First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

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Bryce Hall
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0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.

1 0.9 First ompression (0-6.3 GP) First deompression ( GP) Seond ompression ( GP) Seond deompression ( GP) V/V P (GP) Supplementry Figure 1 Compression ehvior of type-ii glss-like ron (GC) under hydrostti pressure. () An exmple of reorded smple imges in dimond nvil ell during ompression nd deompression. Arrows indite diretions of pressure hnge. () Pressure (P) volume (V) reltions upon ompression to 35.5 GP nd deompression using helium s pressure medium.

Amplitude (V) Amplitude (V) Amplitude (V) 1.2 Compressionl wves Sher wves 0.59 GP d Al 2 O 3 uffer rod Au foil 20 MHz 0.0 - - 1.2 25 MHz 4 5 6 7 8 9 Time (μs) e Glss-like ron Cu 0.

4 GP Supplementry Figure 2 Compressionl nd sher wve signls (,, ) nd orresponding X-ry rdiogrphy imges of type-ii glss-like ron (GC) (d, e, f) t pressures of 0.59, 2.1, nd 4.

2 Amplitude (V) Amplitude (V) Amplitude (V) 1.2 Compressionl wves Sher wves 0.59 GP d Al 2 O 3 uffer rod Au foil 20 MHz MHz Time (μs) e Glss-like ron Cu 0.59 GP Compressionl wves Sher wves 2.1 GP 20 MHz MHz Time (μs) Compressionl wves Sher wves 4.4 GP f 2.1 GP 20 MHz MHz Time (μs) 4.4 GP Supplementry Figure 2 Compressionl nd sher wve signls (,, ) nd orresponding X-ry rdiogrphy imges of type-ii glss-like ron (GC) (d, e, f) t pressures of 0.59, 2.1, nd 4.4 GP, respetively. The ompressionl nd sher wve signls re those from the interfes t nvil/al 2O 3 uffer rod (), Al 2O 3 uffer rod/smple (), nd smple/cu (). The trvel times etween nd re the two-wy signls in the smple.

3 Density (g/m 3 ) Elsti moduli (GP) Elsti wve veloities (km/s) Bulk modulus, K Sher modulus, G Young's modulus, E V p V s Dt dedued from ousti mesurements Dt sed on imging nlysis P (GP) Supplementry Figure 3 Aousti veloities nd dedued densities of type-i (solid symols) nd type-ii glss-like rons (GC) (open symols). () Mesured longitudinl (V p) nd sher (V s) wve veloities t vrious pressures; the errors re less thn %. () The otined elsti moduli t vrious pressures; the errors re less thn the size of the symols. () Densities determined y integrting ousti veloities, together with the results from optil imging mesurements. The rw mterils were ll in plte form.

4 Differentil xil stress (MP) Differentil xil stress (MP) Differentil xil stress (MP) hit point off point 0.5 GP GP 1.5 GP 2.0 GP 2.5 GP Distne (µm) hit point off point 0.5 GP GP 1.5 GP 2.0 GP Distne (µm) E=39.7GP E=39.6GP E=35.1GP E=30.0GP GP GP 1.5 GP 2.0 GP Axil strin (%) Supplementry Figure 4 Trixil deformtion of type-ii () nd I (, ) glss-like ron (GC) under high pressures. (, ) Rw experimentl dt shows piston displement versus differentil stress. () Differentil stress-xil strin urves of type-i GC t vrious onfining pressures from 0.5 to 2.0 GP. The liner portions (indited y the dshed lines) re elsti, with the slopes orresponding to the Young s moduli t vrious pressures. Type-I GC yields t somewht lower strins, ompred to type- II GC (Fig. 3). The rw mterils were the purhsed GC rods.

Supplementry Figure 5 HRTEM imges of type-ii glss-like ron (GC) smples reovered from vrious stges of

A omprison etween nd suggests tht the smple reovered from 5.

5 Supplementry Figure 5 HRTEM imges of type-ii glss-like ron (GC) smples reovered from vrious stges of ompression. All sle rs re 20 nm. () Strting mteril; () reovered from 5.1 GP; () reovered from 13.1 GP. In oth nd, fringes of multi-grphene lyers urved round fullerene-like spheroids (FLS) re seen. A omprison etween nd suggests tht the smple reovered from 5.1 GP did not experiene ny notiele struturl modifition. In, mny res lk FLS, suggesting the prtil ollpse of FLS fter the pressure of 13.1 GP. The losely pked nd strightened frgments of multi-grphene lyers indite the smple ws not reovered. These oservtions re onsistent with the volume mesurements.

6 A Fullerene ggregtes 1.4 nm 9.1 nm 2.1 nm 10.5 nm 3.5 nm 11.9 nm 4.9 nm 13.3 nm 6.3 nm 14.7 nm 7.7 nm B Fullerene ggregtes 2.1 nm 3.5 nm 4.9 nm 6.3 nm 7.7 nm V/V Compression Compression Deompression P (GP) P (GP) Supplementry Figure 6 Compression nd deompression urves for 3D doule-lyer fullerene rrys with vrious sphere dimeters ording to MD simultions. The interlyer distne of doule-lyer fullerene is 0.34 nm for the initil modeling. For simplify, only the outer dimeters re mrked. For exmple, the 1.4 nm outer dimeter fullerene hs inner dimeter of 0.7 nm. () Compression urves of fullerene rrys with sphere dimeters from 0.7 to 14.7 nm. A usp is oserved in the ompression urves when fullerene dimeters re ove 3.5 nm, nd the usps our t lower pressures for fullerenes with lrger dimeters. () Compression nd deompression urves of seleted fullerene rrys. The lrge dimeter fullerene rrys ollpse nd experiene permnent plsti deformtion t the jerk pressures, whih ontrsts the oserved elsti reovery of GC with fullerene dimeter of 5-10 nm.

7 Sher moduli (GP) Bulk moduli (GP) Young's moduli (GP) d V/V P (GP) P (GP) Poisson's rtio, v 15 e P (GP) Supplementry Figure 7 Pressure-indued property hnges of vrious type-ii glss-like ron (GC) smples. () Compression dt sed on the ultrsoni veloity mesurements. (,,d,e) Bulk, sher, Young s moduli, nd Poisson s rtio hnges under pressure. In d, irles represent dt otined y ultrsoni veloity mesurements; tringles re those otined from the stress-strin reltionship in trixil deformtion experiments of GC rods (Fig. 3 nd Supplementry Figure S4). Solid mgent nd red irles re those otined from GC rod smples, nd open irles re those from GC plte smples (see lso Fig. 2). The different type-ii GC smples show slightly different ompressiility, pressuretunle elsti moduli, nd Poisson s rtios.

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint