The effect of inert dopant ions on spin-crossover materials is not simply controlled by chemical pressure

Abstract

[Fe(bpp)₂][BF₄]₂ (bpp = 2,6-bis{pyrazol-1-yl}pyridine) undergoes abrupt thermal spin-crossover (SCO) at 261 K with a small 2–3 K thermal hysteresis. Different compositions of doped materials [Fe_zZn_1−z(bpp)₂][BF₄]₂ and [Fe_zRu_1−z(bpp)₂][BF₄]₂ (0 < z < 1) show similar broadening of the SCO transition with increased doping, but differ in their effect on the transition temperature. Doping with zinc strongly lowers T_½, which is consistent with previous work. In contrast, doping with ruthenium increases T_½ to a smaller degree, which cannot be explained by the chemical pressure arguments that are conventionally applied to doped SCO materials. Mechanoelastic simulations imply that different dopants exert opposite effects on the lattice elastic interactions in the material during the SCO transition. Consistent with that, the materials show a complicated dependence of the crystallographic lattice parameters and thermal expansion properties on the iron spin state, for different dopant ions. These changes correlate with small perturbations to the molecular structure of high-spin [Fe(bpp)₂]²⁺, in the presence of dopants with different geometric preferences and conformational rigidities. We conclude the effect of isomorphous dopants on T_½ reflects how the dopant influences the coordination geometry of the iron centres, as well as the chemical pressure exerted by the dopant ion size.

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Introduction

Spin-crossover (SCO) materials undergo a spin state change under a physical or chemical stimulus.^1–5 The electronic rearrangement is accompanied by structural changes, which impact the colour,⁶ volume,⁷ conductivity,⁸ permittivity⁹ and other materials properties of a solid sample.^10–12 That switching functionality is being exploited in molecular electronics^8,13 and nanoscience,^5,14,15 while SCO materials are being investigated for solid state refrigeration,^16–19 mechanical actuation,^7,20–22 thermochromic printing^23,24 and other macroscopic applications.^6,25–28 Spin-transitions are also useful probes of crystal lattice dynamics, which allow the nucleation, growth and decay of new phases to be observed in real time.^29,30

Most of these applications require materials undergoing first order spin-transitions, which arise from an interplay between the individual switching centres and the surrounding lattice.³¹ Solid solutions of SCO compounds with inert isomorphous dopants have been essential for developing our understanding of that synergy. Early work on doped SCO materials showed how the strength and dimensionality of elastic interactions in a lattice controls the cooperativity of phase transformations,^32,33 leading to the development of Monte Carlo methods for simulating SCO processes.³⁴ More recently, doped SCO materials have shed light on the kinetics of spin state relaxation processes at low temperatures.^33,35,36

Isomorphous M²⁺ dopant ions in an iron(II) SCO material [Fe_zM_1−zL_n]^m+ (M = Mn, Co, Ni, Zn etc.; L = a ligand) reduce the transition cooperativity as z decreases. That reflects the weakening of elastic interactions between the switching centres, as they become separated by dopant molecule spacers in the lattice.^32–34 However, their effect on the transition temperature T_½ is more variable. While increased fractions of Mn²⁺, Co²⁺ or Zn²⁺ dopant ions consistently lower T_½ of an iron(II) SCO compound,^32,36–51 Ni²⁺ dopants have a much smaller effect on T_½ of the same materials (Fig. S1, ESI†).^36,46–54 That is usually explained by the chemical pressure exerted by each dopant ion. The ionic radii of Mn²⁺ (83 pm), Co²⁺ (74.5 pm) and Zn²⁺ (74 pm) resemble high-spin Fe²⁺ (78 pm),⁵⁵ so introducing those dopant ions into the lattice should favour the high-spin state of the SCO material. In contrast, the ionic radius of Ni²⁺ (69 pm) is essentially the average of high-spin (78 pm) and low-spin (61 pm) Fe²⁺, so doping an iron(II) lattice with Ni²⁺ has less effect on its internal chemical pressure.^32–34 By that argument, no dopant ion should increase T_½, since no common metal dications have ionic radii approaching low-spin Fe²⁺.⁵⁶

Chakraborty and co-workers recently reported that [Fe_0.65Ru_0.35(ptz)₆][BF₄]₂ (ptz = 1-propyltetrazole) exhibits T_½ = 135 K,⁵⁷ which is 10 K higher than for [Fe(ptz)₆][BF₄]₂ itself.⁵⁸ That was the first observation of chemical doping leading to stabilisation of the low-spin state of an SCO material. However, interpretation of that result is complicated by a crystallographic phase transition in [Fe(ptz)₆][BF₄]₂, which is associated with the SCO event and influences T_½, but is kinetically slow.^59–62 Other M²⁺ dopant ions in [Fe_zM_1−z(ptz)₆][BF₄]₂ affect T_½ and the phase transition temperature to different degrees, such that the two processes become decoupled at higher dopant levels.⁶³

To clarify that observation, we have investigated the [Fe_zM_1−z(bpp)₂][BF₄]₂ system (Scheme 1; bpp = 2,6-bis{pyrazol-1-yl}pyridine). The parent complex [Fe(bpp)₂][BF₄]₂ undergoes an abrupt spin-transition at T_½ = 261 K with narrow thermal hysteresis, but without a crystallographic phase change.⁶⁴ Previous studies of [Fe_zM_1−z(bpp)₂][BF₄]₂ with M = Co^2+ 42 or Ni^2+ 54 showed typical trends for those dopants. Analogous materials with M = Zn²⁺ and Ru²⁺ are presented here, which confirm those dopant ions have opposing effects on T_½ in the [Fe(bpp)₂][BF₄]₂ lattice.⁶⁵ We show this reflects the geometric preferences and conformational flexibility of the different dopant ions, and how these perturb the local crystal lattice site structure.

Scheme 1 The [Fe_zM_1−z(bpp)₂][BF₄]₂ materials referred to in this study (M²⁺ = Co²⁺, Ni²⁺, Zn²⁺ or Ru²⁺; 0 < z < 1).

