Two-gap 超導體:Ax(NH3)Fe2Se2 (A=Ba, Sr or Ca)的超導性質研究

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(1)國立臺灣師範大學物理學系 Master Thesis 碩士論文. Two-Gap Superconducting Properties of Ax(NH3)Fe2Se2( A=Ba, Sr or Ca) Two-Gap 超導體:Ax(NH3)Fe2Se2 (A=Ba, Sr or Ca)的超導性質研究. Presented by Yu-Bo Li 作者:李育渤 Supervisor: Yung-Yuan Hsu 指導教授:徐鏞元. Department of Physics National Taiwan Normal University January 2018 1.

(2) content 國立臺灣師範大學碩士論文通過簽名表 ......................................................................................... 4 國立台灣師範大學學位論文授權書 ................................................................................................. 5 致謝 ..................................................................................................................................................... 6 摘要 ..................................................................................................................................................... 7 Abstract ............................................................................................................................................... 8 List of the figures and tables ............................................................................................................... 9 Chapter 1 Introduction....................................................................................................................... 13 1-1. Prologue ................................................................................................................................. 13 1-2. Superconductivity of iron-based system ................................................................................ 13 1-3. Motivation .............................................................................................................................. 16 Chapter 2 experimental details .......................................................................................................... 20 2-1. Preparation of -FeSe .......................................................................................................... 20 2-2. Preparation of Ax(NH3)Fe2Se2 (A = Ba, Sr or Ca) ................................................................. 25 2-3. Analysis of structure by X-ray diffraction ............................................................................. 27 2-4. Magnetism measurements ...................................................................................................... 28 2-5. Electric Resistance measurement ........................................................................................... 30 Measurement system ................................................................................................................. 30 Closed-cycle refrigerator system ............................................................................................... 32 Instrument setup ........................................................................................................................ 34 measurement control by LabVIEW ........................................................................................... 36 Data selection ............................................................................................................................ 36 Heat Controller .......................................................................................................................... 36 Chapter 3 Result and Discussion ....................................................................................................... 37 3-1. The selection of Fe1+xSe ......................................................................................................... 37 3-2. Result of Ax(NH3)Fe2Se2 (A=Ba, Sr or Ca) ........................................................................... 42 2.

(3) 3-3. Superconducting properties of Ba x(NH3)Fe2Se2 and 2-gap superconducting model discussion ....................................................................................................................................................... 48 Chapter 4 Conclusion ........................................................................................................................ 60 Reference ........................................................................................................................................... 62. 3.

(4) 國立臺灣師範大學碩士論文通過簽名表. 4.

(5) 國立台灣師範大學學位論文授權書. 5.

(6) 致謝首先要感謝徐鏞元老師、簡守廷學長 & 楊名正學長，謝謝他們用耐心包容跟教導我，在當時，我其實是一個不怎麼樣的學生，但是老師跟學長們還是不厭其煩地教導我，以及給予實驗上的一些意見好讓我的實驗順遂一點，最後實驗成功了，也非常謝謝你們。也感謝古煥球老師 & 鄭武漢先生在 SQUID 上的幫助。再來要感謝的是中央研究院的陳洋元老師以及陳銘堯老師跟駱芳鈺老師在 X-RAY 方面上的協助。還要感謝同學李家逵陳俊諭的陪伴。最後要感謝爸爸、媽媽、哥哥以及滿天神佛的幫助跟支持，謝謝。. 6.

(7) 摘要高純度超導體 Ax(NH3)Fe2Se2 (A =鋇, 鍶 or 鈣)是經由氨熱法將鹼土金族鑲入 -FeSe 裡，製作出來的樣本是純超導，在過去 245-phase 的反鐵磁相會跟超導相一起共存，這是一個很頭痛的問題，因為反鐵磁相會影響超導性質的基本量測。利用氨熱法製作的樣本之基礎超導性質像超導臨界溫度 Tc (Tc = 39 K for A =鋇, 44 K for 鍶和 43 K for 鈣)，然而 Tc 的增高引起了大家對於 Ax(NH3)Fe2Se2 (A = alkali 或 alkaliearth) 產生了高度的興趣，不只是好奇為何 Tc 會增高，還包含了一連串超導性質與機制。而經由 X-ray 的測量後，我們發現 Bax(NH3)Fe2Se2 與 Srx(NH3)Fe2Se2 的 c-axis 的變化，進而讓鐵硒原本的三維費米面轉化為近似二維費米面，除此之外，這篇論文還會提供基本的超導性質像超導低臨界場 Bc1(0 K) (30 G for A =鋇和 24 G for A = 鍶) 和超導高臨界場 Bc2(0 K) (13.4 T for A =鋇和 60.7 T for A =鍶)隱喻了 Ax(NH3)Fe2Se2 (A =鋇, 鍶 or 鈣)是 two-gap model、超導相干長度(0) (4.96 nm for A = Ba 和 2.33 nm for A = Sr)、Ginzburg-Landau parameters (102.4 for A = Ba 和 266 for A = Sr)、超導穿透深度 penetration depths (0) (508.2 nm for A = Ba 和 620 nm for A = Sr)以及超導能隙分別為1 = 6.47 meV 和 2 = 1.06 meV。. 氨. 鋇. 氨熱法: ammonothermal · 7. 鋇: barium · 7. 超. 鍶. 超導: superconductor · 7. 鍶: strontium · 7. 超導性質: superconducting properties · 7. 鐵鈣鐵硒: iron-selenium · 7 鈣: calcium · 7. 7.

(8) Abstract High purity samples of Ax(NH3)Fe2Se2 (A = barium, strontium and calcium) superconductors were successfully synthesized by intercalating alkaliearth metals into tetragonal -FeSe by liquid ammonia. The ammonothermal method employed is known for capable of preparing single phase alkali/alkaliearth-intercalated iron-basic superconductors. The coexistence of antiferromagnitism in the alkali-containing iron-selenium superconductors synthesized by conventional thermal process is a huge barrier interfering detail studies of superconductivity. Beside the pure phase for superconductivity discussion, the enhancement of critical temperature Tc (Tc = 39 K for A = Ba, 44 K for Sr and 43 K for Ca) after alkali/alkaliearth intercalation into -FeSe attracts even more interests. In this work, the details of -FeSe preparation, ammonothermal intercalation process, lattice structure and magnetic properties measurements are described and used for physical parameters derivation. The elongated c-axis and almost unchanged a-axis of Bax(NH3)Fe2Se2 and Srx(NH3)Fe2Se2, comparing with -FeSe, suggested an unchanged intra-Fe2Se2-layer structure and the Tc enhancement is due to a 3D to 2D-like Fermi surface transformation. The superconducting properties coherent lengths (0) (4.96 nm for A = Ba and 2.33 nm for A = Sr), Ginzburg-Landau parameters (102.4 for A = Ba and 266 for A = Sr)and penetration depths (0) (508.2 nm for A = Ba and 620 nm for A = Sr) obtained from the extrapolated lower and upper critical fields Bc1(0 K) (30 G for A = Ba and 24 G for A = Sr) and Bc2(0 K) (13.4 T for A = Ba and 60.7 T for A = Sr) indicates that both compounds are typical type-II superconductors. The temperature dependence of 1/2(T) of Bax(NH3)Fe2Se2 deduced from the low field magnetic susceptibility shows a two-gap s-wave behaviour with superconducting gaps of 1 = 6.47 meV and 2 = 1.06 meV.. 氨. 鋇. 氨熱法: ammonothermal · 7. 鋇: barium · 7. 超. 鍶. 超導: superconductor · 7. 鍶: strontium · 7. 超導性質: superconducting properties · 7. 鐵鈣鐵硒: iron-selenium · 7 鈣: calcium · 7. 8.

