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Polymorphic phase transitions in mixed alkali magnesium fluoride solid solutions
Pergamon
Materials Research Bulletin 35 (2000) 341–349
Polymorphic phase transitions in mixed alkali magnesium fluoride solid solutions Robert W. Smitha,*, W.N. Meib, J.W. Flockenb, M.J. Dudikb, J.R. Hardyc a
Department of Chemistry, University of Nebraska at Omaha, Omaha, NE 68182-0109, USA b Department of Physics, University of Nebraska at Omaha, Omaha, NE 68182-0266, USA c Department of Physics and Center for Electro-Optics, University of Nebraska-Lincoln, Lincoln, NE 68588-0111, USA (Refereed) Received 17 May 1999; accepted 24 May 1999
Abstract Phase transitions in the miscible solid solution Na1⫺xKxMgF3 were examined over a wide range of compositions by computer molecular dynamics, X-ray diffraction, and thermal analysis in order to characterize the polymorphic phase transitions as a function of alkali-metal content. The pure NaMgF3 composition has a single orthorhombic-to-cubic transition at 1038 K, but computer modeled compositions with K⫹ partially substituted for Na⫹ ions have at least two polymorphic transitions. The models also indicate that the transition temperatures decrease with increasing potassium content. Results from thermal analyses and from literature give similar results. Computer simulations, experimental data, and literature values all show a room-temperature transition for the composition around Na0.65K0.35MgF3. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Fluorides; C. Differential scanning calorimetry (DSC); C. X-ray diffraction; D. Lattice dynamics; D. Phase transitions
* Corresponding author. Tel.: ⫹402-554-3592; fax: ⫹402-554-3888. E-mail address: robert㛭[email protected] (R.W. Smith). 0025-5408/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 5 - 5 4 0 8 ( 0 0 ) 0 0 2 3 2 - 4
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1. Introduction We are interested in modeling fluoroperovskites by computer simulations in order to design ferroelectric and related materials. In the past, we have examined fluorides of formula ABF3, where A is an alkali and B is an alkaline earth metal [1–3]; these studies have included both pure materials and mixed solid solutions. To date, we have primarily modeled fluorides in which the potentials of the cation-fluoride ionic pairs can be reliably characterized by the Gordon-Kim modified electron-gas theory [4]. Using this technique, we are able to successfully model the physical properties of these materials using relatively small 320-ion samples. This small sample size greatly reduces the time and cost of our computer simulations, and the advantage of vetting materials for improved properties through molecular modeling is obvious. A logical progression for our efforts was to extend our studies to materials with larger degrees of covalency in the cation-fluoride bonds. Any significant degree of covalency particularly affects the long-range ionic pair potentials. Specifically, the precise charges resident on the various ions must be known to successfully model their behavior. Recently, this technique was used to successfully model the onset of superionicity in the mineral neighborite, NaMgF3, a fluoroperovskite [5]. The magnesium-fluoride bonds in this material display a significant degree of covalency, so that the magnesium and fluoride ions are not of integer charge. In these simulations, charges of ⫹1.37 and ⫺0.79 for the magnesium and fluoride ions, respectively, were used. We sought to extend this work by determining whether we could accurately model solid solutions of mixed alkali magnesium fluorides. One indication of our ability to do so would be accurate predictions of the polymorphic phase-transition temperatures in a mixed alkali magnesium fluoride. In the course of such work, we examined the solid solution Na1⫺xKxMgF3 by both thermal analysis and computer simulation. From both efforts, we find that partial substitution of potassium for sodium causes the single orthorhombic-to-cubic transition in NaMgF3 to split into at least two polymorphic transitions and that the transition temperature decreases with increasing potassium content. The composition with a roomtemperature transition is that with x ⬇ 0.35. We report here the results of our computer simulations of the polymorphic phase transitions and how the simulations compare with experimental phase transitions of actual samples and with results from the literature.
2. Experimental 2.1. Calculations The general methods of lattice statics and molecular dynamics used here are the same as we have detailed previously [6]. The pair potentials were derived using first-principles, Gordon–Kim techniques with no modifications or fits to any experimental values, except for physical constants. These potentials were then fitted to algebraic forms in order to perform analytical differentiation, the choice of the equation depending upon the range of the ionic interactions, i.e.,
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Fig. 1. Variation of sample dimensions with temperature for 320-ion cell with composition Na0.8125K0.1875MgF3 by computer molecular dynamics (1 Bohr ⫽ 0.52917 Å).
