What are minerals?!1. Crystalline solids. 2. natural and inorganic. 3. definite chemical composition!Crystals: internal periodic structure"Geometrical+crystal+shapes+suggest+ordered+structures:+Atomic+order.+The importance of Atomic Order!The importance of Atomic Order!How to Learn the Atomic Order?!How to Learn the Atomic Order?!• Put X-ray beams through crystals.!• X-rays are short electromagnetic waves of wavelength (l) between 0.1 and 10 Angstroms.!• If waves hit periodic array with spacing d > l then diffraction occurs: XRD!Introduc8on+to+X‐ray+genera8on+and+crystallography+• +Discovery+of+X‐rays+• +Con8nuous+and+characteris8c+X‐rays+• +Bragg’s+Law+• +Diffrac8on+techniques+• +Single+crystal+methods+• +Powder+method+• +Rela8onship+to+Miller+Indices+and+Unit+Cells+Discovery+of+X‐rays+X‐rays+were+accidentally+discovered+by+Wilhelm'C.'Roentgen'in+1895+while+experimen8ng+with+“cathode+rays”+produced+in+sealed,+glass+discharge+tubes.+Now+we+know+that+it+was+electrons,+emiUed+from+the+cathode,+which+struck+the+glass+walls+of+the+tube+thereby+causing+another+type+of+weak+radia8on;+this+caused+nearby+materials+in+the+lab+to+“glow+in+the+dark”+or+fluoresce.++Roentgen+correctly+inferred+that+a+new+type+of+radia8on+was+being+produced,+which+he+named+X‐radia4on.++He+was+never+able+to+measure+the+wavelength+of+X‐rays,+but+he+discovered+that+most+substances+(including+human+8ssues)+were+nearly+transparent+to+them.+Schema8c+Crooke’s+Tube+First+medical+x‐ray?+Anna+Roentgen’s+hand+How+are+X‐rays+generated?+X‐rays+arise+as+a+result+of+changing+energy+states+of+electrons+bound+within+an+single+atom,+molecule,+or+mineral.++Must+excite+an+“inner”+shell+electron+to+a+higher+energy+state,+say+by+interac8on+with+an+energe8c+photon+(quan8zed+bit+of+EM+radia8on).+Discussed+on+next+slide.+If+energy+is+conserved+in+the+collision,+then+Ex‐ray'='E2electron'–'E1electron'='hv!Photon+may+be+absorbed,+raising+Eelectron+or+it+may+emiUed,+when+an+electron’s+“falls”++from+a+higher+energy+state+to+a+lower+one.+X‐rays:+part+of+the+EM+spectrum+Electromagne8c+(EM)+radia8on+shows+characteris8cs+of+both+waves+and+par8cles.+Use+the+“wave”+model+for+some+aspects+and+“par8cle”+model+for+others.+E'='hv'='hc/λ!Einstein’s+rela8onship+tells+us++that+the+E,+energy,+of+an+EM++wave+is+quan8zed+(discrete)+and+depends+on+its+frequency.+Con8nuous+and+Characteris8c+X‐rays++Two+types+of+X‐rays+have+been+recognized:+1) Con8nuum+radia8on+that+arises+by+electron++++++++slowing+or+“braking”+2)+Characteris8c+radia8on+that+depends+on+Z,+++++++++the+mean+atomic+number+of+the+atom+Characteris8c+X‐rays+Henry+Moseley+was+a+brilliant+graduate+student+under+Ernest+Rutherford,+the+first+person+to+establish+that+a+dense+atomic+nucleus+exists.+He+was+killed+in+ac8on+at+Gallipoli+in+1915+in+WWI.+Moseley+studied+the+systema8cs+of+characteris8c+X‐rays+and+discovered+that+the+frequency+(or+wavelength)+of+X‐rays+were+dependent+on+the+mean+atomic+number+of+the+atom+under+study.+This+will+allow+us+to+determine+the+chemical+composi8on+of+minerals+using+X‐ray+spectroscopic+techniques+that+we+will+discuss+later.+What'is'X‐ray'Diffrac4on'?'The'atomic'planes'of'a'crystal'cause'an'incident'beam'of'X‐rays'to'interfere'with'one'another'as'they'leave'the'crystal.'The'phenomenon'is'called'X‐ray'diffrac4on.'X‐ray+Diffrac8on+Diffrac4on'is+a+general+term+used+to+describe+the+bending+of+a+wave+around+an+object.+The+basic+principles+were+discovered+by+Christriaan'Huygens,+a+contemporary+of+Isaac+Newton.+Crystals+must+have+regular,+ordered+arrangements+of+atoms.+When+X‐rays+interact+with+such+a+regular+array,+the+EM+radia8on+is+absorbed+by+the+electrons+and+re‐emiUed,+crea8ng+a+new+point+source+of+an+X‐ray+wavelet.++These+waves+are+governed+by+Huygen’s+principle+and+may+combine+(construc8vely+interfere)+to+yield+secondary+waves+that+radiate+away+from+individual+atoms+in+the+crystal.+Max'von'Laue'discovered+that+crystals+diffract+X‐rays+and+was+awarded+the+Noble+Prize+in+1914.+Diffrac8on+of+EM+radia8on,+including+X‐rays,+occurs+because+of+its+coherent,+wave‐like+behavior.++This+will+allow+us+to+treat+incident,+monochroma8c+X‐rays+as+planar+waves.+Bragg’s+Law+William+Henry+Bragg+and+William+Lawrence+Bragg,+a+father++and+son+team+awarded+the+Nobel+Prize+in+Physics+in+1915+Based+their+work+on+the+analysis+of++Max+von+Laue+in+1914++When+Bragg+condi8on+is+sa8sfied,+the+X‐Rays+will+construc4vely'interfere.+If+the+Bragg+condi8on+is+NOT+sa8sfied,+then+X‐Rays+will+s8ll+be+diffracted,+but+will+NOT''result+in+coherent+reflec8ons!+To keep parallel beams at angle  in phase:+n l = d sin a means sin a =n l /d Maximum a is 90o – diffraction directly sideward - for which sin a  1 Giving n l /d  1 or n l  d Smallest n l when n = 1 The 'easiest to satisfy for n = 1 So l  d to keep sin a  1 d l !a = 90o Wavelength must be shorter than d!Otherwise, no diffraction!!Application of XRD!1. Measure the average spacing between layers or rows of atoms!2. Determine the orientation of a single crystal or grain!3. Find the crystal structure of an unknown material!X-Ray diffraction: Laue photographic method!Therefore: X-rays are waves !!Crystals are periodic arrays !! l  d !!This 1912 demonstration won Max von Laue the Nobel Prize in physics for 1914.!Laue X-Ray photograph of Vesuvianite!From: http://www.geology.fau.edu/course_inføfall02/gly4200/X-RAY.htm!Vesuvianite: Contact Metamorphic Mineral!Formula: Ca10(Mg,Fe)2Al4Si9O34(OH)4 System: Tetragonal Hardness: 61⁄2 http://www.mindat.org/min-4223.html!Basic+X‐Ray+Diffrac8on+Geometries+Single+crystal,+monochroma8c+X‐ray+beam+Mul8ple+crystals,+monochroma8c+X‐ray+beam+Debye‐Scherrer+Camera+Debye‐Scherrer+method+Crystal+face+reflec8ons+2