Relationship among Chemical Element Properties, Bulk Additive

Two fundamental chemical element properties, melting point and ... correspondent zinc compounds, and two selected chemical element properties was firs...
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3166

Chem. Mater. 1999, 11, 3166-3170

Relationship among Chemical Element Properties, Bulk Additive Properties, and Crystal Structures of Binary Zinc Compounds Ping Wu* Institute of High Performance Computing, 89B Science Park Drive #01-05/08 The Rutherford, Singapore Science Park I, Singapore 118261

Hong Mei Jin and Yi Li Department of Materials Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260 Received April 27, 1999. Revised Manuscript Received August 18, 1999

Two fundamental chemical element properties, melting point and pseudopotential radii, were found to be strongly correlated not only to the effects of additives in galvanizing but also to the crystal structures of their correspondent binary zinc compounds, based on experimental data from the literature. It was suggested that both the bulk properties (such as galvanizing effects in this study) and crystal structures might be regulated by the same set of constituent chemical element properties. Although most chemical elements, as well as crystal structures of binary compounds, are well investigated and understood, our knowledge of bulk properties of known systems is still less comprehensive. In this study, a correlation between effects of additives in galvanizing, through the behaviors of their correspondent zinc compounds, and two selected chemical element properties was first established, based on available literature data. The selected two element properties were, then, used to correlate to the crystal structures of binary zinc compounds, which will further reveal the relationship between bulk properties and the relevant structures. Predictions of new additives that may enhance the galvanizing process were made, based on the developed correlation. The mechanism of chemical behaviors of constituent elements both in the galvanizing process and in crystal formation might be revealed since only two well-studied chemical element properties were involved in the correlation. It was shown that diffusion might play a key role in both galvanizing and the relevant crystal formation process. This research may provide an interesting approach in the design of new chemicals when there is a lack of bulk property data but a wealth of structural information.

I. Introduction Powerful computational quantum chemistry techniques have made it possible to study individual atoms with regard to their roles in determining the structures and functions of simple chemicals. The sample sizes in these studies are normally in the order of 10 atoms, even on high performance computers. Alternative methods such as correlation techniques must then be developed for large and complex chemicals. Structure mapping1,2 is one such successful approach. It correlates the crystal structures of materials to their chemical element properties. Property mapping3 is another approach that correlates bulk properties to their chemical element properties. Property maps, and especially structure * Corresponding author. E-mail: [email protected]. Telephone: (65) 770-9212. Fax: (65) 778-0522. (1) Pettifor, D. G. In Intermetallic Compounds Principles and Practice, Volume 1-Principles; John Wiley & Sons: New York, 1995; pp 419-438. (2) Zunger, A. In Structure and Bonding in Crystals;Keeffe M. O′, Navrotsky A., Eds.; Academic Press: London, 1981; pp 73-132. (3) ) Rabe, K. M.; Phillips, J. C.; Villars, P.; Brown I. D. Phys. Rev. B 1992, 45, 7650.

maps have, therefore, been widely used in searching chemicals with either specific bulk properties or crystal structures. Structure and property relationship is a classical and well-studied research area. Even commercial software4 provides functions to predict the bulk properties of chemicals from their structural information. But it still remains, in most cases, as an empirical approach. This study indicated that a few fundamental element properties might regulate both property and the relevant structure. It might not only form the basis but also provide an opportunity to improve the quality of the observed relationship between structure and property of chemicals. II. Chemical Element Properties and the Effects of Element Additives in Galvanizing In a galvanizing process, element additives such as Ni or V were added in the molten zinc bath to influence the physical and chemical behaviors of the Fe-Zn (4) Cerius2, Molecular Simulations Inc.: San Diego, CA, 1997.

10.1021/cm990243u CCC: $18.00 © 1999 American Chemical Society Published on Web 10/13/1999

Binary Zinc Compounds

Chem. Mater., Vol. 11, No. 11, 1999 3167

coatings on steel articles. In our previous study,5 a correlation between galvanizing effects of element additives to fundamental element properties was established based on limited literature data. However, the enormous available crystal structure information was ignored. To design new alloy additives, it is necessary to include binary compound data such as the chemical stoichiometry and the crystal structure in the correlation.6 As in our previous study,5 the experimental data by Sebisty7were applied, who measured the effects of additives such as Ag, Co, Mg, Th, U, Ti, V, Ni, Cr, Zr, Mn, and rare-earth-metal elements (RE) on the steel weight loss in the galvanizing of rimmed steel at 460 °C. Sebisty’s study showed that Zr, Mn, Ni, V, Ti, and Cr were effective in reducing iron weight loss, and others either increased (like Ag, Co and Mg) or had minor effects (like U and Th) on iron weight loss. When an element additive, A, is added in a pure molten zinc bath, a series of AiZnj compounds may form, where i and j define the chemical stoichiometry of the compound. A total of 76 such AiZnj compounds were reported in the literature, which were divided into two classes in Table 1 (in bold type). For each of the 76 records in Table 1, a class label Cp was assigned to be p1 in case of reducing weight loss7,8 (where A is one of Zr, Mn, Ni, V, Ti, Cr, and Cu) and to be p2 if otherwise. To construct a property map, its coordinates, which will be functions of element properties and chemical stoichiometry of the compound, have to be defined. For a close A-Zn atomic pair, the difference between atom A and atom Zn in terms of element property P (i.e., PA for A and PZn for Zn) is

