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phys. stat. sol. (b) 245, No. 8, 1520–1526 (2008) / DOI 10.1002/pssb.200844072 p s sbasic solid state physics

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Correlation between ionic charge and the lattice constant of cubic perovskite solids

A. S. Verma*, 1, A. Kumar2, and S. R. Bhardwaj1

1 Department of Physics, B. S. A. College, Mathura, 281004, India 2 Department of Physics, K. R. (P.G.) College, Mathura, 281001, India

Received 16 February 2008, revised 15 April 2008, accepted 25 April 2008 Published online 10 June 2008

PACS 61.50.Ah, 71.15.Ap * Corresponding author: e-mail ajay_phy@rediffmail.com, Phone: +91 565 2423417, Mobil: +91 9412884655

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Most of the physical world around us and a large part of modern technology are based on solid materials. The extensive research devoted to the physics and chemistry of solids during the last quarter of a century has led to great advances in understanding of the properties of solids in general. So it is interesting to study the behav-ior and various properties of different solids. There is a great deal of interest, both experimental and theoretical in the solid-state properties of complex structured solids such as perovskites. The properties of these materials have ren-dered possible the development and fabrication of various technological devices. The investigations on these solids are of great importance, to get information on their proper-ties in order to improve the devices in future modelling. Perovskite is one of the most frequently encountered struc-tures in solid-state physics, and it accommodates most of the metallic ions in the periodic table with a significant number of different anions. These solids are currently gain-ing considerable importance in the field of electrical ce-ramics, refractories, geophysics, astrophysics, particle ac-celerators, fission, fusion reactors, heterogeneous catalysis, etc. [1–4]. Additionally, they have received great attention as high-temperature proton conductors with the possibility of applications in fuel cells or hydrogen sensors. During the last few years, many experimental and theoretical in-vestigations were devoted to the study of perovskite solids:

typically ABX3 (A: large cation with different valence, B: transition metal and X: oxides and halides). In the perovskite structure, which is shown in Fig. 1, B cations are coordinated by six X anions, while A cations present a coordination number of 12 (also coordinated by X anions). The X anions have coordination number 2, being coordi-nated by two B cations, since the distance A–X is about 40% larger than the B–X bond distance. The cubic perovskite is called the ideal perovskite, which is the sub-ject of this study. This class of materials has great potential for a variety of device applications due to their simple crystal structures and unique ferroelectric and dielectric properties. The structural, dielectric and optical properties of the perovskites are very important. The energy gap lies in the visible region of the spectrum and this is one reason why these materials are interesting [5–12]. However, there are very few studies that have focused on the evolution of the bonding mechanism of ferroelectric perovskite materi-als. The lattice constant of these solids may be measured by experimental means such as X-ray, electron or neutron diffraction techniques. However, these techniques are usu-ally complicated, difficult and time consuming. Advances in high-performance computing techniques allow materials scientists to evaluate lattice constants based on empirical methods. Empirical relations have become widely recog-

In this paper we present lattice constant values for cubic perovskite solids with the product of ionic charges and aver-age ionic radii rav (Å). The lattice constant of these compounds exhibit a linear relationship when plotted on a log–log scale against the average ionic radii rav (Å), but fall on different straight lines according to the ionic charge prod-

uct of the compounds. We have applied the proposed relation to ABX3 (A: large cation with different valence, B: transition metal and X: oxides and halides) and found a better agree-ment with the experimental data as compared to the values evaluated by earlier researchers.

phys. stat. sol. (b) 245, No. 8 (2008) 1521

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Figure 1 Ideal cubic perovskite structure. nized as the method of choice for computational solid-state studies. In modern high-speed computer techniques, they allow researchers to investigate many structural and physi-cal properties of materials simply by computation or simu-lation instead of by traditional experiments. In many cases empirical relations do not give highly accurate results for each specific material, but they can still be very useful. In particular, the simplicity of empirical relations allows a broader class of researchers to calculate useful proper- ties, and often trends become more evident. Empirical con-cepts such as valence, empirical radii, electronegativity, ionicity and plasmon energy are then useful [13, 14]. These concepts are directly associated with the character of the chemical bond and thus provide means for explaining and classifying many basic properties of molecules and solids. Recently, the present authors [15–19] have been evaluated the electronic, mechanical and optical properties of binary and complex crystals with the help of ionic charge theory of solids. This is due to the fact that the ionic charge depends on the number of valence electrons, which changes when a metal forms a compound. Therefore we thought it would be of interest to give an alternative expla-nation for the lattice constants of perovskite solids. 2 Theory, results and discussion The lattice con-stant values for perovskite solids is of recognized impor-tance, owing to the development of new solids designed for different applications, such as ferroelectric thin films, microwave and semiconductor technologies, etc. [5]. Some empirical models were established that can perdict lattice constant of perovskites from selected atomic peroperties of their constituent elements. Recently, the methodology de-veloped by Jiang et al. [6], which allows one to predict the

