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SUPPLEMENTARY INFORMATIONDOI: 10.1038/NCHEM.2462

Encoding Complexity within Supramolecular

Analogues of Frustrated Magnets

SUPPLEMENTARY INFORMATION

Andrew B. Cairns,1,2 Matthew J. Cliffe,1,3 Joseph A. M. Paddison,1,4,5

Dominik Daisenberger,6 Matthew G. Tucker,4,6 Francois-Xavier Coudert,7∗

and Andrew L. Goodwin1∗

1Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory,

South Parks Road, Oxford OX1 3QR, U.K.2European Synchrotron Radiation Facility, 71 avenue des Martyrs,

38043 Grenoble, France3Department of Chemistry, University of Cambridge, Lensfield Road,

Cambridge CB2 1EW, U.K.4ISIS Facility, Rutherford Appleton Laboratory, Harwell Oxford, Didcot,

Oxfordshire OX11 0QX, U.K.5School of Physics, Georgia Institute of Technology, 837 State Street,

Atlanta, GA 30332, U.S.A.6Diamond Light Source, Chilton, Oxfordshire, OX11 0DE, U.K.

7Institut de Recherche de Chimie Paris, CNRS – Chimie ParisTech,

11 rue Pierre et Marie Curie, 75005 Paris, France

∗To whom correspondence should be addressed;

E-mail: [email protected], [email protected].

1

Encoding Complexity within Supramolecular

Analogues of Frustrated Magnets

SUPPLEMENTARY INFORMATION

Andrew B. Cairns,1,2 Matthew J. Cliffe,1,3 Joseph A. M. Paddison,1,4,5

Dominik Daisenberger,6 Matthew G. Tucker,4,6 Francois-Xavier Coudert,7∗

and Andrew L. Goodwin1∗

1Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory,

South Parks Road, Oxford OX1 3QR, U.K.2European Synchrotron Radiation Facility, 71 avenue des Martyrs,

38043 Grenoble, France3Department of Chemistry, University of Cambridge, Lensfield Road,

Cambridge CB2 1EW, U.K.4ISIS Facility, Rutherford Appleton Laboratory, Harwell Oxford, Didcot,

Oxfordshire OX11 0QX, U.K.5School of Physics, Georgia Institute of Technology, 837 State Street,

Atlanta, GA 30332, U.S.A.6Diamond Light Source, Chilton, Oxfordshire, OX11 0DE, U.K.

7Institut de Recherche de Chimie Paris, CNRS – Chimie ParisTech,

11 rue Pierre et Marie Curie, 75005 Paris, France

∗To whom correspondence should be addressed;

E-mail: [email protected], [email protected].

1

© 2016 Macmillan Publishers Limited. All rights reserved.



ContentsSupplementary Discussion S1: Atypical Diffraction Profile in Au1/2Ag1/2(CN) 3

Supplementary Discussion S2: Mapping of Bilinear Biquadratic XY Phase Diagram 4

Supplementary Discussion S3: High-Pressure X-ray Diffraction Study of AgCN 5

Supplementary Figure S1: X-ray Powder Diffraction Pattern of Au1/2Ag1/2(CN) 6

Supplementary Figure S2: Proposed Crystalline Approximants for Au1/2Ag1/2(CN) 7

Supplementary Figure S3: X-ray Diffraction by Structural Analogues of BLBQ Phases 8

Supplementary Figure S4: Additional QMC Au1/2Ag1/2(CN) Configuration 9

Supplementary Figure S5: Linear and Bulk Compressibility of AgCN 10

Supplementary Figure S6: High-Pressure X-ray Diffraction Pattern of AgCN 11

Supplementary Figure S7: Non-Equilibrium QMC Configuration Using Full DFT Potential 12

Supplementary References 13

2




Supplementary Discussion S1:

Confirmation of Atypical Diffraction Profile in Au1/2Ag1/2(CN)A sample of Au1/2Ag1/2(CN) was prepared as follows. Equimolar quantities of AgNO3 (Sigma Aldrich,>99%) and KAu(CN)2 (Sigma Aldrich, 98%) were dissolved in water and the two solutions added toone another while stirring. An off-white precipitate formed. The solid product was isolated by vacuumfiltration, washed (H2O) and oven dried (vacuum, 50 ◦C, overnight). The product was treated as if itwere light sensitive.

In order to confirm that the unusual peak shape variation reported in Ref. S1—and used as the basisfor the argument in the main text regarding screw dislocation inclusion—was a reproducible propertyof this phase, high-resolution X-ray powder diffraction data were collected for our own Au1/2Ag1/2(CN)sample. These data were collected at room temperature using a PANalytical Empyrean X-ray diffrac-tometer (Cu Kα1 radiation). The data themselves, together with a Rietveld fit obtained using an AuCN-like structural model and a Stephens (hkl)-dependent anisotropic peak shape,S2 are identical to thediffraction pattern reported in Ref. S1 and given in Fig. 3(b) of the main text [Supplementary Figure S1].