QAZn ) PA - PZn

(1)

Subsequently, in a regular solution,9 a property map coordinate, Op (in respect to element property P), was defined as follows:

Op ) YAYZnQAZn

(2)

Here, YA ) i/(i + j) and YZn ) j/(i + j). YAYZn is proportional to the total number of A-Zn pairs and Op is, therefore, the overall element property difference of all nearest neighbor atomic pairs in the compound.6 A few element properties such as atomic number (AN),10 valence electron number (V),11 electronegativity (X),11 pseudopotential radii (R),11 and melting point (T)10 were selected to define the property map coordinates based on eqs 1 and 2. In Table 1 each record has five predictor variables, O1, O2, O3, O4 and O5, based on element properties AN, V, X, R, and T, respectively. Coordinates O4 and O5 were selected to construct the property map as shown in Figure 1, on which all class p1 compounds are located within a downward-triangle zone, namely (5) Hongmei, J.; Yi, L.; Ping, W. J. Mater. Res. 1999, 5, 1791. (6) Ping, W.; Kokliang, H. Chem. Mater. 1999, 11 (4), 858. (7) Sebisty, J. J.; Palmer, R. H. In Proceedings 7th International Conference on Hot Dip Galvanizing Interlaken, Pergamon Press: Paris, 1964; pp 235-266. (8) Katiforis, N.; Papadimitriou, G. Surf. Coat. Technol. 1996, 78, 185. (9) Ping, W.; Eriksson, G.; Pelton, A. D. J. Am. Ceram. Soc. 1993, 76, 2065. (10) Samsonov, G. V. Handbook of the Physicochemical Properties of the Elements; Imprint New York, IFI/Plenum: New York, 1968; pp 10-132. (11) Villars, P.; Hulliger, F. J. Less-Common Met. 1987, 132, 289.

z1. Most of the class p2 compounds are in a tetragon zone, namely z2. Therefore class p1 and p2 compounds are well separated in Figure 1, which leads to a simple correlation between galvanizing effects and constituent chemical element properties, T and R. III. Correlation of Crystal Structures and Chemical Element Properties of Binary Zinc Compounds A total of 54 binary zinc systems and 221 binary Zn compounds are reported in the literature. The observed 221 compounds, AiZnj, belong to 70 distinctly different structure types by the space group theory. It is, therefore, almost impossible to extract any meaningful connections of compounds either within the same or among different structure types. To reduce the number of distinctly different structure types, Villars12 developed the atomic environmental approach to redefine the structure type by the total number of atoms (CN) in only a few immediate layers of atom around the central A atom. CN is defined as the coordination number of A atoms in a AiZnj compound. For all 221 compounds, the traditional defined structure types, and the CN values, which range from 4 to 24, are listed in Table 1. After such treatment the number of structure types was reduced from the original 70 to 17, but it is still too large a number for correlation development. Classical pattern recognition techniques, available in S-PLUS,13 like the partioning around medoids,14 which is similar to the well-known k-means method,15 were used to further reduce the number of structure types to three, i.e., CN e 10, 10 < CN e 14, and CN > 14. A new class label Cs of s1, s2, or s3 was assigned to each compound according to its new structure type as shown in Table 1. A structure map shown in Figure 2 was constructed by applying the same coordinates (O4 and O5) as in the property map. All s1 compounds are located within zone z3 where O4 is negative. Most s2 compounds are in the z1 zone and some are in the z2 zone. However, almost all s3 compounds are in the z2 zone except five s3 compounds in the z1 zone. Since Figure 1 and Figure 2 have the same coordinates, a correlation between structure and property may be developed. It is very interesting that compounds belong to class p1 are actually labeled as s2 on Figure 2. However, not all s2 compounds occupy the same area as class p1 compounds do. Some of the s2 compounds occupy the area of p2 compounds (z2 zone). IV. Discussion In galvanizing, the zinc atoms and the additive atoms (A) which make up the molten bath interact with one another in various ways. The extent to which they do so and the resulting changes in behavior will determine the local configuration of atoms (or structural geometry) as well as the bulk properties of the system. It is of (12) Villars, P. In Intermetallic Compounds Principles and Practice, Volume 1-Principles; John Wiley & Sons: New York, 1995; pp 227275. (13) (13) S-PLUS5 for Unix Guide to Statistics; Data Analysis Products Division, Mathsoft: Seattle: WA, 1999. (14) S-PLUS5 for Unix Guide to Statistics; Data Analysis Products Division, Mathsoft: Seattle: WA, 1999; pp 583-586 (15) S-PLUS5 for Unix Guide to Statistics, Data Analysis Products Division, Mathsoft: Seattle: WA, 1999; pp 581-582

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Wu et al.

Table 1. Structure Type, Coordination Number, Five Predictor Variables, and Class Labels of Zinc Binary Systems compd

struct type

CN

O1

O2

O3 (eV1/2)

O4 (au)

O5 (°C)

Cp Cs

compd

Ag5Zn8 Ag5Zn95 AgZn Al86Zn14 As2Zn3 AsZn Au3Zn Au5Zn3 Au80Zn20 AuZn AuZn3 BaZn BaZn13 BaZn2 BaZn5 CaZn CaZn11 CaZn13 CaZn2 CaZn5 Cd2Zn98 Cd96Zn4 Ce13Zn58 Ce2Zn17 Ce3Zn11 Ce3Zn22 CeZn CeZn11 CeZn3 CeZn2 CeZn5 CoZn13 CrZn13 Cu2Zn98 Cu5Zn8 Cu70Zn30 CuZn CuZn3 Dy13Zn58 Dy2Zn17 Dy3Zn11 Dy6Zn23 DyZn DyZn12 DyZn3 DyZn5 Er2Zn17 Er2Zn9 Er6Zn23 ErZn ErZn12 ErZn2 ErZn3 ErZn5 EuZn11 EuZn13 EuZn2 EuZn5 Fe11Zn39 Fe3Zn10 Fe68Zn32 FeZn13 Ga2Zn98 Gd13Zn58 Gd2Zn17 Gd3Zn11 Gd3Zn22 Gd6Zn23 GdZn12 GdZn5 Hg2Zn98 HgZn3 Ho13Zn58 Ho2Zn17 Ho5Zn23 HoZn12 HoZn2 HoZn3 HoZn5 Ir2Zn11 La2Zn17 La3Zn22

Cu5Zn8 Mg AgZn Cu5Zn8 Mn2O3 CdSb Au3Zn Au5Zn3 Cu ClCs H3U ClCs NaZn13 CeCu2 BaZn5 BCr BaCd11 NaZn13 CeCu2 CaCu5 Mg Mg Cd58Gd13 Th2Zn17 Al11La3 Pu3Zn22 ClCs BaCd11 YZn3 CeCu2 CaCu5 CoZn13 CoZn13 Mg Cu5Zn8 Cu ClCs CuZn3 Gd13Zn58 Ni17Th2 Al11La3 Mn23Th6 ClCs Mn12Th YZn3 YZn5 Ni17Th2 Gd13Zn58 Mn23Th6 ClCs Mn12Th CeCu2 YZn3 ErZn5 BaCd11 NaZn13 CeCu2 CaCu5 Fe11Zn39 Cu5Zn8 W CoZn13 Mg Cd58Gd13 Th2Zn17 Al11La3 Pu3Zn22 Mn23Th6 Mn12Th CaCu5 Mg AgCd Gd13Zn58 Ni17Th2 Mn23Th6 Mn12Th CeCu2 YZn3 ErZn5 Cu5Zn8 Th2Zn17 Pu3Zn22

12 12 14 12 6 5 12 14 12 14 12 14 24 16 21 17 22 24 16 18 12 12 14 18 19 20 14 22 17 16 18 12 12 12 12 12 14 14 14 18 20 17 14 20 17 18 18 14 17 14 20 16 17 16 22 24 16 18 12 12 14 12 12 14 18 20 20 17 20 18 12 12 14 18 17 20 16 17 16 12 19 20

4.024 0.808 4.250 -2.047 0.720 0.750 9.188 11.484 7.840 12.250 9.188 6.500 1.724 5.778 3.611 -2.500 -0.764 -0.663 -2.222 -1.389 0.353 0.691 4.188 2.637 4.714 2.957 7.000 2.139 5.250 6.222 3.889 -0.199 -0.398 -0.020 -0.237 -0.210 -0.250 -0.188 5.385 3.391 6.061 5.907 9.000 2.556 6.750 5.000 3.579 5.653 6.235 9.500 2.698 8.444 7.125 5.278 2.521 2.189 7.333 4.583 -0.686 -0.710 -0.870 -0.265 0.020 5.085 3.202 5.724 3.590 5.579 2.414 4.722 0.980 9.375 5.534 3.485 5.427 2.627 8.222 6.938 5.139 6.118 2.543 2.851

-0.237 -0.048 -0.250 -1.084 -1.680 -1.750 -0.188 -0.234 -0.160 -0.250 -0.188 -2.500 -0.663 -2.222 -1.389 -2.500 -0.764 -0.663 -2.222 -1.389 0.000 0.000 -1.346 -0.848 -1.515 -0.950 -2.250 -0.688 -1.688 -2.000 -1.250 -0.199 -0.398 -0.020 -0.237 -0.210 -0.250 -0.188 -1.346 -0.848 -1.515 -1.477 -2.250 -0.639 -1.688 -1.250 -0.848 -1.339 -1.477 -2.250 -0.639 -2.000 -1.688 -1.250 -0.688 -0.597 -2.000 -1.250 -0.686 -0.710 -0.870 -0.265 -0.176 -1.346 -0.848 -1.515 -0.950 -1.477 -0.639 -1.250 0.000 0.000 -1.346 -0.848 -1.320 -0.639 -2.000 -1.688 -1.250 -0.391 -0.848 -0.950

