877:
586:
872:{\displaystyle \mathbf {B} ={\begin{bmatrix}1&0&0&6&6&0&0\\0&1.5&0&1&0&0&1\\0&0&1&0&0&1&0\\0&0&0&1&1&0&0\\0&0&0&0&1&0&0\\0&0&0&0&0&1&0\\0&0&0&0&0&0&2\end{bmatrix}}}
1313:, normalized to sum up to 100% as seen above, contains the final batch composition in wt%: 39.216 sand, 16.012 trona, 10.242 lime, 16.022 albite, 4.699 orthoclase, 7.276 dolomite, 6.533 borax. If this batch is melted to a glass, the desired composition given above is obtained. During glass melting,
1305:
1077:
970:
1170:
1332:
If the number of glass and batch components is not equal, if it is impossible to exactly obtain the desired glass composition using the selected batch ingredients, or if the matrix equation is not soluble for other reasons (i.e., the rows/columns are
138:
1175:
989:
46:
The raw materials mixture for glass melting is termed "batch". The batch must be measured properly to achieve a given, desired glass formulation. This batch calculation is based on the common
882:
1082:
1434:
544:
The batching matrix B indicates the relation of the molarity in the batch (columns) and in the glass (rows). For example, the batch component SiO
1929:
980:, is given here. After multiplication with the appropriate molar masses of the batch ingredients one obtains the batch mass fraction matrix M
55:
1300:{\displaystyle \mathbf {M_{B}(100\%normalized)} ={\begin{bmatrix}39.216\\16.012\\10.242\\16.022\\4.699\\7.276\\6.533\end{bmatrix}}}
1481:
2030:
1072:{\displaystyle \mathbf {N_{B}} ={\begin{bmatrix}0.82087\\0.08910\\0.12870\\0.03842\\0.01062\\0.04962\\0.02155\end{bmatrix}}}
576:
of the glass is simply determined by dividing the desired wt% concentrations by the appropriate molar masses, e.g., for SiO
965:{\displaystyle \mathbf {N_{G}} ={\begin{bmatrix}1.1151\\0.1936\\0.1783\\0.0490\\0.0106\\0.0496\\0.0431\end{bmatrix}}}
167:
1165:{\displaystyle \mathbf {M_{B}} ={\begin{bmatrix}49.321\\20.138\\12.881\\20.150\\5.910\\9.150\\8.217\end{bmatrix}}}
1954:
1750:
1355:
1866:
1843:
572:, and so on. For the example given above, the complete batching matrix is listed below. The molarity matrix N
1699:
1442:
1474:
17:
1338:
1770:
552:
to the glass, therefore, the intersection of the first column and row shows "1". Trona adds 1.5 mol Na
1730:
1651:
1541:
267:. The formulas and molar masses of the glass and batch components are listed in the following table:
2035:
1999:
1631:
186:
An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67
1994:
1861:
1467:
1803:
1611:
1374:
Y. B. Peng, Xingye Lei, D. E. Day: "A computer programme for optimising batch calculations";
1324:
Simple glass batch calculation can be found at the website of the
University of Washington.
1959:
1833:
1745:
1581:
1571:
155:
151:
1871:
8:
1979:
1906:
1901:
1823:
1798:
1765:
1626:
1886:
1808:
1556:
1546:
1334:
478:
260:
1964:
1934:
1891:
1828:
1813:
1725:
1616:
163:
47:
1755:
1740:
1510:
1949:
1944:
1793:
1689:
1666:
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1646:
1641:
1636:
1596:
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225:
217:
206:
187:
1911:
1881:
1876:
1388:
1314:
229:
2024:
1818:
1775:
1681:
1656:
1551:
202:
1621:
1984:
1939:
1896:
1586:
1561:
1515:
194:
2009:
1974:
1694:
1576:
1441:. U.S. Department of Energy, Pacific Northwest Laboratory. Archived from
1350:
154:
of the batch and glass components respectively, and B being the batching
1405:
1079:
879:
2004:
1969:
1838:
1606:
1601:
1459:
441:
256:
175:
171:
1422:
248:
159:
34:
is used to determine the correct mix of raw materials (batch) for a
1989:
1760:
1536:
1531:
1709:
1785:
1591:
400:
252:
133:{\displaystyle N_{B}=(B^{T}\cdot B)^{-1}\cdot B^{T}\cdot N_{G}}
1704:
1671:
1505:
1490:
1406:
Calculating batch weights with a programmable microcalculator
1327:
1318:
514:
332:
264:
244:
35:
174:
by weight (wt%) can easily be derived using the appropriate
240:
1241:
1106:
1013:
906:
603:
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1085:
992:
885:
589:
58:
1299:
1164:
1071:
964:
871:
132:
1229:
1190:
2022:
1337:), the batch composition must be determined by
276:Desired concentration of glass component, wt%
1930:Conservation and restoration of glass objects
1475:
976:The resulting molarity matrix of the batch, N
1412:, vol. 43, no 11, November 1986, p 488–491.
