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A Simple Method for the Prediction of the Detonation Performances of Metal-Containing Explosives Yuan Wang,† Jichuan Zhang,† Hui Su,† Shenghua Li,*,† Shaowen Zhang,‡ and Siping Pang*,† †

School of Materials Science & Engineering, Beijing Institute of Technology, Beijing 100081, China School of Chemistry, Beijing Institute of Technology, Beijing 100081, China

‡

ABSTRACT: Accurate prediction to the detonation performances of different kinds of energetic materials has attracted significant attention in the area of high energy density materials (HEDMs). A common approach for the estimation of CHNO explosives is the Kamlet−Jacobs (K-J) equation. However, with the development of energetic materials, the components of explosives are no longer restricted to CHNO elements. In this study, we have extended the K-J equation to the calculation of certain metal-containing explosives. A new empirical method, in which metal elements are assumed to form metallic oxides, has been developed on the basis of the largest exothermic principle. In this method, metal oxides can be deemed as inert solids that release heat other than gases. To evaluate the prediction accuracy of new method, a commercial program EXPLO5 has been employed for the calculation. The difference involved in the ways of treating products has been taken into account, and the detonation parameters from two methods were subject to close comparison. The results suggest that the mean absolute values (MAVs) of relative deviation for detonation velocity (D) and detonation pressure (P) are less than 5%. Overall, this new method has exhibited excellent accuracy and simplicity, affording an efficient way to estimate the performance of explosives without relying on sophisticated computer programs. Therefore, it will be helpful in designing and synthesizing new metallic energetic compounds.

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INTRODUCTION Energetic compounds are one of the most important components of organics, and they generally possess the special properties of energy storage and stability. It is challenging to design and synthesize new energetic compounds, especially with substantially improved properties. The essential step for the development of new energetic compounds is to accurately predict their detonation properties, which often play an important role in energy levels and potential applications. In the past decades, excellent progress has been made to the prediction of detonation performances, and numerous equations have been proposed. Among them, The Kamlet-Jacobs equation was representative,1−4 which can be used to estimate the detonation velocity (D) and detonation pressure (P) of CHNO explosives. The empirical equation is fairly accurate, and there is generally less than 3% difference4 between the calculated results and the experimental data. It works very well for new high energy density materials (HEDMs), which are composed of C, H, N, and O elements. Notably, good accuracy could also be obtained when the K-J equation was extended to calculate F or Cl elements containing explosives.5 However, more wide-ranging energetic metal salts or energetic metal complexes are not accessible with such desk calculation. With the development of energetic materials, the compositions of explosives are no longer restricted to CHNO elements. Alkali metal salts,6−9 heavy metal salts,10 and metal coordination compounds11−13 have become new members of HEDMs. However, the traditional K-J equation cannot meet the rising © 2014 American Chemical Society

demand from emerging novel materials. Recently, a few coded programs like Cheetah14 and EXPLO515 have been developed for the calculation of organometallic compounds, but they usually cannot tolerate certain specific elements such as Ag, Cd, and so forth. With the most updated versions, the applicability of these programs has been improved; however, the scope of calculation is still limited, especially for metal-containing explosives; plus, the high cost of commercial programs also substantially restrict their applications. Herein, we report a simple and efficient method to the prediction of detonation performances for metal containing explosives. Many metallic explosives such as alkali metal salts, alkaline earth metal salts, and transition metal complexes have been analyzed by this method. In addition, the reliability of this novel method has also been demonstrated by comparing with EXPLO5 v 6.01,15 and the deviations of these two different methods have also been determined.

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THEORETICAL METHODS The famous K-J equation was deduced from the RUBY code,16 which uses BKW equation as the core algorithm.17,18 In the process of simplification, Kamlet proposed his own way to determine detonation products. Instead of the Gibbs free energy minimum method adopted by RUBY and EXPLO5,15,16 Received: March 22, 2014 Revised: May 12, 2014 Published: June 2, 2014 4575

dx.doi.org/10.1021/jp502857d | J. Phys. Chem. A 2014, 118, 4575−4581

The Journal of Physical Chemistry A

Article

Table 1. Heats of Formation of Detonation Productsa

a

compound

H2O

CO2

CO

NH3

Li2O

Na2O

K2O

HOF/kJ·mol−1 compound

−242 MgO

−393 CaO

−110.5 SrO

−46 BaO

−597.9 CuO

−416 CdO

−361 Ag2O

HOF/kJ·mol−1

−602

−635

−592

548

−156

−258

−31

The experimental data were obtained from NIST Chemistry WebBook.20

Table 2. Detonation Products of Explosives Estimated by Two Methods

a

explosive

detonation products (new method)