(9) List of the figures and tables Fig.1-1 Fig. 1-2. Fig.1-3 Fig. 1-4. Fig. 1-5. Crystal structures from left to right are FeSe, LiFeAs, BaFe2As2, LiFeAsO[ (Kordyuk, 2012)] ...................................................................... Low field susceptibility data of various FexSe, showing that β-Fe1.03Se is nonsuperconducting and that superconductivity improves going from β-Fe1.02Se to β-Fe1.01Se. For comparison, the susceptibility of a sample poisoned with oxygen, similar to previous work, is also shown (dashed Line) ........................................................................................................... Temperature dependence of the resistivity with various Te concentrations at zero magnetic field ................................................................................... (a)X-ray diffraction pattern of the crystal containing both 30 K superconducting phase and 44 K antiferromagnetic phase. Lower:X-ray diffraction pattern of the crystal with only a 30 K phase. (b) SEM image of the crystal with 44 K 245 phase. Dashed blue line indicates the border of Region I, in which EDX gives K:Fe:Se ratio of 0.9:2.17:2. The rest of the area is labeled as Region II, in which K5Fe5Se ratio is 0.8:1.7:2. The light green ellipse represents the laser spot in Raman measurements.................. Zero-field-cooling (blue) and field-cooling (red) measurement of temperature-dependence magnetization of Ba0.8Fe2Se2 by SQUID. Criticle. temperature Tc of Ba0.8Fe2Se2 is 39 K. Left inset is magnetic field-dependence magnetization. Right inset is temperature-dependence resistivity ...................................................................................................... Fig. 1-6 ZFC and field-cooled measurements on the three samples of Li0.6(1) (NH/D2)0.2(1) (NH/D3)0.8(1) Fe2Se2 measured using µSR and NPD. Red symbols: µSR sample; blue symbols: H-containing NPD sample; green symbols: D-containing NPD sample ............................................................ Fig. 2-1 Binary phase diagram of Fe1+xSe. [ (Schuster, Mikler, & Komarek, 1979)] Fig. 2-2 Binary phase diagram of Fe1+xSe below 480oC [ (McQueen, et al., 2009)] Fig. 2-3 Selenium oxides glued to the wall in Left quartz tube. Right quartz tube is quite clear ..................................................................................................... Fig. 2-4 In the begin, the samples were sealed in single quartz tube. The quartz tube was crack finally .......................................................................................... Fig. 2-5 (a) Smaller quartz .............................................................................................. Fig. 2-5(b) Smaller quartz .............................................................................................. Fig. 2-6 -Fe1+xSe in Double quartz tube no crack ................................................... Fig. 2-7 Ammonothermal Method Schematic diagram ............................................. 9. 14. 15 15. 16. 17. 18 21 22 22 23 23 24 24 26.

(10) Fig. 2-8 Fig. 2-9 Fig. 2-10. Fig. 2-11 Fig. 2-12 Fig. 2-13 Fig. 2-14 Fig. 3-1 Fig. 3-2 Fig. 3-3 Fig. 3-4 Fig. 3-5 Fig. 3-6 Fig. 3-7 Fig. 3-8. Fig. 3-9. Equipment for ammonalthermal methods .................................................... Block Diagram of powder x-ray diffractometer .......................................... Block diagram of SQUID detector model SPMS for magnetization and Magnetic susceptibility measurement system of SQUID (QUANTUM DESIGN,MPMS/MPMS-7 systems) ......................................................... MPMS Response to Dipole Point Source of SQUID (QUANTUM DESIGN, MPMS/MPMS-7 systems) ........................................................ Schematic circuit of electrical resistance measurement............................... Schematic diagram of closed-cycle refrigerator .......................................... Schematic diagram of closed-cycle refrigerator with resistence box and sample holder ............................................................................................... X-ray diffraction pattern of Fe1.0081Se which was sealed in single quartz tube. Hex mean the hexagonal phase(2q=41.6o) ........................................ X-ray diffraction pattern of Fe1.01Se which was sealed in single quartz tube. Hex mean the hexagonal phase(2q=41.7o) ........................................ X-ray diffraction pattern of Fe1.012Se which was sealed in single quartz. 26 27. tube. Hex mean the hexagonal phase(2=41.9o) ........................................ Smaller quartz .............................................................................................. Smaller quartz .............................................................................................. X-ray diffraction pattern of superconducting Fe1.01Se which was sealed in double quartz tube. No hexagonal phase was observed ............................... X-ray diffraction pattern of superconducting Fe1.012Se which was sealed in double quartz tube. No hexagonal phase was observed ............................... Bulk superconducting transition of Fe1.008Se(black spots) and Fe1.01Se(purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G. The critical temperature Tc of Fe1.008Se(black spots) and Fe1.01Se(purple spots) are separately 9.4 K and 8.8 K ........................................................................... Bulk superconducting transition of Bax(NH3)Fe2Se2 (black spots) and Fe1.01Se(purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G for Bax(NH3)Fe2Se2 and 1 G for Fe1.01Se. The critical temperature Tc of. 29 40 40. 30 30 31 33 36 38 39. 41 41. 42. Bax(NH3)Fe2Se2 (black spots) and Fe1.01Se(purple spots) are separately 40 K and 10.5 K. The amount of ammonia inserted to autoclave was. Fig. 3-10. according to the ratio of liquid ammonia and -Fe1.01Se plus Barium is 17.5 c.c./g .................................................................................................... 43 Bulk superconducting transition of Srx(NH3)Fe2Se2 (black spots) Magnetic susceptibility measured with sample cooled undergoes zero field 10.