Y Short range: (r) ⫽ A ⫺ B r⫺6 Y Intermediate range: (r) ⫽ rk exp[⫺␣ r] ¥ Cn rn (n ⫽ 0 – 6) Y Long range: (r) ⫽ D exp[⫺ r2] The values of the constants were determined using a “best fit” procedure in which the values of the potentials and the first and second derivatives were matched at the boundaries. We emphasize that this parameterization was only carried out in order to determine analytically the first and second derivatives of the interionic forces and involved no fitting to experimental data. Thus, all theoretical values reported here are a result of a priori pair potentials unmodified by any experimental parameter. The ionic charges on each of the ions were the same as those used in the modeling of superionicity in NaMgF3 mentioned previously, i.e., ⫹1, ⫹1.37, and ⫺0.79 for the alkali–metal, magnesium, and fluoride ions, respectively. Lattice-statics computations were then performed on a 40-ion sample of NaMgF3 using these potentials. The sample was quenched to a state with minimum energy (where the lattice parameters and ionic positions were relaxed), resulting in a stable configuration with negligible lattice stresses on each ion. The sample was then doubled along each axis to obtain a 320-ion sample, i.e., 64 Na⫹, 64 Mg⫹1.37, and 192 F⫺0.79. Molecular dynamics was then used to verify the ground state by alternately heating and cooling the sample several times. If the sample returned to the same minimum energy state each time, it was assumed to be the ground state. Doped samples were obtained by replacing Na⫹ ions with K⫹ ions at randomly selected sites. Polymorphic phase transitions were observed by heating a sample to 2000 K, cooling it at 50 K increments, thermalizing at each temperature for 180 ps, and measuring the internal angles, lattice constants, and specific heat. Plots of these parameters as a function of temperature were then obtained; discontinuities in the plots were used as “markers” for the transitions. Fig. 1 shows a sample plot.
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Fig. 2. Variation of unit-cell volume for Na1⫺xKxMgF3 in Pbnm at room temperature from powder X-ray diffraction.
2.2. Synthesis and X-ray diffraction Actual samples of the solid solution were prepared by grinding the desired stoichiometric ratio of sodium fluoride, potassium fluoride, and magnesium fluoride to a fine powder and placing it in a platinum boat. The samples were then heated to 970 K under flowing N2 for 10 h, reground to a fine powder, and reheated to 1070 K under flowing N2 for another 10 h. Samples were confirmed to be single-phase by X-ray powder diffraction conducted on a Rigaku powder diffractometer equipped with a graphite monochromator and copper anode. Unit-cell parameters were obtained from a least-squares fit of the 2 values measured between 20° and 70°; 2 values were corrected with silicon (NIST Standard Reference Material 640b) as an internal standard. The room-temperature orthorhombic cell volume varied linearly with potassium content as shown in Fig. 2. 2.3. Thermal analysis Transition temperatures were determined from differential thermal analysis (DTA) for transitions above 900 K and differential scanning calorimetry (DSC) for transitions below 900 K. Measurements were conducted on a DuPont Thermal Analyzer 2000 that was calibrated with barium carbonate (mp 1083 K), potassium chromate (mp 938 K), potassium perchlorate (mp 573 K), and indium metal (mp 430 K). About 30 mg of each sample was heated at 10 K/min from room temperature through the phase transition. All samples with
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Fig. 3. DTA trace for NaMgF3.
potassium content at or below 28% showed an exothermic transition on the heating leg and a corresponding endothermic transition on the cooling leg. No transitions were observed above room temperature on either leg for samples with potassium content above 28%. In all cases, the transition temperature was taken to be the point where the ⌬T vs. T curve showed an abrupt change in slope. All calibration runs were conducted similarly. Fig. 3 shows a sample DTA trace for NaMgF3.