lattice constant of cubic perovskites by using the known ionic radii of the cations and anion. According to him the lattice constant may be determine by the following re-lation,

a = 1.8836(rB + rX) + 1.4898[rA + rX/ 2 (rB + rX)]

– 1.2062 , (1)

where rA, rB and rX are the ionic radii of A, B and X3, re-spectively. According to Ye et al. [20], the lattice constant of the ideal perovskite oxides (ABO3) can be linearly correlated to some atomic parameters as,

a = 0.3166rA + 1.422rB – 0.1708XA + 0.0562XB

– 0.0066(ZB – ZA) + 2.706 , (2)

where rA, rB, XA, XB, ZA and ZB are the ionic radii, electro-negativity and valence number of ions A and B, respec-tively. Any change in the crystallographic environment of an atom is related to the core electrons via the valence electrons. The change in wavefunction that occurs for the outer electrons usually means a displacement of electric charge in the valence shell so that the interaction between valence, shell and core electrons is changed. This leads to a change in binding energy of the inner electron and to a shift in the position of the absorption edge. Because Eq. (2) depends on the number of valence electrons, the ionic charge also depends on the number of valence electrons, which changes when a metal forms a compound. Therefore, we thought it would be of interest to give an alternative explanation for lattice constants of cubic perovskite solids in terms of ionic charge. The lattice constants of perovskite solids exhibit a linear relationship when plotted against av-erage ionic radii rav (Å), but fall on different straight lines according to the ionic charge product of the compounds, which is presented in Fig. 2. In Fig. 2, we observe that in the plot of experimental lattice constants and average ionic radii, the perovskite oxides lie on lines nearly parallel to the line for perovskite halides. From Fig. 2, it is quite ob-vious that the lattice constant trends in these compounds increases with increased average ionic radii and fall on straight lines according to the ionic charge product of the solids. In previous studies, [15–19], we proposed simple ex-pressions for the electronic, optical and mechanical proper-ties such as heteropolar energy gaps (Ec), average energy gaps (Eg), crystal ionicity (f i), dielectric constant (ε∞), elec-tronic susceptibility (χ), cohesive energy (Ecoh), bulk modulus (B) and microhardness (H) of rocksalt, zinc blende and chalcopyrite structured solids in terms of the product of ionic charges of cation and anion by the follow-ing relations:

bulk modulus (B in GPa) = C (Z1Z2)D d –3 , (3)

lattice energy (U in kcal/mol) = C (Z1Z2)D/ d , (4)

dielectric constant (ε∞) = C (Z1Z2)D d 2 , (5)

1522 A. S. Verma et al.: Correlation between ionic charge and lattice constant of cubic perovskite solids

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0.03 0.05 0.07 0.11 0.13 0.15 0.190.01 0.230.09 0.17

0.50

0.55

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0.65

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0.45

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CsCdF3

GdCrO3

RbUO3

K(Ta,Nb)O3

BaPrO3

BaIrO3

SrNbO3

EuCrO3

GdAlO3

PrVO3

CsIO3

CsCaCl3

CsSrF3

CsPbBr3

CsHgBr3

CsTmCl3

CsCdCl3

Z Z = 6A X

Z Z = 3A X

Z Z = 12A X

Z Z = 18A X

log

a(Å

)

log r (Å)av

Lattice constants of cubic perovskite solids

È È

ÈÈ

Figure 2 Plot of log a (lattice constant in Å) against log rav (average ionic radii in Å) for perovskite oxides and halides. In the plots of log a and log rav, perovskite oxides lie on lines nearly parallel to the line for perovskite halides. In this plot all experimental data (lat-tice constant and ionic radii) are taken from Ref. [5].

where C and D are constants, which depend upon crystal structures and d is the nearest-neighbour distance in Å. Z1 and Z2 are the ionic charges on the cation and anion, re-spectively. According to Fig. 1, A is a bigger cation (such as Na+, K+, Ca+2, Sr+2, Ba+2, etc.), B is a smaller cation (such as Ti+4, Nb+5, Mn+4, Zr+4, etc.) and X is an anion (such as O–2, F–1, Cl–1, Br–1, etc.). Furthermore, cubic perovskite oxide solids can be defined in different systems like as A+1B+5O3, A

+2B+4O3 and A+3B+3O3. The Krishnan–Roy theory [25], Jayaraman et al. [26] and Sirdeshmukh and Subhadra [27] found that substantially reduced ionic charges must be used to get better agreement with experi-mental values. To obtain better agreement between ex-perimental and theoretical data for perovskite-type crystal structure compounds, relations (1) and (2) may be ex-tended to:

lattice constant (a in Å) = k (ZAZX)s rav , (6)

where ZA and ZX are the ionic charge on the A and X3, re-spectively, k and s are constants whose values for cubic perovskite solids are 3 and 0.06, rav is the average ionic ra-dii of ABX3 in Å and it can be calculated by rav = (rA + rB + rX)/3. The values so obtained are presented in Tables 1, 2 and 3. The main advantage of Eq. (6) is the simplicity of the formula, which does not require any experimental data expect for the ionic radii of perovskite solids. We note that the evaluated values are in close agreement with the ex-perimental and theoretical data as compared to the values

reported by previous researchers so far. These results show that our current method is quite reasonable and can give us a useful guide in calculating and predicting the more com-plex class of perovskite solids.

3 Conclusion We come to the conclusion that the product of ionic charges of any compound is a key param-eter for calculating physical properties. Furthermore, we found that in the compounds investigated here, the lattice constant exhibit a linear relationship when plotted on a log–log scale against the average ionic radii rav (Å), but fall on four straight lines according to the ionic charge product of the compounds, which is presented in Fig. 2. We ob-serve that in the plot of lattice constant and ionic radii, the monovalent and divalent perovskite oxides lie on lines nearly parallel to the line for the trivalent perovskite oxides and the perovskite oxides lie on lines nearly parallel to the line for the perovskite halides. From the results and discus-sion obtained by using the proposed empirical relation, it is quite obvious that the lattice constant reflecting the struc-tural property can be expressed in terms of product of ionic charges and ionic radii of these materials. The calculated values are presented in Tables 1, 2 and 3. An excellent agreement between the author’s calculated values of lattice constant and the values reported by different researchers has been found. The lattice constants evaluated in this work hardly deviate (0.1–10%) from experimental data. The values evaluated show a systematic trend and are con-

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Table 1 Values of lattice constant (in Å) for perovskite solids. The value of the product of ionic charge (ZAZX) = 6 for perovskite ox-ides and (ZAZX) = 3 for perovskite halides.

solid rA (Å) [5]

rB (Å) [5]

rX (Å) [5]

a (Å) exp. [5]

a (Å) [5]

a (Å) [6]

a (Å) (this work)