(11) Fig. 3-11. Fig. 3-12. Fig. 3-13. Fig. 3-14. Fig. 3-15. Fig. 3-16. cooling(ZFC) with Ba =5 G. The critical temperature Tc of Srx(NH3)Fe2Se2 (black spots) is 45 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and b-Fe1.01Se plus strontium is 2.19 c.c./g ..................................................................................................... 44 Bulk superconducting transition of Cax(NH3)Fe2Se2 (red spots) and Fe1.01Se(blue spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G for Cax(NH3)Fe2Se2 and 5 G for Fe1.01Se. The critical temperature Tc of Cax(NH3)Fe2Se2 (red spots) and Fe1.01Se(blue spots) are separately 43 K and 9 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and b-Fe1.01Se plus calcium is 2.19 c.c./g .................................... 45 Bulk superconducting transition of Bax(NH3)Fe2Se2. Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC,black spot) and filed cooling(FC,black hole) with Ba =10 G. The critical temperature Tc of Bax(NH3)Fe2Se2 are 40 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and -Fe1.01Se plus Barium is 18.37 c.c./g ................................... 46 Powder X-ray diffraction patterns of Bax(NH3)Fe2Se2 and. The small peaks corresponding to hexagonal δ-FeSe are labeled by ”H”, iron oxide by ”Fe2O3” and unknown phases by asteroids ............................................. 47 Bulk superconducting transition of Cax(NH3)Fe2Se2 (purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =2 G. The critical temperature Tc of Cax(NH3)Fe2Se2 (red spots) are 43 K and T of D2 is 12 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and -Fe1.01Se plus calcium is 8.75 c.c./g .................................... 48 The superconducting Ba-T phase diagram of Bax(NH3)Fe2Se2 derived from magnetic measurements. The Bc1(0) ∼30 G was obtained by simple extrapolation and the linear fitting of Bc2(T) was shown by solid curves. The dashed line with Birr is only a guide to the eyes ................................... 50 Conparation of prefect Meissner effect and imperfect Meissner effect. The black zone in the circle is mean the sample is in Meissner state. Then we will get the magnetic susceptibility is. 0. The white zone in the circle is. mean the sample is in vortex state. And the magnetic susceptibility is. (T).  is penetration depth ....................................................................... Fig. 3-17 a Scale under the scope. In order to estimate the size of powder of the 11. 51.

(12) Ax(NH3)Fe2Se2. The distance between two minor ticks which close eachother is 1 mm. The distance between two major ticks is 10 mm .......... Fig. 3-17 b These black spot are powder of Ax(NH3)Fe2Se2( A = Ba or Ca ) .............. Fig. 3-17 c This photo is highlight-photo of Fig. 3-17 b ................................................ Fig. 3-18 The temperature dependence of (1/λ)2 , proportional to superfluid density, of Bax(NH3)Fe2Se2 estimated from low-field magnetic susceptibility. The data can be well described by a two-gap s-wave model (solid brown curve) with a larger gap ∆1 = 6.47 meV and a smaller gap ∆2 = 1.06 meV. The dashed curves are the individual contributions of each gap. The single-gap BCS behavior is shown in green for comparison......................................... Fig. 3-19 Superconducting gap versus distance between the iron-selenide-faces. Non-empty-sample-spot is mean i=1. Empty-sample-spot is mean i=2. This figure show us that enhancement of the distance between the iron-selenide-faces will affect the superconducting gap. Black squares (■). 52 53 54. 57. are the experiment data of FeSe0.85[ (Khasanov, et al., 2008)]. Red triangles (▲) are the experiment data of FeSe0.5Te0.5[ (Biswas, Balakrishnan, Paul, Tomy, Lees, & Hillier, 2010)]. Brown triangles (◄) are the experiment data of Li0.6(NH3)Fe2Se2 [ (Burrard-Lucas, et al., 2013)]. Green triangles (►) are the experiment data of Li(C5H5N)0.2Fe2Se2[ (Biswas, et al., 2013)]. Purple stars (★) are the experiment data of Bax(NH3)Fe2Se2 that produce by us. .......................................................................................................... Fig. 3-20. 58. Superconducting gap  versus critical temperature Tc. The increasing of superconducting gap enhance Tc. Black squares (■) are the experiment data of FeSe0.85[ (Khasanov, et al., 2008)]. Red triangles (▲) are the experiment data of FeSe0.5Te0.5[ (Biswas, Balakrishnan, Paul, Tomy, Lees, & Hillier, 2010)]. Brown triangles (◄) are the experiment data of Li0.6(NH3)Fe2Se2 [ (Burrard-Lucas, et al., 2013)]. Green triangles (►) are the experiment data of Li(C5H5N)0.2Fe2Se2[ (Biswas, et al., 2013)]. Purple stars (★) are the experiment data of Bax(NH3)Fe2Se2 that produce by us. The solid lines are guides to the eyes ............................................................ Fig. 4-1 Thermal treatment processes ................................................................ Table 4-1 superconducting properties .................................................................... 12. 59 61 62.

(13) Chapter 1 Introduction 1-1. Prologue Superconductivity of mercury with superconducting critical temperature Tc ~ 4.2 K has been discovered since 1911 by Heike Onnes, a large number of the researchers attend to the study of superconductors and benefits for humans. Due to the transferring the electricity without loss of energy is good applications on energy issue. So optimizing and raising the efficacy of the superconductors, e.g. superconducting volume or critical temperature Tc, is important and crucial. And the first goal is exploring the high Tc. In the beginning of the exploring superconductors with high Tc, the result is bland. Until 1987, exploring of superconductor YBCO that superconducting critical temperature Tc = 93 K is lager than 77 K shocked the world.[Wu] Eventually, the record of superconducting Tc was broken by TlBaCaCuO4.5+y with Tc is lager than 120 K.[ (25)] However, the record of the critical temperature Tc can not be raised by all methods no matter physical or chemical. So researchers shifted the goal from the serials of cuprate-superconductors to non-cuprate-superconductors. In 2001, non-cuprate-superconductor MgB2 with Tc = 39 K was discovered.[ (26)]. 1-2. Superconductivity of iron-based system Serials of iron-based oxypnictide superconductors named 1111-system were explored in 2008, e.g., LaFeAsO1-xFx with Tc = 26 K [ (28)] and 43 K after 4G Pa-pressured [ (29)], La1-xSrxFeAsO with Tc = 25 K [ (30)], SmFeAsO0.9F0.1 with Tc = 55 K[ (31), (32)], LaFe1-xCoxAsO [ (33)], Gd1-xThxCoAsO [ (34)] and LaFeAsO1- [ (35)]. Then the superconductor of 122-system named Ba1-xKxFe2As2 with Tc = 38 K that produced by substituting the part of barium by kalium.[ (36)] These compound share the similar and square sheet, e.g. Pb-O structure as shown as Fig.1-1 caused by 4 rectangle planes (1/4Fe-1/4B-1/4Fe-1/4B, B = As or Se) and share the same edge. [ (3)]. 13.