3. Results and discussion NaMgF3 (also known as the mineral neighborite) has a distorted perovskite structure [7] with the orthorhombic space group Pbnm at room temperature. NaMgF3 transforms directly to the ideal cubic perovskite structure in Pm3m at 1038 K [8] with no intervening transition to a higher symmetry phase; the transition has a latent heat of 2.3 kJ/mol [9]. KMgF3, on the other hand, crystallizes only in the cubic Pm3m perovskite structure, at least down to 123 K [10]. Transitions in materials from the Pbnm structure to the Pm3m structure can occur as cation displacements and/or octahedral tilts. Theoretically, three transitions are possible, i.e., from Pbnm to a higher symmetry, orthorhombic structure, thence to a tetragonal structure, and finally to the Pm3m structure. Whether one, two, or three transitions occur depends on the nature of the tilts or displacements involved.
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Fig. 4. Variation of Tc with composition in Na1⫺xKxMgF3 (data from Zhao, ref. 11, Fig. 8).
Zhao [11] has recently studied the transitions in the Na1⫺xKxMgF3 system through high-resolution X-ray diffraction and Rietveld analysis of powder samples at various temperatures. His work shows that partial substitution of potassium for sodium causes the single transition in NaMgF3 to split into two transitions: a lower temperature Pbnm to P4/mbm transition and a higher temperature P4/mbm to Pm3m transition. The phase-transition temperatures decrease with increasing potassium content; the compositions with the tetragonal structure at 300 K have approximately 0.34 ⬍ x ⬍ 0.37. Fig. 4 summarizes this work. The variation of Tc with alkali–metal composition from our computer simulations is shown in Fig. 5. Samples analyzed had zero to twenty-four random potassium ion substitutions (at increments of five) onto the 64 sodium ion sites. Transitions for each of these “samples” were usually marked by distinct changes that occurred in the interaxis angle vs. temperature plots. At high temperatures, all interaxis angles are 90° and all three lattice constants are equal. At the transition temperature, one of the interaxis angles changes abruptly from 90° by as much as 0.9°, and at a similar temperature, the cell lengths of the 320-ion system begin to diverge. The latter effect is more pronounced in the higher potassium concentrations. Transitions in the specific heat vs. temperature plots are indicated as a peak in the baseline. When more than one type of plot showed a distinctive transition, the corresponding temperatures were averaged to get the values shown in Fig. 5. In spite of these discernible effects, some interpretation of the data is required to determine transition temperatures. In particular, it is unrealistic to expect our imperfect 320-ion cell to reproduce the macroscopic symmetries of the low-temperature phases of the doped systems; specifically, the interaxial angles may well deviate from 90° (as indeed would those of a
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347
Fig. 5. Variation of Tc with composition in Na1⫺xKxMgF3 from computer simulations.
correspondingly small sample of a real crystal) even though they should not do so in an orthorhombic or tetragonal structure. What we do observe are clear changes in the average angles and/or cell lengths at specific temperatures which signify static ordering of the magnesium-centered octahedral rotations, i.e., phase transitions. And we clearly reproduce Zhou’s major result, which is the existence of two transitions in the doped phases. Our computer simulations also show that the composition with a room-temperature transition has x ⬇ 0.35. We monitored the room-temperature symmetry of the actual samples in our study by observing the reflections that disappear or merge as the symmetry changes from Pbnm to Pm3m as potassium replaces sodium. Our X-ray diffraction data indicate that the roomtemperature symmetry becomes cubic as the composition approaches Na0.62K0.38MgF3, since the diffraction pattern of this composition exhibits only the cubic reflections; Table 1 lists its indexed reflections. All compositions through 32% potassium exhibited at least a vestige of the orthorhombic peaks. Table 2 lists the unit-cell parameters determined from the powder X-ray diffraction data for compositions that have a cubic perovskite structure at room temperature. Fig. 6 shows the variation of Tc with composition from our experimental thermal analyses. We observed two transitions for the 4% potassium substituted compositions with the lower temperature transition having a markedly smaller latent heat than the higher temperature transition. For compositions with potassium content greater than 4%, we only observed a single transition, apparently because significant potassium content causes the lower temperature transition to have a latent heat too small to detect. This is reasonable, since greater
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Table 1 Indexing for Na0.62K0.38MgF3 in Pm3m d(obs) (Å)
h
k
l
3.9186 2.7727 2.2625 1.9598 1.7519 1.6000 1.3854
1 1 1 2 2 2 2
0 1 1 0 1 1 2
0 0 1 0 0 1 0
Table 2 Unit-cell parameters for Na1⫺xKxMgF3 in Pm3m x a(Å)
0.38 3.9187(4)
0.60 3.9530(5)
0.80 3.9742(3)
1.00 3.9904(4)
potassium content produces smaller angular deviations from octahedral collinearity and smaller energy differences between the respective crystal structures. Each successive composition with greater potassium content had a smaller latent heat until it became so small beyond the 28% composition that no transition could be detected. Nevertheless, the plot of Tc as a function of composition follows the higher temperature transition of ref. 11.
Fig. 6. Variation of Tc with composition in Na1⫺xKxMgF3 from thermal analyses.
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4. Conclusions We have demonstrated that the substitution of potassium for sodium in NaMgF3 leads to a decrease in the structural phase-transition temperature in a way that makes it feasible to “design” materials with a preferred transition temperature for use in detectors or transducers. Moreover, we have shown that standard molecular dynamics simulations can give results in reasonable agreement with experiment even for materials with significant degrees of covalency and over a wide compositional range. At the same time, we acknowledge that this type of system may represent the current boundaries of our abilities to do so because of its high degree of covalency and the small latent heats associated with the phase transitions.
Acknowledgments This material is based upon work supported by the Nebraska Research Initiative and the U.S. Army Research Office under grant numbers DAAG55-98-1-0273 and DAAG55-97-10106.
References [1] J.W. Flocken, R.A. Guenther, J.R. Hardy, L.L. Boyer, Phys Rev Lett 56 (16) (1986) 1738 –1741. [2] P.J. Edwardson, L.L. Boyer, R.L. Newman, D.H. Fox, J.R. Hardy, J.W. Flocken, R.A. Guenther, W.N. Mei, Phys Rev B 39 (13) (1989) 9738 –9741. [3] J.W. Flocken, R.W. Smith, J.R. Hardy, E.S. Stevenson, J. Swearingen, Mater Res Bull 31 (9) (1996) 1093–1099. [4] R.G. Gordon, Y.S. Kim, J Chem Phys 56 (6) (1972) 3122–3133. [5] L.X. Zhou, J.R. Hardy, H.Z. Cao, Geophys Res Lett 24 (7) (1997) 747–750. [6] Z. Mo, J.W. Flocken, R.A. Guenther, W.N. Mei, Ferroelectrics 120 (1991) 157–165. [7] M. O’Keeffe, B.G. Hyde, J.-O. Bovin, Phys Chem Miner 4 (1979) 299 –305. [8] Y. Zhao, D.J. Weidner, J.B. Parise, D.E. Cox, Phys Earth Planet Inter 76 (1993) 1–16. [9] L. Topor, A. Navrotsky, Y. Zhao, D.J. Weidner, J Solid State Chem 132 (1997) 131–138. [10] L.A. Muradian, V.E. Zavodnik, I.P. Makarova, K.S. Aleksandrov, V.I. Simonov, Kristallografiya 29 (1984) 392–394. [11] Y. Zhao, J Solid State Chem 141 (1998) 121–132.
Materials Research Bulletin 35 (2000) 341–349
Polymorphic phase transitions in mixed alkali magnesium fluoride solid solutions Robert W. Smitha,*, W.N. Meib, J.W. Flockenb, M.J. Dudikb, J.R. Hardyc a
Department of Chemistry, University of Nebraska at Omaha, Omaha, NE 68182-0109, USA b Department of Physics, University of Nebraska at Omaha, Omaha, NE 68182-0266, USA c Department of Physics and Center for Electro-Optics, University of Nebraska-Lincoln, Lincoln, NE 68588-0111, USA (Refereed) Received 17 May 1999; accepted 24 May 1999
Abstract Phase transitions in the miscible solid solution Na1⫺xKxMgF3 were examined over a wide range of compositions by computer molecular dynamics, X-ray diffraction, and thermal analysis in order to characterize the polymorphic phase transitions as a function of alkali-metal content. The pure NaMgF3 composition has a single orthorhombic-to-cubic transition at 1038 K, but computer modeled compositions with K⫹ partially substituted for Na⫹ ions have at least two polymorphic transitions. The models also indicate that the transition temperatures decrease with increasing potassium content. Results from thermal analyses and from literature give similar results. Computer simulations, experimental data, and literature values all show a room-temperature transition for the composition around Na0.65K0.35MgF3. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Fluorides; C. Differential scanning calorimetry (DSC); C. X-ray diffraction; D. Lattice dynamics; D. Phase transitions
* Corresponding author. Tel.: ⫹402-554-3592; fax: ⫹402-554-3888. E-mail address: robert㛭[email protected] (R.W. Smith). 0025-5408/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 5 - 5 4 0 8 ( 0 0 ) 0 0 2 3 2 - 4
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R.W. Smith et al. / Materials Research Bulletin 35 (2000) 341–349
