Thermodynamics of Cu 47 Ti 34 Zr 11 Ni 8,Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 and Zr 57 Cu 15.4 Ni 12.6 Al 10 Nb 5 bulk metallic glass forming alloys

Size: px

Start display at page:

Download "Thermodynamics of Cu 47 Ti 34 Zr 11 Ni 8,Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 and Zr 57 Cu 15.4 Ni 12.6 Al 10 Nb 5 bulk metallic glass forming alloys"

Esther Lindsey
5 years ago
Views:

1 JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER MAY 2000 Thermodynmics of Cu 47 Ti 34 Zr 11 Ni 8,Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5 ulk metllic glss forming lloys S. C. Glde, ) R. Busch, ) D. S. Lee, c) nd W. L. Johnson Division of Engineering nd Applied Science, Cliforni Institute of Technology, Psden, Cliforni R. K. Wunderlich nd H. J. Fecht Mterils Science, University of Ulm, Alert-Einstein-Alle 47, D Ulm, Germny Received 14 Decemer 1999; ccepted for puliction 18 Ferury 2000 The differences in the thermodynmic functions etween the liquid nd the crystlline sttes of three ulk metllic glss forming lloys, Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5, were clculted. The het cpcity ws mesured in the crystlline solid, the morphous solid, the supercooled liquid, nd the equilirium liquid. Using these het cpcity dt nd the hets of fusion of the lloys, the differences in the thermodynmic functions etween the liquid nd the crystlline sttes were determined. The Gis free energy difference etween the liquid nd the crystlline sttes gives qulittive mesure of the glss forming ility of these lloys. Using the derived entropy difference, the Kuzmnn tempertures for these lloys were determined Americn Institute of Physics. S I. INTRODUCTION Metllic glsses re reltively new clss of mterils. They were first otined from metllic melt y rpid quenching pproximtely 10 6 Ks 1 ) in 1961 y Duwez et l. 1 Recently, new metllic glss forming compositions hve een developed, including L Al Ni, 2 Zr Ni Al Cu, 3 Mg Cu Y, 4 Zr Ti Cu Ni Be, 5 nd Cu Ti Zr Ni. 6 The est glss former out of these lloys is Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5, with criticl cooling rte for glss formtion of 1 K s 1. 7 Due to the improved glss forming ility of these lloys, experiments on the thermophysicl properties in the glssy stte nd in the supercooled liquid cn now e performed, including mesurements of specific het cpcity, 8,9 viscosity, 10 tomic diffusion coefficient, 11 nd the coefficient of therml expnsion. 12 In this rticle, we investigte the thermodynmics of three ulk glss forming lloys: Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N With criticl cooling rtes from 10 to 250 K s 1, these lloys hve moderte glss forming ility compred to Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be However, these glsses re mong the est noneryllium contining glsses, mking them esier to process nd to hndle. After mesuring the het cpcity of these lloys in the crystlline solid, the morphous solid, the supercooled liquid, nd the equilirium liquid, the differences in thermodynmic functions etween the liquid nd the crystlline sttes cn e determined. The Gis free energy difference gives qulittive mesure of the stility of the glss compred to the crystlline stte. II. EXPERIMENTAL METHODS We prepred the lloys in n rc melter with titnium gettered, ultrhigh purity rgon tmosphere, with elements of purities from 99.9% to %. The nominl compositions of the lloys prepred were Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5. To otin morphous smples for differentil scnning clorimetry DSC experiments, we melted the lloys in qurtz tues in rdio frequency induction furnce nd then injection cst the melt with rgon into copper mold. The molten metls were held in the qurtz tues for s short time s possile usully 10 s to void ny contmintion. In previous work done on SiC composites with Cu 47 Ti 34 Zr 11 Ni 8 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5 s the mtrix mteril, silicon dditions to the lloy improved the therml stility of the morphous solid. 14,15 We do not see this improvement in the therml stility of the morphous solid, so the silicon contmintion from melting these lloys in qurtz tues is thought to e less thn 0.5% tomic. A DSC Perkin Elmer DSC-7 ws used to determine the solute specific het cpcity of the lloys. Heting smple t K s 1 nd then holding it t constnt temperture results in step in het flux given y Q Q t Q t Q t c dt dt, Ṫ 0 Ṫ 0 1 where ( Q/ t) Ṫ 0 is the power required to het the smple nd smple pn t constnt heting rte, ( Q/ t) Ṫ 0 is the power needed to hold the smple nd smple pn t con Author to whom correspondence should e ddressed; electronic mil: sglde@cltech.edu Current ddress: Deprtment of Mechnicl Engineering, Oregon Stte University, Corvllis, OR c Current ddress: Symyx Technologies, Snt Clr, CA /2000/87(10)/7242/7/$ Americn Institute of Physics

2 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l FIG. 1. Therml ehvior of Cu 47 Ti 34 Zr 11 Ni 8 upon heting. The lower temperture dt were otined with DSC heting rte of K s 1 nd the higher temperture dt were otined with DTA heting rte of Ks 1. The onset of the glss trnsition, T g, the onset of crystlliztion, T x, the solidus temperture, T solidus, the temperture t the pek of the melting endotherm, T pek, nd the liquidus temperture, T liquidus, re indicted. The exothermic hump fter the melting pek is due to the rection of the lloy with the grphite crucile. stnt temperture, nd c is the het cpcity of the smple nd smple pn. By performing these het flux steps every 20 K on the metl smple in the smple pn, spphire stndrd in the smple pn, nd the smple pn y itself, the solute specific het cpcity of the metl smple cn e determined y Q metl Q pn c p T metl m spphire metl Q spphire Q pn m metl spphire c p T spphire, 2 where m i is mss, i is molr mss, nd c p (T) spphire is the het cpcity of spphire. 9 The solute specific het cpcity of the supercooled liquid immeditely fter the glss trnsition could not e mesured using the method descried ove ecuse these lloys re not very stle ginst crystlliztion in this temperture rnge. To determine the specific het cpcity in this TABLE I. Glss trnsition tempertures, crystlliztion tempertures, solidus tempertures, pek tempertures pek of the melting endotherm, liquidus tempertures, nd the hets of fusion for the three lloys. The solidus nd liquidus tempertures of Cu 47 Ti 34 Zr 11 Ni 8 mesured in this study differ from the previously reported vlues of 1105 nd 1160 K, respectively see Ref. 6. Lin performed DTA experiments using lumin cruciles, while we performed the DTA experiments using grphite cruciles. The difference in the vlues mesured is ttriuted to the rection of the lloy with the lumin cruciles. T g T x T solidus T pek T liquidus H f kj g tom 1 Cu 47 Ti 34 Zr 11 Ni Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti Zr 57 Cu 15.4 Ni 12.6 Al 10 N Mesured with heting rte of K s 1. Mesured with heting rte of K s 1. FIG. 2. The specific het cpcity of the crystlline solid, the morphous lloy, the supercooled liquid mesured with constnt heting rte experiments, nd the undercooled liquid nd the equilirium liquid mesured with c modultion clorimetry for: Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd c Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5. For Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, the equilirium liquid dt were not mesured, ut vlue of 42.5 J g tom 1 K 1 t 1085 K ws ssigned to llow the determintion of the fitting constnt for the liquid specific het cpcity. The lines on the grphs re the fits to Eqs. 7 nd 8.

3 7244 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l. TABLE II. Fitting constnts for the het cpcity dt, using c p,crystl (T) 3R T T 2 to fit the crystlline stte het cpcity dt nd c p,liquid (T) 3R ct dt 2 to fit the liquid het cpcity dt. J g tom 1 K 2 J g tom 1 K 3 c J g tom 1 K 2 d J g tom 1 K Cu 47 Ti 34 Zr 11 Ni Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti Zr 57 Cu 15.4 Ni 12.6 Al 10 N temperture rnge, constnt heting rte DSC experiments were performed t 0.333, 0.667, 1.33, nd 3.33 K s 1. The specific het cpcity is determined y Q c p,glss Ṫm c p,crystl scling constnt, 3 where Q is the power input, Ṫ is the heting rte, m is the mss, nd is the molr mss. The DSC ws clirted for ech heting rte to ccount for the shift in temperture with different heting rtes. Alternting current c modultion clorimetry 16,17 ws used to mesure the specific het cpcity of the undercooled liquid nd the equilirium liquid. The c modultion clorimetry technique ws performed using TEMPUS Tiegelfreies Elektromgnetisches Prozessieren Unter Schwerelosigkeit, see Ref. 18, n electromgnetic processing fcility tht flew on ord the Ntionl Aeronutics nd Spce Administrtion s NASA spce shuttle. c modultion clorimetry is noncontct technique for mesuring het cpcity; y modulting the power input to the smple nd mesuring the temperture response, the het cpcity cn e determined. Two time constnts re importnt in this experimentl method: c p A T T 0 nd 2 3c p 4 3, 5 R th where c p is the smple het cpcity, A is the smple surfce re, T is the totl hemisphericl emissivity of the smple surfce, is the Stefn Boltzmn constnt, T 0 is the smple temperture, R is the smple rdius, nd th is the smple therml conductivity. 1 is the externl relxtion time due to rditive het loss nd 2 is the internl relxtion time due to the finite therml conductivity of the smple. Het cpcity is determined y P m c p f, 1, 2 T m, 6 where f is correction function for rdition loss nd finite therml conductivity, P m ( ) is the power of modultion, T m ( ) is the mplitude of temperture response to the power modultion, nd is the frequency of modultion. Modultion frequencies of 0.08 nd 0.12 Hz were used in these experiments. A differentil therml nlyzer Perkin Elmer DTA-7, using heting rte of K s 1, ws used to determine the hets of fusion, the solidus tempertures, nd the liquidus tempertures of these lloys. Grphite cruciles were used in these experiments to minimize the rection etween the molten lloy nd crucile. III. RESULTS Upon heting n morphous lloy t constnt heting rte, the lloy goes through the glss trnsition, crystllizes, nd then melts. This ehvior is shown in Fig. 1, DSC scn nd differentil therml nlysis DTA scn of Cu 47 Ti 34 Zr 11 Ni 8. The onset of the glss trnsition T g is indicted y smll endothermic rise. Crystlliztion egins t T x 717 K, with three exothermic peks. Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5 oth hve single crystlliztion pek fter heting through the glss trnsition. For Cu 47 Ti 34 Zr 11 Ni 8, melting egins t the solidus temperture of 1114 K, with the lloy eing completely molten t the liquidus temperture of 1128 K. Integrting the re of the melting pek, we find tht the het of fusion is 11.3 kj g tom 1 for Cu 47 Ti 34 Zr 11 Ni 8. The chrcteristic tempertures s well s the hets of fusion of Cu 47 Ti 34 Zr 11 Ni 8 nd the other two lloys, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5, re summrized in Tle I. The specific het cpcity of the crystlline solid, the morphous solid, the supercooled liquid, nd the equilirium liquid for ech lloy is shown in Figs. 2 2 c. The specific het cpcity for the crystlline nd the morphous sttes ws determined y DSC experiments, while the specific het cpcity of the undercooled liquid nd the equilirium liquid ws determined y c modultion clorimetry. Since the morphous solid is not in thermodynmic equilirium or metstle equilirium in the glss trnsition region, het cpcity dt in this region re not included. The het cpcity of crystl well ove the Deye temperture cn e descried y 19 c p,crystl T 3R T T 2. 7 The het cpcity of n undercooled liquid cn e descried y c p,liquid T 3R ct dt 2, 8 where R J g tom 1 K 1, nd,, c, nd d re fitting constnts. The constnts for oth fits to the specific het cpcity dt for ech lloy re summrized in Tle II.

4 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l FIG. 3. The clculted difference in enthlpy etween the liquid nd the crystlline sttes s function of temperture for Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5,nd c Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5. Also indicted on these plots re the Kuzmnn temperture T K, the glss trnsition temperture T g onset with heting rte of K s 1, nd the temperture t which the Gis free energy of the liquid nd the crystlline sttes re tken to e equl, T f. The specific het cpcity of Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 in the undercooled liquid nd equilirium liquid ws not mesured with c modultion clorimetry. However, the specific het cpcity of the liquid for mny metllic glss forming FIG. 4. The clculted difference in entropy etween the liquid nd the crystlline sttes for Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd c Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5. Indicted on these plots re the Kuzmnn temperture T K, the glss trnsition temperture T g onset with heting rte of K s 1, nd the temperture t which the Gis free energy of the liquid nd the crystlline sttes re tken to e equl T f. lloys, including Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5, 8 nd Mg 65 Cu 25 Y 10, 9 is pproximtely 40 J g tom 1 K 1 t the melting temperture. For Cu 47 Ti 34 Zr 11 Ni 8 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5 this work, the het cpcity ner the melting temperture is pproximtely 45 J g tom 1 K 1.

