phonopy phonon-dispersion phonon-dos MedeA phonopy phonopy, phonopy MedeA phonopy MedeA Moruzzi Quasi-harmonic MedeA,Quasi-harmonic phonopy phonopy.
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- ひさとも さんきち
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1 phonopy phonon
2 phonopy phonon-dispersion phonon-dos MedeA phonopy phonopy, phonopy MedeA phonopy MedeA Moruzzi Quasi-harmonic MedeA,Quasi-harmonic phonopy phonopy.
3 phonopy MedeA phonopy MedeA VASP(Vienna Ab-initio Simulation Package) phonon-dos Quasi-harmonic Maple (Bulk modulus) (Debye Temperature)
4 phonopy phonopy MedeA MedeA Quasi-harmonic Quasi-harmonic
5 1 MedeA phonopy phonopy MedeA phonopy MedeA phonopy 1.1 phonopy phonon-dispersion Python Linux phonopy APT(Advanced Packaging Tool) Ubuntu Ubuntu VirtualBox, Vagrant 6 phonopy [4]. 1.2 MedeA,,,,, 3
6 MedeA MedeA- Phonon Job Server/Task Server MedeA [9]. 1.3 phonopy MedeA phonopy Al MedeA VASP phonopy VASP 1 15 phonopy phonopy MedeA phonopy phonopy 1.1: MedeA phonopy. MedeA Phonopy VASP
7 EAM LJ 2.1:. EAM,LJ etc VASP(Vienna Ab-initio Simulation Package) VASP VASP VASP 5
8 VASP munual VASP 1. ω k ( ). phonon K [KJ/mol] : 400K. 6
9 2.1.4 x y z phonopy POSCAR 2.2: F (a, T ) = E(a) + 0 D(ω)f(ω, T ) dω (2.1) a T. E(a) 7
10 . 0 D(ω)f(ω, T ) dω Phonon 2.2. F (a, T ) = k B T ln ( hω 2 sinh( 4πk B T )) dω. (2.2) (2.2). k h. [7] phonon-dos phonon-dos phonon VASP VASP VASP k ω phonon-dos phonon-dos (2.2) 2.2 Quasi-harmonic Quasi-harmonic Maple Maple 1. VASP E V ( ) 2. E V fitting ( ) 8
11 3. Debye Debye ( ) 4. ( 2.2.5, ) Maple Maple Maple C BASIC.[5] Maple quasi-harmonic Lennard-Jones Morse Morse Morse 2 r E V E V 2 E(r) = a + be r + ce 2 r (2.3) Morse E(r) = A 2De (r r 0) + De 2 (r r 0). (2.4) 9
12 a = A. (2.5) b c = 2e r 0. (2.6) D = b2 4c. (2.7) Moruzzi. [8] 2.3: 2. 10
13 2.2.3 (Bulk modulus) x = e r (2.8) (2.3) E = a + bx + cx 2 (2.9) P.[6] P = E V. (2.10) E x P =. (2.11) V x V V = 4 3 r3 (2.12) (2.8) r V r = ln x (2.13) ( ) 3 ln x. (2.14) V = 4 3 x (2.11) P P = x 3 (b + 2cx). (2.15) 4 ln x2 11
14 B B = V P V (2.16) (2.15) P = V P x. (2.17) V x (2.17) (2.16), (2.15) (2.17) x 3 B = 12 ln x ( (b + 4cx) 2 ) (b + 2cx). (2.18) ln x a,b,c :. Θ D [Ry/a.u. 3 ] [ev/a 3 ],[GPa],[kbar] Quasi-harmonic. 12
15 2.2.4 (Debye Temperature) = v s k (2.19) v s g( ) g( ) = V k2 2 2 dk d = V v 3 s (2.20) v s k 1/v 3 s g( ) = V ( 1 v 3 l + 2 v 3 t ) (2.21) 3 1 (longitudinal) 2 (transverse) v t v l 1 v 3 s = 1 v 3 l + 2 v 3 t (2.22) ( V vl v 3 t ) 3 D = 3 (2.23) 3 3 v 3 = 1 v 3 l + 2 v 3 t (2.24) 13
16 2.23 V 6 2 v 3 3 D = 1 (2.25) v ( ) B( ) v = B (2.26) = M V (2.27) V V = 4 3 r3 (2.28) v = r3 B (2.29) ( 3 D = r 3 v3 = r3 ) 1 ( 4 r 3 3 ) 3 ( ) 3 2 B 2 M (2.30) D = (6 2 ) 1 3 ( ) B r3 M (2.31) k B Θ D = h 2 D (2.32) k B D k B h D 2.31 Θ D = ( ) 1 h (6 2 ) K B 4 6 B r3 M. (2.33) 14