1. Introduction We are interested in modeling fluoroperovskites by computer simulations in order to design ferroelectric and related materials. In the past, we have examined fluorides of formula ABF3, where A is an alkali and B is an alkaline earth metal [1–3]; these studies have included both pure materials and mixed solid solutions. To date, we have primarily modeled fluorides in which the potentials of the cation-fluoride ionic pairs can be reliably characterized by the Gordon-Kim modified electron-gas theory [4]. Using this technique, we are able to successfully model the physical properties of these materials using relatively small 320-ion samples. This small sample size greatly reduces the time and cost of our computer simulations, and the advantage of vetting materials for improved properties through molecular modeling is obvious. A logical progression for our efforts was to extend our studies to materials with larger degrees of covalency in the cation-fluoride bonds. Any significant degree of covalency particularly affects the long-range ionic pair potentials. Specifically, the precise charges resident on the various ions must be known to successfully model their behavior. Recently, this technique was used to successfully model the onset of superionicity in the mineral neighborite, NaMgF3, a fluoroperovskite [5]. The magnesium-fluoride bonds in this material display a significant degree of covalency, so that the magnesium and fluoride ions are not of integer charge. In these simulations, charges of ⫹1.37 and ⫺0.79 for the magnesium and fluoride ions, respectively, were used. We sought to extend this work by determining whether we could accurately model solid solutions of mixed alkali magnesium fluorides. One indication of our ability to do so would be accurate predictions of the polymorphic phase-transition temperatures in a mixed alkali magnesium fluoride. In the course of such work, we examined the solid solution Na1⫺xKxMgF3 by both thermal analysis and computer simulation. From both efforts, we find that partial substitution of potassium for sodium causes the single orthorhombic-to-cubic transition in NaMgF3 to split into at least two polymorphic transitions and that the transition temperature decreases with increasing potassium content. The composition with a roomtemperature transition is that with x ⬇ 0.35. We report here the results of our computer simulations of the polymorphic phase transitions and how the simulations compare with experimental phase transitions of actual samples and with results from the literature.
2. Experimental 2.1. Calculations The general methods of lattice statics and molecular dynamics used here are the same as we have detailed previously [6]. The pair potentials were derived using first-principles, Gordon–Kim techniques with no modifications or fits to any experimental values, except for physical constants. These potentials were then fitted to algebraic forms in order to perform analytical differentiation, the choice of the equation depending upon the range of the ionic interactions, i.e.,
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343
Fig. 1. Variation of sample dimensions with temperature for 320-ion cell with composition Na0.8125K0.1875MgF3 by computer molecular dynamics (1 Bohr ⫽ 0.52917 Å).
Y Short range: (r) ⫽ A ⫺ B r⫺6 Y Intermediate range: (r) ⫽ rk exp[⫺␣ r] ¥ Cn rn (n ⫽ 0 – 6) Y Long range: (r) ⫽ D exp[⫺ r2] The values of the constants were determined using a “best fit” procedure in which the values of the potentials and the first and second derivatives were matched at the boundaries. We emphasize that this parameterization was only carried out in order to determine analytically the first and second derivatives of the interionic forces and involved no fitting to experimental data. Thus, all theoretical values reported here are a result of a priori pair potentials unmodified by any experimental parameter. The ionic charges on each of the ions were the same as those used in the modeling of superionicity in NaMgF3 mentioned previously, i.e., ⫹1, ⫹1.37, and ⫺0.79 for the alkali–metal, magnesium, and fluoride ions, respectively. Lattice-statics computations were then performed on a 40-ion sample of NaMgF3 using these potentials. The sample was quenched to a state with minimum energy (where the lattice parameters and ionic positions were relaxed), resulting in a stable configuration with negligible lattice stresses on each ion. The sample was then doubled along each axis to obtain a 320-ion sample, i.e., 64 Na⫹, 64 Mg⫹1.37, and 192 F⫺0.79. Molecular dynamics was then used to verify the ground state by alternately heating and cooling the sample several times. If the sample returned to the same minimum energy state each time, it was assumed to be the ground state. Doped samples were obtained by replacing Na⫹ ions with K⫹ ions at randomly selected sites. Polymorphic phase transitions were observed by heating a sample to 2000 K, cooling it at 50 K increments, thermalizing at each temperature for 180 ps, and measuring the internal angles, lattice constants, and specific heat. Plots of these parameters as a function of temperature were then obtained; discontinuities in the plots were used as “markers” for the transitions. Fig. 1 shows a sample plot.