Results

The starting materials [M′(bpp)₂][BF₄]₂ (M′ = Fe,⁶⁴ Zn⁶⁶ and Ru⁶⁷) are crystallographically isomorphous. Co-crystallizing the iron complex with different mole ratios of the appropriate dopant from nitromethane, using diethyl ether vapour as the anti-solvent, yielded polycrystalline [Fe_zZn_1−z(bpp)₂][BF₄]₂ (1a–1e) and [Fe_zRu_1−z(bpp)₂][BF₄]₂ (2a–2d). Samples of 1a–1e are yellow in colour which becomes paler as z decreases, while 2a–2d become darker brown with increased ruthenium content.⁶⁸ The materials are phase-pure and isomorphous with the precursor complexes by powder diffraction (Fig. S2 and S3, ESI†). EDX analysis and magnetic measurements confirm the composition of each material is consistent with the stoichiometry of its crystallisation mixture (Table 1).

Table 1 Analytical data for the new solid solution materials in this work. The stoichiometry z is the average of the three metal ion ratio calculations in the Table

	z	C found (calcd)	H found (calcd)	N found (calcd)	Fe:M calculated from:
					Synthesis stoichiometry	EDX^a	Magnetic data^b
a Errors on the EDX data are between ±0.01–0.05 (Table S1). b Calculated assuming χMT = 3.5 cm^3 mol^−1 K for high-spin Fe(II), and χMT = 0 for low-spin Fe(II) and the diamagnetic dopant ions. Estimated errors on these values are ±0.02.
M = Zn
1a	0.89	40.7(40.5)	2.73(2.78)	21.6(21.5)	0.89 : 0.11	0.90 : 0.10	0.89 : 0.11
1b	0.69	40.2(40.3)	2.68(2.77)	21.4(21.4)	0.68 : 0.32	0.70 : 0.30	0.69 : 0.31
1c	0.51	40.1(40.2)	2.69(2.76)	21.1(21.3)	0.50 : 0.50	0.55 : 0.45	0.49 : 0.51
1d	0.26	40.0(40.1)	2.82(2.75)	21.1(21.3)	0.28 : 0.72	0.24 : 0.76	0.27 : 0.73
1e	0.07	40.2(40.0)	2.87(2.75)	21.0(21.2)	0.08 : 0.92	0.06 : 0.94	0.07 : 0.93
M = Ru
2a	0.88	39.9(40.2)	2.97(2.76)	20.9(21.3)	0.88 : 0.12	0.84 : 0.16	0.91 : 0.09
2b	0.67	39.4(39.6)	2.78(2.72)	20.7(21.0)	0.69 : 0.31	0.65 : 0.35	0.67 : 0.33
2c	0.49	38.9(39.2)	2.79(2.69)	20.4(20.8)	0.50 : 0.50	0.50 : 0.50	0.48 : 0.52
2d	0.14	38.0(38.3)	2.48(2.63)	19.9(20.3)	0.15 : 0.85	0.14 : 0.86	0.14 : 0.86

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SCO in the new materials was monitored by magnetic susceptibility measurements (Fig. 1). The FeZn materials 1a–1e show the expected trend, in that increasing zinc concentration leads to broadening of the transition, while significantly lowering T_½.^{32,40,43–49} Ruthenium doping in 2a–2d has a similar influence on the SCO cooperativity as the zinc dopant at each dopant concentration. However, the two dopant ions have opposite effects on the transition temperature, in that T_½ in 2a–2d increases at higher ruthenium dopant levels (Fig. 1 and 2). The larger population of low-spin iron centres in the ruthenium-doped materials at room temperature is consistent with their brown colouration.⁶⁸

Fig. 1 Spin-crossover in [Fe(bpp)₂][BF₄]₂ and its solid solutions, from magnetic susceptibility data measured at a scan rate of 2 K min⁻¹. Data are plotted as the fraction of the sample that is high-spin at each temperature (γ_HS), and the transition midpoint at γ_HS = 0.5 is marked with a dashed line. Data points from each compound are linked by spline curves for clarity, Data for [Fe(bpp)₂][BF₄]₂ are taken from ref. 54.

Fig. 2 Variation of T_½ with composition in [Fe_zM_1−z(bpp)₂][BF₄]₂ with different dopant ions, from magnetic susceptibility data measured at a 2 K min⁻¹ scan rate (Fig. 1). Data for M = Ni and Co are taken from ref. 42 and 54.

These trends were confirmed by differential scanning calorimetry (DSC) measurements (Fig. S6 and S7, ESI†). The transition temperatures measured by DSC and the magnetic data show minor differences, which we attribute to the different temperature ramps employed for the measurements (Table 2). However, the DSC data confirm T_½ in [Fe_zM_1−z(bpp)₂][BF₄]₂ decreases with z when M = Zn, but increases when M = Ru. ΔH and ΔS for the spin-transitions decrease more slowly with increased doping for M = Ru than for M = Zn at small dopant concentrations. DSC measurements at larger dopant levels were not achieved, because their endotherms were too weak or outside the temperature range of our calorimeter (T_min = 190 K).

Table 2 SCO parameters for the materials in this work. ΔH and ΔS are quoted per mole of iron in the solid solutions. Estimated errors on T_½ from the DSC data are ±0.2 K

	Magnetic measurements		DSC
	T ½↓/K	T ½↑/K	T ½↑/K	ΔH/kJ mol^−1	ΔS/J mol^−1 K^−1
a Taken from ref. 54. b DSC endotherms for 1c and 2d were too weak to be accurately measured. c Outside the temperature range of our calorimeter.
[Fe(bpp)2][BF4]2^a	261.0	262.5	263.2	21.8(2)	82.9(8)
M = Zn
1a	251.1	251.3	255.0	13.3(2)	52.2(8)
1b	233.6	233.2	237.7	6.6(4)	28(2)
1c	217.2	216.5	—^b	—	—
1d	193	193	—^c	—	—
1e	166	—	—^c	—	—
M = Ru
2a	264.1	265.0	269.1	18.6(2)	69.0(8)
2b	268.5	269.4	271.0	11.2(3)	41.3(11)
2c	272.7	272.7	274.6	8.4(7)	30(3)
2d	279	279	—^b	—	—

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The materials’ SCO profiles were simulated using a 3D mechanoelastic approach.^69–71 The sample used is a lattice of 6400 molecules, represented as balls situated at the sites of a face-centered cubic structure of five interconnected layers with open boundary conditions (Fig. 3). All the bulk molecules have twelve nearest neighbours (six on the same layer and six on the adjacent layers), which are linked by springs.