(14) Fig.1-1. Crystal structures from left to right are FeSe, LiFeAs, BaFe2As2, LiFeAsO[ (3)].. In 2008, iron-based superconductors -β-FeSe was developed and the Tc ≃ 8 K(fig. 1-2) [ (1)]. This study has attracted much interest duo to simple lattice structure and sharing a common electronic origin for superconducting mechanism with the much complicated iron-arsenide systems [ (2), (3)]. The Tc of iron-selenide can be raised upto 14.5 K by tellurium partial substitution on selenium site(fig.1-3) [ (4)].. 14.

(15) Fig. 1-2 Low field susceptibility data of various FexSe, showing that β-Fe1.03Se is nonsuperconducting and that superconductivity improves going from β-Fe1.02Se to β-Fe1.01Se. For comparison, the susceptibility of a sample poisoned with oxygen, similar to previous work, is also shown (dashed Line).. Fig.1-3 Temperature dependence of the resistivity with various Te concentrations at zero magnetic field.. 15.

(16) 1-3. Motivation In 2013, superconductor KFe2Se2 was explored [ (7)] by a method that produce of BaFe2As2. But K0.8Fe1.6Se2 with antiferromagnetism coupled with KFe2Se2.. Fig. 1-4 (a) X-ray diffraction pattern of the crystal containing both 30 K superconducting phase and 44 K antiferromagnetic phase. Lower:X-ray diffraction pattern of the crystal with only a 30 K phase. (b) SEM image of the crystal with 44 K 245 phase. Dashed blue line indicates the border of Region I, in which EDX gives K:Fe:Se ratio of 0.9:2.17:2. The rest of the area is labeled as Region II, in which K5Fe5Se ratio is 0.8:1.7:2. The light green ellipse represents the laser spot in Raman measurements.. 16.

(17) Unfortunately antiferromagnetism would affect the measurement of basic superconducting properties and mechanism. Therefore we need a method to solve this problem of antiferromagnetism. However, Bax(NH3)Fe2Se2 produced by ammono-thermal method. was. discovered. and. no. antiferromagnetism. would. be. coupled. with. superconductivity.[ (14), (15)]. Fig. 1-5 Zero-field-cooling (blue) and field-cooling (red) measurement of temperature-dependence magnetization of Ba0.8Fe2Se2 by SQUID. Criticle temperature Tc of Ba0.8Fe2Se2 is 39 K. Left inset is magnetic field-dependence magnetization. Right inset is temperature-dependence resistivity.. 17.

(18) Fig. 1-6 ZFC and field-cooled measurements on the three samples of Li0.6(1) (NH/D2)0.2(1) (NH/D3)0.8(1) Fe2Se2 measured using µSR and NPD. Red symbols: µSR sample; blue symbols: H-containing NPD sample; green symbols: D-containing NPD sample.. 18.

(19) The neutron diffraction studies indicated that ammonia molecules were inserted together with lithium atoms in-between the Fe2Se2-layers in the Tc = 43 K Lix(NH3)Fe2Se2 superconductor[ (15)].. It has been found that Tc of the iron-selenides systems increases. with an increasing adjacent Fe2Se2-layers distance [ (7)]. On the other hand, structural variations of intra-Fe2Se2-layer and electron doping as the origin of Tc enhancement after the Li and NH3 intercalation is also reported. [ (15), (16)]. Definitly. ammono-thermal. method is a good way to help researchers get pure superconductivity without antiferromagnetism and more information by basic study and measurement.. Finally, we. would offer the basic superconducting properties critical temoerature Tc, length of a-axis, length of c-axis, lower critical field Bc1, higher critical field Bc2, Ginzburg-Landau parameter , coherent length , penetration depth and supercondicting gap i = 1 or 2 of Ax(NH3)Fe2Se2 (A = Ba, Sr or Ca) that produced by ammno-thermal method and its' detail.. 19.

(20) Chapter 2 experimental details 2-1. Preparation of -FeSe Iron granules (99.98%, Alfa Aesar) and Selenium shot (99.999%, Alfa Aesar) were mixed with a proper molar ratio (1+x:1, x = 0.005~0.012) and loaded into a one-end-sealed home-made quartz crucible (outer diameter of 10 mm, length of 30mm and wall thickness of 1.25 mm) and fill with argon. Then the crucible was sealed in a 90 mm long quartz tube with inner diameter of 15 mm. The quartz tube was slowly heated in a high-temperature furnace from room temperature to 750oC in 8 hours (93.75 oC /h) and kept for about 2.5 days to ensure complete reaction of selenium and iron. The sample was further heated to 1075 oC in 4 hours (81.25 OC/h) and kept about 1 day for proper melting and mixing. The sample was then quenched to 400 oC in 3~5 minutes and annealed for 4~6 days. Finally, the quartz tube was quenched in liquid nitrogen. To prepare high quality  -FeSe samples, the first soaking duration is vital that it must be long enough to ensure the Fe-Se reaction is complete. The completeness of reaction can be easily distinguished from the color of the quartz tube. If there is un-reacted selenium vapor, the tube will show a light-red-wine color. As shown in Figure 2-1, there is a wide temperature range for the Fe-Se reaction. However, different choice of temperature will change the FeSe solid-Se vapor equilibrium, and further change the final product properties. Another key point is the annealing temperature, see Figure 2-2, that it should not be too high to crystallize into  -FeSe phase. In order to prepare high quality  -FeSe with high superconducting Tc and no hexagonal non-superconducting hexagonal -FeSe phase or other impurities, some details of procedures were worth to be marked. The most important one is that the cooling rate of reacted FeSe from 1075oC to 400oC was much slower than the quartz tube, which makes 20.

(21) the contacting region of the quartz tube with the FeSe bulk to become cracked cracked. If the samples were prepared by simply load the ingredients into a single walled quartz tube, there will be air leaking through the crack and resulted in formation of of unwanted hexagonal-FeSe, FeOx and SeO2 (dark red on the quartz wall) impurities as shown as figure 22-3 and figure 2-4. To avoid cracking of the quartz tube, home-made home made quartz crucibles (outer diameter of 10 mm, length of 30mm and wall thickness of 1.25 mm) were used to hold the reaction ingredients inside the evacuated quartz tube. One more important thing about the quartz crucibles is that their bottom should have as less contact area with the outer tube as possible(see fig. 2-4, 4, fig. 2-5(a), 2 fig. 2-5(b) and fig. 2-6).. Fig. 2-1. 2 Binary phase diagram of Fe1+xSe. [ (27)]. 21.

(22) Fig. 2-2. Binary phase diagram of Fe1+xSe from temperature T = 280 oC to 480 oC [Phys. Rev. B 79 (2009) 014522]. Fig. 2-3 Selenium oxides glued to the wall in Left quartz tube. Right quartz tube is quite clear.. 22.