% error

CsIO3 1.88 0.95 1.35 4.674 4.539 4.596 4.653 0.4 RbUO3 1.72 0.76 1.35 4.323 4.234 4.286 4.266 1.3 KUO3 1.64 0.76 1.35 4.290 4.203 4.218 4.176 2.7 RbPaO3 1.72 0.78 1.35 4.368 4.259 4.311 4.286 1.9 KPaO3 1.64 0.78 1.35 4.341 4.229 4.243 4.200 3.2 KTaO3 1.64 0.64 1.35 3.988 4.053 4.072 4.042 1.4 KNbO3 1.64 0.64 1.35 4.007 4.053 4.072 3.877 3.2 NaTaO3 1.39 0.64 1.35 3.881 3.952 3.886 3.765 3.0 NaAlO3 1.39 0.535 1.35 3.730 3.823 3.762 3.648 2.2 NaWO3 1.39 0.62 1.35 3.850 3.927 3.861 3.741 2.8 CsCdF3 1.88 0.95 1.285 4.470 4.430 4.475 4.396 1.7 CsCaF3 1.88 1.00 1.285 4.523 4.496 4.539 4.448 1.7 CsHgF3 1.88 1.02 1.285 4.570 4.523 4.565 4.470 2.2 CsSrF3 1.88 1.18 1.285 4.750 4.747 4.781 4.640 2.3 CsEuF3 1.88 1.17 1.285 4.780 4.729 4.767 4.630 3.1 CsPbF3 1.88 1.19 1.285 4.800 4.575 4.795 4.653 3.1 CsYbF3 1.88 1.02 1.285 4.610 4.523 4.565 4.470 3.0 CsCaCl3 1.88 1.00 1.79 5.396 5.360 5.391 4.989 7.5 CsCdCl3 1.88 0.95 1.79 5.210 5.289 5.321 4.935 5.3 CsPbCl3 1.88 1.19 1.79 5.605 5.639 5.667 5.191 7.4 CsHgCl3 1.88 1.02 1.79 5.410 5.389 5.420 5.008 7.4 CsEuCl3 1.88 1.17 1.79 5.627 5.610 5.637 5.169 8.1 CsTmCl3 1.88 1.03 1.79 5.476 5.404 5.406 5.021 8.3 CsYbCl3 1.88 1.02 1.79 5.437 5.389 5.420 5.008 7.9 CsHgBr3 1.88 1.02 1.95 5.770 5.668 5.690 5.182 10 CsPbBr3 1.88 1.19 1.95 5.874 5.921 5.941 5.361 8.7 RbZnF3 1.72 0.74 1.285 4.122 4.102 4.143 4.000 3.0 RbCoF3 1.72 0.745 1.285 4.141 4.108 4.143 4.006 3.3 RbVF3 1.72 0.79 1.285 4.170 4.165 4.203 4.054 2.8 RbFeF3 1.72 0.78 1.285 4.174 4.152 4.191 4.044 3.1 RbMnF3 1.72 0.83 1.285 4.240 4.215 4.252 4.095 3.4 RbCdF3 1.72 0.95 1.285 4.398 4.373 4.405 4.223 4.0 RbCaF3 1.72 1.00 1.285 4.452 4.440 4.471 4.278 3.9 RbHgF3 1.72 1.02 1.285 4.470 4.468 4.498 4.300 3.8 RbPdF3 1.72 0.86 1.285 4.298 4.254 4.290 4.127 4.0 RbYbF3 1.72 1.02 1.285 4.530 4.468 4.498 4.300 5.1 RbPbF3 1.72 1.19 1.285 4.790 4.705 4.732 4.480 6.5 KCdF3 1.64 0.95 1.285 4.293 4.344 4.341 4.140 3.6 KMgF3 1.64 0.72 1.285 3.989 4.046 4.048 3.895 2.4 KNiF3 1.64 0.69 1.285 4.013 4.009 4.012 3.861 3.8 KZnF3 1.64 0.74 1.285 4.056 4.070 4.072 3.916 3.5 KCoF3 1.64 0.745 1.285 4.071 4.077 4.072 3.919 3.7 KVF3 1.64 0.79 1.285 4.100 4.134 4.134 3.967 3.2 KFeF3 1.64 0.78 1.285 4.121 4.121 4.121 3.957 4.0 KMnF3 1.64 0.83 1.285 4.189 4.185 4.184 4.012 4.2 NaVF3 1.39 0.79 1.285 3.940 4.037 3.955 3.701 6.1 AgMgF3 1.48 0.72 1.285 3.918 3.982 3.930 3.724 5.0 AgNiF3 1.48 0.69 1.285 3.936 3.944 3.892 3.691 6.2 AgZnF3 1.48 0.74 1.285 3.972 4.004 3.955 3.743 5.8 AgCoF3 1.48 0.745 1.285 3.983 4.013 3.955 3.749 5.9 AgMnF3 1.48 0.83 1.285 4.030 4.124 4.072 3.839 4.7 LiBaF3 1.61 0.76 1.285 3.992 4.084 3.984 3.903 2.2 NH4ZnF3 1.80 0.74 1.285 4.115 4.134 4.128 4.086 0.7 NH4CoF3 1.80 0.745 1.285 4.129 4.140 4.128 4.092 0.9 NH4FeF3 1.80 0.78 1.285 4.177 4.183 4.176 4.127 1.2

1524 A. S. Verma et al.: Correlation between ionic charge and lattice constant of cubic perovskite solids

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Table 1 Continued.

solid rA (Å) [5]

rB (Å) [5]

rX (Å) [5]

a (Å) exp. [5]

a (Å) [5]

a (Å) [6]

a (Å) (this work)