detonation products (EXPLO5)a

1−1a 1−2b 1−3a 1−4b 1−5c 1−6c 2−1a

0.5Li2O + 2.5H2O + 3N2 + 2C 0.5Na2O + 1.5H2O + 3N2 + 2C 0.5Li2O + 3H2O + 2.5N2 + 0.75CO2 + 0.25C 0.5Na2O + 2H2O + 2.5N2 + 0.75CO2 + 0.25C 0.5K2O + 2H2O + 2.5N2 + 0.75CO2 + 1.25C 0.5K2O + H2O + 3.5N2 + 1.25CO2 + 0.75C MgO + 5.5H2O + 1.33NH3 + 4.33N2 + 2C

2−2b

CaO + 4H2O + 1.33NH3 + 4.33N2 + 2C

2−3b 2−4c 2−5d

CaO + 3N2 + 0.5CO2 + 0.5C SrO + 4H2O + 1.33NH3 + 4.33N2 + 2C BaO + 4H2O + 1.33NH3 + 4.33N2 + 2C

0.5Li2CO3(l) + 1.48H2O + 2.67N2 + 0.66NH3 + 1.48C + 0.03H2 0.5Na2CO3 + 0.48H2O + 2.67N2 + 0.65NH3 + 1.48C + 0.03H2 0.5Li2CO3(l) + 2.73H2O + 2.46N2 + 0.08NH3 + 0.12CH2O2 + 0.15CO2 + 0.23CO + 0.02H2 0.5Na2CO3 + 1.77H2O + 2.46N2 + 0.07NH3 + 0.10CH2O2 + 0.14CO2 + 0.26CO + 0.02H2 0.5K2CO3 + 1.36H2O + 2.40N2 + 0.19NH3 + 0.29CH2O2 + 0.08CO2 + 0.39CO + 0.71C + 0.03H2 0.5K2CO3 + 0.78H2O + 3.47N2 + 0.06NH3 + 0.09CO2 + 0.31CO + 0.98C + 0.11CH2O2 Mg(OH)2 + 3.25H2O + 4.14N2 + 1.62NH3 + 0.34CH2O2 + 0.03CO2 + 0.46CO + 0.95C + 0.24H2 + 0.09HCN + 0.05CH3OH + 0.03C2H4 Ca(OH)2(l) + 2.10H2O + 4.19N2 + 1.54NH3 + 0.30CH2O2 + 0.23CO + 1.29C + 0.11H2 + 0.08HCN + 0.04CH3OH + 0.02C2H4 CaO(l) + 3N2 + 0.20CO2 + 0.61CO + 0.20C

2−6d 2−7d 2−8d 2−9d 2−10d 3−1a 3−2a 3−3a

BaO + 3H2O + 2NH3 + 4N2 + 2C BaO + 2H2O + 3N2 + 0.5CO2 + 0.5C BaO + 5H2O + 6N2 + CO2 + C BaO + 4H2O + 6N2 + 4C BaO + 5H2O + 6N2 + 4C Cu + 3H2O + 6N2 + 0.5CO2 + 3.5C Cu + 2.33NH3 + 4.33N2 + 2C 2Cu + 4H2O + 8NH3 + 10N2 + 4C

3−4b 3−5c

CdO + H2O + 2.67NH3 + 4.67N2 + 2C Ag + H2O + 1.67NH3 + 2.17N2 + 2C

BaO(l) + 3.04H2O + 4.19N2 + 1.56NH3 + 0.27CH2O2 + 0.02CO2 + 0.34CO + 1.22C + 0.19H2 + 0.07HCN + 0.04CH3OH BaO + 3H2O + 1.96NH3 + 4.02N2 + 2C BaO + 2H2O + 3N2 + 0.5O2 + C BaO + 4.3H2O + 5.97N2 + 0.60CH2O2 + 0.58 CO2 + 0.33CO + 0.48C BaO + 3.68H2O + 5.92N2 + 0.17NH3 + 0.07CO2 + 0.07CO + 3.81C BaO + 4.21H2O + 5.81N2 + 0.38NH3 + 0.16CH2O2 + 0.09CO2 + 0.28CO + 3.46C Cu(l) + 2.81H2O + 5.98N2 + 0.04NH3 + 0.16CO + 0.39CO2 + 3.32 C + 0.13CH2O2 Cu(l) + 2.30NH3 + 4.35N2 + 2C + 0.03H2 2 Cu(l) + 3.68H2O + 10.20N2 + 7.51NH3 + 0.16CO + 3.46C + 0.62H2 + 0.09HCN + 0.06CH2O2 + 0.06CH4 + 0.04CH3OH + 0.06C2H4

Blanks in the column are due to elements in these compounds (2−4c, 3−4b, and 3−5c) beyond the calculation capability of EXPLO5.