5 7246 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l. TABLE III. The Kuzmnn tempertures, the glss trnsition tempertures mesured with heting rte of K s 1, nd the entropies of fusion for the three lloys. T K T g S f J g tom 1 K 1 Cu 47 Ti 34 Zr 11 Ni Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti Zr 57 Cu 15.4 Ni 12.6 Al 10 N Therefore, specific het cpcity of 42.5 J g tom 1 K 1 t 1085 K ws ssigned to Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, so tht the fitting constnts for the liquid specific het cpcity could e determined. It is expected tht this vlue is within 10% of the ctul vlue. The difference in the specific het cpcity of the liquid nd the crystlline sttes, c p l x, ws clculted. With these dt, the differences in the thermodynmic functions of the liquid nd the crystlline sttes cn e determined. The clculted difference in enthlpy is given y H l x T H f T T f c p l x T dt 9 nd is shown in Figs. 3 3 c for these lloys. In this eqution, H f is the enthlpy of fusion nd T f is the temperture t which the Gis free energy of the liquid nd the crystlline sttes re equl. The difference in the enthlpy etween the liquid nd the crystlline sttes t the glss trnsition mesured with rte of K s 1 is the mount of enthlpy frozen into the liquid t T g. T f, the temperture t which the Gis free energy of the liquid nd the crystlline sttes re equl, is not known exctly for these lloys. However, the Gis free energy of the liquid nd the crystlline sttes re equl to one nother etween the solidus nd liquidus tempertures. T f ws tken to e the temperture t which the endothermic pek is mximum during melting determined with the DTA, T pek,s listed in Tle I. The clculted difference in entropy etween the liquid nd crystlline sttes is given y S l x T T S f f c l x p T dt 10 T T nd is shown in Figs. 4 4 c for these lloys. T pek is used in plce of T f in this clcultion. S f, the entropy of fusion, is given y FIG. 5. The clculted difference in the Gis free energy etween the liquid nd the crystlline sttes for Cu 47 Ti 34 Zr 11 Ni 8, Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd c Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5. Indicted on these plots re the Kuzmnn temperture T K, the glss trnsition temperture T g onset with heting rte of K s 1, nd the temperture t which the Gis free energy of the liquid nd the crystlline sttes re tken to e equl T f. S f H f. 11 T f Entropy of fusion dt re found in Tle III. Similr to the H l x (T) function tht ws clculted, there is residul entropy frozen into the glss elow the glss trnsition temperture. The T K indicted on these plots is the clculted Kuzmnn temperture. The Kuzmnn temperture is the isentropic temperture, the temperture t which the entropy of the liquid is equl to the entropy of the crystl. This temperture is commonly elieved to e the lowest temperture t which supercooled liquid cn exist without either spontneously crystllizing or forming glss. 20 Kuzmnn temperture dt re found in Tle III. It is importnt to note tht the entropy difference tht is clculted from the het cpcity dt is the totl entropy difference etween the liq-

