Calorimetric Studies and Thermodynamic Modeling of Ag–Mg–Ti Liquid Alloys
Abstract
:1. Introduction
2. Materials and Methods
3. Results and Discussion
Number of Dropped Moles ni [mol] | Heat Effect ∆HSignal ·K [kJ] | Drop Enthalpy HDISS-i [kJ] | Mole Fraction xi | Integral Molar Enthalpy ∆mixH [kJ/mol] | Partial Molar Enthalpy [kJ/mol] | Standard Uncertainties u(∆mixH) [kJ/mol] |
---|---|---|---|---|---|---|
Series A: (Ag0.90Mg0.10)1−xTix Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.013123 mol; K = 0.000007076 kJ/μVs; TD = 298 K; TM = 1294 K; = 39.7295 kJ/mol; = 38.9594 kJ/mol; = 42.9264 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000151 kJ/μVs. | ||||||
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.001461 | −0.015129 | −0.072 | 0.1002 | −4.939 | −49.3 | 0.025 |
nTi | ∆HSignal ·K | HDISS-Ti | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.0003384 | 0.014117 | −0.0004 | 0.0227 | −4.855 | −1.2 | 0.05 |
0.0003928 | −0.019389 | −0.0362 | 0.0477 | −7.097 | −92.3 * | 0.08 |
0.0004930 | 0.015384 | −0.0058 | 0.0774 | −7.241 | −11.7 * | 0.10 |
0.0005515 | 0.018455 | −0.0052 | 0.1085 | −7.316 | −9.5 * | 0.13 |
0.0010258 | 0.035827 | −0.0082 | 0.1611 | −7.357 | −8.0 * | 0.18 |
0.0011239 | 0.041276 | −0.0070 | 0.2121 | −7.287 | −6.2 * | 0.23 |
Series A’: (Ag0.90Mg0.10)1−xTix Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.013419 mol; K = 0.000008991 kJ/μVs; TD = 298 K; TM = 1297 K; = 39.8299 kJ/mol; = 39.8299 kJ/mol; = 43.0337 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000151 kJ/μVs. | ||||||
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.001489 | −0.010079 | −0.068 | 0.0999 | −4.579 | −45.8 | 0.012 |
nTi | ∆HSignal ·K | HDISS-Ti | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.0002402 | 0.009602 | −0.0007 | 0.0159 | −4.555 | −3.1 | 0.02 |
0.0005369 | 0.022891 | −0.0002 | 0.0495 | −4.412 | −0.4 | 0.05 |
0.0007584 | 0.025723 | −0.0069 | 0.0934 | −4.629 | −9.1 | 0.08 |
0.0006246 | 0.014385 | −0.0125 | 0.1266 | −5.192 | −20.0 | 0.09 |
0.0007145 | −0.019600 | −0.0503 | 0.1617 | −7.814 | −70.5 * | 0.11 |
0.0014164 | 0.048640 | −0.0123 | 0.2235 | −7.879 | −8.7 * | 0.15 |
Series B: (Ag0.70Mg0.30)1−xTix Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.013119 mol; K = 0.000007296 kJ/μVs; TD = 298 K; TM = 1294 K; = 39.7295 kJ/mol; = 38.9594 kJ/mol; = 42.9264 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000030 kJ/μVs. | ||||||
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.005624 | −0.003969 | −0.223 | 0.3001 | −11.902 | −39.7 | 0.001 |