(23) Fig. 2-4 In the begin, the samples were sealed in single quartz tube. The quartz tube was crack finally.. Fig. 2-5 (a) Smaller quartz. 23.

(24) Fig. 2-5(b) Smaller quartz. Fig. 2-6 -Fe1+xSe in Double quartz tube no crack. 24.

(25) 2-2. Preparation of Ax(NH3)Fe2Se2 (A = Ba, Sr or Ca) The alkaline earths metal (Ba, Sr or Ca) and ammonia molecule intercalated Ax(NH3)Fe2Se2. (A. =. Ba,. Sr. or. Ca). superconductors. were. prepared. by. ammonothermo-reaction. The previous prepared  -FeSe and alkaline earths metal were placed into the autoclave with desired ratio (2:0.8 in molar ratio) with magnetic stirrer. Little amount of fresh n-hexane was used to avoid unwanted oxidation of the alkaline earth metal and  -FeSe powder. The autoclave was then evacuated carefully for no residual n-hexane before the introduction of ammonia into the autoclave. Gaseous ammonia (99.9 %) was then injected into the autoclave to a pressure slightly greater than atmosphere pressure. After closing the valve, the autoclave was cooled by merging into liquid nitrogen for ammonia condensation. The ammonia injection valve was opened when the pressure inside the autoclave was lowered to allow ammonia gas flowing in for condensation. The injected amount of ammonia gas was monitored by a flow meter until desired volume. The filled autoclave was left in room temperature for 3.5~4 days for reaction with continuous stirring using magnetic stirrer.. The volume of ammonia was determined by the dissolved concentration of alkaline earth metal to liquid ammonia to be between 0.1~0.3 at%. In addition, to ensure complete intercalation reaction, the ammonia liquid inside autoclave should be at least of 5 mm deep (A +  -FeSe : ammonia ~ 1 g : 8.75 ml, A = Ba, Sr or Ca).. 25.

(26) Fig. 2-7. Ammonothermal Method Schematic diagram. Fig. 2-8 Equipment for ammonalthermal methods.. 26.

(27) 2-3. Analysis of structure by X-ray diffraction The powder X-ray diffraction patterns of the prepared samples were be performed partially in the Physics Institute of Academia Sinica and others were measured in Department of Physics in National Taiwan University. The former is made by a Rigaku XXXX diffractometer with a Cuα (λ = 1.54187 Å) anode under 45 kV accelerating voltage and 40 mA electron beam current. The later was carry out by a Rigaku Rotating Anode XXX diffractometer with 50 kV accelerating voltage and 100 mA electron beam current. The scanning range of the 2 is from 10o to 50o with a 0.02o step, in the cases using NTU diffractometer a 0.025o step for continuous mode and 0.01o step for incontinuous mode were used. The schematic diagram in Fig. 2-9 shows the operating concepts of the instruments.. Fig. 2-9. Block Diagram of powder x-ray diffractometer 27.

(28) 2-4. Magnetism measurements The magnetization and magnetic susceptibility measurements were carried out by a QUANTUM DESIGN MPMS2 superconducting quantum interference device (SQUID) magnetometer with a temperature control module that provides an active-regulated, precision thermal environment over range from 2 to 350 K and applied magnetic field from 5 gauss to 1 tesla. The superconducting magnet system provides a reversible field operation ±1 T using a non-overshoot technique for irreversibility of magnetic susceptibility measurement. The SQUID detector system that includes model 2000 SQUID amplified control electronics, sensing pick-up and special filter with full computer control via the HP-150 interfaced computer. The block diagram of SQUID detector system is shown in Fig. 2-10 and Fig. 2-11. The sample was loaded in a capsule and attached to the sample holder by a clear plastic straw. After putting into the sample chamber, the sample position was carefully calibrated to make it site at the center of SQUID detecting coil array. The data were measured and stored automatically by the MPMSR2 software. For zero-field cooled (ZFC) measurements, the “Magnetic reset” option was used to quench the superconducting magnet before cooling procedure to reduce the residual or remnant field to less than 0.2 G. Due to the temperature control mechanism, whenever the temperature was raised from lower than 4.4 K to higher than 4.5 K the sample was heated to a temperature higher than its Tc and field was set to zero before cooling down to the measurement temperature. These additional operations were added under the consideration of the limitation of the SQUID temperature control processes, to ensure all cooling processes are truly under ZFC mode.. 28.

(29) Fig. 2-10. Block diagram of SQUID detector model SPMS for magnetization and Magnetic susceptibility measurement system of SQUID (QUANTUM DESIGN, MPMS/MPMS-7 systems) MPMS response to Dipole Point Source. Fig. 2-11. MPMS Response to Dipole Point Source of SQUID (QUANTUM DESIGN, MPMS/MPMS-7 systems). 29.

(30) 2-5. Electric Resistance measurement The system will separate three parts to description in this section:. Measurement system Resistance of sample is measured by four-probe technique. The schematic diagram show as this below: The power of circuit comes from lock-in amplifier then connects to the resistance switching box. On the other hand, the Rreg not only can prevent the total current overload but control the total current during measure. The different temperature will caused the total resistance changed dramatically only if this Rreg is 10 to 100 times than sample which is measured. The work of Rref helped us to calculate the total current in this circuit. Two volts of Rref and Rsample are measured by two lock-in amplifier which are connected to computer and controlled by LabVIEW. Rreg: prevent the total current overload Rreg. Rref: convert this volt for current Resistance switching box. Lock-in generator Rrf Measured by Lock-in amplifyer Sample. Sample space. I+ V+. V- I-. Rreg: total six resistance can be switched (1, 10, 100, 1K, 10K, 100K Ω). 30.

(31) Rref: total six resistance can be switched (0.1, 1, 10, 100, 1K, 10K Ω). Fig. 2-12 Schematic circuit of electrical resistance measurement. 31.

(32) Closed-cycle refrigerator system Basic principle: The principle of closed-cycle refrigerator is called Gifford-McMahon (GM) refrigerator. Here have 4 steps to cool the metal which is chose. PH. TL. TH. Switching valve. Displacer. Cold finger. PL. QH. Heat exchanger. Shield QL. Fig. 2-13 Schematic diagram of closed-cycle refrigerator. Step1 (a) to (b): while high pressure enters the space, the displacer is moved to the left. High pressure gas is set at the right. Step2 (b) to (c): the valve is switched from high to low pressure. The high pressure gas expends then absorbs heat from TL state. Step3 (c) to (d): the displacer is reset to the right and let the displacer pass through low temperature gas. Step3 (d) to (a): through the high pressure in the left space and repeat Step1 again.. 32.

