Data Collection. Overview. Methods. Counter Methods. Crystal Quality with -Scans

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Mabel Haynes
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$Data Collection Overview with a unit cell, possible space group and computer reference frame (orientation matrix); the location of diffracted x-rays can be calculated (h k l) and intercepted by$ $film Weissenberg and precession photos measure intensity relative to a calibration strip of film 2. automatic diffractometer a.$

1 Data Collection Overview with a unit cell, possible space group and computer reference frame (orientation matrix); the location of diffracted x-rays can be calculated (h k l) and intercepted by something sensitive to x-rays (film or electronic devise) integrated intensity: total number of photons from (h k l) Methods Counter Methods 1. film Weissenberg and precession photos measure intensity relative to a calibration strip of film 2. automatic diffractometer a. single-point detector computer-controlled crystal oriention so diffracted beam goes into the detector scintillation counter collimated x-ray Miller plane 2 beam stop scintillation counter NaI(Tl) energy is transferred to Tl atoms that produce a flash of light; light intensity is proportional to x-ray intensity; photocathode converts the light to voltage Crystal Quality with -Scans Crystal Quality with -Scans sphere of reflection good crystal partial twin twin not centered Lorentzian 1

$_diffrn_measurement_method \w _diffrn_measurement_method \w 2\q 2.$ scan rate usually variable depending on intensity weak reflections scanned more slowly fast pre-scan to

scan rate usually variable depending on intensity weak reflections scanned more slowly fast pre-scan to

background peak scanned on either side to fix baseline scan range 1 o below K 1 to 1 o above K 2 4.

Resolution Resolution protein crystallographers usually use resolution: sin same information as maximum 2, but

data are collected to /sin of at least 1.

2 Data Collection 1. scan method usually or 2 ( 2). _diffrn_measurement_method \w _diffrn_measurement_method \w 2\q Data Collection 1. scan method usually or 2 ( 2). 2. scan rate usually variable depending on intensity weak reflections scanned more slowly fast pre-scan to determine best rate 4.0 to 29.3 o /min 3. background peak scanned on either side to fix baseline scan range 1 o below K 1 to 1 o above K 2 4. maximum 2 depends on instrument, quality, and size of crystal; intensities go down with 2 usually o Resolution Resolution protein crystallographers usually use resolution: sin same information as maximum 2, but refers to the resolution of detail (atoms) in the final structure 4Å 8Å 16Å 32Å for small-molecule studies the data are collected to /sin of at least 1.7 Å ( max > 25 for MoK, max > 67 for CuK ) Intensities Standard Deviation intensity, I, is measured in counts (photons) I = r(s RB) r = scan rate, o /min s = total scan count R = scan to background time ratio B = background count can also calculate esd: estimated standard deviation I2 = r 2 (s + R 2 B) used in weighing reflections 2

Decay Correction x-rays can damage crystal while data collected minimize exposure by

occurs, data usually adjusted with a linear correction 3 or more check reflections

throughout collection Data each data point consist of a number of parameters:

depending on: crystal size, contents, symmetry fit to a decay curve and scale

_diffrn_standards_interval_time? _diffrn_standards_decay_%? 11234943211 Methods 1.

$strip of film 2. automatic diffractometer Image Plate a.$ into the detector scintillation counter b.

3 Decay Correction x-rays can damage crystal while data collected minimize exposure by turning off X-ray beam when crystal is repositioned between data points when decay occurs, data usually adjusted with a linear correction 3 or more check reflections are remeasured periodically (every xxx reflections, every x hours of exposure) throughout collection Data each data point consist of a number of parameters: profile I I h, k, l 2,,, left and right background measure reflections depending on: crystal size, contents, symmetry fit to a decay curve and scale reflections accordingly _diffrn_standards_number? _diffrn_standards_interval_count? _diffrn_standards_interval_time? _diffrn_standards_decay_%? Methods 1. film Weissenberg and precession photos measure intensity relative to a calibration strip of film 2. automatic diffractometer Image Plate a. single-point detector computer-controlled crystal oriention so diffracted beam goes into the detector scintillation counter b. area detector image plates, multi-wire proportional counters, and charge-coupled devises (CCD) detail of data collection depend on manufacturer Mulitwire Proportional Counter CCD 3