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Fig. 2. Variation of unit-cell volume for Na1⫺xKxMgF3 in Pbnm at room temperature from powder X-ray diffraction.
2.2. Synthesis and X-ray diffraction Actual samples of the solid solution were prepared by grinding the desired stoichiometric ratio of sodium fluoride, potassium fluoride, and magnesium fluoride to a fine powder and placing it in a platinum boat. The samples were then heated to 970 K under flowing N2 for 10 h, reground to a fine powder, and reheated to 1070 K under flowing N2 for another 10 h. Samples were confirmed to be single-phase by X-ray powder diffraction conducted on a Rigaku powder diffractometer equipped with a graphite monochromator and copper anode. Unit-cell parameters were obtained from a least-squares fit of the 2 values measured between 20° and 70°; 2 values were corrected with silicon (NIST Standard Reference Material 640b) as an internal standard. The room-temperature orthorhombic cell volume varied linearly with potassium content as shown in Fig. 2. 2.3. Thermal analysis Transition temperatures were determined from differential thermal analysis (DTA) for transitions above 900 K and differential scanning calorimetry (DSC) for transitions below 900 K. Measurements were conducted on a DuPont Thermal Analyzer 2000 that was calibrated with barium carbonate (mp 1083 K), potassium chromate (mp 938 K), potassium perchlorate (mp 573 K), and indium metal (mp 430 K). About 30 mg of each sample was heated at 10 K/min from room temperature through the phase transition. All samples with
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345
Fig. 3. DTA trace for NaMgF3.
potassium content at or below 28% showed an exothermic transition on the heating leg and a corresponding endothermic transition on the cooling leg. No transitions were observed above room temperature on either leg for samples with potassium content above 28%. In all cases, the transition temperature was taken to be the point where the ⌬T vs. T curve showed an abrupt change in slope. All calibration runs were conducted similarly. Fig. 3 shows a sample DTA trace for NaMgF3.
3. Results and discussion NaMgF3 (also known as the mineral neighborite) has a distorted perovskite structure [7] with the orthorhombic space group Pbnm at room temperature. NaMgF3 transforms directly to the ideal cubic perovskite structure in Pm3m at 1038 K [8] with no intervening transition to a higher symmetry phase; the transition has a latent heat of 2.3 kJ/mol [9]. KMgF3, on the other hand, crystallizes only in the cubic Pm3m perovskite structure, at least down to 123 K [10]. Transitions in materials from the Pbnm structure to the Pm3m structure can occur as cation displacements and/or octahedral tilts. Theoretically, three transitions are possible, i.e., from Pbnm to a higher symmetry, orthorhombic structure, thence to a tetragonal structure, and finally to the Pm3m structure. Whether one, two, or three transitions occur depends on the nature of the tilts or displacements involved.
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Fig. 4. Variation of Tc with composition in Na1⫺xKxMgF3 (data from Zhao, ref. 11, Fig. 8).