(33) PH. TH. TL. PH. Displacer. TH. TL. Displacer. PL. PL. (a) PH. TH. (b). TL. PH. TH. TL. Displacer. Displacer. PL. PL. (c). (d). The 4 Kelvin Closed Cycle Refrigerator Systems from Janis and SHI Sumitomo (SHI) 4 K Refrigerator - RDK-408D2 have two GM refrigerator stages and the working gas is helium. The system can cool down the cold finger (sample holder) to 4.2 Kelvin at second stage. The connection between lock-in, resistance switching box, heater and closed cycle system will show in next paragraph.. 33.

(34) Instrument setup: The R-T measurement system is connected by total 22 enameled insulated wires from sample holder space to thermometer and resistance switch box. From the fig, the sample space is desired to place 3 samples which are measured in the same while (12 enameled wire need to be used) for convenience and advanced hardware in the future. The two sensors are placed in different position. The sensor I is contacted well to the cold finger in order to detect the temperature right at the place and the sensor II is placed to the sample holder because the distance between sensor I and sample holder which is removable provides the temperature which have a gradient, also, the sensor II can avoid the different temperature from sensor II to sample when they are closed (8 enameled wire need to be used). Last one thing is heater which is placed at near the cold finger and is used to control temperature at the second between the measurements from this moment to next one. This heating controller usually needs couple, one of them offers a main power to resist the power of cold head and another one maintain the temperature which is set. But now this system has one heater to control for desire. Because the well two layer shielding can resist the radiation and offer a vacuum space to defend the thermal convection from gas, the system can be consider a thermal equilibrium state during measurement from 4 K to 280 K (4 enameled wire need to be used).. 34.

(35) Lock-in amplifier Thermometer. Helium Refrigerator. Lock-in amplifier. Resistance Cold head. switching box. Connect to sample and circuit. I. Thermometer sensor I III. II Thermometer sensor II Sample space. sensor II. Sample holder Fig. 2-14 Schematic diagram of closed-cycle refrigerator with resistence box and sample holder. 35.

(36) measurement control by LabVIEW This program is desired to calculate the resistance of sample when the specific temperature is stood still then plot and save data. One of two functions is data selection, another one is desired as a controller for heater in this program.. Data selection: The basic idea is that we want to clean up the data which isn’t need, so the data is selected in a specific range. For temperature, the condition of the data which is decided to save is how different from the last point that have been saved to newest one. Constrain of decision is not the same for every range (for instance, form 273 K to 200K, per 1 K saved one point). In order to save the phase transition in R-T diagram precisely, for the resistance part, the condition is that the newest one value of resistance is different from the last one about 5 %. If the condition is agreed, the data will be saved and become the last one data.. Heat Controller: This heat controller relies on the temperature which is detected by Sensor I to optimize the value of PID and power limit. The first point about temperature controller is that PID of thermometer is needed to be found for each range of specific temperature and every PID accompany different power limit must to fix one. Due to the data will out of control during the sensitive of PID and power limit switching, the program has to by pass the unreal data about combination of data selection and heat controller by case selection.. 36.

(37) Chapter 3 Result and Discussion 3-1. The selection of Fe1+xSe. Fig. 3-1 X-ray diffraction pattern of Fe1.0081Se which was sealed in single quartz tube. Hex mean the hexagonal phase(2q=41.6o).. 37.

(38) Fig. 3-2 X-ray diffraction pattern of Fe1.01Se which was sealed in single quartz tube. Hex mean the hexagonal phase(2q=41.7o).. Fig. 3-3 X-ray diffraction pattern of Fe1.012Se which was sealed in single quartz tube. Hex 38.

(39) mean the hexagonal phase(2=41.9o).. Fig. 3-4 Smaller quartz. 39.

(40) Fig. 3-5 Smaller quartz. Fig. 3-6 X-ray diffraction pattern of superconducting Fe1.01Se which was sealed in double quartz tube. No hexagonal phase was observed.. 40.

(41) Fig. 3-7 X-ray diffraction pattern of superconducting Fe1.012Se which was sealed in double quartz tube. No hexagonal phase was observed.. Fig. 3-8 Bulk superconducting transition of Fe1.008Se(black spots) and Fe1.01Se(purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G. The critical temperature Tc of Fe1.008Se(black spots) and Fe1.01Se(purple spots) are separately 9.4 K and 8.8 K.. 41.

(42) 3-2. Result of Ax(NH3)Fe2Se2 (A=Ba, Sr or Ca). Fig. 3-9 Bulk superconducting transition of Bax(NH3)Fe2Se2 (black spots) and Fe1.01Se(purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G for Bax(NH3)Fe2Se2 and 1 G for Fe1.01Se. The critical temperature Tc of Bax(NH3)Fe2Se2 (black spots) and Fe1.01Se(purple spots) are separately 40 K and 10.5 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and -Fe1.01Se plus Barium is 17.5 c.c./g.. 42.

(43) Fig. 3-10 Bulk superconducting transition of Srx(NH3)Fe2Se2 (black spots) Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G. The critical temperature Tc of Srx(NH3)Fe2Se2 (black spots) is 45 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and b-Fe1.01Se plus strontium is 2.19 c.c./g.. 43.

(44) Fig. 3-11 Bulk superconducting transition of Cax(NH3)Fe2Se2 (red spots) and Fe1.01Se(blue spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =5 G for Cax(NH3)Fe2Se2 and 5 G for Fe1.01Se. The critical temperature Tc of Cax(NH3)Fe2Se2 (red spots) and Fe1.01Se(blue spots) are separately 43 K and 9 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and b-Fe1.01Se plus calcium is 2.19 c.c./g.. 44.

(45) Fig. 3-12 Bulk superconducting transition of Bax(NH3)Fe2Se2. Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC,black spot) and filed cooling(FC,black hole) with Ba =10 G. The critical temperature Tc of Bax(NH3)Fe2Se2 are 40 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and -Fe1.01Se plus Barium is 18.37 c.c./g.. The powder X-ray diffraction patterns of Ax(NH3)Fe2Se2 (A = Ba or Sr), as shown in Figure 3-13, can be well indexed by body-centered-tetragonal (bct) Li0.6(NH3)Fe2Se2- type structure (space group: I4/mmm) [ (15)]. Minor phases of impurities were barely observed for hexagonal FeSe (marked by “H” and iron oxide (by “Fe2O3”), and unknown phases (by asteroids). No trace of superconducting precursor β-FeSe was observed. The derived lattice parameters for A = Ba are a = 0.3787 nm and c = 1.6885 nm, and for A = Sr are a = 0.3834 nm and c = 1.7318 nm. The greatly elongated c-axes observed are consistent with the literatures and can be attributed to NH3 molecules co-intercalation [ (14), (15), (18), (19)].. 45.

