Mechanical Characterization of Anhydrous Microporous Aluminophosphate Materials: Tridimensional Incompressibility, Ductility, Isotropy and Negative Linear Compressibility
Abstract
:1. Introduction
2. Methods
3. Results and Discussion
3.1. Crystal Structures
3.2. Stiffness Tensors and Mechanical Stability
3.3. Mechanical Properties
3.4. Mechanical Properties as a Function of the Orientation of the Applied Strain
3.5. Compressibility Functions
3.6. Negative Linear Compressibility (NLC) in ALPO-18
3.6.1. Isotropic Negative Linear Compressibility (INLC)
3.6.2. Anisotropic Negative Volumetric Compressibility (ANVC) Effect
3.6.3. Effect of Dispersion Interactions in the NLC Effect of ALPO-18
3.7. Effect of Hydration in the Mechanical Properties of ALPO-18
3.8. Effect of Aging in the Elastic Properties of VPI-5
3.9. Effect of Pressure Polymorphism
3.9.1. VPI-5
3.9.2. ALPO-5
3.10. Comparison with Experimental Data
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | ||||||||
---|---|---|---|---|---|---|---|---|
VPI-5 | ||||||||
PBE | 18.5665 | 18.5665 | 8.5330 | 90.0 | 90.0 | 120.0 | 2547.3630 | 1.431 |
PBE + Disp | 18.5253 | 18.5253 | 8.5234 | 90.0 | 90.0 | 120.0 | 2533.2330 | 1.439 |
PBEsol | 18.5430 | 18.5430 | 8.5398 | 90.0 | 90.0 | 120.0 | 2542.9495 | 1.433 |
Exp [4] | 18.6005(6) | 18.6005(6) | 8.3664(4) | 90.0 | 90.0 | 120.0 | 2506.7931 | 1.455 |
ALPO-8 | ||||||||
PBE | 33.5899 | 14.7280 | 8.5334 | 90.0 | 90.0 | 90.0 | 4221.5557 | 1.727 |
PBE + Disp | 33.3954 | 14.6915 | 8.5222 | 90.0 | 90.0 | 90.0 | 4181.1994 | 1.744 |
PBEsol | 33.5175 | 14.7223 | 8.5398 | 90.0 | 90.0 | 90.0 | 4213.9746 | 1.730 |
Exp [6] | 33.29(2) | 14.76(2) | 8.257(4) | 90.0 | 90.0 | 90.0 | 4057.1628 | 1.797 |
ALPO-5 | ||||||||
PBE | 13.8671 | 13.8671 | 8.5350 | 90.0 | 90.0 | 120.0 | 1421.3670 | 1.710 |
PBE + Disp | 13.8401 | 13.8401 | 8.5261 | 90.0 | 90.0 | 120.0 | 1414.3565 | 1.718 |
PBEsol | 13.8645 | 13.8645 | 8.5382 | 90.0 | 90.0 | 120.0 | 1421.3642 | 1.710 |
Exp [9] | 13.718(1) | 13.718(1) | 8.4526(5) | 90.0 | 90.0 | 120.0 | 1377.5347 | 1.765 |
ALPO-18 | ||||||||
PBE | 13.5704 | 12.6773 | 18.4699 | 90.0 | 90.01 | 90.0 | 3177.4870 | 1.529 |
PBE + Disp | 13.5561 | 12.6613 | 18.4442 | 90.0 | 90.02 | 90.0 | 3165.7084 | 1.535 |
PBEsol | 13.5788 | 12.6705 | 18.4592 | 90.0 | 90.01 | 90.0 | 3175.9001 | 1.530 |
Exp [10] | 13.7114(1) | 12.7314(1) | 18.5703(1) | 90.0 | 90.01(1) | 90.0 | 3241.7302 | 1.500 |
ALPO-18 | ||||||||
PBE | 9.3276 | 9.4113 | 18.3376 | 88.24 | 91.77 | 88.97 | 1607.9391 | 1.957 |
PBE + Disp | 9.2582 | 9.3513 | 18.2448 | 87.99 | 91.81 | 89.32 | 1577.6793 | 1.995 |
PBEsol | 9.2487 | 9.3723 | 18.2507 | 88.66 | 91.93 | 88.54 | 1580.1187 | 1.992 |
Exp [11] | 9.251 | 9.362 | 18.428 | 90.89 | 96.35 | 90.87 | 1585.7971 | 1.985 |
ALPO-31 | ||||||||
PBE | 20.9724 | 20.9724 | 5.0778 | 90.0 | 90.0 | 120.0 | 1934.2242 | 1.884 |
PBE + Disp | 20.9230 | 20.9230 | 5.0683 | 90.0 | 90.0 | 120.0 | 1921.5046 | 1.897 |
PBEsol | 20.9635 | 20.9635 | 5.0767 | 90.0 | 90.0 | 120.0 | 1932.1567 | 1.886 |
Exp [12] | 20.827(1) | 20.827(1) | 5.003(1) | 90.0 | 90.0 | 120.0 | 1879.3798 | 1.940 |
VPI-5 | ALPO-8 | ALPO-5 | ALPO-18 | ALPO-31 | |
---|---|---|---|---|---|
11 | 85.17 | 82.23 | 124.23 | 105.68 | 109.15 |
22 | 85.17 | 102.00 | 124.23 | 98.33 | 109.15 |
33 | 158.27 | 187.62 | 192.56 | 105.82 | 138.05 |
44 | 19.10 | 23.94 | 26.24 | 13.99 | 30.81 |
55 | 19.10 | 25.96 | 26.24 | 18.71 | 30.81 |
