Introduction ============ .. warning:: This manual refers to the 'Vlieg' calculation available in Diffcalc I. By default Diffcalc II now uses its 'You' engine. This manual will be updated soon. For now the developer guide shows how the new constraint system works. This manual assumes that you are running Diffcalc within the external framework of the GDA or Minigda and that Diffcalc has been configured for the six circle diffractometer pictured here: .. figure:: images/sixcircle_gamma_on_arm.* :scale: 50 :align: center Gamma-on-delta six-circle diffractometer, modified from Elias Vlieg & Martin Lohmeier (1993) Your Diffcalc configuration will have been customised for the geometry of your diffractometer and possibly the types of experiment you perform. For example: a five-circle diffractometer might be missing the Gamma circle above, some six-circle modes and the option to fix gamma that would otherwise exist in some modes. The laboratory, crystal and reciprocal-lattice coordinate frames are defined with respect to the beam and to gravity to be (for a cubic crystal): .. figure:: images/fix.png :align: center Laboratory and illustratrive crystal coordinate frames for a cubic crystal The crystal lattice basis vectors are defined within the Cartesian crystal coordinate frame to be: .. figure:: images/unit_cell.* :align: center :scale: 100 Unit cell defined in crystal coordinate frame .. _overview: Overview ======== The following assumes that the diffractometer has been properly levelled, aligned with the beam and zeroed. See the `SPEC fourc manual `__. Before moving in hkl space you must calculate a UB matrix by specifying the crystal's lattice parameters (which define the B matrix) and finding two reflections (from which the U matrix can be inferred); and, optionally for surface-diffraction experiments, determine how the surface of the crystal is oriented with respect to the phi axis. Once a UB matrix has been calculated, the diffractometer may be driven in hkl coordinates. A valid diffractometer setting maps easily into a single hkl value. However for a diffractometer with more than three circles there are excess degrees of freedom when calculating a diffractometer setting from an hkl value. Diffcalc provides modes for using up the excess degrees of freedom. Diffcalc does not perform scans directly. Instead, scannables that use diffcalc to map between reciprocal lattice space and real diffractometer settings are scanned using the Gda's (or minigda's) generic scan mechanism. Theory ------ Thanks to Elias Vlieg for sharing his dos based ``DIF`` software that Diffcalc has borrowed heavily from. (See also the THANKS.txt file). See the papers (included in ``docs/ref``): * Busing & Levi (1966), "Angle Calculations for 3- and 4- Circle X-ray and Neutron Diffractometers", Acta Cryst. 22, 457 * Elias Vlieg & Martin Lohmeier (1993), "Angle Calculations for a Six-Circle Surface X-ray Diffractometer", J. Appl. Cryst. 26, 706-716 Getting Help ============ There are few commands to remember. If a command is called without arguments, Diffcalc will prompt for arguments and provide sensible defaults which can be chosen by pressing enter. The ``helpub`` and ``helphkl`` commands provide help with the crystal orientation and hkl movement phases of an experiment respectively:: >>> helpub Diffcalc -------- helpub ['command'] - lists all ub commands, or one if command is given helphkl ['command'] - lists all hkl commands, or one if command is given UB State -------- newub 'name' - starts a new ub calculation with no lattice or reflection list loadub 'name' - loads an existing ub calculation: lattice and reflection list saveubas 'name' - saves the ubcalculation with a new name (other changes autosaved) ub - shows the complete state of the ub calculation UB lattice ---------- setlat - prompts user to enter lattice parameters (in Angstroms and Deg.) setlat 'name' a - assumes