Intrinsic thermal expansion and tunability of thermal expansion coefficient in Ni-substituted Co2V2O7

Framework oxide materials are well-known for exhibiting not only negative thermal expansion (NTE), but also demonstrating thermal expansion that can be controlled using composition as a tuning parameter. In this work, we study the intrinsic thermal expansion properties of Co2V2O7, which has shown bulk linear NTE, and attempt to understand how substituting Ni2+ for Co2+ will affect the thermal expansion. The isomorphic solid solution is synthesized through solid-state methods and characterized using x-ray diffraction (XRD), diffuse reflectance spectroscopy, and neutron diffraction. The size difference between Ni2+ and Co2+ as well as the polyhedral volume of each Co2+ metal coordination environment in the crystal structure allows Ni2+ to partially be directed toward one crystallographic site over the other. Variable temperature synchrotron XRD data are employed to understand intrinsic thermal expansion. Across the solid solution, no intrinsic NTE is observed at the microscopic level, yet a degree of tunability in the thermal expansion coefficient with Ni substitution is demonstrated. The disparities between the intrinsic and bulk thermal expansion properties suggest that a morphological mechanism may have resulted in NTE in the bulk.


Introduction
Conventionally, positive thermal expansion (PTE) is observed in materials.Negative thermal expansion (NTE) behavior is a fundamentally intriguing and practically useful thermophysical property in which materials decrease in dimension or volume as temperature is increased.NTE materials can be used as thermal compensators when composited with other materials and used to counteract the detrimental effects that PTE can have.For example, common materials steel and aluminum have linear coefficients of thermal expansion of approximately 12 ppm • C −1 and 24 ppm • C −1 , respectively.As a result, if a 1 m rod of each experiences a 100 • C temperature increase, steel would elongate by 1.2 mm and aluminum would elongate by 2.4 mm.While these changes are nearly impossible to detect by eye, these small variations can cause performance degradation, thermal shock, and ultimate failure of materials, which can be catastrophic as seen in the 2004 Charles De Gaulle Airport terminal collapse [1].Thus, the ability to understand and control NTE materials can benefit many applications where dimensional control at various temperatures is important, such as in multi-layer ceramic capacitors [2], solid oxide fuel cells [3], piezoelectric sensors [4], or in precise machining equipment [5].Thus, beyond discovery and study of NTE materials, understanding how to control the thermal expansion of materials is crucial in creating more robust materials.
The first observation of contraction with heating dates back to studies of the 'density anomaly of water' in the 17th century [6], and revealed that water shows NTE in the range of 0 • C-4 • C. The phenomenon was first reported in solid materials (quartz and vitreous silica) centuries later in 1907 [7,8], yet NTE is only observed in limited ranges -e.g. in β-quartz, at temperatures above ≈600 • C [9].Unusual thermal expansion behavior was reported in ZrW 2 O 6 , a framework oxide material, first in 1968 [10].Then in 1996, large, persistent NTE (-9 ppm • C −1 ) over a very large temperature range (-273 • C to 777 • C) was reported in ZrW 2 O 6 , [11] which garnered great interest in the thermal expansion of other framework oxides.Since this report on a material exhibiting large NTE over a temperature range of more than a few tens of degrees, there has been considerable interest in framework oxide materials having characteristics that may result in NTE-namely, a 