nTi | ∆HSignal ·K | HDISS-Ti | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.0004262 | −0.001736 | −0.020 | 0.0222 | −12.682 | −47.0 | 0.001 |
0.0004492 | 0.006449 | −0.013 | 0.0446 | −13.046 | −28.6 | 0.003 |
0.0004283 | 0.013037 | −0.005 | 0.0650 | −13.034 | −12.5 | 0.005 |
0.0008816 | 0.033552 | −0.004 | 0.1044 | −12.690 | −4.9 | 0.012 |
0.0009171 | 0.042679 | 0.003 | 0.1420 | −12.006 | 3.6 | 0.020 |
0.0009150 | 0.039681 | 0.000 | 0.1765 | −11.506 | 0.4 | 0.027 |
0.0011365 | 0.060138 | 0.011 | 0.2157 | −10.483 | 10.0 | 0.037 |
0.0023398 | 0.080252 | −0.020 | 0.2856 | −10.318 | −8.6 * | 0.049 |
Series C: (Ag0.50Mg0.50)1−xTix Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.010210 mol; K = 0.000007166 kJ/μVs; TD = 298 K; TM = 1298 K; = 39.8634 kJ/mol; = 39.0967 kJ/mol; = 43.0695 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000123 kJ/μVs. | ||||||
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.003670 | −0.012785 | −0.156 | 0.2644 | −11.258 | −42.6 | 0.016 |
0.003275 | 0.048014 | −0.080 | 0.4048 | −13.774 | −24.4 | 0.064 |
0.003279 | 0.088052 | −0.040 | 0.5003 | −13.529 | −12.2 | 0.138 |
nTi | ∆HSignal ·K | HDISS-Ti | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.0005160 | 0.019757 | −0.0025 | 0.0246 | −13.313 | −4.8 | 0.154 |
0.0003990 | 0.019514 | 0.0023 | 0.0429 | −12.955 | 5.8 | 0.169 |
0.0004304 | 0.011631 | −0.0069 | 0.0618 | −13.016 | −16.0 | 0.179 |
0.0008649 | 0.037429 | 0.0002 | 0.0976 | −12.511 | 0.2 | 0.207 |
0.0008712 | 0.114159 | 0.0766 | 0.1310 | −8.789 | 88.0 * | 0.290 |
0.0022124 | 0.072838 | −0.0224 | 0.2058 | −8.906 | −10.1 * | 0.339 |
Series D: (Ag0.30Mg0.70)1−xTix Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.010581 mol; K = 0.000007126 kJ/μVs; TD = 298 K; TM = 1297 K; = 39.8299 kJ/mol; = 39.0624 kJ/mol; = 43.0337 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000334 kJ/μVs. | ||||||
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.00822 | 0.060154 | −0.261 | 0.4373 | −13.885 | −31.7 | 0.150 |
0.00822 | 0.233755 | −0.087 | 0.6085 | −12.894 | −10.6 | 0.555 |
0.00824 | 0.281176 | −0.041 | 0.7000 | −11.036 | −4.9 | 0.929 |
nTi | ∆HSignal ·K | HDISS-Ti | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.0003928 | 0.008879 | −0.0080 | 0.0110 | −11.140 | −20.4 | 0.385 |
0.0004241 | 0.011736 | −0.0065 | 0.0226 | −11.189 | −15.4 | 0.401 |
0.0005223 | 0.017379 | −0.0051 | 0.0366 | −11.169 | −9.8 | 0.423 |
0.0009150 | 0.033982 | −0.0054 | 0.0601 | −11.040 | −5.9 | 0.465 |