Fig. 3 Left: The simulation model comprising a five-layer fcc lattice containing high-spin (red), low-spin (blue) and dopant (yellow) molecule sites. Right: The links between molecules within and between the lattice layers (blue) and between two consecutive layers (green).

The molecules can flip between spin states according to the Monte Carlo Arrhenius probabilities (eqn (1) and (2)):^34,72

where D and E_a are respectively the HS-LS energy difference and the transition activation energy for non-interacting molecules; g is the degeneracy ratio between the high- and low-spin states; T is the temperature; κ is a scaling factor between the local pressure and the activation energy; and τ is a scaling constant, chosen so the above probabilities are well below unity at any temperature. The key parameter in the above probabilities, responsible for the cooperativity in the system, is the local pressure force p_i, defined as the sum of elastic forces applied to a molecule by all neighbouring springs (eqn (3)):where δx_ij is positive for compressed springs and negative for elongated ones, and k is the elastic constant of the spring connecting each molecule pair. Thus, the switching probability is determined by the elongation of the springs: in the pure high-spin or low-spin states and in the absence of dopants, all the springs have their natural length. When a molecule flips, its size changes which elongates or compresses the neighbouring springs. Propagation of this perturbation induces all molecules in the system to change their absolute and relative positions.

During a Monte Carlo Step (MCS), all the molecules are checked to establish if they change state, by comparing the individual switching probability with a randomly generated number. After the completion of each MCS, the new equilibrium positions of the molecules are computed by solving differential equations considering the new molecular sizes. In this simulation we used a temperature sweep rate of 0.001 K per MCS, which is small enough to obtain a quasi-static thermal transition while minimizing kinetic effects. The radius of the molecules (including the ligand sphere) is 0.22 nm for HS and 0.20 nm for LS, with a distance of 1 nm between the centres of adjacent Fe ions.³² The scaling factor κ takes the value 1450 × 10⁻¹⁴ J N⁻¹, similar to that in previous studies.⁷³

First we determined which values of the elastic spring constant k give the best fit for the thermal transition loop from the pure iron compound, setting the experimental values for D and g (g = exp{DS/k_B}). We found a value of k = 5 N m⁻¹ within the layers in the lattice, which corresponds to a relatively high cooperativity, and ten times smaller between the layers. Recent experiments showed the stiffness of springs between molecules in different spin states can differ by 25–50%,⁷⁴ but this difference does not qualitatively change the simulation results.⁷⁵ Hence, to minimise the number of fitted parameters, we employed a single value of k between SCO molecules, irrespective of their state.

We introduced dopants into the system by randomly replacing fractions of SCO molecules with dopant molecules, represented as balls of a different radius. The radius of the zinc dopant molecules was set at 0.216 nm which is close to iron in its high-spin state, while the radius of the ruthenium dopant is 0.210 nm, the average of the two iron spin states in the model. Dopants are linked to neighbouring SCO molecules by different elastic constants, which depend on the state of the SCO molecules (k = k_DL or k = k_DH for springs linking dopants with low-spin and high-spin iron sites, respectively; Fig. 4). No other assumptions were made, and other parameters used to reproduce SCO in the pure iron compound were kept constant.

Fig. 4 Left: Schematic of an expanded layer of the simulation system showing dopants replacing SCO molecules, and their links with SCO nearest neighbours (HS = high-spin, LS = low-spin). The experimental (data points) and simulated (lines) thermal SCO transitions in 1a–1e (centre) and 2a–2d (right). The simulations show the equilibrated spin state population at each temperature for the in silico lattice in Fig. 3, using the dopant concentration and force constant parameters described in the text.⁷⁷

Fig. 4 presents simulations obtained with the following parameters: for Zn dopants, k_DL = 6 N m⁻¹ and k_DH = 4 N m⁻¹; and for Ru dopants, k_DL = 3 N m⁻¹ and k_DH = 7 N m⁻¹. This reproduces the shift of T_½ to lower temperatures for Zn doping and to higher temperatures for Ru doping, as observed experimentally. That is, the Zn(II) dopant ions in 1a–1e and the Ru(II) dopants in 2a–2d exert opposite influences on the lattice energetics of SCO in [Fe(bpp)₂][BF₄]₂.

Full crystallographic refinements were achieved from both spin states of 1c, 2c and [Fe_0.5Ni_0.5(bpp)₂][BF₄]₂ (3c),⁵⁴ using synchrotron radiation to maximize the resolution of the datasets. The structures were first refined as crystallographically ordered molecules, with mixed-composition metal atom sites.^{36,40,41,45,76} The bond lengths and angles in the low-spin crystals, and in high-spin 1c, are a good match for the weighted average values calculated from the two component molecules. However, the high-spin structures of 2c and 3c show some deviation from expectation (Table 3). Most notably, the trans-N{pyridyl}–M–N{pyridyl} angle (ϕ)⁷⁸ is larger than expected by 4–5σ, and is essentially equal to that of the ruthenium or nickel dopant molecule.^67,79

Table 3 Summary structural data from the crystallographic refinements of 1c–3c. The italicised values are weighted averages calculated from high-spin [Fe(bpp)₂][BF₄]₂ and the appropriate dopant complex, based on the metal compositions refined in the low temperature analyses (cf.eqn (4)). Complete lists of the bond lengths and angles are in Tables S3–S5 (ESI)^a

