magnetic_refinements
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magnetic_refinements [2012/06/22 10:09] – johnsoevans | magnetic_refinements [2022/11/03 15:08] (current) – external edit 127.0.0.1 | ||
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+ | ====== Magnetic Refinements ====== | ||
+ | Topas v5 will perform magnetic refinements. | ||
+ | |||
+ | Two common pitfalls are comparing moments between different pieces of software (there are several different conventions in use) and scaling moments appropriately when the magnetic cell size is different to the nuclear. | ||
+ | |||
+ | One way of checking refinements (to make sure no symmetry bugs) is to write everything out in p1 using a command like: | ||
+ | |||
+ | <code topas> | ||
+ | in_str_format</ | ||
+ | |||
+ | and then checking the refinement in P1 (1.1). | ||
+ | |||
+ | <code topas> | ||
+ | |||
+ | ====== Topas Coordinate System ====== | ||
+ | |||
+ | The topas coordinate system is in Bohr Magneton/ | ||
+ | This is the reduced lattice coordinate system, where the magnetic metric tensor (M) is the same metric used for interatomic distances (G). | ||
+ | |||
+ | The refined moments can be displayed in alternate systems using macros as shown in the following: | ||
+ | |||
+ | site Fe2_1 x 0.00000 y 0.75000 z 0.00000 occ Fe+2 1 beq 1 mlx 0.00000 mly 0.00000 mlz @ 0.26118` | ||
+ | MM_CrystalAxis_Display( 0.00033`, 0.00000, 3.08356`) | ||
+ | MM_Cartesian_Display(-0.96490`, | ||
+ | |||
+ | In this example it's a monoclinic cell with a 18.254469 b 5.689239 c 11.428258 be 108.24182 and moments along c. These are 3.084 BM from the crystalaxis display which is equivalent to (0.9649^2 + 0^2 + 2.92859^2)^0.5 from the Cartesian. | ||
+ | |||
+ | There are also macros available which let you refine in other coordinate systems. | ||
+ | |||
+ | Let X correspond to cross product. | ||
+ | |||
+ | Reciprocal lattice is: | ||
+ | | ||
+ | a* = b X c | ||
+ | b* = c X a | ||
+ | c* = a X b | ||
+ | |||
+ | In MM_Cartesian_Refine, | ||
+ | |||
+ | ax i | ||
+ | bx i + by j | ||
+ | cx i + cy j + cx k | ||
+ | |||
+ | where i, j, k are unit Cartesian vectors, Or, | ||
+ | |||
+ | i || a | ||
+ | j || a X (a X b) = a X c* | ||
+ | k || a X b = c* | ||
+ | |||
+ | ====== Crystal coordinate systems for defining components of magnetic moments ====== | ||
+ | |||
+ | [N.B. This is a frozen summary. | ||
+ | |||
+ | (1) Bohr Magneton/ | ||
+ | This is the reduced lattice coordinate system, where the magnetic metric tensor (M) is the same metric used for interatomic distances (G). | ||
+ | |||
+ | (2) Bohr Magneton units, with x||a, y||b and z||c | ||
+ | This is the crystal-axis coordinate system, where components of the moment are defined by their projections along the lattice basis vectors. | ||
+ | If we define L = {{a, | ||
+ | |||
+ | (3) Bohr Magneton units, with x||a, y||b* and z||(a x b*) | ||
+ | This is an orthonormal coordinate system defined by a and b*. The magnetic metric tensor is the identity matrix. | ||
+ | |||
+ | (4) Bohr Magneton units, with x||a, y||(c* x a) and z||c* | ||
+ | This is an orthonormal coordinate system defined by a and c*. The magnetic metric tensor is the identity matrix. | ||
+ | |||
+ | (5) Bohr Magneton units for the magnitude, plus two spherical-coordinate angles measured relative to the X and Z axes of system (4). | ||
+ | φ runs from 0 to 2π in the XY plane, and θ runs from 0 to π relative to Z. | ||
+ | |||
+ | ==== Usage ==== | ||
+ | |||
+ | |||
+ | FULLPROF: Systems (2) and (5) can both be used for refinements. | ||
+ | |||
+ | JANA: System (1) is used internally; but systems (2) and (5) can both be used for refinements. | ||
+ | |||
+ | GSAS: Systems (4) is used for refinements; | ||
+ | |||
+ | TOPAS: The parameters of system (1) are explicitly defined (in an unreleased version), though built-in macros for systems (2) and (4) are available for refinements. | ||
+ | |||
+ | ==== Comments ==== | ||
+ | |||
+ | (1) For atomic positions, reduced lattice coordinates are unitless and independent of the cell parameters. | ||
+ | |||
+ | (2) Crystal-axis coordinates have intuitive units (Bohr magnetons) and are easy communicate. | ||
+ | |||
+ | (3) This system does not appear to be in common use. | ||
+ | |||
+ | (4) Orthonormal coordinates are advantageous because of the ease with which the components of the moment are related to its magnitude. |