0.0010592 | 0.037067 | −0.0085 | 0.0859 | −10.958 | −8.0 | 0.510 |
0.0015606 | 0.054283 | −0.0129 | 0.1214 | −10.853 | −8.2 | 0.574 |
0.0017674 | 0.067073 | −0.0090 | 0.1585 | −10.609 | −5.1 | 0.649 |
0.0019700 | 0.062100 | −0.0227 | 0.1963 | −10.650 | −11.5 * | 0.715 |
0.0019930 | 0.056292 | −0.0295 | 0.2312 | −10.830 | −14.8 * | 0.773 |
Number of Dropped Moles ni [mol] | Heat Effect ∆HSignal ·K [kJ] | Drop Enthalpy HDISS-i [kJ] | Mole Fraction xi | Integral Molar Enthalpy ∆mixH [kJ/mol] | Partial Molar Enthalpy [kJ/mol] | Standard Uncertainties u(∆mixH) [kJ/mol] |
---|---|---|---|---|---|---|
Series E: (Ag0.95Ti0.05)1−xMgx Atmosphere: Argon at pressure p = 0.1 MPa. Starting parameters: nAg = 0.025064 mol; K = 0.000006794 kJ/μVs; TD = 298 K; TM = 1296 K; = 39.7964 kJ/mol; = 39.0281 kJ/mol; = 42.9979 kJ/mol. Standard uncertainties: u(nAg) = 0.0000009 mol; u(nMg) = 0.0000041 mol; u(nTi) = 0.0000021; u(TD) = 1 K; u(TM) = 1 K; u(p) = 10 kPa; u(K) = 0.000000158 kJ/μVs. | ||||||
nTi | ∆HSignal ·K | HDISS-Mg | xTi | ∆mixH | ΔTi | u(∆mixH) |
0.00125 | 0.020789 | −0.033 | 0.0475 | −1.251 | −26.4 | 0.018 |
nMg | ∆HSignal ·K | HDISS-Mg | xMg | ∆mixH | ΔMg | u(∆mixH) |
0.00109 | −0.009531 | −0.0519 | 0.0396 | −3.097 | −47.8 | 0.026 |
0.00123 | −0.005510 | −0.0534 | 0.0808 | −4.828 | −43.5 | 0.031 |
0.00160 | −0.010782 | −0.0731 | 0.1293 | −6.991 | −45.8 | 0.039 |
0.00170 | −0.003057 | −0.0694 | 0.1757 | −8.793 | −40.8 | 0.042 |
0.00156 | −0.005299 | −0.0662 | 0.2141 | −10.359 | −42.4 | 0.045 |
0.00592 | 0.088317 | −0.1428 | 0.3322 | −12.425 | −24.1 | 0.097 |
0.00583 | 0.108936 | −0.1184 | 0.4182 | −13.444 | −20.3 | 0.153 |
0.00569 | 0.165765 | −0.0565 | 0.4833 | −13.049 | −9.9 | 0.229 |
0.00804 | 0.228579 | −0.0853 | 0.5537 | −12.717 | −10.6 | 0.320 |
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Chemical Name | Source | Purity [mass%] | Purification Method | Analysis Method |
---|---|---|---|---|
Magnesium | Goodfellow Cambridge Ltd., Huntingdon, England | 99.9 | None | Certified purity |
Silver | Innovator Sp. z o.o., Gliwice, Poland | 99.9 | None | Certified purity |
Titanium | Alfa Aesar, Thermo Scientific Kandel GmBH, Kandel, Germany | 99.99 | None | Certified purity |
Argon | Pioniergas, Kraków, Poland | 99.9999 | None | Certified purity |
Points of Intersection | A | A’ | B | C | E |
---|---|---|---|---|---|
1 | −4.855 | −4.412 | −4.828 | ||
2 | −13.046 | −12.425 | |||
3 | −13.313 | −13.049 |
System | Interaction Parameters [J/mol] | Reference |
---|---|---|
Ag–Mg | −53,346.5 | [5] |
−3694 | ||