1482:
1468:
1328:Advanced batch calculation by optimization
1395:, vol. 62, no 3-4, March 2005, p 109–112.
1489:
1389:Automation of Batch Formula Calculation
14:
2023:
1172: or
181:
158:. The symbol "" stands for the matrix
1463:
556:O to the glass; albite adds 6 mol SiO
288:Molar mass of batch component, g/mol
279:Molar mass of glass component, g/mol
1387:M. M. Khaimovich, K. Yu. Subbotin: "
24:
1378:, vol. 32, 1991, no. 4, p 123–130.
170:. From the molarities matrices N,
25:
2047:
1317:(from trona, lime, dolomite) and
1226:
1223:
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1211:
1208:
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1199:
1196:
1193:
1185:
1181:
1092:
1088:
999:
995:
892:
888:
591:
239:, and as raw materials are used
2000:Radioactive waste vitrification
1955:Glass fiber reinforced concrete
1356:Calculation of glass properties
1321:(from trona, borax) evaporate.
1427:
1415:
1398:
1381:
1368:
150:being the molarities 1-column
92:
72:
13:
1:
2031:Glass engineering and science
1867:Chemically strengthened glass
1361:
166:, and the sign "·" means the
1700:Glass-ceramic-to-metal seals
41:
7:
1423:Free glass batch calculator
1344:
285:Formula of batch component
273:Formula of glass component
10:
2052:
1439:Battelle PNNL MST Handbook
1920:
1852:
1784:
1731:Chemical vapor deposition
1718:
1680:
1652:Ultra low expansion glass
1542:Borophosphosilicate glass
1524:
1498:
1970:Glass-reinforced plastic
1632:Sodium hexametaphosphate
162:operation, "" indicates
1862:Anti-reflective coating
1736:Glass batch calculation
1617:Photochromic lens glass
1339:optimization techniques
28:Glass batch calculation
1301:
1166:
1073:
966:
873:
134:
1995:Prince Rupert's drops
1844:Transparent materials
1804:Gradient-index optics
1612:Phosphosilicate glass
1302:
1167:
1074:
967:
874:
580:67/60.0843 = 1.1151.
135:
1960:Glass ionomer cement
1834:Photosensitive glass
1761:Liquidus temperature
1582:Fluorosilicate glass
1176:
1083:
990:
883:
587:
56:
1980:Glass-to-metal seal
1902:Self-cleaning glass
1824:Optical lens design
182:Example calculation
1965:Glass microspheres
1887:Hydrogen darkening
1809:Hydrogen darkening
1557:Chalcogenide glass
1547:Borosilicate glass
1410:Glass and Ceramics
1393:Glass and Ceramics
1335:linearly dependent
1297:
1291:
1162:
1156:
1069:
1063:
962:
956:
869:
863:
130:
2018:
2017:
1935:Glass-coated wire
1907:sol–gel technique
1892:Insulated glazing
1829:Photochromic lens
1814:Optical amplifier
1766:sol–gel technique
1351:Glass ingredients
542:
541:
48:linear regression
16:(Redirected from
2043:
1756:Ion implantation
1511:Glass transition
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1376:Glass technology
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282:Batch component
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164:matrix inversion
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2036:Glass chemistry
2021:
2020:
2019:
2014:
1950:Glass electrode
1945:Glass databases
1922:
1916:
1854:
1848:
1780:
1714:
1690:Bioactive glass
1676:
1662:Vitreous enamel
1647:Thoriated glass
1642:Tellurite glass
1627:Soda–lime glass
1597:Gold ruby glass
1567:Cranberry glass
1520:
1494:
1488:
1458:
1457:
1448:
1446:
1435:"Glass Melting"
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1404:A. I. Priven: "
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564:O, and 1 mol Al
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1912:Tempered glass
1909:
1904:
1899:
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1884:
1882:DNA microarray
1879:
1877:Dealkalization
1874:
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1751:Glass modeling
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1682:Glass-ceramics
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1622:Silicate glass
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1493:science topics
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1326:
1315:carbon dioxide
1310:
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1111:
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608:
605:
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602:
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573:
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561:
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553:
549:
548:adds 1 mol SiO
545:
540:
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536:
532:
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168:scalar product
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62:
43:
40:
32:glass batching
9:
6:
4:
3:
2:
2048:
2037:
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2029:
2028:
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2011:
2008:
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1819:Optical fiber
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1807:
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1800:
1797:
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1776:Vitrification
1774:
1772:
1769:
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1757:
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1749:
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1746:Glass melting
1744:
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1741:Glass forming
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1660:
1658:
1657:Uranium glass
1655:
1653:
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1637:Soluble glass
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1552:Ceramic glaze
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1527:
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1501:
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1462:
1445:on 2010-05-05
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1322:
1320:
1316:
1307:
1292:
1286:
1279:
1272:
1265:
1258:
1251:
1244:
1238:
1233:
1157:
1151:
1144:
1137:
1130:
1123:
1116:
1109:
1103:
1098:
1064:
1058:
1051:
1044:
1037:
1030:
1023:
1016:
1010:
1005:
985:
957:
951:
944:
937:
930:
923:
916:
909:
903:
898:
864:
858:
853:
848:
843:
838:
833:
828:
821:
816:
811:
806:
801:
796:
791:
784:
779:
774:
769:
764:
759:
754:
747:
742:
737:
732:
727:
722:
717:
710:
705:
700:
695:
690:
685:
680:
673:
668:
663:
658:
653:
648:
643:
636:
631:
626:
621:
616:
611:
606:
600:
595:
583:
582:
581:
537:
518:
516:
513:
510:
507:
497:
496:
492:
482:
480:
477:
474:
471:
468:
467:
463:
445:
443:
440:
437:
434:
427:
426:
422:
404:
402:
399:
396:
393:
383:
382:
378:
372:
369:
366:
363:
360:
359:
355:
336:
334:
331:
328:
325:
318:
317:
313:
307:
304:
301:
298:
292:
291:
287:
284:
281:
278:
275:
272:
271:
268:
266:
262:
258:
254:
250:
246:
242:
238:
227:
223:
215:
204:
200:
192:
179:
177:
173:
169:
165:
161:
157:
153:
140:
125:
121:
117:
112:
108:
104:
99:
96:
88:
85:
80:
76:
69:
64:
60:
51:
49:
39:
37:
33:
29:
19:
1985:Porous glass
1940:Safety glass
1897:Porous glass
1855:modification
1735:
1667:Wood's glass
1587:Fused quartz
1562:Cobalt glass
1516:Supercooling
1447:. Retrieved
1443:the original
1438:
1429:
1417:
1409:
1400:
1392:
1383:
1375:
1370:
1331:
1323:
1309:The matrix M
1308:
986:
974:
543:
185:
176:molar masses
141:
52:
45:
31:
27:
26:
2010:Glass fiber
1975:Glass cloth
1719:Preparation
1695:CorningWare
1577:Flint glass
1572:Crown glass
1525:Formulation
172:percentages
18:Glass batch
2025:Categories
2005:Windshield
1839:Refraction
1799:Dispersion
1607:Milk glass
1602:Lead glass
1449:2008-01-26
1421:See also:
1362:References
560:, 1 mol Na
442:Orthoclase
257:orthoclase
50:equation:
1872:Corrosion
1771:Viscosity
1726:Annealing
1197:%
538:381.3721
493:184.4014
464:556.6631
423:524.4460
397:101.9613
379:100.0872
356:226.0262
160:transpose
118:⋅
105:⋅
97:−
86:⋅
42:Principle
1990:Pre-preg
1794:Achromat
1537:Bioglass
1532:AgInSbTe
1345:See also
511:69.6202
479:Dolomite
475:40.3044
438:94.1960
367:56.0774
329:61.9789
314:60.0843
302:60.0843
261:dolomite
152:matrices
1921:Diverse
1853:Surface
1710:Zerodur
1059:0.02155
1052:0.04962
1045:0.01062
1038:0.03842
1031:0.12870
1024:0.08910
1017:0.82087
483:MgCa(CO
1923:topics
1786:Optics
1592:GeSbTe
1499:Basics
1266:16.022
1259:10.242
1252:16.012
1245:39.216
1131:20.150
1124:12.881
1117:20.138
1110:49.321
952:0.0431
945:0.0496
938:0.0106
931:0.0490
924:0.1783
917:0.1936
910:1.1151
401:Albite
263:, and
253:albite
156:matrix
142:with N
38:melt.
1705:Macor
1672:ZBLAN
1506:Glass
1491:Glass
1319:water
1287:6.533
1280:7.276
1273:4.699
1152:8.217
1145:9.150
1138:5.910
515:Borax
458:*6SiO
417:*6SiO
370:Lime
333:Trona
305:Sand
265:borax
245:trona
201:, 10
193:, 12
146:and N
36:glass
531:*10H
469:MgO
450:O*Al
409:O*Al
373:CaCO
361:CaO
341:H(CO
249:lime
241:sand
228:, 3
224:, 2
216:, 1
205:, 5
1408:";
1391:";
1194:100
649:1.5
364:10
349:*2H
326:12
308:SiO
299:67
293:SiO
226:MgO
203:CaO
188:SiO
30:or
2027::
1437:.
1341:.
984::
535:O
519:Na
508:3
472:2
435:1
432:O
405:Na
394:5
384:Al
353:O
337:Na
323:O
319:Na
259:,
255:,
251:,
247:,
243:,
207:Al
195:Na
178:.
1483:e
1476:t
1469:v
1452:.
1311:B
1293:]
1239:[
1234:=
1230:)
1227:d
1224:e
1221:z
1218:i
1215:l
1212:a
1209:m
1206:r
1203:o
1200:n
1191:(
1186:B
1182:M
1158:]
1104:[
1099:=
1093:B
1089:M
1065:]
1011:[
1006:=
1000:B
996:N
982:B
978:B
958:]
904:[
899:=
893:G
889:N
865:]
859:2
854:0
849:0
844:0
839:0
834:0
829:0
822:0
817:1
812:0
807:0
802:0
797:0
792:0
785:0
780:0
775:1
770:0
765:0
760:0
755:0
748:0
743:0
738:1
733:1
728:0
723:0
718:0
711:0
706:1
701:0
696:0
691:1
686:0
681:0
674:1
669:0
664:0
659:1
654:0
644:0
637:0
632:0
627:6
622:6
617:0
612:0
607:1
601:[
596:=
592:B
578:2
574:G
570:3
568:O
566:2
562:2
558:2
554:2
550:2
546:2
533:2
529:7
527:O
525:4
523:B
521:2
504:3
502:O
500:2
498:B
489:2
487:)
485:3
460:2
456:3
454:O
452:2
448:2
446:K
430:2
428:K
419:2
415:3
413:O
411:2
407:2
390:3
388:O
386:2
375:3
351:2
347:2
345:)
343:3
339:3
321:2
310:2
295:2
236:3
234:O
232:2
230:B
222:O
220:2
218:K
213:3
211:O
209:2
199:O
197:2
190:2
148:G
144:B
126:G
122:N
113:T
109:B
100:1
93:)
89:B
81:T
77:B
73:(
70:=
65:B
61:N
20:)
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