	1c		2c		3c
	HS, 300 K	LS, 100 K	HS, 350 K	LS, 100 K	HS, 350 K	LS, 100 K
a HS = high-spin, LS = low-spin. b γ is the average bpp ligand bite angle in the model, which is sensitive to the spin state and the composition of the metal content in the crystal. c ϕ is the trans-N{pyridyl}–M–N{pyridyl} bond angle.
M–N{pyridyl}average	2.114(6) {2.114(6)}	1.996(2) {1.993(4)}	2.058(6) {2.074(5)}	1.950(3) {1.962(4)}	2.065(6) {2.065{3}}	1.959(2) {1.962(3)}
M–N{pyrazolyl}average	2.184(10) {2.183(10)}	2.067(3) {2.069(5)}	2.119(12) {2.137(8)}	2.026(4) {2.034(7)}	2.143(13) {2.144(6)}	2.041(4) {2.049(4)}
γ/deg^b	73.8(5) {73.8(4)}	77.19(14) {77.4(3)}	75.8(5) {75.9(3)}	79.03(17) {79.2(3)}	75.2(4) {75.3(2)}	78.38(14) {78.37(18)}
ϕ/deg^c	173.8(2) {173.5(2)}	175.47(8) {175.70(17)}	177.6(3) {175.7(2)}	177.94(11) {178.1(2)}	176.6(3) {175.20(12)}	177.32(8) {177.43(11)}

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The observed ϕ should be a weighted average of the iron and dopant molecule values (eqn (4)):⁷⁶

ϕ_obs = zϕ{Fe} + (1 − z)ϕ{M} (4)

Eqn (4) estimates ϕ{Fe, HS} = 173.8(3)° for high-spin 1c at 300 K; 176.9(4)° for 2c at 350 K; and 176.2(3)° for 3c at 350 K. For comparison, [Fe(bpp)₂][BF₄]₂ exhibits ϕ{Fe, HS} = 173.15(10)° at 290 K.⁶⁴ Hence, the high-spin [Fe(bpp)₂]²⁺ centres in 1c are unchanged by zinc doping within experimental error, but may adapt their geometries to the demands of the more rigid dopant molecules in 2c and 3c.⁸⁰ These small deviations will have little effect on the ligand field of the iron centres but should influence the lattice energy of the high-spin materials, thus changing the energetics of SCO.⁸¹ This is discussed further below.

Whole molecule disorder models were constructed from the 100 K datasets of each crystal, to resolve their [Fe(bpp)₂]²⁺ and [M(bpp)₂]²⁺ (M = Zn, Ru or Ni) moieties. These refined without geometric restraints, although thermal parameter constraints were sometimes required between equivalent atoms in the two partial molecules. That allowed the metal composition of each crystal to be refined, which lay in the range 0.46 ≤ z ≤ 0.54. The most precise disorder refinement is for 1c (Fig. 5), because the geometry of its [Zn(bpp)₂]²⁺ dopant is most different from the low-spin [Fe(bpp)₂]²⁺ centres. Hence, those components are distinguished most clearly by the disorder model.

Fig. 5 The asymmetric unit of 1c at 100 K showing the resolved [Fe(bpp)₂]²⁺ (dark colouration) and [Zn(bpp)₂]²⁺ (pale colouration) cation sites, which refined independently without restraints. Displacement ellipsoids are at the 50% probability level, and H atoms are omitted for clarity. Colour code: C, white or dark grey; B, pink; F, yellow; Fe, dark green; N, pale or dark blue; Zn, pale green.

The geometries of [Fe(bpp)₂]²⁺ and [Zn(bpp)₂]²⁺ in 1c are identical to the single-component crystals [Fe(bpp)₂][BF₄]₂ and [Zn(bpp)₂][BF₄]₂, within experimental error (Table S3, ESI†). The cation disorder refinements of 2c and 3c are less accurate and deviate slightly from expectation, particularly in their Fe–N{pyridyl} and M–N{pyridyl} bond lengths which are more similar than expected (Tables S4 and S5, ESI†). The resolution of the synchrotron diffraction data may be too low to fully define the disorder in that region of the asymmetric unit.

As previously described,⁸² the crystals adopt a “terpyridine embrace” crystal lattice, which is often found in homoleptic complexes of 2,2′:6′,2′′-terpyridine and related ligands.⁸³ The [M(bpp)₂]²⁺ molecules associate into layers in the (001) crystal plane, through four-fold interdigitation of their distal pyrazolyl groups (Fig. 6 and Fig. S11, ESI†). Nearest neighbour cations within the layers are in close contact, through edge-to-face C–H⋯π and face-to-face π⋯π interactions between their pyrazolyl rings. Adjacent layers in the crystal are separated by the BF₄⁻ anions, and are not in direct van der Waals contact.

Fig. 6 Packing diagram of [Fe(bpp)₂][BF₄]₂ at 150 K,⁶⁴ viewed in the plane of the terpyridine embrace cation layers (Fig. S11, ESI†). Alternate cation layers are coloured white and purple, while the BF₄⁻ ions are de-emphasised for clarity. The red arrows show the approximate directions of the principal components of thermal expansion; the vector is oriented along b, perpendicular to the view.

Unit cell data were collected at 10 K intervals between 350 and 100 K, from 1c–3c and the precursor crystals [M′(bpp)₂][BF₄]₂ (M′ = Fe, Zn, Ni and Ru; Fig. 7). The isothermal volume change during the high → low-spin transition of the iron-containing crystals (ΔV_SCO) was calculated at T_½ (Table 4). The magnitude of ΔV_SCO shows significant variation, in the order 1c < 2c ≈ 3c < [Fe(bpp)₂][BF₄]₂. ΔV_SCO for 2c and 3c is 54–62% that of the pure iron complex, reflecting that they contain ca. 50% of the iron content in the pure iron crystal.⁷⁶ Unexpectedly however, 1c shows a much smaller ΔV_SCO which is ca. half that of the other solid solutions. This variation in ΔV_SCO has little effect on the SCO cooperativity in 1c/2c/3c, which is very similar in each material from the magnetic susceptibility data (Fig. S21, ESI†).

