提升能源使用效率與發展可靠的再生能源，是目前能源議題上最重要的二項作為。熱電材料擁有將熱能轉換成電力、將廢熱回收提升能源使用效率的特性，在能源議題上受到重視。熱電元件，若與太陽能加熱系統併用，是具有很大應用潛力的再生能源。Ag-Pb-Sn-Te四元材料系統是重要的熱電材料系統，尤其如PbTe、SnTe及Ag-Pb-Te等化合物，已被認為是極具潛力的熱電材料。相圖是研究相變化、相生成、微結構最直接之依據。相圖可以由實驗測定，也可以利用Calphad方法計算。本研究擬探討具熱電應用重要的四元Ag-Pb-Sn-Te材料系統相圖。Ag-Pb-Sn-Te的六個二元子系統為Ag-Pb、Ag-Sn、Ag-Te、Pb-Sn、Pb-Te、Sn-Te，四個三元子系統為Ag-Pb-Sn、Ag-Pb-Te、Ag-Sn-Te與Pb-Sn-Te。六個二元組成系統、Ag-Pb-Te與Pb-Sn-Te二個組成三元系統的相圖在文獻中已有許多探討，也皆有使用Calphad方法描述的熱力學模型。本研究將整理文獻，直接引用結果，進行相圖計算，不再重複進行探討。針對缺乏相圖實驗結果的Ag-Pb-Sn、Ag-Sn-Te二個三元子系統與Ag-Pb-Sn-Te四元系統，本研究以實驗方法測定350oC與500oC的相平衡結果。依據實驗的結果，以及二元組成系統相圖，建構Ag-Pb-Sn三元系統在350oC與500oC的等溫橫截面圖與Ag-Sn-Te在350 ℃的等溫橫截面圖。依據四元系統的實驗結果，建構四元系統在350oC與500oC的30at.%Te與50at.%Te等值剖面圖。實驗結果顯示，Ag-Pb-Sn的三元系統在350℃時並未發現三元相，穩定存在的相有(Ag)、ζ-Ag4Sn、ε-Ag3Sn 與 liquid相；存在著(Ag)+ζ-Ag4Sn+liquid與 ζ-Ag4Sn+ ε-Ag3Sn+liquid二個三相區。500℃時並未發現三元相，穩定存在的相有(Ag)、ζ-Ag4Sn與liquid相；存在著(Ag)+ζ-Ag4Sn +liquid一個三相區。Ag-Sn-Te的三元系統在350℃時，穩定存在的相有(Ag)、ζ-Ag4Sn、ε-Ag3Sn、liquid、SnTe、(Te)、Ag5Te3、Ag2Te與一個三元相AgSnTe2；存在著(Ag)+ζ-Ag4Sn+Ag2Te、ζ-Ag4Sn+SnTe+Ag2Te、ζ-Ag4Sn+ε-Ag3Sn+SnTe、ε-Ag3Sn+liquid+SnTe、AgSnTe2+SnTe+(Te)、Ag5Te3+ AgSnTe2+(Te)、Ag2Te+ AgSnTe2+ Ag5Te3與 Ag2Te+SnTe+ AgSnTe2八個三相區。本研究也直接使用組成二元系統的Calphad型式熱力學敘述，在未引入三元作用參數條件下，計算了Ag-Pb-Sn 及Ag-Sn-Te 350℃與500℃等溫橫截面相圖。350℃下的計算結果與實驗結果，在定性上十分符合。

Improving energy efficiency and developing renewable energy are the two most important tasks of the current energy challenges. Thermoelectric modules can improve energy usage efficiency by converting waste heat into electricy. If combined with solar heating systems, thermoelectric modules are renewable energy sources. The Ag-Pb-Sn-Te quaternary system is of important thermoelectric application interests, especially PbTe, SnTe and Ag-Pb-Te compounds are all highly promising thermoelectric materials. This study determines the phase diagrams of the quaternary thermoelectric material Ag-Pb-Sn-Te system. The Ag-Pb-Sn-Te has six binary constituent systems, Ag-Pb, Ag-Sn, Ag-Te, Pb-Sn, Pb-Te, and Sn-Te, and four ternary constituent systems, Ag-Pb-Sn, Ag-Pb-Te, Ag-Sn-Te and Pb-Sn-Te. There are phase diagram results of experimental determinations and Calphad-type calculation of the six binary systems and the Ag-Pb-Te and Pb-Sn-Te ternary systems. Regarding these binary and ternary systems of available phase diagrams results, this study gathers and assesses the results of the literature, calculates the phase diagrams, and does not repeat phase diagram determination efforts. This study carries out experimental determinations of the phase equilibria at 350oC and 500oC of the Ag-Pb-Sn, Ag-Sn-Te and Ag-Pb-Sn-Te systems, which are lacking in the literatures. Based on the experimental results and the phase diagrams of the constituent binary systems, the isothermal sections at 350oC and 500oC of the Ag-Pb-Sn ternary system and that at 350oC of the Ag-Sn-Te ternary system are determined. The isoplethal sections of 30at.