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材料研究学报  2014, Vol. 28 Issue (1): 31-43    DOI: 10.11901/1005.3093.2013.663
  本期目录 | 过刊浏览 |
Miedema模型在含O和S熔体与合金中的扩展与应用*
陈伟亮,,宁,唐昭辉,丁学勇()
东北大学材料与冶金学院 沈阳 110004
Extension and Application of Miedema’s Model in O and S Containing Melts and Alloys
Weiliang CHEN,Ning ZHANG,Zhaohui TANG,Xueyong DING()
School of Materials and Metallurgy, Northeastern University, Shenyang 110004
引用本文:

陈伟亮,,宁,唐昭辉,丁学勇. Miedema模型在含O和S熔体与合金中的扩展与应用*[J]. 材料研究学报, 2014, 28(1): 31-43.
Weiliang CHEN, Ning ZHANG, Zhaohui TANG, Xueyong DING, . Extension and Application of Miedema’s Model in O and S Containing Melts and Alloys[J]. Chinese Journal of Materials Research, 2014, 28(1): 31-43.

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摘要: 

将Miedema模型与实验数据相结合得到适于Miedema模型的O和S的参数(O: 电负性7.04、电子密度6.03、摩尔体积4.59; S: 电负性5.8、电子密度3.24、摩尔体积6.97), 计算了141种O的二元化合物和145种S的二元化合物生成焓其平均绝对误差(MAPE)分别为36.8%、32.4%。 结合Ding导出的三元系相互作用系数计算模型, 计算了1873 K时Fe基熔体中O和S与其它元素之间的相互作用系数。与实验数据的比较表明, 除个别元素外, 计算值与实验值之间误差不大且变化趋势比较一致。将误差较大的Nb、Ag、Pt的电负性参数由原来的4.05、4.35、5.65修正为4.31、4.17、5.57, 使用Miedema模型的计算精度有很大的提高。

关键词 材料科学基础学科Miedema模型含O和S熔体与合金相互作用系数参数的修正    
Abstract

Combined Miedema’s model with experimental data provided by Kleppa, the parameters of oxygen and sulfur which were satisfied with Miedema’s model were derived: Oxgen: electronegativity 7.04, electronic density 6.03, molar volume 4.59; Sulfur: electronegativity 5.8, electronic density 3.24, and molar volume 6.97. In comparison with results from literature, those parameters had been turned out to be highly reasonable to Miedema’s model. The mean absolute percentage error of enthalpies of formation of binary alloying oxides and sulfides were 36.8%, 34.2% respectively. Combining Ding’s model, the activities and interaction coefficients between oxygen and other elements of Fe-based alloying melt in 1873 K were derived and further compared with available experimental data. Calculated results were confirmed to be in good agreement with available experimental data, except some special cases. Therefore the long-term problem related with the parameters of oxygen and sulfur for Miedema’s model has been resolved successfully by this method. In particular, the special cases Nb, Pt, Ag-their electronegativities(4.05, 5.65, 4.35) were revised to be 4.31, 5.57 and 4.17, respectively, and the revised parameters were much more reasonable than the original parameters.

Key wordsfoundational discipline in materials science    Miedema’s model    oxygen and sulfur containing melts and alloys    interaction coefficients    revision of parameters
收稿日期: 2013-09-12     
基金资助:*国家自然科学基金51174048 资助项目。
图1  过渡元素氧化物生成焓实验值与计算值的比较
Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ] Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ]
Sc2O3 -381.764 -345.005 -341.329 CeO2 -362.889 -346.538 -348.575
Y2O3 -355.439 -350.970 -349.580 Ce2O3 -359.238 -351.035 -350.514
La2O3 -358.740 -350.775 -350.702 CeO1.72 -366.048 -351.863 -352.526
TiO -271.332 -320.792 -302.888 CeO1.83 -364.993 -350.472 -351.696
TiO2 -314.916 -305.285 -293.060 Pr2O3 -361.931 -392.932 -382.518
Ti2O3 -300.026 -326.757 -311.466 Pr7O12 -342.632 -387.898 -378.967
Ti3O5 -318.643 -321.200 -306.972 PrO1.833 -333.066 -383.199 -375.059
Ti4O7 -309.502 -317.685 -303.979 PrO2 -316.450 -375.025 -367.933
ZrO2 -365.821 -338.979 -330.139 Nd2O3 -361.581 -350.593 -349.672
HfO2 -381.581 -351.037 -339.316 Sm2O3 -364.728 -351.412 -349.987
VO -215.895 -261.029 -241.936 Eu2O3 -332.544 -351.265 -349.852
V2O3 -243.760 -258.008 -241.508 EuO -295.00 -324.117 -320.167
V2O4 -237.860 -236.011 -222.423 Gd2O3 -365.380 -350.970 -349.580
V2O5 -221.513 -211.273 -200.009 TbO1.72 -350.410 -350.455 -349.799
NbO -209.827 -306.656 -283.019 TbO1.81 -342.314 -348.633 -348.452
NbO2 -264.987 -295.157 -276.932 TbO1.83 -339.958 -348.142 -348.064
Nb2O5 -271.362 -268.916 -253.588 TbO2 -323.842 -342.916 -343.665
Ta2O5 -292.282 -267.213 -252.517 Tb2O3 -373.045 -351.597 -349.714
CrO2 -199.298 -185.376 -170.951 Ho2O3 -376.142 -347.335 -345.757
CrO3 -147.382 -146.466 -135.999 Tm2O3 -377.732 -349.348 -347.184
Cr2O3 -227.940 -204.957 -187.777 Yb2O3 -335.159 -348.651 -346.538
MoO2 -196.313 -214.030 -194.366 Lu2O3 -375.640 -352.388 -349.560
MoO3 -186.272 -174.241 -159.528 CaO -317.544 -283.597 -292.851
WO2 -196.564 -200.640 -179.461 CaO2 -217.568 -299.816 -314.971
WO2.72 -209.987 -173.865 -156.530 SrO -296.018 -275.276 -286.468
WO2.9 -210.273 -167.435 -150.915 SrO2 -211.153 -306.869 -324.179
WO2.96 -210.848 -165.346 -149.085 Dy2O3 -372.620 -350.333 -348.545
WO3 -192.883 -163.970 -147.877 Er2O3 -379.572 -350.715 -348.450
MnO -192.611 -220.677 -206.763 Pt2O3 -17.200 -123.888 -109.852
Mn2O -173.343 -172.952 -160.001 Pm203 -362.00 -354.350 -352.716
Mn2O3 -191.800 -214.350 -202.843 Al2O3 -335.138 -133.255 -135.980
Mn3O4 -198.257 -219.218 -206.851 Li2O -199.577 -144.818 -150.632
MnO2 -173.343 -193.831 -184.631 Li2O2 -158.155 -185.273 -195.531
MnO3.5 -81.009 -136.888 -131.518 NaO2 -86.888 -150.244 -168.986
TcO2 -144.348 -142.045 -125.833 Na2O -139.327 -111.831 -121.998
ReO2 -149.648 -154.220 -134.557 K2O -120.499 -101.843 -113.543
ReO3 -147.277 -125.425 -110.314 K2O2 -123.846 -148.310 -165.773
Re2O7 -140.350 -113.029 -99.633 RbO2 -92.885 -165.548 -188.489
表1  氧化物生成焓的结果比较
Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ] Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ]
Fe0.947O -136.759 -181.379 -162.284 Rb2O -113.0 -99.418 -111.251
FeO -136.022 -180.635 -161.407 RbO -102.500 -145.340 -162.871
Fe2O3 -164.850 -175.606 -158.481 Rb2O3 -105 -164.494 -185.603
Fe3O4 -159.769 -179.547 -161.570 CsO2 -95.395 -165.765 -188.838
RuO2 -101.671 -130.929 -114.703 Cs2O -115.325 -96.347 -108.208
OsO2 -98.324 -133.493 -115.745 Cs2O3 -104.014 -161.853 -182.874
OsO4 -78.820 -88.202 -77.356 BeO -304.177 -70.594 -65.942
CoO -118.972 -158.652 -142.658 MgO -300.621 -177.756 -183.611
Co3O4 -130.003 -156.938 -142.119 ZnO -175.230 -124.300 -128.760
Rh2O3 -71.128 -139.034 -124.998 CdO -129.495 -117.887 -125.878
Rh2O -32.00 -104.419 -91.931 HgO -45.395 -101.212 -110.577
RhO -45.00 -138.666 -123.457 B2O3 -254.387 -52.474 -46.710
IrO2 -80.891 -121.620 -106.023 Ga2O3 -217.819 -133.261 -139.356
NiO -119.851 -148.453 -133.407 In2O3 -185.158 -127.937 -140.029
PdO -57.739 -127.772 -118.532 Tl2O -56.345 -74.196 -82.719
CuO -78.032 -146.924 -145.455 Tl2O3 -78.910 -113.520 -128.458
Cu2O -56.902 -117.606 -114.807 SiO2 -291.977 -89.570 -90.912
Ag2O -10.350 -101.987 -104.071 GeO2 -193.301 -86.068 -92.797
Au2O3 -0.669 -99.794 -98.720 SnO -142.885 -110.728 -119.478
ThO2 -408.805 -369.414 -365.369 SnO2 -193.608 -118.285 -129.519
UO2 -361.633 -313.713 -301.150 PbO -109.031 -91.065 -104.280
UO3 -305.746 -264.824 -256.586 PbO2 -91.490 -99.740 -115.816
U3O8 -324.983 -281.594 -272.158 Pb2O3 -98.340 -100.222 -115.600
U4O9 -345.705 -302.423 -291.146 Pb3O4 -102.669 -98.611 -113.466
PuO -282.420 -304.615 -291.869 As2O3 -130.959 -85.496 -90.205
PuO2 -351.944 -299.882 -292.039 As2O5 -132.096 -75.370 -80.510
Pu2O3 -359.824 -316.338 -305.879 Sb2O3 -144.061 -94.780 -106.615
BaO -276.772 -278.500 -289.899 Sb2O4 -151.192 -93.831 -106.266
BaO2 -211.431 -316.987 -334.600 Sb2O5 -138.843 -88.985 -101.335
Sc2O3 -381.764 -345.005 -341.329 Bi2O3 -114.776 -97.903 -113.273
La2O3 -358.740 -350.775 -350.702 P2O5 -214.995 -36.955 -36.338
续表1  氧化物生成焓的结果比较
图2  过渡元素硫化物生成焓实验值与计算值之间的比较
Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ] Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ]
LaS -228.030 -223.613 -225.623 IrS2.667 -45.004 -30.391 -25.352