17 rb Θ D = M (2.34) v t v l v t = v t = S L (2.35) (2.36) Moruzzi S = 0.30B L = 1.42B v B v = (2.37) 2.31 Θ D (Θ D ) 0 = r0 B M (2.38) r0 [a.u.] M B r0 [kbar] [6] D(y) = 3 y 3 y 0 e x x 4 dx. (2.39) (e x 1) 2 y 0 D 1 y = Θ D [6] K 15
18 2.5:. 2.6:. 16
19 2.2.6 F (r, T ) = E(r) + E D (r, T ) T S D (r, T ). (2.40) T E D S D E D S D E D (r, T ) = 3k B T D ( ΘD T ) + E 0 (2.41) [ ( ) 4 S D (r, T ) = 3k B 3 D ΘD ( ) ] ln 1 e Θ D T (2.42) T E 0 E 0 = 9 8 k BΘ D (2.43) f(r, T ) = E(r) k B T [ D ( ΘD T ) ( ) ] 3 ln 1 e Θ D T k BΘ D. (2.44) 17
20 2.7:. 18
21 3 phonopy MedeA 3.1 MedeA phonopy MedeA Windows GUI phonopy MedeA 1. New bulk System 2. Edit Edit structure Spacegroup Al Spacegroup Fm-3m 3. VASP 4. Add Atom Builders Build supercells 19
22 phonopy 1. POSCAR VASP 2. phonopy 6 MedeA phonopy MedeA phonopy 3.2 MedeA,phonopy VASP INCAR INCAR GUI CUI MedeA 3.1 VASP INCAR DOS, 3.1: MedeA 20
23 phonopy INCAR INCAR PREC = Accurate ENCUT = 300 IBRION = 2 NSW = 60 ISIF = 3 ALGO = V NELM = 60 NELMIN = 12 NELMDL = -12 EDIFF = 1.0e-05 EDIFFG = VOSKOWN = 1 ISPIN = 1 INIWAV = 1 ISTART = 0 ICHARG = 2 LWAVE =.FALSE. LCHARG =.TRUE. ADDGRID =.TRUE. LREAL = Auto MedeA GUI INCAR phonopy MedeA 21
24 3.3 MedeA phonon JobServer/TaskServer phonopy VASP phonon phonopy 1. VASP 2. vasprun POSCAR phonon 6 MedeA 1. VASP MedeA-phonon 2. JobServer 22
25 4 Al,NaCl phonopy,medea Quasiharmonic 4.1 VASP. 4.1:. Al NaCl ( 1.00) ( 1.03) phonopy 4.1 phonopy Al 4.2 NaCl [KJ/mol], [K] NomalCell VolumeExpansionCell 1.03 Al. NaCl Al 23
26 4.1: phonopy Al. 4.2: phonopy NaCl. 24
27 4.1.1 phonopy 4.3 [KJ/mol], 300K phonopy 4.3: phonopy 300K Al. 25
28 4.2 MedeA 4.4 MedeA Al 4.5 NaCl [KJ/mol], [K] 4.5 NomalCell VolumeExpansionCell 1.03 Al K 4.4: MedeA Al. 26
29 NaCl 4.5 Al NaCl 4.5: MedeA NaCl. 27
30 4.2.1 MedeA 4.6 Al 100K,300K,500K MedeA Caluclation-data MedeA fitting 4.6: MedeA. 28
31 4.3 Quasi-harmonic Quasi-harmonic 4.7 NomalCell VolumeExpansionCell K 4.7: Quasiharmonic Al. 29
32 4.3.1 Quasi-harmonic 4.8 [a.u.] [KJ/mol] minimum 4.8:. 30
33 phonopy,medea,quasi-harmonic Al 5.1 [KJ/mol] [K] phonopy MedeA phonopy MedeA Quasi-harmonic phonopy phonopy phonopy 31
34 5.1: Al. 32
35 5.1.2 phonopy,medea,quasi-harmonic Al 300K 5.2 [KJ/mol], Calculation-data MedeA phonopy fitting MedeA,Quasi-harmonic phonopy phonopy phonopy 5.2:. 33
36 6 phonopy MedeA Al,NaCl phonopy phonopy MedeA,Moruzzi Quasi-harmonic Al.,MedeA Quasi-harmonic phonopy phonopy MedeA,Quasi-harmonic phonopy MedeA phonopy 1 MedeA phonopy 1 MedeA,Quasi-harmonic phonopy phonopy MedeA 34
37 35
38 phonopy phonopy VirtualBox,Vagrant,UbuntuOS phonopy apt-get APT VirtualBox VirtualBox OS PC OS OS Ubuntu [1] VirtualBox version for OS X hosts GUI VirtualBox UserManual Vagrant Vagrant VirtualBox Ubuntu [2] MAC OS X Vagrant mac 36