(46) Lager lattice parameters and unit cell volume observed for Sr-compound (V = 0.2542 nm3 ) than Ba-compound (V = 0.2422 nm3 ) suggests a higher content of intercalated metal atoms in the former, which is consistent with the preliminary refinement results that the stoichiometric parameter x of ∼0.25 and ∼0.4 for A = Ba and Sr, respectively. However, due to the signal to noise ratio of the XRD data is not conclusive enough, we left the Ba/Sr content as undetermined in the following discussion.. Fig. 3-13 Powder X-ray diffraction patterns of Bax(NH3)Fe2Se2 and. The small peaks corresponding to hexagonal δ-FeSe are labeled by ”H”, iron oxide by ”Fe2O3” and unknown phases by asteroids.. 46.

(47) Fig. 3-14 Bulk superconducting transition of Cax(NH3)Fe2Se2 (purple spots). Magnetic susceptibility measured with sample cooled undergoes zero field cooling(ZFC) with Ba =2 G. The critical temperature Tc of Cax(NH3)Fe2Se2 (red spots) are 43 K and T of 2 is 12 K. The amount of ammonia inserted to autoclave was according to the ratio of liquid ammonia and -Fe1.01Se plus calcium is 8.75 c.c./g.. 47.

(48) 3-3. Superconducting properties of Ba x(NH3)Fe2Se2 and 2-gap superconducting model discussion The superconducting critical fields, Bc1(T) and Bc2(T), of Bax(NH3)Fe2Se2 obtained from magnetic measurements are summarized in a Ba−T phase diagram as shown in figure 3-15. The irreversible line, Birr, determined from the deviation points of ZFC and FC curves is also shown as a boundary between vortex glass and liquid states. The zero temperature lower critical field Bc1(0) ∼30 G was easily obtained by extrapolation. An empirical value of Bc2(0) = 13.4 T was obtained by using the Werthamer-Helfand-Hohenberg formula with a linear slope dBc2(Tc)/dT = -0.497 T/K. The Ginzburg-Landau parameter κBa = 102 was derived from these extrapolated Bc2(0) and Bc1(0) values by solving Bc2/Bc1 = 2κ 2/lnκ, which indicates that Ba x(NH3)Fe2Se2 is a typical type-II superconductor as expected. Since the superconducting coherent length ξBa(0) = 4.96 nm can be easily derived by using the formula Bc2 = Φ0/2πξ2 , it is straight forward to calculate the magnetic field penetration depth λBa(0) = κξ(0) = 508 nm. Similar analysis was performed on Srx(NH3)Fe2Se2 and the obtained critical fields were Bc2(0) = 61.4 T and Bc1(0) = 24 G, by which the superconducting parameters κSr = 266, ξSr(0) = 2.33 nm, and λSr(0) = 620 nm were derived.. 48.

(49) Fig. 3-15 The superconducting Ba-T phase diagram of Bax(NH3)Fe2Se2 derived from magnetic measurements. The Bc1(0) ∼30 G was obtained by simple extrapolation and the linear fitting of Bc2(T) was shown by solid curves. The dashed line with Birr is only a guide to the eyes.. 49.

(50) Fig. 3-16 Conparation of prefect Meissner effect and imperfect Meissner effect. The black zone in the circle is mean the sample is in Meissner state. Then we will get the magnetic susceptibility is. 0. The white zone in the circle is mean the sample is in vortex state. And. the magnetic susceptibility is. (T).  is penetration depth.. To further investigate superconductivity of the system, temperature dependence of superfluid density, proportional and presented by 1/λ2 , of Ba x(NH3)Fe2Se2 was estimated and plotted in figure 3-18. The London penetration depth λ(T) was derived by solving the equation χ(T)/χ0 =∫(1−3 (λ/ r) cot( r/λ )+3 λ2/r2 )r3g(r) dr /∫r3g(r)dr---------------(1) where χ0 is the susceptibility of perfect diamagnetic spheres and g(r) is the grand size distribution function, which was obtained by counting sample powder grands under an optical microscope as g(r) = 95 exp(−((log r + 0.5)/0.382)2 ).. 50.

(51) Fig. 3-17 a. Scale under the scope. In order to estimate the size of powder of the Ax(NH3)Fe2Se2. The distance between two minor ticks which close eachother is 1 mm. The distance between two major ticks is 10 mm.. 51.

(52) Fig. 3-17 b. These black spot are powder of Ax(NH3)Fe2Se2( A = Ba or Ca ).. 52.

(53) Fig. 3-17 c. This photo is highlight-photo of Fig. 3-17 b.. 53.

(54) The formula, (1), is mean the superconductor would not be completely perfect Meissner state, i.e., no applied field would penetrate into the superconductor that is in perfect Meissner state, in the ordinary way. However, the estimation of magnetic susceptibility χ(T) would be complex when the superconductor is in superconducting state but imperfect Meissner state. In order to solve this problem, we applied formula (1). Since the 10-G applied field became larger than Bc1 for temperature higher than ∼32 K, the penetration depth λ values obtained at those temperature were contaminated by vortex formation, thus 1/λ2 data for T > 32 K were excluded for further discussion. At the low temperature side, 1/λ2 for temperature below 15 K apparently deviated from the saturation behaviour of conventional BCS single-gap model. Referring to similar systems, [ (17), (21)] two-gap model was used for analysis and consistent results were obtained. The temperature dependence of the penetration depth of Bax(NH3)Fe2Se2 was fitted by a weakly coupled two-gap s-wave model [ (20), (21), (22)] λ−2(T)/ λ−2(0) = ω λ−2 (T,∆1)/ λ−2 (0,∆1) + (1 − ω) λ−2 (T,∆2) λ−2 (0,∆2) where λ(0) is the zero temperature penetration depth, ∆i is the ith superconducting gap at T = 0 K and ω is the weighting factor of the first gap [ (21)]. Each component can be expressed within the local London approximation as λ −2 (T)/ λ−2(0) = 1 + 2∫∞ ∆i((∂f/∂E)√(E2−∆i(T)2) )EdE where f = 1/(1 + exp(E/kBT)) is the Fermi function, and the temperature dependence of the gap is approximated as ∆i(T) = ∆i tanh 1.82[1.018(Tc/T − 1)]0.51. [ (17)] The two-gap s-wave model, the brown curve in figure 3-18, describes the temperature dependence of penetration depth very well. The zero temperature gaps values obtained for Ba x(NH3)Fe2Se2 are ∆1 = 6.47 meV and ∆2 = 1.06 meV with ω = 0.69. The derived gap to Tc ratios of 2∆1/kBTc = 3.85 and 2∆2/kBTc = 0.63 are consistent with those in Li(C2H5N)0.2Fe2Se2 (Tc = 40 K) [ (21)] and Li0.6(NH3)Fe2Se2 (Tc = 43 K) [ (15)]. The slightly bigger value for the 2∆1/kBTc, comparing with the BCS value of 2∆0/kBTc = 3.35, suggests that the weak-coupling assumption in the two-gap s-wave model used is a good approximation. Since our samples were randomly orientated powder, the 54.