Fig. 7 Variable temperature unit cell volumes for 1c–3c. Error bars are smaller than the symbols on the graphs. The lines show the thermal expansion linear regression fits for each [M′(bpp)₂][BF₄]₂ component in the crystal, as a pure material (HS = high-spin, LS = low-spin; Fig. S21–S22, ESI†).

Table 4 Absolute and % isothermal changes to the unit cell parameters during high → low-spin SCO in the iron-containing crystals, Δx_SCO (x = a, b, c, β, V). Data for each compound are calculated at T_½ (Table 2), by linear extrapolation of the low-spin and high-spin parameters to that temperature

		ΔaSCO/Å	ΔbSCO/Å	ΔcSCO/Å	ΔβSCO/deg	ΔabSCO^a/Å	ΔVSCO/Å^3
a ΔabSCO denotes the change in the area of the 2D cation layers in the unit cell during SCO, where ab is the product of the a and b unit cell dimensions. b The isothermal ΔVSCO for [Fe(bpp)2][BF4]2 at 30 K has also been measured, at −29.3(5) Å^3 or 2.22%.^86
[Fe(bpp)2][BF4]2	ΔxSCO	+0.0231(6)	+0.074(2)	−0.5570(9)	+2.027(5)	0.82(2)	−30.4(3)^b
	%	+0.27	+0.87	−2.93	+2.11	+1.14	−2.23
1c	ΔxSCO	+0.0153(15)	+0.0428(11)	−0.222(3)	+0.666(13)	0.49(2)	−8.8(4)
	%	+0.18	+0.50	−1.18	+0.69	+0.68	−0.65
2c	ΔxSCO	−0.0093(7)	+0.0103(6)	−0.1993(16)	+0.724(8)	0.008(11)	−16.5(2)
	%	−0.11	+0.12	−1.06	+0.75	+0.01	−1.22
3c	ΔxSCO	−0.0041(8)	+0.0213(10)	−0.264(2)	+0.800(10)	0.146(16)	−18.8(3)
	%	−0.05	+0.25	−1.40	+0.83	+0.20	−1.38

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The largest changes to the lattice during SCO involve the canting of the cation layers (the unit cell β angle), which is greater in the low-spin state; and, the spacing between them (the c dimension), which contracts in the low-spin material (Fig. 6). Both those changes contribute to the negative value of ΔV_SCO, as observed (Fig. 7 and Table 4). Those parameters behave quite consistently in 1c–3c. Rather, the main differences between 1c–3c during SCO lie in the dimensions of the cation layers in the ab plane. SCO in [Fe(bpp)₂][BF₄]₂ causes a small expansion of a and b in the low-spin state, despite the shorter distal Fe–N bond lengths in the low-spin molecule. That layer expansion is replicated in 1c, roughly proportionately with its iron concentration. In contrast, the effect of SCO on a and b in 2c and 3c is much smaller. The expansion of the cation layers during SCO in 1c partly offsets the other changes to the lattice, and is the main origin of its smaller ΔV_SCO volume contraction compared to 2c and 3c.

The area of the cation layers in all the single-component [M′(bpp)₂][BF₄]₂ lattices, as the product of a and b, shows a reasonable linear correlation with the bond angle ϕ (Fig. S23, ESI†). That is, the complex molecules pack less efficiently in two dimensions as ϕ approaches 180°, corresponding to idealised D_2d molecular symmetry. That explains the expansion of a and b in the low spin states of [Fe(bpp)₂][BF₄]₂ and 1c. The change in ab during SCO at T_½ in the iron-containing compounds, Δab_SCO, decreases linearly with Δϕ_SCO{Fe} for their iron centres, as estimated from eqn (4) (Fig. 8).

Fig. 8 The relationship between the changes in ϕ, and the area of the 2D cation layers, during SCO in the iron-containing crystals. The black datapoints are for the iron centres in 1c–3c, calculated from eqn (4), while the grey points are directly measured values averaged between the iron and dopant complex molecules (Tables S2–S4, ESI†). Linear regression lines are included for both sets of data.

The unit cell data were used to calculate linear thermal expansion coefficients (α_V, eqn (5)).^84,85

α_V is the inverse of the bulk modulus of a material, and is related to its compressibility; materials with a higher α_V are more susceptible to deformation. For consistency, the α_V values in Table 5 are scaled against the reference volume (V₀) at 100 K, which was derived by linear extrapolation of the experimental data if required. Although there is evidence of curvature in some of the V vs. T graphs (Fig. 7 and Fig. S21, S22, ESI†), the linear regression fits used to calculate α_V{100 K} all gave R² ≥ 0.97.

Table 5 Linear thermal expansion parameters for the compounds in this work, from single crystal unit cell data (Fig. S21 and S22, ESI). The values are scaled against the unit cell volume (V) at 100 K, which was derived by linear extrapolation of the experimental data if required^a

	α V {100 K}/10^6 K^−1	α TE{100 K}^b/10^6 K^−1	α 3{100 K}/10^6 K^−1
a HS = high-spin, LS = low-spin. b See eqn (6).
[Fe(bpp)2][BF4]2, HS	209(2)	38(3)	167.0(10)
[Fe(bpp)2][BF4]2, LS	160(4)	82.0(15)	76(2)
1c, HS	213(8)	50(4)	158(4)
1c, LS	140(7)	57(3)	80(4)
2c, HS	273(2)	60(4)	208(6)
2c, LS	170(5)	90(2)	78(2)
3c, HS	251(8)	64(4)	182(4)
3c, LS	173(6)	88(3)	81(3)
[Zn(bpp)2][BF4]2	204(7)	70(2)	127(5)
[Ru(bpp)2][BF4]2	180(4)	66.3(16)	98(3)
[Ni(bpp)2][BF4]2	168(4)	83.1(10)	93(3)