cubic setlat 'name' a b - assumes tetragonal setlat 'name' a b c - assumes ortho setlat 'name' a b c gam - assumes mon/hex with gam not equal to 90 setlat 'name' a b c alpha beta gamma - arbitrary UB surface ---------- sigtau [sigma tau] - sets sigma and tau UB reflections -------------- showref - shows full reflection list addref - add reflection addref h k l ['tag'] - add reflection with hardware position and energy addref h k l (p1,p2...pN) energy ['tag']- add reflection with specified position and energy delref num - deletes a reflection (numbered from 1) swapref - swaps first two reflections used for calculating U swapref num1 num2 - swaps two reflections (numbered from 1) UB calculation -------------- setu [((,,),(,,),(,,))] - manually set u matrix setub ((,,),(,,),(,,)) - manually set ub matrix calcub - (re)calculate u matrix from ref1 and ref2 checkub - show calculated and entered hkl values for reflections >>> helphkl Diffcalc -------- helphkl [command] - lists all hkl commands, or one if command is given helpub [command] - lists all ub commands, or one if command is given Settings -------- hklmode [num] - changes mode or shows current and available modes and all settings setalpha [num] - fixes alpha, or shows all settings if no num given setgamma [num] - fixes gamma, or shows all settings if no num given setbetain [num] - fixes betain, or shows all settings if no num given setbetaout [num] - fixes betaout, or shows all settings if no num given trackalpha [boolean] - determines wether alpha parameter will track alpha axis trackgamma [boolean] - determines wether gamma parameter will track gamma axis trackphi [boolean] - determines wether phi parameter will track phi axis setsectorlim [omega_high omega_low phi_high phi_low]- sets sector limits Motion ------ pos hkl [h k l] - move diffractometer to hkl, or read hkl position. Use None to hold a value still sim hkl [h k l] - simulates moving hkl hkl - shows loads of info about current hkl position pos sixc [alpha, delta, gamma, omega, chi, phi,]- move diffractometer to Eularian position. Use None to hold a value still sim sixc [alpha, delta, gamma, omega, chi, phi,]- simulates moving sixc sixc - shows loads of info about current sixc position Diffcalc's Scannables ===================== Please see :ref:`moving-in-hkl-space` and :ref:`scanning-in-hkl-space` for some relevant examples. To list and show the current positions of your beamline's scannables use ``pos`` with no arguments:: >>> pos Results in: **Energy and wavelength scannables**:: energy 12.3984 wl: 1.0000 **Diffractometer scannables**, as a group and in component axes (in the real GDA these have limits):: sixc: alpha: 0.0000 delta: 0.0000 gamma: 0.0000 omega: 0.0000 chi: 0.0000 phi: 0.0000 alpha: 0.0000 chi: 0.0000 delta: 0.0000 gamma: 0.0000 omega: 0.0000 phi: 0.0000 **Dummy counter**, which in this example simply counts at 1hit/s:: cnt: 0.0000 **Hkl scannable**, as a group and in component:: hkl: Error: No UB matrix h: Error: No UB matrix k: Error: No UB matrix l: Error: No UB matrix **Parameter scannables**, used in some modes, these provide a scannable alternative to the series of ``fix`` commands described in :ref:`moving-in-hkl-space`.:: alpha_par:0.00000 azimuth: --- betain: --- betaout: --- gamma_par:0.00000 phi_par: --- Note that where a parameter corresponds with a physical diffractometer axis, it can also be set to track that axis directly. See `Tracking axis`_ below. Crystal orientation =================== Before moving in hkl space you must calculate a UB matrix by specifying the crystal's lattice parameters (which define the B matrix) and finding two reflections (from which the U matrix can be inferred); and, optionally for surface-diffraction experiments, determine how the surface of the crystal is oriented with respect to the phi axis (see :ref:`overview`). Starting a UB calculation ------------------------- A *UB-calculation* contains the description of the crystal-under-test, any saved reflections, sigma & tau (both default to 0), and a B & UB matrix pair if they have been calculated or manually specified. Starting a new UB calculation will clear all of these. Before starting a UB-calculation, the ``ub`` command used to summarise the state of the current UB-calculation, will reflect that no UB-calculation has been started:: >>> ub No UB calculation started. Wavelength: 1.239842 Energy: 10.000000 A new UB-calculation calculation may be started and lattice specified explicitly:: >>> newub 'b16_270608' >>> setlat 'xtal' 3.8401 3.8401 5.43072 90 90 90 or interactively:: >>> newub calculation name: b16_270608 crystal name: xtal a [1]: 3.8401 b [3.8401]: 3.8401 c [3.8401]: 5.43072 alpha [90]: 90 beta [90]: 90 gamma [90]: 90 where a,b and c are the lengths of the three unit cell basis vectors in Angstroms, and alpha, beta and gamma the typically used angles (defined in the figure above) in Degrees. The ``ub`` command will show the state of the current UB-calculation (and the current energy for reference):: UBCalc: b16_270608 ====== Crystal ------- name: xtal lattice: a ,b ,c = 3.84010, 3.84010, 5.43072 alpha, beta , gamma = 90.00000, 90.00000, 90.00000 reciprocal: b1, b2, b3 = 1.63620, 1.63620, 1.15697 beta1, beta2, beta3 = 1.57080, 1.57080, 1.57080 B matrix: 1.6362035642769 -0.0000000000000 -0.000000000000 0.0000000000000 1.6362035642769 -0.000000000000 0.0000000000000 0.0000000000000 1.156970955450 Reflections ----------- energy h k l alpha delta gamma omega chi phi tag UB matrix --------- none calculated Sigma: 0.000000 Tau: 0.000000 Wavelength: 1.000000 Energy: 12.398420 Specifying Sigma and Tau for surface diffraction experiments ------------------------------------------------------------ Sigma and Tau are used in modes that fix either the beam exit or entry angle with respect to the crystal surface, or that keep the surface normal in the horizontal laboratory plane. For non surface-diffraction experiments these can safely be left at zero. For surface diffraction experiments, where not only the crystal's lattice planes must be oriented appropriately but so must the crystal's optical surface, two angles _Tau_ and _Sigma_ define the orientation of the surface with respect to the phi axis. Sigma is (minus) the amount of chi axis rotation and Tau (minus) the amount of phi axis rotation needed to move the surface normal parallel to the omega circle axis. These angles are often determined by reflecting a laser from the surface of the Crystal onto some thing and moving chi and tau until the reflected spot remains stationary with movements of omega. Use ``sigtau`` with no args to set interactively:: >>> pos chi -3.1 chi: -3.1000 >>> pos phi 10.0 phi: 10.0000 >>> sigtau sigma, tau = 0.000000, 0.000000 chi, phi = -3.100000, 10.000000 sigma[ 3.1]: 3.1 tau[-10.0]: 10.0 Sigma and Tau can also be set explicitly:: >>>sigtau 0 0 Managing reflections -------------------- The normal way to calculate a UB matrix is to find the position of **two** reflections with known hkl values. Diffcalc allows many reflections to be recorded but currently only uses the first two when calculating a UB matrix. Add reflection at current location ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is normal to first move to a reflection:: >>> pos en 10 en: 10.0000 >>> pos sixc [5.000, 22.790, 0.000, 1.552, 22.400, 14.255] sixc: alpha: 5.0000 delta: 22.7900 gamma: 0.0000 omega: 1.5520 chi: 22.4000 phi: 14.2550 and then use the ``addref`` command either explicitly:: addref 1 0 1.0628 'optional_tag' or interactively:: >>> addref h: 1 k: 0 l: 1.0628 current pos[y]: y tag: 'tag_string' to add a reflection. Add a reflection manually ~~~~~~~~~~~~~~~~~~~~~~~~~ If a reflection cannot be reached but its position is known (or if its position has been previously determined), a reflection may be