−905.8 | ||
Ag–Ti | −10,011.8 | [This study] |
−18,866.8 | ||
Mg–Ti | 77,020 | [14] |
Ag–Mg–Ti | −198,140.53 | [This study] |
−434,984.54 | ||
59,643.579 |
xAg | xMg | xTi | Ag | Mg | Ti | ∆mixH |
---|---|---|---|---|---|---|
kJ/mol | ||||||
Series A and A’: (Ag0.90Mg0.10)1−xTix alloys at T = 1297 K | ||||||
0.900 | 0.100 | 0.00 | −0.661 | −45.241 | −31.065 | −5.119 |
0.855 | 0.095 | 0.05 | −0.846 | −46.036 | −21.246 | −6.159 |
0.810 | 0.090 | 0.10 | −1.601 | −45.635 | −13.281 | −6.732 |
0.720 | 0.080 | 0.20 | −4.214 | −41.378 | −2.077 | −6.759 |
0.630 | 0.070 | 0.30 | −7.397 | −32.844 | 4.112 | −5.726 |
0.540 | 0.060 | 0.40 | −10.228 | −20.588 | 6.663 | −4.093 |
0.450 | 0.050 | 0.50 | −11.967 | −5.350 | 6.778 | −2.264 |
0.360 | 0.040 | 0.60 | −12.058 | 11.952 | 5.471 | −0.580 |
0.270 | 0.030 | 0.70 | −10.124 | 30.215 | 3.579 | 0.678 |
0.180 | 0.020 | 0.80 | −5.971 | 48.155 | 1.753 | 1.290 |
0.090 | 0.010 | 0.90 | 0.412 | 64.306 | 0.464 | 1.097 |
0.000 | 0.000 | 1.00 | 8.855 | 77.020 | 0.000 | 0.000 |
Series B: (Ag0.70Mg0.30)1−xTix alloys at T = 1297 K | ||||||
0.700 | 0.300 | 0.00 | −5.504 | −25.636 | −37.763 | −11.544 |
0.665 | 0.285 | 0.05 | −5.750 | −26.431 | −21.224 | −12.418 |
0.630 | 0.270 | 0.10 | −7.018 | −26.909 | −8.348 | −12.521 |
0.560 | 0.240 | 0.20 | −11.373 | −26.211 | 8,325 | −10.994 |
0.490 | 0.210 | 0.30 | −16.389 | −22.449 | 15,769 | −8.014 |
0.420 | 0.180 | 0.40 | −20.381 | −15.030 | 16.997 | −4.467 |
0.350 | 0.150 | 0.50 | −22.163 | −3.854 | 14.526 | −1.072 |
0.280 | 0.120 | 0.60 | −21.044 | 10.680 | 10.377 | 1.615 |
0.210 | 0.090 | 0.70 | −16.830 | 27.676 | 6.072 | 3.207 |
0.140 | 0.060 | 0.80 | −9.826 | 45.740 | 2.637 | 3.479 |
0.070 | 0.030 | 0.90 | −0.831 | 62.984 | 0.603 | 2.374 |
0.000 | 0.000 | 1.00 | 8.855 | 77.020 | 0.000 | 0.000 |
Series C: (Ag0.50Mg0.50)1−xTix alloys at T = 1297 K | ||||||
0.500 | 0.500 | 0.00 | −14.260 | −12.413 | −37.016 | −13.337 |
0.475 | 0.475 | 0.05 | −15.927 | −11.731 | −17.137 | −13.994 |
0.450 | 0.450 | 0.10 | −18.502 | −11.589 | −1.920 | −13.733 |
0.400 | 0.400 | 0.20 | −24.897 | −11.623 | 17.046 | −11.199 |
0.350 | 0.350 | 0.30 | −30.906 | −10.332 | 24.498 | −7.084 |
0.300 | 0.300 | 0.40 | −34.669 | −6.209 | 24.377 | −2.513 |
0.250 | 0.250 | 0.50 | −35.001 | 1.576 | 19.947 | 1.617 |
0.200 | 0.200 | 0.60 | −31.394 | 13.172 | 13.795 | 4.633 |
0.150 | 0.150 | 0.70 | −24.019 | 28.056 | 7.831 | 6.087 |
0.100 | 0.100 | 0.80 | −13.724 | 45.025 | 3.286 | 5.759 |
0.050 | 0.050 | 0.90 | −2.032 | 62.198 | 0.717 | 3.653 |