%Te and 50at.%Te at 350oC and 500oC of the Ag-Pb-Sn-Te system are determined based on the quaternary experimental results and the phase diagrams of the constituent ternary systems. There are no ternary compounds in the Ag-Pb-Sn system at 350℃. The stable phases are (Ag), ζ-Ag4Sn, ε-Ag3Sn and liquid. There are two tie-triagles, (Ag)+ζ-Ag4Sn +liquid and ζ-Ag4Sn+ ε-Ag3Sn+liquid. At 500℃, there are no ternary compounds, and the stable phases are (Ag), Ag4Sn and liquid phases. There is a (Ag)+ζ-Ag4Sn +liquid tie-triangle. The stable phases in the Ag-Sn-Te ternary system at 350℃ are (Ag), ζ-Ag4Sn, ε-Ag3Sn, liquid, SnTe, (Te), Ag5Te3, Ag2Te and a ternary AgSnTe2 compound. There are 8 tie-triangles, (Ag)+ζ-Ag4Sn+Ag2Te, ζ-Ag4Sn+SnTe+Ag2Te, ζ-Ag4Sn+ ε-Ag3Sn+SnTe, ε-Ag3Sn+liquid+SnTe, AgSnTe2+SnTe+(Te), Ag5Te3+ AgSnTe2+(Te), Ag2Te+ AgSnTe2+Ag5Te3 and Ag2Te+SnTe+ AgSnTe2. The phase diagrams of Ag-Pb-Te and Pb-Sn-Te ternary systems are also calculated by using the Calphad-type thermodynamic descriptions of the constituent binary systems available in the literatures without introducing ternay interaction parameters. The calculated and experimental reults of the Ag-Pb-Sn 350oC isothermal sections are qualitatively in good agreement.

[1] L. L. N. L, Estimated U. S. Energy Consumption in 2017, (2017).
[2] G. J. Snyder, E. S. Toberer, "Complex thermoelectric materials", Nature Materials, 7(2008) 105-114.
[3] T. M. Tritt, "Thermoelectric Phenomena, Materials, and Applications", Annual. Reviews. Mater. Res. 2011. 41:433–48.
[4]劉倡宜碲化鉍合金薄膜熱電元件的開發，國立台灣大學工學院機械工程研究所碩士論文，2015。
[5] A. J. Minnich, M.S. Dresselhaus, Z. F. Ren, G. Chen, "Bulk nanostructured thermoelectric materials: current research and future prospects", Energy & Environmental Science, 2(2009) 466-479.
[6] R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O’quinn, "Thin-film thermoelectric devices with high room-temperature figures of merit", Nature, 413(2001) 597-602.
[7] Z. H. Dughaish, "Lead telluride as a thermoelectric material for thermoelectric power generation", Physica B: Condensed Matter, 322(2002) 205-223.
[8] Y. Gelbstein, Z. Dashevsky, M. P. Dariel, "High performance n-type PbTe-based materials for thermoelectric applications", Physica B: Condensed Matter, 363 (2005) 196-205.
[9] E. I. Rogacheva, S. N. Grigorov, O. N. Nashchekina, T. V. Tavrina, S. G. Lyubchenko, A. Yu. Sipatov, V. V. Volobuev, A. G. Fedorov, M. S. Dresselhaus, "Growth mechanism and thermoelectric properties of PbTe/SnTe/ PbTe heterostructures", Thin Solid Films, Vol. 493, pp. 41-48, (2005).
[10] G. Tan, F. Shi, S. Hao, L. D. Zhao, H. Chi, X. Zhang, C. Uher, C. Wolverton, V. P. Dravid, M. G. Kanatzidis, "Non-equilibrium processing leads to record high thermoelectric figure of merit in PbTe–SrTe", Nature Communications, DOI: 10.1038/ncomms12167
[11] W. Li, L. L. Zheng, B. H. Ge, S. Lin, X. Zhang, Z. Chen, Y. Chang and Y. Z. Pei*, "Promoting SnTe as an Eco-Friendly Solution for p-PbTe Thermoelectric via Band Convergence and Interstitial Defects.", Adv. Mater. 2017, 29, 1605887.
[12] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E.K. Polychroniadis and M. G. Kanatzidis, "Cubic AgPbmSbTe2+m: New Bulk Thermoelectric Materials with High Figure of Merit for Power Generation. " Science, Vol.303, pp.818-21, (2004).
[13] Gibbs' Phase Rule: Where it all Begins
https://serc.carleton.edu/research_education/equilibria/phaserule.html
[14] B. Predel, M. Hoch, M. Pool, "Phase Diagrams and Heterogeneous Equilibria: A Practical Introduction. ",ISBN 3-540-14011-5, (2003).
[15] I. Karakaya and W. T. Thompson, "The Ag-Pb (Silver-Lead) System ", Bulletin of Alloy Phase Diagrams, Vol. 8(4), pp. 326-334, (1987).
[16] W. Gierlotka, J. Lapsa, and K. Fitzner, "Thermodynamic Description of the Ag-Pb-Te Ternary System", Journal of Phase Equilibria and Diffusion, Vol. 31(6), pp. 509-517, (2010).
[17] I. Karakaya and W. T. Thompson, "The Ag-Sn (Silver-Tin) System", Bulletin Alloy Phase Diagrams, Vol. 8(4), pp. 340-347, (1987).
[18] W. Gierlotka, "Thermodynamic assessment of the Ag-Te binary system", Journal of Alloys and Compounds, Vol. 485, pp. 231-235, (2009).
[19] I. Karakaya, W. T. Thompson, "The Ag-Te (Silver-Tellurium) System", Journal of Phase Equilibria, Vol. 12, No. 1, pp. 56-63, (2010).
[20] C. Kracek, C. J. Ksanda, "Phase relations in the system tellurium-silver", Transactions, American Geophysical Union, Vol. 363, (1940).
[21] C. Kracek, C. J. Ksanda, L. J. Cabri, "Phase relations in the silver - tellurium system", American Mineralogist, Vol. 51, pp. 14-28, (1996).
[22] R. M. Honea, "Empressite and stuetzite redefined", American Mineralogist, Vol. 49, pp. 325-338, (1964).
[23] H. Ohtani, K. Okuda, and K. Ishida, "Thermodynamic Study of Phase Equilibria in the Pb-Sn-Sb System", Journal of Phase Equilibria, Vol. 16(5), pp. 416-429, (1995).
[24] l. Karakaya and W.T. Thompson"The Pb-Sn (Lead-Tin) System", Bulletin of Alloy Phase Diagrams Vol. 9(2), pp147-152, (1988)
[25] J. -C. Lin, K. C. Hsieh, R. C. Sharma, and Y. A. Chang, "The Pb-Te (lead-tellurium) system", Bulletin of Alloy Phase Diagrams, Vol. 10(4), pp. 340-347, (1989).
[26] H. Gravemann, H. J. Wallbaum, "Zur Kenntnis des Dreistoffsystems Kupfer-Blei-Tellur", Zeitschrift Fur Metallkunde, Vol. 47, pp. 433-441, (1956).
[27] M. Moniri, C. Petot, "Study and the Pb-Te System", Journal of Thermal Analysis and Calorimetry, Vol. 24, pp. 195-201, (1978).