(55) influence of temperature variation of λc(T) should be observed in diamagnetic susceptibility. However, by taking typical anisotropy of iron-selenide systems and the obtained λ(0), the estimated value of λc(0) is about 2 µm which is larger than most (∼ 80%) grain size of the powder. When the c-axes of the single crystal grains have large angles to the applied magnetic field, magnetic field penetrates into the grains completely even at low temperature which makes the effects of temperature dependence are not observed. Thus the estimated λ(0) value of ∼506 nm could be regarded as the upper bound of λab(0) and the temperature dependence of 1/λ2 represents the supercurrent behaviour in the Fe2Se2-layer.. 55.

(56) Fig. 3-18 . The temperature dependence of (1/λ)2 , proportional to superfluid density, of Bax(NH3)Fe2Se2 estimated from low-field magnetic susceptibility. The data can be well described by a two-gap s-wave model (solid brown curve) with a larger gap ∆1 = 6.47 meV and a smaller gap ∆2 = 1.06 meV. The dashed curves are the individual contributions of each gap. The single-gap BCS behavior is shown in green for comparison.. 56.

(57) Fig. 3-19 Superconducting gap versus distance between the iron-selenide-faces. Non-empty-sample-spot is mean i=1. Empty-sample-spot is mean i=2. This figure show us that enhancement of the distance between the iron-selenide-faces will affect the superconducting gap. Black squares (■) are the experiment data of FeSe0.85[ (17)]. Red triangles (▲) are the experiment data of FeSe0.5Te0.5[ (23)]. Brown triangles (◄) are the experiment data of Li0.6(NH3)Fe2Se2 [ (15)]. Green triangles (►) are the experiment data of Li(C5H5N)0.2Fe2Se2[ (21)]. Purple stars (★) are the experiment data of Bax(NH3)Fe2Se2 that produce by us.. 57.

(58) Fig. 3-20 Superconducting gap  versus critical temperature Tc. The increasing of superconducting gap enhance Tc. Black squares (■) are the experiment data of FeSe0.85[ (17)]. Red triangles (▲) are the experiment data of FeSe0.5Te0.5[ (23)]. Brown triangles (◄) are the experiment data of Li0.6(NH3)Fe2Se2 [ (15)]. Green triangles (►) are the experiment data of Li(C5H5N)0.2Fe2Se2[ (21)]. Purple stars (★) are the experiment data of Bax(NH3)Fe2Se2 that produce by us. The solid lines are guides to the eyes.. 58.

(59) Finally, we would talk about effect of enhance of c-axis to superconducting gap. As fig. 3-19 shown as that superconducting gap 1 and 2 of FeSe0.85 are 18.5437 (K) and 4.4191 (K) opposite to d what is the distance between Fe-Se layers or distance of C-axis devided by the symmtry of the C-axis is 0.55287 nm. Then 1 and 2 of FeSe0.5Te0.5 are 30.168 (K) and 10.08 (K) opposite to d = 0.6029 nm. 1 and 2 of Li0.6(NH3)Fe2Se2 are 113.305 (K) and 14.835 (K) opposite to d = 0.82613 nm. 1 and 2 of Li0(C5H5N)0.2Fe2Se2 are 79.2 (K) and 11.4 (K) opposite to d = 1.15482 nm. 1 and 2 of Bax(NH3)Fe2Se2 are 37.5375 (K) = 6.47 mev and 6.1425 (K) = 1.06 mev opposite to d = 0.84425 nm. Obviously, the effect of enhance of d make something do work to affect the superconducting gap. Then, as fig. 3-20 shown as, the superconducting gap would change the critical temperature Tc of FeSe0.85 , FeSe0.5Te0.5, Li0.6(NH3)Fe2Se2 and Li0(C5H5N)0.2Fe2Se2 because of the enhancement of c-axis of -FeSe.. 59.

(60) Chapter 4 Conclusion In conclusion, quality of -FeSe is important for high quality superconctors Ax(NH3)Fe2Se2 (A = Ba, Sr or Ca). A recipe for stable synthesis of high quality superconcting -FeSe is described by introducing a quartz crucible tube for avoiding oxygen contamination due to quartz tube crack during the fast cooling from melting temperature. Then the samples undergoes a long low-temperature annealing to form desired tetragonal superconducting structure. The operational steps are listed below (Fig. 4-1): 1. Seal granular iron and selenium in evacuated quartz tube with a inner quartz crucible. 2. Heat the tube slowly to ~750 OC (8 hours). 3. Soaking at 750 OC for 48~60 hours in order that gas of selenium react with iron entirely. 4. Heat up to 1075 OC to melting point for proper mixing (stay for 24 hours). 5. Air quench to 380~410 OC in 2 minutes to avoid formation of unwanted phases. 6. Stay for 144 hours at 380~410 OC forming single phase tetragonal -FeSe. 7. Quench in liquid nitrogen in order to freeze the crystal structure.. Fig. 4-1 Thermal treatment processes In order to produce a good Ax(NH3)Fe2Se2 (A = Ba, Sr or Ca), grind the -FeSe entirely and get the -FeSe, A = Ba, Sr or Ca, a few N-hexane and magnet into container. Then pump the air out, put the container into liquid 60.

(61) nitrogen, insert amount of ammonia by mol-ratio of ammonia to -FeSe is 8.75 c.c.:1 g and let magnet stirring for 3.5~4 days(A = Ba) and 6 days(A = Sr or Ca). The measurement results of X-ray diffraction patterns, and the basic superconducting properties from resistance and magnetic measurements (by SQUID) are concluded as table 4-1, e.g., critical temperature Tc, lower critical field at 0 K Bc1(0 K) , higher critical field at 0 K Bc2(0 K), Ginzburg-Landau parameter coherent length got by Ginzburg-Landau theorypenetration depth got by Ginzburg-Landau theory and superconducting gap i = 1 or 2got by calculating from the formula:  (T)/= ∫[1-3(r)cot(r/r2)]r3g(r)dr/∫r3g(r)dr.. -FeSe Lattice parameters a (Å) c (Å) Superconductivity Tc Bc1(0 K) (G) Bc2(0 K) (T) nm nm nm meV meV. A = Ba. Ax(NH3)Fe2Se2 A = Sr A = Ca. 3.773 5.535. 3.787 16.885. 3.834 17.318. -. 10.5. 39 30 13.4 102 4.96 508 6.47. 45 24 61.4 266 2.33 620. 43. 1.06 Table 4-1 superconducting properties. The elongation of c-axis by intercalation cause the fermi-surface changes from 3-D-like -FeSe to 2-D-like one in Ax(NH3)Fe2Se2 as well as the superconducting critical temperature Tc increase. The analysis in Fig. 3-18 shows that Bax(NH3)Fe2Se2 is an s-wave two-gap superconductor with properties listed above.. 61.

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