-0.088 -0.018 -0.093 0.024 0.199 0.208 -0.047 -0.059 -0.040 -0.063 -0.047 -0.090 -0.024 -0.080 -0.050 -0.068 -0.021 -0.018 -0.060 -0.038 -0.001 -0.002 -0.051 -0.032 -0.057 -0.036 -0.085 -0.026 -0.064 -0.076 -0.047 0.019 0.037 -0.007 -0.085 -0.076 -0.090 -0.068 -0.043 -0.027 -0.049 -0.048 -0.073 -0.021 -0.054 -0.040 -0.023 -0.036 -0.039 -0.060 -0.017 -0.053 -0.045 -0.033 -0.022 -0.019 -0.064 -0.040 0.039 0.041 0.050 0.015 0.005 -0.051 -0.032 -0.057 -0.036 -0.056 -0.024 -0.047 0.001 0.009 -0.036 -0.023 -0.035 -0.017 -0.053 -0.045 -0.033 0.056 -0.008 -0.010

0.117 0.024 0.124 -0.025 -0.112 -0.116 0.146 0.183 0.125 0.195 0.146 0.381 0.101 0.338 0.211 0.280 0.086 0.074 0.249 0.156 0.007 0.013 0.392 0.247 0.441 0.277 0.655 0.200 0.491 0.582 0.364 0.009 0.037 0.003 0.038 0.034 0.040 0.030 0.268 0.169 0.301 0.294 0.448 0.127 0.336 0.249 0.165 0.260 0.287 0.438 0.124 0.389 0.328 0.243 0.157 0.137 0.458 0.286 0.039 0.041 0.050 0.015 -0.004 0.304 0.191 0.342 0.214 0.333 0.144 0.282 0.010 0.099 0.265 0.167 0.260 0.126 0.393 0.332 0.246 0.097 0.113 0.127

128.3 25.7 135.5 29.0 95.5 99.5 120.9 151.2 103.2 161.3 120.9 77.5 20.6 68.9 43.1 105.0 32.1 27.9 93.3 58.3 -1.9 -3.8 56.7 35.7 63.8 40.0 94.8 29.0 71.1 84.2 52.6 71.4 95.4 13.0 157.4 139.7 166.3 124.7 148.1 93.2 166.7 162.4 247.5 70.3 185.6 137.5 103.9 164.1 181.0 275.8 78.3 245.1 206.8 153.2 30.4 26.4 88.4 55.3 191.7 198.3 243.1 74.1 -7.6 133.6 84.1 150.4 94.3 146.5 63.4 124.0 -9.0 -85.9 157.2 99.0 154.2 74.6 233.6 197.1 146.0 263.5 47.2 52.9

p2 s2 p2 s2 p2 s2 s2 s1 s1 s2 s2 s2 s2 s2 s2 s3 s3 s3 s3 s3 s3 s3 s3 s2 s2 p2 s2 p2 s3 p2 s3 p2 s3 p2 s2 p2 s3 p2 s3 p2 s3 p2 s3 p2 s2 p1 s2 p1 s2 p1 s2 p1 s2 p1 s2 p1 s2 s2 s3 s3 s3 s2 s3 s3 s3 s3 s2 s3 s2 s3 s3 s3 s3 s3 s3 s3 s3 p1 s2 p1 s2 p1 s2 p1 s2 s2 s2 s3 s3 s3 s3 s3 s3 s2 s2 s2 s3 s3 s3 s3 s3 s3 s2 p2 s3 p2 s3

Nd2Zn17 Nd3Zn11 Nd3Zn22 NdZn11 NdZn2 NdZn NdZn3 Ni3Zn14 Ni70Zn30 NiZn NiZn3 NiZn8 P2Zn P2Zn3 P4Zn Pd2Zn Pd2Zn3 Pd2Zn9 Pd81Zn19 PdZn PdZn2 Pr13Zn58 Pr2Zn17 Pr3Zn11 Pr3Zn22 PrZn PrZn11 PrZn3 PrZn5 Pt3Zn Pt3Zn10 Pt4Zn7 Pt7Zn12 Pu13Zn58 Pu2Zn17 Pu3Zn22 Pu97Zn3 PuZn2 SZn Sb3Zn4 SbZn Sc3Zn17 ScZn ScZn12 Se2Zn SeZn Sm13Zn58 Sm2Zn17 Sm3Zn11 Sm3Zn22 SmZn SmZn12 SmZn2 SmZn3 SmZn5 SmZn11 Sn17Zn3 SrZn SrZn13 SrZn2 SrZn5 Ta6Zn7 TaZn2 Tb13Zn58 Tb2Zn17 Tb3Zn11 Tb6Zn23 TbZn TbZn12 TbZn2 TbZn3 TeZn Th2Zn ThZn2 ThZn4 Th2Zn17 ThZn9 TiZn16 TiZn2 TiZn3 Tm13Zn58 Tm2Zn17