4 Symmetry amount of independent data limited by: sphere of reflection weak reflections at large 2 symmetry not all data independent 1. Friedel s Law at least half the reflections redundant I hkl = I hkl 2. additional redundancies based on the crystal system monoclinic orthorhombic: I hkl = I hkl I hkl = I hkl = I hkl = I hkl = I hkl I hkl = I hkl = I hkl = I hkl = I hkl = I hkl = I hkl Limiting Sphere Ewald s Sphere crystal limiting sphere radius = 1/d max (from max h, k, and l (or max 2)) c* Unique Data b* Collecting Symmetry Related Reflections b* c* if the crystal allows it (decay not a problem) and you have time, symmetry related reflections can be measured and averaged improves statistics and gives an idea of crystal quality a* triclinic one index 0 two indices a* c* a* orthorhombic b* all indices 0 monoclinic k and h or l 0 l or h _diffrn_reflns_av_r_equivalents (R int ) ( I ) / I for symmetry-equivalent reflections ( I ) is the average absolute difference between I (average I) and the individual symmetry-equivalent I s equivalent reflections are averaged to during Data Reduction Bottom Line on Data Collection Data Reduction solving a structure means to rephase the scattered x-rays (lens), which requires the amplitudes and phases of the scattered x-rays obtain the most, good (usable), unique data possible more data means better statistical determination of structure for any wave: amplitude is proportional to the square root of the intensity amplitudes derived from x-ray data are called: Structure Factors F hkl F hkl I F s are converted to F observed or F o with several corrections based on decay, absorption and the geometry of data collection Data Reduction 4

5 Decay using check reflections, the decay rate can be estimated: 1300 Empirical Absorption Correction ψ scans find several reflections with near 90 o ; rotate crystal around and measure how the intensity changes Relative Intensity y = x º steps (36 data points) Time (hours) _exptl_absorpt_correction_t_min _exptl_absorpt_correction_t_max Absorption Correction Cif Definitions Geometric Corrections Lp analytical cylinder analytical from crystal shape cylindrical F hkl = KI hkl Lp empirical empirical from intensities gaussian integration multi-scan none numerical Gaussian from crystal shape integration from crystal shape symmetry related measurements no absorption correction applied numerical from crystal shape K L scale factor Lorentz factor depends on crystal size and x-ray intensity estimated early and refined at the end time for a reflection to pass through Ewald s Sphere depends on the 2 angle psi-scan ψ scan corrections refdelf refined from F sphere spherical Lorentz Factor - L Geometric Corrections Lp F hkl = KI hkl Lp K scale factor. depends on crystal size and x-ray intensity estimated early and refined at the end L Lorentz factor time for a reflection to pass through Ewald s Sphere depends on the 2 angle for a single-point diffractometer: p Polarization reflected x-ray is partially polarized L = 1/sin2 5

6 Polarization - p Geometric Corrections Lp I F hkl = KI hkl Lp I I I K scale factor. depends on crystal size and x-ray intensity. estimated early and refined at the end p = (1 + cos 2 2)/2 L p Lorentz factor polarization eime for a reflection to pass through Ewald s Sphere depends on the 2 angle eeflected x-ray is partially polarized esually called the 1/Lp correction Structure Factors Scattering Factors the idea in solving a crystal structure: 1. measure reflections and reduce data to F o h k l I σ I h k l F σ F 2. guess structure; calculate structure factors that would result from that structure: F c 3. compare F o and F c ; improve guess, calculate new structure factors (F c ) that result from improved structure 4. continue process until F o and F c match within statistically acceptable error and structure is chemically reasonable = KI o Lp to calculate F c, it is necessary to know the scattering power of each atom in the cell and how it contributes to structure factor Scattering Factors function of: 1. number of e in atom 2. scattering angle (Bragg) Scattering Factors Number of e x-ray hitting e causes it to oscillate at same frequency wavelet emitted with amplitude to oscillation magnitude each e wave adds to scattered x-ray from atom Scattering Factor Curve of Carbon f o gives a scattered wave with an amplitude to total e sin/ = 1/2d 6