6 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l TABLE IV. The criticl cooling rtes nd the reduced glss trnsition tempertures for the three lloys in this work nd two other metllic glss forming lloys, in order of decresing glss forming ility. Criticl cooling rte Ks 1 T rg Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be Zr 57 Cu 15.4 Ni 12.6 Al 10 N Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti c Mg 65 Cu 25 Y Cu 47 Ti 34 Zr 11 Ni Determined using the onset of the glss trnsition mesured with heting rte of K s 1 nd the liquidus temperture mesured with heting rte of K s 1. See Ref. 8. c See Ref. 9. FIG. 6. The clculted difference in the Gis free energy etween the liquid nd the crystlline sttes for numer of glss forming lloys see Ref. 9. uid nd the crystlline sttes nd not the configurtionl entropy difference. The totl entropy difference etween the liquid nd the crystlline sttes includes configurtionl entropy, communl entropy, nd virtionl entropy. Thus, this clculted Kuzmnn temperture does not necessrily represent the temperture where the configurtionl entropy of the liquid vnishes. The clculted difference in the Gis free energy etween the liquid nd crystlline sttes is given y G T f l x H T f c l x p T T dt T T S f f c l x p T T T dt 12 nd is shown in Figs. 5 5 c for these lloys. IV. DISCUSSION A comprison of the Gis free energy difference etween the liquid nd the crystl for severl metllic glss forming lloys 9 is shown in Fig. 6, long with the estimted criticl cooling rtes for these lloys. In generl, the lower the Gis free energy difference etween the liquid nd the crystlline sttes, the etter the glss forming ility of the lloy ccording to the criticl cooling rte. It is importnt to note tht this Gis free energy difference is the driving force for crystlliztion only in the cse of polymorphic trnsformtion. If the crystlliztion is not polymorphic s is the cse for mny metllic glss forming compositions, this free energy difference is the lower limit of the thermodynmic driving force for crystlliztion. Also, in generl, the smller the entropy of fusion, the etter is the glss forming ility of these metllic glsses. This is understood y the Turnull pproximtion 21 G l x H f T S f, 13 which is good pproximtion immeditely elow the melting point. Initilly, s the liquid is undercooled, the entropy of fusion S f determines the rte t which G l x chnges. Another prmeter tht is qulittive indictor of the glss forming ility in glss forming lloys is the reduced glss trnsition temperture T rg. The reduced glss trnsition temperture is given y T rg T g, 14 T m where T g is the glss trnsition temperture nd T m is the melting temperture. It is mesure of the time spent in the supercooled liquid regime when cooling the liquid from the melt. Lrger reduced glss trnsition tempertures indicte etter glss forming ility; the temperture intervl etween the melting temperture nd glss trnsition temperture is smller, decresing the likelihood of crystlliztion. Vlues of the criticl cooling rtes nd T rg for the three lloys in this work nd two other metllic glss forming lloys re given in Tle IV. V. SUMMARY AND CONCLUSION The thermodynmic functions of three ulk glss forming lloys, Cu 47 Ti 34 Zr 11 Ni 8, nd Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5, nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5, were determined. To do this, the het cpcity in the crystlline solid, the morphous solid, the supercooled liquid, nd the equilirium liquid, nd the hets of fusion for these lloys were mesured. The Gis free energy difference etween the liquid nd the crystlline sttes gives qulittive mesure of the glss forming ility of these glss forming lloys. ACKNOWLEDGMENTS The uthors thnk S. Bossuyt, H. Choi-Yim, nd C. C. Hys for ssistnce in the lortory nd John Hygrth of Teledyne Wh-Chng for providing mteril for the TEMPUS smples. They lso thnk Tem TEMPUS for helping mke the MSL-1 spce shuttle flight experiments successful. This work ws supported y NASA Grnt No. 4NAG S.C.G. cknowledges fellowship support from NDSEG.

7 7248 J. Appl. Phys., Vol. 87, No. 10, 15 My 2000 Glde et l. 1 W. Klement, R. H. Willens, nd P. Duwez, Nture London 187, A. Inoue, T. Zhng, nd T. Msumoto, Mter. Trns., JIM 31, T. Zhng, A. Inoue, nd T. Msumoto, Mter. Trns., JIM 32, A. Inoue, A. Kto, T. Zhng, S. G. Kim, nd T. Msumoto, Mter. Trns., JIM 32, A. Peker nd W. L. Johnson, Appl. Phys. Lett. 63, X. H. Lin nd W. L. Johnson, J. Appl. Phys. 78, Y. J. Kim, R. Busch, W. L. Johnson, A. J. Rullison, nd W. K. Rhim, Appl. Phys. Lett. 65, R. Busch, Y. J. Kim, nd W. L. Johnson, J. Appl. Phys. 77, R. Busch, W. Liu, nd W. L. Johnson, J. Appl. Phys. 83, A. Msuhr, R. Busch, nd W. L. Johnson, J. Non-Cryst. Solids 252, U. Geyer, S. Schneider, W. L. Johnson, Y. Qui, T. A. Tomrello, nd M. P. Mcht, Phys. Rev. Lett. 75, K. Ohsk, S. K. Chung, W. K. Rhim, A. Peker, D. Scruggs, nd W. L. Johnson, Appl. Phys. Lett. 70, X. H. Lin, Ph.D. thesis, Cliforni Institute of Technology, H. Choi-Yim, R. Busch, nd W. L. Johnson, J. Appl. Phys. 83, H. Choi-Yim, R. Busch, U. Köster, nd W. L. Johnson, Act Mter. 47, H. J. Fecht nd W. L. Johnson, Rev. Sci. Instrum. 62, R. K. Wunderlich nd H. J. Fecht, Int. J. Thermophys. 17, J. Szekely, E. Schwrtz, nd R. Hyers, JOM 47, O. Kuschewski, C. B. Alcock, nd P. J. Spencer, Mterils Thermochemistry, 6th ed. Permgon, New York, W. Kuzmnn, Chem. Rev. 43, D. Turnull, J. Appl. Phys. 21,

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het