struct type

CN

Th2Zn17 18 Al11La3 20 pu3Zn22 20 BaCd11 22 CeCu2 16 ClCs 14 YZn3 17 Cu5Zn8 12 Cu 12 AuCu 12 NiZn3 12 NiZn8 11 P2Zn 4 Mn2O3 6 As4Mg 4 Co2Si 13 ClCs 14 Cu5Zn8 12 Cu 12 AuCu 12 PdZn2 13 Gd13Zn58 14 Ni17Th2 18 BaCd11 20 Pu3Zn22 20 ClCs 14 BaCd11 22 YZn3 17 CaCu5 18 AuCu3 12 Pt3Zn10 12 Pt4Zn7 10 Pt7Zn12 17 Cd58Gd13 14 Th2Zn17 18 Pu3Zn22 20 Cu 12 Cu2Mg 16 ClNa 6 Sb3Zn4 4 Cdsb 5 Be17Ru3 16 ClCs 14 Mn12Th 20 Fes2 4 SZn 4 Gd13Zn58 14 Ni17Th2 18 Al11La3 20 Pu3Zn22 20 ClCs 14 Mn12Th 20 CeCu2 16 YZn3 17 CaCu5 18 SmZn11 18 CW 14 BFe 17 NaZn13 24 CeCu2 16 CaCu5 12 Fe7W6 14 MgNi2 16 Gd13Zn58 14 Ni17Th2 18 Al11La3 20 Mn23Th6 17 HgMn 14 Mn12Th 20 CeCu2 16 YZn3 17 ClNa 6 Al2Cu 15 AlB2 20 Al4Ba 22 Ni17Th2 18 CaCu5 18 TiZn16 15 MgZn2 16 AuCu3 13 Gd13Zn58 14 Th2Zn17 18

O1

O2

O3 (eV1/2)

O4 (au)

O5 (°C)

2.825 5.051 3.168 2.292 6.667 7.500 5.625 -0.291 -0.420 -0.500 -0.375 -0.198 -3.333 -3.600 -2.400 3.556 3.840 2.380 2.918 4.000 3.556 4.338 2.731 4.883 3.062 7.250 2.215 5.438 4.028 9.000 8.521 11.107 11.169 9.573 6.028 6.758 1.862 14.222 -3.500 5.143 5.250 -1.148 -2.250 -0.639 0.889 1.000 4.786 3.014 5.388 3.379 8.000 2.272 7.111 6.000 4.444 2.444 2.550 2.000 0.531 1.778 1.111 10.686 9.556 5.235 3.296 5.893 5.743 8.750 2.485 7.778 6.563 2.694 13.333 13.333 9.600 5.651 5.400 -0.443 -1.778 -1.500 5.833 3.673

-0.848 -1.515 -0.950 -0.688 -2.000 -2.250 -1.688 -0.291 -0.420 -0.500 -0.375 -0.198 -1.556 -1.680 -1.120 -0.444 -0.480 -0.298 -0.365 -0.500 -0.444 -1.346 -0.848 -1.515 -0.950 -2.250 -0.688 -1.688 -1.250 -0.375 -0.355 -0.463 -0.465 -1.346 -0.848 -0.950 -0.262 -2.000 -1.500 -1.714 -1.750 -1.148 -2.250 -0.639 -1.333 -1.500 -1.346 -0.848 -1.515 -0.950 -2.250 -0.639 -2.000 -1.688 -1.250 -0.688 -1.020 -2.500 -0.663 -2.222 -1.389 -1.740 -1.556 -1.346 -0.848 -1.515 -1.477 -2.250 -0.639 -2.000 -1.688 -1.102 -2.000 -2.000 -1.440 -0.848 -0.810 -0.443 -2.000 -1.500 -1.346 -0.848

-0.023 -0.040 -0.025 -0.018 -0.053 -0.060 -0.045 0.047 0.067 0.080 0.060 0.032 0.196 0.211 0.141 0.142 0.154 0.095 0.117 0.160 0.142 -0.051 -0.032 -0.057 -0.036 -0.085 -0.026 -0.064 -0.047 0.088 0.083 0.109 0.109 -0.021 -0.013 -0.015 -0.004 -0.031 0.303 0.171 0.175 0.008 0.015 0.004 0.244 0.275 -0.036 -0.023 -0.040 -0.025 -0.060 -0.017 -0.053 -0.045 -0.033 -0.018 0.056 -0.078 -0.021 -0.069 -0.043 0.124 0.111 -0.036 -0.023 -0.040 -0.039 -0.060 -0.017 -0.053 -0.045 0.115 -0.031 -0.031 -0.022 -0.013 -0.013 0.023 0.093 0.079 -0.036 -0.023

0.199 0.355 0.223 0.161 0.469 0.528 0.396 0.044 0.063 0.075 0.056 0.030 -0.142 -0.154 -0.102 0.127 0.137 0.085 0.104 0.143 0.127 0.389 0.245 0.438 0.275 0.650 0.199 0.488 0.361 0.154 0.146 0.190 0.191 0.453 0.285 0.320 0.088 0.673 -0.200 -0.028 -0.029 0.111 0.218 0.062 -0.132 -0.149 0.338 0.213 0.381 0.239 0.565 0.160 0.502 0.424 0.314 0.173 0.000 0.333 0.088 0.296 0.185 0.226 0.202 1.796 1.131 2.022 1.971 3.003 0.853 2.669 2.252 -0.026 0.689 0.689 0.496 0.292 0.279 0.039 0.156 0.131 0.257 0.162