7 Scattering Factors Dependence scattering factor would always be atomic number of the atom if all e at a point; however, a real atom has volume in phase if = 0 o f o 3.00 Scattering Factor Curve of Carbon point real atom 2.00 increasingly out of phase at > 0 o sin/ Scattering Factor Calculation Anomalous Dispersion 6 f (sinθ/λ) = a i e b i (sinθ/λ)2 Atom a 1 a 2 a 3 a 4 a 5 a 6 b 1 b 2 b 3 b 4 b 5 b 6 Carbon if an atom absorbs x-rays before re-emitting, the phase changes; intensity is also changed f o anom = f o + f atom, + if atom, intensity change phase change Freidel s Law violated for noncentrosymmetric space groups numbers for every atom are part structure solution software Multiwavelength Anomalous Diffraction (MAD) phasing Temperature Factor Temperature Factor scattering factor based on a spherical, stationary, atoms but atoms are in constant motio; magnitude depends on mass, bond strength and temperature 4.00 f o 3.00 B = e B(sinθ/λ)2 f= f o thermal motion spreads e density over a larger volume, causing scattering to drop off more rapidly sin/ effective volume B = 8 2 u 2 u 2 = mean-square amplitude B (in Å 2 ) is the temperature factor or thermal parameter 7

8 Temperature Factor f = f o e B(sin/) 2 = f o e B/4 (1/d hkl ) 2 B = 8 2 u 2 mean-square amplitude hkl plane U = B / 8 2 typical values for U: 0.05 Å 2 B: 4 Å 2 isotropic: spherical anisotropic: ellipsoid Wilson Plot a method to estimate overall temperature factor and scale factor I relative = (F relative ) 2 I absolute = I abs = Arthur J. C. Wilson Canadian N f 2 oi average intensity depends on what is in cell, not where it is. N f 2 oie 2B(sinθ/λ)2 N atoms in cell ln I rel N 2 foi I rel N 2 foi Wilson Plot e 2B(sin/) N 2 2 I abs = foi I = C I rel abs e 2B(sin/) N 2 2 rel f I = C oi = C e 2B(sin/) 2 = lnc 2B(sin/) 2 y = b + m x ln N I rel f 2 oi Wilson Plot 3.5 k = (1/C) lnc 1/ slope = 2B (sin/) 2 (Å 2 ) each point represents ~100 reflections of similar sin/ F abs = k F rel ~10-15% accurate Wilson Plot U = B 8π 2 E hkl2 = N F hkl 2 f 2 j j = 1 average E 2 average E 2 1 average E E > 1 E > 2 E > 3 Other Statistics normalized structure factors ( point atoms ) = integer (usually 1) related to symmetry centrosymmetric noncentrosymmetric % 36.8% 5.0% 1.8% 0.3% 0.01% P1 Z = 4 x, y, z x, y, z HO H O crystallographic 1 O H O OH H OH approximate 1 HO H O 8

PSD '18 -- Xray lecture 4. Laue conditions Fourier Transform The reciprocal lattice data collection

PSD '18 -- Xray lecture 4. Laue conditions Fourier Transform The reciprocal lattice data collection PSD '18 -- Xray lecture 4 Laue conditions Fourier Transform The reciprocal lattice data collection 1 Fourier Transform The Fourier Transform is a conversion of one space into another space with reciprocal