Kamlet, the corresponding products generated from detonation can be assumed in the following two equilibriums (Scheme 1): Scheme 1. Two Equilibriums Considered in the H2O−CO2 Arbitrary Theory

Kamlet’s method not only made the calculating process easier but also was not affected the accuracy. At the same time, EXPLO5 uses BKW equation as well. So, basically speaking, the K-J method shares the same origin with EXPLO5. Our method used the hypothesis of BKW equation and arbitrary theory of the K-J method to perform calculations. Metal atoms are treated as reductants in the molecules and the heat released in the process of oxidation reaction increases the temperature of gases. Calculating methods are explained in further detail below. Key equations concluded by Kamlet and Jacobs1−4 are given as follows: D = 1.01(NM1/2Q1/2)1/2 (1 + 1.30ρ0 )

(1)

P = 1.55ρ0 2 NM1/2Q1/2

(2)

Q=

ΔH0 = − 41.2 kcal/mol

(4)

H 2 + CO ⇌ H 2O + C ΔH0 = −31.4 kcal/mol

(5)

2CO ⇌ CO2 + C

As mentioned by Kamlet, for practical calculational purposes, equilibrium 5 may be considered as invariantly to the right at all loading densities under consideration. Reaction 4, on the other hand, is in a region of shifting equilibrium and may be considered as predominantly to the right only at the higher loading densities (i.e., greater than 1.6 or 1.7 g·cm−3).1 In practice, an H atom should have higher priority than a C atom, because 1 mol of H2O has a lower heat of formation than 0.5 mol of CO2 when 1 mol of O atom is consumed; furthermore, the N value in the K-J equation should also increase. Typically, when the K-J equation is employed for calculation, the overall process can be described as follows: for the explosives composed of C, H, N, and O elements, all N atoms are converted to N2; O atoms form H2O with H atoms first and then form CO2 with C atoms; the remaining C atoms are retained in solid state; if there are O atoms left, they will form O2.19

−[ΔHf (detonation products) − ΔHf (explosive)] formula weight of explosive (3)

To calculate the D and P values of a given compound, one should first determine its density (ρ), heat of formation (HOF), heat of detonation (Q), moles of detonation gases per gram of explosive (N), and average molecular weight of gases (M). According to the largest exothermic principle proposed by 4576



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EXPLO5 gives out more elaborate minor products. Their detonation products are covered in the following section. Alkali Metal Salts. Alkali metal salts are one of the most significant components in energetic salts, and they are served as precursors for alkylated derivatives or coloring agents in modern pyrotechnics.21,22 In addition, they are also important intermediates for the synthesis of nonmetal energetic salts.8,23 However, the energetic properties of alkali metal salts are not comprehensively investigated in most cases.24 Proper evaluation to the energetic performances of such energetic compounds is highly desirable. In this work, a series of lithium salts, sodium salts, and potassium salts have been extensively studied (Scheme 2), and the calculated results are shown in Table 3. Deviations of D and P can be determined by subtracting K-J results from the EXPLO5 results. The relative deviations (RD) are the ratios of the deviations to K-J values. On the basis of the results of D and P, we conclude that the energetic levels of these compounds are between TNT and RDX, suggesting that they should be decent energetic materials. Notably, it appears that the detonation products estimated by two methods are different, as illustrated in Table 2. Contrast to the new method, EXPLO5 treats metal atoms as carbonates instead of oxides, which apparently has led to the increase of Q and decrease of gas release, simultaneously. These two aspects show very different effects on the D and P. On one hand, increased Q contributes to the increase of D and P. On the other hand, less gas products lead to the decrease of N and M, which results in the negative influence. Therefore, the final values of D and P are related to the combination of Q, N, and M. Interestingly, the smallest deviation for D is 0.02 km·s−1 in compound 1−3a, which has exhibited the smallest relative deviation as well. In addition, it appears that compound 1−5c has the finest accordance of P, exhibiting a deviation of 0.01 GPa, almost negligible. On the other hand, the large relative deviations are generally about 10%; however, the large deviations for both D and P are not evident in one compound simultaneously. The mean absolute values of relative deviation for D and P are 3.67% and 5.89%, and the standard deviations (SD) of D and P are 0.39 km·s−1 and 1.58 GPa, respectively. Alkaline Earth Metal Salts. Alkaline earth metals are similar to alkali metals in terms of chemical properties, and they are extensively used in pyrotechnics and primary explosives.10,25 Most studies on these special metal salts have been conducted to mainly explore their configurations and thermal stabilities.10,26 In this work, we have specifically predicted the energetic performances of alkaline earth metal salts, which