---

The α_V{100 K} coefficients in Table 5 are typical for molecular crystals.^84,85 While they show some variation, α_V{100 K} for the high-spin iron-containing materials is consistently larger than for their low-spin states.^76,87–89 The dopants [Ni(bpp)₂][BF₄]₂ and [Ru(bpp)₂][BF₄]₂ yield α_V{100 K} values close to the low-spin iron crystals, whereas for [Zn(bpp)₂][BF₄]₂ it is nearer the high-spin iron range. α_V{100 K} coefficients calculated using published unit cell data from other iron(II) SCO molecular materials and their zinc(II) analogs also conform to these trends (Table S14, ESI†). In particular, α_V{100K} for the zinc complexes is always 82–94% of the value for the isomorphous high-spin iron(II) complex.⁸⁹

More insight is provided by the principal anisotropic components of the thermal expansion, which follow the same pattern in each crystal (Table S13, ESI†).⁹⁰ The two smallest component vectors (α₁ and α₂ in the Table) are oriented within the cation layers in the crystal. The largest component, α₃, the most deformable direction in the lattice, lies approximately perpendicular to the cation layers (Fig. 6). Since the intermolecular interactions in the lattice are weakest in that direction, these results are consistent with expectations.

The 2D thermal expansion coefficient of the terpyridine embrace cation layers, α_TE, is given by the sum in eqn (6).

α_TE = α₁ + α₂ (6)

Two trends are apparent when comparing the high-spin and low-spin forms of the iron-containing crystals (Table 5). First is that, for most of the crystals, α_TE[LS] > α_TE[HS]. The possible exception is 1c, where the difference between α_TE in the two spin states lies within the experimental error. That trend in α_TE does not reflect the deformability of the metal coordination sphere, which should be more rigid for low-spin iron(II).⁸⁰ Moreover, α_TE for the precursor crystals [M′(bpp)₂][BF₄]₂ also follows the trend M′ = Zn ≈ Ni < Ru. That is, the most conformationally rigid low-spin d⁶ ruthenium(II) complex molecule forms crystals with the most deformable cation layers.

The second observation, exhibited by all the iron-containing crystals, is that α₃{HS} = 2–3 × α₃{LS}. That is, high → low-spin SCO makes the crystal more deformable in the plane of the terpyridine embrace layers, but more rigid when deformed perpendicular to the cation layers. That is again mirrored in the [M′(bpp)₂][BF₄]₂ precursor crystals, where α₃ follows the trend M′ = Zn > Ni ≈ Ru. Thus, crystals of the largest and most flexible zinc(II) and high-spin iron(II) complexes are most susceptible to deformation between the cation layers. Of all these parameters, α₃ shows the most significant differences between the spin states, which is the origin of the consistent reduction in α_V during SCO.

Discussion

Derivatives of [Fe(bpp)₂][BF₄]₂ doped with inert metal ions, of formula [Fe_zM_1−z(bpp)₂][BF₄]₂, have now been produced with M = Co, Ni, Zn and Ru (Fig. 2). The first three dopant ions stabilise the high-spin state of the materials, in the expected order M = Co ≈ Zn > Ni for a given composition z (Fig. S1, ESI†).^32,33,48,49 In contrast, doping with Ru increases the transition temperature T_½, stabilising the low-spin state. Such trends have previously been explained by chemical pressure arguments, where larger dopant ions progressively stabilise the larger high-spin form of the iron centres.^32–34 While no ionic radius for Ru²⁺ is available,⁵⁵ the relative sizes of the dopant ions can be expressed by the octahedral coordination volume (V_Oh⁹¹) in their isomorphous [M′(bpp)₂][BF₄]₂ crystals. The trend in V_Oh runs as follows:

M′ = Fe{HS} [12.378(9) ų] > Zn [12.251(12)] > Co [12.012(6)]

>Ni [11.320(5)] ≈ Ru [11.279(10)] ≫ Fe{LS} [9.620(5)]

On that basis, precedent predicts that [Fe_zM_1−z(bpp)₂][BF₄]₂ should behave similarly when M = Ni and Ru, as they do when M = Zn and Co (Fig. 2). Hence, the stabilisation of the low-spin state in [Fe(bpp)₂][BF₄]₂ by doping with ruthenium(II) cannot be rationalised from chemical pressure considerations.

Mechanoelastic simulations of the SCO curves show these trends can be explained, if the [Zn(bpp)₂]²⁺ dopant molecules in 1a–1e and the [Ru(bpp)₂]²⁺ dopant in 2a–2d exert opposite influences on the energetics of the [Fe_zM_1−z(bpp)₂][BF₄]₂ lattice. That is, intermolecular elastic interactions are stronger in the low-spin state of 1a–1e, and in the high-spin state of 2a–2d (Fig. 4). This is supported by a crystallographic comparison of [Fe_zM_1−z(bpp)₂][BF₄]₂ (z ≈ 0.5; M = Zn, 1c; M = Ru, 2c; M = Ni, 3c), which implies those three dopant ions affect the iron lattice in different ways. That is clear in their lattice properties, where the isothermal volume change during SCO (ΔV_SCO) in 1c is only ca half the value for 2c and 3c. The difference mostly reflects the low-spin unit cell of 1c, whose volume is significantly larger than for the other two materials (Fig. 7).

These changes in ΔV_SCO are anisotropic in nature (Table 4), so they do not simply originate from the different ionic radii of the dopant metal ions. Rather, they reflect the dimensions of the cation layers, which become measurably larger during SCO in 1c but are almost unchanged in 2c and 3c (Table 4). This in turn correlates with the molecular structure changes during SCO at the iron sites in 1c–3c (Fig. 8).

Related observations can be made from the thermal expansion coefficients of each material. All the iron-containing crystals are less deformable in their low-spin states (smaller α_V, Table 5), which reflects significant changes perpendicular to the cation layers during SCO. The cation layers themselves show the opposite trend, in being more deformable in the low-spin crystals than in their high-spin state (larger α_TE). However that trend is less pronounced in 1c than in the other iron-containing crystals, where α_TE in both spin states lies within experimental error. That is more evidence that the lattice properties of 1c are different from 2c and 3c.