Zhao [11] has recently studied the transitions in the Na1⫺xKxMgF3 system through high-resolution X-ray diffraction and Rietveld analysis of powder samples at various temperatures. His work shows that partial substitution of potassium for sodium causes the single transition in NaMgF3 to split into two transitions: a lower temperature Pbnm to P4/mbm transition and a higher temperature P4/mbm to Pm3m transition. The phase-transition temperatures decrease with increasing potassium content; the compositions with the tetragonal structure at 300 K have approximately 0.34 ⬍ x ⬍ 0.37. Fig. 4 summarizes this work. The variation of Tc with alkali–metal composition from our computer simulations is shown in Fig. 5. Samples analyzed had zero to twenty-four random potassium ion substitutions (at increments of five) onto the 64 sodium ion sites. Transitions for each of these “samples” were usually marked by distinct changes that occurred in the interaxis angle vs. temperature plots. At high temperatures, all interaxis angles are 90° and all three lattice constants are equal. At the transition temperature, one of the interaxis angles changes abruptly from 90° by as much as 0.9°, and at a similar temperature, the cell lengths of the 320-ion system begin to diverge. The latter effect is more pronounced in the higher potassium concentrations. Transitions in the specific heat vs. temperature plots are indicated as a peak in the baseline. When more than one type of plot showed a distinctive transition, the corresponding temperatures were averaged to get the values shown in Fig. 5. In spite of these discernible effects, some interpretation of the data is required to determine transition temperatures. In particular, it is unrealistic to expect our imperfect 320-ion cell to reproduce the macroscopic symmetries of the low-temperature phases of the doped systems; specifically, the interaxial angles may well deviate from 90° (as indeed would those of a
R.W. Smith et al. / Materials Research Bulletin 35 (2000) 341–349
347
Fig. 5. Variation of Tc with composition in Na1⫺xKxMgF3 from computer simulations.
correspondingly small sample of a real crystal) even though they should not do so in an orthorhombic or tetragonal structure. What we do observe are clear changes in the average angles and/or cell lengths at specific temperatures which signify static ordering of the magnesium-centered octahedral rotations, i.e., phase transitions. And we clearly reproduce Zhou’s major result, which is the existence of two transitions in the doped phases. Our computer simulations also show that the composition with a room-temperature transition has x ⬇ 0.35. We monitored the room-temperature symmetry of the actual samples in our study by observing the reflections that disappear or merge as the symmetry changes from Pbnm to Pm3m as potassium replaces sodium. Our X-ray diffraction data indicate that the roomtemperature symmetry becomes cubic as the composition approaches Na0.62K0.38MgF3, since the diffraction pattern of this composition exhibits only the cubic reflections; Table 1 lists its indexed reflections. All compositions through 32% potassium exhibited at least a vestige of the orthorhombic peaks. Table 2 lists the unit-cell parameters determined from the powder X-ray diffraction data for compositions that have a cubic perovskite structure at room temperature. Fig. 6 shows the variation of Tc with composition from our experimental thermal analyses. We observed two transitions for the 4% potassium substituted compositions with the lower temperature transition having a markedly smaller latent heat than the higher temperature transition. For compositions with potassium content greater than 4%, we only observed a single transition, apparently because significant potassium content causes the lower temperature transition to have a latent heat too small to detect. This is reasonable, since greater
348
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Table 1 Indexing for Na0.62K0.38MgF3 in Pm3m d(obs) (Å)
h
k
l
3.9186 2.7727 2.2625 1.9598 1.7519 1.6000 1.3854
1 1 1 2 2 2 2
0 1 1 0 1 1 2
0 0 1 0 0 1 0
Table 2 Unit-cell parameters for Na1⫺xKxMgF3 in Pm3m x a(Å)
0.38 3.9187(4)
0.60 3.9530(5)
0.80 3.9742(3)
1.00 3.9904(4)
potassium content produces smaller angular deviations from octahedral collinearity and smaller energy differences between the respective crystal structures. Each successive composition with greater potassium content had a smaller latent heat until it became so small beyond the 28% composition that no transition could be detected. Nevertheless, the plot of Tc as a function of composition follows the higher temperature transition of ref. 11.
Fig. 6. Variation of Tc with composition in Na1⫺xKxMgF3 from thermal analyses.
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4. Conclusions We have demonstrated that the substitution of potassium for sodium in NaMgF3 leads to a decrease in the structural phase-transition temperature in a way that makes it feasible to “design” materials with a preferred transition temperature for use in detectors or transducers. Moreover, we have shown that standard molecular dynamics simulations can give results in reasonable agreement with experiment even for materials with significant degrees of covalency and over a wide compositional range. At the same time, we acknowledge that this type of system may represent the current boundaries of our abilities to do so because of its high degree of covalency and the small latent heats associated with the phase transitions.
Acknowledgments This material is based upon work supported by the Nebraska Research Initiative and the U.S. Army Research Office under grant numbers DAAG55-98-1-0273 and DAAG55-97-10106.
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