56.2 100.5 63.0 45.6 132.7 149.3 111.9 150.3 217.1 258.5 193.9 102.1 -83.3 -90.0 -60.0 251.8 271.9 168.5 206.7 283.3 251.8 76.6 48.2 86.2 54.1 128.0 39.1 96.0 71.1 253.7 240.2 313.1 314.8 33.1 20.8 23.3 6.4 49.1 -76.0 51.9 53.0 142.8 280.0 79.5 -44.0 -49.5 97.7 61.5 109.9 69.0 163.3 46.4 145.1 122.4 90.7 49.9 -23.8 87.3 23.1 77.6 48.5 644.9 576.7 140.3 88.3 157.9 153.9 234.5 66.6 208.4 175.9 3.7 296.9 296.9 213.8 125.8 120.2 69.3 296.9 234.6 168.4 106.0

Cp Cs p2 p2 p2 p2 p2 p2 p2 p1 p1 p1 p1

p2 p2 p2 p2 p2 p2 p2

p2

p2 p2 p2 p2 p2 p1 p1 p1

s3 s3 s3 s3 s3 s2 s3 s2 s2 s2 s2 s1 s1 s1 s1 s2 s2 s2 s2 s2 s2 s2 s3 s3 s3 s2 s3 s3 s3 s2 s2 s2 s3 s2 s3 s3 s2 s3 s1 s1 s1 s3 s2 s3 s1 s1 s2 s3 s3 s3 s2 s3 s2 s3 s3 s3 s2 s3 s3 S3 s2 s2 s3 s2 s3 s3 s3 s2 s3 s3 s3 s1 s3 s3 s3 s3 s3 s3 s3 s2 s2 s3

Binary Zinc Compounds

Chem. Mater., Vol. 11, No. 11, 1999 3169 Table 1. Continued

compd

struct type

CN

O1

O2

LaZn13 LaZn5 LaZn LiZn LiZn99 Lu13Zn58 Lu2Zn17 Lu6Zn23 LuZn12 LuZn2 LuZn3 LuZn5 LuZn Mg2Zn11 Mg97Zn3 Mg51Zn20 Mg4Zn7 MgZn2 Mn60Zn40 MnZn MnZn13 MnZn3 MoZn7 NaZn13 Nb2Zn3 Nb3Zn7 NbZn2 NbZn3 Nd13Zn58

NaZn13 CaCu5 ClCs NaTl Mg Gd13Zn58 Th2Zn17 Mn23Th6 Mn12Th CeCu2 YZn3 ErZn5 ClCs Mg2Zn11 Mg Mg51Zn20 Mg4Zn7 MgZn2 Mn Mg CoZn13 Cu Ca7Ge NaZn13 Fe7W6 Cu MgNi2 AuCu3 Gd13Zn58

24 12 14 14 12 14 19 17 20 16 17 16 14 17 12 17 17 12 12 12 12 12 12 24 12 12 16 12 14

1.791 3.750 6.750 -6.750 -0.267 6.133 3.861 6.728 2.911 9.111 7.688 5.694 10.250 -1.695 -0.524 -2.467 -4.165 -4.000 -1.200 -1.250 -0.332 -0.938 1.313 -1.260 2.640 2.310 2.444 2.063 4.487

-0.597 -1.250 -2.250 -2.750 -0.109 -1.346 -0.848 -1.477 -0.639 -2.000 -1.688 -1.250 -2.250 -0.942 -0.291 -1.371 -2.314 -2.222 -1.200 -1.250 -0.332 -0.938 -0.656 -0.730 -1.680 -1.470 -1.556 -1.313 -1.346

O3 (eV1/2)

O4 (au)

O5 (°C)

Cp Cs

-0.006 0.080 33.2 p2 -0.013 0.167 69.6 p1 -0.023 0.300 125.3 p1 -0.135 -0.067 -59.8 -0.005 -0.003 -2.4 -0.036 0.223 185.9 -0.023 0.140 117.1 -0.039 0.244 204.0 -0.017 0.106 88.3 -0.053 0.331 276.2 -0.045 0.279 233.1 -0.033 0.207 172.6 -0.060 0.373 310.8 -0.012 0.014 21.7 p2 -0.004 0.004 6.7 p2 -0.018 0.021 31.5 p2 -0.030 0.035 53.2 p2 -0.029 0.033 51.1 p2 0.144 0.082 198.0 p2 0.150 0.085 206.3 p1 0.040 0.023 54.7 p1 0.113 0.064 154.7 p1 0.055 0.092 240.4 p1 -0.036 0.051 -24.6 0.142 0.211 491.5 0.124 0.185 430.1 0.131 0.196 455.1 0.111 0.165 384.0 -0.036 0.316 89.3 p2

s3 s2 s2 s2 s2 s2 s3 s3 s3 s3 s3 s3 s2 s3 s2 s3 s3 s2 s2 s2 s2 s2 s2 s3 s2 s2 s3 s2 s2

compd

struct type

CN

O1

O2

O3 (eV1/2)