'flexible' structure allowed by corner-shared polyhedra in the structure.Several thorough review articles discuss advances in controllability and understanding of NTE materials [5,[12][13][14], and show that NTE can exist in many types of compounds with various structure types and compositions.However, not all NTE materials display such behavior through the same mechanism.The diversity in materials exhibiting NTE is paralleled by the diversity in mechanisms of NTE they exhibit, and are categorized broadly as structural, electronic, and morphological [15].In comparison to other mechanisms, those that exhibit structural NTE (including framework oxides like ZrW 2 O 6 ) tend to have a wider temperature range but smaller overall NTE magnitude.This can be useful when the application to be controlled operates at a large range of temperatures but needs fine tuning as far as the coefficient of thermal expansion (CTE) is concerned.
The search for other materials exhibiting structural NTE (beyond serendipitous 'search and screen' methods) has been supported by efforts to predict which materials have certain structural characteristics that should lead to NTE, including the concept of average atomic volume (AAV).AAV is calculated from simple crystallographic parameters in both isotropic [16] and anisotropic materials [17] spanning several material classes, and the calculated AAV can be compared to a threshold value to determine whether or not NTE can be expected.According to the AAV trend, materials with a calculated AAV of ≈16 Å 3 and above tend to exhibit NTE.Though robust for many materials, including ZrW 2 O 8 mentioned above, some framework oxides with AAV below 16 Å 3 exhibit NTE, thus they would not be detected by this proxy.Specifically, materials in the A 2 Q 2 O 7 (A = divalent metal; Q = P, V) family such as α -Cu 2 P 2 O 7 (AAV = 10.97Å 3 ) [18], β -Cu 2 P 2 O 7 (AAV = 10.91 Å 3 ), [19] and α -Zn 2 V 2 O 7 (AAV = 13.24Å 3 ) [20] which have all shown NTE.Thus, we find this family of materials worthy of further study to explore whether or not NTE is exhibited and, if so, how it manifests.
Beyond materials simply exhibiting NTE in a certain temperature range, it is also beneficial to understand how to control the thermal expansion (i.e. the CTE) in materials such that it may be tuned to fit specific needs [14].Several studies of framework oxides exhibiting NTE have shown that isovalent substitution allows for tunability of the CTE.In ZrV 2 O 7 (space group Pa 3, No. 205), substituting P for V can tune the CTE and percent relative expansion [21].Similar tunability is observed when substituting Zn for Cu [19] or V for P [22] in Cu 2 P 2 O 7 (space groups C2/c, No. 15 and C2/m, No. 12), and when substituting P for V in Zn 2 V 2 O 7 (space group C2/c, No. 15) [23].Many oxides in the A 2 Q 2 O 7 family are amenable to isovalent site substitution, thus it is also worthwhile to explore how isovalent substitution affects thermal expansion in these materials.
Herein, we present a study of the intrinsic thermal expansion properties of the Ni-substituted transition metal framework oxide Co 2 V 2 O 7 (space group P2 1 /c).NTE has been observed above 500 • C in bulk dilatometric studies of the unsubstituted Co 2 V 2 O 7 [24], thus the primary goal of this work is to investigate the intrinsic thermal expansion properties of this material on the unit cell level using variable temperature synchrotron x-ray diffraction (VTXRD).Furthermore, since other A 2 Q 2 O 7 materials show that site substitution can allow for controllability of the thermal expansion coefficient, we attempt isovalent substitution of Ni 2+ on Co 2+ sites to understand if any control can be garnered over the thermal expansion properties using composition as a tuning parameter.