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Mapping of Bilinear Biquadratic XY Phase DiagramThe claim is made in the main text that the various phases in the BLBQ XY phase diagram can be distin-guished on the basis of the diffraction patterns of the corresponding Au1/2Ag1/2(CN) structure models.Supplementary Figure S3 illustrates the relevant X-ray diffraction patterns calculated for three key phases(other than the ferroquadrupolar phase discussed in the main text). In each case the diffraction profile isdiagnostic and noticeably different to that observed experimentally. For completeness we note that theantiferroquadrupolar (AFQ) phase is most ordered in the unique case for J1 = 0, J2 > 0; the diffractionpatterns for the chiral disordered phases on either side (grey regions of Supplementary Figure S3(a))obey similar reflection conditions to the AFQ phase but admit additional diffuse scattering and peakbroadening contributions that are not observed experimentally.

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High-Pressure X-ray Diffraction Study of AgCNThe high-pressure behaviour of AgCN was explored using variable-pressure synchrotron X-ray powderdiffraction measurements carried out using the I15 beamline at the Diamond Light Source, U.K. A smallpowder sample of AgCN (Sigma Aldrich, 99%) was placed in the pre-indented rhenium gasket of agas membrane diamond anvil cell (DAC) together with a single ruby sphere for pressure calibration. Awater-free methanol/ethanol mixture (4:1) was used as the pressure transmitting medium. A focussedX-ray beam of wavelength λ = 0.309960 A was selected using a Si(111) monochromator and datawere collected using a Mar345 2D detector that was positioned ∼350 mm from the sample. Duringdata collection the DAC was rocked by 7◦ in order to improve powder averaging. Instrument setup wascalibrated using a CeO2 standard and data integration was carried out using FIT2D.S3, S4 Pawley andRietveld refinements were carried out using TOPAS Academic v.4.1. (Refs. S5, S6) in space group R3m(ambient phase) and P6/mmm (high-pressure phase, a(P6/mmm) � 1√

3a(R3m)).

Synchrotron X-ray diffraction data were collected over the pressure range 0 < p < 20.5GPa, notingthat deviation from hydrostatic conditions is expected at pressure points greater than ca 10 GPa. Thediffraction data were dominated by the ambient-pressure AgCN phase (R3m) for all pressure points;however, a series of additional reflections were observed at higher pressures, culminating in the AuCN-like phase discussed below. Pawley refinement of the lattice parameters for the ambient-pressure phasewas possible at all pressures. The observed pressure dependence of the unit cell parameters is shownin Supplementary Figure S5. The main structural change is a large and rapid decrease in the a,b planeresulting from weak inter-chain interactions. Calculation of linear compressibilities using the PASCalsoftware (Ref. S7) gives the values Ka = +5.9(3)TPa−1 and Kc = −0.01(20)TPa−1 for the pressurerange 0 < p < 20.5GPa. Equation-of-state fits to the volume compressibility are not especially robust;the fit shown in the right-hand panel of Supplementary Figure S5 results from a very small bulk modulusB0 < 5GPa and a very large and positive first derivative of the bulk modulus B′ = dB/dp � 4.

At a pressure of 20.5 GPa a set of additional peaks appeared. The reflection conditions observedwere inconsistent with all maximal subgroups of R3m but could instead be indexed on the basis of anadditional AuCN-like phase with c approximately unchanged and a reduced by the expected factor of∼

√3 [Supplementary Figure S6]. Given that the applied pressure exceeds the hydrostatic limit of our

pressure transmitting medium, we do not wish to attach too great a significance to this apparent partially-complete phase transition. However, we note that the progression from the ambient-pressure AgCNphase (electrostatics-dominated) to an AuCN-like phase (metallophilicity-dominated) at high pressuresis consistent with the change in electrostatic and metallophilic interaction strengths as the inter-chainseparation is reduced. The ∼20% decrease in the a lattice parameter observed between 0 and 20.5 GPacorresponds to an increase in electrostatic interaction energies by a factor of 1/(0.8) � 1.2, but anincrease in metallophilic interaction energies by a much larger factor of 1/(0.8)6 � 3.8. This may besufficient to invert the sign of the effective inter-chain coupling parameter J described in the main text.

5




Supplementary Figure S1: Rietveld refinement of X-ray diffraction data for as-synthesised

Au1/2Ag1/2(CN) using a Stephens anisotropic peak shape.S2 Refined lattice parameters: a =

3.4233(6) A, c = 5.1560(8) A. Data are shown as black markers, fit as a red line, and difference (data

− fit) as a blue line, displaced downwards by five units. Tick marks (green) indicate expected peak

positions.