O4 (au)

O5 (°C)

Tm6Zn23 TmZn12 TmZn2 TmZn3 TmZn TmZn5 U2Zn17 UZn12 V4Zn5 VZn3 Y2Zn17 Y3Zn11 YZn3 YZn5 Y2Zn9 YZn12 Y6Zn23 Yb2Zn17 Yb3Zn11 Yb3Zn17 Yb13Zn58 YbZn11 YbZn13 YbZn2 ZnZr2 ZrZn Zn2Zr Zn22Zr

Mn23Th6 Mn12Th CeCu2 YZn3 ClCs ErZn5 U2Zn17 UZn12 V4Zn5 AuCu3 Ni17Th2 Al11La3 YZn3 CaCu5 Y2Zn9 Mn12Th Mn23Th6 Ni17Th2 Al11La3 Be17Ru3 Gd13Zn58 BaCd11 NaZn13 CeCu2 MoSi2 ClCs Cu2Mg Al18Cr22Mg3

17 20 16 17 14 16 18 18 14 12 18 20 17 12 17 20 17 18 20 16 14 22 24 16 14 14 16 12

6.400 2.769 8.667 7.313 9.750 5.417 5.839 4.402 -1.728 -1.313 0.848 1.515 1.688 1.250 1.339 0.639 1.477 3.767 6.735 5.100 0.666 3.056 2.653 8.889 2.222 2.500 2.222 0.416

-1.477 -0.639 -2.000 -1.688 -2.250 -1.250 -0.848 -0.639 -1.728 -1.313 -0.848 -1.515 -1.688 -1.250 -1.339 -0.639 -1.477 -0.848 -1.515 -1.148 -0.150 -0.688 -0.597 -2.000 -1.778 -2.000 -1.778 -0.333

-0.039 -0.017 -0.053 -0.045 -0.060 -0.033 0.024 0.018 0.193 0.146 -0.003 -0.005 0.146 -0.004 -0.004 -0.002 -0.005 -0.032 -0.057 -0.043 -0.006 -0.026 -0.023 -0.076 0.058 0.065 0.058 0.011

0.282 0.122 0.382 0.323 0.430 0.239 0.267 0.202 0.136 0.103 0.100 0.178 0.103 0.147 0.158 0.075 0.174 0.161 0.288 0.218 0.028 0.131 0.113 0.380 0.210 0.236 0.210 0.039

184.8 80.0 250.2 211.1 281.5 156.4 67.2 50.6 366.2 278.1 104.3 186.4 207.6 153.8 164.7 78.6 181.6 38.1 68.2 51.6 6.7 30.9 26.9 90.0 318.4 358.3 318.4 59.6

Cp Cs

p2 p2 p1 p1

p1 p1 p1 p1

s3 s3 s3 s3 s2 s3 s3 s3 s2 s2 s3 s3 s3 s2 s3 s3 s3 s3 s3 s3 s2 s3 s3 s3 s2 s2 s3 s2

Figure 1. Two-dimensional property map for 76 compounds

greatest importance in chemistry to understand what fundamental parameters regulate these interactions. A simple theory is to look at the interaction between two close atom pairs, either alike or otherwise. This is because it determines if an A atom prefers another A or Zn as its closest neighbor, which will result in the observed stable crystal structures of AiZnj compounds and property of the system. Equation 1 gives a quantity to describe such interaction of an unlike atom pair (AZn) in terms of a specific element property (or mechanism of behavior), with a reference state of an A-A pair and a Zn-Zn pair. Equation 2 just magnifies the interaction by the number of close unlike atom pairs in the system. The applied atomic environment approach gives geometrical information about the short-range atomic arrangements in the structures. Daams16 found low coordination numbers, CN < 9, for the p elements (compounds), CN numbers between 9 and 14 for the d elements, and CN > 12 for the s and f elements, which

Figure 2. Two-dimensional structure map for all binary zinc compounds

is quite close to the classification of the three structure types in this study. Therefore, compounds within each of the three structure types may share some common similarities in electron structures of short-range atoms. O4 and O5, based on R and T, respectively, were found strongly correlated to the property and the structure as shown in Figures 1 and 2. Therefore, both the property and structure may be regulated by R and T. Furthermore, a strong correlation between T and the selfdiffusion energy D17,18 was reported. So the diffusion of additives may play a key role in determining both the (16) Daams, J. L. C. In Intermetallic Compounds Principles and Practice, Volume 1-Principles; John Wiley & Sons: New York, 1995; pp 363-383. (17) Rice, S. A.; Nachtrieb, N. H. J. Chem. Phys. 1959, 31, 139. (18) Tiwari, G. P. Z. Metallkd. 1981, 72, 211.