Experimental
Stoichiometric amounts of starting materials CoCO 3 (99.5%,ThermoScientific), NiO (99.998%,Alfa Aesar), V 2 O 5 (99.60%,Alfa Aesar), and (NH 4 ) 2 HPO 4 (98%, Alfa Aesar) were weighed and ground together in an agate mortar with pestle for 10 min to total amounts of 500 mg and 5 g (for neutron diffraction measurements).For 500 mg samples, the powder was pelletized into a 6 mm diameter pellet.Pellets were placed in open alumina crucibles and heated in a box furnace to 750 • C at a rate of 10 • C min −1 , and held at the highest temperature for 4 h before the furnace was turned off and allowed to cool.For 5 g samples, the same procedure was used except samples were pelletized into 25 mm diameter pellets to accommodate the larger amount of powder, and samples were annealed at 750 • C for 24 h.For clarity, samples will be referred to according to their nominal Ni compositions (i.e.x = 0.0, 0.5, and so on).
All samples were first verified using room temperature laboratory x-ray diffraction (XRD) using a Rigaku Miniflex II Diffractometer (Cu Kα, λ = 1.54).For further characterization, diffuse reflectance data were measured between 280 nm and 2400 nm using a Jasco V-770 Spectrophotometer and transformed using Tauc plots to extract optical onsets.A BaSO 4 standard was used as a white reference.
High-resolution diffraction data were collected on 500 mg samples using synchrotron radiation at room temperature and at varying temperatures up to 700 • C at beamline 11-BM at the Advanced Photon Source (Argonne National Laboratory, λ = 0.458953 Å).For VTXRD measurements, samples were loaded into 0.8 mm fused silica capillaries and sealed on each end with modeling clay.Each sample was heated with the beamline's dedicated Cyberstar Hot Gas Blower.Samples were measured for 30 min at 50 • C, then in 50 • C increments from 300 • C to 700 • C. Samples were allowed to equilibrate for 1 min at each temperature before measurement.Since the approximate region of interest/onset of NTE was known to be above 500 • C from He et al [24] high temperature measurements were restricted to this range to be economical in utilizing synchrotron time.After the highest temperature measurement, samples were cooled to 50 • C, then the hot air blower was removed and the sample was allowed to equilibrate to ambient temperature for 1 min before a final data acquisition.VTXRD data were analyzed using sequential Rietveld refinement.Coefficients of thermal expansion were computed using the PASCal software [25].
Neutron powder diffraction data were collected on separate 5 g samples at room temperature at the POWGEN diffractometer at the Spallation Neutron Source at Oak Ridge National Laboratory.Patterns were collected using a center wavelength of the neutron packet of 1.5 Å.A small portion of these 5 g samples were also loaded into 0.8 mm diameter Kapton capillaries, each end sealed with modeling clay, and samples were measured for 1 h at beamline 2-1 at the Stanford Synchrotron Radiation Lightsource (SSRL, λ = 0.72 803 Å).Data on 5 g samples from POWGEN and SSRL were used for combined neutron and synchrotron refinement, and the resultant lattice parameters were compared to those obtained from Rietveld refinement of the initial 500 mg samples on which VTXRD measurements were carried out.Rietveld refinements of all diffraction data were performed using TOPAS [26].Structure visualization and calculation of parameters such as polyhedral volume and distortion index, D, were performed using VESTA-3 [27].