La2S3 -244.350 -237.854 -231.552 IrS3 -52.512 -28.090 -23.323
TiS -135.981 -185.881 -178.313 Ir2S3 -42.012 -39.747 -34.454
TiS2 -135.701 -163.1533 -146.881 NiS0.840 -44.804 -57.282 -52.221
TiS3 -104.751 -128.902 -113.422 NiS -43.935 -57.597 -51.612
Ti2S3 -123.603 -180.455 -166.413 NiS2 -43.801 -46.436 -39.411
ZrS2 -192.464 -198.988 -183.623 Ni3S2 -43.266 -54.724 -51.012
TaS2 -117.995 -141.454 -125.194 Ni3S4 -43.042 -55.023 -48.023
CrS -73.886 -87.913 -77.945 Ni0.958S -47.603 -57.451 -51.274
CrS1.170 -76.161 -86.688 -75.702 Ni7S6 -44.834 -57.392 -52.213
CrS1.2 -70.012 -86.329 -75.211 PdS -44.055 -64.981 -64.062
CrS1.330 -67.092 -84.432 -72.882 PdS2 -30.273 -56.587 -52.431
Cr2S3 -67.204 -81.410 -69.583 Pd3S -24.131 -39.157 -41.613
MoS2 -92.051 -78.280 -65.012 Pd16S7 -26.802 -47.248 -49.723
MoS3 -77.402 -61.621 -50.093 Pd4S -22.083 -31.319 -33.432
Mo2S3 -81.424 -86.959 -73.912 PtS -41.954 -49.431 -48.161
WS2 -86.473 -65.340 -52.651 PtS2 -36.820 -43.503 -39.802
MnS -107.101 -109.966 -101.182 CuS -26.553 -63.528 -54.554
MnS2 -74.612 -89.471 -77.833 Cu2S -27.062 -54.238 -49.625
ReS2 -59.553 -40.590 -31.264 Ag2S -10.861 -48.996 -44.677
ReS3 -52.092 -31.937 -24.093 ThS -197.703 -225.789 -226.55
Re2S7 -50.161 -28.554 -21.452 ThS2 -208.674 -230.375 -216.587
Fe0.877S -56.192 -66.604 -57.201 Th2S3 -216.803 -239.228 -231.366
Fe0.9S -50.463 -66.812 -57.522 US -158.992 -183.131 -178.075
Fe0.920S -50.684 -66.961 -57.772 US2 -175.732 -170.438 -155.153
表2  硫化物生成焓的结果比较
Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ] Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ]
Fe0.940S -50.842 -67.080 -57.993 U2S3 -170.803 -184.121 -172.082
Fe0.960S -50.641 -67.173 -58.193 PuS -219.664 -186.726 -181.671
Fe0.980S -50.863 -67.239 -58.362 Pu2S3 -197.903 -185.014 -172.994
FeS -50.844 -67.282 -58.513 SrS -234.303 -210.985 -214.153
FeS2 -57.181 -54.830 -45.092 BaS -230.122 -218.100 -223.112
RuS2 -68.622 -37.259 -30.421 CaS -236.601 -211.529 -212.552
OsS2 -49.233 -34.694 -27.462 PrS -225.944 -244.154 -242.091
CoS0.890 -50.034 -61.243 -54.992 Pr3S4 -222.053 -249.773 -240.971
CoS -49.002 -61.307 -54.421 NdS -225.942 -223.330 -224.300
CoS2 -51.042 -49.469 -41.593 Nd2S3 -237.601 -234.611 -227.102
Co3S4 -68.373 -58.593 -50.663 Rh2S3 -26.383 -52.541 -47.043
IrS2 -44.353 -35.719 -30.271 WS2 -86.393 -65.340 -52.654
Ge2S3 -52.002 -32.249 -24.131 NbS2 -118.154 -141.094 -124.652
HgS -26.672 -46.955 -39.224 NbS -105.004 -158.961 -149.731
InS -66.941 -62.771 -54.903 Nb2S3 -118.003 -155.364 -140.662
In2S3 -71.133 -64.215 -54.051 SmS -215.483 -223.494 -224.133
In5S6 -70.372 -64.481 -55.462 YS -230.003 -223.309 -223.872
InS1.33 -72.103 -64.691 -55.093 VS -142.124 -129.545 -119.553
P4S3 -32.031 4.771 8.614 CeS -228.003 -223.641 -225.182
P4S5 -33.885 4.999 8.595 Ce2S3 -237.652 -236.535 -229.673
P4S6 -34.723 5.000 8.5922 CeS1.333 -236.122 -235.838 -231.604
P4S7 -29.395 4.590 7.661 DyS -230.002 -222.817 -222.816
P4S10 -22.094 3.838 6.262 Dy2S3 -244.001 -231.454 -222.893
Sb2S3 -28.352 -38.733 -29.953 ErS -230.003 -222.712 -222.332
SiS2 -71.131 -23.702 -16.014 Er2S3 -247.004 -230.369 -221.421
SnS -53.971 -52.468 -44.832 EuS -209.005 -223.433 -224.042
SnS2 -51.182 -51.117 -40.931 EuS1.333 -212.024 -233.861 -228.534
Sn2S3 -52.723 -54.212 -44.602 GdS -230.003 -223.309 -223.875
Sn3S4 -52.904 -54.445 -45.303 Gd2S3 -241.002 -233.474 -225.512
Tl2S -31.663 -39.799 -35.414 HfS2 -195.001 -201.736 -185.451
ZnS -95.922 -57.093 -48.492 HfS3 -156.003 -163.354 -146.022
Na2S -122.031 -78.327 -76.674 HoS -230.004 -220.921 -220.703
Na2S2 -98.324 -107.633 -101.457 Ho2S3 -245.002 -229.097 -220.384
Na2S3 -86.533 -109.608 -99.568 LuS -230.001 -223.733 -222.932
Na2S4 -68.552 -101.1412 -89.563 Lu2S3 -249.005 -230.149 -220.721
K2S2 -107.752 -109.043 -105.312 AsS -14.054 -24.198 -17.392
K2S3 -93.564 -120.019 -112.573 As2S3 -16.603 -24.234 -16.743
K2S -125.523 -75.100 -73.761 AlS -132.002 -57.115 -48.274
K2S4 -77.622 -118.078 -107.903 Al2S3 -144.801 -54.740 -44.522
续表2-1  硫化物生成焓的结果比较
Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ] Comp Δ H e x p Δ H c a l Δ H l i t [ 10 ]
K2S5 -70.86 -110.518 -99.005 B2S3 -50.463 7.553 12.401
K2S6 -58.533 -101.255 -89.402 Bi2S3 -28.624 -44.812 -35.282
BeS -117.152 -4.354 2.301 CdS -74.683 -57.632 -49.593
MgS -172.864 -103.605 -95.803 EuS -209.202 -149.488 -145.002
PbS -49.323 -44.049 -36.234 GaS -104.601 -60.910 -52.562
SiS2 -78.331 -23.702 -16.011 Ga2S3 -103.262 -59.830 -49.661
Rb2S -121.333 -74.446 -73.254 GeS2 -52.304 -29.147 -21.292
Cs2S -114.003 -73.184 -72.101 GeS -38.001 -33.246 -25.873
Li2S -223.004 -98.996 -98.045
续表2-2  硫化物生成焓的结果比较
图3  Fe 基溶液1873 K时第五主族元素与对应的 ε O j 实验值与计算值之间的关系
Element Lit[10] Cal Exp[11] Element Lit[10] Cal Exp[11]
Ca -28.38 -23.85 Be 12.02 14.13
Sc -20.16 -18.11 B 20.13 21.91 -13.20
Ti -15.82 -15.55 C 32.21 34.90 -19.96
V -10.44 -10.48 N 42.90 46.91 -7.30
Cr -4.56 -4.70 -11.68 Na -20.10 -14.67
Mn -7.63 -6.90 -4.73 Mg -9.61 -5.72
Co 2.92 3.44 1.89 Al 5.49 8.71
Ni 4.66 5.36 1.40 Si 13.04 16.09 -7.09
Cu -3.26 -0.58 -3.56 P 27.94 30.88 9.36
Sr -31.73 -26.84 K -28.47 -22.69
Y -21.50 -18.88 Zn 1.71 5.39
Zr -17.67 -16.54 Ga 3.44 7.21
Nb -12.50 -13.01 Ge 9.67 13.61
