. These must match labels specified as _atom_site.label in the atom list. The torsion-angle definition should be that of Klyne and Prelog (1960). Reference: Klyne, W. & Prelog, V. (1960).
Experientia, 16, 521-523. Description of steric relationships across single bonds.
_geom_torsion.min
CIF
Minimum torsion angle; see _geom_torsion.max.
_geom_torsion.site_ssg_symmetry_1
CIF
The symmetry code of each atom site as the symmetry operation number 'n' and the higher-dimensional translation 'm1...mp'. These numbers are combined to form the code 'n m1...mp' or n_m1...mp. The character string n_m1...mp is composed as follows: 'n' refers to the symmetry operation that is applied to the superspace coordinates. It must match a number given in _space_group_symop_ssg_id. 'm1...mp' refer to the translations that are subsequently applied to the symmetry-transformed coordinates to generate the atom used in calculating the angle. These translations (t1,...tp) are related to (m1...mp) by the relations m1=5+t1, ..., mp=5+tp. By adding 5 to the translations, the use of negative numbers is avoided. The number 'p' must agree with (_cell_modulation_dimension + 3). If there are no cell translations, the translation number may be omitted. If no symmetry operations or translations are applicable, then a single full stop '.' is used.
Examples:
4
7_645
_geom_torsion.site_ssg_symmetry_2
CIF
Symmetry code of described in _geom_torsion.site_ssg_symmetry_1.
_geom_torsion.site_ssg_symmetry_3
CIF
Symmetry code of described in _geom_torsion.site_ssg_symmetry_1.
_geom_torsion.site_ssg_symmetry_4
CIF
Symmetry code of described in _geom_torsion.site_ssg_symmetry_1.
_geom_torsion.angle
CIF
Angle defined by the sites identified by _geom_torsion.id. The torsion-angle definition should be that of Klyne and Prelog. The vector direction *_label_2 to *_label_3 is the viewing direction, and the torsion angle is the angle of twist required to superimpose the projection of the vector between site 2 and site 1 onto the projection of the vector between site 3 and site 4. Clockwise torsions are positive, anticlockwise torsions are negative. Ref: Klyne, W. & Prelog, V. (1960). Experientia, 16, 521-523.
_geom_torsion.angle_su
CIF
Standard Uncertainty of the torsion angle.
SPACE_GROUP
CIF
_space_group.ssg_IT_number
CIF
Superspace-group number from International Tables for Crystallography, Vol. C (2006). Valid only for one-dimensional modulated structures. Reference: International Tables for Crystallography (2006). Vol. C,
Chapter 9.8. John Wiley & Sons, Ltd. Incommensurate and commensurate modulated structures
_space_group.ssg_name
CIF
Superspace-group symbol conforming to an alternative definition from that given in _space_group_ssg_name_IT and _space_group_ssg_name_WJJ for one-dimensional modulated structures or to the superspace-group name for higher dimensions. When necessary, indicate the origin and the setting. Use a colon ':' as a separator between the different parts of the superspace-group symbol. Within each part, leave a space between each component. Rules for the notation for Hermann-Mauguin and Hall symbols (if present) are given in the symmetry CIF dictionary (cif_sym.dic) and, partially, in _space_group_ssg_name_IT and _space_group_ssg_name_WJJ. For composites described in a single data block, the superspace group describes the symmetry of the whole structure. The symmetry of each subsystem can be derived using the appropriate W matrices.
Example:
W:-P -2xb -2ya:q q
_space_group.ssg_name_IT
CIF
Superspace-group symbol as given in International Tables for Crystallography, Vol. C (2006). Valid only for one-dimensional modulated structures. The symbol is divided into three parts: the Hermann-Mauguin space-group symbol of the reference structure, the modulation wave vector and the phase shift (or internal translation) associated with each component of the space group. Each component of the space-group name is separated by a space. Subscripts should appear without special symbols and bars should be given as negative signs. The components of the modulation wave vector (in parentheses) and the phase shifts are also separated by a space. For composites described in a single data block, the superspace group describes the symmetry of the whole structure. The symmetry of each subsystem can be derived using the appropriate W matrices. Reference: International Tables for Crystallography (2006). Vol. C,
Chapter 9.8. John Wiley & Sons, Ltd. Incommensurate and commensurate modulated structures
Example:
P n m a (0 0 ) 0 s 0
_space_group.ssg_name_WJJ
CIF
Superspace-group symbol as given by de Wolff, Janssen & Janner (1981). Valid only for one-dimensional modulated structures. The symbol is divided into three parts separated by colons ':': the superspace lattice symbol, the Hermann-Mauguin space-group symbol of the reference structure and the phase shift (or internal translation) associated with each component of the space group. Each component of the space-group name is separated by a space. Subscripts should appear without special symbols and bars should be given as negative signs. The phase shifts are also separated by a space. For composites described in a single data block, the superspace group describes the symmetry of the whole structure. The symmetry of each subsystem can be derived using the appropriate W matrices. Reference: Wolff, P. M. de, Janssen, T. & Janner, A. (1981).
Acta Cryst. A37, 625-636. The superspace groups for incommensurate crystal structures with a one-dimensional modulation
Example:
P:P c m n:s s -1
_space_group.ssg_WJJ_code
CIF
Superspace-group code as given by de Wolff, Janssen & Janner (1981). Valid only for one-dimensional modulated structures. Reference: Wolff, P. M. de, Janssen, T. & Janner, A. (1981).
Acta Cryst. A37, 625-636. The superspace groups for incommensurate crystal structures with a one-dimensional modulation
Example:
28a.10.1/2
Revision history
Version 3.0 (2014-06-27) Initial conversion to DDLm (Syd Hall)
Version 3.1 (2016-11-17) Substantial edits to conform to current DDLm, CIF2 syntax (James Hester).
Version 3.2 (2017-03-11) Returned all additional indices to main dictionary, removed category_id
from templates(James Hester)
Version 3.2.1 (2019-09-25) Corrected a typo in the definition of the _geom_torsion.angle data item. Changed the content type of multiple data items from 'Count' to 'Integer' and assigned the appropriate enumeration range if needed.
International Tables for Crystallography
Volume G: Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon
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An essential guide and reference to CIF for programmers, data managers handling crystal-structure information and practising crystallographers.