Structural characterization
The structure is comprised of two crystallographically distinct A sites which the divalent metal can occupy, herein referred to as A1 and A2, which are pseudo-octahedrally coordinated to oxygen atoms and edge-shared to one another through sharing two oxygen atoms.The A1 and A2 pseudo-octahedra are slightly different in size with A1 having average volume and average bond length values of 2.072 Å and 11.729 Å 3 , A2 having average volume and average bond length values of 2.092 Å and 12.091 Å 3 (when A = Co).These values are extracted from neutron diffraction data refinement (described below), but trends are in good agreement with previously published crystallographic data [28].The two crystallographically unique V sites are both tetrahedrally coordinated, and corner-shared with one another to form (V 2 O 7 ) 4− dimers, and further corner shared with the A sites.This corner sharing is hypothesized as important in NTE materials for flexibility [11].Figure 1(b) shows detail of the edge-sharing of the A sites as well as the slight asymmetry of the octahedral coordination.The V1 and V2 polyhedra (figure 1(c)) are slightly closer in volume than the two A sites, differing by under 3% (additional details in table S3 of the supplementary data).
Figure 2 shows the results of Rietveld refinement of 50 • C synchrotron XRD patterns for samples x = 0.0 through x = 2.0 as fit to the Co 2 V 2 O 7 structure in space group P2 1 /c.Samples x = 0.5 through x = 1.5 showed additional peaks corresponding to an impurity of Ni metal.x = 0.5 and x = 1.5 resulted in below 1 wt% of Ni, but x = 1.0 showed 3.81 wt% Ni; results from Rietveld refinement of this sample with contributions from each phase are plotted in figure S1 of the supplementary data.
The series results in a complete, isostructural solid-solution as the Co/Ni ratio is varied, as evident from the excellent agreement between the data and model as well as the relatively flat difference pattern for each refinement.Figure 3 shows the lattice parameters resulting from Rietveld refinements in figure 2. The unit cell lengths, a, b, and c, the variable angle β, and the overall unit cell volume all decrease with increasing Ni content.This is in good agreement with the fact that 6-coordinate Co 2+ has an ionic radius of 0.745 Å while 6-coordinate Ni 2+ has a smaller ionic radius of 0.69 Å [29].XRD cannot discern Co from Ni since they only differ by one electron thus precise compositional information cannot be gleaned from these data, but this monotonically decreasing trend in lattice parameters suggests that the smaller Ni is gradually being included in the structure.Furthermore, the literature reported lattice parameters of the end members are also in good agreement (within 1%) with those reported here [28].
Synchrotron XRD is insufficient to fully characterize the Co/Ni ratio in these materials because of the lack of difference in electron count between Co and Ni, thus they are not discernable using this technique.However, neutron diffraction can provide compositional information because of the differing coherent neutron scattering cross sections, σ c , of Co and Ni (σ c equal to 0.779 barn and 13.3 barn, respectively [30]).However, since V is virtually invisible to neutron diffraction (σ c equal to 0.0184 barn) [30]), neutron diffraction data alone would be insufficient to fully characterize these materials.Thus, combined refinement  of neutron diffraction and synchrotron XRD data was used for further characterization.Time-of-flight neutron diffraction at POWGEN (Oak Ridge National Laboratory Spallation Neutron Source) was employed to further characterize these materials.As compared to synchrotron x-rays, neutron beams are relatively weak, and x-rays scatter from the entire electron cloud yet neutrons scatter off of the relatively small nucleus.As such, larger sample masses are required to obtain high-quality neutron diffraction patterns.For these measurements, sample synthesis was modified slightly (experimental details, vide supra) to scale samples up to 5 g.The majority of each 5 g sample was reserved for neutron diffraction at POWGEN, and small portions of these samples were measured via synchrotron diffraction at beamline 2-1 at the Stanford Synchrotron Radiation Lightsource (λ = 0.72 803 Å).Select combined refinements of x = 0.0 and x = 1.0 data are shown in figures 4(a) and (b); additional refinements are in figure S2 of the supplementary data.Since compositional information (5 g samples) and variable temperature synchrotron data (500 mg samples) were  not collected on the same samples figure 4(c) shows a comparison of the lattice parameters of the main phase.Within error, the 5 g and 500 mg samples' lattice parameters are in excellent agreement, thus we are confident that the compositions of each set of samples are comparable.Detailed lattice parameters are listed in table S1.
Figure 4(a) shows the resultant synchrotron x-ray and neutron diffraction fits to solely the Co 2 V 2 O 7 phase for x = 0.0; the data are fit well by the model and no secondary crystalline phase was detected.Figure 4(b) shows the resultant Rietveld refinement as x = 1.0 is fit to both the main Co 2 V 2 O 7 phase and a secondary crystalline phase, CoV 2 O 6 .While the synchrotron data are satisfactorily fit in all cases, the mixed occupancy phases show higher residuals for the fit to the neutron diffraction data (table S2).The neutron diffraction data show peaks in the difference pattern indicating at least once unidentified impurity phase.However, the peaks corresponding to the main phase are fit well and, while there could be slight compositional differences from what is expected, we can still garner information from refinement of the main phase.
Since neutron diffraction data are able to differentiate between Co and Ni, the site occupancies on the A site were investigated.Co occupancy was allowed to refine and the total site occupancy was constrained to unity.As previously discussed and shown in figure 1(b), there are two 6-coordinate transition metal sites which Co 2+ and Ni 2+ can occupy, A1 and A2, with polyhedral volumes of 11.729 Å 3 and 12.091 Å 3 , respectively.Thus, these data can allow some insight into whether the size of the substituting ion could be exploited in order to direct certain sized ions to certain sites.The data show that the overall experimental compositions are all within 10% of the experimental x values.Furthermore, the 'coloring problem' [31] Table 1.Results of Rietveld refinement of variable-temperature synchrotron XRD samples (500 mg samples) and samples analyzed for compositional information by neutron diffraction (5 g samples) are tabulated.Ni occupancies were allowed to refine freely, and the total occupancy of each A site was constrained to unity.(i.e.preferential substitution of the substituting ion on certain sites) matches the prediction that the smaller Ni 2+ preferentially occupies the smaller A1 site since between 55% and 80% of the total Ni composition in each sample occupies the A1 site.Additional compositional details can be found in table 1.