To preserve Kamlet’s method, the H2O−CO2 arbitrary theory is employed to determine the detonation products from metal-containing explosives. In most cases, metal atoms are converted to their oxidation states, emitting more heat after detonation. Otherwise, metal atoms can be treated as their reduction state, if the HOF of metallic oxides is higher than that of H2O, or there is no O atom in the molecule. Besides, O atoms form H2O with H atoms first and the remaining ones form CO2 with C atoms. However, if the amount of O atoms is not sufficient to oxidize all H atoms, the remaining H atoms can produce NH3 with N atoms, and the rest of the N atoms are released as N2 gas. On the other hand, the remaining C atoms are retained in the solid state if they are not completely oxidized by O atoms. If there are redundant O atoms, however, they can be expelled as O2. The heat of formation for detonation products was summarized in Table 1. Metallic oxides are treated as inert solids, thus no gas is produced, only heat emits in the explosion process. The detonation products from the explosives examined in this study are listed in Table 2.

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RESULTS AND DISCUSSION Table 2 shows the different ways of treating products adopted by the new method and EXPLO5. Metallic products, deduced Scheme 2. Molecular Formulas of Alkali Metal Salts Calculated in the Study

by the different methods, are diverse. However, the main gas products including H2O and N2 are basically the same although Table 3. Results and Deviations of Alkali Metal Salts compound g

1−1a 1−2bg 1−3ah 1−4bh 1−5ci 1−6cj

ρ/g·cm−3 a

HOF/kJ·mol−1

Q/J·g−1 b

D/km·s−1 b

P/GPab

D(D)/km·s−1 c

D(P)/GPad

RD(D)/%e

RD(P)/%f

1.76 1.94 1.61 1.73 1.92 1.92

−410 9k −610k −360k 438l 256m

2940.18/3456.03 3491.87/4402.70 4055.43/4497.56 3622.83/4435.52 6950.5/7680.22 5148.55/6024.98

6.80/7.54 7.01/7.62 7.37/7.39 7.03/6.99 8.26/8.33 7.78/8.04

20.19/19.38 22.77/23.78 22.51/20.10 21.43/19.23 31.46/31.47 27.87/28.38

0.74 0.61 0.02 −0.05 0.07 0.04

−0.82 1.01 −2.41 −2.19 0.01 −1.65

10.96 8.71 0.27 −0.66 0.84 0.56

−4.04 4.44 −10.69 −10.24 0.03 −5.92

k

a

Crystal density. bValues in front of slashes refer to results calculated by the new method and ones behind slashes refer to results calculated by EXPLO5. cDeviation of detonation velocity. dDeviation of detonation pressure. eRelative deviation of detonation velocity. fRelative deviation of detonation pressure. gReference 6. hReference 7. iReference 8. jReference 9. kCalculated values based on measured heats of combustion. lCalculated results obtained by Gaussian 03 combined with the Born−Haber cycle method. mCalculated results obtained by Gaussian 09 with the CBS-4 M method. 4577



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Scheme 3. Molecular Formulas of Alkaline Earth Metal Salts Calculated in the Study

Table 4. Results and Deviations of Alkaline Earth Metal Salts compound b

2−1a 2−2bb 2−3bc 2−4cb 2−5db 2−6dd 2−7dd 2−8dd 2−9dd 2−10dd

ρ/g·cm−3 a

HOF/kJ·mol−1 f

Q/J·g−1

D/km·s−1

P/GPa

D(D)/km·s−1

D(P)/GPa

RD(D)/%

RD(P)/%

1.68 1.90 2.00e 2.09 2.21 2.13 2.91 2.33 2.30 2.15

955 1530 32.8g 1140 895 −925 −660 −797 −612 −317

9606.95/9598.25 10791.67/9715.88 5141.58/4424.17 8036.48 6286.13/5998.13 1168.21/1209.63 1886.20/1278.55 2896.26/2816.06 2047.57/2070.43 3135.81/3093.05