At the molecular level, the crystallographic metric parameters in high-spin 2c and 3c deviate slightly from expectation, when considered as an average of their component molecules. This is most obvious in the ϕ angle, which is larger than predicted for high-spin 2c and 3c based on the structures of their pure component molecules (Table 3). In contrast ϕ for high-spin 1c, and for all of the low-spin crystals, are essentially equal to the expected values.

The plasticity of the coordination sphere in [M′(bpp)₂]²⁺ should vary according to the d-electron configuration of M′, as M′ = Fe{HS} > Zn > Ni > Fe{LS} ≈ Ru.⁸⁰ Hence, this variation in ϕ implies the molecular geometry of high-spin [Fe(bpp)₂]²⁺ in 2c and 3c may be influenced by the presence of more rigid dopant molecules. That in turn correlates with the observed structural differences between 1c–3c during SCO, which appear to reflect the influence of ϕ on their crystal packing rather than the size of the dopant ions (Fig. 8).

T _½ in salts of [Fe(bpp)₂]²⁺ derivatives with terpyridine embrace crystal packing correlates linearly with the change in Θ during SCO (ΔΘ_SCO, Fig. 9).^92,93Θ is a torsion angle parameter, defined in the ESI,† which reflects the position of the metal coordination geometry along the O_h → D_3h distortion pathway.⁹¹ While Θ is a function of the whole metal coordination sphere, ϕ and Θ are approximately proportional to each other when other metric parameters are unchanged.⁷⁸

Fig. 9 The relationship between ΔΘ_SCO{Fe} and the lattice contribution to T_½, ΔT(latt),⁹³ for salts of [Fe(bpp)₂]²⁺ derivatives with terpyridine embrace crystal packing. The green data points and line show the published correlation,⁹² while 1c–3c are plotted in black.⁹⁴

Data in Fig. 9 are plotted as ΔT(latt), which is the lattice contribution to T_½ separated from the molecular ligand field component, which is estimated from solution measurements (eqn (7)).^93,94

ΔT(latt) = T_½(solid) − T_½(solution) (7)

The slope of Fig. 9 describes the coupling between the molecular geometry rearrangement and the lattice energy change during SCO in terpyridine embrace crystals.⁹⁵

The average ΔΘ_SCO for the mixed-metal sites in 1c–3c (Tables S2–S4, ESI†) bears no relation to the correlation in Fig. 9. However, Θ_SCO for their iron centres can be extracted from these averaged values, by correction for Θ of the dopant molecule (eqn (8), cf.eqn (4)).

Θ_obs = zΘ{Fe} + (1 − z)Θ{M} (8)

The corrected values ΔΘ_SCO{Fe} are shown in Fig. 9. 1c lies significantly below the correlation line for undoped materials, implying its ΔT(latt) (and T_½) are lower than predicted from the structural properties of its iron centres. That is, the lattice in 1c stabilises its high-spin state more efficiently than in the pure iron complex. In contrast, 2c and 3c are both a similar distance above the main correlation. That suggests their ΔT(latt) and T_½ are slightly higher than expected on structural grounds, and to a similar degree. Hence, the doped lattices in 2c and 3c influence T_½ to a similar degree, but differently from 1c.

Lastly, since 2c and 3c both lie a similar distance above the main correlation line in Fig. 9, we conclude the higher T_½ in 2c compared to 3c is also a function of ΔΘ_SCO; that is, how their iron coordination geometries are modified by the presence of ruthenium(II) and nickel(II) dopants.

Conclusions

The effect of dopant ions ‘M’ on SCO in [Fe_zM_1−z(bpp)₂][BF₄]₂ is more complicated than expected, based on previous work.^32–34 Most unexpectedly, T_½ increases with increased ruthenium doping in [Fe_zRu_1−z(bpp)₂][BF₄]₂ (2a–2d; Table 1). That cannot be explained from the ionic radius of Ru²⁺, which is too large to stabilise the low-spin state of the iron lattice. Rather, it reflects that different dopant ions cause opposite perturbations to the energetics of SCO in the host lattice (Fig. 4). Since another ruthenium-doped SCO crystal also exhibits a higher T_½ than the parent iron complex,⁵⁷ that might be a general observation.

Crystallographic analysis of [Fe_zM_1−z(bpp)₂][BF₄]₂ (z ≈ 0.5) with M = Zn, Ru and Ni correlates these macroscopic observations with their structures at the molecular level. Small but consistent trends in their molecular structures, unit cell parameters and thermal expansion coefficients imply the influence of zinc dopants on the materials’ structures differs from doping with nickel or ruthenium. That is clearly expressed in the structure:function correlation in Fig. 9. This shows 2c and 3c behave broadly consistently with each other, with their doped lattices stabilizing the low-spin state of the material compared to the undoped material. However 1c behaves differently, in that its zinc-doped lattice strongly stabilises the high-spin state. The structure:function properties of the two types of doped material must be considered separately.

We conclude that large dopant ions like zinc(II) in 1c indeed lower T_½ as previously understood, which is reflected in its smaller ΔV_SCO unit cell volume change (Fig. 7).^32–34 However Fig. 8 implies the more distorted coordination geometry of the zinc(II) dopant complex, and its impact on the structure of the iron sites in the material, contributes to ΔV_SCO as much as the ionic radius of the zinc(II) ion. In contrast the ruthenium(II) and nickel(II) dopants in 2c and 3c exert more moderate, and very similar, chemical pressure on the [Fe(bpp)₂][BF₄]₂ lattice (Fig. 9). In that case, the variation of T_½ with composition reflects the different influences of those two dopant ions on the molecular structure of the iron switching centres, and how that feeds through to the bulk lattice (Fig. 8 and 9).