Diffuse reflectance spectroscopy
Diffuse reflectance spectroscopy (DRS) data are presented in figure 5(a) with extracted absorption onset energies as extracted from Tauc plots are plotted in figure 5(b).Data for Tauc plots were plotted as (α × hν) 1/2 since, according to DFT studies, the end members exhibit indirect gaps [32].The absorption onset blue shifts from x = 0.0 to x = 2.0 (1.72 eV and 2.17 eV, respectively).A prior study exists understanding the identities of the peaks in the DRS spectra of the end members [32].According to this study, the absorption edges were experimentally determined to be 1.62 eV for the Co end member (T 1g → 4 T 1g ) and 2.23 eV for the Ni end member ( 3 A 2g → 3 T 1g , in relatively good agreement with extrapolated absorption edges in this study.The additional peak at 1400 nm in the near-IR region for Co can be attributed to 4 T 1g → 4 T 2g ), and peaks at 715 nm and 1400 nm in Ni are attributed to 3 A 2g → 3 T 1g (F) and 3 A sg → 3 T 2g transitions, respectively.Thus, the number of absorption peaks and their approximate energies for the expected transitions in the present samples are in good agreement with this prior study.

Thermal expansion properties
This study of Co 2 V 2 O 7 was motivated by an observation of NTE above 500 • C in this material, yet these thermal expansion data were collected using a dilatometer which yields linear thermal expansion data of bulk samples [24].The primary aim of the current work was to understand how NTE manifests in this material by probing changes in the average unit cell to understand the intrinsic mechanism of NTE.Thus, VTXRD data were collected such that the evolution of the average unit cell dimensions as a function of temperature could be elucidated through Rietveld refinement of the diffraction data.Data were collected on 500 mg samples isothermally at 50   In contrast to the prior report on bulk samples measured by dilatometry [24], no NTE is observed in any unit cell direction or in the overall volume.Some differences between the microscopic and bulk thermal expansion properties in an anisotropic material are to be expected [33], and is famously the case in well-known β-eucryptite in which the dilatometric NTE is more than ten times the magnitude of the crystallographic NTE [34].However, the total absence of NTE at the microscopic level was not expected.Though the original work on Co 2 V 2 O 7 suggested a glassy transition could explain the origin of NTE, our data suggest the structure remains throughout the measured temperature range.Figure S3 of the supplementary data shows Rietveld refinements of isothermal measurements are shown at (a) 300 • C (below the previously reported NTE region), (b) 550 • C (at the cusp of the NTE region), and (c) 700 • C (well into or above the NTE region).These refinements show that no new peaks arise or existing peaks are lost as temperature increases, only peak shifting corresponding with PTE is apparent.The structure remains throughout the reported NTE region, thus this anomalous thermal expansion may be explained by microstructural effects in the bulk.For example, colossal NTE behavior in layered ruthenates such as Ca 2 RuO 4 was reported in 2017 [35].The enormity of the NTE (total volume change of 6.7%) cannot be explained solely by the microscopic mechanism but requires some consideration of the microstructure.Although smaller in difference, a similar effect is observed in another framework oxide material, Ta 2 WO 8 [36].While VTXRD data indicate small positive linear thermal expansion (α l = 1.32 × 10 −6 K −1 ), but dilatometry of a sintered sample show small negative linear thermal expansion (α l = −1.69× 10 −6 K −1 ).Further sintering and addition of MgO to decrease pore size result in dilatometry data that are closer to the intrinsic VTXRD data.Thus, while NTE is observed in bulk Ta 2 WO 8 , it is likely a microstructural effect and pore size affects how this manifests.In the current A 2 V 2 O 7 series, this may be an explanation, yet a remaining question is why the NTE only manifests above a particular temperature.
In the present samples, the addition of Ni 2+ on the Co 2+ does allow for some tuning of the CTE.The overall decrease in CTE from x = 0.0 to x = 2.0 is about 8.7%.While the thermal expansion is anisotropic across the three crystallographic axes, we further examined which axes were most and least affected by the Ni substitution.The change in slope across the series for the a axis is the highest percent decrease at 9.5%, and the least affected was the b axis with a percent decrease of 4.8%.Figure 7 shows the CTE for (a) the a, b, and c crystallographic directions and (b) the overall volume as generated by PASCal [25].These data show additional subtleties, such as the marked decrease in CTE from x = 0.0 to x = 1.5, then there is a slight increase along most axes (except a) for the Ni end member.Overall, it seems the addition of Ni creates more rigidity in the structure allowing for less flexibility and a lower CTE, yet when the A site is fully occupied with Ni, the trend is disrupted.This suggests that there may be a particular advantage to having disordered/mixed occupancy sites when attempting to tune the rigidity and overall thermal expansion in this structure.However, the present VTXRD data are likely unsuitable to elucidate intricacies in oxygen occupancies and atomic positions atoms given the low number of electrons.Furthermore, results from diffraction techniques can disagree with 'true' bond lengths yielded by local structure techniques such as EXAFS or pair distribution function measurements since diffraction yields an 'average' atomic position that can be clouded by anisotropic vibration [19].Thus, additional techniques that understand the temperature dependence of the oxygen positions and occupancy (such as variable temperature neutron diffraction) and the local structure to reveal true bond lengths (such as temperature dependent EXAFS or pair distribution function measurements) are required to understand which bonds' rigidity are most affected by the inclusion of Ni.