9.17/9.07 9.81/10.30 7.29/7.62 9.06 8.30/8.22 5.22/5.69 6.78/6.51 7.49/7.57 6.31/6.75 6.83/6.96

35.75/34.49 44.10/46.79 25.03/25.63 39.67 34.27/35.04 13.27/13.05 25.97/23.53 28.66/28.72 20.23/20.69 22.86/22.32

−0.09 0.49 0.33

−1.26 2.7 0.6

−1.04 4.98 4.56

−3.54 6.12 2.4

−0.08 0.47 −0.27 0.08 0.44 0.13

0.77 −0.22 −2.44 0.06 0.46 −0.54

−0.98 9.03 −3.98 1.09 6.9 1.96

2.25 −1.66 −9.39 0.21 2.25 −2.36

a

Crystal density. bReference 26. cReference 25. dReference 10. eCalculated value, method not mentioned. fCalculated values based on measured heats of combustion. gCalculated results obtained by Gaussian 09 with the CBS-4 M method.

maximum deviations for D are 0.08 and 0.49 km·s−1; for P are +0.06 and −2.44 GPa. The minimum relative deviations for D and P are −0.98% and +0.21%, respectively. For compound 2− 8d, however, these two methods have similar detonation products; thus the deviations between them turned out to be minimum. The maximum relative deviation for compound 2− 7d is −9.39%, which presumably should be due to the unusual coexistence of O2 and C in the products, as estimated by

should serve as a salutary complement for this series. The molecular formulas were demonstrated in Scheme 3, and the Q, D, P, and their deviations were summarized in Table 4. As shown in Table 4, compounds 2−1a, 2−2b, and 2−4c have exhibited large and positive Q values, which is mainly due to much water release and low HOF of the corresponding metallic oxides. Consequently, the values of D and P have reached a high level in these cases. The minimum and 4578



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Scheme 4. Molecular Formulas of Transition Metal Complexes Calculated in the Study

Chart 1. Detonation Velocities of Energetic Compounds Estimated by the New Method and EXPLO5

Chart 2. Detonation Pressures of Energetic Compounds Estimated by the New Method and EXPLO5

EXPLO5. Most of the relative deviations are smaller than 5%, and the mean absolute values of relative deviation for D and P are 3.84% and 3.35%, respectively. The SD for D and P are 0.30 km·s−1 and 1.28 GPa, respectively. Transition Metal Complexes. Because of unique coordinating characters of transition metals, numerous energetic complexes have been synthesized following the development of HEDMs.11−13,27 These complexes extended the area of metal containing explosive apart from energetic metal salts and have became a new research hotspot.28,29 For instance, copper azole complexes are deemed as promising primary explosives, because they are adequately effective yet more environmentbenign compared with their Pb or Hg counterparts.13,27 Therefore, a thorough evaluation to the properties of such complexes is highly desirable. The molecular formulas of this series are shown in Scheme 4, and the Q, D, and P values of complexes containing Cu, Cd, and Ag elements were summarized in Table 5.

It is worth noting that Cu and Ag atoms were treated as their metallic state according to the H2O−CO2 arbitrary theory, because the corresponding oxides possess higher HOF than H2O. In other words, if 1 mol of O atoms is consumed, much more heat could be released when O atoms react with H atoms rather than metal atoms. To our delight, the products deduced by EXPLO5 have confirmed that this approach is reasonable. On the basis of the results shown in Table 5, the detonation parameters of Cu complexes calculated by two methods are adequately close. The minimum and maximum relative deviations for D and P are 2.06% (min) and 6.64% (max), 0.37% (min) and −5.08% (max). Compared with alkali or alkaline earth metal compounds, the Cu derivatives (3−1a, 3− 2a, and 3−3a) have exhibited lower maximum relative deviations. In addition, the SD of D and P in this series are 0.29 km·s−1 and 0.70 GPa, respectively. One of the major