% error

NH4MnF3 1.80 0.83 1.285 4.241 4.246 4.238 4.182 1.4 NH4MgF3 1.80 0.72 1.285 4.060 4.110 4.104 4.063 0.1 TlCoF3 1.70 0.745 1.285 4.138 4.100 4.133 3.983 3.7 TlFeF3 1.70 0.78 1.285 4.188 4.144 4.181 4.022 4.0 TlMnF3 1.70 0.83 1.285 4.260 4.208 4.243 4.076 4.3 TlCdF3 1.70 0.95 1.285 4.400 4.366 4.396 4.204 4.5 TlPdF3 1.70 0.86 1.285 4.301 4.247 4.280 4.108 4.5 TlMnCl3 1.70 0.83 1.79 5.020 5.064 5.087 4.614 8.1

Table 2 Values of lattice constant (in Å) for perovskite solids. The value of product of ionic charge (ZAZX) = 12 for perovskite oxides.

solid rA(Å) [5]

rB (Å) [5]

rX (Å) [5]

a (Å) exp. [5]

a (Å) [5]

a (Å) [6]

a (Å) (this work)

% error

BaFeO3 1.61 0.585 1.35 3.994 3.975 3.998 4.116 3.1 BaMoO3 1.61 0.65 1.35 4.040 4.053 4.068 4.189 3.7 BaNbO3 1.61 0.68 1.35 4.080 4.091 4.104 4.224 3.5 BaSnO3 1.61 0.69 1.35 4.116 4.103 4.117 4.238 3.0 BaHfO3 1.61 0.71 1.35 4.171 4.128 4.141 4.259 2.1 BaZrO3 1.61 0.72 1.35 4.193 4.141 4.154 4.273 1.9 BaIrO3 1.61 0.625 1.35 4.100 4.023 4.045 4.161 1.5 BaPbO3 1.61 0.775 1.35 4.265 4.211 4.229 4.336 1.7 BaTbO3 1.61 0.76 1.35 4.285 4.192 4.204 4.319 0.8 BaPrO3 1.61 0.85 1.35 4.354 4.310 4.319 4.423 1.6 BaCeO3 1.61 0.87 1.35 4.397 4.336 4.346 4.447 1.1 BaAmO3 1.61 0.85 1.35 4.357 4.310 4.319 4.423 1.5 BaNpO3 1.61 0.87 1.35 4.384 4.336 4.346 4.447 1.4 BaUO3 1.61 0.89 1.35 4.387 4.363 4.372 4.469 1.9 BaPaO3 1.61 0.90 1.35 4.450 4.377 4.386 4.483 0.7 BaThO3 1.61 0.94 1.35 4.480 4.431 4.439 4.527 1.0 BaTiO3 1.61 0.605 1.35 4.012 3.999 4.021 4.137 3.1 SrMnO3 1.44 0.53 1.35 3.806 3.838 3.837 3.855 1.3 SrVO3 1.44 0.58 1.35 3.890 3.898 3.932 3.911 0.5 SrFeO3 1.44 0.585 1.35 3.850 3.904 3.908 3.918 1.8 SrTiO3 1.44 0.605 1.35 3.905 3.929 3.932 3.942 0.9 SrTcO3 1.44 0.645 1.35 3.949 3.979 3.981 3.987 1.0 SrMoO3 1.44 0.65 1.35 3.975 3.985 3.981 3.994 0.5 SrNbO3 1.44 0.68 1.35 4.016 4.023 4.018 4.029 0.3 SrSnO3 1.44 0.69 1.35 4.034 4.036 4.031 4.040 0.1 SrHfO3 1.44 0.71 1.35 4.069 4.062 4.056 4.064 0.1 SrTbO3 1.44 0.76 1.35 4.180 4.127 4.121 4.120 1.4 SrAmO3 1.44 0.85 1.35 4.230 4.248 4.240 4.224 0.1 SrPuO3 1.44 0.86 1.35 4.280 4.261 4.253 4.238 1.0 SrCoO3 1.44 0.53 1.35 3.850 3.838 3.837 3.855 0.1 SrZrO3 1.44 0.72 1.35 4.104 4.075 4.069 4.074 0.7 SrRuO3 1.44 0.68a 1.35 3.930b 3.927b – 4.040 2.8 CaVO3 1.34 0.58 1.35 3.767 3.857 3.838 3.796 0.8 CaTiO3 1.34 0.605 1.35 3.840 3.888 3.838 3.824 0.4

a Ref. [21], b Ref. [22]

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Table 3 Values of lattice constant (in Å) for perovskite solids. The value of product of ionic charge (ZAZX) = 18 for perovskite oxides.

solid rA (Å) [5]

rB (Å) [5]

rX (Å) [5]

a (Å) exp. [5]

a (Å) [5]

a (Å) [6]

a (Å) (this work)