Conclusions
An isomorphic solid solution of Ni-substituted Co 2 V 2 O 7 has been synthesized and characterized using ambient synchrotron XRD and diffuse reflectance spectroscopy.Neutron diffraction data were collected and refined in order to understand true composition of mixed occupancy materials, and the refined compositions were in good agreement with the nominal compositions.VTXRD data were collected across the apparent NTE transition (from 300 • C to 700 • C), yet no intrinsic NTE was observed in this temperature range was demonstrated in bulk linear thermal expansion measurements which suggests morphological mechanism for NTE in the bulk may explain why NTE is absent intrinsically.Ni substitution on the Co site does allow for tunability of the CTE and is most effective in the mixed occupancy species.Future studies will include using variable temperature neutron diffraction to understand the evolution of oxygen composition as a function of temperature, as well as variable temperature x-ray and neutron pair distribution function measurements to understand the evolution of bond lengths to explain the anisotropy in CTE and why Ni substitution increases rigidity and lowers overall CTE.

Figure 1 .
Figure 1.(a) One unit cell of the A2V2O7 (A = Co, Ni) structure in space group P21/c is depicted.6-coordinate A 2+ ions are blue, 4-coordinate V 5+ ions are magenta, and O 2-ions are orange.(b) A sub-motif of the crystal structure depicting the two edge-shared, 6-coordinate transition metal sites occupied Co and/or Ni.When A = Co, the A1 site has a polyhedral volume of 11.729 Å 3 and the A2 site has a larger polyhedral volume of 12.091 Å 3 .(c).A sub-motif of the crystal structure depicting the two corner-shared, 4-coordinate V sites.

Figure 2 .
Figure 2. Rietveld refinement results of synchrotron x-ray diffraction data (11-BM, APS, λ = 0.458 953 Å)are shown.Each sample shows the complete model of all phases fit, where x = 0 and x = 2 are solely fit to the A2V2O7 phase.x = 0.5, x = 1.0, and x = 1.5 contain 0.65%, 3.81%, and 0.39 wt% Ni, respectively.A figure depicting the individual contributions of the main and impurity phases in x = 1.0 are in figure S1 of the supplementary data.

Figure 3 .
Figure 3. Lattice parameters (a) a, (b) b, (c) c, (d)β and (e) unit cell volume as a function of experimental x value as determined from Rietveld refinement of synchrotron x-ray diffraction data are depicted.

Figure 4 .
Figure 4. Results of Rietveld refinement of synchrotron and neutron diffraction data for (a) x = 0.0 and (b) x = 1.0 are shown.Since compositional data from combined refinement and temperature-dependent diffraction data were measured on different samples, (c) depicts the lattice parameter agreement between each sample to suggest that they are comparable.Error bars are smaller than the symbols shown.

Figure 5 .
Figure 5. (a) Diffuse reflectance data on samples x = 0.0 and x = 2.0 are shown as transformed to Kubelka-Munk absorption.The absorption onset in the visible region as extrapolated from Tauc plots is shown for (b) x = 0.0 and (c) x = 2.0.