Table 5. Results and Deviations of Transition Metal Complexes complex b

3−1A 3−2Ac 3−3Ad 3−4Bd 3−5Ce

ρ/g·cma f

2.07 1.99f 1.75g 2.11g 2.47f

HOF/kJ·mol−1 a

Q/J·g−1

D/km·s−1

P/GPa

D(D)/km·s−1

D(P)/GPa

RD(D)/%

RD(P)/%

−83.7 367 2979 1793 −263

2396.57/2366.11 1907.25/1898.64 6501.43/6426.88 6969.61 232.91

6.76/7.00 6.07/6.47 8.21/8.37 8.23 3.58

21.92/20.80 17.32/16.83 29.36/29.47 32.84 6.72

0.24 0.4 0.17

−1.11 −0.49 0.11

3.56 6.64 2.06

−5.08 −2.81 0.37

a

Calculated values based on measured heats of combustion. bReference 11. cReference 12. dReference 27. eReference 13. fCrystal density. Measured with gas pycnometer, 25 °C.

g

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results, which were generated by both the new method and the EXPLO5 program, are very close for compounds 1−3a, 1−4b, 1−5c, and 2−8d. Interestingly, as demonstrated by the deviations and relative deviations of D, there seems to be a good accordance between these two sets of data (Figure 1). Specifically, it appears that the lines are basically above zero, which indicates that it is more likely for EXPLO5 to give higher detonation velocities. Chart 2 shows the statistic detonation pressures of compounds studied, ranging from 20 to 45 GPa. Among them, compounds 1−5c, 2−6d, 2−8d, and 3−3a have exhibited nearly identical results using these two methods. As illustrated in Figure 2, it appears that the deviations of P are floating around zero, which indicates that the results obtained from the extended K-J equation are in good agreement with the ones from EXPLO5, even for different kinds of metallic derivatives. Overall, three series of energetic compounds have been examined in the study, and the D and P deviations are illustrated in Table 6. Notably, it appears that the MAVs of deviations for D are at the same level in all three series, yet the values for P have decreased in sequence. The MAVs of RD are lower than 5%, except for the P value in the first series. Theoretically, the standard deviation (SD) can disclose the extent of data deviation from the average. As shown in Table 6, the second and third series seem to exhibit lower SDs than the first series. Hence, the latter two series should afford more intensive results. In addition, the last column in the table also indicates that all compounds have exhibited DMAV of 0.26 km· s−1 for D, 1.05 GPa for P, and RDMAV of 3.82% for D and 4.10% for P. Compared with the commercial EXPLO5 program, the new approach developed has exhibited decent accuracy, affording a convenient and efficient method for the calculation of metallic energetic materials.

Figure 1. Deviations and relative deviations of detonation velocity between two methods.

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Figure 2. Deviations and relative deviations of detonation pressure between two methods.

CONCLUSION

In conclusion, we have developed a new method for the calculation of metal-containing explosives. The method has exhibited excellent accuracy and simplicity, affording an efficient way to estimate the energetic performance of metallic explosives, without relying on a computer program. When the new method is compared with the commercial program EXPLO5 v 6.01, the mean absolute values (MAVs) of relative deviation for detonation velocity (D) and detonation pressure (P) are less than 5%. In addition, the method can also estimate metal complexes containing special elements such as Cd and Ag, which are not accessible with the commercial program. We anticipate that the new method will be extended to any metal element, making it a powerful tool for the design and synthesis of novel energetic materials.

advantages of our method is that it can be employed to estimate metal complexes containing special elements such as Cd and Ag, which cannot be evaluated with the commercial program. For example, due to the high density and detonation heat, the Cd complex 3−4b possesses the highest P value in this series. In contrast, the Ag complex 3−5c has exhibited the lowest P value, presumably because of its low HOF and less gas production. The calculated D and P and their deviations and relative deviations have been depicted in Charts 1 and 2 and Figures 1 and 2, respectively. Chart 1 shows the D values of compounds examined in this study, which are within the range 6−10 km· s−1, a universal interval for general HEDMs. The estimated Table 6. D and P Deviations of the Three Series 1 a

DMAV RDMAVb SDc

2

3

all

D

P

D

P

D

P

D

P

0.26 3.67 0.39

1.35 5.89 1.58

0.26 3.84 0.30

1.00 3.35 1.28

0.27 4.09 0.29

0.57 2.75 0.70

0.26 3.82 0.34

1.05 4.10 1.35

Refer to mean average values of deviation with unit of km·s−1 (D) or GPa (P). bRefer to mean average values of relative deviation with unit of %. Refer to standard deviation with unit of km·s−1 (D) or GPa (P).

a c

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AUTHOR INFORMATION

Corresponding Authors

*S. Li: tel, +86-010-68918892; e-mail, [email protected]. *S. Pang: tel, +86-010-68913038; e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the opening project of State Key Laboratory of Science and Technology (Beijing Institute of Technology). The opening project number is ZDKT12-03.

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REFERENCES

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