6




Supplementary Figure S2: Representations of the (a) Immm and (b) P6/mmm structural models

proposed for Au1/2Ag1/2(CN) in Ref. S1. Gold and silver atoms are shown in gold and silver, respectively;

C atoms are in black and N atoms in blue. The neutron pair distribution functions T (r) calculated for

these models were equally capable of describing the experimental T (r) data reported in Ref. S1.

7




Supplementary Figure S3: X-ray diffraction patterns calculated for candidate Au1/2Ag1/2(CN) struc-

tures corresponding to BLBQ phases with different J1, J2 combinations. (a) The BLBQ XY magnet

phase diagram,S8 with three extreme Ji combinations indicated by grey (AFQ; J1 = 0, J2 > 0), red

(AFM; J1 > 0, J2 = 0) and blue (FM; J1 < 0, J2 = 0) stars. (b) The X-ray diffraction patterns for the

corresponding Au1/2Ag1/2(CN) configurations, where the horizontal scale has been expanded to show the

low-angle superlattice peak characteristic of the FM phase. This peak is clearly absent in our own X-ray

diffraction data [Supplementary Figure S1], as it was in the data of Ref. S1.

8




Supplementary Figure S4: Illustration of an additional representative Au1/2Ag1/2(CN) configuration,

generated using the quench Monte Carlo method described in the main text. Au and Ag atoms are

shown as gold and silver spheres, respectively; C and N atoms are shown as red spheres. This specific

configuration—which shares all the same basic structural features of that shown in Fig. 3(f) of the main

text—is that from which the finite-temperature X-ray diffraction pattern shown in Fig. 3(b) of the main

text was calculated.

9




Supplementary Figure S5: Pressure response of AgCN up to 20 GPa showing rapid decrease in inter-

chain separation. (a) Upon application of pressure AgCN collapses rapidly in the a direction and is

essentially incompressible in the c direction. This is a result of weak inter-chain interactions allowing

rapid compression perpendicular to the chain axis. (b) Rapid volume collapse fitted to a third-order

Birch-Murnaghan equation of state gives a very large value of B′ and a small bulk modulus B0. Errors

on all measurements are included within the area of the data points.

10




Supplementary Figure S6: Pawley refinement of synchrotron X-ray diffraction data (λ = 0.309960 A)

for AgCN at 20.5 GPa showing emergence of an AuCN-like phase. Data are shown as black markers,

fit as a red line, difference (data − fit) as a blue line displaced downwards by five units. Green tick

marks show expected peak positions for AgCN (R3m) with refined lattice parameters a = 4.766(3) A,

c = 5.287(5) A. Pink tick marks show expected peak positions for an AuCN-like phase of AgCN

(P6/mmm) with refined lattice parameters a = 2.7658(11) A, c = 5.1587(10) A.

11




Supplementary Figure S7: (a) Illustration of a representative QMC Au1/2Ag1/2(CN) configuration, ob-

tained using the full DFT inter-chain interaction potential. For the BLBQ system used to generate the

configurations shown in Fig. 3(f) of the main text and Supplementary Figure S4, the ground-state and

finite-temperature behaviour are sufficiently well understood from theory that the non-equilibrium QMC

configurations can be meaningfully interpreted. By contrast, it is not clear that the configuration shown

here is physically meaningful beyond demonstrating (i) the behaviour of QMC simulations when driven

by the more complex interaction potential, and (ii) that the key structural features—namely, a tendancy

for chains to align with close Ag. . .Au interactions and the presence of screw dislocations—are repro-

duced. (b) The corresponding X-ray diffraction pattern for this model (red line), shown relative to the

experimental data (black line). The topological defect concentration is sufficiently high in the simu-

lated configuration that a number of reflections have broadened completely. The presence of multiple

local minima in the full DFT interaction potential likely accounts for the difficulty in relating the non-

equilibrium QMC configuration to the true equilibrium behaviour in this case.

12




Supplementary References(S1) A. M. Chippindale, et al., J. Am. Chem. Soc. 134, 16387 (2012).(S2) P. W. Stephens, J. Appl. Cryst. 32, 281 (1999).(S3) A. P. Hammersley, FIT2D: An introduction and overview, Tech. Rep. ESRF97HA02T , ESRF

(1997).(S4) A. P. Hammersley, S. O. Svensson, M. Hanfland, A. N. Fitch, D. Hausermann, High Press. Res. 14,

235 (1996).(S5) A. A. Coelho, TOPAS-Academic, version 4.1 (Computer Software). Coelho Software, Brisbane.(S6) A. A. Coelho, TOPAS v4.1: General profile and structure analysis software for powder diffraction

data, Karlsruhe (2007).(S7) M. J. Cliffe, A. L. Goodwin, J. Appl. Cryst. 45, 1321 (2012).(S8) M. Zukovic, T. Idogaki, Physica B 329-333, 1055 (2003).

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