Figure 6 .
Figure 6.Lattice parameters (a) a, (b) b, (c) c, (d)β and (e) unit cell volume resulting from Rietveld refinement of temperature-dependent synchrotron diffraction data for all samples are shown.Data were collected isothermally for 30 min.at 50 • C, then every 50 • C between 300 • C and 700 • C.

figure 6 .
figure6.In contrast to the prior report on bulk samples measured by dilatometry[24], no NTE is observed in any unit cell direction or in the overall volume.Some differences between the microscopic and bulk thermal expansion properties in an anisotropic material are to be expected[33], and is famously the case in well-known β-eucryptite in which the dilatometric NTE is more than ten times the magnitude of the crystallographic NTE[34].However, the total absence of NTE at the microscopic level was not expected.Though the original work on Co 2 V 2 O 7 suggested a glassy transition could explain the origin of NTE, our data suggest the structure remains throughout the measured temperature range.FigureS3of the supplementary data shows Rietveld refinements of isothermal measurements are shown at (a) 300 • C (below the previously reported NTE region), (b) 550 • C (at the cusp of the NTE region), and (c) 700 • C (well into or above the NTE region).These refinements show that no new peaks arise or existing peaks are lost as temperature increases, only peak shifting corresponding with PTE is apparent.The structure remains throughout the reported NTE region, thus this anomalous thermal expansion may be explained by microstructural effects in the bulk.For example, colossal NTE behavior in layered ruthenates such as Ca 2 RuO 4 was reported in 2017[35].The enormity of the NTE (total volume change of 6.7%) cannot be explained solely by the microscopic mechanism but requires some consideration of the microstructure.Although smaller in difference, a similar effect is observed in another framework oxide material, Ta 2 WO 8[36].While VTXRD data indicate small positive linear thermal expansion (α l = 1.32 × 10 −6 K −1 ), but dilatometry of a sintered sample show small negative linear thermal expansion (α l = −1.69× 10 −6 K −1 ).Further sintering and addition of MgO to decrease pore size result in dilatometry data that are closer to the intrinsic VTXRD data.Thus, while NTE is observed in bulk Ta 2 WO 8 , it is likely a microstructural effect and pore size affects how this manifests.In the current A 2 V 2 O 7 series, this may be an explanation, yet a remaining question is why the NTE only manifests above a particular temperature.In the present samples, the addition of Ni 2+ on the Co 2+ does allow for some tuning of the CTE.The overall decrease in CTE from x = 0.0 to x = 2.0 is about 8.7%.While the thermal expansion is anisotropic across the three crystallographic axes, we further examined which axes were most and least affected by the Ni substitution.The change in slope across the series for the a axis is the highest percent decrease at 9.5%, and the least affected was the b axis with a percent decrease of 4.8%.Figure7shows the CTE for (a) the a, b, and c crystallographic directions and (b) the overall volume as generated by PASCal[25].These data show additional subtleties, such as the marked decrease in CTE from x = 0.0 to x = 1.5, then there is a slight increase along most axes (except a) for the Ni end member.Overall, it seems the addition of Ni creates more rigidity in the structure allowing for less flexibility and a lower CTE, yet when the A site is fully occupied with Ni, the trend is disrupted.This suggests that there may be a particular advantage to having disordered/mixed occupancy sites when attempting to tune the rigidity and overall thermal expansion in this structure.However, the present VTXRD data are likely unsuitable to elucidate intricacies in oxygen occupancies and atomic positions atoms given the low number of electrons.Furthermore, results from diffraction techniques can disagree with 'true' bond lengths yielded by local structure techniques such as EXAFS or pair distribution function measurements since diffraction yields an 'average' atomic position that can be clouded by

Figure 7 .
Figure 7. Thermal expansion coefficients for (a) the three principal axes and (b) the unit cell volume generated by PASCal software [25].
• C, then in 50 • C increments between 300 • C and 700 • C upon heating, and finally one additional 'ambient' temperature measurement after the heater was removed.Resultant lattice parameters from Rietveld refinement of VTXRD data are plotted as a function of temperature for each sample in