39 [yanase-no-macbook-pro:~/.vagrant.d] yanase% vagrant plugin install vagrant-vbguest Vagrant, virtualbox Vagrant phonopy [yanase-no-macbook?-pro:~/vagrant] yanase% vagrant up Vagrant ssh yanase% vagrant ssh UbuntuOS UbuntuOS Linux [yanase-no-macbook-pro:~/.vagrant.d] yanase% vagrant box add ubuntu virtualbox/opscode_ubuntu-13.10_chef-provisionerless.box [yanase-no-macbook-pro:~/.vagrant.d] yanase% vagrant init ubuntu phonopy [4] phonopy vagrant Python Python apt-get Vagrant Vagrant 37
40 1. Python python 2. apt-get 3. phonopy 4. phonopy 5. python PATH python 6. phonopy setup.py 1 sudo apt-get install python-dev python-numpy python-matplotlib python-tk python-lxml python-yaml 2 sudo apt-get update --fix-missing 3 mv /vagrant/phonopy rc3.tar.gz. 4 tar xvfz phonopy rc3.tar.gz 5 export PYTHONPATH=/usr/lib/python2.7/ 6 sudo python setup.py install --home=. python PATH PATH echo $PATH PATH=$PATH:/home/vagrant/phonopy rc3/lib/python export PATH setup.py sudo python setup.py build sudo python setup.py install 38
41 phonopy Tutorial 1. Pre-process : 2. : VASP 3. Post-process : Phonon-DOS,FreeEnergy,Phonon-dispersion Pre-process phonopy phonopy -d --dim="2 2 2" % ls disp.yaml POSCAR POSCAR-001 POSCAR-002 POSCAR-003 SPOSCAR SPOSCAR disp.yaml POSCAR-(001,002,003) atom.poscarnumber disp.yaml atom Force constants POSCAR-(001,002,003) VASP VASP POSCAR POSCAR- (001,002,003) VASP INCAR 39
42 PREC = Accurate IBRION = -1 ENCUT = 500 EDIFF = 1.0e-08 ISMEAR = 0; SIGMA = 0.01 IALGO = 38 LREAL =.FALSE. ADDGRID =.TRUE. LWAVE =.FALSE. LCHARG =.FALSE. VASP FORCE-SETS vasp disp POSCAR-number vasprun % phonopy -f disp-001/vasprun.xml disp-002/ vasprun.xml disp-003/vasprun.xml Post-process mesh.conf phonon-dos, mesh.conf emacs ATOM_NAME = Al DIM = MP = Post-process phonon-dos POSCAR,FORCE-SET,mesh.conf mac gnuplot 40
43 phonopy -p mesh.conf Post-process FreeEnergy POSCAR,FORCE-SET,mesh.conf F [KJ/mol] S[J/K/mol] vagrant:~/phonopy rc3/al/al-test$ phonopy -t -p mesh.conf _ _ \ _ \ / _ \ _ \ / _ \ _ \ _) (_) (_) _) _. / _ _ \ / _ _ \ (_). / \, _ _ / Mesh sampling mode Settings: Sampling mesh: [8 8 8] Supercell: [2 2 2] Spacegroup: Fm-3m (225) Calculating force constants... Number of irreducible q-points: 20 Calculating thermal properties rc3 # T [K] F [kj/mol] S [J/K/mol] C_v [J/K/mol] E [kj/mol]
44 Quasi-harmonic restart;with(plots):with(plottools):with(stats):with(linearalgebra): with(linalg):with(listtools):with(combinat,permute):with(statistics): with(stringtools):with(plots):with(linearalgebra):with(stats): # E-V Curve # p1:=[[0.95, ],[0.98, ],[0.99, ], [1.00, ],[1.01, ],[1.02, ], [1.03, ],[1.04, ],[1.05, ], [1.06, ],[1.07, ],[1.08, ]]; # ev Ry (8 SuperCell UnitCell ) for i from 1 to nops(p1) do p1[i][2]:=p1[i][2]*(2/27.2)/8; end do; # Al = for i from 1 to nops(p1) do p1[i][1]:=p1[i][1]* ; end do; # a.u. for i from 1 to nops(p1) do p1[i][1]:=p1[i][1]/ ; end do; 42
45 # data11=[[ (a.u.)],[ (Ry)]] # Al fcc sqrt(2)/2 data11:=convert(transpose(convert(p1,array)),listlist); data1:=[(data11[1]*evalf((sqrt(2)/2))/2),data11[2]]; q1:=convert(transpose(convert(data1,array)),listlist); # fitting fit1:=fit[leastsquare[[x,y], y=a+b*x+c*x^2+d*x^3+e*x^4+f*x^5]](data1); f2:=unapply(rhs(fit1),x); pp1:=pointplot(q1); pp2:=plot(f2(r),r=5..6); display(pp2,pp1,labels=["atomicdistance[a.u.]","bindingenergy[ry]"], labeldirections=[horizontal,vertical]); # Morse f1:=(a,b,c,d,r)->a+b*exp(-d*r)+c*exp(-2*d*r); # x0:=fsolve(diff(f2(x),x),x=5..6); y0:=f2(x0); # fitting.y2 y1:=subs(x=x0,diff(f2(x),x)); y2:=subs(x=x0,diff(f2(x),x,x)); y3:=subs(x=x0,diff(f2(x),x,x,x)); # f1 a,b,c,d,x0 a,b,c,d y0=f1(a,b,c,d,x0); 43
46 # x0 y2 subs(x=x0,diff(f1(a,b,c,d,x),x))=0; y2=subs(x=x0,diff(f1(a,b,c,d,x),x,x)); y3=subs(x=x0,diff(f1(a,b,c,d,x),x,x,x)); # eqs:={y0=f1(a,b,c,d,x0),subs(x=x0,diff(f1(a,b,c,d,x),x))=0,y2=subs(x=x0, diff(f1(a,b,c,d,x),x,x)),y3=subs(x=x0,diff(f1(a,b,c,d,x),x,x,x))}; sol1:=solve(eqs,{a,b,c,d}); # f1 a,b,c,d f3 f3:=unapply(subs(sol1,f1(a,b,c,d,x)),x); pp3:=plot(f3(r),r=5..6,color=blue); display(pp1,pp2,pp3,labels=["atomicdistance[a.u.]","[ry]"], labeldirections=[horizontal,vertical]); P1: [[ a/a0],[ (ev)]] data11: [[ (a.u.)],[ (Ry)]] data1: [[ (a.u.)],[ (Ry)]] q1: data1 list fit1: fitting f2: fit1 pp1,pp2: f1: Morse x0,y0:, y0,y1,y2,y3: f1 0,1,2,3 eqs: y0,y1,y2,y3 sol1: eqs,a,b,c,d f3: f1 a,b,c,d pp3: 44
47 # B1 B2= B1:=unapply((-lambda^3*exp(-lambda*r))/(12*Pi*ln(exp(-lambda*r))),r); B2:=unapply((b+4*c*exp(-lambda*r))-(2/ln(exp(-lambda*r)))* (b+2*c*exp(-lambda*r)),r); # B3(r):=B1(r)*B2(r)*((27.2/2)/( ^3))* *10; #, B:=unapply(B3(r),r); evalf(b(x0));r0:=x0; plot(b(r),r=6..8.5,color=black,labels=["atomicdistance[a.u.]", "BulkModulus\UTF{008E}\UTF{0087}[Kbar]"], labeldirections=[horizontal,vertical]); B1: 2.18 B2: 2.18 B3: B1,B : ev/ GPa B: B1,B2 r0: =x0 45
48 # (Al) M:=26.98; # thetad:=unapply(41.63*(r*b(r)/m)^(1/2),r); plot(thetad(r),r=6..6.4,labels=["atomicdistance[a.u.]","temperature[k]"],labeldirections=[horizontal,vertical]); # Debye:=unapply((3/y^3)*int(exp(x)*x^4/(exp(x)-1)^2,x=0..y),y); # Df:=unapply(Re(evalf(Debye(thetaD(r)/T))),r,T): plot(df(r,300),r=5..6,color=black,labels=["atomicdistance[a.u.]", "DebyeTemperature"],labeldirections=[HORIZONTAL,VERTICAL]); M: thetad: 2.38 Debye: 2.39 Df: 46
49 #Ry: 1Ry= * 10^(-18) [J] #kb: Ry:= *10^(-18); kb:= *10^(-23); # func:=unapply((kb/ry)*t*(df(r,t)-3*ln(1-exp(-thetad(r)/t)))- (9/8)*(kb/Ry)*thetaD(r),r,T): plot(-func(r0,x),x= ); # g:=(-f3(r0)+f3(r)-func(r,t))*10^3: f:=unapply(g,r,t): # f(atomdistance,temperature) p2:=plot(f(r,100),r= ,color=black); p3:=plot(f(r,200),r= ,color=black); p5:=plot(f(r,400),r= ,color=black); p6:=plot(f(r,800),r= ,color=black); # # first100:=evalf(f(5.4,100)): i100:=5.4: for i from 5.4 by to 5.44 do second100:=evalf(f(i,100)): if first100 > second100 then first100:=second100: i100:=i; end if:end do: first100;i100; mi[1]:=[i100,first100]; 47
50 first200:=evalf(f(5.4,200)): i200:=5.4: for i from 5.4 by to 5.44 do second200:=evalf(f(i,200)): if first200 > second200 then first200:=second200; i200:=i; end if:end do: first200;i200; mi[2]:=[i200,first200]; first400:=evalf(f(5.4,400)): i400:=5.44: for i from 5.4 by to 5.44 do second400:=evalf(f(i,400)): if first400 > second400 then first400:=second400; i400:=i; end if: end do: first400; i400; mi[3]:=[i400,first400]; first800:=evalf(f(5.4,800)): i800:=5.4: for i from 5.4 by to 5.44 do second800:=evalf(f(i,800)): if first800 > second800 then first800:=second800; i800:=i; end if: end do: first800; i800; mi[4]:=[i800,first800]; 48
51 #, po1:=pointplot(mi[1]); po2:=pointplot(mi[2]); po3:=pointplot(mi[3]); po4:=pointplot(mi[4]); display(p2,p2,p3,p5,p6,po1,po2,po3,po4,labels=["atomicdistance[a.u.]", "Free energy[mry]"],labeldirections=[horizontal,vertical]); # [mry] pf1:=plot(f(r0,x),x= ,color=red); pf3:=plot(f(r0*1.03,x),x= ,color=green); display(pf1,pf3,labels=["temperature[k]","free energy[mry]"], labeldirections=[horizontal,vertical]); # [KJ/mol] F1:=unapply(f(r0,x)/10^3* * ,x,r): F2:=unapply(f(r0*1.01,x)/10^3* * ,x,r): FE_kj1:=plot(F1(x),x= ,color=red); FE_kj2:=plot(F2(x),x= ,color=blue); display(fe_kj1,fe_kj2,labels=["temperature[k]","free energy[kj/mol]"], labeldirections=[horizontal,vertical]); frac: 2.44 g: 2.40 f: g p2,p3,p5,p6: mi: po1,po2,po3,po4: mi pf1,pf3: F1,F2: mry KJ/mol 49
52 [1] OracleCorporation,Download of Virtualbox, (accessed January 9, 2015). [2] MitchellHashimoto,Vagrant, (accessed January 9, 2015). [3] UbuntuJapaneseTeam,downloadofUbuntu, /vagrant/virtualbox/opscode-ubuntu chef-provisionerless.box (accessed January 9, 2015). [4] OpenSourceDevelopmentNetworkCorporation,SOUCEFORGE.jp, (accessed January 9, 2015). [5], (,2006). [6], - ( 2006). [7], Ti Phonon ( 2014). [8] V. L. Moruzzi, J. F. Janak and K. Schwarz, Calculatedthermalpropertiesofmetals, Phys. Rev. B, 37(1988), [9] Ryoka Systems lnc,medea, (accessed January 9, 2015). 50
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Serverspec でインフラテスト 2018 年 4 月 20 日株式会社フルマークス大久保和彦 目次 1. Serverspec とは 1.1. Serverspecとは 1.2. Serverspecで出来る事 2. セットアップ 2.1. 必要なもの 2.2. インストール 3. デモ 3.1. デモ環境について 3.2. テスト対象サーバーの登録 3.3. サンプルテストの中身 3.4.
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イチからはじめる Linux サーバ構築ハンズオン 事前準備用資料 株式会社リーデックス はじめに 弊社の勉強会にご興味を持っていただきありがとうございます Linuxサーバ構築ハンズオンを受講いただくにあたり 必要なソフトのインストールと環境構築の手順をまとめました 資料はWindows 環境前提で記載してありますが Macでも少しの読み替えで対応できると思います 当日の時間内にインストールからスタートするとインターネットの回線状況によっては環境構築だけで
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1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります
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