0.000 | 0.000 | 1.00 | 8.855 | 77.020 | 0.000 | 0.000 |
Series D: (Ag0.30Mg0.70)1−xTix alloys at T = 1297 K | ||||||
0.300 | 0.700 | 0.00 | −26.360 | −4.307 | −16.539 | −10.923 |
0.285 | 0.665 | 0.05 | −32.359 | −2.322 | 0.080 | −10.762 |
0.270 | 0.630 | 0.10 | −38.140 | −1.256 | 12.461 | −9.843 |
0.240 | 0.560 | 0.20 | −48.008 | −0.482 | 26.862 | −6.419 |
0.210 | 0.490 | 0.30 | −54.285 | 0.412 | 30.980 | −1.904 |
0.180 | 0.420 | 0.40 | −55.933 | 3.184 | 28.491 | 2.666 |
0.150 | 0.350 | 0.50 | −52.554 | 8.951 | 22.431 | 6.465 |
0.120 | 0.280 | 0.60 | −44.391 | 18.191 | 15.195 | 8.884 |
0.090 | 0.210 | 0.70 | −32.325 | 30.742 | 8.539 | 9.524 |
0.060 | 0.140 | 0.80 | −17.880 | 45.799 | 3.578 | 8.202 |
0.030 | 0.070 | 0.90 | −3.219 | 61.919 | 0.787 | 4.946 |
0.000 | 0.000 | 1.00 | 8.855 | 77.020 | 0.000 | 0.000 |
Series E: (Ag0.9525Ti0.0475)1−xMgx alloys at T = 1297 K | ||||||
0.95250 | 0.00 | 0.04750 | −0.142 | −57.701 | −22.948 | −1.226 |
0.90488 | 0.05 | 0.04513 | −0.338 | −51.439 | −22.404 | −3.889 |
0.85725 | 0.10 | 0.04275 | −0.836 | −45.499 | −22.547 | −6.231 |
0.76200 | 0.20 | 0.03800 | −2.760 | −34.665 | −24.180 | −9.955 |
0.66675 | 0.30 | 0.03325 | −5.915 | −25.322 | −26.385 | −12.418 |
0.57150 | 0.40 | 0.02850 | −10.246 | −17.536 | −27.643 | −13.658 |
0.47625 | 0.50 | 0.02375 | −15.640 | −11.317 | −26.376 | −13.733 |
0.38100 | 0.60 | 0.01900 | −21.925 | −6.615 | −20.952 | −12.721 |
0.28575 | 0.70 | 0.01425 | −28.873 | −3.325 | −9.678 | −10.716 |
0.19050 | 0.80 | 0.00950 | −36.200 | −1.283 | 9.195 | −7.835 |
0.09525 | 0.90 | 0.00475 | −43.562 | −0.267 | 37.473 | −4.212 |
0.00000 | 1.00 | 0.00000 | −50.559 | 0.000 | 77.020 | 0.000 |
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Gozdur, W.; Gąsior, W.; Zrobek, M.; Budziak, A.; Dębski, R.; Gierlotka, W.; Pęska, M.; Polański, M.; Dębski, A. Calorimetric Studies and Thermodynamic Modeling of Ag–Mg–Ti Liquid Alloys. Materials 2024, 17, 1786. https://doi.org/10.3390/ma17081786
Gozdur W, Gąsior W, Zrobek M, Budziak A, Dębski R, Gierlotka W, Pęska M, Polański M, Dębski A. Calorimetric Studies and Thermodynamic Modeling of Ag–Mg–Ti Liquid Alloys. Materials. 2024; 17(8):1786. https://doi.org/10.3390/ma17081786
Chicago/Turabian StyleGozdur, Weronika, Władysław Gąsior, Maciej Zrobek, Andrzej Budziak, Roman Dębski, Wojciech Gierlotka, Magda Pęska, Marek Polański, and Adam Dębski. 2024. "Calorimetric Studies and Thermodynamic Modeling of Ag–Mg–Ti Liquid Alloys" Materials 17, no. 8: 1786. https://doi.org/10.3390/ma17081786