% error

EuTiO3 1.23 0.670 1.35 3.905 3.927 3.889 3.864 1.0 EuAlO3 1.23 0.535 1.35 3.725 3.755 3.724 3.704 0.6 EuCrO3 1.23 0.615 1.35 3.803 3.856 3.824 3.800 0.1 EuFeO3 1.23 0.645 1.35 3.836 3.894 3.856 3.836 – CeAlO3 1.34 0.535 1.35 3.772 3.801 3.757 3.836 1.7 GdAlO3 1.22 0.535 1.35 3.710 3.750 3.719 3.693 0.5 GdCrO3 1.22 0.615 1.35 3.795 3.852 3.819 3.789 0.2 GdFeO3 1.22 0.645 1.35 3.820 3.890 3.851 3.825 0.1 LaAlO3 1.36 0.535 1.35 3.778 3.810 3.768 3.861 2.2 LaCrO3 1.36 0.615 1.35 3.874 3.909 3.866 3.953 2.0 LaFeO3 1.36 0.645 1.35 3.920 3.947 3.898 3.989 1.8 LaGaO3 1.36 0.620 1.35 3.874 3.915 3.866 3.961 2.2 LaRhO3 1.36 0.665 1.35 3.940 3.972 3.930 4.014 1.9 LaTiO3 1.36 0.670 1.35 3.920 3.979 3.930 4.021 2.6 LaVO3 1.36 0.640 1.35 3.910 3.940 3.891 3.986 1.9 NdAlO3 1.27 0.535 1.35 3.752 3.772 3.740 3.754 0.1 NdCoO3 1.27 0.545 1.35 3.777 3.784 3.753 3.764 0.3 NdCrO3 1.27 0.615 1.35 3.835 3.872 3.840 3.846 0.3 NdFeO3 1.27 0.645 1.35 3.870 3.910 3.872 3.882 0.3 NdMnO3 1.27 0.645 1.35 3.800 3.910 3.872 3.882 2.2 PrAlO3 1.30 0.535 1.35 3.757 3.784 3.746 3.789 0.9 PrCrO3 1.30 0.615 1.35 3.852 3.884 3.845 3.882 0.8 PrFeO3 1.30 0.645 1.35 3.887 3.923 3.877 3.918 0.8 PrGaO3 1.30 0.620 1.35 3.863 3.891 3.845 3.889 0.7 PrMnO3 1.30 0.645 1.35 3.820 3.923 3.877 3.918 2.6 PrVO3 1.30 0.640 1.35 3.890 3.916 3.871 3.914 0.6 SmAlO3 1.24 0.535 1.35 3.734 3.759 3.729 3.718 0.4 SmCoO3 1.24 0.545 1.35 3.750 3.771 3.742 3.729 0.6 SmVO3 1.24 0.640 1.35 3.890 3.892 3.855 3.843 1.2 SmFeO3 1.24 0.645 1.35 3.845 3.898 3.861 3.846 – YAlO3 1.20 0.535 1.35 3.680 3.742 3.697 3.668 0.3 YCrO3 1.20 0.615 1.35 3.768 3.843 3.798 3.764 0.1 YFeO3 1.20 0.645 1.35 3.785 3.882 3.831 3.800 0.4 BiAlO3 1.03a 0.535 1.35 – 3.723c 3.715c 3.461 – BiGaO3 1.03a 0.620 1.35 – 3.834d 3.821c 3.568 – BiInO3 1.03a 0.800a 1.35 – 4.111c 4.193c 3.782 – BiScO3 1.03a 0.745a 1.35 – 4.080c 3.974c 3.711 –

a Ref. [21], c Ref. [23], d Ref. [24]

sistent with the available data reported so far, which proves the validity of the approach. According to this idea we may evaluate all-important properties of perovskite solids using their ionic charge and average ionic radii, which are basic parameters. It is also noteworthy that the proposed empiri-cal relation is simpler, widely applicable and values ob-tained are in better agreement with experiment data as compared to the empirical relations proposed by previous researchers. We have been reasonably successful in calcu-lating lattice constant using the product of ionic charges and ionic radii of the materials for perovskite solids. It is natural to say that this model can easily be extended to rocksalt, zinc blende and chalcopyrite crystals, for which the work is in progress and will be appearing in a forth-coming paper. Hence, it is possible to predict the order of

physical properties of binary and complex structured solids from their ionic charges. The method presented in this work will be helpful to material scientists for finding new materials with desired lattice constant among a series of structurally similar materials.

References

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