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Wu et al.

bulk properties and the structure, which is in agreement with experiment.19 Similarly, the average atomic radius of a compound, (RA + RZn)/2, was strongly correlated to the shortest interatomic distance d (or bond length) of the compound for a few materials systems:16

d ) k1(RA + RZn)/2 + k2

(3)

where k1 and k2 are independent of the atomic sizes. From eqs 2 and 3, it is clear that O4 is proportional to the shortest interatomic distance d, which may suggest that the bond formation ability of additives (measured by d) is another key factor determining both the bulk properties and the structure. According to the first Hume-Rothery rule,20 solid solutions are not to be expected if the atomic sizes of the solvent and solute differ by more than 15%. It seems only when the size difference is large enough (or larger d), the structure of the solvent may no longer be able to be sustained and a new structure (of intermetallic compound) may be preferred. The slope of a straight line through the origin in Figure 1, L ) O5/O4) ∆T/∆R, is proportional to ∆D/d, which has the same units as a force. d is the shortest effective distance of an atomic diffusion step. L may, therefore, be interpreted as a quantity for the effective diffusion force. For compounds with similar d values, L and ∆D follow the same trend. In Figure 2, when a straight line from each compound point is connected to the origin, every compound will have its own L value. For most cases, when L is small, the compound tends to prefer very complex structures (with CN > 14). When L increases to a critical value, 1408.5 °C/au, which is the slope of the line that separates z1 and z2 zones, the compound tends to prefer a simpler geometry of atoms (with CN e 14). And this is when the A element additive (with regard to AiZnj) starts to show positive effect in reducing weight loss. The exact physical nature of L is not quite clear yet. It may be related to the kinetic energy of atoms. An AiZnj compound may experience phase change from solid to liquid, gas, and plasma, if heated from low to very high temperatures. This is because the kinetic energy of the atoms will increase with heating. When their kinetic energy values are high enough, the old structure can no longer be sustained, and new structures will be adopted. In general, the new structure will become simpler (like the structure in gas is simpler than that in liquid) because the atoms are dynamic enough to break some old bonds and to rearrange others. A few exceptional cases are mainly the rare earth elements, which do form a simple compound when L is less than 1408.5. But these compounds fail to show positive galvanizing effects. It is unclear why they do not fit in the found pattern. Few compounds located close to the origin in Figure 2 also form simple structures when L is less than 1408.5. It may because the A atom in such compound is very close to the Zn atom in size, which reduces the resistance to diffusion. Compounds that have even simpler structures (CN e 10) all fall in the z3 zone where the A atom is smaller than

the Zn atom. It is also very interesting that when L is negative there are only a few compounds forming. New galvanizing additive elements may be predicted if their correspondent binary Zn compounds are located within the z1 zone in Figure 2. It will be a straightforward application if it is known that the studied element forms at least one stable compound with Zn. In such case, at first the O4 and O5 values of the compound may be calculated by using eqs 1 and 2. If its O5/O4 is greater than 1408.5 and O4 > 0 (or this compound falls in the z1 zone in Figure 2), this element will become a potential candidate to reduce weight loss in galvanizing. However, if the compound formation is not clear, empirical methods such as Miedema’s approach for transition metals21 will be applied to predict the compound formation. Miedema’s approach is based on the enthalpy of formation, ∆H, by using two elemental properties of constituent chemical elements: the chemical potential for electronic charge and the electron density at the boundary of the Wigner-Seitz atomic cell. If ∆H is negative, there exists at least one stable compound in the system; otherwise there will be no compound forming. By applying this model, stable compounds are predicted in binary systems of Ru-Zn, Rh-Zn, Hf-Zn, Re-Zn, and Os-Zn. For simplicity the stoichiometry of the compound in each system is assumed as AZn in the study. The predictions are shown in Figure 2. Accordingly, elements such as Nb, Pt, Ta, Re, Os, Hf, Ru, and Rh are the potential candidates of new additives in steel hot dip galvanizing. Experiments to test the model prediction will be carried out in another study. V. Conclusions Two fundamental element properties, T and R, were found to be strongly correlated to both the galvanizing property of additive elements and the crystal structures of their correspondent binary Zn compounds. It is further suggested that diffusion may play a key role in both the galvanizing process and the formation of binary Zn compounds. When the effective diffusion force L in a compound is small, the compound prefers a more complex structure where CN > 14. When L is greater than 1408.5 °C/au, the compound tends to have a less complex structure where 10 < CN e 14. The performance of an additive element in galvanizing seems related to the effective diffusion capability of the element in the compound formation process. This study may provide a useful approach in the design of new chemicals when there are only limited bulk property data but extensive structure information. Acknowledgment. The authors would like to thank Dr.Robert A. Straunghan of IHPC, Singapore, for his advice and contribution in crystal structure classification using S-PLUS. We are also grateful to Dr. Pierre Villars of MPDS, Vitznau, Switzerland, for helpful discussions on his atomic environment approach. CM990243U

(19) Mackowiak, J.; Short, N. R. Int. Met. Rev. 1979, 1, 1. (20) Hume-Rothery, W.; Smallman, R. W.; Haworth, C. W. In The Structure of Metals and Alloys; The Metals and Metallurgy Trust of the Institute of Metals and the Institute of Metallurgists: London, 1969; pp 124-128.

(21) de Boer, F. R.; Boom, R.; Mattens, W. C. M.; Miedema, A R.; Niessen, A. K. In Cohesion in Metals; North-Holland Physics Publishing: Amsterdam, 1988; pp 720-746.