Mo -4.55 -5.12 1.26 As 15.13 18.85
Tc 6.58 6.85 Rb -30.84 -25.04
Ru 8.42 8.67 Cd -0.59 3.70
Rh 8.45 9.38 5.08 In -1.92 2.73
Pd 9.12 11.02 -4.81 Sn 2.54 6.99 -6.50
Ag -5.84 -2.12 -5.81 Sb 5.80 10.45 -12.70
Ba -33.63 -28.68 Cs -33.09 -27.28
La -22.65 -19.75 Hg 0.12 4.64
Hf -17.32 -16.72 Tl -4.14 0.91
Ta -12.52 -12.92 Pb -1.95 3.16
W -2.27 -2.95 4.52 Bi -0.56 4.54
Re 4.58 4.28 Dy -21.19 -18.66
Os 8.40 8.45 Ho -21.20 -18.65
Ir 11.46 11.94 Er -20.90 -18.45
Pt 13.67 14.79 1.52 Tm -20.91 -18.47
Au 7.32 10.20 -8.18 Yb -20.92 -18.48
Nd -21.84 -19.13 Lu -20.64 -18.31
Pm -21.47 -18.87 Th -18.99 -16.94
Sm -21.50 -18.87 U -14.38 -13.76
Eu -21.50 -18.87 Pu -16.24 -15.04
Gd -21.50 -18.88 Ce -22.23 -19.42
Tb -21.18 -18.64 Pr -21.85 -19.13
Li -14.48 -10.01 H 18.97 22.72 3.98
表3   ε O j 实验值与计算值的比较
图4  Fe 基溶液1873 K时第四周期元素与对应的 ε O j 实验值与计算值之间的关系
图5  Fe 基溶液1873 K时第五周期元素与对应的 ε O j 实验值与计算值之间的关系
图6  Fe 基溶液1873 K时第六周期元素与对应的 ε O j 实验值与计算值之间的关系
Element Lit[10] Cal Exp[11] Element Lit[10] Cal Exp[11]
Ca -31.12 -33.12 Au 2.21 1.88 -0.25
Sc -19.95 -22.07 Nd -22.64 -24.75
Ti -13.78 -15.27 Pm -22.09 -24.22
V -8.49 -9.15 -3.89 Sm -22.16 -24.27
Cr -3.33 -3.44 -2.13 Eu -22.16 -24.27
Mn -7.79 -8.54 -5.86 Gd -22.16 -24.27
Co 1.01 0.71 0.58 Tb -21.70 -23.82
Ni 1.91 1.49 -0.054 Dy -21.72 -23.83
Cu -5.23 -5.49 -2.35 Ho -21.77 -23.86
Sr -35.07 -37.04 Er -21.29 -23.40
Y -22.16 -24.27 Tm -21.30 -23.42
Zr -17.03 -18.94 Yb -21.31 -23.43
Nb -9.18 -9.97 -5.63 Lu -20.85 -22.99
Mo -2.29 -2.13 0.35 Th -18.81 -20.85
Tc 4.43 4.32 U -13.17 -14.57
Ru 5.89 5.78 Pu -15.95 -17.69
Rh 4.22 3.59 Ce -23.16 -25.26
Pd 2.45 1.22 Pr -22.64 -24.75
Ag -8.97 -9.20 H 11.49 11.16 2.67
Ba -37.35 -39.43 Li -18.21 -19.38
La -23.71 -25.80 Be 8.56 8.96
Hf -15.70 -17.61 B 16.45 17.01 6.86
Ta -9.45 -10.29 -10.34 C 21.48 20.39 6.26
W -0.17 0.23 6.03 N 25.05 21.70 1.32
Re 4.35 4.70 Na -25.32 -26.02
Os 6.37 6.43 Mg -12.76 -13.50
Ir 7.57 7.20 Al 2.25 2.04 5.06
Pt 7.68 6.75 4.65 Si 8.76 8.76 9.12
In -6.91 -7.17 P 20.50 20.20 4.90
Sn -2.67 -2.88 -3.27 K -34.71 -35.41
Sb -0.40 -0.56 0.67 Zn -2.12 -2.39
Cs -40.06 -40.82 Ga -0.54 -0.81
Hg -5.34 -5.53 Ge 4.20 4.03 3.89
Tl -9.76 -9.91 As 9.26 9.11 0.92
Pb -8.08 -8.17 -41.80 Rb -37.42 -38.16
Bi -6.79 -6.89 Cd -5.33 -5.59
表4   ε S j 实验值与计算值得比较
图7  Fe 基溶液1873 K时第二周期元素与对应的 ε S j 实验值与计算值之间的关系
图8  Fe 基溶液1873 K时第四周期元素与对应的 ε S j 实验值与计算值之间的关系
图9  Fe 基溶液1873 K时第五周期元素与对应的 ε S j 实验值与计算值之间的关系
图10  Fe 基溶液1873 K时第六周期元素与对应的 ε S j 实验值与计算值之间的关系
图11  Nb基二元合金生成焓实验值[22-28]与计算值之间的比较
图12  Ag基化合物实验值与计算值之间的比较
图13  Pt基化合物生成焓实验值与计算值的对比
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