The above implies that salts of [Fe(bpp)₂]²⁺ derivatives with more distorted high-spin molecular geometries and a larger structure change during SCO, should be affected more strongly by ruthenium doping.^96–99 Other moderately sized dopant ions whose coordination geometries impose a regular O_h symmetry preferred by low-spin iron(II) centres, should also increase T_½ most effectively in doped [Fe_zM_1−zL_n] lattices. Current work aims to test those predictions, and to probe the generality of our conclusions.

Finally, “molecular alloying”¹⁰⁰ by chemical doping of different metals, ligands and/or anions into SCO materials has been used to tune T_½ towards room temperature for application purposes.^45,100–106 Up to now, metal doping has only been used in such materials undergoing high temperature SCO, to lower their T_½ towards 300 K.^102,103 This study shows how metal doping can increase T_½ towards a desired range, as well as decreasing it. That could have value for adjusting solid-state refrigerants based on SCO materials, for example, to optimise their performance at room temperature.^16–19 While chemical doping also quenches thermal hysteresis in cooperative SCO materials, that is beneficial for cooling applications requiring a first-order transition that is thermodynamically reversible (ie with no thermal hysteresis).¹⁰⁷

Experimental

The precursor complexes [M′(bpp)₂][BF₄]₂ (M′ = Fe,⁶⁴ Ni,⁷⁹ Zn⁶⁶ and Ru⁶⁷), and [Fe_0.5Ni_0.5(bpp)₂][BF₄]₂ (3c),⁵⁴ were prepared by the literature methods.

Synthesis of [Fe_zZn_1−z(bpp)₂][BF₄]₂ (1a–1e)

Preformed [Fe(bpp)₂][BF₄]₂ and [Zn(bpp)₂][BF₄]₂ were mixed in different mole ratios, to a combined mass of 0.25 g. The combined solids were stirred in nitromethane (25 cm³), until all the solid had dissolved. The solutions were concentrated to ca. 10 cm³, then filtered. Slow diffusion of diethyl ether vapour into the solutions afforded yellow polycrystalline materials, whose colour becomes paler as z decreases. Crystallised yields were in the range 80–85%. The compositions and analytical data for 1a–1e are given in Table 1.

Synthesis of [Fe_zRu_1−z(bpp)₂][BF₄]₂ (2a–2d)

Method as above, using [Ru(bpp)₂][BF₄]₂ (Table 1). Polycrystalline 2a–2d are brown in colour, which becomes darker with increased Ru content.

Single crystal structure analyses

Single crystals of 1c, 2c, 3c and the precursor complexes were grown by vapour diffusion methods as described above. Full datasets of the doped crystals were collected at station I19 of the Diamond synchrotron (λ = 0.6889 Å), while variable temperature unit cell data were measured with an Agilent SuperNova diffractometer using Mo-K_α radiation (λ = 0.7107 Å).

Experimental details and refinement protocols for the full structure determinations are given in the ESI.† The structures were solved by direct methods (SHELX-TL¹⁰⁸), and developed by full least-squares refinement on F² (SHELXL2018¹⁰⁹). Crystallographic figures were produced using XSEED,¹¹⁰ and other publication materials were prepared with OLEX2.¹¹¹

Isotropic and anisotropic thermal expansion parameters at 100 K were calculated with PASCal.⁹⁰ Thermal expansion coefficients at 300 K were derived from linear regression analyses of unit cell data (eqn (1)). Estimated errors on α_V{300 K} are also based on the PASCal calculations.

Other measurements

All physical characterisation was performed using the same sample of each material. CHN elemental microanalyses were performed by the microanalytical service at the London Metropolitan University School of Human Sciences. Energy Dispersive X-Ray (EDX) analysis was carried out using a Jeol JSM-7610F field emission scanning electron microscope with a 15 kV applied voltage; or, with a FEI Nova NanoSEM 450 environmental microscope operating at 3 kV. X-ray powder diffraction data were obtained with a Bruker D8 Advance A25 diffractometer using Cu-K_α radiation (λ = 1.5418 Å). Differential scanning calorimetry (DSC) measurements used a TA Instruments DSC Q20 calorimeter, with heating at a rate of 10 K min⁻¹.

Magnetic susceptibility measurements were performed on a Quantum Design MPMS-2 SQUID or a MPMS-3 SQUID/VSM magnetometer, with an applied field of 5000 G and a scan rate of 2 K min⁻¹. A diamagnetic correction for the samples was estimated from Pascal's constants;¹¹² a diamagnetic correction for the sample holder was also applied. Processing of magnetic data and all graph plotting was performed using using SIGMAPLOT.¹¹³

Author contributions

The project was conceived and supervised by PC and MAH. PG undertook the synthesis and analytical characterisation of the new materials. HBV and NY measured the magnetic susceptibility data, using SQUID magnetometer time provided by OC and TK. CMP collected the crystallographic data, and MAH did the structure refinements and analysis. CE performed the mechanoelastic model simulations and analysed the results. MAH and CE wrote the manuscript draft, which was reviewed and edited by PC. All authors approved the final version of the publication.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors thank Dr Alexander Kulak and Dr Namrah Shahid (University of Leeds) for help with some measurements. PC and MAH's collaboration was funded by the Royal Society, UK (IES\R3\193172). PG gratefully acknowledges financial support by the SERB, India (PDF/2021/004430); PC by the SERB (ECR/2018/000923); and CE by the UEFISCDI, Romania (PN-III-P4-ID-PCE-2020-1946). MAH acknowledges Diamond Light Source for access to beamline I19 (CY26879), which contributed to the results presented here.

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Footnotes

† Electronic supplementary information (ESI) available: X-ray powder diffraction and magnetic susceptibility data; crystallographic experimental data, refinement procedures, Figures and tabulated metric parameters; calculated thermal expansion coefficients from the compounds in this work, and selected literature materials. CCDC 2261786–2261796. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3tc02683c

‡ Current address: Department of Chemistry, Faculty of Science, National Taiwan Normal University, Taipei 11677, Taiwan.

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