added without first moving to it either explicitly:: >>> addref 0 1 1.0628 [5.000, 22.790, 0.000,4.575, 24.275, 101.320] 'optional_tag' or interactively:: >>> addref h: 0 k: 1 l: 1.0628 current pos[y]: n alpha[5.000]: delta[22.79]: gamma[0.000]: omega[1.552]: 4.575 chi[22.40]: 24.275 phi[14.25]: 101.320 en[9.998]: tag: optional_tag2 Edit reflection list ~~~~~~~~~~~~~~~~~~~~ Use ``showref`` to show the reflection list:: >>> showref energy h k l alpha delta gamma omega chi phi tag 1 9.999 1.00 0.00 1.06 5.0000 22.7900 0.0000 1.5520 22.4000 14.2550 1st 2 9.999 0.00 1.00 1.06 5.0000 22.7900 0.0000 4.5750 24.2750 101.32000 2nd Use ``swapref`` to swap reflections:: >>> swapref 1 2 Recalculating UB matrix. >>> showref energy h k l alpha delta gamma omega chi phi tag 1 9.999 0.00 1.00 1.06 5.0000 22.7900 0.0000 4.5750 24.2750 101.3200 2nd 2 9.999 1.00 0.00 1.06 5.0000 22.7900 0.0000 1.5520 22.4000 14.2550 1st Use ``delref`` to delete a reflection:: >>> delref 1 >>> showref energy h k l alpha delta gamma omega chi phi tag 1 9.999 1.00 0.00 1.06 5.0000 22.7900 0.0000 1.5520 22.4000 14.2550 1st Calculating a UB matrix ----------------------- Unless a U or UB matrix has been manually specified, a new UB matrix will be calculated after the second reflection has been found, or whenever one of the first two reflections is changed. Use the command ``calcub`` to force the UB matrix to be calculated from the first two reflections. If you have misidentified a reflection used for the orientation the resulting UB matrix will be incorrect. Always use the ``checkub`` command to check that the computed values agree with the estimated values:: >>>checkub energy h k l h_comp k_comp l_comp tag 1 9.9987 1.00 0.00 1.06 1.0000 0.0000 1.0628 1st 2 9.9987 0.00 1.00 1.06 -0.0329 1.0114 1.0400 2nd Notice that the first reflection will always match, but that the second will not match exactly. (The system of equations used to calculate the U matrix is overdetermined and some information from the second reflection is thrown away.) Manually setting U and UB ------------------------- *To help find the initial reflections* it may be useful to set the U matrix manually---to the identity matrix for example. Use the ``setu`` command to do this. Once set the diffractometer may be driven to the ideal location of a reflection and then the actual reflection sought. Normally this would be done in the default mode, four-circle-bisecting, (see :ref:`moving-in-hkl-space`). In the following example this has been done by setting the alpha to 5 and leaving gamma at 0 (it would be normal to leave alpha at 0):: >>> hklmode 1 1) fourc bisecting alpha: 0.0 gamma: 0.0 >>> setalpha 5 alpha: 0 --> 5.000000 >>> setu row1[1 0 0]: row2[0 1 0]: row3[0 0 1]: >>> sim hkl [1,0,1.0628] # Check it all makes sense sixc would move to: alpha : 5.00000 deg delta : 22.79026 deg gamma : 0.00000 deg omega : 5.82845 deg chi : 24.57658 deg phi : 6.14137 deg theta : 70702.991919 2theta : 23.303705 Bin : 6.969151 Bout : 6.969151 azimuth : 7.262472 >>> pos hkl [1,0,1.0628] hkl: h: 1.00000 k: 0.00000 l: 1.06280 >>> # scan about to find actual reflection >>> addref h[0.0]: 1 k[0.0]: 0 l[0.0]: 1.0628 current pos[y]: y tag: 'ref1' >>> There is currently no way to refine a manually specified U matrix by inferring as much as possible from just one found reflection. .. _moving-in-hkl-space: Moving in hkl space =================== Once a UB matrix has been calculated, the diffractometer may be driven in hkl coordinates. A given diffractometer setting maps easily into a single hkl value. However for a diffractometer with more than three circles there are excess degrees of freedom when calculating a diffractometer setting from an hkl value. Diffcalc provides many for using up the excess degrees of freedom. By default Diffcalc selects four-circle bisecting mode (see below). Note that to play along with the following ``run`` the file in ``example/session/sixc_example.py`` to configure the UB-calculation. Modes ----- Use the command ``hklmode`` to summarise the state of Diffcalc's angle calculator. It shows a list the available modes for your diffractometer and the parameters that must be fixed for each, the current mode and the current parameter settings:: >>> hklmode Available modes: 0) fourc fixed-bandlw (alpha, gamma, blw) (Not impl.) 1) fourc bisecting (alpha, gamma) 2) fourc incoming (alpha, gamma, betain) 3) fourc outgoing (alpha, gamma, betaout) 4) fourc azimuth (alpha, gamma, azimuth) (Not impl.) 5) fourc fixed-phi (alpha, gamma, phi) (Not impl.) 10) fivec bisecting (gamma) 11) fivec incoming (gamma, betain) 12) fivec outgoing (gamma, betaout) 13) fivec bisecting (alpha) 14) fivec incoming (alpha, betain) 15) fivec outgoing (alpha, betaout) 20) zaxis bisecting () 21) zaxis incoming (betain) 22) zaxiz outgoing (betaout) Current mode: 1) fourc bisecting Parameters: alpha: 0.0 gamma: 0.0 betain: --- (not relevant in this mode) betaout: --- (not relevant in this mode) azimuth: --- (not relevant in this mode) phi: --- (not relevant in this mode) blw: --- (not relevant in this mode) Note that 'Not impl.' is short for 'not implemented'. Standby. Your output may differ. For example: - When listed with a typical five-circle diffractometer with no gamma circle: the fourc modes will have no gamma parameter to fix (actually it will have been fixed under the covers to 0), there will be no gamma or alpha parameters to fix in the five circle modes (again, under the covers gamma will have been fixed) and there will be no zaxis modes (as these require six circles, or an actual z-axis diffractometer). - When listed with a typical four-circle diffractometer with no alpha or gamma circle, the four-circle modes will appear with no alpha or gamma parameters (again, they are fixed under the covers), and there will be no five circle or zaxis modes. To change the current mode, call ``hklmode`` with an argument:: >>> hklmode 2 2) fourc incoming alpha: 0.0 gamma: 0.0 betain: --- (The dashes next to the betain parameter indicate that a parameter has not yet been set.) Mode parameters --------------- A parameter can be set using either one of the series of {{{set}}} commands, by moving one of the scannables associated with each parameter or, where appropriate, by asking that a parameter track an axis. Set commands ~~~~~~~~~~~~ Use the series of commands ``set`` to set a parameter:: >>> setalpha 3 alpha: 0 --> 3.000000 >>> setbetain 5 WARNING: The parameter betain is not used in mode 1 betain: --- --> 5.000000 >>> setalpha # With no args, the current value is displayed alpha: 3 >>> setbetain betain: --- Parameter Scannables ~~~~~~~~~~~~~~~~~~~~ In most installations there will be a scannable for each parameter. In this example installation, the parameters which correspond to physical axes have had '_par' appended to their names to prevent clashes. These may be used to change a parameter either with the ``pos`` command or by using them within a scan (see :ref:`scanning-in-hkl-space`).:: >>> pos betain betain: 0.00000 >>> pos betain 5 betain: 5.00000 >>> setbetain betain: 5 >>> pos alpha_par alpha_par:3.00000 >>> setalpha alpha: 3 Tracking Axis ~~~~~~~~~~~~~ Where a parameter matches an axis name, that parameter may be set to track that axis:: >>> pos alpha alpha: 5.0000 >>> hklmode 1 1) fourc bisecting alpha: 0.0 gamma: 0.0 >>> trackalpha alpha: 5 >>> pos alpha alpha: 6.0000 >>> hklmode 1 1) fourc bisecting alpha: 6.0 (tracking physical axis) gamma: 0.0 Although convenient, there is a danger with this method that in geometries where the axes are built from other axes (such as in a kappa geometry), the position of an axis may drift slightly during a scan. Sectors ------- When mapping from reciprocal lattice space to a set of diffractometer settings, there is normally a choice of solutions for the sample orientation. The selected sector mode will determine which solution is used. There is currently only one sector mode: Sector mode: Find first solution within sector limits ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this sector mode, taken from 'DIF', the first solution found within the 'sector limits' is chosen. These are different from the physical or software limits on the axes and can be checked/modified using ``setsectorlim``:: >>> setsectorlim omega_high[270]: omega_low[-90]: phi_high[180]: phi_low[-180]: The hkl scannable ----------------- Once a UB matrix has been calculated, a mode chosen and parmeters set, use the hkl scannable to move to a point in reciprocal lattice space:: >>> pos hkl [1,0,0] hkl: h: 1.00000 k: -0.00000 l: -0.00000 >>> pos sixc sixc: alpha: 3.0000 delta: 17.2252 gamma: 4.0000 omega: 7.5046 chi: -24.6257 phi: 4.8026 >>> pos hkl hkl: h: 1.00000 k: -0.00000 l: -0.00000 >>> hkl hkl: h : 1.000000 k : -0.000000 l : -0.000000 2theta : 18.582618 Bin : -0.387976 Bout : -0.387976 azimuth : 1.646099 Notice that typing ``hkl`` will also display some virtual angles (such as twotheta and Bin), that checking the position with ``pos hkl`` will not. To get this extra information into a scan use the scannable hklverbose instead of hkl:: >>> pos hklverbose [1,0,0] hklverbose: h: 1.00000 k: -0.00000 l: -0.00000 2theta : 18.582618 Bin : -0.387976 Bout :-0.387976 azimuth : 1.646099 The ``sim`` command will report, without moving the diffractometer, where an hkl position would be found:: >>> sim hkl [1,0,0] sixc would move to: alpha : 3.00000 deg delta : 17.22516 deg gamma : 4.00000 deg omega : 7.50461 deg chi : -24.62568 deg phi : 4.80260 deg theta : 70702.991919 2theta : 18.582618 Bin : -0.387976 Bout : -0.387976 azimuth : 1.646099 Moving out of range ~~~~~~~~~~~~~~~~~~~ Not every hkl position can be reached:: >>> pos hkl [10,10,10] Exception: Could not compute delta for this hkl position The diffractometer scannable (sixc) ----------------------------------- We've seen this before, but it also works with sim:: gda>>>sim sixc [3, 17.22516, 4, 7.50461, -24.62568, 4.80260] hkl would move to: h : 1.000000 k : 0.000000 l : -0.000000 .. _scanning-in-hkl-space: Scanning in hkl space ===================== All scans described below use the same generic scanning mechanism provided by the GDA system or by minigda. Here are some examples. Fixed hkl scans --------------- In a 'fixed hkl scan' something (such as energy or Bin) is scanned, and at each step hkl is 'moved' to keep the sample and detector aligned. Also plonk the diffractometer scannable (sixc) on there with no destination to monitor what is actually happening and then throw on a detector (cnt) with an exposure time if appropriate:: >>> #scan scannable_name start stop step [scannable_name [pos or time]].. >>> scan en 9 11 .5 hkl [1,0,0] sixc cnt 1 >>> scan en 9 11 .5 hklverbose [1,0,0] sixc cnt 1 >>> scan betain 4 5 .2 hkl [1,0,0] sixc cnt 1 >>> scan alpha_par 0 10 2 hkl [1,0,0] sixc cnt 1 >>> trackalpha >>> scan alpha 0 10 2 hkl [1,0,0] sixc cnt 1 # Equivalent to last scan Scanning hkl ------------ Hkl, or one component, may also be scanned directly:: >>> scan h .8 1.2 .1 hklverbose sixc cnt 1 At each step, this will read the current hkl position, modify the h component and then move to the resulting vector. There is a danger that with this method k and l may drift. To get around this the start, stop and step values may also be specified as vectors. So for example:: >>> scan hkl [1,0,0] [1,.3,0] [1,0.1,0] cnt1 is equivilant to:: >>> pos hkl [1,0,0] >>> scan k 0 .3 .1 cnt1 but will not suffer from drifting. This method also allows scans along any direction in hkl space to be performed. Multidimension scans -------------------- Two and three dimensional scans:: >>> scan en 9 11 .5 h .9 1.1 .2 hklverbose sixc cnt 1 >>> scan h 1 3 1 k 1 3 1 l 1 3 1 hkl cnt 1 Good luck --- RobW