66 | 21.79 | 23.35 | 28.22 | 28.90 | 23.01 |
12 | 41.59 | 53.01 | 67.80 | 68.62 | 63.13 |
13 | 43.66 | 48.05 | 59.70 | 57.17 | 61.58 |
14 | 0.0 | 0.0 | 0.0 | 0.0 | 5.76 |
15 | 0.0 | 0.0 | 0.0 | −2.42 | 0.46 |
16 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
23 | 43.66 | 51.17 | 59.70 | 52.13 | 61.58 |
24 | 0.0 | 0.0 | 0.0 | 0.0 | −5.76 |
25 | 0.0 | 0.0 | 0.0 | −1.73 | −0.46 |
26 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
34 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
35 | 0.0 | 0.0 | 0.0 | 3.16 | 0.0 |
36 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
45 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
46 | 0.0 | 0.0 | 0.0 | −1.21 | −0.46 |
56 | 0.0 | 0.0 | 0.0 | 0.0 | 5.76 |
Property | VPI-5 | ALPO-8 | ALPO-5 | ALPO-18 | ALPO-31 | |
---|---|---|---|---|---|---|
Bulk modulus | 60.49 0.56 | 68.27 0.87 | 88.22 0.60 | 73.56 0.95 | 80.17 1.16 | |
Shear modulus | 22.67 | 25.56 | 30.24 | 19.34 | 26.41 | |
Young’s modulus | 60.46 | 68.18 | 81.43 | 53.35 | 71.39 | |
Poisson’s ratio | 0.33 | 0.33 | 0.35 | 0.38 | 0.35 | |
Ductility index | 2.66 | 2.67 | 2.92 | 3.80 | 3.04 | |
Intrinsic ductility index | 0.37 | 0.43 | 0.51 | 1.02 | 0.45 | |
Hardness index | 0.94 | 1.22 | 1.13 | 0.63 | 0.70 | |
Universal anisotropy | 0.66 | 0.83 | 0.49 | 0.46 | 0.36 | |
Bulk modulus (SC) | 60.74 0.81 | 72.60 0.42 | 87.27 1.36 | 73.85 2.92 | 90.14 1.56 |
Material | ||||
---|---|---|---|---|
VPI-5 ) | 16.46 | 6.95 | 6.95 | 2.56 |
ALPO-8 ) | 13.77 | 6.93 | 5.04 | 1.81 |
ALPO-5 | 11.45 | 4.61 | 4.61 | 2.25 |
ALPO-18 | 13.54 | 3.40 | 5.17 | 4.97 |
ALPO-31 ) | 11.09 | 4.43 | 4.43 | 2.23 |
VPI-5 | ALPO-5 | ALPO-18W | |
---|---|---|---|
11 | 69.66 | 120.90 | 92.30 |
22 | 68.50 | 127.95 | 103.17 |
33 | 79.68 | 193.34 | 103.75 |
44 | 18.75 | 26.30 | 25.58 |
55 | 19.61 | 26.04 | 24.06 |
66 | 19.38 | 25.61 | 25.81 |
12 | 31.53 | 67.01 | 37.53 |
13 | 14.04 | 60.75 | 42.27 |
14 | 0.0 | 0.0 | −2.52 |
15 | −0.05 | 0.0 | −5.10 |
16 | 0.0 | 0.0 | 7.90 |
23 | 12.60 | 62.53 | 41.38 |
24 | 0.0 | 0.0 | 6.67 |
25 | −0.20 | 0.0 | −0.47 |
26 | 0.0 | 0.0 | 3.03 |
34 | 0.0 | 0.0 | 0.50 |
35 | 0.42 | 0.0 | −3.83 |
36 | 0.0 | 0.0 | −1.19 |
45 | 0.0 | 0.0 | 1.85 |
46 | 0.20 | 0.0 | 0.58 |
56 | 0.0 | 0.0 | 1.37 |
Property | VPI-5 | ALPO-5 | ALPO-18W |
---|---|---|---|
37.06 0.81 | 88.62 0.37 | 58.82 0.94 | |
20.98 | 29.58 | 25.81 | |
54.24 | 79.87 | 67.56 | |
0.26 | 0.35 | 0.31 | |
1.77 | 3.00 | 2.28 | |
0.24 | 0.51 | 0.18 | |
3.10 | 1.02 | 2.11 | |
0.29 | 0.50 | 0.24 | |
33.85 1.90 | 87.71 0.27 | 58.80 1.84 |
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Colmenero, F.; Lobato, Á.; Timón, V. Mechanical Characterization of Anhydrous Microporous Aluminophosphate Materials: Tridimensional Incompressibility, Ductility, Isotropy and Negative Linear Compressibility. Solids 2022, 3, 457-499. https://doi.org/10.3390/solids3030032
Colmenero F, Lobato Á, Timón V. Mechanical Characterization of Anhydrous Microporous Aluminophosphate Materials: Tridimensional Incompressibility, Ductility, Isotropy and Negative Linear Compressibility. Solids. 2022; 3(3):457-499. https://doi.org/10.3390/solids3030032
Chicago/Turabian StyleColmenero, Francisco, Álvaro Lobato, and Vicente Timón. 2022. "Mechanical Characterization of Anhydrous Microporous Aluminophosphate Materials: Tridimensional Incompressibility, Ductility, Isotropy and Negative Linear Compressibility" Solids 3, no. 3: 457-499. https://doi.org/10.3390/solids3030032