[28] R. C. Sharma and Y. A. Chang, "The Sn-Te (Tin-Tellurium) system", Journal of Phase Equilibra, Vol. 17(1), pp. 72-80, (1986).
[29] Y. Liu, D. Liang, and L. Zhang, "Thermodynamic Descriptions for the Sn-Te and Pb-Sn-Te Systems", Journal of Electronic Materials, Vol. 39 (2), pp.246-257, (2010).
[30] A. Kroupa, A. Dinsdale. A. Watson, J. J. Vřešťáld, A. Zemanova and P. Broz, "The Thermodynamic data base COST MP0602 for Materials for high- temperature lead-free soldering", Journal of Mining and Metallurgy: Section B: Metallurgy, Vol. 48(3) B, pp. 339-346, (2012).
[31] C. P. Lin, C. M. Chen, Y. W. Yen, H. J. Wu, S. W. Chen, "Interfacial reactions between high-Pb solders and Ag", Journal of Alloys and Compounds, Vol. 509, pp.3509–3514, (2011).
[32] K. Bergum, T. Ikeda, G. J. Snyder, "Solubility and microstructure in the pseudo-binary PbTe–Ag2Te system ", Journal of Solid State Chemistry,Vol. 184, pp.2543–2552, (2011).
[33] H. J. Wu, W. J. Foo, W. Gierlotka, S. W. Chen, and G. J. Snyder, "The microstructure, liquidus projection and thermodynamic modeling of thermoelectric Ag–Pb–Te system", Materials Chemistry and Physics, Vol. 141, pp. 758-767, (2013).
[34] F. Romermann, R. Blachnik, "The excess enthalpies of liquid
Ag-Ge-Te and Ag-Sn-Te alloys", Zeitschrift fuer Metallkunde, Vol.
92, No.4, pp. 336-344, (2001).
[35] D. M. Wamwangi, "Application of p electron theory to predict new materials for rewritable optical recording", pp141-143(2004).
[36] 邱國峻，國立清華大學化學工程研究所碩士論文，2012。
[37] J. S. Chang, S. W. Chen, K. C. Chiu, H. J. Wu, and J. J. Chen, "Liquidus projection of the Ag-Sn-Te ternary system", Metallurgical and Materials Transactions A, Vol. 45A, pp. 3728-3740, (2014).
[38] J. J. van. Laar, Z. Phys, Chem., Vol. 64, pp. 257-293, (1908).
[39] J. L. Mijering, Philips Res. Repts., Vol. 18, pp. 318-330, (1963).
[40] H. L. Lukas, J. Weiss, and E. T. Henig, "Calphad-Computer coupling of Phase Diagram and Thermochemistry", Vol. 6(3), pp.229-251, (1982).
[41] O. B. Fabrichnaya, S. K. Saxena, P. Richet and E. F. Westrum, "Thermodynamic Data, Models, and Phase Diagrams in Multicomponent Oxide Systems : an Assessment for Materials and Planetary Scientists Based on Calorimetric, Volumetric and Phase Equilibrium Data", ISBN 9783662105047.
[42] W. Gierlotka, Y. Huang, and S.-W. Chen, "Phase Equilibria of Sn-Sb-Ag Ternary System (II): Calculation", Metallurgical and Materials Transctions A, Vol. 39Am pp. 3199-3209, (2008).
[43] Y. Liu, L. Zhang and D. Yu, "Thermodynamic Descriptions for the Cd-Te, Pb-Te, Cd-Pb and Cd-Pb-Te Systems", Journal of Electronic Materials, Vol. 38(10), pp. 2033-2045, (2009).
[44] K. Hsieh, M.-S. Wei,Y.-A. Chang, "Thermodynamic Analysis Of The
Tin-Tellurium System and Calculation Of The Phase Diagram", Z.
Metallkd, Vol.74, pp. 330-337, (1983).
[45] W. Gierlotka∗, J. Łapsa, D. J.-Handzlik, "Thermodynamic description of the Pb–Te system using ionic liquid model", Journal of Alloys and Compounds, Vol.479, pp.152-156, (2009).